id	sid	tid	token	lemma	pos
gi-4940	1	1	plotting	plot	VERB
gi-4940	1	2	the	the	DET
gi-4940	1	3	map	map	NOUN
gi-4940	1	4	projection	projection	NOUN
gi-4940	1	5	graticule	graticule	NOUN
gi-4940	1	6	involving	involve	VERB
gi-4940	1	7	discontinuities	discontinuity	NOUN
gi-4940	1	8	based	base	VERB
gi-4940	1	9	on	on	ADP
gi-4940	1	10	combined	combined	ADJ
gi-4940	1	11	sampling	sample	VERB
gi-4940	1	12	plotting	plot	VERB
gi-4940	1	13	the	the	DET
gi-4940	1	14	map	map	NOUN
gi-4940	1	15	projection	projection	NOUN
gi-4940	1	16	graticule	graticule	NOUN
gi-4940	1	17	involving	involve	VERB
gi-4940	1	18	discontinuities	discontinuity	NOUN
gi-4940	1	19	based	base	VERB
gi-4940	1	20	on	on	ADP
gi-4940	1	21	combined	combine	VERB
gi-4940	1	22	sampling	sampling	NOUN
gi-4940	1	23	tomáš	tomáš	ADP
gi-4940	1	24	bayer	bayer	PROPN
gi-4940	1	25	department	department	PROPN
gi-4940	1	26	of	of	ADP
gi-4940	1	27	applied	apply	VERB
gi-4940	1	28	geoinformatics	geoinformatic	NOUN
gi-4940	1	29	and	and	CCONJ
gi-4940	1	30	cartography	cartography	NOUN
gi-4940	1	31	,	,	PUNCT
gi-4940	1	32	faculty	faculty	NOUN
gi-4940	1	33	of	of	ADP
gi-4940	1	34	science	science	NOUN
gi-4940	1	35	,	,	PUNCT
gi-4940	1	36	charles	charles	PROPN
gi-4940	1	37	university	university	PROPN
gi-4940	1	38	,	,	PUNCT
gi-4940	1	39	czech	czech	PROPN
gi-4940	1	40	republic	republic	PROPN
gi-4940	1	41	bayertom@natur.cuni.cz	bayertom@natur.cuni.cz	PROPN
gi-4940	1	42	abstract	abstract	ADJ
gi-4940	1	43	.	.	PUNCT
gi-4940	2	1	this	this	DET
gi-4940	2	2	article	article	NOUN
gi-4940	2	3	presents	present	VERB
gi-4940	2	4	a	a	DET
gi-4940	2	5	new	new	ADJ
gi-4940	2	6	algorithm	algorithm	NOUN
gi-4940	2	7	for	for	ADP
gi-4940	2	8	interval	interval	NOUN
gi-4940	2	9	plotting	plot	VERB
gi-4940	2	10	the	the	DET
gi-4940	2	11	projection	projection	NOUN
gi-4940	2	12	graticule	graticule	NOUN
gi-4940	2	13	on	on	ADP
gi-4940	2	14	the	the	DET
gi-4940	2	15	interval	interval	NOUN
gi-4940	2	16	ω	ω	NOUN
gi-4940	2	17	=	=	NOUN
gi-4940	2	18	ωϕ	ωϕ	PRON
gi-4940	2	19	×	×	NOUN
gi-4940	2	20	ωλ	ωλ	INTJ
gi-4940	2	21	based	base	VERB
gi-4940	2	22	on	on	ADP
gi-4940	2	23	the	the	DET
gi-4940	2	24	combined	combined	ADJ
gi-4940	2	25	sampling	sampling	NOUN
gi-4940	2	26	technique	technique	NOUN
gi-4940	2	27	.	.	PUNCT
gi-4940	3	1	the	the	DET
gi-4940	3	2	proposed	propose	VERB
gi-4940	3	3	method	method	NOUN
gi-4940	3	4	synthesizes	synthesize	VERB
gi-4940	3	5	the	the	DET
gi-4940	3	6	uniform	uniform	NOUN
gi-4940	3	7	and	and	CCONJ
gi-4940	3	8	adaptive	adaptive	ADJ
gi-4940	3	9	sampling	sampling	NOUN
gi-4940	3	10	approaches	approach	NOUN
gi-4940	3	11	and	and	CCONJ
gi-4940	3	12	treats	treat	VERB
gi-4940	3	13	the	the	DET
gi-4940	3	14	discontinuities	discontinuity	NOUN
gi-4940	3	15	of	of	ADP
gi-4940	3	16	the	the	DET
gi-4940	3	17	coordinate	coordinate	NOUN
gi-4940	3	18	functions	function	NOUN
gi-4940	3	19	f	f	NOUN
gi-4940	3	20	,	,	PUNCT
gi-4940	3	21	g.	g.	PROPN
gi-4940	3	22	a	a	DET
gi-4940	3	23	full	full	ADJ
gi-4940	3	24	set	set	NOUN
gi-4940	3	25	of	of	ADP
gi-4940	3	26	the	the	DET
gi-4940	3	27	projection	projection	ADJ
gi-4940	3	28	constant	constant	ADJ
gi-4940	3	29	values	value	NOUN
gi-4940	3	30	represented	represent	VERB
gi-4940	3	31	by	by	ADP
gi-4940	3	32	the	the	DET
gi-4940	3	33	projection	projection	NOUN
gi-4940	3	34	pole	pole	NOUN
gi-4940	4	1	k	k	PROPN
gi-4940	5	1	=	=	PUNCT
gi-4940	6	1	[	[	X
gi-4940	6	2	ϕk	ϕk	X
gi-4940	6	3	,	,	PUNCT
gi-4940	6	4	λk	λk	X
gi-4940	6	5	]	]	PUNCT
gi-4940	6	6	,	,	PUNCT
gi-4940	6	7	two	two	NUM
gi-4940	6	8	standard	standard	ADJ
gi-4940	6	9	parallels	parallel	VERB
gi-4940	6	10	ϕ′1	ϕ′1	ADJ
gi-4940	6	11	,	,	PUNCT
gi-4940	6	12	ϕ′2	ϕ′2	NOUN
gi-4940	6	13	and	and	CCONJ
gi-4940	6	14	the	the	DET
gi-4940	6	15	central	central	ADJ
gi-4940	6	16	meridian	meridian	PROPN
gi-4940	6	17	shift	shift	NOUN
gi-4940	6	18	λ′0	λ′0	PROPN
gi-4940	6	19	are	be	AUX
gi-4940	6	20	supported	support	VERB
gi-4940	6	21	.	.	PUNCT
gi-4940	7	1	in	in	ADP
gi-4940	7	2	accordance	accordance	NOUN
gi-4940	7	3	with	with	ADP
gi-4940	7	4	the	the	DET
gi-4940	7	5	discontinuity	discontinuity	NOUN
gi-4940	7	6	direction	direction	NOUN
gi-4940	7	7	it	it	PRON
gi-4940	7	8	utilizes	utilize	VERB
gi-4940	7	9	a	a	DET
gi-4940	7	10	subdivision	subdivision	NOUN
gi-4940	7	11	of	of	ADP
gi-4940	7	12	the	the	DET
gi-4940	7	13	given	give	VERB
gi-4940	7	14	latitude	latitude	NOUN
gi-4940	7	15	/	/	SYM
gi-4940	7	16	longitude	longitude	NOUN
gi-4940	7	17	intervals	interval	NOUN
gi-4940	7	18	ωϕ	ωϕ	PRON
gi-4940	7	19	=	=	PUNCT
gi-4940	8	1	[	[	X
gi-4940	8	2	ϕ,ϕ	ϕ,ϕ	ADP
gi-4940	8	3	]	]	X
gi-4940	8	4	,	,	PUNCT
gi-4940	8	5	ωλ	ωλ	ADJ
gi-4940	8	6	=	=	SYM
gi-4940	9	1	[	[	X
gi-4940	9	2	λ	λ	X
gi-4940	9	3	,	,	PUNCT
gi-4940	9	4	λ	λ	X
gi-4940	9	5	]	]	X
gi-4940	9	6	to	to	ADP
gi-4940	9	7	the	the	DET
gi-4940	9	8	set	set	NOUN
gi-4940	9	9	of	of	ADP
gi-4940	9	10	disjoint	disjoint	NOUN
gi-4940	9	11	subintervals	subinterval	NOUN
gi-4940	9	12	ωg	ωg	ADP
gi-4940	9	13	k,ϕ,ω	k,ϕ,ω	PROPN
gi-4940	9	14	g	g	PROPN
gi-4940	9	15	k	k	PROPN
gi-4940	9	16	,	,	PUNCT
gi-4940	9	17	λ	λ	X
gi-4940	9	18	forming	form	VERB
gi-4940	9	19	tiles	tile	NOUN
gi-4940	9	20	without	without	ADP
gi-4940	9	21	the	the	DET
gi-4940	9	22	internal	internal	ADJ
gi-4940	9	23	singularities	singularity	NOUN
gi-4940	9	24	,	,	PUNCT
gi-4940	9	25	containing	contain	VERB
gi-4940	9	26	only	only	ADV
gi-4940	9	27	“	"	PUNCT
gi-4940	9	28	good	good	ADJ
gi-4940	9	29	”	"	PUNCT
gi-4940	9	30	data	datum	NOUN
gi-4940	9	31	;	;	PUNCT
gi-4940	9	32	their	their	PRON
gi-4940	9	33	parameters	parameter	NOUN
gi-4940	9	34	can	can	AUX
gi-4940	9	35	be	be	AUX
gi-4940	9	36	easily	easily	ADV
gi-4940	9	37	adjusted	adjust	VERB
gi-4940	9	38	.	.	PUNCT
gi-4940	10	1	each	each	DET
gi-4940	10	2	graticule	graticule	NOUN
gi-4940	10	3	tile	tile	NOUN
gi-4940	10	4	borders	border	NOUN
gi-4940	10	5	generated	generate	VERB
gi-4940	10	6	over	over	ADP
gi-4940	10	7	ωg	ωg	PROPN
gi-4940	10	8	k	k	PROPN
gi-4940	10	9	=	=	PUNCT
gi-4940	10	10	ωg	ωg	PROPN
gi-4940	10	11	k,ϕ	k,ϕ	VERB
gi-4940	10	12	×ω	×ω	ADV
gi-4940	10	13	g	g	PROPN
gi-4940	10	14	k	k	PROPN
gi-4940	10	15	,	,	PUNCT
gi-4940	10	16	λ	λ	PRON
gi-4940	10	17	run	run	VERB
gi-4940	10	18	along	along	ADP
gi-4940	10	19	the	the	DET
gi-4940	10	20	singularities	singularity	NOUN
gi-4940	10	21	.	.	PUNCT
gi-4940	11	1	for	for	ADP
gi-4940	11	2	combined	combined	ADJ
gi-4940	11	3	sampling	sampling	NOUN
gi-4940	11	4	with	with	ADP
gi-4940	11	5	the	the	DET
gi-4940	11	6	given	give	VERB
gi-4940	11	7	threshold	threshold	NOUN
gi-4940	11	8	α	α	NOUN
gi-4940	11	9	between	between	ADP
gi-4940	11	10	the	the	DET
gi-4940	11	11	adjacent	adjacent	ADJ
gi-4940	11	12	segments	segment	NOUN
gi-4940	11	13	of	of	ADP
gi-4940	11	14	the	the	DET
gi-4940	11	15	polygonal	polygonal	ADJ
gi-4940	11	16	approximation	approximation	NOUN
gi-4940	11	17	,	,	PUNCT
gi-4940	11	18	the	the	DET
gi-4940	11	19	recursive	recursive	ADJ
gi-4940	11	20	approach	approach	NOUN
gi-4940	11	21	has	have	AUX
gi-4940	11	22	been	be	AUX
gi-4940	11	23	used	use	VERB
gi-4940	11	24	;	;	PUNCT
gi-4940	11	25	meridian	meridian	ADJ
gi-4940	11	26	/	/	SYM
gi-4940	11	27	parallel	parallel	ADJ
gi-4940	11	28	offsets	offset	NOUN
gi-4940	11	29	are	be	AUX
gi-4940	11	30	∆ϕ,∆λ	∆ϕ,∆λ	NOUN
gi-4940	11	31	.	.	PUNCT
gi-4940	12	1	finally	finally	ADV
gi-4940	12	2	,	,	PUNCT
gi-4940	12	3	several	several	ADJ
gi-4940	12	4	tests	test	NOUN
gi-4940	12	5	of	of	ADP
gi-4940	12	6	the	the	DET
gi-4940	12	7	proposed	propose	VERB
gi-4940	12	8	algorithms	algorithm	NOUN
gi-4940	12	9	are	be	AUX
gi-4940	12	10	involved	involve	VERB
gi-4940	12	11	.	.	PUNCT
gi-4940	13	1	keywords	keyword	NOUN
gi-4940	13	2	:	:	PUNCT
gi-4940	13	3	digital	digital	ADJ
gi-4940	13	4	cartography	cartography	NOUN
gi-4940	13	5	;	;	PUNCT
gi-4940	13	6	mathematical	mathematical	ADJ
gi-4940	13	7	cartography	cartography	NOUN
gi-4940	13	8	;	;	PUNCT
gi-4940	13	9	adaptive	adaptive	ADJ
gi-4940	13	10	sampling	sampling	NOUN
gi-4940	13	11	;	;	PUNCT
gi-4940	13	12	graticule	graticule	NOUN
gi-4940	13	13	;	;	PUNCT
gi-4940	13	14	meridians	meridian	NOUN
gi-4940	13	15	;	;	PUNCT
gi-4940	13	16	parallels	parallel	NOUN
gi-4940	13	17	;	;	PUNCT
gi-4940	13	18	recursive	recursive	ADJ
gi-4940	13	19	approach	approach	NOUN
gi-4940	13	20	;	;	PUNCT
gi-4940	13	21	map	map	NOUN
gi-4940	13	22	projection	projection	NOUN
gi-4940	13	23	;	;	PUNCT
gi-4940	13	24	great	great	ADJ
gi-4940	13	25	circle	circle	NOUN
gi-4940	13	26	;	;	PUNCT
gi-4940	13	27	discontinuity	discontinuity	NOUN
gi-4940	13	28	;	;	PUNCT
gi-4940	13	29	visualization	visualization	NOUN
gi-4940	13	30	;	;	PUNCT
gi-4940	13	31	sphere	sphere	ADV
gi-4940	13	32	.	.	PUNCT
gi-4940	14	1	1	1	X
gi-4940	14	2	.	.	X
gi-4940	14	3	introduction	introduction	NOUN
gi-4940	14	4	maps	map	NOUN
gi-4940	14	5	are	be	AUX
gi-4940	14	6	an	an	DET
gi-4940	14	7	essential	essential	ADJ
gi-4940	14	8	part	part	NOUN
gi-4940	14	9	of	of	ADP
gi-4940	14	10	our	our	PRON
gi-4940	14	11	history	history	NOUN
gi-4940	14	12	and	and	CCONJ
gi-4940	14	13	cultural	cultural	ADJ
gi-4940	14	14	heritage	heritage	NOUN
gi-4940	14	15	;	;	PUNCT
gi-4940	14	16	a	a	DET
gi-4940	14	17	close	close	ADJ
gi-4940	14	18	attention	attention	NOUN
gi-4940	14	19	is	be	AUX
gi-4940	14	20	paid	pay	VERB
gi-4940	14	21	to	to	ADP
gi-4940	14	22	their	their	PRON
gi-4940	14	23	study	study	NOUN
gi-4940	14	24	and	and	CCONJ
gi-4940	14	25	research	research	NOUN
gi-4940	14	26	.	.	PUNCT
gi-4940	15	1	working	work	VERB
gi-4940	15	2	with	with	ADP
gi-4940	15	3	the	the	DET
gi-4940	15	4	map	map	NOUN
gi-4940	15	5	content	content	NOUN
gi-4940	15	6	,	,	PUNCT
gi-4940	15	7	its	its	PRON
gi-4940	15	8	geometric	geometric	ADJ
gi-4940	15	9	and	and	CCONJ
gi-4940	15	10	spatial	spatial	ADJ
gi-4940	15	11	characteristics	characteristic	NOUN
gi-4940	15	12	described	describe	VERB
gi-4940	15	13	by	by	ADP
gi-4940	15	14	the	the	DET
gi-4940	15	15	map	map	NOUN
gi-4940	15	16	projection	projection	NOUN
gi-4940	15	17	can	can	AUX
gi-4940	15	18	not	not	PART
gi-4940	15	19	be	be	AUX
gi-4940	15	20	ignored	ignore	VERB
gi-4940	15	21	.	.	PUNCT
gi-4940	16	1	the	the	DET
gi-4940	16	2	map	map	NOUN
gi-4940	16	3	projection	projection	NOUN
gi-4940	16	4	p	p	NOUN
gi-4940	16	5	is	be	AUX
gi-4940	16	6	defined	define	VERB
gi-4940	16	7	by	by	ADP
gi-4940	16	8	the	the	DET
gi-4940	16	9	coordinate	coordinate	NOUN
gi-4940	16	10	functions	function	NOUN
gi-4940	16	11	f	f	X
gi-4940	16	12	(	(	PUNCT
gi-4940	16	13	ϕ	ϕ	PROPN
gi-4940	16	14	,	,	PUNCT
gi-4940	16	15	λ	λ	NOUN
gi-4940	16	16	)	)	PUNCT
gi-4940	16	17	,	,	PUNCT
gi-4940	16	18	g(ϕ	g(ϕ	PROPN
gi-4940	16	19	,	,	PUNCT
gi-4940	16	20	λ	λ	NOUN
gi-4940	16	21	)	)	PUNCT
gi-4940	16	22	of	of	ADP
gi-4940	16	23	two	two	NUM
gi-4940	16	24	independent	independent	ADJ
gi-4940	16	25	variables	variable	NOUN
gi-4940	16	26	,	,	PUNCT
gi-4940	16	27	the	the	DET
gi-4940	16	28	latitude	latitude	NOUN
gi-4940	16	29	ϕ	ϕ	PROPN
gi-4940	16	30	,	,	PUNCT
gi-4940	16	31	and	and	CCONJ
gi-4940	16	32	the	the	DET
gi-4940	16	33	longitude	longitude	ADJ
gi-4940	16	34	λ	λ	PROPN
gi-4940	16	35	.	.	PUNCT
gi-4940	17	1	f	f	X
gi-4940	17	2	,	,	PUNCT
gi-4940	17	3	g	g	PROPN
gi-4940	17	4	may	may	AUX
gi-4940	17	5	have	have	VERB
gi-4940	17	6	a	a	DET
gi-4940	17	7	different	different	ADJ
gi-4940	17	8	form	form	NOUN
gi-4940	17	9	;	;	PUNCT
gi-4940	17	10	they	they	PRON
gi-4940	17	11	may	may	AUX
gi-4940	17	12	not	not	PART
gi-4940	17	13	be	be	AUX
gi-4940	17	14	continuous	continuous	ADJ
gi-4940	17	15	,	,	PUNCT
gi-4940	17	16	or	or	CCONJ
gi-4940	17	17	their	their	PRON
gi-4940	17	18	analytic	analytic	ADJ
gi-4940	17	19	form	form	NOUN
gi-4940	17	20	may	may	AUX
gi-4940	17	21	not	not	PART
gi-4940	17	22	exist	exist	VERB
gi-4940	17	23	.	.	PUNCT
gi-4940	18	1	to	to	PART
gi-4940	18	2	avoid	avoid	VERB
gi-4940	18	3	the	the	DET
gi-4940	18	4	discontinuities	discontinuity	NOUN
gi-4940	18	5	,	,	PUNCT
gi-4940	18	6	the	the	DET
gi-4940	18	7	interval	interval	NOUN
gi-4940	18	8	ω	ω	PROPN
gi-4940	18	9	=	=	PUNCT
gi-4940	19	1	ωϕ×ωλ	ωϕ×ωλ	PROPN
gi-4940	19	2	will	will	AUX
gi-4940	19	3	be	be	AUX
gi-4940	19	4	divided	divide	VERB
gi-4940	19	5	into	into	ADP
gi-4940	19	6	the	the	DET
gi-4940	19	7	disjoint	disjoint	NOUN
gi-4940	19	8	set	set	NOUN
gi-4940	19	9	of	of	ADP
gi-4940	19	10	k	k	X
gi-4940	19	11	“	"	PUNCT
gi-4940	19	12	good	good	ADJ
gi-4940	19	13	”	"	PUNCT
gi-4940	19	14	subintervals	subinterval	NOUN
gi-4940	19	15	ωg	ωg	PROPN
gi-4940	19	16	k	k	PROPN
gi-4940	19	17	;	;	PUNCT
gi-4940	19	18	their	their	PRON
gi-4940	19	19	“	"	PUNCT
gi-4940	19	20	boundaries	boundary	NOUN
gi-4940	19	21	”	"	PUNCT
gi-4940	19	22	run	run	VERB
gi-4940	19	23	along	along	ADP
gi-4940	19	24	the	the	DET
gi-4940	19	25	singularities	singularity	NOUN
gi-4940	19	26	.	.	PUNCT
gi-4940	20	1	a	a	DET
gi-4940	20	2	current	current	ADJ
gi-4940	20	3	approach	approach	NOUN
gi-4940	20	4	concentrated	concentrate	VERB
gi-4940	20	5	on	on	ADP
gi-4940	20	6	uniform	uniform	ADJ
gi-4940	20	7	sampling	sampling	NOUN
gi-4940	20	8	of	of	ADP
gi-4940	20	9	the	the	DET
gi-4940	20	10	meridians	meridian	NOUN
gi-4940	20	11	and	and	CCONJ
gi-4940	20	12	parallels	parallel	VERB
gi-4940	20	13	with	with	ADP
gi-4940	20	14	the	the	DET
gi-4940	20	15	steps	step	NOUN
gi-4940	20	16	δϕ	δϕ	NOUN
gi-4940	20	17	,	,	PUNCT
gi-4940	20	18	δλ	δλ	PROPN
gi-4940	20	19	may	may	AUX
gi-4940	20	20	not	not	PART
gi-4940	20	21	be	be	AUX
gi-4940	20	22	sufficient	sufficient	ADJ
gi-4940	20	23	.	.	PUNCT
gi-4940	21	1	despite	despite	SCONJ
gi-4940	21	2	its	its	PRON
gi-4940	21	3	popularity	popularity	NOUN
gi-4940	21	4	,	,	PUNCT
gi-4940	21	5	the	the	DET
gi-4940	21	6	equally	equally	ADV
gi-4940	21	7	spaced	spaced	ADJ
gi-4940	21	8	points	point	NOUN
gi-4940	21	9	can	can	AUX
gi-4940	21	10	not	not	PART
gi-4940	21	11	describe	describe	VERB
gi-4940	21	12	the	the	DET
gi-4940	21	13	meridian	meridian	PROPN
gi-4940	21	14	/	/	SYM
gi-4940	21	15	parallel	parallel	ADJ
gi-4940	21	16	course	course	NOUN
gi-4940	21	17	without	without	ADP
gi-4940	21	18	errors	error	NOUN
gi-4940	21	19	;	;	PUNCT
gi-4940	21	20	the	the	DET
gi-4940	21	21	problems	problem	NOUN
gi-4940	21	22	of	of	ADP
gi-4940	21	23	undersampling	undersample	VERB
gi-4940	21	24	or	or	CCONJ
gi-4940	21	25	oversampling	oversampling	ADJ
gi-4940	21	26	are	be	AUX
gi-4940	21	27	common	common	ADJ
gi-4940	21	28	.	.	PUNCT
gi-4940	22	1	because	because	SCONJ
gi-4940	22	2	of	of	ADP
gi-4940	22	3	the	the	DET
gi-4940	22	4	complex	complex	ADJ
gi-4940	22	5	/	/	SYM
gi-4940	22	6	straight	straight	ADJ
gi-4940	22	7	shapes	shape	NOUN
gi-4940	22	8	of	of	ADP
gi-4940	22	9	the	the	DET
gi-4940	22	10	meridians	meridian	NOUN
gi-4940	22	11	and	and	CCONJ
gi-4940	22	12	parallels	parallel	NOUN
gi-4940	22	13	,	,	PUNCT
gi-4940	22	14	this	this	DET
gi-4940	22	15	technique	technique	NOUN
gi-4940	22	16	is	be	AUX
gi-4940	22	17	not	not	PART
gi-4940	22	18	generally	generally	ADV
gi-4940	22	19	recommended	recommend	VERB
gi-4940	22	20	.	.	PUNCT
gi-4940	23	1	adaptive	adaptive	ADJ
gi-4940	23	2	sampling	sampling	NOUN
gi-4940	23	3	brings	bring	VERB
gi-4940	23	4	several	several	ADJ
gi-4940	23	5	benefits	benefit	NOUN
gi-4940	23	6	,	,	PUNCT
gi-4940	23	7	it	it	PRON
gi-4940	23	8	adapts	adapt	VERB
gi-4940	23	9	to	to	ADP
gi-4940	23	10	a	a	DET
gi-4940	23	11	different	different	ADJ
gi-4940	23	12	curvature	curvature	NOUN
gi-4940	23	13	of	of	ADP
gi-4940	23	14	the	the	DET
gi-4940	23	15	function	function	NOUN
gi-4940	23	16	,	,	PUNCT
gi-4940	23	17	reduces	reduce	VERB
gi-4940	23	18	the	the	DET
gi-4940	23	19	amount	amount	NOUN
gi-4940	23	20	of	of	ADP
gi-4940	23	21	data	datum	NOUN
gi-4940	23	22	and	and	CCONJ
gi-4940	23	23	provides	provide	VERB
gi-4940	23	24	a	a	DET
gi-4940	23	25	natural	natural	ADJ
gi-4940	23	26	and	and	CCONJ
gi-4940	23	27	smooth	smooth	ADJ
gi-4940	23	28	plot	plot	NOUN
gi-4940	23	29	of	of	ADP
gi-4940	23	30	the	the	DET
gi-4940	23	31	function	function	NOUN
gi-4940	23	32	without	without	ADP
gi-4940	23	33	jumps	jump	NOUN
gi-4940	23	34	and	and	CCONJ
gi-4940	23	35	unnatural	unnatural	ADJ
gi-4940	23	36	breaks	break	NOUN
gi-4940	23	37	.	.	PUNCT
gi-4940	24	1	this	this	DET
gi-4940	24	2	technique	technique	NOUN
gi-4940	24	3	is	be	AUX
gi-4940	24	4	popular	popular	ADJ
gi-4940	24	5	in	in	ADP
gi-4940	24	6	computer	computer	NOUN
gi-4940	24	7	graphics	graphic	NOUN
gi-4940	24	8	;	;	PUNCT
gi-4940	24	9	recall	recall	VERB
gi-4940	24	10	the	the	DET
gi-4940	24	11	decasteljau	decasteljau	ADJ
gi-4940	24	12	or	or	CCONJ
gi-4940	24	13	chaikin	chaikin	NOUN
gi-4940	24	14	’s	’s	PART
gi-4940	24	15	algorithms	algorithm	NOUN
gi-4940	24	16	for	for	ADP
gi-4940	24	17	the	the	DET
gi-4940	24	18	curve	curve	NOUN
gi-4940	24	19	approximation	approximation	NOUN
gi-4940	24	20	.	.	PUNCT
gi-4940	25	1	a	a	DET
gi-4940	25	2	combination	combination	NOUN
gi-4940	25	3	of	of	ADP
gi-4940	25	4	the	the	DET
gi-4940	25	5	uniform	uniform	NOUN
gi-4940	25	6	and	and	CCONJ
gi-4940	25	7	adaptive	adaptive	ADJ
gi-4940	25	8	sampling	sampling	NOUN
gi-4940	25	9	techniques	technique	NOUN
gi-4940	25	10	synthesizes	synthesize	VERB
gi-4940	25	11	their	their	PRON
gi-4940	25	12	advantages	advantage	NOUN
gi-4940	25	13	,	,	PUNCT
gi-4940	25	14	which	which	PRON
gi-4940	25	15	is	be	AUX
gi-4940	25	16	discussed	discuss	VERB
gi-4940	25	17	in	in	ADP
gi-4940	25	18	[	[	X
gi-4940	25	19	5	5	NUM
gi-4940	25	20	]	]	PUNCT
gi-4940	25	21	.	.	PUNCT
gi-4940	26	1	taking	take	VERB
gi-4940	26	2	into	into	ADP
gi-4940	26	3	account	account	NOUN
gi-4940	26	4	the	the	DET
gi-4940	26	5	facts	fact	NOUN
gi-4940	26	6	mentioned	mention	VERB
gi-4940	26	7	above	above	ADV
gi-4940	26	8	,	,	PUNCT
gi-4940	26	9	this	this	DET
gi-4940	26	10	technique	technique	NOUN
gi-4940	26	11	may	may	AUX
gi-4940	26	12	provide	provide	VERB
gi-4940	26	13	a	a	DET
gi-4940	26	14	smooth	smooth	ADJ
gi-4940	26	15	and	and	CCONJ
gi-4940	26	16	natural	natural	ADJ
gi-4940	26	17	depiction	depiction	NOUN
gi-4940	26	18	of	of	ADP
gi-4940	26	19	the	the	DET
gi-4940	26	20	graticule	graticule	NOUN
gi-4940	26	21	which	which	PRON
gi-4940	26	22	is	be	AUX
gi-4940	26	23	less	less	ADJ
gi-4940	26	24	data	data	NOUN
gi-4940	26	25	-	-	PUNCT
gi-4940	26	26	redundant	redundant	ADJ
gi-4940	26	27	.	.	PUNCT
gi-4940	27	1	a	a	DET
gi-4940	27	2	full	full	ADJ
gi-4940	27	3	set	set	NOUN
gi-4940	27	4	of	of	ADP
gi-4940	27	5	the	the	DET
gi-4940	27	6	projection	projection	NOUN
gi-4940	27	7	geoinformatics	geoinformatic	NOUN
gi-4940	27	8	fce	fce	VERB
gi-4940	27	9	ctu	ctu	NOUN
gi-4940	27	10	17(2	17(2	NUM
gi-4940	27	11	)	)	PUNCT
gi-4940	27	12	,	,	PUNCT
gi-4940	27	13	2018	2018	NUM
gi-4940	28	1	,	,	PUNCT
gi-4940	28	2	doi:10.14311	doi:10.14311	NOUN
gi-4940	28	3	/	/	SYM
gi-4940	28	4	gi.17.2.3	gi.17.2.3	PROPN
gi-4940	28	5	31	31	NUM
gi-4940	28	6	http://orcid.org/0000-0001-6279-1926	http://orcid.org/0000-0001-6279-1926	PROPN
gi-4940	28	7	http://dx.doi.org/10.14311/gi.17.2.3	http://dx.doi.org/10.14311/gi.17.2.3	PROPN
gi-4940	28	8	http://creativecommons.org/licenses/by/4.0/	http://creativecommons.org/licenses/by/4.0/	PROPN
gi-4940	28	9	t.	t.	PROPN
gi-4940	28	10	bayer	bayer	PROPN
gi-4940	28	11	:	:	PUNCT
gi-4940	28	12	plotting	plot	VERB
gi-4940	28	13	the	the	DET
gi-4940	28	14	map	map	NOUN
gi-4940	28	15	projection	projection	NOUN
gi-4940	28	16	graticule	graticule	NOUN
gi-4940	28	17	with	with	ADP
gi-4940	28	18	discontinuities	discontinuity	NOUN
gi-4940	28	19	constant	constant	ADJ
gi-4940	28	20	values	value	NOUN
gi-4940	28	21	represented	represent	VERB
gi-4940	28	22	by	by	ADP
gi-4940	28	23	the	the	DET
gi-4940	28	24	projection	projection	NOUN
gi-4940	28	25	pole	pole	NOUN
gi-4940	28	26	k	k	PROPN
gi-4940	29	1	=	=	PUNCT
gi-4940	30	1	[	[	X
gi-4940	30	2	ϕk	ϕk	X
gi-4940	30	3	,	,	PUNCT
gi-4940	30	4	λk	λk	X
gi-4940	30	5	]	]	PUNCT
gi-4940	30	6	,	,	PUNCT
gi-4940	30	7	two	two	NUM
gi-4940	30	8	standard	standard	ADJ
gi-4940	30	9	parallels	parallel	VERB
gi-4940	30	10	ϕ′1	ϕ′1	ADJ
gi-4940	30	11	,	,	PUNCT
gi-4940	30	12	ϕ′2	ϕ′2	NOUN
gi-4940	30	13	,	,	PUNCT
gi-4940	30	14	and	and	CCONJ
gi-4940	30	15	the	the	DET
gi-4940	30	16	central	central	ADJ
gi-4940	30	17	meridian	meridian	PROPN
gi-4940	30	18	shift	shift	NOUN
gi-4940	30	19	λ′0	λ′0	PROPN
gi-4940	30	20	is	be	AUX
gi-4940	30	21	supported	support	VERB
gi-4940	30	22	.	.	PUNCT
gi-4940	31	1	they	they	PRON
gi-4940	31	2	have	have	VERB
gi-4940	31	3	a	a	DET
gi-4940	31	4	strong	strong	ADJ
gi-4940	31	5	influence	influence	NOUN
gi-4940	31	6	on	on	ADP
gi-4940	31	7	the	the	DET
gi-4940	31	8	shape	shape	NOUN
gi-4940	31	9	of	of	ADP
gi-4940	31	10	the	the	DET
gi-4940	31	11	graticule	graticule	NOUN
gi-4940	31	12	.	.	PUNCT
gi-4940	32	1	the	the	DET
gi-4940	32	2	last	last	ADJ
gi-4940	32	3	parameter	parameter	NOUN
gi-4940	32	4	makes	make	VERB
gi-4940	32	5	the	the	DET
gi-4940	32	6	process	process	NOUN
gi-4940	32	7	of	of	ADP
gi-4940	32	8	the	the	DET
gi-4940	32	9	graticule	graticule	NOUN
gi-4940	32	10	reconstruction	reconstruction	NOUN
gi-4940	32	11	more	more	ADV
gi-4940	32	12	difficult	difficult	ADJ
gi-4940	32	13	;	;	PUNCT
gi-4940	32	14	an	an	DET
gi-4940	32	15	intersection	intersection	NOUN
gi-4940	32	16	of	of	ADP
gi-4940	32	17	the	the	DET
gi-4940	32	18	meridian	meridian	PROPN
gi-4940	32	19	m(λ′0	m(λ′0	PROPN
gi-4940	32	20	)	)	PUNCT
gi-4940	32	21	with	with	ADP
gi-4940	32	22	the	the	DET
gi-4940	32	23	parallel	parallel	ADJ
gi-4940	32	24	p(ϕ	p(ϕ	NOUN
gi-4940	32	25	)	)	PUNCT
gi-4940	32	26	as	as	ADV
gi-4940	32	27	well	well	ADV
gi-4940	32	28	as	as	ADP
gi-4940	32	29	with	with	ADP
gi-4940	32	30	the	the	DET
gi-4940	32	31	meridian	meridian	PROPN
gi-4940	32	32	m(λ	m(λ	PROPN
gi-4940	32	33	)	)	PUNCT
gi-4940	32	34	need	need	VERB
gi-4940	32	35	to	to	PART
gi-4940	32	36	be	be	AUX
gi-4940	32	37	determined	determine	VERB
gi-4940	32	38	.	.	PUNCT
gi-4940	33	1	another	another	DET
gi-4940	33	2	essential	essential	ADJ
gi-4940	33	3	subproblem	subproblem	NOUN
gi-4940	33	4	is	be	AUX
gi-4940	33	5	represented	represent	VERB
gi-4940	33	6	by	by	ADP
gi-4940	33	7	the	the	DET
gi-4940	33	8	automatic	automatic	ADJ
gi-4940	33	9	detection	detection	NOUN
gi-4940	33	10	of	of	ADP
gi-4940	33	11	the	the	DET
gi-4940	33	12	discontinuities	discontinuity	NOUN
gi-4940	33	13	;	;	PUNCT
gi-4940	33	14	this	this	DET
gi-4940	33	15	issue	issue	NOUN
gi-4940	33	16	refers	refer	VERB
gi-4940	33	17	to	to	ADP
gi-4940	33	18	many	many	ADJ
gi-4940	33	19	coordinate	coordinate	NOUN
gi-4940	33	20	functions	function	NOUN
gi-4940	33	21	f	f	NOUN
gi-4940	33	22	,	,	PUNCT
gi-4940	33	23	g.	g.	PROPN
gi-4940	33	24	finally	finally	ADV
gi-4940	33	25	,	,	PUNCT
gi-4940	33	26	all	all	DET
gi-4940	33	27	algorithms	algorithm	NOUN
gi-4940	33	28	will	will	AUX
gi-4940	33	29	be	be	AUX
gi-4940	33	30	tested	test	VERB
gi-4940	33	31	on	on	ADP
gi-4940	33	32	the	the	DET
gi-4940	33	33	real	real	ADJ
gi-4940	33	34	cartographic	cartographic	ADJ
gi-4940	33	35	data	datum	NOUN
gi-4940	33	36	represented	represent	VERB
gi-4940	33	37	by	by	ADP
gi-4940	33	38	several	several	ADJ
gi-4940	33	39	projections	projection	NOUN
gi-4940	33	40	.	.	PUNCT
gi-4940	34	1	to	to	PART
gi-4940	34	2	illustrate	illustrate	VERB
gi-4940	34	3	the	the	DET
gi-4940	34	4	behavior	behavior	NOUN
gi-4940	34	5	,	,	PUNCT
gi-4940	34	6	properties	property	NOUN
gi-4940	34	7	,	,	PUNCT
gi-4940	34	8	and	and	CCONJ
gi-4940	34	9	drawbacks	drawback	NOUN
gi-4940	34	10	of	of	ADP
gi-4940	34	11	the	the	DET
gi-4940	34	12	proposed	propose	VERB
gi-4940	34	13	methods	method	NOUN
gi-4940	34	14	,	,	PUNCT
gi-4940	34	15	the	the	DET
gi-4940	34	16	projections	projection	NOUN
gi-4940	34	17	with	with	ADP
gi-4940	34	18	more	more	ADJ
gi-4940	34	19	singularities	singularity	NOUN
gi-4940	34	20	will	will	AUX
gi-4940	34	21	be	be	AUX
gi-4940	34	22	preferred	prefer	VERB
gi-4940	34	23	;	;	PUNCT
gi-4940	34	24	the	the	DET
gi-4940	34	25	fournier	fournier	PROPN
gi-4940	34	26	i.	i.	PROPN
gi-4940	34	27	projection	projection	PROPN
gi-4940	34	28	represents	represent	VERB
gi-4940	34	29	a	a	DET
gi-4940	34	30	typical	typical	ADJ
gi-4940	34	31	candidate	candidate	NOUN
gi-4940	34	32	.	.	PUNCT
gi-4940	35	1	apart	apart	ADV
gi-4940	35	2	from	from	ADP
gi-4940	35	3	current	current	ADJ
gi-4940	35	4	outcomes	outcome	NOUN
gi-4940	35	5	in	in	ADP
gi-4940	35	6	the	the	DET
gi-4940	35	7	cartographic	cartographic	ADJ
gi-4940	35	8	or	or	CCONJ
gi-4940	35	9	gis	gis	NOUN
gi-4940	35	10	software	software	NOUN
gi-4940	35	11	tools	tool	NOUN
gi-4940	35	12	,	,	PUNCT
gi-4940	35	13	several	several	ADJ
gi-4940	35	14	specific	specific	ADJ
gi-4940	35	15	applications	application	NOUN
gi-4940	35	16	may	may	AUX
gi-4940	35	17	occur	occur	VERB
gi-4940	35	18	.	.	PUNCT
gi-4940	36	1	let	let	VERB
gi-4940	36	2	us	we	PRON
gi-4940	36	3	mention	mention	VERB
gi-4940	36	4	the	the	DET
gi-4940	36	5	problem	problem	NOUN
gi-4940	36	6	of	of	ADP
gi-4940	36	7	the	the	DET
gi-4940	36	8	unknown	unknown	ADJ
gi-4940	36	9	map	map	NOUN
gi-4940	36	10	projection	projection	NOUN
gi-4940	36	11	analysis	analysis	NOUN
gi-4940	36	12	.	.	PUNCT
gi-4940	37	1	providing	provide	VERB
gi-4940	37	2	the	the	DET
gi-4940	37	3	visualization	visualization	NOUN
gi-4940	37	4	of	of	ADP
gi-4940	37	5	the	the	DET
gi-4940	37	6	results	result	NOUN
gi-4940	37	7	of	of	ADP
gi-4940	37	8	the	the	DET
gi-4940	37	9	detection	detection	NOUN
gi-4940	37	10	algorithm	algorithm	NOUN
gi-4940	37	11	illustrates	illustrate	VERB
gi-4940	37	12	its	its	PRON
gi-4940	37	13	efficiency	efficiency	NOUN
gi-4940	37	14	,	,	PUNCT
gi-4940	37	15	which	which	PRON
gi-4940	37	16	,	,	PUNCT
gi-4940	37	17	from	from	ADP
gi-4940	37	18	the	the	DET
gi-4940	37	19	“	"	PUNCT
gi-4940	37	20	raw	raw	ADJ
gi-4940	37	21	numbers	number	NOUN
gi-4940	37	22	”	"	PUNCT
gi-4940	37	23	,	,	PUNCT
gi-4940	37	24	may	may	AUX
gi-4940	37	25	not	not	PART
gi-4940	37	26	be	be	AUX
gi-4940	37	27	apparent	apparent	ADJ
gi-4940	37	28	.	.	PUNCT
gi-4940	38	1	this	this	DET
gi-4940	38	2	paper	paper	NOUN
gi-4940	38	3	is	be	AUX
gi-4940	38	4	organized	organize	VERB
gi-4940	38	5	as	as	SCONJ
gi-4940	38	6	follows	follow	VERB
gi-4940	38	7	.	.	PUNCT
gi-4940	39	1	in	in	ADP
gi-4940	39	2	section	section	NOUN
gi-4940	39	3	3	3	NUM
gi-4940	39	4	the	the	DET
gi-4940	39	5	mathematical	mathematical	ADJ
gi-4940	39	6	background	background	NOUN
gi-4940	39	7	of	of	ADP
gi-4940	39	8	the	the	DET
gi-4940	39	9	solution	solution	NOUN
gi-4940	39	10	is	be	AUX
gi-4940	39	11	described	describe	VERB
gi-4940	39	12	.	.	PUNCT
gi-4940	40	1	section	section	NOUN
gi-4940	40	2	4	4	NUM
gi-4940	40	3	is	be	AUX
gi-4940	40	4	devoted	devote	VERB
gi-4940	40	5	to	to	ADP
gi-4940	40	6	the	the	DET
gi-4940	40	7	proposed	propose	VERB
gi-4940	40	8	combined	combined	ADJ
gi-4940	40	9	sampling	sampling	NOUN
gi-4940	40	10	algorithm	algorithm	NOUN
gi-4940	40	11	,	,	PUNCT
gi-4940	40	12	the	the	DET
gi-4940	40	13	properties	property	NOUN
gi-4940	40	14	of	of	ADP
gi-4940	40	15	which	which	PRON
gi-4940	40	16	in	in	ADP
gi-4940	40	17	section	section	NOUN
gi-4940	40	18	5	5	NUM
gi-4940	40	19	will	will	AUX
gi-4940	40	20	serve	serve	VERB
gi-4940	40	21	to	to	PART
gi-4940	40	22	analyze	analyze	VERB
gi-4940	40	23	its	its	PRON
gi-4940	40	24	behavior	behavior	NOUN
gi-4940	40	25	on	on	ADP
gi-4940	40	26	real	real	ADJ
gi-4940	40	27	data	datum	NOUN
gi-4940	40	28	.	.	PUNCT
gi-4940	41	1	2	2	X
gi-4940	41	2	.	.	X
gi-4940	41	3	related	relate	VERB
gi-4940	41	4	work	work	NOUN
gi-4940	41	5	the	the	DET
gi-4940	41	6	polygonal	polygonal	ADJ
gi-4940	41	7	approximation	approximation	NOUN
gi-4940	41	8	of	of	ADP
gi-4940	41	9	the	the	DET
gi-4940	41	10	parametric	parametric	ADJ
gi-4940	41	11	curve	curve	NOUN
gi-4940	41	12	based	base	VERB
gi-4940	41	13	on	on	ADP
gi-4940	41	14	adaptive	adaptive	ADJ
gi-4940	41	15	sampling	sampling	NOUN
gi-4940	41	16	is	be	AUX
gi-4940	41	17	mentioned	mention	VERB
gi-4940	41	18	in	in	ADP
gi-4940	41	19	several	several	ADJ
gi-4940	41	20	papers	paper	NOUN
gi-4940	41	21	:	:	PUNCT
gi-4940	41	22	the	the	DET
gi-4940	41	23	refinement	refinement	NOUN
gi-4940	41	24	criteria	criterion	NOUN
gi-4940	41	25	in	in	ADP
gi-4940	41	26	[	[	X
gi-4940	41	27	12	12	NUM
gi-4940	41	28	]	]	PUNCT
gi-4940	41	29	,	,	PUNCT
gi-4940	41	30	the	the	DET
gi-4940	41	31	approximation	approximation	NOUN
gi-4940	41	32	by	by	ADP
gi-4940	41	33	polygonal	polygonal	ADJ
gi-4940	41	34	curves	curve	NOUN
gi-4940	41	35	in	in	ADP
gi-4940	41	36	[	[	X
gi-4940	41	37	7	7	NUM
gi-4940	41	38	]	]	PUNCT
gi-4940	41	39	,	,	PUNCT
gi-4940	41	40	the	the	DET
gi-4940	41	41	spatial	spatial	ADJ
gi-4940	41	42	approximation	approximation	NOUN
gi-4940	41	43	of	of	ADP
gi-4940	41	44	implicit	implicit	ADJ
gi-4940	41	45	curves	curve	NOUN
gi-4940	41	46	in	in	ADP
gi-4940	41	47	[	[	X
gi-4940	41	48	17	17	NUM
gi-4940	41	49	]	]	PUNCT
gi-4940	41	50	,	,	PUNCT
gi-4940	41	51	[	[	X
gi-4940	41	52	10	10	NUM
gi-4940	41	53	]	]	PUNCT
gi-4940	41	54	,	,	PUNCT
gi-4940	41	55	the	the	DET
gi-4940	41	56	affine	affine	NOUN
gi-4940	41	57	arithmetic	arithmetic	NOUN
gi-4940	41	58	working	work	VERB
gi-4940	41	59	in	in	ADP
gi-4940	41	60	triangulated	triangulate	VERB
gi-4940	41	61	models	model	NOUN
gi-4940	41	62	in	in	ADP
gi-4940	41	63	[	[	X
gi-4940	41	64	21	21	NUM
gi-4940	41	65	]	]	PUNCT
gi-4940	41	66	.	.	PUNCT
gi-4940	42	1	the	the	DET
gi-4940	42	2	curve	curve	NOUN
gi-4940	42	3	interpolation	interpolation	NOUN
gi-4940	42	4	algorithms	algorithm	NOUN
gi-4940	42	5	preserving	preserve	VERB
gi-4940	42	6	its	its	PRON
gi-4940	42	7	speed	speed	NOUN
gi-4940	42	8	are	be	AUX
gi-4940	42	9	described	describe	VERB
gi-4940	42	10	in	in	ADP
gi-4940	42	11	[	[	X
gi-4940	42	12	23	23	NUM
gi-4940	42	13	]	]	PUNCT
gi-4940	42	14	,	,	PUNCT
gi-4940	43	1	[	[	X
gi-4940	43	2	25	25	NUM
gi-4940	43	3	]	]	PUNCT
gi-4940	43	4	,	,	PUNCT
gi-4940	43	5	[	[	X
gi-4940	43	6	26	26	NUM
gi-4940	43	7	]	]	PUNCT
gi-4940	43	8	,	,	PUNCT
gi-4940	43	9	the	the	DET
gi-4940	43	10	adaptive	adaptive	ADJ
gi-4940	43	11	-	-	PUNCT
gi-4940	43	12	feed	feed	NOUN
gi-4940	43	13	rate	rate	NOUN
gi-4940	43	14	technique	technique	NOUN
gi-4940	43	15	in	in	ADP
gi-4940	43	16	[	[	X
gi-4940	43	17	27	27	NUM
gi-4940	43	18	]	]	PUNCT
gi-4940	43	19	.	.	PUNCT
gi-4940	44	1	however	however	ADV
gi-4940	44	2	,	,	PUNCT
gi-4940	44	3	the	the	DET
gi-4940	44	4	map	map	NOUN
gi-4940	44	5	projections	projection	NOUN
gi-4940	44	6	are	be	AUX
gi-4940	44	7	never	never	ADV
gi-4940	44	8	defined	define	VERB
gi-4940	44	9	by	by	ADP
gi-4940	44	10	the	the	DET
gi-4940	44	11	implicit	implicit	ADJ
gi-4940	44	12	equations	equation	NOUN
gi-4940	44	13	.	.	PUNCT
gi-4940	45	1	there	there	PRON
gi-4940	45	2	are	be	VERB
gi-4940	45	3	several	several	ADJ
gi-4940	45	4	papers	paper	NOUN
gi-4940	45	5	focused	focus	VERB
gi-4940	45	6	on	on	ADP
gi-4940	45	7	the	the	DET
gi-4940	45	8	approximation	approximation	NOUN
gi-4940	45	9	and	and	CCONJ
gi-4940	45	10	drawing	draw	VERB
gi-4940	45	11	the	the	DET
gi-4940	45	12	functions	function	NOUN
gi-4940	45	13	or	or	CCONJ
gi-4940	45	14	surfaces	surface	NOUN
gi-4940	45	15	containing	contain	VERB
gi-4940	45	16	discontinuities	discontinuity	NOUN
gi-4940	45	17	.	.	PUNCT
gi-4940	46	1	the	the	DET
gi-4940	46	2	interpolation	interpolation	NOUN
gi-4940	46	3	and	and	CCONJ
gi-4940	46	4	approximation	approximation	NOUN
gi-4940	46	5	of	of	ADP
gi-4940	46	6	the	the	DET
gi-4940	46	7	piece	piece	NOUN
gi-4940	46	8	-	-	PUNCT
gi-4940	46	9	wise	wise	ADJ
gi-4940	46	10	smooth	smooth	ADJ
gi-4940	46	11	functions	function	NOUN
gi-4940	46	12	are	be	AUX
gi-4940	46	13	discussed	discuss	VERB
gi-4940	46	14	in	in	ADP
gi-4940	46	15	[	[	X
gi-4940	46	16	2	2	NUM
gi-4940	46	17	]	]	PUNCT
gi-4940	46	18	,	,	PUNCT
gi-4940	46	19	[	[	X
gi-4940	46	20	9	9	NUM
gi-4940	46	21	]	]	PUNCT
gi-4940	46	22	.	.	PUNCT
gi-4940	47	1	several	several	ADJ
gi-4940	47	2	detection	detection	NOUN
gi-4940	47	3	methods	method	NOUN
gi-4940	47	4	for	for	ADP
gi-4940	47	5	the	the	DET
gi-4940	47	6	localization	localization	NOUN
gi-4940	47	7	of	of	ADP
gi-4940	47	8	the	the	DET
gi-4940	47	9	singularities	singularity	NOUN
gi-4940	47	10	of	of	ADP
gi-4940	47	11	surfaces	surface	NOUN
gi-4940	47	12	can	can	AUX
gi-4940	47	13	be	be	AUX
gi-4940	47	14	found	find	VERB
gi-4940	47	15	in	in	ADP
gi-4940	47	16	[	[	X
gi-4940	47	17	13	13	NUM
gi-4940	47	18	]	]	PUNCT
gi-4940	47	19	,	,	PUNCT
gi-4940	47	20	[	[	X
gi-4940	47	21	22	22	NUM
gi-4940	47	22	]	]	PUNCT
gi-4940	47	23	,	,	PUNCT
gi-4940	47	24	[	[	X
gi-4940	47	25	19	19	NUM
gi-4940	47	26	]	]	PUNCT
gi-4940	47	27	,	,	PUNCT
gi-4940	47	28	[	[	X
gi-4940	47	29	11	11	NUM
gi-4940	47	30	]	]	PUNCT
gi-4940	47	31	,	,	PUNCT
gi-4940	47	32	[	[	X
gi-4940	47	33	18	18	NUM
gi-4940	47	34	]	]	PUNCT
gi-4940	47	35	,	,	PUNCT
gi-4940	47	36	[	[	X
gi-4940	47	37	1	1	NUM
gi-4940	47	38	]	]	PUNCT
gi-4940	47	39	,	,	PUNCT
gi-4940	47	40	[	[	X
gi-4940	47	41	8	8	NUM
gi-4940	47	42	]	]	PUNCT
gi-4940	47	43	,	,	PUNCT
gi-4940	47	44	the	the	DET
gi-4940	47	45	combined	combine	VERB
gi-4940	47	46	sampling	sampling	NOUN
gi-4940	47	47	technique	technique	NOUN
gi-4940	47	48	in	in	ADP
gi-4940	47	49	[	[	X
gi-4940	47	50	5	5	NUM
gi-4940	47	51	]	]	PUNCT
gi-4940	47	52	.	.	PUNCT
gi-4940	48	1	the	the	DET
gi-4940	48	2	reconstructed	reconstructed	ADJ
gi-4940	48	3	projection	projection	NOUN
gi-4940	48	4	graticule	graticule	NOUN
gi-4940	48	5	and	and	CCONJ
gi-4940	48	6	its	its	PRON
gi-4940	48	7	plot	plot	NOUN
gi-4940	48	8	may	may	AUX
gi-4940	48	9	be	be	AUX
gi-4940	48	10	utilized	utilize	VERB
gi-4940	48	11	in	in	ADP
gi-4940	48	12	many	many	ADJ
gi-4940	48	13	cartographic	cartographic	ADJ
gi-4940	48	14	or	or	CCONJ
gi-4940	48	15	gis	gis	NOUN
gi-4940	48	16	applications	application	NOUN
gi-4940	48	17	.	.	PUNCT
gi-4940	49	1	an	an	DET
gi-4940	49	2	interesting	interesting	ADJ
gi-4940	49	3	application	application	NOUN
gi-4940	49	4	is	be	AUX
gi-4940	49	5	represented	represent	VERB
gi-4940	49	6	by	by	ADP
gi-4940	49	7	the	the	DET
gi-4940	49	8	analysis	analysis	NOUN
gi-4940	49	9	of	of	ADP
gi-4940	49	10	the	the	DET
gi-4940	49	11	unknown	unknown	ADJ
gi-4940	49	12	map	map	NOUN
gi-4940	49	13	projection	projection	NOUN
gi-4940	49	14	described	describe	VERB
gi-4940	49	15	in	in	ADP
gi-4940	49	16	[	[	X
gi-4940	49	17	6	6	NUM
gi-4940	49	18	]	]	PUNCT
gi-4940	49	19	,	,	PUNCT
gi-4940	49	20	[	[	X
gi-4940	49	21	4	4	X
gi-4940	49	22	]	]	PUNCT
gi-4940	49	23	providing	provide	VERB
gi-4940	49	24	the	the	DET
gi-4940	49	25	visualization	visualization	NOUN
gi-4940	49	26	of	of	ADP
gi-4940	49	27	results	result	NOUN
gi-4940	49	28	of	of	ADP
gi-4940	49	29	the	the	DET
gi-4940	49	30	detection	detection	NOUN
gi-4940	49	31	algorithms	algorithm	NOUN
gi-4940	49	32	,	,	PUNCT
gi-4940	49	33	typically	typically	ADV
gi-4940	49	34	the	the	DET
gi-4940	49	35	reconstructed	reconstructed	ADJ
gi-4940	49	36	projection	projection	NOUN
gi-4940	49	37	graticule	graticule	NOUN
gi-4940	49	38	.	.	PUNCT
gi-4940	50	1	3	3	X
gi-4940	50	2	.	.	NOUN
gi-4940	50	3	map	map	NOUN
gi-4940	50	4	projection	projection	NOUN
gi-4940	50	5	and	and	CCONJ
gi-4940	50	6	its	its	PRON
gi-4940	50	7	properties	property	NOUN
gi-4940	50	8	let	let	VERB
gi-4940	50	9	s2	s2	NOUN
gi-4940	50	10	be	be	AUX
gi-4940	50	11	a	a	DET
gi-4940	50	12	sphere	sphere	NOUN
gi-4940	50	13	of	of	ADP
gi-4940	50	14	the	the	DET
gi-4940	50	15	radius	radius	NOUN
gi-4940	50	16	r	r	NOUN
gi-4940	50	17	in	in	ADP
gi-4940	50	18	r3	r3	PROPN
gi-4940	50	19	(	(	PUNCT
gi-4940	50	20	reference	reference	NOUN
gi-4940	50	21	surface	surface	NOUN
gi-4940	50	22	,	,	PUNCT
gi-4940	50	23	earth	earth	NOUN
gi-4940	50	24	)	)	PUNCT
gi-4940	50	25	,	,	PUNCT
gi-4940	50	26	a	a	PRON
gi-4940	50	27	=	=	X
gi-4940	50	28	(	(	PUNCT
gi-4940	50	29	0	0	NUM
gi-4940	50	30	,	,	PUNCT
gi-4940	50	31	0	0	NUM
gi-4940	50	32	,	,	PUNCT
gi-4940	50	33	r	r	NOUN
gi-4940	50	34	)	)	PUNCT
gi-4940	50	35	,	,	PUNCT
gi-4940	50	36	b	b	X
gi-4940	50	37	=	=	SYM
gi-4940	50	38	(	(	PUNCT
gi-4940	50	39	0	0	NUM
gi-4940	50	40	,	,	PUNCT
gi-4940	50	41	0,−r	0,−r	PROPN
gi-4940	50	42	)	)	PUNCT
gi-4940	50	43	north	north	NOUN
gi-4940	50	44	and	and	CCONJ
gi-4940	50	45	south	south	ADJ
gi-4940	50	46	poles	pole	NOUN
gi-4940	50	47	of	of	ADP
gi-4940	50	48	s2	s2	PROPN
gi-4940	50	49	,	,	PUNCT
gi-4940	50	50	and	and	CCONJ
gi-4940	50	51	σ	σ	VERB
gi-4940	50	52	a	a	DET
gi-4940	50	53	plane	plane	NOUN
gi-4940	50	54	.	.	PUNCT
gi-4940	51	1	for	for	ADP
gi-4940	51	2	a	a	DET
gi-4940	51	3	current	current	ADJ
gi-4940	51	4	point	point	NOUN
gi-4940	51	5	q	q	NOUN
gi-4940	52	1	=	=	PUNCT
gi-4940	52	2	[	[	X
gi-4940	52	3	ϕ	ϕ	X
gi-4940	52	4	,	,	PUNCT
gi-4940	52	5	λ	λ	X
gi-4940	52	6	]	]	X
gi-4940	52	7	∈	∈	PROPN
gi-4940	52	8	s2	s2	PROPN
gi-4940	52	9	,	,	PUNCT
gi-4940	52	10	different	different	ADJ
gi-4940	52	11	from	from	ADP
gi-4940	52	12	a	a	DET
gi-4940	52	13	,	,	PUNCT
gi-4940	52	14	b	b	NOUN
gi-4940	52	15	,	,	PUNCT
gi-4940	52	16	and	and	CCONJ
gi-4940	52	17	its	its	PRON
gi-4940	52	18	image	image	NOUN
gi-4940	52	19	p	p	NOUN
gi-4940	52	20	′	′	NOUN
gi-4940	52	21	=	=	PUNCT
gi-4940	53	1	[	[	X
gi-4940	53	2	x	x	X
gi-4940	53	3	,	,	PUNCT
gi-4940	53	4	y	y	PROPN
gi-4940	53	5	]	]	PUNCT
gi-4940	53	6	∈	∈	PROPN
gi-4940	53	7	σ	σ	PROPN
gi-4940	53	8	,	,	PUNCT
gi-4940	53	9	the	the	DET
gi-4940	53	10	map	map	NOUN
gi-4940	53	11	projection	projection	NOUN
gi-4940	53	12	p	p	NOUN
gi-4940	53	13	:	:	PUNCT
gi-4940	53	14	s2	s2	PROPN
gi-4940	53	15	−	−	PROPN
gi-4940	53	16	{	{	PUNCT
gi-4940	53	17	a	a	PROPN
gi-4940	53	18	,	,	PUNCT
gi-4940	53	19	b	b	NOUN
gi-4940	53	20	}	}	PUNCT
gi-4940	53	21	→	→	SYM
gi-4940	53	22	σ	σ	PROPN
gi-4940	53	23	,	,	PUNCT
gi-4940	53	24	p(q	p(q	PROPN
gi-4940	53	25	)	)	PUNCT
gi-4940	53	26	=	=	SYM
gi-4940	54	1	p	p	PROPN
gi-4940	54	2	′	′	NOUN
gi-4940	54	3	,	,	PUNCT
gi-4940	54	4	is	be	AUX
gi-4940	54	5	defined	define	VERB
gi-4940	54	6	by	by	ADP
gi-4940	54	7	the	the	DET
gi-4940	54	8	coordinate	coordinate	NOUN
gi-4940	54	9	functions	function	NOUN
gi-4940	54	10	f	f	NOUN
gi-4940	54	11	,	,	PUNCT
gi-4940	54	12	g	g	PROPN
gi-4940	54	13	,	,	PUNCT
gi-4940	54	14	of	of	ADP
gi-4940	54	15	two	two	NUM
gi-4940	54	16	independent	independent	ADJ
gi-4940	54	17	variables	variable	NOUN
gi-4940	54	18	ϕ	ϕ	PROPN
gi-4940	54	19	,	,	PUNCT
gi-4940	54	20	λ	λ	X
gi-4940	54	21	x	x	SYM
gi-4940	54	22	=	=	SYM
gi-4940	54	23	f	f	X
gi-4940	54	24	(	(	PUNCT
gi-4940	54	25	ϕ	ϕ	NOUN
gi-4940	54	26	,	,	PUNCT
gi-4940	54	27	λ	λ	PROPN
gi-4940	54	28	)	)	PUNCT
gi-4940	54	29	,	,	PUNCT
gi-4940	54	30	y	y	PROPN
gi-4940	54	31	=	=	SYM
gi-4940	54	32	g(ϕ	g(ϕ	PROPN
gi-4940	54	33	,	,	PUNCT
gi-4940	54	34	λ	λ	NOUN
gi-4940	54	35	)	)	PUNCT
gi-4940	54	36	,	,	PUNCT
gi-4940	54	37	(	(	PUNCT
gi-4940	54	38	3.1	3.1	NUM
gi-4940	54	39	)	)	PUNCT
gi-4940	54	40	which	which	PRON
gi-4940	54	41	are	be	AUX
gi-4940	54	42	continuous	continuous	ADJ
gi-4940	54	43	with	with	ADP
gi-4940	54	44	their	their	PRON
gi-4940	54	45	first	first	ADJ
gi-4940	54	46	order	order	NOUN
gi-4940	54	47	partial	partial	ADJ
gi-4940	54	48	derivatives	derivative	NOUN
gi-4940	54	49	,	,	PUNCT
gi-4940	54	50	finite	finite	NOUN
gi-4940	54	51	,	,	PUNCT
gi-4940	54	52	and	and	CCONJ
gi-4940	54	53	independent	independent	ADJ
gi-4940	54	54	.	.	PUNCT
gi-4940	55	1	a	a	DET
gi-4940	55	2	transformation	transformation	NOUN
gi-4940	55	3	between	between	ADP
gi-4940	55	4	the	the	DET
gi-4940	55	5	normal	normal	ADJ
gi-4940	55	6	and	and	CCONJ
gi-4940	55	7	oblique	oblique	ADJ
gi-4940	55	8	aspects	aspect	NOUN
gi-4940	55	9	is	be	AUX
gi-4940	55	10	performed	perform	VERB
gi-4940	55	11	using	use	VERB
gi-4940	55	12	the	the	DET
gi-4940	55	13	laws	law	NOUN
gi-4940	55	14	of	of	ADP
gi-4940	55	15	sphergeoinformatics	sphergeoinformatic	NOUN
gi-4940	55	16	fce	fce	VERB
gi-4940	55	17	ctu	ctu	NOUN
gi-4940	55	18	17(2	17(2	NUM
gi-4940	55	19	)	)	PUNCT
gi-4940	55	20	,	,	PUNCT
gi-4940	55	21	2018	2018	NUM
gi-4940	55	22	32	32	NUM
gi-4940	55	23	t.	t.	NOUN
gi-4940	55	24	bayer	bayer	PROPN
gi-4940	55	25	:	:	PUNCT
gi-4940	55	26	plotting	plot	VERB
gi-4940	55	27	the	the	DET
gi-4940	55	28	map	map	NOUN
gi-4940	55	29	projection	projection	NOUN
gi-4940	55	30	graticule	graticule	NOUN
gi-4940	55	31	with	with	ADP
gi-4940	55	32	discontinuities	discontinuity	NOUN
gi-4940	55	33	ical	ical	PROPN
gi-4940	55	34	trigonometry	trigonometry	NOUN
gi-4940	55	35	sinϕ′	sinϕ′	PART
gi-4940	55	36	=	=	NOUN
gi-4940	55	37	sinϕk	sinϕk	NOUN
gi-4940	55	38	sinϕ+	sinϕ+	ADP
gi-4940	55	39	cosϕk	cosϕk	ADV
gi-4940	55	40	cosϕ	cosϕ	NOUN
gi-4940	55	41	cos	cos	PROPN
gi-4940	55	42	∆λ	∆λ	PROPN
gi-4940	55	43	,	,	PUNCT
gi-4940	55	44	(	(	PUNCT
gi-4940	55	45	3.2	3.2	NUM
gi-4940	55	46	)	)	PUNCT
gi-4940	55	47	tanλ′	tanλ′	VERB
gi-4940	56	1	=	=	NOUN
gi-4940	56	2	cosϕ	cosϕ	PRON
gi-4940	56	3	sin	sin	NOUN
gi-4940	56	4	∆λ	∆λ	PROPN
gi-4940	56	5	cosϕ	cosϕ	NOUN
gi-4940	56	6	sinϕk	sinϕk	NOUN
gi-4940	56	7	cos	cos	ADP
gi-4940	56	8	∆λ−	∆λ−	PROPN
gi-4940	56	9	sinϕ	sinϕ	PROPN
gi-4940	56	10	cosϕk	cosϕk	ADV
gi-4940	56	11	,	,	PUNCT
gi-4940	56	12	(	(	PUNCT
gi-4940	56	13	3.3	3.3	NUM
gi-4940	56	14	)	)	PUNCT
gi-4940	56	15	where	where	SCONJ
gi-4940	56	16	ϕ′	ϕ′	NOUN
gi-4940	56	17	,	,	PUNCT
gi-4940	56	18	λ′	λ′	PROPN
gi-4940	56	19	are	be	AUX
gi-4940	56	20	the	the	DET
gi-4940	56	21	spherical	spherical	ADJ
gi-4940	56	22	coordinates	coordinate	NOUN
gi-4940	56	23	related	relate	VERB
gi-4940	56	24	to	to	ADP
gi-4940	56	25	k.	k.	NOUN
gi-4940	56	26	the	the	DET
gi-4940	56	27	inverse	inverse	NOUN
gi-4940	56	28	transformation	transformation	NOUN
gi-4940	56	29	has	have	VERB
gi-4940	56	30	the	the	DET
gi-4940	56	31	form	form	NOUN
gi-4940	56	32	of	of	ADP
gi-4940	56	33	sinϕ	sinϕ	NOUN
gi-4940	56	34	=	=	PROPN
gi-4940	56	35	sinϕk	sinϕk	NOUN
gi-4940	56	36	sinϕ′	sinϕ′	VERB
gi-4940	57	1	−	−	PROPN
gi-4940	57	2	cosϕk	cosϕk	INTJ
gi-4940	57	3	cosϕ′	cosϕ′	X
gi-4940	57	4	cosλ′	cosλ′	NOUN
gi-4940	57	5	,	,	PUNCT
gi-4940	57	6	(	(	PUNCT
gi-4940	57	7	3.4	3.4	NUM
gi-4940	57	8	)	)	PUNCT
gi-4940	57	9	tan	tan	NOUN
gi-4940	57	10	∆λ	∆λ	PROPN
gi-4940	57	11	=	=	PUNCT
gi-4940	57	12	cosϕ′	cosϕ′	X
gi-4940	58	1	sinλ′	sinλ′	PROPN
gi-4940	58	2	cosϕ′	cosϕ′	X
gi-4940	58	3	sinϕk	sinϕk	NOUN
gi-4940	58	4	cosλ′	cosλ′	PROPN
gi-4940	59	1	+	+	CCONJ
gi-4940	59	2	sinϕ′	sinϕ′	X
gi-4940	59	3	cosϕk	cosϕk	INTJ
gi-4940	59	4	,	,	PUNCT
gi-4940	59	5	(	(	PUNCT
gi-4940	59	6	3.5	3.5	NUM
gi-4940	59	7	)	)	PUNCT
gi-4940	59	8	where	where	SCONJ
gi-4940	59	9	∆λ	∆λ	PROPN
gi-4940	59	10	=	=	SYM
gi-4940	59	11	λ−λk	λ−λk	PROPN
gi-4940	59	12	.	.	PUNCT
gi-4940	60	1	a	a	DET
gi-4940	60	2	meridian	meridian	NOUN
gi-4940	60	3	of	of	ADP
gi-4940	60	4	the	the	DET
gi-4940	60	5	sphere	sphere	NOUN
gi-4940	60	6	s2	s2	NOUN
gi-4940	60	7	is	be	AUX
gi-4940	60	8	a	a	DET
gi-4940	60	9	curve	curve	NOUN
gi-4940	60	10	m(ϕ	m(ϕ	NOUN
gi-4940	60	11	,	,	PUNCT
gi-4940	60	12	λc	λc	NOUN
gi-4940	60	13	)	)	PUNCT
gi-4940	60	14	,	,	PUNCT
gi-4940	60	15	ϕ	ϕ	PROPN
gi-4940	60	16	∈	∈	PROPN
gi-4940	61	1	[	[	X
gi-4940	61	2	−π	−π	ADP
gi-4940	61	3	2	2	NUM
gi-4940	61	4	,	,	PUNCT
gi-4940	61	5	π	π	PROPN
gi-4940	61	6	2	2	NUM
gi-4940	61	7	]	]	PUNCT
gi-4940	61	8	,	,	PUNCT
gi-4940	61	9	λc	λc	X
gi-4940	61	10	=	=	SYM
gi-4940	61	11	const	const	PROPN
gi-4940	61	12	;	;	PUNCT
gi-4940	61	13	its	its	PRON
gi-4940	61	14	image	image	NOUN
gi-4940	61	15	in	in	ADP
gi-4940	61	16	p	p	PROPN
gi-4940	61	17	is	be	AUX
gi-4940	61	18	m̃(ϕ	m̃(ϕ	PROPN
gi-4940	61	19	,	,	PUNCT
gi-4940	61	20	λc	λc	NOUN
gi-4940	61	21	)	)	PUNCT
gi-4940	61	22	=	=	SYM
gi-4940	62	1	(	(	PUNCT
gi-4940	62	2	f	f	X
gi-4940	62	3	(	(	PUNCT
gi-4940	62	4	ϕ	ϕ	NOUN
gi-4940	62	5	,	,	PUNCT
gi-4940	62	6	λc	λc	NOUN
gi-4940	62	7	)	)	PUNCT
gi-4940	62	8	,	,	PUNCT
gi-4940	62	9	g(ϕ	g(ϕ	PROPN
gi-4940	62	10	,	,	PUNCT
gi-4940	62	11	λc	λc	NOUN
gi-4940	62	12	)	)	PUNCT
gi-4940	62	13	)	)	PUNCT
gi-4940	62	14	.	.	PUNCT
gi-4940	63	1	a	a	DET
gi-4940	63	2	parallel	parallel	NOUN
gi-4940	63	3	of	of	ADP
gi-4940	63	4	the	the	DET
gi-4940	63	5	sphere	sphere	NOUN
gi-4940	63	6	s2	s2	NOUN
gi-4940	63	7	in	in	ADP
gi-4940	63	8	r3	r3	PROPN
gi-4940	63	9	is	be	AUX
gi-4940	63	10	a	a	DET
gi-4940	63	11	curve	curve	NOUN
gi-4940	63	12	p(ϕc	p(ϕc	NOUN
gi-4940	63	13	,	,	PUNCT
gi-4940	63	14	λ	λ	PROPN
gi-4940	63	15	)	)	PUNCT
gi-4940	63	16	,	,	PUNCT
gi-4940	64	1	λ	λ	PROPN
gi-4940	64	2	∈	∈	PROPN
gi-4940	65	1	[	[	X
gi-4940	65	2	−π	−π	PROPN
gi-4940	65	3	,	,	PUNCT
gi-4940	65	4	π	π	PROPN
gi-4940	65	5	]	]	X
gi-4940	65	6	,	,	PUNCT
gi-4940	65	7	ϕc	ϕc	NOUN
gi-4940	65	8	=	=	SYM
gi-4940	65	9	const	const	PROPN
gi-4940	65	10	;	;	PUNCT
gi-4940	65	11	its	its	PRON
gi-4940	65	12	image	image	NOUN
gi-4940	65	13	in	in	ADP
gi-4940	65	14	p	p	PROPN
gi-4940	65	15	is	be	AUX
gi-4940	65	16	p̃(ϕc	p̃(ϕc	NOUN
gi-4940	65	17	,	,	PUNCT
gi-4940	65	18	λ	λ	X
gi-4940	65	19	)	)	PUNCT
gi-4940	65	20	=	=	SYM
gi-4940	66	1	(	(	PUNCT
gi-4940	66	2	f	f	X
gi-4940	66	3	(	(	PUNCT
gi-4940	66	4	ϕc	ϕc	PROPN
gi-4940	66	5	,	,	PUNCT
gi-4940	66	6	λ	λ	PROPN
gi-4940	66	7	)	)	PUNCT
gi-4940	66	8	,	,	PUNCT
gi-4940	66	9	g(ϕc	g(ϕc	PROPN
gi-4940	66	10	,	,	PUNCT
gi-4940	66	11	λ	λ	NOUN
gi-4940	66	12	)	)	PUNCT
gi-4940	66	13	)	)	PUNCT
gi-4940	66	14	.	.	PUNCT
gi-4940	67	1	in	in	ADP
gi-4940	67	2	the	the	DET
gi-4940	67	3	simplified	simplified	ADJ
gi-4940	67	4	notation	notation	NOUN
gi-4940	67	5	m(λ	m(λ	PROPN
gi-4940	67	6	)	)	PUNCT
gi-4940	67	7	represents	represent	VERB
gi-4940	67	8	a	a	DET
gi-4940	67	9	meridian	meridian	NOUN
gi-4940	67	10	of	of	ADP
gi-4940	67	11	the	the	DET
gi-4940	67	12	longitude	longitude	ADJ
gi-4940	67	13	λ	λ	PROPN
gi-4940	67	14	,	,	PUNCT
gi-4940	67	15	p(ϕ	p(ϕ	PROPN
gi-4940	67	16	)	)	PUNCT
gi-4940	67	17	a	a	DET
gi-4940	67	18	parallel	parallel	NOUN
gi-4940	67	19	of	of	ADP
gi-4940	67	20	the	the	DET
gi-4940	67	21	latitude	latitude	NOUN
gi-4940	67	22	ϕ	ϕ	PROPN
gi-4940	67	23	and	and	CCONJ
gi-4940	67	24	m̃(λ	m̃(λ	PROPN
gi-4940	67	25	)	)	PUNCT
gi-4940	67	26	,	,	PUNCT
gi-4940	67	27	p̃(ϕ	p̃(ϕ	PROPN
gi-4940	67	28	)	)	PUNCT
gi-4940	67	29	their	their	PRON
gi-4940	67	30	projected	project	VERB
gi-4940	67	31	variants	variant	NOUN
gi-4940	67	32	.	.	PUNCT
gi-4940	68	1	3.1	3.1	NUM
gi-4940	68	2	.	.	NOUN
gi-4940	68	3	map	map	NOUN
gi-4940	68	4	projection	projection	NOUN
gi-4940	68	5	singularities	singularity	NOUN
gi-4940	68	6	during	during	ADP
gi-4940	68	7	the	the	DET
gi-4940	68	8	graticule	graticule	NOUN
gi-4940	68	9	construction	construction	NOUN
gi-4940	68	10	,	,	PUNCT
gi-4940	68	11	several	several	ADJ
gi-4940	68	12	types	type	NOUN
gi-4940	68	13	of	of	ADP
gi-4940	68	14	singularities	singularity	NOUN
gi-4940	68	15	occur	occur	VERB
gi-4940	68	16	;	;	PUNCT
gi-4940	68	17	see	see	VERB
gi-4940	68	18	fig	fig	NOUN
gi-4940	68	19	.	.	PUNCT
gi-4940	69	1	3.2	3.2	NUM
gi-4940	69	2	.	.	PUNCT
gi-4940	70	1	the	the	DET
gi-4940	70	2	sampling	sample	VERB
gi-4940	70	3	algorithm	algorithm	NOUN
gi-4940	70	4	should	should	AUX
gi-4940	70	5	be	be	AUX
gi-4940	70	6	adapted	adapt	VERB
gi-4940	70	7	to	to	ADP
gi-4940	70	8	these	these	DET
gi-4940	70	9	facts	fact	NOUN
gi-4940	70	10	.	.	PUNCT
gi-4940	71	1	a	a	DET
gi-4940	71	2	meridian	meridian	NOUN
gi-4940	71	3	or	or	CCONJ
gi-4940	71	4	a	a	DET
gi-4940	71	5	parallel	parallel	NOUN
gi-4940	71	6	may	may	AUX
gi-4940	71	7	intersect	intersect	VERB
gi-4940	71	8	a	a	DET
gi-4940	71	9	singularity	singularity	NOUN
gi-4940	71	10	or	or	CCONJ
gi-4940	71	11	may	may	AUX
gi-4940	71	12	be	be	AUX
gi-4940	71	13	coincident	coincident	ADJ
gi-4940	71	14	.	.	PUNCT
gi-4940	72	1	there	there	PRON
gi-4940	72	2	are	be	VERB
gi-4940	72	3	several	several	ADJ
gi-4940	72	4	simple	simple	ADJ
gi-4940	72	5	strategies	strategy	NOUN
gi-4940	72	6	for	for	ADP
gi-4940	72	7	handling	handle	VERB
gi-4940	72	8	and	and	CCONJ
gi-4940	72	9	detecting	detect	VERB
gi-4940	72	10	the	the	DET
gi-4940	72	11	discontinuities	discontinuity	NOUN
gi-4940	72	12	;	;	PUNCT
gi-4940	72	13	their	their	PRON
gi-4940	72	14	overview	overview	NOUN
gi-4940	72	15	can	can	AUX
gi-4940	72	16	be	be	AUX
gi-4940	72	17	found	find	VERB
gi-4940	72	18	in	in	ADP
gi-4940	72	19	[	[	X
gi-4940	72	20	15	15	NUM
gi-4940	72	21	]	]	PUNCT
gi-4940	72	22	,	,	PUNCT
gi-4940	72	23	[	[	X
gi-4940	72	24	3	3	NUM
gi-4940	72	25	]	]	PUNCT
gi-4940	72	26	,	,	PUNCT
gi-4940	72	27	[	[	X
gi-4940	72	28	16	16	NUM
gi-4940	72	29	]	]	PUNCT
gi-4940	72	30	,	,	PUNCT
gi-4940	72	31	[	[	X
gi-4940	72	32	5	5	NUM
gi-4940	72	33	]	]	PUNCT
gi-4940	72	34	.	.	PUNCT
gi-4940	73	1	our	our	PRON
gi-4940	73	2	approach	approach	NOUN
gi-4940	73	3	is	be	AUX
gi-4940	73	4	based	base	VERB
gi-4940	73	5	on	on	ADP
gi-4940	73	6	the	the	DET
gi-4940	73	7	lr	lr	NOUN
gi-4940	73	8	criterion	criterion	NOUN
gi-4940	73	9	described	describe	VERB
gi-4940	73	10	in	in	ADP
gi-4940	73	11	[	[	X
gi-4940	73	12	20	20	NUM
gi-4940	73	13	]	]	PUNCT
gi-4940	73	14	.	.	PUNCT
gi-4940	74	1	coincidence	coincidence	NOUN
gi-4940	74	2	with	with	ADP
gi-4940	74	3	the	the	DET
gi-4940	74	4	infinite	infinite	ADJ
gi-4940	74	5	singularity	singularity	NOUN
gi-4940	74	6	.	.	PUNCT
gi-4940	75	1	if	if	SCONJ
gi-4940	75	2	the	the	DET
gi-4940	75	3	meridian	meridian	PROPN
gi-4940	75	4	m(λ	m(λ	PROPN
gi-4940	75	5	)	)	PUNCT
gi-4940	75	6	coincides	coincide	VERB
gi-4940	75	7	with	with	ADP
gi-4940	75	8	the	the	DET
gi-4940	75	9	infinite	infinite	ADJ
gi-4940	75	10	singularity	singularity	NOUN
gi-4940	75	11	c	c	NOUN
gi-4940	75	12	,	,	PUNCT
gi-4940	75	13	λ	λ	X
gi-4940	75	14	=	=	SYM
gi-4940	75	15	c	c	NOUN
gi-4940	75	16	,	,	PUNCT
gi-4940	75	17	then	then	ADV
gi-4940	75	18	,	,	PUNCT
gi-4940	75	19	lim	lim	PROPN
gi-4940	75	20	λ→c±	λ→c±	PROPN
gi-4940	75	21	f	f	PROPN
gi-4940	75	22	(	(	PUNCT
gi-4940	75	23	ϕ	ϕ	PROPN
gi-4940	75	24	,	,	PUNCT
gi-4940	75	25	λ	λ	NOUN
gi-4940	75	26	)	)	PUNCT
gi-4940	75	27	=	=	NOUN
gi-4940	75	28	∞∨	∞∨	PROPN
gi-4940	75	29	lim	lim	NOUN
gi-4940	75	30	λ→c±	λ→c±	PROPN
gi-4940	75	31	f	f	PROPN
gi-4940	75	32	(	(	PUNCT
gi-4940	75	33	ϕ	ϕ	PROPN
gi-4940	75	34	,	,	PUNCT
gi-4940	75	35	λ	λ	NOUN
gi-4940	75	36	)	)	PUNCT
gi-4940	75	37	=	=	SYM
gi-4940	75	38	−∞∨	−∞∨	PROPN
gi-4940	75	39	lim	lim	PROPN
gi-4940	75	40	λ→c±	λ→c±	PROPN
gi-4940	75	41	g(ϕ	g(ϕ	PROPN
gi-4940	75	42	,	,	PUNCT
gi-4940	75	43	λ	λ	NOUN
gi-4940	75	44	)	)	PUNCT
gi-4940	76	1	=	=	NOUN
gi-4940	76	2	∞∨	∞∨	PROPN
gi-4940	76	3	lim	lim	PROPN
gi-4940	76	4	λ→c±	λ→c±	PROPN
gi-4940	76	5	g(ϕ	g(ϕ	PROPN
gi-4940	76	6	,	,	PUNCT
gi-4940	76	7	λ	λ	NOUN
gi-4940	76	8	)	)	PUNCT
gi-4940	76	9	=	=	SYM
gi-4940	76	10	−∞	−∞	PROPN
gi-4940	76	11	,	,	PUNCT
gi-4940	76	12	(	(	PUNCT
gi-4940	76	13	case	case	NOUN
gi-4940	76	14	a	a	X
gi-4940	76	15	)	)	PUNCT
gi-4940	76	16	,	,	PUNCT
gi-4940	76	17	or	or	CCONJ
gi-4940	76	18	,	,	PUNCT
gi-4940	76	19	lim	lim	PROPN
gi-4940	76	20	λ→c±	λ→c±	PROPN
gi-4940	76	21	f	f	PROPN
gi-4940	76	22	(	(	PUNCT
gi-4940	76	23	ϕ	ϕ	PROPN
gi-4940	76	24	,	,	PUNCT
gi-4940	76	25	λ	λ	NOUN
gi-4940	76	26	)	)	PUNCT
gi-4940	77	1	=	=	SYM
gi-4940	77	2	±∞∨	±∞∨	PROPN
gi-4940	77	3	lim	lim	PROPN
gi-4940	77	4	λ→c±	λ→c±	PROPN
gi-4940	77	5	f	f	PROPN
gi-4940	77	6	(	(	PUNCT
gi-4940	77	7	ϕ	ϕ	PROPN
gi-4940	77	8	,	,	PUNCT
gi-4940	77	9	λ	λ	NOUN
gi-4940	77	10	)	)	PUNCT
gi-4940	77	11	=	=	SYM
gi-4940	77	12	∓∞∨	∓∞∨	PROPN
gi-4940	77	13	lim	lim	PROPN
gi-4940	77	14	λ→c±	λ→c±	PROPN
gi-4940	77	15	g(ϕ	g(ϕ	PROPN
gi-4940	77	16	,	,	PUNCT
gi-4940	77	17	λ	λ	NOUN
gi-4940	77	18	)	)	PUNCT
gi-4940	77	19	=	=	SYM
gi-4940	77	20	±∞∨	±∞∨	PROPN
gi-4940	77	21	lim	lim	PROPN
gi-4940	77	22	λ→c±	λ→c±	PROPN
gi-4940	77	23	g(ϕ	g(ϕ	PROPN
gi-4940	77	24	,	,	PUNCT
gi-4940	77	25	λ	λ	NOUN
gi-4940	77	26	)	)	PUNCT
gi-4940	77	27	=	=	SYM
gi-4940	77	28	∓∞	∓∞	PROPN
gi-4940	77	29	,	,	PUNCT
gi-4940	77	30	(	(	PUNCT
gi-4940	77	31	case	case	NOUN
gi-4940	77	32	b	b	X
gi-4940	77	33	)	)	PUNCT
gi-4940	77	34	for	for	ADP
gi-4940	77	35	any	any	DET
gi-4940	77	36	ϕ	ϕ	PROPN
gi-4940	77	37	∈	∈	PROPN
gi-4940	77	38	(	(	PUNCT
gi-4940	77	39	−π/2	−π/2	PROPN
gi-4940	77	40	,	,	PUNCT
gi-4940	77	41	π/2	π/2	NUM
gi-4940	77	42	)	)	PUNCT
gi-4940	77	43	.	.	PUNCT
gi-4940	78	1	using	use	VERB
gi-4940	78	2	the	the	DET
gi-4940	78	3	leftand	leftand	NOUN
gi-4940	78	4	right	right	NOUN
gi-4940	78	5	-	-	PUNCT
gi-4940	78	6	boundaries	boundary	NOUN
gi-4940	78	7	(	(	PUNCT
gi-4940	78	8	c+	c+	NOUN
gi-4940	78	9	ε	ε	PROPN
gi-4940	78	10	)	)	PUNCT
gi-4940	78	11	and	and	CCONJ
gi-4940	78	12	(	(	PUNCT
gi-4940	78	13	c−	c−	X
gi-4940	78	14	ε	ε	PROPN
gi-4940	78	15	)	)	PUNCT
gi-4940	78	16	in	in	ADP
gi-4940	78	17	case	case	NOUN
gi-4940	78	18	a	a	X
gi-4940	78	19	,	,	PUNCT
gi-4940	78	20	the	the	DET
gi-4940	78	21	original	original	ADJ
gi-4940	78	22	projected	project	VERB
gi-4940	78	23	meridian	meridian	PROPN
gi-4940	78	24	m̃(c	m̃(c	PROPN
gi-4940	78	25	)	)	PUNCT
gi-4940	78	26	is	be	AUX
gi-4940	78	27	replaced	replace	VERB
gi-4940	78	28	with	with	ADP
gi-4940	78	29	m̃(c	m̃(c	PROPN
gi-4940	78	30	)	)	PUNCT
gi-4940	78	31	=	=	SYM
gi-4940	79	1	0.5	0.5	NUM
gi-4940	79	2	[	[	PUNCT
gi-4940	79	3	m̃(c−	m̃(c−	NUM
gi-4940	79	4	ε	ε	PROPN
gi-4940	79	5	)	)	PUNCT
gi-4940	79	6	+	+	CCONJ
gi-4940	79	7	m̃(c+	m̃(c+	PROPN
gi-4940	79	8	ε	ε	PROPN
gi-4940	79	9	)	)	PUNCT
gi-4940	79	10	]	]	PUNCT
gi-4940	79	11	.	.	PUNCT
gi-4940	80	1	for	for	ADP
gi-4940	80	2	case	case	NOUN
gi-4940	80	3	b	b	X
gi-4940	80	4	,	,	PUNCT
gi-4940	80	5	the	the	DET
gi-4940	80	6	original	original	ADJ
gi-4940	80	7	meridian	meridian	PROPN
gi-4940	80	8	m(λ	m(λ	PROPN
gi-4940	80	9	)	)	PUNCT
gi-4940	80	10	is	be	AUX
gi-4940	80	11	replaced	replace	VERB
gi-4940	80	12	with	with	ADP
gi-4940	80	13	two	two	NUM
gi-4940	80	14	new	new	ADJ
gi-4940	80	15	meridians	meridian	NOUN
gi-4940	80	16	m−(λ→	m−(λ→	X
gi-4940	80	17	c−	c−	ADJ
gi-4940	80	18	)	)	PUNCT
gi-4940	80	19	,	,	PUNCT
gi-4940	80	20	and	and	CCONJ
gi-4940	80	21	m+(λ	m+(λ	NOUN
gi-4940	80	22	→	→	SYM
gi-4940	80	23	c+	c+	X
gi-4940	80	24	)	)	PUNCT
gi-4940	80	25	.	.	PUNCT
gi-4940	81	1	analogously	analogously	ADV
gi-4940	81	2	,	,	PUNCT
gi-4940	81	3	cases	case	NOUN
gi-4940	81	4	c	c	NOUN
gi-4940	81	5	,	,	PUNCT
gi-4940	81	6	d	d	NOUN
gi-4940	81	7	occur	occur	VERB
gi-4940	81	8	,	,	PUNCT
gi-4940	81	9	if	if	SCONJ
gi-4940	81	10	a	a	DET
gi-4940	81	11	parallel	parallel	ADJ
gi-4940	81	12	p(ϕ	p(ϕ	NOUN
gi-4940	81	13	)	)	PUNCT
gi-4940	81	14	coincides	coincide	VERB
gi-4940	81	15	with	with	ADP
gi-4940	81	16	the	the	DET
gi-4940	81	17	infinite	infinite	ADJ
gi-4940	81	18	singularity	singularity	NOUN
gi-4940	81	19	c	c	NOUN
gi-4940	81	20	,	,	PUNCT
gi-4940	82	1	lim	lim	PROPN
gi-4940	82	2	ϕ→c±	ϕ→c±	PROPN
gi-4940	82	3	f	f	PROPN
gi-4940	82	4	(	(	PUNCT
gi-4940	82	5	ϕ	ϕ	PROPN
gi-4940	82	6	,	,	PUNCT
gi-4940	82	7	λ	λ	NOUN
gi-4940	82	8	)	)	PUNCT
gi-4940	82	9	=	=	NOUN
gi-4940	82	10	∞∨	∞∨	PROPN
gi-4940	82	11	lim	lim	PROPN
gi-4940	82	12	ϕ→c±	ϕ→c±	PROPN
gi-4940	82	13	f	f	PROPN
gi-4940	82	14	(	(	PUNCT
gi-4940	82	15	ϕ	ϕ	PROPN
gi-4940	82	16	,	,	PUNCT
gi-4940	82	17	λ	λ	NOUN
gi-4940	82	18	)	)	PUNCT
gi-4940	82	19	=	=	SYM
gi-4940	82	20	−∞∨	−∞∨	PROPN
gi-4940	82	21	lim	lim	PROPN
gi-4940	82	22	ϕ→c±	ϕ→c±	PROPN
gi-4940	82	23	g(ϕ	g(ϕ	PROPN
gi-4940	82	24	,	,	PUNCT
gi-4940	82	25	λ	λ	NOUN
gi-4940	82	26	)	)	PUNCT
gi-4940	82	27	=	=	NOUN
gi-4940	82	28	∞∨	∞∨	PROPN
gi-4940	82	29	lim	lim	PROPN
gi-4940	82	30	ϕ→c±	ϕ→c±	PROPN
gi-4940	82	31	g(ϕ	g(ϕ	PROPN
gi-4940	82	32	,	,	PUNCT
gi-4940	82	33	λ	λ	NOUN
gi-4940	82	34	)	)	PUNCT
gi-4940	82	35	=	=	SYM
gi-4940	82	36	−∞	−∞	NOUN
gi-4940	82	37	,	,	PUNCT
gi-4940	82	38	or	or	CCONJ
gi-4940	82	39	,	,	PUNCT
gi-4940	82	40	if	if	SCONJ
gi-4940	82	41	,	,	PUNCT
gi-4940	82	42	lim	lim	PROPN
gi-4940	82	43	ϕ→c±	ϕ→c±	PROPN
gi-4940	82	44	f	f	PROPN
gi-4940	82	45	(	(	PUNCT
gi-4940	82	46	ϕ	ϕ	PROPN
gi-4940	82	47	,	,	PUNCT
gi-4940	82	48	λ	λ	NOUN
gi-4940	82	49	)	)	PUNCT
gi-4940	82	50	=	=	SYM
gi-4940	82	51	±∞∨	±∞∨	PROPN
gi-4940	82	52	lim	lim	PROPN
gi-4940	82	53	ϕ→c±	ϕ→c±	PROPN
gi-4940	82	54	f	f	PROPN
gi-4940	82	55	(	(	PUNCT
gi-4940	82	56	ϕ	ϕ	PROPN
gi-4940	82	57	,	,	PUNCT
gi-4940	82	58	λ	λ	NOUN
gi-4940	82	59	)	)	PUNCT
gi-4940	82	60	=	=	SYM
gi-4940	83	1	∓∞∨	∓∞∨	PROPN
gi-4940	83	2	lim	lim	PROPN
gi-4940	83	3	ϕ→c±	ϕ→c±	PROPN
gi-4940	83	4	g(ϕ	g(ϕ	PROPN
gi-4940	83	5	,	,	PUNCT
gi-4940	83	6	λ	λ	NOUN
gi-4940	83	7	)	)	PUNCT
gi-4940	83	8	=	=	SYM
gi-4940	83	9	±∞∨	±∞∨	PROPN
gi-4940	83	10	lim	lim	PROPN
gi-4940	83	11	ϕ→c±	ϕ→c±	PROPN
gi-4940	83	12	g(ϕ	g(ϕ	PROPN
gi-4940	83	13	,	,	PUNCT
gi-4940	83	14	λ	λ	NOUN
gi-4940	83	15	)	)	PUNCT
gi-4940	83	16	=	=	PUNCT
gi-4940	84	1	∓∞.	∓∞.	NOUN
gi-4940	84	2	geoinformatics	geoinformatic	NOUN
gi-4940	84	3	fce	fce	VERB
gi-4940	84	4	ctu	ctu	NOUN
gi-4940	84	5	17(2	17(2	NUM
gi-4940	84	6	)	)	PUNCT
gi-4940	84	7	,	,	PUNCT
gi-4940	84	8	2018	2018	NUM
gi-4940	84	9	33	33	NUM
gi-4940	84	10	t.	t.	NOUN
gi-4940	84	11	bayer	bayer	PROPN
gi-4940	84	12	:	:	PUNCT
gi-4940	84	13	plotting	plot	VERB
gi-4940	84	14	the	the	DET
gi-4940	84	15	map	map	NOUN
gi-4940	84	16	projection	projection	NOUN
gi-4940	84	17	graticule	graticule	NOUN
gi-4940	84	18	with	with	ADP
gi-4940	84	19	discontinuities	discontinuity	NOUN
gi-4940	84	20	−90	−90	NOUN
gi-4940	84	21	−60	−60	NOUN
gi-4940	84	22	−30	−30	NOUN
gi-4940	84	23	0	0	NUM
gi-4940	84	24	30	30	NUM
gi-4940	84	25	60	60	NUM
gi-4940	84	26	90	90	NUM
gi-4940	84	27	−10	−10	NOUN
gi-4940	84	28	−5	−5	ADV
gi-4940	84	29	0	0	NUM
gi-4940	84	30	5	5	NUM
gi-4940	84	31	10	10	NUM
gi-4940	84	32	hassler	hassler	PROPN
gi-4940	84	33	projection	projection	PROPN
gi-4940	84	34	−90	−90	PROPN
gi-4940	84	35	−60	−60	NOUN
gi-4940	84	36	−30	−30	NOUN
gi-4940	84	37	0	0	NUM
gi-4940	84	38	30	30	NUM
gi-4940	84	39	60	60	NUM
gi-4940	84	40	90	90	NUM
gi-4940	84	41	0	0	NUM
gi-4940	84	42	−50	−50	NOUN
gi-4940	84	43	100	100	NUM
gi-4940	84	44	150	150	NUM
gi-4940	84	45	gnomonic	gnomonic	ADJ
gi-4940	84	46	projection	projection	NOUN
gi-4940	84	47	−180	−180	NOUN
gi-4940	84	48	−120	−120	ADV
gi-4940	84	49	−60	−60	NOUN
gi-4940	84	50	0	0	NUM
gi-4940	85	1	60	60	NUM
gi-4940	85	2	120	120	NUM
gi-4940	85	3	180	180	NUM
gi-4940	85	4	0	0	NUM
gi-4940	85	5	50	50	NUM
gi-4940	85	6	100	100	NUM
gi-4940	85	7	150	150	NUM
gi-4940	85	8	apianus	apianus	PROPN
gi-4940	85	9	projection	projection	NOUN
gi-4940	85	10	f	f	PROPN
gi-4940	85	11	(	(	PUNCT
gi-4940	85	12	λ	λ	INTJ
gi-4940	85	13	)	)	PUNCT
gi-4940	86	1	[	[	X
gi-4940	86	2	k	k	X
gi-4940	86	3	m	m	VERB
gi-4940	86	4	]	]	X
gi-4940	86	5	−180	−180	NOUN
gi-4940	87	1	−120	−120	ADV
gi-4940	87	2	−60	−60	NOUN
gi-4940	87	3	0	0	NUM
gi-4940	88	1	60	60	NUM
gi-4940	88	2	120	120	NUM
gi-4940	88	3	180	180	NUM
gi-4940	88	4	−150	−150	ADJ
gi-4940	88	5	−100	−100	NOUN
gi-4940	88	6	−50	−50	NOUN
gi-4940	88	7	0	0	NUM
gi-4940	88	8	50	50	NUM
gi-4940	88	9	100	100	NUM
gi-4940	88	10	150	150	NUM
gi-4940	88	11	nicolosi	nicolosi	NOUN
gi-4940	88	12	projection	projection	NOUN
gi-4940	88	13	λ	λ	PROPN
gi-4940	89	1	[	[	X
gi-4940	89	2	deg]λ	deg]λ	PROPN
gi-4940	89	3	[	[	X
gi-4940	89	4	deg	deg	X
gi-4940	89	5	]	]	X
gi-4940	89	6	ϕ	ϕ	PROPN
gi-4940	90	1	[	[	X
gi-4940	90	2	deg	deg	X
gi-4940	90	3	]	]	X
gi-4940	90	4	ϕ	ϕ	PROPN
gi-4940	91	1	[	[	X
gi-4940	91	2	deg	deg	X
gi-4940	91	3	]	]	X
gi-4940	91	4	f	f	X
gi-4940	91	5	(	(	PUNCT
gi-4940	91	6	λ	λ	INTJ
gi-4940	91	7	)	)	PUNCT
gi-4940	92	1	[	[	X
gi-4940	92	2	k	k	X
gi-4940	92	3	m	m	VERB
gi-4940	92	4	]	]	X
gi-4940	92	5	f	f	X
gi-4940	92	6	(	(	PUNCT
gi-4940	92	7	ϕ	ϕ	NOUN
gi-4940	92	8	)	)	PUNCT
gi-4940	93	1	[	[	X
gi-4940	93	2	k	k	X
gi-4940	93	3	m	m	VERB
gi-4940	93	4	]	]	X
gi-4940	93	5	g	g	PROPN
gi-4940	93	6	(	(	PUNCT
gi-4940	93	7	ϕ	ϕ	NOUN
gi-4940	93	8	)	)	PUNCT
gi-4940	94	1	[	[	X
gi-4940	94	2	k	k	X
gi-4940	94	3	m	m	VERB
gi-4940	94	4	]	]	X
gi-4940	94	5	a	a	X
gi-4940	94	6	)	)	PUNCT
gi-4940	94	7	b	b	NOUN
gi-4940	94	8	)	)	PUNCT
gi-4940	94	9	c	c	NOUN
gi-4940	94	10	)	)	PUNCT
gi-4940	94	11	d	d	NOUN
gi-4940	94	12	)	)	PUNCT
gi-4940	94	13	figure	figure	NOUN
gi-4940	94	14	3.1	3.1	NUM
gi-4940	94	15	:	:	PUNCT
gi-4940	94	16	discontinuities	discontinuity	NOUN
gi-4940	94	17	of	of	ADP
gi-4940	94	18	the	the	DET
gi-4940	94	19	coordinate	coordinate	NOUN
gi-4940	94	20	functions	function	NOUN
gi-4940	94	21	f	f	NOUN
gi-4940	94	22	,	,	PUNCT
gi-4940	94	23	g	g	PROPN
gi-4940	94	24	and	and	CCONJ
gi-4940	94	25	asymptotes	asymptote	VERB
gi-4940	94	26	:	:	PUNCT
gi-4940	94	27	the	the	DET
gi-4940	94	28	removable	removable	ADJ
gi-4940	94	29	discontinuity	discontinuity	NOUN
gi-4940	94	30	(	(	PUNCT
gi-4940	94	31	hassler	hassler	PROPN
gi-4940	94	32	projection	projection	PROPN
gi-4940	94	33	)	)	PUNCT
gi-4940	94	34	,	,	PUNCT
gi-4940	94	35	the	the	DET
gi-4940	94	36	infinite	infinite	ADJ
gi-4940	94	37	discontinuity	discontinuity	NOUN
gi-4940	94	38	(	(	PUNCT
gi-4940	94	39	gnomonic	gnomonic	ADJ
gi-4940	94	40	projection	projection	NOUN
gi-4940	94	41	)	)	PUNCT
gi-4940	94	42	at	at	ADP
gi-4940	94	43	ϕ	ϕ	NOUN
gi-4940	94	44	=	=	SYM
gi-4940	94	45	0	0	PROPN
gi-4940	94	46	,	,	PUNCT
gi-4940	94	47	the	the	DET
gi-4940	94	48	infinite	infinite	ADJ
gi-4940	94	49	discontinuity	discontinuity	NOUN
gi-4940	94	50	(	(	PUNCT
gi-4940	94	51	apianus	apianu	NOUN
gi-4940	94	52	and	and	CCONJ
gi-4940	94	53	nicolosi	nicolosi	NOUN
gi-4940	94	54	projections	projection	NOUN
gi-4940	94	55	)	)	PUNCT
gi-4940	94	56	at	at	ADP
gi-4940	94	57	λ	λ	X
gi-4940	94	58	=	=	SYM
gi-4940	94	59	0	0	PROPN
gi-4940	94	60	.	.	PUNCT
gi-4940	95	1	for	for	ADP
gi-4940	95	2	case	case	NOUN
gi-4940	95	3	c	c	NOUN
gi-4940	95	4	,	,	PUNCT
gi-4940	95	5	the	the	DET
gi-4940	95	6	originally	originally	ADV
gi-4940	95	7	projected	project	VERB
gi-4940	95	8	parallel	parallel	ADJ
gi-4940	95	9	p̃(c	p̃(c	PROPN
gi-4940	95	10	)	)	PUNCT
gi-4940	95	11	may	may	AUX
gi-4940	95	12	be	be	AUX
gi-4940	95	13	replaced	replace	VERB
gi-4940	95	14	with	with	ADP
gi-4940	95	15	the	the	DET
gi-4940	95	16	average	average	ADJ
gi-4940	95	17	p̃(c	p̃(c	PROPN
gi-4940	95	18	)	)	PUNCT
gi-4940	95	19	=	=	PUNCT
gi-4940	96	1	0.5	0.5	NUM
gi-4940	96	2	[	[	X
gi-4940	96	3	p̃(c−	p̃(c−	NOUN
gi-4940	96	4	ε	ε	NOUN
gi-4940	96	5	)	)	PUNCT
gi-4940	96	6	+	+	CCONJ
gi-4940	96	7	p̃(c+	p̃(c+	PROPN
gi-4940	96	8	ε	ε	PROPN
gi-4940	96	9	)	)	PUNCT
gi-4940	96	10	]	]	PUNCT
gi-4940	96	11	,	,	PUNCT
gi-4940	96	12	(	(	PUNCT
gi-4940	96	13	3.6	3.6	NUM
gi-4940	96	14	)	)	PUNCT
gi-4940	96	15	for	for	ADP
gi-4940	96	16	case	case	NOUN
gi-4940	96	17	d	d	X
gi-4940	96	18	the	the	DET
gi-4940	96	19	parallel	parallel	ADJ
gi-4940	96	20	p(ϕ	p(ϕ	NOUN
gi-4940	96	21	)	)	PUNCT
gi-4940	96	22	is	be	AUX
gi-4940	96	23	replaced	replace	VERB
gi-4940	96	24	with	with	ADP
gi-4940	96	25	two	two	NUM
gi-4940	96	26	new	new	ADJ
gi-4940	96	27	parallels	parallel	NOUN
gi-4940	96	28	p−(ϕ→	p−(ϕ→	PROPN
gi-4940	96	29	c−	c−	PROPN
gi-4940	96	30	)	)	PUNCT
gi-4940	96	31	,	,	PUNCT
gi-4940	96	32	and	and	CCONJ
gi-4940	96	33	p+(ϕ→	p+(ϕ→	X
gi-4940	96	34	c+	c+	PROPN
gi-4940	96	35	)	)	PUNCT
gi-4940	96	36	.	.	PUNCT
gi-4940	97	1	the	the	DET
gi-4940	97	2	removable	removable	ADJ
gi-4940	97	3	discontinuities	discontinuity	NOUN
gi-4940	97	4	may	may	AUX
gi-4940	97	5	be	be	AUX
gi-4940	97	6	treated	treat	VERB
gi-4940	97	7	analogously	analogously	ADV
gi-4940	97	8	to	to	ADP
gi-4940	97	9	cases	case	NOUN
gi-4940	97	10	a	a	DET
gi-4940	97	11	,	,	PUNCT
gi-4940	97	12	c	c	X
gi-4940	97	13	,	,	PUNCT
gi-4940	97	14	the	the	DET
gi-4940	97	15	jump	jump	NOUN
gi-4940	97	16	discontinuities	discontinuity	NOUN
gi-4940	97	17	analogously	analogously	ADV
gi-4940	97	18	to	to	ADP
gi-4940	97	19	cases	case	NOUN
gi-4940	97	20	b	b	PROPN
gi-4940	97	21	,	,	PUNCT
gi-4940	97	22	d.	d.	PROPN
gi-4940	97	23	an	an	DET
gi-4940	97	24	example	example	NOUN
gi-4940	97	25	of	of	ADP
gi-4940	97	26	the	the	DET
gi-4940	97	27	coincidence	coincidence	NOUN
gi-4940	97	28	with	with	ADP
gi-4940	97	29	the	the	DET
gi-4940	97	30	discontinuities	discontinuity	NOUN
gi-4940	97	31	can	can	AUX
gi-4940	97	32	be	be	AUX
gi-4940	97	33	found	find	VERB
gi-4940	97	34	in	in	ADP
gi-4940	97	35	fig	fig	NOUN
gi-4940	97	36	.	.	PUNCT
gi-4940	98	1	3.2	3.2	NUM
gi-4940	98	2	.	.	PUNCT
gi-4940	98	3	intersection	intersection	NOUN
gi-4940	98	4	of	of	ADP
gi-4940	98	5	the	the	DET
gi-4940	98	6	singularity	singularity	NOUN
gi-4940	98	7	.	.	PUNCT
gi-4940	99	1	the	the	DET
gi-4940	99	2	singularity	singularity	NOUN
gi-4940	99	3	may	may	AUX
gi-4940	99	4	not	not	PART
gi-4940	99	5	affect	affect	VERB
gi-4940	99	6	the	the	DET
gi-4940	99	7	entire	entire	ADJ
gi-4940	99	8	meridian	meridian	NOUN
gi-4940	99	9	or	or	CCONJ
gi-4940	99	10	parallel	parallel	NOUN
gi-4940	99	11	,	,	PUNCT
gi-4940	99	12	but	but	CCONJ
gi-4940	99	13	only	only	ADV
gi-4940	99	14	some	some	DET
gi-4940	99	15	inferior	inferior	ADJ
gi-4940	99	16	points	point	NOUN
gi-4940	99	17	.	.	PUNCT
gi-4940	100	1	the	the	DET
gi-4940	100	2	meridian	meridian	PROPN
gi-4940	100	3	m(λ	m(λ	PROPN
gi-4940	100	4	)	)	PUNCT
gi-4940	100	5	intersects	intersect	VERB
gi-4940	100	6	the	the	DET
gi-4940	100	7	infinite	infinite	ADJ
gi-4940	100	8	singularity	singularity	NOUN
gi-4940	100	9	c	c	NOUN
gi-4940	100	10	at	at	ADP
gi-4940	100	11	the	the	DET
gi-4940	100	12	point	point	NOUN
gi-4940	100	13	qi	qi	NOUN
gi-4940	100	14	=	=	PUNCT
gi-4940	101	1	[	[	X
gi-4940	101	2	ϕi	ϕi	X
gi-4940	101	3	=	=	SYM
gi-4940	101	4	c	c	NOUN
gi-4940	101	5	,	,	PUNCT
gi-4940	101	6	λ	λ	X
gi-4940	101	7	]	]	X
gi-4940	101	8	,	,	PUNCT
gi-4940	102	1	if	if	SCONJ
gi-4940	102	2	lim	lim	PROPN
gi-4940	102	3	ϕi→c±	ϕi→c±	PROPN
gi-4940	102	4	f	f	PROPN
gi-4940	102	5	(	(	PUNCT
gi-4940	102	6	ϕi	ϕi	PROPN
gi-4940	102	7	,	,	PUNCT
gi-4940	102	8	λ	λ	NOUN
gi-4940	102	9	)	)	PUNCT
gi-4940	102	10	=	=	NOUN
gi-4940	102	11	∞∨	∞∨	PROPN
gi-4940	102	12	lim	lim	NOUN
gi-4940	103	1	ϕi→c+	ϕi→c+	PROPN
gi-4940	103	2	f	f	PROPN
gi-4940	103	3	(	(	PUNCT
gi-4940	103	4	ϕi	ϕi	PROPN
gi-4940	103	5	,	,	PUNCT
gi-4940	103	6	λ	λ	NOUN
gi-4940	103	7	)	)	PUNCT
gi-4940	103	8	=	=	SYM
gi-4940	103	9	−∞∨	−∞∨	PROPN
gi-4940	103	10	lim	lim	PROPN
gi-4940	103	11	ϕi→c±	ϕi→c±	PROPN
gi-4940	103	12	g(ϕi	g(ϕi	PROPN
gi-4940	103	13	,	,	PUNCT
gi-4940	103	14	λ	λ	X
gi-4940	103	15	)	)	PUNCT
gi-4940	103	16	=	=	NOUN
gi-4940	103	17	∞∨	∞∨	PROPN
gi-4940	103	18	lim	lim	PROPN
gi-4940	103	19	ϕi→c±	ϕi→c±	PROPN
gi-4940	103	20	g(ϕi	g(ϕi	PROPN
gi-4940	103	21	,	,	PUNCT
gi-4940	103	22	λ	λ	X
gi-4940	103	23	)	)	PUNCT
gi-4940	103	24	=	=	SYM
gi-4940	103	25	−∞	−∞	PROPN
gi-4940	103	26	,	,	PUNCT
gi-4940	103	27	(	(	PUNCT
gi-4940	103	28	case	case	NOUN
gi-4940	103	29	e	e	NOUN
gi-4940	103	30	)	)	PUNCT
gi-4940	103	31	,	,	PUNCT
gi-4940	103	32	or	or	CCONJ
gi-4940	103	33	,	,	PUNCT
gi-4940	103	34	if	if	SCONJ
gi-4940	103	35	lim	lim	PROPN
gi-4940	103	36	ϕi→c±	ϕi→c±	PROPN
gi-4940	103	37	f	f	PROPN
gi-4940	103	38	(	(	PUNCT
gi-4940	103	39	ϕi	ϕi	PROPN
gi-4940	103	40	,	,	PUNCT
gi-4940	103	41	λ	λ	NOUN
gi-4940	103	42	)	)	PUNCT
gi-4940	104	1	=	=	SYM
gi-4940	104	2	±∞∨	±∞∨	PROPN
gi-4940	104	3	lim	lim	PROPN
gi-4940	104	4	ϕi→c±	ϕi→c±	PROPN
gi-4940	104	5	f	f	PROPN
gi-4940	104	6	(	(	PUNCT
gi-4940	104	7	ϕi	ϕi	PROPN
gi-4940	104	8	,	,	PUNCT
gi-4940	104	9	λ	λ	NOUN
gi-4940	104	10	)	)	PUNCT
gi-4940	104	11	=	=	SYM
gi-4940	105	1	∓∞∨	∓∞∨	PROPN
gi-4940	105	2	lim	lim	PROPN
gi-4940	105	3	ϕi→c±	ϕi→c±	PROPN
gi-4940	105	4	g(ϕi	g(ϕi	PROPN
gi-4940	105	5	,	,	PUNCT
gi-4940	105	6	λ	λ	X
gi-4940	105	7	)	)	PUNCT
gi-4940	105	8	=	=	SYM
gi-4940	105	9	±∞∨	±∞∨	PROPN
gi-4940	105	10	lim	lim	PROPN
gi-4940	105	11	ϕi→c±	ϕi→c±	PROPN
gi-4940	105	12	g(ϕi	g(ϕi	PROPN
gi-4940	105	13	,	,	PUNCT
gi-4940	105	14	λ	λ	X
gi-4940	105	15	)	)	PUNCT
gi-4940	105	16	=	=	SYM
gi-4940	105	17	∓∞	∓∞	PROPN
gi-4940	105	18	,	,	PUNCT
gi-4940	105	19	representing	represent	VERB
gi-4940	105	20	case	case	NOUN
gi-4940	105	21	f.	f.	NOUN
gi-4940	105	22	for	for	ADP
gi-4940	105	23	case	case	NOUN
gi-4940	105	24	e	e	NOUN
gi-4940	105	25	,	,	PUNCT
gi-4940	105	26	the	the	DET
gi-4940	105	27	projected	project	VERB
gi-4940	105	28	meridian	meridian	PROPN
gi-4940	105	29	point	point	PROPN
gi-4940	105	30	qi	qi	PROPN
gi-4940	105	31	is	be	AUX
gi-4940	105	32	replaced	replace	VERB
gi-4940	105	33	with	with	ADP
gi-4940	105	34	the	the	DET
gi-4940	105	35	average	average	NOUN
gi-4940	105	36	xi	xi	X
gi-4940	105	37	=	=	SYM
gi-4940	105	38	0.5	0.5	NUM
gi-4940	105	39	(	(	PUNCT
gi-4940	105	40	f	f	X
gi-4940	105	41	(	(	PUNCT
gi-4940	105	42	c−	c−	X
gi-4940	105	43	ε	ε	PROPN
gi-4940	105	44	,	,	PUNCT
gi-4940	105	45	λ	λ	NOUN
gi-4940	105	46	)	)	PUNCT
gi-4940	106	1	+	+	NUM
gi-4940	106	2	f	f	X
gi-4940	106	3	(	(	PUNCT
gi-4940	106	4	c+	c+	NOUN
gi-4940	106	5	ε	ε	PROPN
gi-4940	106	6	,	,	PUNCT
gi-4940	106	7	λ	λ	NOUN
gi-4940	106	8	)	)	PUNCT
gi-4940	106	9	)	)	PUNCT
gi-4940	106	10	,	,	PUNCT
gi-4940	106	11	yi	yi	NOUN
gi-4940	106	12	=	=	SYM
gi-4940	106	13	0.5	0.5	NUM
gi-4940	106	14	(	(	PUNCT
gi-4940	106	15	g(c−	g(c−	NOUN
gi-4940	106	16	ε	ε	PROPN
gi-4940	106	17	,	,	PUNCT
gi-4940	106	18	λ	λ	NOUN
gi-4940	106	19	)	)	PUNCT
gi-4940	106	20	+	+	ADJ
gi-4940	106	21	g(c+	g(c+	ADJ
gi-4940	106	22	ε	ε	PROPN
gi-4940	106	23	,	,	PUNCT
gi-4940	106	24	λ	λ	NOUN
gi-4940	106	25	)	)	PUNCT
gi-4940	106	26	)	)	PUNCT
gi-4940	106	27	.	.	PUNCT
gi-4940	107	1	treating	treat	VERB
gi-4940	107	2	case	case	NOUN
gi-4940	107	3	f	f	NOUN
gi-4940	107	4	is	be	AUX
gi-4940	107	5	more	more	ADV
gi-4940	107	6	difficult	difficult	ADJ
gi-4940	107	7	,	,	PUNCT
gi-4940	107	8	the	the	DET
gi-4940	107	9	entire	entire	ADJ
gi-4940	107	10	meridian	meridian	PROPN
gi-4940	107	11	m(λ	m(λ	PROPN
gi-4940	107	12	)	)	PUNCT
gi-4940	107	13	needs	need	NOUN
gi-4940	107	14	be	be	AUX
gi-4940	107	15	split	split	VERB
gi-4940	107	16	into	into	ADP
gi-4940	107	17	two	two	NUM
gi-4940	107	18	parts	part	NOUN
gi-4940	107	19	at	at	ADP
gi-4940	107	20	c	c	X
gi-4940	107	21	m(λ	m(λ	PROPN
gi-4940	107	22	)	)	PUNCT
gi-4940	107	23	=	=	PUNCT
gi-4940	108	1	〈	〈	PROPN
gi-4940	108	2	〈	〈	PROPN
gi-4940	108	3	m−(ϕi	m−(ϕi	NOUN
gi-4940	108	4	,	,	PUNCT
gi-4940	108	5	λ	λ	PROPN
gi-4940	108	6	)	)	PUNCT
gi-4940	108	7	,	,	PUNCT
gi-4940	108	8	ϕ	ϕ	NOUN
gi-4940	108	9	≤	≤	PROPN
gi-4940	108	10	ϕi	ϕi	ADP
gi-4940	108	11	<	<	X
gi-4940	108	12	c	c	NOUN
gi-4940	108	13	〉	〉	NOUN
gi-4940	108	14	,	,	PUNCT
gi-4940	108	15	〈	〈	PROPN
gi-4940	108	16	m+(ϕi	m+(ϕi	NOUN
gi-4940	108	17	,	,	PUNCT
gi-4940	108	18	λ	λ	NOUN
gi-4940	108	19	)	)	PUNCT
gi-4940	108	20	,	,	PUNCT
gi-4940	108	21	c	c	X
gi-4940	108	22	<	<	X
gi-4940	108	23	ϕi	ϕi	ADP
gi-4940	108	24	≤	≤	PROPN
gi-4940	108	25	ϕ	ϕ	PROPN
gi-4940	108	26	〉	〉	NOUN
gi-4940	108	27	〉	〉	NOUN
gi-4940	108	28	,	,	PUNCT
gi-4940	108	29	geoinformatics	geoinformatic	NOUN
gi-4940	108	30	fce	fce	VERB
gi-4940	108	31	ctu	ctu	NOUN
gi-4940	108	32	17(2	17(2	NUM
gi-4940	108	33	)	)	PUNCT
gi-4940	108	34	,	,	PUNCT
gi-4940	109	1	2018	2018	NUM
gi-4940	109	2	34	34	NUM
gi-4940	109	3	t.	t.	NOUN
gi-4940	109	4	bayer	bayer	PROPN
gi-4940	109	5	:	:	PUNCT
gi-4940	109	6	plotting	plot	VERB
gi-4940	109	7	the	the	DET
gi-4940	109	8	map	map	NOUN
gi-4940	109	9	projection	projection	NOUN
gi-4940	109	10	graticule	graticule	NOUN
gi-4940	109	11	with	with	ADP
gi-4940	109	12	discontinuities	discontinuity	NOUN
gi-4940	109	13	a	a	DET
gi-4940	109	14	k	k	X
gi-4940	109	15	m(l	m(l	PROPN
gi-4940	109	16	k	k	PROPN
gi-4940	109	17	)	)	PUNCT
gi-4940	109	18	ºm	ºm	PROPN
gi-4940	109	19	(	(	PUNCT
gi-4940	109	20	0	0	NUM
gi-4940	109	21	)	)	PUNCT
gi-4940	109	22	m	m	VERB
gi-4940	109	23	(	(	PUNCT
gi-4940	109	24	l	l	NOUN
gi-4940	109	25	0	0	NUM
gi-4940	109	26	)	)	PUNCT
gi-4940	110	1	l	l	NOUN
gi-4940	110	2	k	k	X
gi-4940	110	3	l	l	NOUN
gi-4940	110	4	0	0	PUNCT
gi-4940	110	5	m(0	m(0	NOUN
gi-4940	110	6	)	)	PUNCT
gi-4940	110	7	l	l	NOUN
gi-4940	110	8	k	k	PROPN
gi-4940	110	9	±p	±p	PROPN
gi-4940	110	10	m(l	m(l	PROPN
gi-4940	110	11	k	k	PROPN
gi-4940	110	12	±p	±p	PROPN
gi-4940	110	13	)	)	PUNCT
gi-4940	110	14	m(±p	m(±p	NOUN
gi-4940	110	15	)	)	PUNCT
gi-4940	110	16	figure	figure	NOUN
gi-4940	110	17	3.2	3.2	NUM
gi-4940	110	18	:	:	PUNCT
gi-4940	110	19	coincidence	coincidence	NOUN
gi-4940	110	20	with	with	ADP
gi-4940	110	21	the	the	DET
gi-4940	110	22	singularities	singularity	NOUN
gi-4940	110	23	:	:	PUNCT
gi-4940	110	24	the	the	DET
gi-4940	110	25	meridian	meridian	PROPN
gi-4940	110	26	m(λk	m(λk	PROPN
gi-4940	110	27	)	)	PUNCT
gi-4940	110	28	passing	pass	VERB
gi-4940	110	29	the	the	DET
gi-4940	110	30	transformed	transform	VERB
gi-4940	110	31	pole	pole	NOUN
gi-4940	110	32	k	k	PROPN
gi-4940	110	33	,	,	PUNCT
gi-4940	110	34	the	the	DET
gi-4940	110	35	meridian	meridian	PROPN
gi-4940	110	36	m(λk	m(λk	PROPN
gi-4940	110	37	±	±	PROPN
gi-4940	110	38	π	π	PROPN
gi-4940	110	39	)	)	PUNCT
gi-4940	110	40	“	"	PUNCT
gi-4940	110	41	opposite	opposite	ADJ
gi-4940	110	42	”	"	PUNCT
gi-4940	110	43	the	the	DET
gi-4940	110	44	transformed	transform	VERB
gi-4940	110	45	pole	pole	NOUN
gi-4940	110	46	,	,	PUNCT
gi-4940	110	47	and	and	CCONJ
gi-4940	110	48	the	the	DET
gi-4940	110	49	meridian	meridian	PROPN
gi-4940	110	50	m(±π	m(±π	PROPN
gi-4940	110	51	)	)	PUNCT
gi-4940	110	52	;	;	PUNCT
gi-4940	110	53	the	the	DET
gi-4940	110	54	azimuthal	azimuthal	ADJ
gi-4940	110	55	projection	projection	NOUN
gi-4940	110	56	.	.	PUNCT
gi-4940	111	1	projected	project	VERB
gi-4940	111	2	separately	separately	ADV
gi-4940	111	3	.	.	PUNCT
gi-4940	112	1	analogously	analogously	ADV
gi-4940	112	2	,	,	PUNCT
gi-4940	112	3	cases	case	VERB
gi-4940	112	4	g	g	NOUN
gi-4940	112	5	,	,	PUNCT
gi-4940	112	6	h	h	NOUN
gi-4940	112	7	occur	occur	VERB
gi-4940	112	8	,	,	PUNCT
gi-4940	112	9	if	if	SCONJ
gi-4940	112	10	a	a	DET
gi-4940	112	11	parallel	parallel	ADJ
gi-4940	112	12	p(ϕ	p(ϕ	NOUN
gi-4940	112	13	)	)	PUNCT
gi-4940	112	14	intersects	intersect	VERB
gi-4940	112	15	the	the	DET
gi-4940	112	16	infinite	infinite	ADJ
gi-4940	112	17	singularity	singularity	NOUN
gi-4940	112	18	at	at	ADP
gi-4940	112	19	the	the	DET
gi-4940	112	20	point	point	NOUN
gi-4940	112	21	qi	qi	NOUN
gi-4940	113	1	=	=	PUNCT
gi-4940	114	1	[	[	X
gi-4940	114	2	ϕ	ϕ	NOUN
gi-4940	114	3	,	,	PUNCT
gi-4940	114	4	c	c	PROPN
gi-4940	114	5	=	=	SYM
gi-4940	114	6	λi	λi	PROPN
gi-4940	114	7	]	]	X
gi-4940	114	8	,	,	PUNCT
gi-4940	114	9	lim	lim	PROPN
gi-4940	114	10	λi→c±	λi→c±	PROPN
gi-4940	114	11	f	f	PROPN
gi-4940	114	12	(	(	PUNCT
gi-4940	114	13	ϕ	ϕ	NOUN
gi-4940	114	14	,	,	PUNCT
gi-4940	114	15	λi	λi	NOUN
gi-4940	114	16	)	)	PUNCT
gi-4940	115	1	=	=	NOUN
gi-4940	115	2	∞∨	∞∨	PROPN
gi-4940	115	3	lim	lim	PROPN
gi-4940	115	4	λi→c±	λi→c±	PROPN
gi-4940	115	5	f	f	PROPN
gi-4940	115	6	(	(	PUNCT
gi-4940	115	7	ϕ	ϕ	NOUN
gi-4940	115	8	,	,	PUNCT
gi-4940	115	9	λi	λi	NOUN
gi-4940	115	10	)	)	PUNCT
gi-4940	115	11	=	=	SYM
gi-4940	115	12	−∞∨	−∞∨	PROPN
gi-4940	115	13	lim	lim	PROPN
gi-4940	115	14	λi→c±	λi→c±	PROPN
gi-4940	115	15	g(ϕ	g(ϕ	PROPN
gi-4940	115	16	,	,	PUNCT
gi-4940	115	17	λi	λi	NOUN
gi-4940	115	18	)	)	PUNCT
gi-4940	115	19	=	=	NOUN
gi-4940	115	20	∞∨	∞∨	PROPN
gi-4940	115	21	lim	lim	PROPN
gi-4940	115	22	λi→c±	λi→c±	PROPN
gi-4940	115	23	g(ϕ	g(ϕ	PROPN
gi-4940	115	24	,	,	PUNCT
gi-4940	115	25	λi	λi	NOUN
gi-4940	115	26	)	)	PUNCT
gi-4940	115	27	=	=	SYM
gi-4940	115	28	−∞	−∞	NOUN
gi-4940	115	29	,	,	PUNCT
gi-4940	115	30	or	or	CCONJ
gi-4940	115	31	,	,	PUNCT
gi-4940	115	32	if	if	SCONJ
gi-4940	115	33	,	,	PUNCT
gi-4940	115	34	lim	lim	PROPN
gi-4940	115	35	λi→c±	λi→c±	PROPN
gi-4940	115	36	f	f	PROPN
gi-4940	115	37	(	(	PUNCT
gi-4940	115	38	ϕ	ϕ	NOUN
gi-4940	115	39	,	,	PUNCT
gi-4940	115	40	λi	λi	NOUN
gi-4940	115	41	)	)	PUNCT
gi-4940	116	1	=	=	SYM
gi-4940	116	2	±∞∨	±∞∨	PROPN
gi-4940	116	3	lim	lim	PROPN
gi-4940	116	4	λi→c±	λi→c±	PROPN
gi-4940	116	5	f	f	PROPN
gi-4940	116	6	(	(	PUNCT
gi-4940	116	7	ϕ	ϕ	NOUN
gi-4940	116	8	,	,	PUNCT
gi-4940	116	9	λi	λi	NOUN
gi-4940	116	10	)	)	PUNCT
gi-4940	116	11	=	=	SYM
gi-4940	116	12	∓∞∨	∓∞∨	PROPN
gi-4940	116	13	lim	lim	PROPN
gi-4940	116	14	λi→c±	λi→c±	PROPN
gi-4940	116	15	g(ϕ	g(ϕ	PROPN
gi-4940	116	16	,	,	PUNCT
gi-4940	116	17	λi	λi	NOUN
gi-4940	116	18	)	)	PUNCT
gi-4940	116	19	=	=	SYM
gi-4940	116	20	±∞∨	±∞∨	PROPN
gi-4940	116	21	lim	lim	PROPN
gi-4940	116	22	λi→c±	λi→c±	PROPN
gi-4940	116	23	g(ϕ	g(ϕ	PROPN
gi-4940	116	24	,	,	PUNCT
gi-4940	116	25	λi	λi	NOUN
gi-4940	116	26	)	)	PUNCT
gi-4940	116	27	=	=	PUNCT
gi-4940	116	28	∓∞.	∓∞.	NOUN
gi-4940	116	29	for	for	ADP
gi-4940	116	30	case	case	NOUN
gi-4940	116	31	g	g	NOUN
gi-4940	116	32	,	,	PUNCT
gi-4940	116	33	the	the	DET
gi-4940	116	34	projected	project	VERB
gi-4940	116	35	parallel	parallel	ADJ
gi-4940	116	36	point	point	NOUN
gi-4940	116	37	qi	qi	PROPN
gi-4940	116	38	is	be	AUX
gi-4940	116	39	replaced	replace	VERB
gi-4940	116	40	with	with	ADP
gi-4940	116	41	the	the	DET
gi-4940	116	42	average	average	NOUN
gi-4940	116	43	xi	xi	X
gi-4940	116	44	=	=	SYM
gi-4940	116	45	0.5	0.5	NUM
gi-4940	116	46	(	(	PUNCT
gi-4940	116	47	f	f	PROPN
gi-4940	116	48	(	(	PUNCT
gi-4940	116	49	ϕ	ϕ	NOUN
gi-4940	116	50	,	,	PUNCT
gi-4940	116	51	c−	c−	X
gi-4940	116	52	ε	ε	PROPN
gi-4940	116	53	)	)	PUNCT
gi-4940	117	1	+	+	NUM
gi-4940	117	2	f	f	X
gi-4940	117	3	(	(	PUNCT
gi-4940	117	4	ϕ	ϕ	NOUN
gi-4940	117	5	,	,	PUNCT
gi-4940	117	6	c+	c+	X
gi-4940	117	7	ε	ε	PROPN
gi-4940	117	8	)	)	PUNCT
gi-4940	117	9	)	)	PUNCT
gi-4940	117	10	,	,	PUNCT
gi-4940	117	11	yi	yi	NOUN
gi-4940	117	12	=	=	SYM
gi-4940	117	13	0.5	0.5	NUM
gi-4940	117	14	(	(	PUNCT
gi-4940	117	15	g(ϕ	g(ϕ	PROPN
gi-4940	117	16	,	,	PUNCT
gi-4940	117	17	c−	c−	X
gi-4940	117	18	ε	ε	PROPN
gi-4940	117	19	)	)	PUNCT
gi-4940	117	20	+	+	NOUN
gi-4940	117	21	g(ϕ	g(ϕ	NOUN
gi-4940	117	22	,	,	PUNCT
gi-4940	117	23	c+	c+	X
gi-4940	117	24	ε	ε	PROPN
gi-4940	117	25	)	)	PUNCT
gi-4940	117	26	)	)	PUNCT
gi-4940	117	27	,	,	PUNCT
gi-4940	117	28	however	however	ADV
gi-4940	117	29	,	,	PUNCT
gi-4940	117	30	for	for	ADP
gi-4940	117	31	case	case	NOUN
gi-4940	117	32	h	h	NOUN
gi-4940	117	33	,	,	PUNCT
gi-4940	117	34	the	the	DET
gi-4940	117	35	parallel	parallel	ADJ
gi-4940	117	36	p(ϕ	p(ϕ	NOUN
gi-4940	117	37	)	)	PUNCT
gi-4940	117	38	needs	need	VERB
gi-4940	117	39	to	to	PART
gi-4940	117	40	be	be	AUX
gi-4940	117	41	split	split	VERB
gi-4940	117	42	into	into	ADP
gi-4940	117	43	two	two	NUM
gi-4940	117	44	parts	part	NOUN
gi-4940	117	45	at	at	ADP
gi-4940	117	46	c	c	PROPN
gi-4940	117	47	p(ϕ	p(ϕ	PROPN
gi-4940	117	48	)	)	PUNCT
gi-4940	117	49	=	=	PUNCT
gi-4940	117	50	〈	〈	PROPN
gi-4940	117	51	〈	〈	PROPN
gi-4940	117	52	p−(ϕ	p−(ϕ	PROPN
gi-4940	117	53	,	,	PUNCT
gi-4940	117	54	λi	λi	NOUN
gi-4940	117	55	)	)	PUNCT
gi-4940	117	56	,	,	PUNCT
gi-4940	117	57	λ	λ	X
gi-4940	117	58	≤	≤	NUM
gi-4940	117	59	λi	λi	ADP
gi-4940	117	60	<	<	X
gi-4940	117	61	c	c	NOUN
gi-4940	117	62	〉	〉	NOUN
gi-4940	117	63	,	,	PUNCT
gi-4940	117	64	〈	〈	PROPN
gi-4940	117	65	p+(ϕ	p+(ϕ	NOUN
gi-4940	117	66	,	,	PUNCT
gi-4940	117	67	λi	λi	CCONJ
gi-4940	117	68	)	)	PUNCT
gi-4940	117	69	,	,	PUNCT
gi-4940	117	70	c	c	X
gi-4940	117	71	<	<	X
gi-4940	117	72	λi	λi	X
gi-4940	117	73	≤	≤	VERB
gi-4940	117	74	λ	λ	PROPN
gi-4940	117	75	〉	〉	NOUN
gi-4940	117	76	〉	〉	NOUN
gi-4940	117	77	.	.	PUNCT
gi-4940	118	1	the	the	DET
gi-4940	118	2	removable	removable	ADJ
gi-4940	118	3	discontinuities	discontinuity	NOUN
gi-4940	118	4	may	may	AUX
gi-4940	118	5	be	be	AUX
gi-4940	118	6	treated	treat	VERB
gi-4940	118	7	analogously	analogously	ADV
gi-4940	118	8	to	to	ADP
gi-4940	118	9	cases	case	NOUN
gi-4940	118	10	e	e	NOUN
gi-4940	118	11	,	,	PUNCT
gi-4940	118	12	g	g	PROPN
gi-4940	118	13	,	,	PUNCT
gi-4940	118	14	the	the	DET
gi-4940	118	15	jump	jump	NOUN
gi-4940	118	16	discontinuities	discontinuity	NOUN
gi-4940	118	17	analogously	analogously	ADV
gi-4940	118	18	to	to	ADP
gi-4940	118	19	cases	case	NOUN
gi-4940	118	20	f	f	PROPN
gi-4940	118	21	,	,	PUNCT
gi-4940	118	22	h.	h.	PROPN
gi-4940	118	23	geoinformatics	geoinformatic	NOUN
gi-4940	118	24	fce	fce	VERB
gi-4940	118	25	ctu	ctu	NOUN
gi-4940	118	26	17(2	17(2	NUM
gi-4940	118	27	)	)	PUNCT
gi-4940	118	28	,	,	PUNCT
gi-4940	118	29	2018	2018	NUM
gi-4940	118	30	35	35	NUM
gi-4940	118	31	t.	t.	NOUN
gi-4940	118	32	bayer	bayer	NOUN
gi-4940	118	33	:	:	PUNCT
gi-4940	118	34	plotting	plot	VERB
gi-4940	118	35	the	the	DET
gi-4940	118	36	map	map	NOUN
gi-4940	118	37	projection	projection	NOUN
gi-4940	118	38	graticule	graticule	NOUN
gi-4940	118	39	with	with	ADP
gi-4940	118	40	discontinuities	discontinuity	NOUN
gi-4940	118	41	q	q	X
gi-4940	119	1	i	i	PRON
gi-4940	119	2	q	q	NOUN
gi-4940	119	3	i-1	i-1	ADJ
gi-4940	119	4	q	q	PROPN
gi-4940	119	5	i-2	i-2	PROPN
gi-4940	119	6	q	q	PROPN
gi-4940	120	1	i+1	i+1	SYM
gi-4940	120	2	q	q	X
gi-4940	121	1	i+2	i+2	X
gi-4940	121	2	q	q	X
gi-4940	122	1	i+2	i+2	PRON
gi-4940	122	2	q	q	NOUN
gi-4940	123	1	i+1	i+1	X
gi-4940	123	2	q	q	NOUN
gi-4940	124	1	i	i	PRON
gi-4940	124	2	q	q	NOUN
gi-4940	124	3	i-1	i-1	NUM
gi-4940	124	4	q	q	PROPN
gi-4940	124	5	i-2	i-2	PROPN
gi-4940	124	6	p(φ	p(φ	PROPN
gi-4940	124	7	)	)	PUNCT
gi-4940	124	8	m(λ	m(λ	PROPN
gi-4940	124	9	)	)	PUNCT
gi-4940	124	10	m(λ	m(λ	PROPN
gi-4940	124	11	‘	'	PUNCT
gi-4940	124	12	)	)	PUNCT
gi-4940	124	13	p(φ	p(φ	NOUN
gi-4940	124	14	‘	'	PUNCT
gi-4940	124	15	)	)	PUNCT
gi-4940	124	16	m(λ	m(λ	ADJ
gi-4940	124	17	)	)	PUNCT
gi-4940	124	18	m(λ	m(λ	PROPN
gi-4940	124	19	‘	'	PUNCT
gi-4940	124	20	)	)	PUNCT
gi-4940	124	21	p(φ	p(φ	NOUN
gi-4940	124	22	)	)	PUNCT
gi-4940	124	23	p(φ	p(φ	NOUN
gi-4940	124	24	‘	'	PUNCT
gi-4940	124	25	)	)	PUNCT
gi-4940	124	26	b	b	PROPN
gi-4940	124	27	φ	φ	NOUN
gi-4940	124	28	‘	'	PUNCT
gi-4940	124	29	b	b	NOUN
gi-4940	124	30	l‘i	l‘i	NOUN
gi-4940	124	31	i	i	PRON
gi-4940	124	32	figure	figure	VERB
gi-4940	124	33	3.3	3.3	NUM
gi-4940	124	34	:	:	PUNCT
gi-4940	124	35	boundaries	boundary	NOUN
gi-4940	124	36	bϕ′i	bϕ′i	PROPN
gi-4940	124	37	,	,	PUNCT
gi-4940	124	38	bλ′i	bλ′i	PROPN
gi-4940	124	39	and	and	CCONJ
gi-4940	124	40	their	their	PRON
gi-4940	124	41	backward	backward	ADJ
gi-4940	124	42	projections	projection	NOUN
gi-4940	124	43	to	to	ADP
gi-4940	124	44	the	the	DET
gi-4940	124	45	(	(	PUNCT
gi-4940	124	46	ϕ	ϕ	NOUN
gi-4940	124	47	,	,	PUNCT
gi-4940	124	48	λ	λ	NOUN
gi-4940	124	49	)	)	PUNCT
gi-4940	124	50	directions	direction	NOUN
gi-4940	124	51	.	.	PUNCT
gi-4940	125	1	detection	detection	NOUN
gi-4940	125	2	of	of	ADP
gi-4940	125	3	singularities	singularity	NOUN
gi-4940	125	4	.	.	PUNCT
gi-4940	126	1	for	for	ADP
gi-4940	126	2	parametric	parametric	ADJ
gi-4940	126	3	functions	function	NOUN
gi-4940	126	4	f	f	X
gi-4940	126	5	,	,	PUNCT
gi-4940	126	6	g	g	PROPN
gi-4940	126	7	it	it	PRON
gi-4940	126	8	is	be	AUX
gi-4940	126	9	necessary	necessary	ADJ
gi-4940	126	10	to	to	PART
gi-4940	126	11	recognize	recognize	VERB
gi-4940	126	12	whether	whether	SCONJ
gi-4940	126	13	a	a	DET
gi-4940	126	14	singularity	singularity	NOUN
gi-4940	126	15	refers	refer	VERB
gi-4940	126	16	to	to	ADP
gi-4940	126	17	ϕ	ϕ	NOUN
gi-4940	126	18	or	or	CCONJ
gi-4940	126	19	λ	λ	NOUN
gi-4940	126	20	coordinate	coordinate	NOUN
gi-4940	126	21	.	.	PUNCT
gi-4940	127	1	therefore	therefore	ADV
gi-4940	127	2	,	,	PUNCT
gi-4940	127	3	each	each	DET
gi-4940	127	4	sampled	sample	VERB
gi-4940	127	5	point	point	NOUN
gi-4940	127	6	qi	qi	NOUN
gi-4940	127	7	=	=	SYM
gi-4940	128	1	[	[	X
gi-4940	128	2	ϕi	ϕi	ADP
gi-4940	128	3	,	,	PUNCT
gi-4940	128	4	λi	λi	X
gi-4940	128	5	]	]	X
gi-4940	128	6	and	and	CCONJ
gi-4940	128	7	its	its	PRON
gi-4940	128	8	boundary	boundary	ADJ
gi-4940	128	9	b(qi	b(qi	PROPN
gi-4940	128	10	,	,	PUNCT
gi-4940	128	11	ε	ε	PROPN
gi-4940	128	12	)	)	PUNCT
gi-4940	128	13	will	will	AUX
gi-4940	128	14	be	be	AUX
gi-4940	128	15	checked	check	VERB
gi-4940	128	16	for	for	ADP
gi-4940	128	17	a	a	DET
gi-4940	128	18	discontinuity	discontinuity	NOUN
gi-4940	128	19	.	.	PUNCT
gi-4940	129	1	suppose	suppose	VERB
gi-4940	129	2	bϕi	bϕi	NOUN
gi-4940	129	3	=	=	PUNCT
gi-4940	130	1	[	[	X
gi-4940	130	2	ϕi	ϕi	ADP
gi-4940	130	3	−	−	PROPN
gi-4940	130	4	ε	ε	PROPN
gi-4940	130	5	,	,	PUNCT
gi-4940	130	6	ϕi	ϕi	ADP
gi-4940	130	7	+	+	CCONJ
gi-4940	130	8	ε	ε	PROPN
gi-4940	130	9	]	]	PUNCT
gi-4940	130	10	,	,	PUNCT
gi-4940	130	11	bλi	bλi	PROPN
gi-4940	130	12	=	=	PUNCT
gi-4940	131	1	[	[	X
gi-4940	131	2	λi	λi	X
gi-4940	131	3	−	−	PROPN
gi-4940	131	4	ε	ε	PROPN
gi-4940	131	5	,	,	PUNCT
gi-4940	131	6	λi	λi	X
gi-4940	131	7	+	+	CCONJ
gi-4940	131	8	ε	ε	X
gi-4940	131	9	]	]	PUNCT
gi-4940	131	10	to	to	PART
gi-4940	131	11	be	be	AUX
gi-4940	131	12	the	the	DET
gi-4940	131	13	projections	projection	NOUN
gi-4940	131	14	of	of	ADP
gi-4940	131	15	b(qi	b(qi	PROPN
gi-4940	131	16	,	,	PUNCT
gi-4940	131	17	ε	ε	PROPN
gi-4940	131	18	)	)	PUNCT
gi-4940	131	19	to	to	ADP
gi-4940	131	20	the	the	DET
gi-4940	131	21	(	(	PUNCT
gi-4940	131	22	ϕ	ϕ	NOUN
gi-4940	131	23	,	,	PUNCT
gi-4940	131	24	λ	λ	NOUN
gi-4940	131	25	)	)	PUNCT
gi-4940	131	26	directions	direction	NOUN
gi-4940	131	27	and	and	CCONJ
gi-4940	132	1	qϕi+l	qϕi+l	NUM
gi-4940	132	2	=	=	SYM
gi-4940	133	1	[	[	X
gi-4940	133	2	ϕi	ϕi	X
gi-4940	133	3	+	+	X
gi-4940	133	4	lh	lh	PROPN
gi-4940	133	5	,	,	PUNCT
gi-4940	133	6	λi	λi	AUX
gi-4940	133	7	]	]	X
gi-4940	133	8	∈	∈	PROPN
gi-4940	133	9	bϕi	bϕi	NOUN
gi-4940	133	10	,	,	PUNCT
gi-4940	133	11	qλi+l	qλi+l	PUNCT
gi-4940	133	12	=	=	PUNCT
gi-4940	134	1	[	[	X
gi-4940	134	2	ϕi	ϕi	ADP
gi-4940	134	3	,	,	PUNCT
gi-4940	134	4	λi	λi	X
gi-4940	134	5	+	+	CCONJ
gi-4940	134	6	lh	lh	PROPN
gi-4940	134	7	]	]	X
gi-4940	134	8	∈	∈	PROPN
gi-4940	134	9	bλi	bλi	PROPN
gi-4940	134	10	,	,	PUNCT
gi-4940	134	11	where	where	SCONJ
gi-4940	134	12	h	h	NOUN
gi-4940	134	13	=	=	SYM
gi-4940	134	14	ε/2	ε/2	PROPN
gi-4940	134	15	,	,	PUNCT
gi-4940	134	16	l	l	NOUN
gi-4940	134	17	=	=	SYM
gi-4940	134	18	−2,−1	−2,−1	ADJ
gi-4940	134	19	,	,	PUNCT
gi-4940	134	20	0	0	NUM
gi-4940	134	21	,	,	PUNCT
gi-4940	134	22	1	1	NUM
gi-4940	134	23	,	,	PUNCT
gi-4940	134	24	2	2	NUM
gi-4940	134	25	,	,	PUNCT
gi-4940	134	26	to	to	PART
gi-4940	134	27	be	be	AUX
gi-4940	134	28	5	5	NUM
gi-4940	134	29	sampled	sample	VERB
gi-4940	134	30	points	point	NOUN
gi-4940	134	31	.	.	PUNCT
gi-4940	135	1	if	if	SCONJ
gi-4940	135	2	any	any	DET
gi-4940	135	3	point	point	NOUN
gi-4940	135	4	of	of	ADP
gi-4940	135	5	bϕi	bϕi	NOUN
gi-4940	135	6	is	be	AUX
gi-4940	135	7	singular	singular	ADJ
gi-4940	135	8	,	,	PUNCT
gi-4940	135	9	the	the	DET
gi-4940	135	10	singularity	singularity	NOUN
gi-4940	135	11	has	have	VERB
gi-4940	135	12	a	a	DET
gi-4940	135	13	direction	direction	NOUN
gi-4940	135	14	of	of	ADP
gi-4940	135	15	the	the	DET
gi-4940	135	16	meridian	meridian	PROPN
gi-4940	135	17	m(λi	m(λi	PROPN
gi-4940	135	18	)	)	PUNCT
gi-4940	135	19	and	and	CCONJ
gi-4940	135	20	analogously	analogously	ADV
gi-4940	135	21	for	for	ADP
gi-4940	135	22	bλi	bλi	PROPN
gi-4940	135	23	.	.	PUNCT
gi-4940	136	1	for	for	ADP
gi-4940	136	2	the	the	DET
gi-4940	136	3	oblique	oblique	ADJ
gi-4940	136	4	aspect	aspect	NOUN
gi-4940	136	5	of	of	ADP
gi-4940	136	6	p	p	NOUN
gi-4940	136	7	,	,	PUNCT
gi-4940	136	8	bϕ′i	bϕ′i	PROPN
gi-4940	136	9	=	=	PUNCT
gi-4940	137	1	[	[	X
gi-4940	137	2	ϕ′i−ε	ϕ′i−ε	X
gi-4940	137	3	,	,	PUNCT
gi-4940	137	4	ϕ′i+ε	ϕ′i+ε	NOUN
gi-4940	137	5	]	]	PUNCT
gi-4940	137	6	,	,	PUNCT
gi-4940	137	7	bλ′i	bλ′i	X
gi-4940	137	8	=	=	PUNCT
gi-4940	138	1	[	[	X
gi-4940	138	2	λ′i−ε	λ′i−ε	X
gi-4940	138	3	,	,	PUNCT
gi-4940	138	4	λ′i+ε	λ′i+ε	NOUN
gi-4940	138	5	]	]	PUNCT
gi-4940	138	6	represent	represent	VERB
gi-4940	138	7	the	the	DET
gi-4940	138	8	projections	projection	NOUN
gi-4940	138	9	of	of	ADP
gi-4940	138	10	b(qi	b(qi	PROPN
gi-4940	138	11	,	,	PUNCT
gi-4940	138	12	ε	ε	PROPN
gi-4940	138	13	)	)	PUNCT
gi-4940	138	14	to	to	ADP
gi-4940	138	15	the	the	DET
gi-4940	138	16	(	(	PUNCT
gi-4940	138	17	ϕ′	ϕ′	PROPN
gi-4940	138	18	,	,	PUNCT
gi-4940	138	19	λ′	λ′	NUM
gi-4940	138	20	)	)	PUNCT
gi-4940	138	21	directions	direction	NOUN
gi-4940	138	22	and	and	CCONJ
gi-4940	138	23	qϕ′	qϕ′	NOUN
gi-4940	139	1	i+l	i+l	NOUN
gi-4940	139	2	=	=	SYM
gi-4940	140	1	[	[	X
gi-4940	140	2	ϕ′i	ϕ′i	NOUN
gi-4940	140	3	+	+	CCONJ
gi-4940	140	4	lh	lh	PROPN
gi-4940	140	5	,	,	PUNCT
gi-4940	140	6	λ′i	λ′i	X
gi-4940	140	7	]	]	X
gi-4940	140	8	∈	∈	PROPN
gi-4940	140	9	bϕ′i	bϕ′i	NOUN
gi-4940	140	10	,	,	PUNCT
gi-4940	140	11	qλ′i+l	qλ′i+l	ADV
gi-4940	140	12	=	=	SYM
gi-4940	141	1	[	[	X
gi-4940	141	2	ϕ′i	ϕ′i	NOUN
gi-4940	141	3	,	,	PUNCT
gi-4940	141	4	λ′i	λ′i	X
gi-4940	142	1	+	+	CCONJ
gi-4940	142	2	lh	lh	PROPN
gi-4940	142	3	]	]	X
gi-4940	142	4	∈	∈	PROPN
gi-4940	142	5	bλ′i	bλ′i	NOUN
gi-4940	142	6	are	be	AUX
gi-4940	142	7	the	the	DET
gi-4940	142	8	5	5	NUM
gi-4940	142	9	sampled	sample	VERB
gi-4940	142	10	points	point	NOUN
gi-4940	142	11	.	.	PUNCT
gi-4940	143	1	if	if	SCONJ
gi-4940	143	2	all	all	DET
gi-4940	143	3	points	point	NOUN
gi-4940	143	4	of	of	ADP
gi-4940	143	5	bϕ′i	bϕ′i	PROPN
gi-4940	143	6	are	be	AUX
gi-4940	143	7	singular	singular	ADJ
gi-4940	143	8	,	,	PUNCT
gi-4940	143	9	the	the	DET
gi-4940	143	10	singularity	singularity	NOUN
gi-4940	143	11	has	have	VERB
gi-4940	143	12	a	a	DET
gi-4940	143	13	direction	direction	NOUN
gi-4940	143	14	of	of	ADP
gi-4940	143	15	the	the	DET
gi-4940	143	16	meridian	meridian	PROPN
gi-4940	143	17	m(λ′i	m(λ′i	PROPN
gi-4940	143	18	)	)	PUNCT
gi-4940	143	19	and	and	CCONJ
gi-4940	143	20	analogously	analogously	ADV
gi-4940	143	21	for	for	ADP
gi-4940	143	22	bλ′i	bλ′i	PROPN
gi-4940	143	23	.	.	PUNCT
gi-4940	144	1	while	while	SCONJ
gi-4940	144	2	bϕi	bϕi	NOUN
gi-4940	144	3	,	,	PUNCT
gi-4940	144	4	bλi	bλi	NOUN
gi-4940	144	5	refer	refer	NOUN
gi-4940	144	6	to	to	ADP
gi-4940	144	7	directions	direction	NOUN
gi-4940	144	8	of	of	ADP
gi-4940	144	9	the	the	DET
gi-4940	144	10	geographic	geographic	PROPN
gi-4940	144	11	meridian	meridian	PROPN
gi-4940	144	12	/	/	SYM
gi-4940	144	13	parallel	parallel	ADJ
gi-4940	144	14	,	,	PUNCT
gi-4940	144	15	bϕ′i	bϕ′i	PROPN
gi-4940	144	16	,	,	PUNCT
gi-4940	144	17	bλ′i	bλ′i	PROPN
gi-4940	144	18	are	be	AUX
gi-4940	144	19	aligned	align	VERB
gi-4940	144	20	with	with	ADP
gi-4940	144	21	the	the	DET
gi-4940	144	22	transformed	transform	VERB
gi-4940	144	23	meridian	meridian	PROPN
gi-4940	144	24	/	/	SYM
gi-4940	144	25	parallel	parallel	ADJ
gi-4940	144	26	directions	direction	NOUN
gi-4940	144	27	,	,	PUNCT
gi-4940	144	28	see	see	VERB
gi-4940	144	29	fig	fig	NOUN
gi-4940	144	30	.	.	PUNCT
gi-4940	145	1	3.3	3.3	NUM
gi-4940	145	2	.	.	PUNCT
gi-4940	146	1	depending	depend	VERB
gi-4940	146	2	on	on	ADP
gi-4940	146	3	the	the	DET
gi-4940	146	4	direction	direction	NOUN
gi-4940	146	5	,	,	PUNCT
gi-4940	146	6	the	the	DET
gi-4940	146	7	coordinates	coordinate	NOUN
gi-4940	146	8	xi	xi	PROPN
gi-4940	146	9	,	,	PUNCT
gi-4940	146	10	yi	yi	PROPN
gi-4940	146	11	are	be	AUX
gi-4940	146	12	labeled	label	VERB
gi-4940	146	13	with	with	ADP
gi-4940	146	14	ϕ	ϕ	PROPN
gi-4940	146	15	,	,	PUNCT
gi-4940	146	16	λ	λ	PROPN
gi-4940	146	17	.	.	PUNCT
gi-4940	147	1	the	the	DET
gi-4940	147	2	infinite	infinite	ADJ
gi-4940	147	3	discontinuities	discontinuity	NOUN
gi-4940	147	4	of	of	ADP
gi-4940	147	5	coordinates	coordinate	NOUN
gi-4940	147	6	xϕ′	xϕ′	VERB
gi-4940	147	7	i−k	i−k	NOUN
gi-4940	147	8	,	,	PUNCT
gi-4940	147	9	yϕ′	yϕ′	PROPN
gi-4940	147	10	i−k	i−k	NOUN
gi-4940	147	11	in	in	ADP
gi-4940	147	12	the	the	DET
gi-4940	147	13	latitude	latitude	NOUN
gi-4940	147	14	/	/	SYM
gi-4940	147	15	longitude	longitude	NOUN
gi-4940	147	16	directions	direction	NOUN
gi-4940	147	17	are	be	AUX
gi-4940	147	18	tested	test	VERB
gi-4940	147	19	by	by	ADP
gi-4940	147	20	comparing	compare	VERB
gi-4940	147	21	with	with	ADP
gi-4940	147	22	the	the	DET
gi-4940	147	23	coordinate	coordinate	NOUN
gi-4940	147	24	thresholds	threshold	VERB
gi-4940	147	25	x	x	PRON
gi-4940	147	26	,	,	PUNCT
gi-4940	147	27	y.	y.	PROPN
gi-4940	147	28	subsequently	subsequently	ADV
gi-4940	147	29	,	,	PUNCT
gi-4940	147	30	the	the	DET
gi-4940	147	31	jump	jump	NOUN
gi-4940	147	32	discontinuity	discontinuity	NOUN
gi-4940	147	33	is	be	AUX
gi-4940	147	34	detected	detect	VERB
gi-4940	147	35	using	use	VERB
gi-4940	147	36	lr	lr	PROPN
gi-4940	147	37	criteria	criterion	NOUN
gi-4940	147	38	lrx(ϕ′i	lrx(ϕ′i	PROPN
gi-4940	147	39	,	,	PUNCT
gi-4940	147	40	λ′i	λ′i	NOUN
gi-4940	147	41	)	)	PUNCT
gi-4940	147	42	=	=	SYM
gi-4940	148	1	∣∣f	∣∣f	ADP
gi-4940	148	2	2	2	NUM
gi-4940	148	3	r	r	NOUN
gi-4940	148	4	−	−	NOUN
gi-4940	148	5	f	f	NOUN
gi-4940	148	6	2	2	NUM
gi-4940	148	7	l	l	NOUN
gi-4940	148	8	∣∣	∣∣	NUM
gi-4940	148	9	f	f	NOUN
gi-4940	148	10	2	2	NUM
gi-4940	148	11	r	r	NOUN
gi-4940	148	12	+	+	NOUN
gi-4940	148	13	f	f	PROPN
gi-4940	148	14	2	2	NUM
gi-4940	148	15	l	l	NOUN
gi-4940	148	16	,	,	PUNCT
gi-4940	148	17	lry(ϕ′i	lry(ϕ′i	NOUN
gi-4940	148	18	,	,	PUNCT
gi-4940	148	19	λ′i	λ′i	NOUN
gi-4940	148	20	)	)	PUNCT
gi-4940	148	21	=	=	SYM
gi-4940	148	22	∣∣g2	∣∣g2	NOUN
gi-4940	148	23	r	r	NOUN
gi-4940	148	24	−g2	−g2	ADJ
gi-4940	148	25	l	l	NOUN
gi-4940	148	26	∣∣	∣∣	X
gi-4940	148	27	g2	g2	PROPN
gi-4940	148	28	r	r	PROPN
gi-4940	148	29	+	+	PROPN
gi-4940	148	30	g2	g2	PROPN
gi-4940	148	31	l	l	NOUN
gi-4940	148	32	,	,	PUNCT
gi-4940	148	33	where	where	SCONJ
gi-4940	148	34	fr	fr	PROPN
gi-4940	148	35	=	=	PUNCT
gi-4940	148	36	3fi−	3fi−	NUM
gi-4940	148	37	4fi+1	4fi+1	NUM
gi-4940	149	1	+	+	NOUN
gi-4940	149	2	fi+2	fi+2	PROPN
gi-4940	149	3	,	,	PUNCT
gi-4940	149	4	fl	fl	NOUN
gi-4940	149	5	=	=	SYM
gi-4940	149	6	3fi−	3fi−	NUM
gi-4940	149	7	4fi−1	4fi−1	PROPN
gi-4940	149	8	+	+	CCONJ
gi-4940	149	9	fi−2	fi−2	PROPN
gi-4940	149	10	,	,	PUNCT
gi-4940	149	11	and	and	CCONJ
gi-4940	149	12	gr	gr	NOUN
gi-4940	149	13	=	=	SYM
gi-4940	149	14	3gi−	3gi−	NUM
gi-4940	149	15	4gi+1	4gi+1	NOUN
gi-4940	150	1	+	+	NOUN
gi-4940	150	2	gi+2	gi+2	NOUN
gi-4940	150	3	,	,	PUNCT
gi-4940	150	4	gl	gl	NOUN
gi-4940	150	5	=	=	PUNCT
gi-4940	150	6	3gi	3gi	PROPN
gi-4940	151	1	−	−	PROPN
gi-4940	152	1	4gi−1	4gi−1	NUM
gi-4940	152	2	+	+	NUM
gi-4940	152	3	gi−2	gi−2	NOUN
gi-4940	152	4	.	.	PUNCT
gi-4940	153	1	if	if	SCONJ
gi-4940	153	2	lrx(ϕ′i	lrx(ϕ′i	PROPN
gi-4940	153	3	,	,	PUNCT
gi-4940	153	4	λ′i	λ′i	X
gi-4940	153	5	+	+	CCONJ
gi-4940	153	6	lh	lh	PROPN
gi-4940	153	7	)	)	PUNCT
gi-4940	153	8	>	>	X
gi-4940	154	1	lr	lr	X
gi-4940	154	2	∨	∨	NUM
gi-4940	154	3	lry(ϕ′i	lry(ϕ′i	NOUN
gi-4940	154	4	,	,	PUNCT
gi-4940	154	5	λ′i	λ′i	X
gi-4940	154	6	+	+	CCONJ
gi-4940	154	7	lh	lh	PROPN
gi-4940	154	8	)	)	PUNCT
gi-4940	154	9	>	>	X
gi-4940	155	1	lr	lr	PROPN
gi-4940	155	2	,	,	PUNCT
gi-4940	155	3	l	l	NOUN
gi-4940	155	4	=	=	SYM
gi-4940	155	5	−2,−1	−2,−1	ADJ
gi-4940	155	6	,	,	PUNCT
gi-4940	155	7	0	0	NUM
gi-4940	155	8	,	,	PUNCT
gi-4940	155	9	1	1	NUM
gi-4940	155	10	,	,	PUNCT
gi-4940	155	11	2	2	NUM
gi-4940	155	12	,	,	PUNCT
gi-4940	155	13	then	then	ADV
gi-4940	155	14	,	,	PUNCT
gi-4940	155	15	f	f	PROPN
gi-4940	155	16	or	or	CCONJ
gi-4940	155	17	g	g	PROPN
gi-4940	155	18	(	(	PUNCT
gi-4940	155	19	or	or	CCONJ
gi-4940	155	20	both	both	PRON
gi-4940	155	21	)	)	PUNCT
gi-4940	155	22	are	be	AUX
gi-4940	155	23	probably	probably	ADV
gi-4940	155	24	not	not	PART
gi-4940	155	25	smooth	smooth	ADJ
gi-4940	155	26	at	at	ADP
gi-4940	155	27	qi	qi	PROPN
gi-4940	155	28	;	;	PUNCT
gi-4940	155	29	a	a	DET
gi-4940	155	30	discontinuity	discontinuity	NOUN
gi-4940	155	31	is	be	AUX
gi-4940	155	32	aligned	align	VERB
gi-4940	155	33	with	with	ADP
gi-4940	155	34	the	the	DET
gi-4940	155	35	λ′	λ′	NOUN
gi-4940	155	36	direction	direction	NOUN
gi-4940	155	37	.	.	PUNCT
gi-4940	156	1	otherwise	otherwise	ADV
gi-4940	156	2	,	,	PUNCT
gi-4940	156	3	if	if	SCONJ
gi-4940	156	4	lrx(ϕ′i	lrx(ϕ′i	PROPN
gi-4940	156	5	+	+	CCONJ
gi-4940	156	6	lh	lh	PROPN
gi-4940	156	7	,	,	PUNCT
gi-4940	156	8	λ′i	λ′i	PROPN
gi-4940	156	9	)	)	PUNCT
gi-4940	156	10	>	>	X
gi-4940	156	11	lr	lr	X
gi-4940	156	12	∨	∨	NUM
gi-4940	156	13	lry(ϕ′i	lry(ϕ′i	NOUN
gi-4940	156	14	+	+	CCONJ
gi-4940	156	15	lh	lh	PROPN
gi-4940	156	16	,	,	PUNCT
gi-4940	156	17	λ′i	λ′i	PROPN
gi-4940	156	18	)	)	PUNCT
gi-4940	156	19	>	>	X
gi-4940	157	1	lr	lr	PROPN
gi-4940	157	2	,	,	PUNCT
gi-4940	157	3	a	a	DET
gi-4940	157	4	discontinuity	discontinuity	NOUN
gi-4940	157	5	is	be	AUX
gi-4940	157	6	aligned	align	VERB
gi-4940	157	7	with	with	ADP
gi-4940	157	8	the	the	DET
gi-4940	157	9	ϕ′	ϕ′	PROPN
gi-4940	157	10	direction	direction	NOUN
gi-4940	157	11	,	,	PUNCT
gi-4940	157	12	where	where	SCONJ
gi-4940	157	13	lr	lr	NOUN
gi-4940	157	14	=	=	NOUN
gi-4940	157	15	0.8	0.8	NUM
gi-4940	157	16	represents	represent	VERB
gi-4940	157	17	the	the	DET
gi-4940	157	18	threshold	threshold	NOUN
gi-4940	157	19	.	.	PUNCT
gi-4940	158	1	if	if	SCONJ
gi-4940	158	2	a	a	DET
gi-4940	158	3	discontinuity	discontinuity	NOUN
gi-4940	158	4	is	be	AUX
gi-4940	158	5	detected	detect	VERB
gi-4940	158	6	,	,	PUNCT
gi-4940	158	7	the	the	DET
gi-4940	158	8	backward	backward	ADJ
gi-4940	158	9	projection	projection	NOUN
gi-4940	158	10	of	of	ADP
gi-4940	158	11	bϕ′i	bϕ′i	PROPN
gi-4940	158	12	,	,	PUNCT
gi-4940	158	13	bλ′i	bλ′i	NOUN
gi-4940	158	14	to	to	PART
gi-4940	158	15	bϕi	bϕi	VERB
gi-4940	158	16	,	,	PUNCT
gi-4940	158	17	bλi	bλi	PROPN
gi-4940	158	18	is	be	AUX
gi-4940	158	19	performed	perform	VERB
gi-4940	158	20	;	;	PUNCT
gi-4940	158	21	see	see	VERB
gi-4940	158	22	fig	fig	NOUN
gi-4940	158	23	.	.	PUNCT
gi-4940	159	1	3.3	3.3	NUM
gi-4940	159	2	.	.	PUNCT
gi-4940	160	1	in	in	ADP
gi-4940	160	2	practice	practice	NOUN
gi-4940	160	3	,	,	PUNCT
gi-4940	160	4	only	only	ADV
gi-4940	160	5	the	the	DET
gi-4940	160	6	internal	internal	ADJ
gi-4940	160	7	points	point	NOUN
gi-4940	160	8	qϕ′	qϕ′	NOUN
gi-4940	160	9	i+l	i+l	NUM
gi-4940	160	10	of	of	ADP
gi-4940	160	11	bϕ′i	bϕ′i	PROPN
gi-4940	160	12	,	,	PUNCT
gi-4940	160	13	and	and	CCONJ
gi-4940	160	14	qλ′i+l	qλ′i+l	ADV
gi-4940	160	15	of	of	ADP
gi-4940	160	16	bλ′i	bλ′i	PROPN
gi-4940	160	17	are	be	AUX
gi-4940	160	18	converted	convert	VERB
gi-4940	160	19	to	to	ADP
gi-4940	160	20	the	the	DET
gi-4940	160	21	normal	normal	ADJ
gi-4940	160	22	aspect	aspect	NOUN
gi-4940	160	23	using	use	VERB
gi-4940	160	24	eqs	eqs	PROPN
gi-4940	160	25	.	.	PROPN
gi-4940	160	26	3.4	3.4	NUM
gi-4940	160	27	,	,	PUNCT
gi-4940	160	28	3.5	3.5	NUM
gi-4940	160	29	and	and	CCONJ
gi-4940	160	30	their	their	PRON
gi-4940	160	31	direction	direction	NOUN
gi-4940	160	32	is	be	AUX
gi-4940	160	33	checked	check	VERB
gi-4940	160	34	.	.	PUNCT
gi-4940	161	1	subsequently	subsequently	ADV
gi-4940	161	2	,	,	PUNCT
gi-4940	161	3	the	the	DET
gi-4940	161	4	meridian	meridian	PROPN
gi-4940	161	5	/	/	SYM
gi-4940	161	6	parallel	parallel	NOUN
gi-4940	161	7	is	be	AUX
gi-4940	161	8	shifted	shift	VERB
gi-4940	161	9	or	or	CCONJ
gi-4940	161	10	split	split	VERB
gi-4940	161	11	at	at	ADP
gi-4940	161	12	qi	qi	NOUN
gi-4940	161	13	=	=	PUNCT
gi-4940	162	1	[	[	X
gi-4940	162	2	ϕi	ϕi	ADP
gi-4940	162	3	,	,	PUNCT
gi-4940	162	4	λi	λi	NOUN
gi-4940	162	5	]	]	PUNCT
gi-4940	162	6	.	.	PUNCT
gi-4940	162	7	geoinformatics	geoinformatic	NOUN
gi-4940	162	8	fce	fce	VERB
gi-4940	162	9	ctu	ctu	NOUN
gi-4940	162	10	17(2	17(2	NUM
gi-4940	162	11	)	)	PUNCT
gi-4940	162	12	,	,	PUNCT
gi-4940	162	13	2018	2018	NUM
gi-4940	162	14	36	36	NUM
gi-4940	162	15	t.	t.	NOUN
gi-4940	162	16	bayer	bayer	PROPN
gi-4940	162	17	:	:	PUNCT
gi-4940	162	18	plotting	plot	VERB
gi-4940	162	19	the	the	DET
gi-4940	162	20	map	map	NOUN
gi-4940	162	21	projection	projection	NOUN
gi-4940	162	22	graticule	graticule	NOUN
gi-4940	162	23	with	with	ADP
gi-4940	162	24	discontinuities	discontinuity	NOUN
gi-4940	162	25	a	a	DET
gi-4940	162	26	km	km	NOUN
gi-4940	162	27	2	2	NUM
gi-4940	162	28	m	m	NOUN
gi-4940	162	29	3	3	NUM
gi-4940	162	30	m(l	m(l	NOUN
gi-4940	162	31	c	c	PROPN
gi-4940	162	32	)	)	PUNCT
gi-4940	162	33	p(j	p(j	PROPN
gi-4940	162	34	c	c	NOUN
gi-4940	162	35	)	)	PUNCT
gi-4940	162	36	p(j	p(j	PROPN
gi-4940	162	37	3	3	NUM
gi-4940	162	38	)	)	PUNCT
gi-4940	162	39	m	m	VERB
gi-4940	162	40	(	(	PUNCT
gi-4940	162	41	0	0	NUM
gi-4940	162	42	)	)	PUNCT
gi-4940	162	43	m	m	VERB
gi-4940	162	44	(	(	PUNCT
gi-4940	162	45	l	l	NOUN
gi-4940	162	46	0	0	NUM
gi-4940	162	47	)	)	PUNCT
gi-4940	162	48	l	l	NOUN
gi-4940	163	1	k	k	X
gi-4940	163	2	l	l	NOUN
gi-4940	163	3	c	c	NOUN
gi-4940	163	4	l	l	NOUN
gi-4940	163	5	0	0	PUNCT
gi-4940	163	6	m(0	m(0	NOUN
gi-4940	163	7	)	)	PUNCT
gi-4940	163	8	l	l	NOUN
gi-4940	163	9	1	1	NUM
gi-4940	163	10	l	l	NOUN
gi-4940	163	11	2	2	NUM
gi-4940	163	12	m(l	m(l	NOUN
gi-4940	163	13	2	2	NUM
gi-4940	163	14	)	)	PUNCT
gi-4940	163	15	m(l	m(l	NOUN
gi-4940	163	16	1	1	NUM
gi-4940	163	17	)	)	PUNCT
gi-4940	163	18	l	l	NOUN
gi-4940	164	1	=	=	NOUN
gi-4940	164	2	p	p	NOUN
gi-4940	164	3	m	m	VERB
gi-4940	164	4	1	1	NUM
gi-4940	164	5	figure	figure	NOUN
gi-4940	164	6	3.4	3.4	NUM
gi-4940	164	7	:	:	PUNCT
gi-4940	164	8	the	the	DET
gi-4940	164	9	intersections	intersection	NOUN
gi-4940	164	10	of	of	ADP
gi-4940	164	11	the	the	DET
gi-4940	164	12	meridian	meridian	PROPN
gi-4940	164	13	m′(λ′0	m′(λ′0	PROPN
gi-4940	164	14	)	)	PUNCT
gi-4940	164	15	,	,	PUNCT
gi-4940	164	16	parallel	parallel	ADJ
gi-4940	164	17	p(ϕc	p(ϕc	NOUN
gi-4940	164	18	)	)	PUNCT
gi-4940	164	19	,	,	PUNCT
gi-4940	164	20	and	and	CCONJ
gi-4940	164	21	the	the	DET
gi-4940	164	22	meridian	meridian	PROPN
gi-4940	164	23	m(λc	m(λc	PROPN
gi-4940	164	24	)	)	PUNCT
gi-4940	164	25	lead	lead	VERB
gi-4940	164	26	to	to	ADP
gi-4940	164	27	the	the	DET
gi-4940	164	28	ϕ/λ	ϕ/λ	PROPN
gi-4940	164	29	interval	interval	NOUN
gi-4940	164	30	partition	partition	NOUN
gi-4940	164	31	into	into	ADP
gi-4940	164	32	two	two	NUM
gi-4940	164	33	/	/	SYM
gi-4940	164	34	three	three	NUM
gi-4940	164	35	subintervals	subinterval	NOUN
gi-4940	164	36	;	;	PUNCT
gi-4940	164	37	a	a	PRON
gi-4940	164	38	represents	represent	VERB
gi-4940	164	39	the	the	DET
gi-4940	164	40	north	north	NOUN
gi-4940	164	41	pole	pole	NOUN
gi-4940	164	42	,	,	PUNCT
gi-4940	164	43	k	k	PROPN
gi-4940	164	44	the	the	DET
gi-4940	164	45	transformed	transform	VERB
gi-4940	164	46	pole	pole	NOUN
gi-4940	164	47	.	.	PUNCT
gi-4940	165	1	3.2	3.2	NUM
gi-4940	165	2	.	.	PUNCT
gi-4940	165	3	intersection	intersection	NOUN
gi-4940	165	4	of	of	ADP
gi-4940	165	5	the	the	DET
gi-4940	165	6	great	great	ADJ
gi-4940	165	7	circle	circle	NOUN
gi-4940	165	8	and	and	CCONJ
gi-4940	165	9	meridian	meridian	PROPN
gi-4940	165	10	/	/	SYM
gi-4940	165	11	parallel	parallel	ADJ
gi-4940	165	12	arcs	arc	NOUN
gi-4940	165	13	finding	find	VERB
gi-4940	165	14	an	an	DET
gi-4940	165	15	intersection	intersection	NOUN
gi-4940	165	16	of	of	ADP
gi-4940	165	17	the	the	DET
gi-4940	165	18	great	great	ADJ
gi-4940	165	19	circle	circle	NOUN
gi-4940	165	20	arc	arc	NOUN
gi-4940	165	21	and	and	CCONJ
gi-4940	165	22	the	the	DET
gi-4940	165	23	meridian	meridian	PROPN
gi-4940	165	24	/	/	SYM
gi-4940	165	25	parallel	parallel	ADJ
gi-4940	165	26	arc	arc	NOUN
gi-4940	165	27	on	on	ADP
gi-4940	165	28	the	the	DET
gi-4940	165	29	sphere	sphere	NOUN
gi-4940	165	30	represents	represent	VERB
gi-4940	165	31	an	an	DET
gi-4940	165	32	essential	essential	ADJ
gi-4940	165	33	problem	problem	NOUN
gi-4940	165	34	of	of	ADP
gi-4940	165	35	the	the	DET
gi-4940	165	36	graticule	graticule	NOUN
gi-4940	165	37	construction	construction	NOUN
gi-4940	165	38	algorithm	algorithm	NOUN
gi-4940	165	39	.	.	PUNCT
gi-4940	166	1	while	while	SCONJ
gi-4940	166	2	p(ϕ),m(λ	p(ϕ),m(λ	NOUN
gi-4940	166	3	)	)	PUNCT
gi-4940	166	4	refer	refer	VERB
gi-4940	166	5	to	to	ADP
gi-4940	166	6	the	the	DET
gi-4940	166	7	normal	normal	ADJ
gi-4940	166	8	aspect	aspect	NOUN
gi-4940	166	9	,	,	PUNCT
gi-4940	166	10	commas	comma	NOUN
gi-4940	166	11	in	in	ADP
gi-4940	166	12	the	the	DET
gi-4940	166	13	labels	label	NOUN
gi-4940	166	14	indicate	indicate	VERB
gi-4940	166	15	the	the	DET
gi-4940	166	16	oblique	oblique	ADJ
gi-4940	166	17	aspect	aspect	NOUN
gi-4940	166	18	.	.	PUNCT
gi-4940	167	1	the	the	DET
gi-4940	167	2	parallel	parallel	ADJ
gi-4940	167	3	p(ϕc	p(ϕc	NOUN
gi-4940	167	4	)	)	PUNCT
gi-4940	167	5	sampled	sample	VERB
gi-4940	167	6	on	on	ADP
gi-4940	167	7	ωλ	ωλ	NOUN
gi-4940	167	8	=	=	SYM
gi-4940	168	1	[	[	X
gi-4940	168	2	−π	−π	X
gi-4940	168	3	,	,	PUNCT
gi-4940	168	4	π	π	X
gi-4940	168	5	]	]	X
gi-4940	168	6	intersects	intersects	NOUN
gi-4940	168	7	m′(λ′0	m′(λ′0	NOUN
gi-4940	168	8	)	)	PUNCT
gi-4940	168	9	in	in	ADP
gi-4940	168	10	at	at	ADP
gi-4940	168	11	most	most	ADV
gi-4940	168	12	two	two	NUM
gi-4940	168	13	points	point	NOUN
gi-4940	168	14	m1	m1	NOUN
gi-4940	168	15	=	=	PUNCT
gi-4940	169	1	[	[	X
gi-4940	169	2	ϕ1	ϕ1	NOUN
gi-4940	169	3	,	,	PUNCT
gi-4940	169	4	λ1	λ1	PROPN
gi-4940	169	5	]	]	PUNCT
gi-4940	169	6	,	,	PUNCT
gi-4940	169	7	m2	m2	PROPN
gi-4940	169	8	=	=	PUNCT
gi-4940	170	1	[	[	X
gi-4940	170	2	ϕ2	ϕ2	ADV
gi-4940	170	3	,	,	PUNCT
gi-4940	170	4	λ2	λ2	PROPN
gi-4940	170	5	]	]	PUNCT
gi-4940	170	6	where	where	SCONJ
gi-4940	170	7	λ1	λ1	PROPN
gi-4940	170	8	≥	≥	NOUN
gi-4940	170	9	λ2	λ2	NOUN
gi-4940	170	10	,	,	PUNCT
gi-4940	170	11	and	and	CCONJ
gi-4940	170	12	ϕ1	ϕ1	NOUN
gi-4940	170	13	=	=	SYM
gi-4940	170	14	ϕ2	ϕ2	ADV
gi-4940	170	15	=	=	SYM
gi-4940	170	16	ϕc	ϕc	NOUN
gi-4940	170	17	.	.	PUNCT
gi-4940	171	1	the	the	DET
gi-4940	171	2	interval	interval	NOUN
gi-4940	171	3	will	will	AUX
gi-4940	171	4	be	be	AUX
gi-4940	171	5	split	split	VERB
gi-4940	171	6	into	into	ADP
gi-4940	171	7	the	the	DET
gi-4940	171	8	three	three	NUM
gi-4940	171	9	parts	part	NOUN
gi-4940	171	10	given	give	VERB
gi-4940	171	11	by	by	ADP
gi-4940	171	12	the	the	DET
gi-4940	171	13	longitude	longitude	ADJ
gi-4940	171	14	subintervals	subinterval	NOUN
gi-4940	171	15	ωλ,1	ωλ,1	PROPN
gi-4940	172	1	=	=	PUNCT
gi-4940	173	1	[	[	X
gi-4940	173	2	−π	−π	ADJ
gi-4940	173	3	,	,	PUNCT
gi-4940	173	4	λ2	λ2	PROPN
gi-4940	173	5	)	)	PUNCT
gi-4940	173	6	,	,	PUNCT
gi-4940	173	7	ωλ,2	ωλ,2	NOUN
gi-4940	173	8	=	=	SYM
gi-4940	173	9	(	(	PUNCT
gi-4940	173	10	λ2	λ2	PROPN
gi-4940	173	11	,	,	PUNCT
gi-4940	173	12	λ1	λ1	PROPN
gi-4940	173	13	)	)	PUNCT
gi-4940	173	14	,	,	PUNCT
gi-4940	173	15	ωλ,3	ωλ,3	NOUN
gi-4940	173	16	=	=	SYM
gi-4940	173	17	(	(	PUNCT
gi-4940	173	18	λ1	λ1	PROPN
gi-4940	173	19	,	,	PUNCT
gi-4940	173	20	π	π	NOUN
gi-4940	173	21	]	]	X
gi-4940	173	22	.	.	PUNCT
gi-4940	174	1	if	if	SCONJ
gi-4940	174	2	λ′0	λ′0	PROPN
gi-4940	174	3	=	=	SYM
gi-4940	174	4	0	0	PROPN
gi-4940	174	5	,	,	PUNCT
gi-4940	174	6	then	then	ADV
gi-4940	174	7	m1	m1	PROPN
gi-4940	175	1	=	=	PUNCT
gi-4940	176	1	[	[	X
gi-4940	176	2	ϕc	ϕc	X
gi-4940	176	3	,	,	PUNCT
gi-4940	176	4	λk	λk	X
gi-4940	176	5	]	]	PUNCT
gi-4940	176	6	,	,	PUNCT
gi-4940	176	7	m2	m2	PROPN
gi-4940	176	8	=	=	PROPN
gi-4940	177	1	[	[	X
gi-4940	177	2	ϕc	ϕc	X
gi-4940	177	3	,	,	PUNCT
gi-4940	177	4	λk	λk	PROPN
gi-4940	177	5	±	±	NUM
gi-4940	177	6	π	π	NOUN
gi-4940	177	7	]	]	X
gi-4940	177	8	.	.	PUNCT
gi-4940	178	1	depending	depend	VERB
gi-4940	178	2	on	on	ADP
gi-4940	178	3	λk	λk	ADP
gi-4940	178	4	,	,	PUNCT
gi-4940	178	5	the	the	DET
gi-4940	178	6	longitude	longitude	ADJ
gi-4940	178	7	interval	interval	NOUN
gi-4940	178	8	ωλ	ωλ	INTJ
gi-4940	178	9	will	will	AUX
gi-4940	178	10	be	be	AUX
gi-4940	178	11	split	split	VERB
gi-4940	178	12	into	into	ADP
gi-4940	178	13	three	three	NUM
gi-4940	178	14	parts	part	NOUN
gi-4940	178	15	ωλ,1	ωλ,1	PROPN
gi-4940	178	16	,	,	PUNCT
gi-4940	178	17	ωλ,2	ωλ,2	NOUN
gi-4940	178	18	,	,	PUNCT
gi-4940	178	19	ωλ,3	ωλ,3	NOUN
gi-4940	178	20	.	.	PUNCT
gi-4940	179	1	if	if	SCONJ
gi-4940	179	2	λk	λk	PROPN
gi-4940	179	3	≥	≥	X
gi-4940	179	4	0	0	NUM
gi-4940	179	5	ωλ,1	ωλ,1	X
gi-4940	179	6	=	=	PUNCT
gi-4940	180	1	[	[	X
gi-4940	180	2	−π	−π	PROPN
gi-4940	180	3	,	,	PUNCT
gi-4940	180	4	λk	λk	ADP
gi-4940	180	5	−	−	PROPN
gi-4940	180	6	π	π	PROPN
gi-4940	180	7	)	)	PUNCT
gi-4940	180	8	,	,	PUNCT
gi-4940	180	9	ωλ,2	ωλ,2	NOUN
gi-4940	180	10	=	=	SYM
gi-4940	180	11	(	(	PUNCT
gi-4940	180	12	λk	λk	INTJ
gi-4940	180	13	−	−	PROPN
gi-4940	180	14	π	π	PROPN
gi-4940	180	15	,	,	PUNCT
gi-4940	180	16	λk	λk	PROPN
gi-4940	180	17	)	)	PUNCT
gi-4940	180	18	,	,	PUNCT
gi-4940	180	19	ωλ,3	ωλ,3	NOUN
gi-4940	180	20	=	=	SYM
gi-4940	180	21	(	(	PUNCT
gi-4940	180	22	λk	λk	X
gi-4940	180	23	,	,	PUNCT
gi-4940	180	24	π	π	PROPN
gi-4940	180	25	]	]	X
gi-4940	180	26	,	,	PUNCT
gi-4940	180	27	otherwise	otherwise	ADV
gi-4940	180	28	,	,	PUNCT
gi-4940	180	29	ωλ,1	ωλ,1	PROPN
gi-4940	180	30	=	=	PUNCT
gi-4940	181	1	[	[	X
gi-4940	181	2	−π	−π	PROPN
gi-4940	181	3	,	,	PUNCT
gi-4940	181	4	λk	λk	X
gi-4940	181	5	)	)	PUNCT
gi-4940	181	6	,	,	PUNCT
gi-4940	181	7	ωλ,2	ωλ,2	NOUN
gi-4940	181	8	=	=	SYM
gi-4940	181	9	(	(	PUNCT
gi-4940	181	10	λk	λk	ADP
gi-4940	181	11	,	,	PUNCT
gi-4940	181	12	λk	λk	X
gi-4940	181	13	+	+	NUM
gi-4940	181	14	π	π	NOUN
gi-4940	181	15	)	)	PUNCT
gi-4940	181	16	,	,	PUNCT
gi-4940	181	17	ωλ,3	ωλ,3	NOUN
gi-4940	181	18	=	=	SYM
gi-4940	181	19	(	(	PUNCT
gi-4940	181	20	λk	λk	X
gi-4940	181	21	+	+	NUM
gi-4940	181	22	π	π	PROPN
gi-4940	181	23	,	,	PUNCT
gi-4940	181	24	π	π	PROPN
gi-4940	181	25	]	]	X
gi-4940	181	26	.	.	PUNCT
gi-4940	182	1	geoinformatics	geoinformatic	NOUN
gi-4940	182	2	fce	fce	VERB
gi-4940	182	3	ctu	ctu	NOUN
gi-4940	182	4	17(2	17(2	NUM
gi-4940	182	5	)	)	PUNCT
gi-4940	182	6	,	,	PUNCT
gi-4940	183	1	2018	2018	NUM
gi-4940	183	2	37	37	NUM
gi-4940	183	3	t.	t.	NOUN
gi-4940	183	4	bayer	bayer	PROPN
gi-4940	183	5	:	:	PUNCT
gi-4940	183	6	plotting	plot	VERB
gi-4940	183	7	the	the	DET
gi-4940	183	8	map	map	NOUN
gi-4940	183	9	projection	projection	NOUN
gi-4940	183	10	graticule	graticule	NOUN
gi-4940	183	11	with	with	ADP
gi-4940	183	12	discontinuities	discontinuity	NOUN
gi-4940	183	13	for	for	ADP
gi-4940	183	14	λ′0	λ′0	NOUN
gi-4940	184	1	=	=	SYM
gi-4940	184	2	0	0	PROPN
gi-4940	185	1	the	the	DET
gi-4940	185	2	meridians	meridian	NOUN
gi-4940	185	3	m′(0	m′(0	NOUN
gi-4940	185	4	)	)	PUNCT
gi-4940	185	5	and	and	CCONJ
gi-4940	185	6	m(λc	m(λc	NOUN
gi-4940	185	7	)	)	PUNCT
gi-4940	185	8	have	have	VERB
gi-4940	185	9	just	just	ADV
gi-4940	185	10	two	two	NUM
gi-4940	185	11	intersections	intersection	NOUN
gi-4940	185	12	at	at	ADP
gi-4940	185	13	the	the	DET
gi-4940	185	14	poles	pole	NOUN
gi-4940	185	15	:	:	PUNCT
gi-4940	185	16	m3	m3	PROPN
gi-4940	185	17	=	=	PUNCT
gi-4940	186	1	[	[	X
gi-4940	186	2	π2	π2	X
gi-4940	186	3	,	,	PUNCT
gi-4940	186	4	·	·	PUNCT
gi-4940	186	5	]	]	X
gi-4940	186	6	≡	≡	PROPN
gi-4940	186	7	a	a	X
gi-4940	186	8	,	,	PUNCT
gi-4940	186	9	m4	m4	PROPN
gi-4940	186	10	=	=	PUNCT
gi-4940	187	1	[	[	X
gi-4940	187	2	−π	−π	ADP
gi-4940	187	3	2	2	NUM
gi-4940	187	4	,	,	PUNCT
gi-4940	187	5	·	·	PUNCT
gi-4940	187	6	]	]	PUNCT
gi-4940	187	7	≡	≡	PROPN
gi-4940	187	8	b	b	PROPN
gi-4940	187	9	;	;	PUNCT
gi-4940	187	10	the	the	DET
gi-4940	187	11	latitude	latitude	NOUN
gi-4940	187	12	interval	interval	NOUN
gi-4940	187	13	ωϕ	ωϕ	PRON
gi-4940	187	14	of	of	ADP
gi-4940	187	15	the	the	DET
gi-4940	187	16	meridian	meridian	PROPN
gi-4940	187	17	m(λc	m(λc	PROPN
gi-4940	187	18	)	)	PUNCT
gi-4940	187	19	does	do	AUX
gi-4940	187	20	not	not	PART
gi-4940	187	21	need	need	VERB
gi-4940	187	22	to	to	PART
gi-4940	187	23	be	be	AUX
gi-4940	187	24	split	split	VERB
gi-4940	187	25	,	,	PUNCT
gi-4940	187	26	see	see	VERB
gi-4940	187	27	fig	fig	NOUN
gi-4940	187	28	.	.	PUNCT
gi-4940	188	1	3.4	3.4	NUM
gi-4940	188	2	.	.	PUNCT
gi-4940	189	1	if	if	SCONJ
gi-4940	189	2	λ′0	λ′0	PROPN
gi-4940	189	3	6=	6=	PROPN
gi-4940	189	4	0	0	NUM
gi-4940	189	5	,	,	PUNCT
gi-4940	189	6	at	at	ADP
gi-4940	189	7	most	most	ADJ
gi-4940	189	8	one	one	NUM
gi-4940	189	9	intersection	intersection	NOUN
gi-4940	189	10	,	,	PUNCT
gi-4940	189	11	m3	m3	PROPN
gi-4940	189	12	=	=	PUNCT
gi-4940	190	1	[	[	X
gi-4940	190	2	ϕ3	ϕ3	NOUN
gi-4940	190	3	,	,	PUNCT
gi-4940	190	4	λc	λc	X
gi-4940	190	5	]	]	PUNCT
gi-4940	190	6	exists	exist	VERB
gi-4940	190	7	.	.	PUNCT
gi-4940	191	1	to	to	PART
gi-4940	191	2	avoid	avoid	VERB
gi-4940	191	3	the	the	DET
gi-4940	191	4	singularity	singularity	NOUN
gi-4940	191	5	,	,	PUNCT
gi-4940	191	6	the	the	DET
gi-4940	191	7	meridian	meridian	PROPN
gi-4940	191	8	m(λc	m(λc	PROPN
gi-4940	191	9	)	)	PUNCT
gi-4940	191	10	sampled	sample	VERB
gi-4940	191	11	in	in	ADP
gi-4940	191	12	ωϕ	ωϕ	ADP
gi-4940	191	13	=	=	PUNCT
gi-4940	192	1	[	[	X
gi-4940	192	2	−π	−π	ADP
gi-4940	192	3	2	2	NUM
gi-4940	192	4	,	,	PUNCT
gi-4940	192	5	π	π	PROPN
gi-4940	192	6	2	2	NUM
gi-4940	192	7	]	]	PUNCT
gi-4940	192	8	will	will	AUX
gi-4940	192	9	be	be	AUX
gi-4940	192	10	split	split	VERB
gi-4940	192	11	into	into	ADP
gi-4940	192	12	two	two	NUM
gi-4940	192	13	parts	part	NOUN
gi-4940	192	14	given	give	VERB
gi-4940	192	15	by	by	ADP
gi-4940	192	16	the	the	DET
gi-4940	192	17	latitude	latitude	NOUN
gi-4940	192	18	subintervals	subinterval	NOUN
gi-4940	192	19	ωϕ,1	ωϕ,1	PROPN
gi-4940	192	20	=	=	PUNCT
gi-4940	193	1	[	[	X
gi-4940	193	2	−π2	−π2	NOUN
gi-4940	193	3	,	,	PUNCT
gi-4940	193	4	ϕ3	ϕ3	PROPN
gi-4940	193	5	)	)	PUNCT
gi-4940	193	6	,	,	PUNCT
gi-4940	193	7	ωϕ,1	ωϕ,1	PROPN
gi-4940	193	8	=	=	PRON
gi-4940	193	9	(	(	PUNCT
gi-4940	193	10	ϕ3	ϕ3	PROPN
gi-4940	193	11	,	,	PUNCT
gi-4940	193	12	π	π	PROPN
gi-4940	193	13	2	2	NUM
gi-4940	193	14	]	]	PUNCT
gi-4940	193	15	.	.	PUNCT
gi-4940	194	1	intersection	intersection	NOUN
gi-4940	194	2	of	of	ADP
gi-4940	194	3	two	two	NUM
gi-4940	194	4	planes	plane	NOUN
gi-4940	194	5	.	.	PUNCT
gi-4940	195	1	suppose	suppose	VERB
gi-4940	195	2	the	the	DET
gi-4940	195	3	planes	plane	NOUN
gi-4940	195	4	ρ1(n1	ρ1(n1	VERB
gi-4940	195	5	)	)	PUNCT
gi-4940	195	6	,	,	PUNCT
gi-4940	195	7	ρ2(n2	ρ2(n2	ADV
gi-4940	195	8	)	)	PUNCT
gi-4940	195	9	given	give	VERB
gi-4940	195	10	by	by	ADP
gi-4940	195	11	the	the	DET
gi-4940	195	12	normal	normal	ADJ
gi-4940	195	13	vectors	vector	NOUN
gi-4940	195	14	n1	n1	NOUN
gi-4940	195	15	=	=	SYM
gi-4940	195	16	(	(	PUNCT
gi-4940	195	17	n1,x	n1,x	PROPN
gi-4940	195	18	,	,	PUNCT
gi-4940	195	19	n1,yn1,z	n1,yn1,z	NOUN
gi-4940	195	20	)	)	PUNCT
gi-4940	195	21	,	,	PUNCT
gi-4940	195	22	n2	n2	NOUN
gi-4940	195	23	=	=	SYM
gi-4940	195	24	(	(	PUNCT
gi-4940	195	25	n2,x	n2,x	PROPN
gi-4940	195	26	,	,	PUNCT
gi-4940	195	27	n2,yn2,z	n2,yn2,z	PROPN
gi-4940	195	28	)	)	PUNCT
gi-4940	195	29	,	,	PUNCT
gi-4940	195	30	the	the	DET
gi-4940	195	31	points	point	NOUN
gi-4940	195	32	q1	q1	PROPN
gi-4940	195	33	∈	∈	PROPN
gi-4940	195	34	ρ1	ρ1	NOUN
gi-4940	195	35	,	,	PUNCT
gi-4940	195	36	q2	q2	PROPN
gi-4940	195	37	∈	∈	PROPN
gi-4940	195	38	ρ2	ρ2	PROPN
gi-4940	195	39	and	and	CCONJ
gi-4940	195	40	an	an	DET
gi-4940	195	41	arbitrary	arbitrary	ADJ
gi-4940	195	42	point	point	NOUN
gi-4940	195	43	q0	q0	NOUN
gi-4940	195	44	=	=	PUNCT
gi-4940	196	1	[	[	X
gi-4940	196	2	x0	x0	PROPN
gi-4940	196	3	,	,	PUNCT
gi-4940	196	4	y0	y0	PROPN
gi-4940	196	5	,	,	PUNCT
gi-4940	196	6	y0	y0	PROPN
gi-4940	196	7	]	]	PUNCT
gi-4940	196	8	.	.	PUNCT
gi-4940	197	1	the	the	DET
gi-4940	197	2	intersection	intersection	NOUN
gi-4940	197	3	point	point	NOUN
gi-4940	197	4	m	m	VERB
gi-4940	197	5	=	=	PUNCT
gi-4940	198	1	[	[	X
gi-4940	198	2	xm	xm	X
gi-4940	198	3	,	,	PUNCT
gi-4940	198	4	ym	ym	INTJ
gi-4940	198	5	,	,	PUNCT
gi-4940	198	6	zm	zm	PROPN
gi-4940	198	7	]	]	PUNCT
gi-4940	198	8	which	which	PRON
gi-4940	198	9	lies	lie	VERB
gi-4940	198	10	on	on	ADP
gi-4940	198	11	both	both	DET
gi-4940	198	12	planes	plane	NOUN
gi-4940	198	13	ρ1	ρ1	NOUN
gi-4940	198	14	,	,	PUNCT
gi-4940	198	15	ρ2	ρ2	NOUN
gi-4940	198	16	will	will	AUX
gi-4940	198	17	be	be	AUX
gi-4940	198	18	chosen	choose	VERB
gi-4940	198	19	to	to	PART
gi-4940	198	20	minimize	minimize	VERB
gi-4940	198	21	the	the	DET
gi-4940	198	22	norm	norm	NOUN
gi-4940	198	23	[	[	X
gi-4940	198	24	14	14	NUM
gi-4940	198	25	]	]	SYM
gi-4940	198	26	min	min	NOUN
gi-4940	198	27	‖m	‖m	NOUN
gi-4940	198	28	−q0‖22	−q0‖22	NOUN
gi-4940	198	29	,	,	PUNCT
gi-4940	198	30	subject	subject	ADJ
gi-4940	198	31	to	to	ADP
gi-4940	198	32	(	(	PUNCT
gi-4940	198	33	m	m	NOUN
gi-4940	198	34	−q1)n1	−q1)n1	NOUN
gi-4940	198	35	=	=	SYM
gi-4940	198	36	0	0	NUM
gi-4940	198	37	,	,	PUNCT
gi-4940	198	38	(	(	PUNCT
gi-4940	198	39	m	m	PROPN
gi-4940	198	40	−q2)n2	−q2)n2	ADJ
gi-4940	198	41	=	=	NOUN
gi-4940	198	42	0	0	NUM
gi-4940	198	43	.	.	PUNCT
gi-4940	199	1	it	it	PRON
gi-4940	199	2	leads	lead	VERB
gi-4940	199	3	to	to	ADP
gi-4940	199	4	the	the	DET
gi-4940	199	5	system	system	NOUN
gi-4940	199	6	of	of	ADP
gi-4940	199	7	linear	linear	PROPN
gi-4940	199	8	equations	equation	NOUN
gi-4940	199	9	with	with	ADP
gi-4940	199	10	the	the	DET
gi-4940	199	11	lagrange	lagrange	PROPN
gi-4940	199	12	multipliers	multiplier	NOUN
gi-4940	199	13	λ1	λ1	PROPN
gi-4940	199	14	,	,	PUNCT
gi-4940	199	15	λ2	λ2	NOUN
gi-4940	199	16	and	and	CCONJ
gi-4940	199	17	the	the	DET
gi-4940	199	18	solution	solution	NOUN
gi-4940	199	19	s	s	PART
gi-4940	199	20	=	=	NOUN
gi-4940	199	21	a−1b	a−1b	NOUN
gi-4940	199	22	,	,	PUNCT
gi-4940	199	23	where	where	SCONJ
gi-4940	199	24	s	s	NOUN
gi-4940	199	25	=	=	NOUN
gi-4940	199	26			NOUN
gi-4940	200	1	xm	xm	PROPN
gi-4940	200	2	ym	ym	PROPN
gi-4940	201	1	zm	zm	PROPN
gi-4940	201	2	λ1	λ1	PROPN
gi-4940	201	3	λ2	λ2	PROPN
gi-4940	201	4			NOUN
gi-4940	201	5	,	,	PUNCT
gi-4940	201	6	a	a	DET
gi-4940	201	7	=	=	NOUN
gi-4940	201	8			NOUN
gi-4940	201	9	2	2	NUM
gi-4940	201	10	0	0	NUM
gi-4940	201	11	0	0	NUM
gi-4940	202	1	n1,x	n1,x	PROPN
gi-4940	202	2	n2,x	n2,x	PROPN
gi-4940	202	3	0	0	NUM
gi-4940	202	4	2	2	NUM
gi-4940	202	5	0	0	NUM
gi-4940	203	1	n1,y	n1,y	PROPN
gi-4940	203	2	n2,y	n2,y	PROPN
gi-4940	203	3	0	0	NUM
gi-4940	203	4	0	0	NUM
gi-4940	203	5	2	2	NUM
gi-4940	203	6	n1,z	n1,z	PROPN
gi-4940	203	7	n2,z	n2,z	PROPN
gi-4940	203	8	n1,x	n1,x	PROPN
gi-4940	203	9	n1,y	n1,y	PROPN
gi-4940	203	10	n1,z	n1,z	PROPN
gi-4940	203	11	0	0	NUM
gi-4940	203	12	0	0	NUM
gi-4940	203	13	n2,x	n2,x	PROPN
gi-4940	203	14	n2,y	n2,y	PROPN
gi-4940	203	15	n2,z	n2,z	PROPN
gi-4940	203	16	0	0	NUM
gi-4940	203	17	0	0	NUM
gi-4940	203	18			NOUN
gi-4940	203	19	,	,	PUNCT
gi-4940	203	20	b	b	X
gi-4940	203	21	=	=	SYM
gi-4940	203	22			NOUN
gi-4940	203	23	2x0	2x0	NUM
gi-4940	203	24	2y0	2y0	NUM
gi-4940	203	25	2z0	2z0	NUM
gi-4940	203	26	x1n1,x	x1n1,x	PROPN
gi-4940	203	27	+	+	CCONJ
gi-4940	203	28	y1n1,y	y1n1,y	PROPN
gi-4940	203	29	+	+	CCONJ
gi-4940	203	30	z1n1,z	z1n1,z	PROPN
gi-4940	203	31	x2n2,x	x2n2,x	NOUN
gi-4940	203	32	+	+	CCONJ
gi-4940	203	33	y2n2,y	y2n2,y	PROPN
gi-4940	203	34	+	+	CCONJ
gi-4940	203	35	z2n2,z	z2n2,z	PROPN
gi-4940	203	36			VERB
gi-4940	203	37	.	.	PUNCT
gi-4940	204	1	because	because	SCONJ
gi-4940	204	2	a	a	PRON
gi-4940	204	3	is	be	AUX
gi-4940	204	4	sparse	sparse	ADJ
gi-4940	204	5	and	and	CCONJ
gi-4940	204	6	symmetric	symmetric	ADJ
gi-4940	204	7	,	,	PUNCT
gi-4940	204	8	its	its	PRON
gi-4940	204	9	inversion	inversion	NOUN
gi-4940	204	10	can	can	AUX
gi-4940	204	11	be	be	AUX
gi-4940	204	12	found	find	VERB
gi-4940	204	13	in	in	ADP
gi-4940	204	14	the	the	DET
gi-4940	204	15	analytic	analytic	ADJ
gi-4940	204	16	form	form	NOUN
gi-4940	204	17	.	.	PUNCT
gi-4940	205	1	let	let	VERB
gi-4940	205	2	us	we	PRON
gi-4940	205	3	put	put	VERB
gi-4940	205	4	k0	k0	PROPN
gi-4940	205	5	=	=	PROPN
gi-4940	205	6	n2	n2	PROPN
gi-4940	205	7	1,x	1,x	NUM
gi-4940	205	8	,	,	PUNCT
gi-4940	205	9	k1	k1	NOUN
gi-4940	205	10	=	=	SYM
gi-4940	205	11	n2	n2	PROPN
gi-4940	205	12	1,y	1,y	NUM
gi-4940	205	13	,	,	PUNCT
gi-4940	205	14	k2	k2	NOUN
gi-4940	205	15	=	=	SYM
gi-4940	205	16	n2	n2	ADJ
gi-4940	205	17	1,z	1,z	NUM
gi-4940	205	18	,	,	PUNCT
gi-4940	206	1	k3	k3	PROPN
gi-4940	206	2	=	=	PROPN
gi-4940	206	3	n2	n2	PROPN
gi-4940	206	4	2,x	2,x	PROPN
gi-4940	206	5	,	,	PUNCT
gi-4940	206	6	k4	k4	NOUN
gi-4940	206	7	=	=	SYM
gi-4940	206	8	n2	n2	PROPN
gi-4940	206	9	2,y	2,y	NUM
gi-4940	206	10	,	,	PUNCT
gi-4940	206	11	k5	k5	PROPN
gi-4940	206	12	=	=	PROPN
gi-4940	206	13	n2	n2	PROPN
gi-4940	206	14	2,z	2,z	PROPN
gi-4940	206	15	,	,	PUNCT
gi-4940	206	16	k6	k6	PROPN
gi-4940	206	17	=	=	PROPN
gi-4940	206	18	k0	k0	PROPN
gi-4940	206	19	+	+	CCONJ
gi-4940	206	20	k1	k1	PROPN
gi-4940	206	21	k7	k7	PROPN
gi-4940	206	22	=	=	PUNCT
gi-4940	207	1	k3	k3	PROPN
gi-4940	207	2	+	+	CCONJ
gi-4940	207	3	k4	k4	ADJ
gi-4940	207	4	,	,	PUNCT
gi-4940	207	5	k8	k8	NOUN
gi-4940	207	6	=	=	PRON
gi-4940	207	7	k3	k3	PROPN
gi-4940	207	8	+	+	CCONJ
gi-4940	207	9	k5	k5	PROPN
gi-4940	207	10	,	,	PUNCT
gi-4940	207	11	k9	k9	NOUN
gi-4940	207	12	=	=	PROPN
gi-4940	207	13	k4	k4	PROPN
gi-4940	207	14	+	+	CCONJ
gi-4940	207	15	k5	k5	PROPN
gi-4940	207	16	,	,	PUNCT
gi-4940	207	17	k10	k10	PROPN
gi-4940	207	18	=	=	SYM
gi-4940	207	19	n1,xn2,x	n1,xn2,x	PROPN
gi-4940	207	20	,	,	PUNCT
gi-4940	207	21	k11	k11	PROPN
gi-4940	207	22	=	=	SYM
gi-4940	207	23	n1,xn2,x	n1,xn2,x	PROPN
gi-4940	207	24	,	,	PUNCT
gi-4940	207	25	k12	k12	NOUN
gi-4940	207	26	=	=	SYM
gi-4940	207	27	n1,zn2,z	n1,zn2,z	PROPN
gi-4940	207	28	,	,	PUNCT
gi-4940	207	29	k13	k13	NOUN
gi-4940	207	30	=	=	SYM
gi-4940	207	31	n1,xn2,y	n1,xn2,y	PROPN
gi-4940	207	32	,	,	PUNCT
gi-4940	207	33	k14	k14	PROPN
gi-4940	207	34	=	=	PUNCT
gi-4940	207	35	n1,xn2,z	n1,xn2,z	PROPN
gi-4940	207	36	,	,	PUNCT
gi-4940	207	37	k15	k15	PROPN
gi-4940	207	38	=	=	SYM
gi-4940	207	39	n1,yn2,x	n1,yn2,x	PROPN
gi-4940	207	40	,	,	PUNCT
gi-4940	207	41	k16	k16	PROPN
gi-4940	207	42	=	=	SYM
gi-4940	207	43	n1,yn2,z	n1,yn2,z	PROPN
gi-4940	207	44	,	,	PUNCT
gi-4940	207	45	k17	k17	PROPN
gi-4940	207	46	=	=	SYM
gi-4940	207	47	n1,zn2,y	n1,zn2,y	PROPN
gi-4940	207	48	,	,	PUNCT
gi-4940	207	49	k18	k18	PROPN
gi-4940	207	50	=	=	PUNCT
gi-4940	207	51	n1,zn2,x	n1,zn2,x	PROPN
gi-4940	207	52	,	,	PUNCT
gi-4940	207	53	k19	k19	PROPN
gi-4940	207	54	=	=	SYM
gi-4940	207	55	k15n2,y	k15n2,y	PROPN
gi-4940	207	56	,	,	PUNCT
gi-4940	207	57	k20	k20	NOUN
gi-4940	207	58	=	=	SYM
gi-4940	207	59	k17n2,z	k17n2,z	PROPN
gi-4940	207	60	,	,	PUNCT
gi-4940	207	61	k21	k21	NOUN
gi-4940	207	62	=	=	SYM
gi-4940	207	63	k15n1,x	k15n1,x	PROPN
gi-4940	207	64	,	,	PUNCT
gi-4940	207	65	k22	k22	NOUN
gi-4940	207	66	=	=	SYM
gi-4940	207	67	k13n1,y	k13n1,y	PROPN
gi-4940	207	68	,	,	PUNCT
gi-4940	207	69	k23	k23	PROPN
gi-4940	207	70	=	=	PROPN
gi-4940	207	71	k0	k0	PROPN
gi-4940	207	72	+	+	CCONJ
gi-4940	207	73	k1	k1	PROPN
gi-4940	207	74	+	+	CCONJ
gi-4940	207	75	k2	k2	ADJ
gi-4940	207	76	,	,	PUNCT
gi-4940	207	77	k24	k24	NOUN
gi-4940	207	78	=	=	PUNCT
gi-4940	207	79	k3	k3	VERB
gi-4940	207	80	+	+	CCONJ
gi-4940	207	81	k4	k4	ADJ
gi-4940	207	82	+	+	CCONJ
gi-4940	207	83	k5	k5	PROPN
gi-4940	207	84	,	,	PUNCT
gi-4940	207	85	then	then	ADV
gi-4940	207	86	det(a	det(a	PROPN
gi-4940	207	87	)	)	PUNCT
gi-4940	208	1	=	=	PUNCT
gi-4940	209	1	2(k0k9	2(k0k9	NUM
gi-4940	209	2	−	−	NOUN
gi-4940	209	3	2k10k12	2k10k12	NUM
gi-4940	210	1	+	+	CCONJ
gi-4940	211	1	k2k7	k2k7	CCONJ
gi-4940	211	2	−	−	PROPN
gi-4940	211	3	2k11(k10	2k11(k10	NUM
gi-4940	211	4	+	+	CCONJ
gi-4940	211	5	k12	k12	NOUN
gi-4940	211	6	)	)	PUNCT
gi-4940	212	1	+	+	CCONJ
gi-4940	212	2	k1k8	k1k8	NOUN
gi-4940	212	3	)	)	PUNCT
gi-4940	212	4	,	,	PUNCT
gi-4940	212	5	and	and	CCONJ
gi-4940	212	6	the	the	DET
gi-4940	212	7	elements	element	NOUN
gi-4940	212	8	of	of	ADP
gi-4940	212	9	a−1	a−1	PROPN
gi-4940	212	10	are	be	AUX
gi-4940	212	11	a11	a11	PROPN
gi-4940	212	12	=	=	SYM
gi-4940	212	13	(	(	PUNCT
gi-4940	212	14	k18	k18	PROPN
gi-4940	212	15	−	−	PROPN
gi-4940	213	1	k16)(k18	k16)(k18	PROPN
gi-4940	213	2	−	−	PROPN
gi-4940	213	3	k16	k16	PROPN
gi-4940	213	4	)	)	PUNCT
gi-4940	213	5	det(a	det(a	PROPN
gi-4940	213	6	)	)	PUNCT
gi-4940	213	7	,	,	PUNCT
gi-4940	213	8	a12	a12	NOUN
gi-4940	213	9	=	=	SYM
gi-4940	213	10	(	(	PUNCT
gi-4940	213	11	k14	k14	PROPN
gi-4940	213	12	−	−	PROPN
gi-4940	213	13	k17)(k18	k17)(k18	PROPN
gi-4940	214	1	−	−	PROPN
gi-4940	214	2	k16	k16	PROPN
gi-4940	214	3	)	)	PUNCT
gi-4940	214	4	det(a	det(a	PROPN
gi-4940	214	5	)	)	PUNCT
gi-4940	214	6	,	,	PUNCT
gi-4940	214	7	a13	a13	NOUN
gi-4940	214	8	=	=	SYM
gi-4940	214	9	(	(	PUNCT
gi-4940	214	10	k13	k13	VERB
gi-4940	214	11	−	−	PROPN
gi-4940	214	12	k15)(k16	k15)(k16	NOUN
gi-4940	214	13	−	−	PROPN
gi-4940	214	14	k18	k18	PROPN
gi-4940	214	15	)	)	PUNCT
gi-4940	214	16	det(a	det(a	PROPN
gi-4940	214	17	)	)	PUNCT
gi-4940	214	18	,	,	PUNCT
gi-4940	214	19	a14	a14	PROPN
gi-4940	214	20	=	=	SYM
gi-4940	214	21	2(−k19	2(−k19	NUM
gi-4940	214	22	−	−	NOUN
gi-4940	214	23	k20	k20	NOUN
gi-4940	214	24	+	+	CCONJ
gi-4940	214	25	n1,xk9	n1,xk9	NOUN
gi-4940	214	26	)	)	PUNCT
gi-4940	214	27	det(a	det(a	PROPN
gi-4940	214	28	)	)	PUNCT
gi-4940	214	29	,	,	PUNCT
gi-4940	214	30	a15	a15	NOUN
gi-4940	214	31	=	=	SYM
gi-4940	214	32	2[n1,yk15	2[n1,yk15	PROPN
gi-4940	214	33	−	−	PROPN
gi-4940	214	34	k22	k22	NOUN
gi-4940	214	35	+	+	CCONJ
gi-4940	214	36	n1,z(k17	n1,z(k17	PROPN
gi-4940	214	37	−	−	PROPN
gi-4940	214	38	k14	k14	PROPN
gi-4940	214	39	)	)	PUNCT
gi-4940	214	40	]	]	PUNCT
gi-4940	215	1	det(a	det(a	NOUN
gi-4940	215	2	)	)	PUNCT
gi-4940	215	3	,	,	PUNCT
gi-4940	215	4	a22	a22	X
gi-4940	215	5	=	=	SYM
gi-4940	215	6	(	(	PUNCT
gi-4940	215	7	k17	k17	PROPN
gi-4940	215	8	−	−	PROPN
gi-4940	215	9	k14)(k17	k14)(k17	PROPN
gi-4940	215	10	−	−	PROPN
gi-4940	215	11	k14	k14	PROPN
gi-4940	215	12	)	)	PUNCT
gi-4940	215	13	det(a	det(a	PROPN
gi-4940	215	14	)	)	PUNCT
gi-4940	215	15	,	,	PUNCT
gi-4940	215	16	a23	a23	PROPN
gi-4940	215	17	=	=	PUNCT
gi-4940	215	18	(	(	PUNCT
gi-4940	215	19	k13	k13	VERB
gi-4940	215	20	−	−	PROPN
gi-4940	215	21	k15)(k17	k15)(k17	PROPN
gi-4940	215	22	−	−	PROPN
gi-4940	215	23	k14	k14	PROPN
gi-4940	215	24	)	)	PUNCT
gi-4940	215	25	det(a	det(a	PROPN
gi-4940	215	26	)	)	PUNCT
gi-4940	215	27	,	,	PUNCT
gi-4940	215	28	a24	a24	PROPN
gi-4940	215	29	=	=	NOUN
gi-4940	215	30	2[n1,yk8	2[n1,yk8	NUM
gi-4940	215	31	−	−	PROPN
gi-4940	215	32	n2,y(k10	n2,y(k10	PROPN
gi-4940	215	33	+	+	CCONJ
gi-4940	215	34	k12	k12	NOUN
gi-4940	215	35	)	)	PUNCT
gi-4940	215	36	]	]	PUNCT
gi-4940	216	1	det(a	det(a	NOUN
gi-4940	216	2	)	)	PUNCT
gi-4940	216	3	,	,	PUNCT
gi-4940	216	4	a25	a25	NOUN
gi-4940	216	5	=	=	SYM
gi-4940	216	6	2[n1,xk13	2[n1,xk13	PROPN
gi-4940	217	1	−	−	NOUN
gi-4940	217	2	k21	k21	NOUN
gi-4940	217	3	+	+	CCONJ
gi-4940	217	4	n1,z(k18	n1,z(k18	PROPN
gi-4940	217	5	−	−	PROPN
gi-4940	217	6	k16	k16	PROPN
gi-4940	217	7	)	)	PUNCT
gi-4940	217	8	]	]	PUNCT
gi-4940	218	1	det(a	det(a	NOUN
gi-4940	218	2	)	)	PUNCT
gi-4940	218	3	,	,	PUNCT
gi-4940	218	4	a33	a33	NUM
gi-4940	218	5	=	=	SYM
gi-4940	218	6	(	(	PUNCT
gi-4940	218	7	k15	k15	PROPN
gi-4940	218	8	−	−	PROPN
gi-4940	218	9	k13)(k15	k13)(k15	PROPN
gi-4940	218	10	−	−	PROPN
gi-4940	218	11	k13	k13	PROPN
gi-4940	218	12	)	)	PUNCT
gi-4940	218	13	det(a	det(a	PROPN
gi-4940	218	14	)	)	PUNCT
gi-4940	218	15	,	,	PUNCT
gi-4940	218	16	a34	a34	NOUN
gi-4940	218	17	=	=	SYM
gi-4940	218	18	2[n1,zk7	2[n1,zk7	NUM
gi-4940	218	19	−	−	NOUN
gi-4940	219	1	n2,z(k10	n2,z(k10	NOUN
gi-4940	219	2	+	+	CCONJ
gi-4940	219	3	k11	k11	NOUN
gi-4940	219	4	)	)	PUNCT
gi-4940	219	5	]	]	PUNCT
gi-4940	220	1	det(a	det(a	NOUN
gi-4940	220	2	)	)	PUNCT
gi-4940	220	3	,	,	PUNCT
gi-4940	220	4	a35	a35	X
gi-4940	220	5	=	=	SYM
gi-4940	220	6	2[n2,zk6	2[n2,zk6	NUM
gi-4940	220	7	−	−	NOUN
gi-4940	221	1	n1,z(k10	n1,z(k10	NOUN
gi-4940	221	2	+	+	CCONJ
gi-4940	221	3	k11	k11	NOUN
gi-4940	221	4	)	)	PUNCT
gi-4940	221	5	]	]	PUNCT
gi-4940	222	1	det(a	det(a	NOUN
gi-4940	222	2	)	)	PUNCT
gi-4940	222	3	,	,	PUNCT
gi-4940	222	4	a44	a44	PROPN
gi-4940	222	5	=	=	SYM
gi-4940	222	6	−4k24	−4k24	PROPN
gi-4940	222	7	det(a	det(a	PROPN
gi-4940	222	8	)	)	PUNCT
gi-4940	222	9	,	,	PUNCT
gi-4940	222	10	a45	a45	PROPN
gi-4940	222	11	=	=	SYM
gi-4940	222	12	4(k10	4(k10	PROPN
gi-4940	222	13	+	+	CCONJ
gi-4940	222	14	k11	k11	NOUN
gi-4940	222	15	+	+	CCONJ
gi-4940	222	16	k12	k12	NOUN
gi-4940	222	17	)	)	PUNCT
gi-4940	222	18	det(a	det(a	PROPN
gi-4940	222	19	)	)	PUNCT
gi-4940	222	20	,	,	PUNCT
gi-4940	222	21	a55	a55	X
gi-4940	222	22	=	=	SYM
gi-4940	222	23	−4k23	−4k23	PROPN
gi-4940	222	24	det(a	det(a	PROPN
gi-4940	222	25	)	)	PUNCT
gi-4940	222	26	.	.	PUNCT
gi-4940	223	1	the	the	DET
gi-4940	223	2	direction	direction	NOUN
gi-4940	223	3	n	n	PROPN
gi-4940	223	4	of	of	ADP
gi-4940	223	5	the	the	DET
gi-4940	223	6	line	line	NOUN
gi-4940	223	7	of	of	ADP
gi-4940	223	8	intersection	intersection	NOUN
gi-4940	223	9	is	be	AUX
gi-4940	223	10	given	give	VERB
gi-4940	223	11	by	by	ADP
gi-4940	223	12	the	the	DET
gi-4940	223	13	cross	cross	NOUN
gi-4940	223	14	product	product	NOUN
gi-4940	223	15	n	n	PROPN
gi-4940	223	16	=	=	SYM
gi-4940	223	17	n1	n1	PROPN
gi-4940	223	18	×	×	PROPN
gi-4940	223	19	n2	n2	NOUN
gi-4940	223	20	,	,	PUNCT
gi-4940	223	21	its	its	PRON
gi-4940	223	22	parametric	parametric	ADJ
gi-4940	223	23	equation	equation	NOUN
gi-4940	223	24	is	be	AUX
gi-4940	223	25	(	(	PUNCT
gi-4940	223	26	x	x	NOUN
gi-4940	223	27	,	,	PUNCT
gi-4940	223	28	y	y	PROPN
gi-4940	223	29	,	,	PUNCT
gi-4940	223	30	z	z	NOUN
gi-4940	223	31	)	)	PUNCT
gi-4940	223	32	=	=	SYM
gi-4940	224	1	(	(	PUNCT
gi-4940	224	2	xm	xm	PROPN
gi-4940	224	3	,	,	PUNCT
gi-4940	224	4	ym	ym	INTJ
gi-4940	224	5	,	,	PUNCT
gi-4940	224	6	zm	zm	PROPN
gi-4940	224	7	)	)	PUNCT
gi-4940	225	1	+	+	CCONJ
gi-4940	225	2	α(nx	α(nx	NOUN
gi-4940	225	3	,	,	PUNCT
gi-4940	225	4	ny	ny	NOUN
gi-4940	225	5	,	,	PUNCT
gi-4940	225	6	nz	nz	PROPN
gi-4940	225	7	)	)	PUNCT
gi-4940	225	8	,	,	PUNCT
gi-4940	225	9	where	where	SCONJ
gi-4940	225	10	α	α	PRON
gi-4940	225	11	∈	∈	PROPN
gi-4940	226	1	[	[	X
gi-4940	226	2	0	0	NUM
gi-4940	226	3	,	,	PUNCT
gi-4940	226	4	1	1	NUM
gi-4940	226	5	]	]	PUNCT
gi-4940	226	6	.	.	PUNCT
gi-4940	227	1	geoinformatics	geoinformatic	NOUN
gi-4940	227	2	fce	fce	VERB
gi-4940	227	3	ctu	ctu	NOUN
gi-4940	227	4	17(2	17(2	NUM
gi-4940	227	5	)	)	PUNCT
gi-4940	227	6	,	,	PUNCT
gi-4940	227	7	2018	2018	NUM
gi-4940	227	8	38	38	NUM
gi-4940	227	9	t.	t.	NOUN
gi-4940	227	10	bayer	bayer	NOUN
gi-4940	227	11	:	:	PUNCT
gi-4940	227	12	plotting	plot	VERB
gi-4940	227	13	the	the	DET
gi-4940	227	14	map	map	NOUN
gi-4940	227	15	projection	projection	NOUN
gi-4940	227	16	graticule	graticule	NOUN
gi-4940	227	17	with	with	ADP
gi-4940	227	18	discontinuities	discontinuity	NOUN
gi-4940	227	19	intersection	intersection	NOUN
gi-4940	227	20	of	of	ADP
gi-4940	227	21	the	the	DET
gi-4940	227	22	line	line	NOUN
gi-4940	227	23	and	and	CCONJ
gi-4940	227	24	sphere	sphere	NOUN
gi-4940	227	25	.	.	PUNCT
gi-4940	228	1	it	it	PRON
gi-4940	228	2	is	be	AUX
gi-4940	228	3	necessary	necessary	ADJ
gi-4940	228	4	to	to	PART
gi-4940	228	5	test	test	VERB
gi-4940	228	6	,	,	PUNCT
gi-4940	228	7	whether	whether	SCONJ
gi-4940	228	8	the	the	DET
gi-4940	228	9	line	line	NOUN
gi-4940	228	10	of	of	ADP
gi-4940	228	11	intersection	intersection	NOUN
gi-4940	228	12	intersects	intersect	VERB
gi-4940	228	13	a	a	DET
gi-4940	228	14	sphere	sphere	NOUN
gi-4940	228	15	s2	s2	NOUN
gi-4940	228	16	of	of	ADP
gi-4940	228	17	the	the	DET
gi-4940	228	18	radius	radius	NOUN
gi-4940	228	19	r	r	NOUN
gi-4940	228	20	with	with	ADP
gi-4940	228	21	the	the	DET
gi-4940	228	22	center	center	NOUN
gi-4940	228	23	c	c	NOUN
gi-4940	229	1	=	=	PUNCT
gi-4940	230	1	[	[	X
gi-4940	230	2	xc	xc	X
gi-4940	230	3	,	,	PUNCT
gi-4940	230	4	yc	yc	PROPN
gi-4940	230	5	,	,	PUNCT
gi-4940	230	6	zc	zc	NOUN
gi-4940	230	7	]	]	X
gi-4940	230	8	,	,	PUNCT
gi-4940	230	9	given	give	VERB
gi-4940	230	10	by	by	ADP
gi-4940	230	11	(	(	PUNCT
gi-4940	230	12	xm	xm	PROPN
gi-4940	230	13	+	+	CCONJ
gi-4940	230	14	αnx	αnx	PROPN
gi-4940	230	15	−	−	PROPN
gi-4940	230	16	xc)2	xc)2	PROPN
gi-4940	230	17	+	+	CCONJ
gi-4940	230	18	(	(	PUNCT
gi-4940	230	19	ym	ym	NOUN
gi-4940	230	20	+	+	CCONJ
gi-4940	230	21	αny	αny	ADJ
gi-4940	231	1	−	−	PUNCT
gi-4940	231	2	yc)2	yc)2	NOUN
gi-4940	231	3	+	+	CCONJ
gi-4940	231	4	(	(	PUNCT
gi-4940	231	5	zm	zm	PROPN
gi-4940	231	6	+	+	PROPN
gi-4940	231	7	αnz	αnz	PROPN
gi-4940	231	8	−	−	PROPN
gi-4940	231	9	zc)2	zc)2	NOUN
gi-4940	231	10	=	=	SYM
gi-4940	231	11	r2	r2	PROPN
gi-4940	231	12	.	.	PUNCT
gi-4940	232	1	it	it	PRON
gi-4940	232	2	leads	lead	VERB
gi-4940	232	3	to	to	ADP
gi-4940	232	4	the	the	DET
gi-4940	232	5	quadratic	quadratic	ADJ
gi-4940	232	6	equation	equation	NOUN
gi-4940	232	7	for	for	ADP
gi-4940	232	8	α	α	NOUN
gi-4940	232	9	,	,	PUNCT
gi-4940	232	10	where	where	SCONJ
gi-4940	232	11	a	a	DET
gi-4940	232	12	=	=	SYM
gi-4940	232	13	n2	n2	NOUN
gi-4940	232	14	x	x	PUNCT
gi-4940	233	1	+	+	PUNCT
gi-4940	233	2	n2	n2	PROPN
gi-4940	233	3	y	y	PROPN
gi-4940	233	4	+	+	CCONJ
gi-4940	233	5	n2	n2	PROPN
gi-4940	233	6	z	z	PROPN
gi-4940	233	7	,	,	PUNCT
gi-4940	233	8	b	b	X
gi-4940	233	9	=	=	SYM
gi-4940	233	10	2(xmnx	2(xmnx	PROPN
gi-4940	233	11	−	−	PROPN
gi-4940	233	12	nxxc	nxxc	NOUN
gi-4940	233	13	+	+	CCONJ
gi-4940	233	14	ymny	ymny	PROPN
gi-4940	233	15	−	−	PROPN
gi-4940	233	16	nyyc	nyyc	ADJ
gi-4940	233	17	+	+	NUM
gi-4940	233	18	zmnz	zmnz	NOUN
gi-4940	233	19	−	−	NOUN
gi-4940	233	20	zmzc	zmzc	NOUN
gi-4940	233	21	)	)	PUNCT
gi-4940	233	22	,	,	PUNCT
gi-4940	233	23	c	c	X
gi-4940	233	24	=	=	SYM
gi-4940	233	25	(	(	PUNCT
gi-4940	233	26	xm	xm	PROPN
gi-4940	233	27	−	−	PROPN
gi-4940	233	28	xc)2	xc)2	PROPN
gi-4940	234	1	+	+	CCONJ
gi-4940	234	2	(	(	PUNCT
gi-4940	234	3	ym	ym	NOUN
gi-4940	234	4	−	−	PROPN
gi-4940	234	5	yc)2	yc)2	NOUN
gi-4940	234	6	+	+	CCONJ
gi-4940	234	7	(	(	PUNCT
gi-4940	234	8	zm	zm	PROPN
gi-4940	234	9	−	−	PROPN
gi-4940	234	10	zc)2	zc)2	PROPN
gi-4940	234	11	−r2	−r2	PROPN
gi-4940	234	12	.	.	PROPN
gi-4940	234	13	for	for	ADP
gi-4940	234	14	the	the	DET
gi-4940	234	15	discriminantd	discriminantd	NOUN
gi-4940	234	16	>	>	X
gi-4940	234	17	0	0	NUM
gi-4940	234	18	,	,	PUNCT
gi-4940	234	19	there	there	PRON
gi-4940	234	20	are	be	VERB
gi-4940	234	21	two	two	NUM
gi-4940	234	22	intersectionsm1	intersectionsm1	NOUN
gi-4940	235	1	=	=	PUNCT
gi-4940	236	1	[	[	X
gi-4940	236	2	x1	x1	PROPN
gi-4940	236	3	,	,	PUNCT
gi-4940	236	4	y1	y1	PROPN
gi-4940	236	5	,	,	PUNCT
gi-4940	236	6	z1	z1	PROPN
gi-4940	236	7	]	]	PUNCT
gi-4940	236	8	,	,	PUNCT
gi-4940	236	9	andm2	andm2	PUNCT
gi-4940	237	1	=	=	PUNCT
gi-4940	238	1	[	[	X
gi-4940	238	2	x2	x2	PROPN
gi-4940	238	3	,	,	PUNCT
gi-4940	238	4	y2	y2	PROPN
gi-4940	238	5	,	,	PUNCT
gi-4940	238	6	z2	z2	PROPN
gi-4940	238	7	]	]	PUNCT
gi-4940	238	8	,	,	PUNCT
gi-4940	238	9	determined	determine	VERB
gi-4940	238	10	from	from	ADP
gi-4940	238	11	(	(	PUNCT
gi-4940	238	12	x1,2	x1,2	ADJ
gi-4940	238	13	,	,	PUNCT
gi-4940	238	14	y1,2	y1,2	ADJ
gi-4940	238	15	,	,	PUNCT
gi-4940	238	16	z1,2	z1,2	ADJ
gi-4940	238	17	)	)	PUNCT
gi-4940	238	18	=	=	SYM
gi-4940	238	19	(	(	PUNCT
gi-4940	238	20	xm	xm	PROPN
gi-4940	238	21	,	,	PUNCT
gi-4940	238	22	ym	ym	INTJ
gi-4940	238	23	,	,	PUNCT
gi-4940	238	24	zm	zm	PROPN
gi-4940	238	25	)	)	PUNCT
gi-4940	239	1	+	+	CCONJ
gi-4940	239	2	α1,2(nx	α1,2(nx	NOUN
gi-4940	239	3	,	,	PUNCT
gi-4940	239	4	ny	ny	NOUN
gi-4940	239	5	,	,	PUNCT
gi-4940	239	6	nz	nz	PROPN
gi-4940	239	7	)	)	PUNCT
gi-4940	239	8	.	.	PUNCT
gi-4940	240	1	if	if	SCONJ
gi-4940	240	2	d	d	PROPN
gi-4940	240	3	=	=	SYM
gi-4940	240	4	0	0	NUM
gi-4940	240	5	,	,	PUNCT
gi-4940	240	6	then	then	ADV
gi-4940	240	7	m1	m1	PROPN
gi-4940	240	8	≡m2	≡m2	NUM
gi-4940	240	9	;	;	PUNCT
gi-4940	240	10	for	for	ADP
gi-4940	240	11	d	d	PROPN
gi-4940	240	12	<	<	X
gi-4940	240	13	0	0	PROPN
gi-4940	240	14	the	the	DET
gi-4940	240	15	line	line	NOUN
gi-4940	240	16	does	do	AUX
gi-4940	240	17	not	not	PART
gi-4940	240	18	intersect	intersect	VERB
gi-4940	240	19	the	the	DET
gi-4940	240	20	sphere	sphere	NOUN
gi-4940	240	21	.	.	PUNCT
gi-4940	241	1	the	the	DET
gi-4940	241	2	cartesian	cartesian	ADJ
gi-4940	241	3	coordinates	coordinate	NOUN
gi-4940	241	4	of	of	ADP
gi-4940	241	5	intersections	intersection	NOUN
gi-4940	241	6	need	need	VERB
gi-4940	241	7	to	to	PART
gi-4940	241	8	be	be	AUX
gi-4940	241	9	converted	convert	VERB
gi-4940	241	10	to	to	ADP
gi-4940	241	11	the	the	DET
gi-4940	241	12	spherical	spherical	NOUN
gi-4940	241	13	,	,	PUNCT
gi-4940	241	14	where	where	SCONJ
gi-4940	241	15	ϕ1,2	ϕ1,2	PROPN
gi-4940	241	16	=	=	SYM
gi-4940	241	17	arcsin	arcsin	PROPN
gi-4940	241	18	(	(	PUNCT
gi-4940	241	19	z1,2/	z1,2/	NUM
gi-4940	241	20	√	√	NUM
gi-4940	241	21	x2	x2	NOUN
gi-4940	241	22	1,2	1,2	NUM
gi-4940	241	23	+	+	CCONJ
gi-4940	241	24	y2	y2	NOUN
gi-4940	241	25	1,2	1,2	NUM
gi-4940	241	26	+	+	CCONJ
gi-4940	241	27	z2	z2	PROPN
gi-4940	241	28	1,2	1,2	NUM
gi-4940	241	29	)	)	PUNCT
gi-4940	241	30	,	,	PUNCT
gi-4940	241	31	λ1,2	λ1,2	NOUN
gi-4940	241	32	=	=	PUNCT
gi-4940	241	33	atan2(y1,2	atan2(y1,2	ADJ
gi-4940	241	34	,	,	PUNCT
gi-4940	241	35	x1,2	x1,2	NUM
gi-4940	241	36	)	)	PUNCT
gi-4940	241	37	.	.	PUNCT
gi-4940	242	1	practical	practical	ADJ
gi-4940	242	2	computation	computation	NOUN
gi-4940	242	3	.	.	PUNCT
gi-4940	243	1	the	the	DET
gi-4940	243	2	meridian	meridian	PROPN
gi-4940	243	3	plane	plane	NOUN
gi-4940	243	4	%	%	NOUN
gi-4940	243	5	1	1	NUM
gi-4940	243	6	containing	contain	VERB
gi-4940	243	7	m(λc	m(λc	NOUN
gi-4940	243	8	)	)	PUNCT
gi-4940	243	9	passes	pass	VERB
gi-4940	243	10	through	through	ADP
gi-4940	243	11	the	the	DET
gi-4940	243	12	points	point	NOUN
gi-4940	243	13	p5	p5	ADJ
gi-4940	244	1	=	=	PUNCT
gi-4940	245	1	[	[	X
gi-4940	245	2	ϕ5	ϕ5	NOUN
gi-4940	245	3	,	,	PUNCT
gi-4940	245	4	λc	λc	X
gi-4940	245	5	]	]	X
gi-4940	245	6	,	,	PUNCT
gi-4940	245	7	p6	p6	PROPN
gi-4940	245	8	=	=	PUNCT
gi-4940	246	1	[	[	X
gi-4940	246	2	ϕ6λc	ϕ6λc	X
gi-4940	246	3	]	]	X
gi-4940	246	4	,	,	PUNCT
gi-4940	246	5	and	and	CCONJ
gi-4940	246	6	p7	p7	ADJ
gi-4940	246	7	=	=	PUNCT
gi-4940	247	1	[	[	X
gi-4940	247	2	ϕ7	ϕ7	PROPN
gi-4940	247	3	,	,	PUNCT
gi-4940	247	4	λc	λc	X
gi-4940	247	5	]	]	X
gi-4940	247	6	,	,	PUNCT
gi-4940	247	7	where	where	SCONJ
gi-4940	247	8	ϕ5	ϕ5	NOUN
gi-4940	248	1	=	=	PUNCT
gi-4940	248	2	−π	−π	ADP
gi-4940	248	3	2	2	NUM
gi-4940	249	1	+	+	CCONJ
gi-4940	249	2	ε	ε	PROPN
gi-4940	249	3	,	,	PUNCT
gi-4940	249	4	ϕ6	ϕ6	PROPN
gi-4940	249	5	=	=	SYM
gi-4940	249	6	0	0	PROPN
gi-4940	249	7	,	,	PUNCT
gi-4940	249	8	ϕ7	ϕ7	X
gi-4940	250	1	=	=	PUNCT
gi-4940	250	2	π	π	PROPN
gi-4940	250	3	2	2	X
gi-4940	250	4	−	−	NOUN
gi-4940	250	5	ε	ε	PROPN
gi-4940	250	6	.	.	PUNCT
gi-4940	250	7	analogously	analogously	PROPN
gi-4940	250	8	,	,	PUNCT
gi-4940	250	9	the	the	DET
gi-4940	250	10	parallel	parallel	ADJ
gi-4940	250	11	plane	plane	NOUN
gi-4940	250	12	%	%	NOUN
gi-4940	250	13	2	2	NUM
gi-4940	250	14	containing	contain	VERB
gi-4940	250	15	p(ϕc	p(ϕc	NOUN
gi-4940	250	16	,	,	PUNCT
gi-4940	250	17	λ	λ	X
gi-4940	250	18	)	)	PUNCT
gi-4940	250	19	is	be	AUX
gi-4940	250	20	given	give	VERB
gi-4940	250	21	by	by	ADP
gi-4940	250	22	the	the	DET
gi-4940	250	23	points	point	NOUN
gi-4940	250	24	p8	p8	X
gi-4940	250	25	=	=	PUNCT
gi-4940	251	1	[	[	X
gi-4940	251	2	ϕc	ϕc	X
gi-4940	251	3	,	,	PUNCT
gi-4940	251	4	λ8	λ8	NOUN
gi-4940	251	5	]	]	PUNCT
gi-4940	251	6	,	,	PUNCT
gi-4940	251	7	p9	p9	PROPN
gi-4940	251	8	=	=	PUNCT
gi-4940	252	1	[	[	X
gi-4940	252	2	ϕc	ϕc	X
gi-4940	252	3	,	,	PUNCT
gi-4940	252	4	λ9	λ9	NOUN
gi-4940	252	5	]	]	PUNCT
gi-4940	252	6	,	,	PUNCT
gi-4940	252	7	and	and	CCONJ
gi-4940	252	8	p10	p10	NOUN
gi-4940	252	9	=	=	PUNCT
gi-4940	253	1	[	[	X
gi-4940	253	2	ϕc	ϕc	NOUN
gi-4940	253	3	,	,	PUNCT
gi-4940	253	4	λ10	λ10	PROPN
gi-4940	253	5	]	]	PUNCT
gi-4940	253	6	,	,	PUNCT
gi-4940	253	7	where	where	SCONJ
gi-4940	253	8	λ8	λ8	NOUN
gi-4940	253	9	=	=	SYM
gi-4940	253	10	−π	−π	PROPN
gi-4940	253	11	+	+	CCONJ
gi-4940	253	12	ε	ε	PROPN
gi-4940	253	13	,	,	PUNCT
gi-4940	253	14	λ9	λ9	ADJ
gi-4940	253	15	=	=	SYM
gi-4940	253	16	0	0	NUM
gi-4940	253	17	,	,	PUNCT
gi-4940	253	18	λ10	λ10	NOUN
gi-4940	253	19	=	=	SYM
gi-4940	253	20	π	π	PROPN
gi-4940	253	21	−	−	X
gi-4940	253	22	ε	ε	PROPN
gi-4940	253	23	,	,	PUNCT
gi-4940	253	24	and	and	CCONJ
gi-4940	253	25	the	the	DET
gi-4940	253	26	meridian	meridian	PROPN
gi-4940	253	27	plane	plane	NOUN
gi-4940	253	28	%	%	NOUN
gi-4940	253	29	3	3	NUM
gi-4940	253	30	containing	contain	VERB
gi-4940	253	31	m′(ϕ′	m′(ϕ′	ADV
gi-4940	253	32	,	,	PUNCT
gi-4940	253	33	λ′0	λ′0	PROPN
gi-4940	253	34	)	)	PUNCT
gi-4940	253	35	centered	center	VERB
gi-4940	253	36	at	at	ADP
gi-4940	253	37	λ′0	λ′0	PROPN
gi-4940	253	38	is	be	AUX
gi-4940	253	39	given	give	VERB
gi-4940	253	40	by	by	ADP
gi-4940	253	41	three	three	NUM
gi-4940	253	42	points	point	NOUN
gi-4940	253	43	p11	p11	NOUN
gi-4940	253	44	=	=	PUNCT
gi-4940	254	1	[	[	X
gi-4940	254	2	ϕ′11	ϕ′11	NOUN
gi-4940	254	3	,	,	PUNCT
gi-4940	254	4	λ	λ	NOUN
gi-4940	254	5	′	′	NOUN
gi-4940	254	6	0	0	NUM
gi-4940	254	7	]	]	PUNCT
gi-4940	254	8	,	,	PUNCT
gi-4940	254	9	p12	p12	ADJ
gi-4940	254	10	=	=	PUNCT
gi-4940	255	1	[	[	X
gi-4940	255	2	ϕ′12	ϕ′12	NOUN
gi-4940	255	3	,	,	PUNCT
gi-4940	255	4	λ	λ	NOUN
gi-4940	255	5	′	′	NOUN
gi-4940	255	6	0	0	NUM
gi-4940	255	7	]	]	PUNCT
gi-4940	255	8	,	,	PUNCT
gi-4940	255	9	and	and	CCONJ
gi-4940	255	10	p13	p13	NOUN
gi-4940	255	11	=	=	SYM
gi-4940	256	1	[	[	X
gi-4940	256	2	ϕ′13	ϕ′13	NOUN
gi-4940	256	3	,	,	PUNCT
gi-4940	256	4	λ	λ	INTJ
gi-4940	256	5	′	′	NOUN
gi-4940	256	6	0	0	NUM
gi-4940	256	7	]	]	PUNCT
gi-4940	256	8	,	,	PUNCT
gi-4940	256	9	where	where	SCONJ
gi-4940	256	10	ϕ′11	ϕ′11	NOUN
gi-4940	256	11	=	=	NOUN
gi-4940	257	1	−π	−π	ADP
gi-4940	257	2	2	2	NUM
gi-4940	257	3	+	+	CCONJ
gi-4940	257	4	ε	ε	PROPN
gi-4940	257	5	,	,	PUNCT
gi-4940	257	6	ϕ′12	ϕ′12	NOUN
gi-4940	257	7	=	=	SYM
gi-4940	257	8	0	0	NUM
gi-4940	257	9	,	,	PUNCT
gi-4940	257	10	ϕ′13	ϕ′13	NOUN
gi-4940	257	11	=	=	SYM
gi-4940	257	12	π	π	PROPN
gi-4940	257	13	2	2	X
gi-4940	257	14	−	−	NOUN
gi-4940	257	15	ε	ε	PROPN
gi-4940	257	16	.	.	PROPN
gi-4940	257	17	1	1	NUM
gi-4940	257	18	.	.	PUNCT
gi-4940	258	1	the	the	DET
gi-4940	258	2	inverse	inverse	NOUN
gi-4940	258	3	transformation	transformation	NOUN
gi-4940	258	4	initially	initially	ADV
gi-4940	258	5	,	,	PUNCT
gi-4940	258	6	the	the	DET
gi-4940	258	7	spherical	spherical	ADJ
gi-4940	258	8	coordinates	coordinate	NOUN
gi-4940	259	1	[	[	X
gi-4940	259	2	ϕ′i	ϕ′i	NOUN
gi-4940	259	3	,	,	PUNCT
gi-4940	259	4	λ′i	λ′i	X
gi-4940	259	5	]	]	PUNCT
gi-4940	259	6	of	of	ADP
gi-4940	259	7	points	point	NOUN
gi-4940	259	8	p11	p11	NOUN
gi-4940	259	9	,	,	PUNCT
gi-4940	259	10	p12	p12	VERB
gi-4940	259	11	,	,	PUNCT
gi-4940	259	12	p13	p13	NOUN
gi-4940	259	13	related	relate	VERB
gi-4940	259	14	to	to	ADP
gi-4940	259	15	the	the	DET
gi-4940	259	16	pole	pole	NOUN
gi-4940	259	17	k	k	PROPN
gi-4940	260	1	=	=	PUNCT
gi-4940	261	1	[	[	X
gi-4940	261	2	ϕk	ϕk	X
gi-4940	261	3	,	,	PUNCT
gi-4940	261	4	λk	λk	X
gi-4940	261	5	]	]	PUNCT
gi-4940	261	6	are	be	AUX
gi-4940	261	7	transformed	transform	VERB
gi-4940	261	8	to	to	ADP
gi-4940	261	9	the	the	DET
gi-4940	261	10	normal	normal	ADJ
gi-4940	261	11	aspect	aspect	NOUN
gi-4940	261	12	using	use	VERB
gi-4940	261	13	eqs	eqs	PROPN
gi-4940	261	14	.	.	PROPN
gi-4940	261	15	3.4	3.4	NUM
gi-4940	261	16	,	,	PUNCT
gi-4940	261	17	3.5	3.5	NUM
gi-4940	261	18	,	,	PUNCT
gi-4940	261	19	where	where	SCONJ
gi-4940	261	20	i	i	PRON
gi-4940	261	21	=	=	NOUN
gi-4940	261	22	11	11	NUM
gi-4940	261	23	,	,	PUNCT
gi-4940	261	24	12	12	NUM
gi-4940	261	25	,	,	PUNCT
gi-4940	261	26	13	13	NUM
gi-4940	261	27	.	.	NOUN
gi-4940	262	1	2	2	NUM
gi-4940	262	2	.	.	X
gi-4940	263	1	the	the	DET
gi-4940	263	2	transformation	transformation	NOUN
gi-4940	263	3	to	to	ADP
gi-4940	263	4	the	the	DET
gi-4940	263	5	geocentric	geocentric	ADJ
gi-4940	263	6	coordinates	coordinate	NOUN
gi-4940	263	7	the	the	DET
gi-4940	263	8	spherical	spherical	ADJ
gi-4940	263	9	coordinates	coordinate	NOUN
gi-4940	263	10	[	[	X
gi-4940	263	11	ϕi	ϕi	ADP
gi-4940	263	12	,	,	PUNCT
gi-4940	263	13	λi	λi	AUX
gi-4940	263	14	]	]	PUNCT
gi-4940	263	15	of	of	ADP
gi-4940	263	16	points	point	NOUN
gi-4940	263	17	p5	p5	ADJ
gi-4940	263	18	−	−	PROPN
gi-4940	263	19	p13	p13	NOUN
gi-4940	263	20	are	be	AUX
gi-4940	263	21	transformed	transform	VERB
gi-4940	263	22	to	to	ADP
gi-4940	263	23	the	the	DET
gi-4940	263	24	cartesian	cartesian	ADJ
gi-4940	263	25	geocentric	geocentric	ADJ
gi-4940	263	26	coordinates	coordinate	NOUN
gi-4940	263	27	xi	xi	PROPN
gi-4940	263	28	,	,	PUNCT
gi-4940	263	29	yi	yi	PROPN
gi-4940	263	30	,	,	PUNCT
gi-4940	263	31	zi	zi	NOUN
gi-4940	263	32	,	,	PUNCT
gi-4940	263	33	where	where	SCONJ
gi-4940	263	34	xi	xi	X
gi-4940	263	35	=	=	SYM
gi-4940	263	36	cosϕi	cosϕi	NOUN
gi-4940	263	37	cosλi	cosλi	NOUN
gi-4940	263	38	,	,	PUNCT
gi-4940	263	39	yi	yi	NOUN
gi-4940	263	40	=	=	SYM
gi-4940	263	41	cosϕi	cosϕi	NOUN
gi-4940	263	42	sinλi	sinλi	NOUN
gi-4940	263	43	,	,	PUNCT
gi-4940	263	44	zi	zi	NOUN
gi-4940	263	45	=	=	SYM
gi-4940	263	46	sinϕi	sinϕi	PROPN
gi-4940	263	47	,	,	PUNCT
gi-4940	263	48	i	i	PRON
gi-4940	263	49	=	=	NOUN
gi-4940	263	50	5	5	NUM
gi-4940	263	51	,	,	PUNCT
gi-4940	263	52	...	...	PUNCT
gi-4940	263	53	,	,	PUNCT
gi-4940	263	54	13	13	NUM
gi-4940	263	55	.	.	X
gi-4940	264	1	3	3	X
gi-4940	264	2	.	.	X
gi-4940	264	3	find	find	VERB
gi-4940	264	4	the	the	DET
gi-4940	264	5	analytic	analytic	ADJ
gi-4940	264	6	representation	representation	NOUN
gi-4940	264	7	of	of	ADP
gi-4940	264	8	planes	plane	NOUN
gi-4940	264	9	the	the	DET
gi-4940	264	10	meridian	meridian	PROPN
gi-4940	264	11	plane	plane	NOUN
gi-4940	264	12	of	of	ADP
gi-4940	264	13	m′(λ′0	m′(λ′0	NOUN
gi-4940	264	14	)	)	PUNCT
gi-4940	264	15	is	be	AUX
gi-4940	264	16	given	give	VERB
gi-4940	264	17	by	by	ADP
gi-4940	264	18	the	the	DET
gi-4940	264	19	vectors	vector	NOUN
gi-4940	264	20	u1	u1	NOUN
gi-4940	264	21	,	,	PUNCT
gi-4940	264	22	v1	v1	NOUN
gi-4940	264	23	,	,	PUNCT
gi-4940	264	24	where	where	SCONJ
gi-4940	264	25	u1	u1	NOUN
gi-4940	264	26	=	=	SYM
gi-4940	264	27	p12−p11	p12−p11	ADJ
gi-4940	264	28	,	,	PUNCT
gi-4940	264	29	v1	v1	NOUN
gi-4940	264	30	=	=	SYM
gi-4940	264	31	p13−p11	p13−p11	NOUN
gi-4940	264	32	.	.	PUNCT
gi-4940	265	1	the	the	DET
gi-4940	265	2	vectors	vector	NOUN
gi-4940	265	3	u2	u2	VERB
gi-4940	265	4	,	,	PUNCT
gi-4940	265	5	v2	v2	PROPN
gi-4940	265	6	of	of	ADP
gi-4940	265	7	the	the	DET
gi-4940	265	8	second	second	ADJ
gi-4940	265	9	meridian	meridian	PROPN
gi-4940	265	10	plane	plane	NOUN
gi-4940	265	11	m(λc	m(λc	NOUN
gi-4940	265	12	)	)	PUNCT
gi-4940	265	13	are	be	AUX
gi-4940	265	14	u2	u2	NOUN
gi-4940	265	15	=	=	PUNCT
gi-4940	265	16	p6−p5	p6−p5	NOUN
gi-4940	265	17	,	,	PUNCT
gi-4940	265	18	v2	v2	PROPN
gi-4940	265	19	=	=	SYM
gi-4940	265	20	p7−p5	p7−p5	NOUN
gi-4940	265	21	,	,	PUNCT
gi-4940	265	22	and	and	CCONJ
gi-4940	265	23	the	the	DET
gi-4940	265	24	vectors	vector	NOUN
gi-4940	265	25	u3	u3	PROPN
gi-4940	265	26	,	,	PUNCT
gi-4940	265	27	v3	v3	PROPN
gi-4940	265	28	of	of	ADP
gi-4940	265	29	the	the	DET
gi-4940	265	30	parallel	parallel	ADJ
gi-4940	265	31	plane	plane	NOUN
gi-4940	265	32	p(ϕc	p(ϕc	NOUN
gi-4940	265	33	)	)	PUNCT
gi-4940	265	34	are	be	AUX
gi-4940	265	35	u3	u3	NOUN
gi-4940	265	36	=	=	SYM
gi-4940	265	37	p9−p8	p9−p8	NOUN
gi-4940	265	38	,	,	PUNCT
gi-4940	265	39	v3	v3	PROPN
gi-4940	265	40	=	=	PUNCT
gi-4940	265	41	p10−p8	p10−p8	PROPN
gi-4940	265	42	.	.	PUNCT
gi-4940	266	1	find	find	VERB
gi-4940	266	2	the	the	DET
gi-4940	266	3	vectors	vector	NOUN
gi-4940	266	4	n1	n1	NOUN
gi-4940	266	5	,	,	PUNCT
gi-4940	266	6	n2	n2	NOUN
gi-4940	266	7	,	,	PUNCT
gi-4940	266	8	n3	n3	ADJ
gi-4940	266	9	perpendicular	perpendicular	NOUN
gi-4940	266	10	to	to	PART
gi-4940	266	11	u1	u1	VERB
gi-4940	266	12	,	,	PUNCT
gi-4940	266	13	v1	v1	NOUN
gi-4940	266	14	,	,	PUNCT
gi-4940	266	15	u2	u2	NOUN
gi-4940	266	16	,	,	PUNCT
gi-4940	266	17	v2	v2	NOUN
gi-4940	266	18	,	,	PUNCT
gi-4940	266	19	and	and	CCONJ
gi-4940	266	20	u3	u3	PROPN
gi-4940	266	21	,	,	PUNCT
gi-4940	266	22	v3	v3	PROPN
gi-4940	266	23	using	use	VERB
gi-4940	266	24	the	the	DET
gi-4940	266	25	cross	cross	NOUN
gi-4940	266	26	products	product	NOUN
gi-4940	266	27	n1	n1	NOUN
gi-4940	266	28	=	=	SYM
gi-4940	266	29	u1	u1	PROPN
gi-4940	266	30	×	×	PROPN
gi-4940	266	31	v1	v1	NOUN
gi-4940	266	32	,	,	PUNCT
gi-4940	266	33	n2	n2	NOUN
gi-4940	266	34	=	=	PROPN
gi-4940	266	35	u2	u2	PROPN
gi-4940	266	36	×	×	PROPN
gi-4940	266	37	v2	v2	PROPN
gi-4940	266	38	,	,	PUNCT
gi-4940	266	39	n3	n3	NOUN
gi-4940	266	40	=	=	PUNCT
gi-4940	266	41	u3	u3	PROPN
gi-4940	266	42	×	×	PROPN
gi-4940	266	43	v3	v3	PROPN
gi-4940	266	44	.	.	PUNCT
gi-4940	267	1	4	4	X
gi-4940	267	2	.	.	X
gi-4940	267	3	compute	compute	VERB
gi-4940	267	4	the	the	DET
gi-4940	267	5	line	line	NOUN
gi-4940	267	6	of	of	ADP
gi-4940	267	7	intersection	intersection	NOUN
gi-4940	267	8	for	for	ADP
gi-4940	267	9	the	the	DET
gi-4940	267	10	meridian	meridian	PROPN
gi-4940	267	11	planes	plane	NOUN
gi-4940	267	12	m′(λ′0	m′(λ′0	PROPN
gi-4940	267	13	)	)	PUNCT
gi-4940	267	14	,	,	PUNCT
gi-4940	267	15	and	and	CCONJ
gi-4940	267	16	m(λc	m(λc	NOUN
gi-4940	267	17	)	)	PUNCT
gi-4940	267	18	,	,	PUNCT
gi-4940	267	19	set	set	VERB
gi-4940	267	20	:	:	PUNCT
gi-4940	267	21	q1	q1	PROPN
gi-4940	267	22	≡	≡	PROPN
gi-4940	267	23	p11	p11	NOUN
gi-4940	267	24	,	,	PUNCT
gi-4940	267	25	q2	q2	PROPN
gi-4940	267	26	≡	≡	PROPN
gi-4940	267	27	p5	p5	PROPN
gi-4940	267	28	;	;	PUNCT
gi-4940	267	29	for	for	ADP
gi-4940	267	30	the	the	DET
gi-4940	267	31	meridian	meridian	PROPN
gi-4940	267	32	m′(λ′0	m′(λ′0	PROPN
gi-4940	267	33	)	)	PUNCT
gi-4940	267	34	and	and	CCONJ
gi-4940	267	35	parallel	parallel	ADJ
gi-4940	267	36	p(ϕc	p(ϕc	NOUN
gi-4940	267	37	)	)	PUNCT
gi-4940	267	38	planes	plane	NOUN
gi-4940	267	39	,	,	PUNCT
gi-4940	267	40	set	set	VERB
gi-4940	267	41	:	:	PUNCT
gi-4940	267	42	q1	q1	PROPN
gi-4940	267	43	≡	≡	PROPN
gi-4940	267	44	p11	p11	NOUN
gi-4940	267	45	,	,	PUNCT
gi-4940	267	46	q2	q2	PROPN
gi-4940	267	47	≡	≡	PROPN
gi-4940	267	48	p8	p8	PROPN
gi-4940	267	49	,	,	PUNCT
gi-4940	267	50	compute	compute	NOUN
gi-4940	267	51	q0	q0	NOUN
gi-4940	267	52	=	=	PUNCT
gi-4940	267	53	(	(	PUNCT
gi-4940	267	54	p11	p11	NOUN
gi-4940	267	55	+	+	CCONJ
gi-4940	267	56	p12	p12	ADJ
gi-4940	267	57	+	+	CCONJ
gi-4940	267	58	p13)/3	p13)/3	NOUN
gi-4940	267	59	.	.	PUNCT
gi-4940	268	1	evaluate	evaluate	VERB
gi-4940	268	2	the	the	DET
gi-4940	268	3	line	line	NOUN
gi-4940	268	4	of	of	ADP
gi-4940	268	5	intersection	intersection	NOUN
gi-4940	268	6	,	,	PUNCT
gi-4940	268	7	compute	compute	VERB
gi-4940	268	8	the	the	DET
gi-4940	268	9	cross	cross	NOUN
gi-4940	268	10	products	product	NOUN
gi-4940	268	11	n1,2	n1,2	PROPN
gi-4940	268	12	=	=	SYM
gi-4940	268	13	n1	n1	PROPN
gi-4940	268	14	×	×	PROPN
gi-4940	268	15	n2	n2	NOUN
gi-4940	268	16	,	,	PUNCT
gi-4940	268	17	n1,3	n1,3	PROPN
gi-4940	268	18	=	=	SYM
gi-4940	268	19	n1×n3	n1×n3	PROPN
gi-4940	268	20	,	,	PUNCT
gi-4940	268	21	where	where	SCONJ
gi-4940	268	22	the	the	DET
gi-4940	268	23	direction	direction	NOUN
gi-4940	268	24	n	n	PROPN
gi-4940	268	25	of	of	ADP
gi-4940	268	26	both	both	DET
gi-4940	268	27	lines	line	NOUN
gi-4940	268	28	of	of	ADP
gi-4940	268	29	intersection	intersection	NOUN
gi-4940	268	30	is	be	AUX
gi-4940	268	31	n	n	PRON
gi-4940	268	32	≡	≡	PROPN
gi-4940	268	33	n1,2	n1,2	PROPN
gi-4940	268	34	,	,	PUNCT
gi-4940	268	35	or	or	CCONJ
gi-4940	268	36	n	n	PRON
gi-4940	268	37	≡	≡	PROPN
gi-4940	268	38	n1,3	n1,3	PROPN
gi-4940	268	39	.	.	PROPN
gi-4940	269	1	5	5	NUM
gi-4940	269	2	.	.	X
gi-4940	269	3	intersection	intersection	NOUN
gi-4940	269	4	of	of	ADP
gi-4940	269	5	the	the	DET
gi-4940	269	6	line	line	NOUN
gi-4940	269	7	and	and	CCONJ
gi-4940	269	8	sphere	sphere	NOUN
gi-4940	269	9	let	let	VERB
gi-4940	269	10	s2	s2	PROPN
gi-4940	269	11	be	be	AUX
gi-4940	269	12	the	the	DET
gi-4940	269	13	sphere	sphere	NOUN
gi-4940	269	14	of	of	ADP
gi-4940	269	15	the	the	DET
gi-4940	269	16	radius	radius	NOUN
gi-4940	269	17	r	r	NOUN
gi-4940	269	18	=	=	SYM
gi-4940	269	19	1	1	NUM
gi-4940	269	20	centered	center	VERB
gi-4940	269	21	at	at	ADP
gi-4940	269	22	c	c	NOUN
gi-4940	269	23	=	=	PUNCT
gi-4940	270	1	[	[	X
gi-4940	270	2	0	0	NUM
gi-4940	270	3	,	,	PUNCT
gi-4940	270	4	0	0	NUM
gi-4940	270	5	,	,	PUNCT
gi-4940	270	6	0	0	NUM
gi-4940	270	7	]	]	PUNCT
gi-4940	270	8	.	.	PUNCT
gi-4940	271	1	depending	depend	VERB
gi-4940	271	2	on	on	ADP
gi-4940	271	3	the	the	DET
gi-4940	271	4	sign	sign	NOUN
gi-4940	271	5	of	of	ADP
gi-4940	271	6	the	the	DET
gi-4940	271	7	discriminantd	discriminantd	NOUN
gi-4940	271	8	,	,	PUNCT
gi-4940	271	9	evaluate	evaluate	VERB
gi-4940	271	10	the	the	DET
gi-4940	271	11	intersectionsm1	intersectionsm1	NOUN
gi-4940	271	12	=	=	PUNCT
gi-4940	272	1	[	[	X
gi-4940	272	2	x1	x1	PROPN
gi-4940	272	3	,	,	PUNCT
gi-4940	272	4	y1	y1	PROPN
gi-4940	272	5	,	,	PUNCT
gi-4940	272	6	z1],m2	z1],m2	PROPN
gi-4940	272	7	=	=	PUNCT
gi-4940	273	1	[	[	X
gi-4940	273	2	x2	x2	PROPN
gi-4940	273	3	,	,	PUNCT
gi-4940	273	4	y2	y2	PROPN
gi-4940	273	5	,	,	PUNCT
gi-4940	273	6	z2	z2	PROPN
gi-4940	273	7	]	]	PUNCT
gi-4940	273	8	of	of	ADP
gi-4940	273	9	the	the	DET
gi-4940	273	10	geoinformatics	geoinformatic	NOUN
gi-4940	273	11	fce	fce	VERB
gi-4940	273	12	ctu	ctu	NOUN
gi-4940	273	13	17(2	17(2	NUM
gi-4940	273	14	)	)	PUNCT
gi-4940	273	15	,	,	PUNCT
gi-4940	273	16	2018	2018	NUM
gi-4940	273	17	39	39	NUM
gi-4940	273	18	t.	t.	NOUN
gi-4940	273	19	bayer	bayer	NOUN
gi-4940	273	20	:	:	PUNCT
gi-4940	273	21	plotting	plot	VERB
gi-4940	273	22	the	the	DET
gi-4940	273	23	map	map	NOUN
gi-4940	273	24	projection	projection	NOUN
gi-4940	273	25	graticule	graticule	NOUN
gi-4940	273	26	with	with	ADP
gi-4940	273	27	discontinuities	discontinuity	NOUN
gi-4940	273	28	-18	-18	PUNCT
gi-4940	273	29	0.0	0.0	NUM
gi-4940	273	30	-15	-15	SYM
gi-4940	273	31	0.0	0.0	NUM
gi-4940	273	32	-12	-12	NUM
gi-4940	273	33	0.0	0.0	NUM
gi-4940	273	34	-90	-90	NUM
gi-4940	273	35	.0	.0	NUM
gi-4940	273	36	-60	-60	SYM
gi-4940	274	1	.0	.0	NUM
gi-4940	275	1	-30.0	-30.0	NOUN
gi-4940	275	2	0.030.0	0.030.0	NUM
gi-4940	275	3	60.0	60.0	NUM
gi-4940	275	4	90	90	NUM
gi-4940	275	5	.0	.0	NUM
gi-4940	275	6	12	12	NUM
gi-4940	275	7	0.0	0.0	NUM
gi-4940	275	8	15	15	NUM
gi-4940	275	9	0.0	0.0	NUM
gi-4940	275	10	18	18	NUM
gi-4940	275	11	0.0	0.0	NUM
gi-4940	275	12	15.015.0	15.015.0	NUM
gi-4940	275	13	-16	-16	PROPN
gi-4940	275	14	5.0	5.0	NUM
gi-4940	275	15	-16	-16	SYM
gi-4940	275	16	5.0	5.0	NUM
gi-4940	275	17	-90.0	-90.0	NOUN
gi-4940	275	18	-90.0	-90.0	NOUN
gi-4940	275	19	-	-	PUNCT
gi-4940	275	20	90.0	90.0	NUM
gi-4940	275	21	-75.0	-75.0	NOUN
gi-4940	275	22	-75.0	-75.0	NOUN
gi-4940	276	1	-75.0	-75.0	NOUN
gi-4940	277	1	-60.0	-60.0	NOUN
gi-4940	277	2	-60.0	-60.0	INTJ
gi-4940	278	1	-60.0	-60.0	NOUN
gi-4940	278	2	-45.0	-45.0	NUM
gi-4940	278	3	-45.0	-45.0	NUM
gi-4940	278	4	-45.0	-45.0	PROPN
gi-4940	278	5	-30.0	-30.0	PROPN
gi-4940	278	6	-30.0	-30.0	NOUN
gi-4940	278	7	-30.0	-30.0	PROPN
gi-4940	278	8	-15.0	-15.0	PRON
gi-4940	278	9	-15	-15	NUM
gi-4940	278	10	.0	.0	NUM
gi-4940	278	11	-15.0	-15.0	PUNCT
gi-4940	278	12	0.0	0.0	NUM
gi-4940	278	13	0.0	0.0	NUM
gi-4940	278	14	0.0	0.0	NUM
gi-4940	278	15	15.0	15.0	NUM
gi-4940	278	16	15	15	NUM
gi-4940	278	17	.0	.0	NUM
gi-4940	278	18	15.0	15.0	NUM
gi-4940	278	19	30.0	30.0	NUM
gi-4940	278	20	30	30	NUM
gi-4940	278	21	.0	.0	NUM
gi-4940	278	22	30.0	30.0	NUM
gi-4940	278	23	45.0	45.0	NUM
gi-4940	278	24	45	45	NUM
gi-4940	278	25	.0	.0	NUM
gi-4940	278	26	45.0	45.0	NUM
gi-4940	278	27	60.0	60.0	NUM
gi-4940	278	28	60	60	NUM
gi-4940	278	29	.0	.0	NUM
gi-4940	278	30	60.0	60.0	NUM
gi-4940	278	31	75.0	75.0	NUM
gi-4940	278	32	75	75	NUM
gi-4940	278	33	.0	.0	NUM
gi-4940	278	34	75.0	75.0	NUM
gi-4940	278	35	90.090	90.090	NUM
gi-4940	278	36	.0	.0	NUM
gi-4940	278	37	90.0	90.0	NUM
gi-4940	278	38	-18	-18	SYM
gi-4940	278	39	0.0	0.0	NUM
gi-4940	278	40	-15	-15	NUM
gi-4940	278	41	0.0	0.0	NUM
gi-4940	278	42	-12	-12	NUM
gi-4940	278	43	0.0	0.0	NUM
gi-4940	278	44	-90	-90	NUM
gi-4940	278	45	.0	.0	NUM
gi-4940	278	46	-60	-60	SYM
gi-4940	279	1	.0	.0	NUM
gi-4940	280	1	-30.0	-30.0	NOUN
gi-4940	280	2	0.030.0	0.030.0	NUM
gi-4940	280	3	60.0	60.0	NUM
gi-4940	280	4	90	90	NUM
gi-4940	280	5	.0	.0	NUM
gi-4940	280	6	12	12	NUM
gi-4940	280	7	0.0	0.0	NUM
gi-4940	280	8	15	15	NUM
gi-4940	280	9	0.0	0.0	NUM
gi-4940	280	10	18	18	NUM
gi-4940	280	11	0.0	0.0	NUM
gi-4940	280	12	15.015.0	15.015.0	NUM
gi-4940	280	13	-16	-16	PROPN
gi-4940	280	14	5.0	5.0	NUM
gi-4940	280	15	-16	-16	NUM
gi-4940	280	16	5.0	5.0	NUM
gi-4940	280	17	-90.0	-90.0	NOUN
gi-4940	281	1	-75.0	-75.0	NOUN
gi-4940	282	1	-60.0	-60.0	NOUN
gi-4940	283	1	-45.0	-45.0	NUM
gi-4940	283	2	-30	-30	SYM
gi-4940	283	3	.0	.0	NUM
gi-4940	283	4	-15	-15	SYM
gi-4940	284	1	.0	.0	NUM
gi-4940	284	2	0.0	0.0	NUM
gi-4940	284	3	15.0	15.0	NUM
gi-4940	284	4	30.0	30.0	NUM
gi-4940	284	5	45.0	45.0	NUM
gi-4940	284	6	60.0	60.0	NUM
gi-4940	284	7	75.0	75.0	NUM
gi-4940	284	8	90.0	90.0	NUM
gi-4940	284	9	a	a	DET
gi-4940	284	10	)	)	PUNCT
gi-4940	284	11	b	b	NOUN
gi-4940	284	12	)	)	PUNCT
gi-4940	284	13	figure	figure	NOUN
gi-4940	284	14	4.1	4.1	NUM
gi-4940	284	15	:	:	PUNCT
gi-4940	284	16	the	the	DET
gi-4940	284	17	hassler	hassler	PROPN
gi-4940	284	18	projection	projection	NOUN
gi-4940	284	19	in	in	ADP
gi-4940	284	20	the	the	DET
gi-4940	284	21	oblique	oblique	ADJ
gi-4940	284	22	aspect	aspect	NOUN
gi-4940	284	23	,	,	PUNCT
gi-4940	284	24	k	k	X
gi-4940	284	25	=	=	PUNCT
gi-4940	285	1	[	[	X
gi-4940	285	2	50	50	NUM
gi-4940	285	3	◦	◦	NOUN
gi-4940	285	4	,	,	PUNCT
gi-4940	285	5	15	15	NUM
gi-4940	285	6	◦	◦	NOUN
gi-4940	285	7	]	]	PUNCT
gi-4940	285	8	;	;	PUNCT
gi-4940	285	9	the	the	DET
gi-4940	285	10	singularities	singularity	NOUN
gi-4940	285	11	involved	involve	VERB
gi-4940	285	12	a	a	PRON
gi-4940	285	13	)	)	PUNCT
gi-4940	285	14	and	and	CCONJ
gi-4940	285	15	treated	treat	VERB
gi-4940	285	16	b	b	NUM
gi-4940	285	17	)	)	PUNCT
gi-4940	285	18	.	.	PUNCT
gi-4940	286	1	planes	plane	NOUN
gi-4940	286	2	%	%	NOUN
gi-4940	286	3	2	2	NUM
gi-4940	287	1	and	and	CCONJ
gi-4940	287	2	%	%	NOUN
gi-4940	287	3	3	3	X
gi-4940	287	4	.	.	PUNCT
gi-4940	288	1	the	the	DET
gi-4940	288	2	planes	plane	NOUN
gi-4940	288	3	%	%	NOUN
gi-4940	288	4	1	1	NUM
gi-4940	288	5	,	,	PUNCT
gi-4940	288	6	%	%	INTJ
gi-4940	288	7	3	3	NUM
gi-4940	288	8	have	have	VERB
gi-4940	288	9	two	two	NUM
gi-4940	288	10	intersections	intersection	NOUN
gi-4940	288	11	denoted	denote	VERB
gi-4940	288	12	as	as	ADP
gi-4940	288	13	m3	m3	PROPN
gi-4940	288	14	=	=	PUNCT
gi-4940	289	1	[	[	X
gi-4940	289	2	x3	x3	ADJ
gi-4940	289	3	,	,	PUNCT
gi-4940	289	4	y3	y3	NOUN
gi-4940	289	5	,	,	PUNCT
gi-4940	289	6	z3	z3	PROPN
gi-4940	289	7	]	]	PUNCT
gi-4940	289	8	and	and	CCONJ
gi-4940	289	9	m4	m4	PROPN
gi-4940	289	10	=	=	PUNCT
gi-4940	290	1	[	[	X
gi-4940	290	2	x4	x4	PROPN
gi-4940	290	3	,	,	PUNCT
gi-4940	290	4	y4	y4	PROPN
gi-4940	290	5	,	,	PUNCT
gi-4940	290	6	z4	z4	PROPN
gi-4940	290	7	]	]	PUNCT
gi-4940	290	8	.	.	PUNCT
gi-4940	291	1	6	6	NUM
gi-4940	291	2	.	.	X
gi-4940	291	3	transformation	transformation	NOUN
gi-4940	291	4	to	to	ADP
gi-4940	291	5	spherical	spherical	ADJ
gi-4940	291	6	coordinates	coordinate	NOUN
gi-4940	291	7	finally	finally	ADV
gi-4940	291	8	,	,	PUNCT
gi-4940	291	9	the	the	DET
gi-4940	291	10	cartesian	cartesian	ADJ
gi-4940	291	11	coordinates	coordinate	NOUN
gi-4940	291	12	of	of	ADP
gi-4940	291	13	the	the	DET
gi-4940	291	14	intersections	intersection	NOUN
gi-4940	291	15	m1	m1	NOUN
gi-4940	291	16	,	,	PUNCT
gi-4940	291	17	m2	m2	PROPN
gi-4940	291	18	,	,	PUNCT
gi-4940	291	19	m3	m3	PROPN
gi-4940	291	20	will	will	AUX
gi-4940	291	21	be	be	AUX
gi-4940	291	22	converted	convert	VERB
gi-4940	291	23	to	to	ADP
gi-4940	291	24	the	the	DET
gi-4940	291	25	spherical	spherical	NOUN
gi-4940	291	26	.	.	PUNCT
gi-4940	292	1	4	4	X
gi-4940	292	2	.	.	X
gi-4940	292	3	graticule	graticule	NOUN
gi-4940	292	4	reconstruction	reconstruction	NOUN
gi-4940	292	5	using	use	VERB
gi-4940	292	6	the	the	DET
gi-4940	292	7	combined	combine	VERB
gi-4940	292	8	sampling	sampling	NOUN
gi-4940	292	9	let	let	VERB
gi-4940	292	10	ω	ω	NOUN
gi-4940	292	11	=	=	PRON
gi-4940	292	12	ωϕ	ωϕ	PRON
gi-4940	292	13	×	×	NOUN
gi-4940	292	14	ωλ	ωλ	VERB
gi-4940	292	15	,	,	PUNCT
gi-4940	292	16	where	where	SCONJ
gi-4940	292	17	ωϕ	ωϕ	ADV
gi-4940	292	18	=	=	PUNCT
gi-4940	293	1	[	[	X
gi-4940	293	2	ϕ,ϕ	ϕ,ϕ	ADP
gi-4940	293	3	]	]	X
gi-4940	293	4	,	,	PUNCT
gi-4940	293	5	and	and	CCONJ
gi-4940	293	6	ωλ	ωλ	VERB
gi-4940	293	7	=	=	PUNCT
gi-4940	293	8	[	[	X
gi-4940	293	9	λ	λ	X
gi-4940	293	10	,	,	PUNCT
gi-4940	293	11	λ	λ	PROPN
gi-4940	293	12	]	]	PUNCT
gi-4940	293	13	,	,	PUNCT
gi-4940	293	14	be	be	AUX
gi-4940	293	15	the	the	DET
gi-4940	293	16	subdomain	subdomain	NOUN
gi-4940	293	17	,	,	PUNCT
gi-4940	293	18	inside	inside	ADP
gi-4940	293	19	which	which	PRON
gi-4940	293	20	the	the	DET
gi-4940	293	21	polygonal	polygonal	ADJ
gi-4940	293	22	approximation	approximation	NOUN
gi-4940	293	23	of	of	ADP
gi-4940	293	24	the	the	DET
gi-4940	293	25	meridians	meridian	NOUN
gi-4940	293	26	/	/	SYM
gi-4940	293	27	parallels	parallel	NOUN
gi-4940	293	28	is	be	AUX
gi-4940	293	29	constructed	construct	VERB
gi-4940	293	30	.	.	PUNCT
gi-4940	294	1	the	the	DET
gi-4940	294	2	points	point	NOUN
gi-4940	294	3	pi	pi	NOUN
gi-4940	294	4	=	=	PUNCT
gi-4940	294	5	(	(	PUNCT
gi-4940	294	6	f	f	X
gi-4940	294	7	(	(	PUNCT
gi-4940	294	8	ϕi	ϕi	PROPN
gi-4940	294	9	,	,	PUNCT
gi-4940	294	10	λc	λc	NOUN
gi-4940	294	11	)	)	PUNCT
gi-4940	294	12	,	,	PUNCT
gi-4940	294	13	g(ϕi	g(ϕi	NOUN
gi-4940	294	14	,	,	PUNCT
gi-4940	294	15	λc	λc	NOUN
gi-4940	294	16	)	)	PUNCT
gi-4940	294	17	)	)	PUNCT
gi-4940	294	18	,	,	PUNCT
gi-4940	294	19	1	1	NUM
gi-4940	294	20	≤	≤	NUM
gi-4940	294	21	i	i	PRON
gi-4940	294	22	≤	≤	PROPN
gi-4940	294	23	nϕ	nϕ	VERB
gi-4940	294	24	,	,	PUNCT
gi-4940	294	25	ϕi	ϕi	ADP
gi-4940	294	26	∈	∈	PROPN
gi-4940	294	27	ωϕ	ωϕ	PRON
gi-4940	294	28	approximate	approximate	VERB
gi-4940	294	29	the	the	DET
gi-4940	294	30	meridian	meridian	PROPN
gi-4940	294	31	m(λc	m(λc	PROPN
gi-4940	294	32	)	)	PUNCT
gi-4940	294	33	,	,	PUNCT
gi-4940	294	34	and	and	CCONJ
gi-4940	294	35	analogously	analogously	ADV
gi-4940	294	36	for	for	ADP
gi-4940	294	37	the	the	DET
gi-4940	294	38	parallel	parallel	NOUN
gi-4940	294	39	.	.	PUNCT
gi-4940	295	1	the	the	DET
gi-4940	295	2	combined	combined	ADJ
gi-4940	295	3	sampling	sample	VERB
gi-4940	295	4	procedure	procedure	NOUN
gi-4940	295	5	represents	represent	VERB
gi-4940	295	6	a	a	DET
gi-4940	295	7	generalization	generalization	NOUN
gi-4940	295	8	of	of	ADP
gi-4940	295	9	the	the	DET
gi-4940	295	10	curve	curve	NOUN
gi-4940	295	11	sampling	sample	VERB
gi-4940	295	12	procedure	procedure	NOUN
gi-4940	295	13	discussed	discuss	VERB
gi-4940	295	14	in	in	ADP
gi-4940	295	15	[	[	X
gi-4940	295	16	5	5	NUM
gi-4940	295	17	]	]	PUNCT
gi-4940	295	18	.	.	PUNCT
gi-4940	296	1	it	it	PRON
gi-4940	296	2	starts	start	VERB
gi-4940	296	3	with	with	ADP
gi-4940	296	4	the	the	DET
gi-4940	296	5	uniform	uniform	ADJ
gi-4940	296	6	sampling	sample	VERB
gi-4940	296	7	procedure	procedure	NOUN
gi-4940	296	8	,	,	PUNCT
gi-4940	296	9	which	which	PRON
gi-4940	296	10	after	after	SCONJ
gi-4940	296	11	d	d	NOUN
gi-4940	296	12	steps	step	NOUN
gi-4940	296	13	transforms	transform	VERB
gi-4940	296	14	to	to	ADP
gi-4940	296	15	adaptive	adaptive	ADJ
gi-4940	296	16	sampling	sampling	NOUN
gi-4940	296	17	.	.	PUNCT
gi-4940	297	1	a	a	DET
gi-4940	297	2	refinement	refinement	NOUN
gi-4940	297	3	criterion	criterion	NOUN
gi-4940	297	4	is	be	AUX
gi-4940	297	5	based	base	VERB
gi-4940	297	6	on	on	ADP
gi-4940	297	7	the	the	DET
gi-4940	297	8	angular	angular	ADJ
gi-4940	297	9	difference	difference	NOUN
gi-4940	297	10	αi	αi	NOUN
gi-4940	297	11	of	of	ADP
gi-4940	297	12	segments	segment	NOUN
gi-4940	297	13	formed	form	VERB
gi-4940	297	14	by	by	ADP
gi-4940	297	15	three	three	NUM
gi-4940	297	16	adjacent	adjacent	ADJ
gi-4940	297	17	points	point	NOUN
gi-4940	297	18	(	(	PUNCT
gi-4940	297	19	pi−1	pi−1	NOUN
gi-4940	297	20	,	,	PUNCT
gi-4940	297	21	pi	pi	NOUN
gi-4940	297	22	,	,	PUNCT
gi-4940	297	23	pi+1	pi+1	NOUN
gi-4940	297	24	)	)	PUNCT
gi-4940	297	25	.	.	PUNCT
gi-4940	298	1	4.1	4.1	NUM
gi-4940	298	2	.	.	PUNCT
gi-4940	299	1	graticule	graticule	NOUN
gi-4940	299	2	construction	construction	NOUN
gi-4940	299	3	with	with	ADP
gi-4940	299	4	singularities	singularity	NOUN
gi-4940	299	5	the	the	DET
gi-4940	299	6	proposed	propose	VERB
gi-4940	299	7	algorithm	algorithm	NOUN
gi-4940	299	8	based	base	VERB
gi-4940	299	9	on	on	ADP
gi-4940	299	10	the	the	DET
gi-4940	299	11	stack	stack	NOUN
gi-4940	299	12	s	s	PART
gi-4940	299	13	implementation	implementation	NOUN
gi-4940	299	14	is	be	AUX
gi-4940	299	15	described	describe	VERB
gi-4940	299	16	in	in	ADP
gi-4940	299	17	alg	alg	PROPN
gi-4940	299	18	.	.	PROPN
gi-4940	300	1	1	1	NUM
gi-4940	300	2	.	.	PUNCT
gi-4940	300	3	the	the	DET
gi-4940	300	4	basic	basic	ADJ
gi-4940	300	5	idea	idea	NOUN
gi-4940	300	6	is	be	AUX
gi-4940	300	7	to	to	PART
gi-4940	300	8	find	find	VERB
gi-4940	300	9	a	a	DET
gi-4940	300	10	set	set	NOUN
gi-4940	300	11	of	of	ADP
gi-4940	300	12	disjoint	disjoint	NOUN
gi-4940	300	13	subsets	subset	NOUN
gi-4940	300	14	ωg	ωg	ADP
gi-4940	300	15	ϕ	ϕ	PROPN
gi-4940	300	16	,	,	PUNCT
gi-4940	300	17	ω	ω	PROPN
gi-4940	300	18	g	g	NOUN
gi-4940	300	19	ϕ	ϕ	NOUN
gi-4940	300	20	⊆	⊆	NUM
gi-4940	300	21	ωϕ	ωϕ	NOUN
gi-4940	300	22	,	,	PUNCT
gi-4940	300	23	and	and	CCONJ
gi-4940	300	24	ω	ω	NUM
gi-4940	300	25	g	g	PROPN
gi-4940	300	26	λ	λ	PROPN
gi-4940	300	27	,	,	PUNCT
gi-4940	300	28	ω	ω	PROPN
gi-4940	300	29	g	g	NOUN
gi-4940	300	30	λ	λ	PROPN
gi-4940	300	31	⊆	⊆	NUM
gi-4940	300	32	ωλ	ωλ	ADJ
gi-4940	300	33	,	,	PUNCT
gi-4940	300	34	where	where	SCONJ
gi-4940	300	35	ωg	ωg	ADP
gi-4940	300	36	=	=	PROPN
gi-4940	300	37	ωg	ωg	PROPN
gi-4940	300	38	ϕ×ω	ϕ×ω	PROPN
gi-4940	300	39	g	g	PROPN
gi-4940	300	40	λ	λ	PROPN
gi-4940	300	41	,	,	PUNCT
gi-4940	300	42	containing	contain	VERB
gi-4940	300	43	“	"	PUNCT
gi-4940	300	44	good	good	ADJ
gi-4940	300	45	”	"	PUNCT
gi-4940	300	46	data	datum	NOUN
gi-4940	300	47	without	without	ADP
gi-4940	300	48	singularities	singularity	NOUN
gi-4940	300	49	that	that	PRON
gi-4940	300	50	allow	allow	VERB
gi-4940	300	51	for	for	ADP
gi-4940	300	52	adaptive	adaptive	ADJ
gi-4940	300	53	sampling	sampling	NOUN
gi-4940	300	54	.	.	PUNCT
gi-4940	301	1	over	over	ADP
gi-4940	301	2	each	each	DET
gi-4940	301	3	ωg	ωg	PROPN
gi-4940	301	4	j	j	PROPN
gi-4940	301	5	,	,	PUNCT
gi-4940	301	6	the	the	DET
gi-4940	301	7	borders	border	NOUN
gi-4940	301	8	of	of	ADP
gi-4940	301	9	which	which	PRON
gi-4940	301	10	run	run	VERB
gi-4940	301	11	along	along	ADP
gi-4940	301	12	discontinuities	discontinuity	NOUN
gi-4940	301	13	the	the	DET
gi-4940	301	14	graticule	graticule	NOUN
gi-4940	301	15	fragment	fragment	NOUN
gi-4940	301	16	is	be	AUX
gi-4940	301	17	constructed	construct	VERB
gi-4940	301	18	.	.	PUNCT
gi-4940	302	1	the	the	DET
gi-4940	302	2	entire	entire	ADJ
gi-4940	302	3	graticule	graticule	NOUN
gi-4940	302	4	is	be	AUX
gi-4940	302	5	put	put	VERB
gi-4940	302	6	together	together	ADV
gi-4940	302	7	from	from	ADP
gi-4940	302	8	these	these	DET
gi-4940	302	9	fragments	fragment	NOUN
gi-4940	302	10	.	.	PUNCT
gi-4940	303	1	the	the	DET
gi-4940	303	2	point	point	NOUN
gi-4940	303	3	qi	qi	NOUN
gi-4940	304	1	=	=	PUNCT
gi-4940	304	2	[	[	X
gi-4940	304	3	ϕi	ϕi	ADP
gi-4940	304	4	,	,	PUNCT
gi-4940	304	5	λi	λi	AUX
gi-4940	304	6	]	]	X
gi-4940	304	7	is	be	AUX
gi-4940	304	8	“	"	PUNCT
gi-4940	304	9	good	good	ADJ
gi-4940	304	10	”	"	PUNCT
gi-4940	304	11	if	if	SCONJ
gi-4940	304	12	no	no	DET
gi-4940	304	13	singularity	singularity	NOUN
gi-4940	304	14	at	at	ADP
gi-4940	304	15	f	f	PROPN
gi-4940	304	16	(	(	PUNCT
gi-4940	304	17	qi	qi	PROPN
gi-4940	304	18	)	)	PUNCT
gi-4940	304	19	and	and	CCONJ
gi-4940	304	20	g(qi	g(qi	PROPN
gi-4940	304	21	)	)	PUNCT
gi-4940	304	22	occurs	occur	VERB
gi-4940	304	23	.	.	PUNCT
gi-4940	305	1	unlike	unlike	ADP
gi-4940	305	2	the	the	DET
gi-4940	305	3	one	one	NUM
gi-4940	305	4	-	-	PUNCT
gi-4940	305	5	dimensional	dimensional	ADJ
gi-4940	305	6	version	version	NOUN
gi-4940	305	7	of	of	ADP
gi-4940	305	8	the	the	DET
gi-4940	305	9	problem	problem	NOUN
gi-4940	305	10	,	,	PUNCT
gi-4940	305	11	ω	ω	PROPN
gi-4940	305	12	is	be	AUX
gi-4940	305	13	partitioned	partition	VERB
gi-4940	305	14	in	in	ADP
gi-4940	305	15	two	two	NUM
gi-4940	305	16	orthogonal	orthogonal	ADJ
gi-4940	305	17	directions	direction	NOUN
gi-4940	305	18	(	(	PUNCT
gi-4940	305	19	ϕ	ϕ	NOUN
gi-4940	305	20	,	,	PUNCT
gi-4940	305	21	λ	λ	NOUN
gi-4940	305	22	)	)	PUNCT
gi-4940	305	23	.	.	PUNCT
gi-4940	306	1	let	let	VERB
gi-4940	306	2	the	the	DET
gi-4940	306	3	j	j	PROPN
gi-4940	306	4	−	−	X
gi-4940	306	5	th	th	X
gi-4940	306	6	interval	interval	NOUN
gi-4940	306	7	ωj	ωj	ADP
gi-4940	306	8	=	=	SYM
gi-4940	306	9	ωϕ,j	ωϕ,j	SYM
gi-4940	306	10	×	×	PROPN
gi-4940	306	11	ωλ	ωλ	PROPN
gi-4940	306	12	,	,	PUNCT
gi-4940	306	13	j	j	PROPN
gi-4940	306	14	,	,	PUNCT
gi-4940	306	15	where	where	SCONJ
gi-4940	306	16	ωϕ,j	ωϕ,j	X
gi-4940	306	17	=	=	PUNCT
gi-4940	307	1	[	[	X
gi-4940	307	2	ϕ	ϕ	X
gi-4940	307	3	j	j	PROPN
gi-4940	307	4	,	,	PUNCT
gi-4940	307	5	ϕj	ϕj	ADP
gi-4940	307	6	]	]	X
gi-4940	307	7	,	,	PUNCT
gi-4940	307	8	ωλ	ωλ	PROPN
gi-4940	307	9	,	,	PUNCT
gi-4940	307	10	j	j	PROPN
gi-4940	308	1	=	=	PUNCT
gi-4940	309	1	[	[	AUX
gi-4940	309	2	λj	λj	X
gi-4940	309	3	,	,	PUNCT
gi-4940	309	4	λj	λj	PROPN
gi-4940	309	5	]	]	X
gi-4940	309	6	,	,	PUNCT
gi-4940	309	7	contain	contain	VERB
gi-4940	309	8	a	a	DET
gi-4940	309	9	singularity	singularity	NOUN
gi-4940	309	10	c	c	NOUN
gi-4940	309	11	,	,	PUNCT
gi-4940	309	12	c	c	PROPN
gi-4940	309	13	∈	∈	PROPN
gi-4940	309	14	ω	ω	PROPN
gi-4940	309	15	,	,	PUNCT
gi-4940	309	16	with	with	ADP
gi-4940	309	17	the	the	DET
gi-4940	309	18	unknown	unknown	ADJ
gi-4940	309	19	direction	direction	NOUN
gi-4940	309	20	stored	store	VERB
gi-4940	309	21	in	in	ADP
gi-4940	309	22	the	the	DET
gi-4940	309	23	stack	stack	NOUN
gi-4940	309	24	s	s	NOUN
gi-4940	309	25	,	,	PUNCT
gi-4940	309	26	and	and	CCONJ
gi-4940	309	27	ε	ε	PROPN
gi-4940	309	28	,	,	PUNCT
gi-4940	309	29	ε	ε	PROPN
gi-4940	309	30	>	>	X
gi-4940	309	31	0	0	PROPN
gi-4940	309	32	,	,	PUNCT
gi-4940	309	33	be	be	AUX
gi-4940	309	34	the	the	DET
gi-4940	309	35	numerical	numerical	ADJ
gi-4940	309	36	threshold	threshold	NOUN
gi-4940	309	37	.	.	PUNCT
gi-4940	310	1	suppose	suppose	VERB
gi-4940	310	2	∆ϕ	∆ϕ	NOUN
gi-4940	310	3	to	to	PART
gi-4940	310	4	be	be	AUX
gi-4940	310	5	the	the	DET
gi-4940	310	6	latitude	latitude	NOUN
gi-4940	310	7	offset	offset	VERB
gi-4940	310	8	between	between	ADP
gi-4940	310	9	parallels	parallel	NOUN
gi-4940	310	10	and	and	CCONJ
gi-4940	310	11	∆λ	∆λ	PROPN
gi-4940	310	12	to	to	PART
gi-4940	310	13	be	be	AUX
gi-4940	310	14	the	the	DET
gi-4940	310	15	longitude	longitude	ADJ
gi-4940	310	16	offset	offset	NOUN
gi-4940	310	17	between	between	ADP
gi-4940	310	18	meridians	meridian	NOUN
gi-4940	310	19	.	.	PUNCT
gi-4940	311	1	geoinformatics	geoinformatic	NOUN
gi-4940	311	2	fce	fce	VERB
gi-4940	311	3	ctu	ctu	NOUN
gi-4940	311	4	17(2	17(2	NUM
gi-4940	311	5	)	)	PUNCT
gi-4940	311	6	,	,	PUNCT
gi-4940	311	7	2018	2018	NUM
gi-4940	311	8	40	40	NUM
gi-4940	311	9	t.	t.	NOUN
gi-4940	311	10	bayer	bayer	NOUN
gi-4940	311	11	:	:	PUNCT
gi-4940	311	12	plotting	plot	VERB
gi-4940	311	13	the	the	DET
gi-4940	311	14	map	map	NOUN
gi-4940	311	15	projection	projection	NOUN
gi-4940	311	16	graticule	graticule	NOUN
gi-4940	311	17	with	with	ADP
gi-4940	311	18	discontinuities	discontinuity	NOUN
gi-4940	311	19	algorithm	algorithm	NOUN
gi-4940	311	20	1	1	NUM
gi-4940	311	21	combined	combine	VERB
gi-4940	311	22	sampling	sample	VERB
gi-4940	311	23	with	with	ADP
gi-4940	311	24	the	the	DET
gi-4940	311	25	singularities	singularity	NOUN
gi-4940	311	26	,	,	PUNCT
gi-4940	311	27	the	the	DET
gi-4940	311	28	stack	stack	NOUN
gi-4940	311	29	implementation	implementation	NOUN
gi-4940	311	30	.	.	PUNCT
gi-4940	312	1	1	1	NUM
gi-4940	312	2	:	:	PUNCT
gi-4940	312	3	function	function	NOUN
gi-4940	312	4	graticule(lϕ,lλ	graticule(lϕ,lλ	NOUN
gi-4940	312	5	,	,	PUNCT
gi-4940	312	6	ωϕ	ωϕ	PRON
gi-4940	312	7	,	,	PUNCT
gi-4940	312	8	ωλ,∆ϕ,∆λ	ωλ,∆ϕ,∆λ	PRON
gi-4940	312	9	,	,	PUNCT
gi-4940	312	10	p	p	X
gi-4940	312	11	,	,	PUNCT
gi-4940	312	12	s	s	X
gi-4940	312	13	,	,	PUNCT
gi-4940	312	14	d	d	NOUN
gi-4940	312	15	,	,	PUNCT
gi-4940	312	16	d	d	PROPN
gi-4940	312	17	,	,	PUNCT
gi-4940	312	18	ε	ε	PROPN
gi-4940	312	19	,	,	PUNCT
gi-4940	312	20	α	α	NOUN
gi-4940	312	21	)	)	PUNCT
gi-4940	312	22	2	2	NUM
gi-4940	312	23	:	:	PUNCT
gi-4940	312	24	s	s	NOUN
gi-4940	312	25	=	=	NOUN
gi-4940	312	26	∅	∅	NOUN
gi-4940	312	27	,	,	PUNCT
gi-4940	312	28	s	s	NOUN
gi-4940	312	29	=	=	NOUN
gi-4940	312	30	0	0	NUM
gi-4940	312	31	3	3	NUM
gi-4940	312	32	:	:	PUNCT
gi-4940	312	33	s	s	X
gi-4940	312	34	←	←	PROPN
gi-4940	312	35	ωj	ωj	ADP
gi-4940	312	36	=	=	PUNCT
gi-4940	312	37	ωϕ	ωϕ	PRON
gi-4940	312	38	×ωλ	×ωλ	VERB
gi-4940	312	39	4	4	NUM
gi-4940	312	40	:	:	PUNCT
gi-4940	312	41	while	while	SCONJ
gi-4940	312	42	s	s	PROPN
gi-4940	312	43	6=	6=	PROPN
gi-4940	312	44	∅	∅	NOUN
gi-4940	312	45	do	do	VERB
gi-4940	312	46	5	5	NUM
gi-4940	312	47	:	:	PUNCT
gi-4940	312	48	ωj	ωj	ADP
gi-4940	312	49	=	=	PUNCT
gi-4940	312	50	ωϕ,j	ωϕ,j	PUNCT
gi-4940	312	51	×ωλ	×ωλ	PROPN
gi-4940	312	52	,	,	PUNCT
gi-4940	312	53	j	j	PROPN
gi-4940	312	54	=	=	SYM
gi-4940	312	55	s.pop	s.pop	PROPN
gi-4940	312	56	(	(	PUNCT
gi-4940	312	57	)	)	PUNCT
gi-4940	312	58	6	6	NUM
gi-4940	312	59	:	:	PUNCT
gi-4940	312	60	ωj,1	ωj,1	NOUN
gi-4940	312	61	=	=	SYM
gi-4940	312	62	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	312	63	×ωλ	×ωλ	VERB
gi-4940	312	64	,	,	PUNCT
gi-4940	312	65	j,1	j,1	X
gi-4940	312	66	=	=	SYM
gi-4940	312	67	ωj	ωj	ADP
gi-4940	312	68	,	,	PUNCT
gi-4940	313	1	ωj,2	ωj,2	NOUN
gi-4940	313	2	=	=	SYM
gi-4940	313	3	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	313	4	×ωλ	×ωλ	NOUN
gi-4940	313	5	,	,	PUNCT
gi-4940	313	6	j,2	j,2	NOUN
gi-4940	313	7	=	=	SYM
gi-4940	313	8	ωj	ωj	ADP
gi-4940	313	9	7	7	NUM
gi-4940	313	10	:	:	PUNCT
gi-4940	313	11	k	k	X
gi-4940	313	12	=	=	SYM
gi-4940	313	13	0	0	NUM
gi-4940	313	14	8	8	NUM
gi-4940	313	15	:	:	PUNCT
gi-4940	313	16	try	try	VERB
gi-4940	313	17	9	9	NUM
gi-4940	313	18	:	:	PUNCT
gi-4940	313	19	lϕ,j	lϕ,j	X
gi-4940	313	20	=	=	SYM
gi-4940	313	21	∅	∅	NOUN
gi-4940	313	22	,	,	PUNCT
gi-4940	313	23	lλ	lλ	INTJ
gi-4940	313	24	,	,	PUNCT
gi-4940	313	25	j	j	NOUN
gi-4940	314	1	=	=	NOUN
gi-4940	314	2	∅	∅	NOUN
gi-4940	314	3	10	10	NUM
gi-4940	314	4	:	:	PUNCT
gi-4940	314	5	meridians(lλ	meridians(lλ	PROPN
gi-4940	314	6	,	,	PUNCT
gi-4940	314	7	j	j	PROPN
gi-4940	314	8	,	,	PUNCT
gi-4940	314	9	ωϕ,j	ωϕ,j	X
gi-4940	314	10	,	,	PUNCT
gi-4940	314	11	ωλ	ωλ	PROPN
gi-4940	314	12	,	,	PUNCT
gi-4940	314	13	j	j	PROPN
gi-4940	314	14	,	,	PUNCT
gi-4940	314	15	∆λ	∆λ	PROPN
gi-4940	314	16	,	,	PUNCT
gi-4940	314	17	p	p	X
gi-4940	314	18	,	,	PUNCT
gi-4940	314	19	d	d	X
gi-4940	314	20	,	,	PUNCT
gi-4940	314	21	d	d	PROPN
gi-4940	314	22	,	,	PUNCT
gi-4940	314	23	ε	ε	PROPN
gi-4940	314	24	,	,	PUNCT
gi-4940	314	25	α	α	NOUN
gi-4940	314	26	)	)	PUNCT
gi-4940	314	27	11	11	NUM
gi-4940	314	28	:	:	PUNCT
gi-4940	314	29	parallels(lϕ,j	parallels(lϕ,j	PROPN
gi-4940	314	30	,	,	PUNCT
gi-4940	314	31	ωϕ,j	ωϕ,j	X
gi-4940	314	32	,	,	PUNCT
gi-4940	314	33	ωλ	ωλ	PROPN
gi-4940	314	34	,	,	PUNCT
gi-4940	314	35	j	j	PROPN
gi-4940	314	36	,	,	PUNCT
gi-4940	314	37	∆ϕ,p	∆ϕ,p	NOUN
gi-4940	314	38	,	,	PUNCT
gi-4940	314	39	d	d	NOUN
gi-4940	314	40	,	,	PUNCT
gi-4940	314	41	d	d	PROPN
gi-4940	314	42	,	,	PUNCT
gi-4940	314	43	ε	ε	PROPN
gi-4940	314	44	,	,	PUNCT
gi-4940	314	45	α	α	NOUN
gi-4940	314	46	)	)	PUNCT
gi-4940	314	47	12	12	NUM
gi-4940	314	48	:	:	PUNCT
gi-4940	314	49	lϕ	lϕ	PROPN
gi-4940	314	50	←	←	PROPN
gi-4940	314	51	lϕ,j	lϕ,j	X
gi-4940	314	52	,	,	PUNCT
gi-4940	314	53	lλ	lλ	INTJ
gi-4940	314	54	←	←	PROPN
gi-4940	314	55	lλ	lλ	PROPN
gi-4940	314	56	,	,	PUNCT
gi-4940	314	57	j	j	PROPN
gi-4940	314	58	13	13	NUM
gi-4940	314	59	:	:	PUNCT
gi-4940	314	60	catch	catch	NOUN
gi-4940	314	61	(	(	PUNCT
gi-4940	314	62	singularitylaterror	singularitylaterror	NOUN
gi-4940	314	63	e	e	NOUN
gi-4940	314	64	)	)	PUNCT
gi-4940	314	65	14	14	NUM
gi-4940	314	66	:	:	PUNCT
gi-4940	314	67	if	if	SCONJ
gi-4940	314	68	(	(	PUNCT
gi-4940	314	69	s	s	X
gi-4940	314	70	<	<	X
gi-4940	314	71	s	s	NOUN
gi-4940	314	72	)	)	PUNCT
gi-4940	314	73	then	then	ADV
gi-4940	314	74	15	15	NUM
gi-4940	314	75	:	:	PUNCT
gi-4940	315	1	processint(ωϕ,j	processint(ωϕ,j	PROPN
gi-4940	315	2	,	,	PUNCT
gi-4940	315	3	e.ϕi	e.ϕi	PROPN
gi-4940	315	4	,	,	PUNCT
gi-4940	315	5	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	315	6	,	,	PUNCT
gi-4940	315	7	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	315	8	,	,	PUNCT
gi-4940	315	9	k	k	PROPN
gi-4940	315	10	,	,	PUNCT
gi-4940	315	11	s	s	PROPN
gi-4940	315	12	,	,	PUNCT
gi-4940	315	13	ε	ε	PROPN
gi-4940	315	14	)	)	PUNCT
gi-4940	315	15	16	16	NUM
gi-4940	315	16	:	:	PUNCT
gi-4940	315	17	catch	catch	NOUN
gi-4940	315	18	(	(	PUNCT
gi-4940	315	19	singularitylonerror	singularitylonerror	NOUN
gi-4940	315	20	e	e	NOUN
gi-4940	315	21	)	)	PUNCT
gi-4940	315	22	17	17	NUM
gi-4940	315	23	:	:	PUNCT
gi-4940	315	24	if	if	SCONJ
gi-4940	315	25	(	(	PUNCT
gi-4940	315	26	s	s	X
gi-4940	315	27	<	<	X
gi-4940	315	28	s	s	NOUN
gi-4940	315	29	)	)	PUNCT
gi-4940	315	30	then	then	ADV
gi-4940	315	31	18	18	NUM
gi-4940	315	32	:	:	PUNCT
gi-4940	315	33	processint(ωλ	processint(ωλ	NOUN
gi-4940	315	34	,	,	PUNCT
gi-4940	315	35	j	j	PROPN
gi-4940	315	36	,	,	PUNCT
gi-4940	315	37	e.λi	e.λi	PROPN
gi-4940	315	38	,	,	PUNCT
gi-4940	315	39	ωλ	ωλ	ADJ
gi-4940	315	40	,	,	PUNCT
gi-4940	315	41	j,1	j,1	NOUN
gi-4940	315	42	,	,	PUNCT
gi-4940	315	43	ωλ	ωλ	ADJ
gi-4940	315	44	,	,	PUNCT
gi-4940	315	45	j,2	j,2	NOUN
gi-4940	315	46	,	,	PUNCT
gi-4940	315	47	k	k	PROPN
gi-4940	315	48	,	,	PUNCT
gi-4940	315	49	s	s	PROPN
gi-4940	315	50	,	,	PUNCT
gi-4940	315	51	ε	ε	PROPN
gi-4940	315	52	)	)	PUNCT
gi-4940	315	53	19	19	NUM
gi-4940	315	54	:	:	PUNCT
gi-4940	315	55	catch	catch	NOUN
gi-4940	315	56	(	(	PUNCT
gi-4940	315	57	singularityerror	singularityerror	NOUN
gi-4940	315	58	e	e	NOUN
gi-4940	315	59	)	)	PUNCT
gi-4940	315	60	20	20	NUM
gi-4940	315	61	:	:	PUNCT
gi-4940	315	62	if	if	SCONJ
gi-4940	315	63	(	(	PUNCT
gi-4940	315	64	s	s	X
gi-4940	315	65	>	>	X
gi-4940	315	66	s	s	PROPN
gi-4940	315	67	)	)	PUNCT
gi-4940	315	68	then	then	ADV
gi-4940	315	69	21	21	NUM
gi-4940	315	70	:	:	PUNCT
gi-4940	315	71	lϕ	lϕ	PROPN
gi-4940	315	72	=	=	X
gi-4940	315	73	∅,lλ	∅,lλ	ADV
gi-4940	315	74	=	=	SYM
gi-4940	315	75	∅	∅	NOUN
gi-4940	315	76	22	22	NUM
gi-4940	315	77	:	:	PUNCT
gi-4940	315	78	return	return	VERB
gi-4940	315	79	23	23	NUM
gi-4940	315	80	:	:	PUNCT
gi-4940	315	81	else	else	ADV
gi-4940	315	82	24	24	NUM
gi-4940	315	83	:	:	PUNCT
gi-4940	315	84	if	if	SCONJ
gi-4940	315	85	(	(	PUNCT
gi-4940	315	86	k	k	X
gi-4940	315	87	>	>	X
gi-4940	315	88	0	0	NUM
gi-4940	315	89	)	)	PUNCT
gi-4940	315	90	then	then	ADV
gi-4940	315	91	25	25	NUM
gi-4940	315	92	:	:	PUNCT
gi-4940	315	93	s	s	X
gi-4940	315	94	←	←	PROPN
gi-4940	315	95	ωj,1	ωj,1	NOUN
gi-4940	315	96	26	26	NUM
gi-4940	315	97	:	:	PUNCT
gi-4940	315	98	else	else	ADV
gi-4940	315	99	if	if	SCONJ
gi-4940	315	100	(	(	PUNCT
gi-4940	315	101	k	k	X
gi-4940	315	102	>	>	X
gi-4940	315	103	1	1	NUM
gi-4940	315	104	)	)	PUNCT
gi-4940	315	105	then	then	ADV
gi-4940	315	106	27	27	NUM
gi-4940	315	107	:	:	PUNCT
gi-4940	315	108	s	s	PART
gi-4940	315	109	←	←	PROPN
gi-4940	315	110	ωj,2	ωj,2	NOUN
gi-4940	315	111	initially	initially	ADV
gi-4940	315	112	,	,	PUNCT
gi-4940	315	113	ωg	ωg	PROPN
gi-4940	315	114	≡	≡	PROPN
gi-4940	315	115	ω	ω	PROPN
gi-4940	315	116	is	be	AUX
gi-4940	315	117	set	set	VERB
gi-4940	315	118	,	,	PUNCT
gi-4940	315	119	so	so	SCONJ
gi-4940	315	120	ωg	ωg	ADP
gi-4940	315	121	ϕ	ϕ	PROPN
gi-4940	315	122	≡	≡	PROPN
gi-4940	315	123	ωϕ	ωϕ	PRON
gi-4940	315	124	,	,	PUNCT
gi-4940	315	125	ωg	ωg	PROPN
gi-4940	315	126	ϕ	ϕ	PROPN
gi-4940	315	127	≡	≡	PROPN
gi-4940	315	128	ωϕ.	ωϕ.	ADP
gi-4940	315	129	all	all	PRON
gi-4940	315	130	adaptively	adaptively	ADV
gi-4940	315	131	sampled	sample	VERB
gi-4940	315	132	meridian	meridian	PROPN
gi-4940	315	133	/	/	SYM
gi-4940	315	134	parallel	parallel	ADJ
gi-4940	315	135	points	point	NOUN
gi-4940	315	136	qi	qi	PRON
gi-4940	315	137	are	be	AUX
gi-4940	315	138	checked	check	VERB
gi-4940	315	139	for	for	ADP
gi-4940	315	140	the	the	DET
gi-4940	315	141	discontinuities	discontinuity	NOUN
gi-4940	315	142	.	.	PUNCT
gi-4940	316	1	if	if	SCONJ
gi-4940	316	2	a	a	DET
gi-4940	316	3	discontinuity	discontinuity	NOUN
gi-4940	316	4	c	c	NOUN
gi-4940	316	5	is	be	AUX
gi-4940	316	6	found	find	VERB
gi-4940	316	7	,	,	PUNCT
gi-4940	316	8	it	it	PRON
gi-4940	316	9	is	be	AUX
gi-4940	316	10	classified	classify	VERB
gi-4940	316	11	,	,	PUNCT
gi-4940	316	12	and	and	CCONJ
gi-4940	316	13	its	its	PRON
gi-4940	316	14	direction	direction	NOUN
gi-4940	316	15	is	be	AUX
gi-4940	316	16	determined	determine	VERB
gi-4940	316	17	.	.	PUNCT
gi-4940	317	1	depending	depend	VERB
gi-4940	317	2	on	on	ADP
gi-4940	317	3	c	c	PROPN
gi-4940	317	4	value	value	NOUN
gi-4940	317	5	,	,	PUNCT
gi-4940	317	6	the	the	DET
gi-4940	317	7	lower	low	ADJ
gi-4940	317	8	/	/	SYM
gi-4940	317	9	upper	upper	ADJ
gi-4940	317	10	bound	bind	VERB
gi-4940	317	11	of	of	ADP
gi-4940	317	12	ωϕ,j	ωϕ,j	PUNCT
gi-4940	317	13	or	or	CCONJ
gi-4940	317	14	ωλ	ωλ	ADJ
gi-4940	317	15	,	,	PUNCT
gi-4940	317	16	j	j	PROPN
gi-4940	317	17	is	be	AUX
gi-4940	317	18	shifted	shift	VERB
gi-4940	317	19	,	,	PUNCT
gi-4940	317	20	or	or	CCONJ
gi-4940	317	21	,	,	PUNCT
gi-4940	317	22	a	a	DET
gi-4940	317	23	split	split	NOUN
gi-4940	317	24	to	to	ADP
gi-4940	317	25	two	two	NUM
gi-4940	317	26	disjoint	disjoint	NOUN
gi-4940	317	27	intervals	interval	NOUN
gi-4940	317	28	is	be	AUX
gi-4940	317	29	performed	perform	VERB
gi-4940	317	30	:	:	PUNCT
gi-4940	317	31	ωϕ,j	ωϕ,j	X
gi-4940	317	32	=	=	PUNCT
gi-4940	318	1	〈	〈	PROPN
gi-4940	318	2	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	318	3	,	,	PUNCT
gi-4940	318	4	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	318	5	〉	〉	NUM
gi-4940	318	6	,	,	PUNCT
gi-4940	318	7	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	318	8	=	=	PUNCT
gi-4940	319	1	[	[	X
gi-4940	319	2	ϕ	ϕ	X
gi-4940	319	3	j	j	PROPN
gi-4940	319	4	,	,	PUNCT
gi-4940	319	5	c−	c−	X
gi-4940	319	6	ε	ε	PROPN
gi-4940	319	7	]	]	X
gi-4940	319	8	,	,	PUNCT
gi-4940	319	9	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	319	10	=	=	PUNCT
gi-4940	320	1	[	[	X
gi-4940	320	2	c+	c+	NOUN
gi-4940	320	3	ε	ε	VERB
gi-4940	320	4	,	,	PUNCT
gi-4940	320	5	ϕj	ϕj	ADP
gi-4940	320	6	]	]	X
gi-4940	320	7	,	,	PUNCT
gi-4940	320	8	ωλ	ωλ	PROPN
gi-4940	320	9	,	,	PUNCT
gi-4940	320	10	j	j	PROPN
gi-4940	320	11	=	=	SYM
gi-4940	320	12	〈	〈	PROPN
gi-4940	320	13	ωλ	ωλ	ADJ
gi-4940	320	14	,	,	PUNCT
gi-4940	320	15	j,1	j,1	NOUN
gi-4940	320	16	,	,	PUNCT
gi-4940	320	17	ωλ	ωλ	ADJ
gi-4940	320	18	,	,	PUNCT
gi-4940	320	19	j,2	j,2	NOUN
gi-4940	320	20	〉	〉	NUM
gi-4940	320	21	,	,	PUNCT
gi-4940	320	22	ωλ	ωλ	ADJ
gi-4940	320	23	,	,	PUNCT
gi-4940	320	24	j,1	j,1	X
gi-4940	320	25	=	=	PUNCT
gi-4940	321	1	[	[	X
gi-4940	321	2	λj	λj	X
gi-4940	321	3	,	,	PUNCT
gi-4940	321	4	c−	c−	X
gi-4940	321	5	ε	ε	PROPN
gi-4940	321	6	]	]	PUNCT
gi-4940	321	7	,	,	PUNCT
gi-4940	321	8	ωλ	ωλ	ADJ
gi-4940	321	9	,	,	PUNCT
gi-4940	321	10	j,2	j,2	NOUN
gi-4940	321	11	=	=	PUNCT
gi-4940	322	1	[	[	X
gi-4940	322	2	c+	c+	NOUN
gi-4940	322	3	ε	ε	PROPN
gi-4940	322	4	,	,	PUNCT
gi-4940	322	5	λj	λj	X
gi-4940	322	6	]	]	X
gi-4940	322	7	.	.	PUNCT
gi-4940	323	1	otherwise	otherwise	ADV
gi-4940	323	2	,	,	PUNCT
gi-4940	323	3	the	the	DET
gi-4940	323	4	polygonal	polygonal	ADJ
gi-4940	323	5	approximation	approximation	NOUN
gi-4940	323	6	lλ	lλ	PROPN
gi-4940	323	7	,	,	PUNCT
gi-4940	323	8	j	j	PROPN
gi-4940	323	9	of	of	ADP
gi-4940	323	10	the	the	DET
gi-4940	323	11	meridian	meridian	PROPN
gi-4940	323	12	m(λ	m(λ	PROPN
gi-4940	323	13	)	)	PUNCT
gi-4940	323	14	or	or	CCONJ
gi-4940	323	15	lϕ,j	lϕ,j	X
gi-4940	323	16	of	of	ADP
gi-4940	323	17	the	the	DET
gi-4940	323	18	parallel	parallel	ADJ
gi-4940	323	19	p(ϕ	p(ϕ	NOUN
gi-4940	323	20	)	)	PUNCT
gi-4940	323	21	is	be	AUX
gi-4940	323	22	constructed	construct	VERB
gi-4940	323	23	.	.	PUNCT
gi-4940	324	1	all	all	DET
gi-4940	324	2	disjoint	disjoint	ADJ
gi-4940	324	3	polygonal	polygonal	ADJ
gi-4940	324	4	approximations	approximation	NOUN
gi-4940	324	5	lj	lj	PRON
gi-4940	324	6	are	be	AUX
gi-4940	324	7	stored	store	VERB
gi-4940	324	8	in	in	ADP
gi-4940	324	9	the	the	DET
gi-4940	324	10	lists	list	NOUN
gi-4940	324	11	of	of	ADP
gi-4940	324	12	meridians	meridian	NOUN
gi-4940	324	13	lλ	lλ	ADV
gi-4940	324	14	and	and	CCONJ
gi-4940	324	15	parallels	parallel	VERB
gi-4940	324	16	lϕ.	lϕ.	ADP
gi-4940	324	17	recall	recall	PROPN
gi-4940	324	18	s	s	PRON
gi-4940	324	19	to	to	PART
gi-4940	324	20	be	be	AUX
gi-4940	324	21	the	the	DET
gi-4940	324	22	amount	amount	NOUN
gi-4940	324	23	of	of	ADP
gi-4940	324	24	ωϕ,j	ωϕ,j	PUNCT
gi-4940	324	25	,	,	PUNCT
gi-4940	324	26	and	and	CCONJ
gi-4940	324	27	ωλ	ωλ	VERB
gi-4940	324	28	,	,	PUNCT
gi-4940	324	29	j	j	PROPN
gi-4940	324	30	splits	split	VERB
gi-4940	324	31	.	.	PUNCT
gi-4940	325	1	the	the	DET
gi-4940	325	2	procedure	procedure	NOUN
gi-4940	325	3	can	can	AUX
gi-4940	325	4	be	be	AUX
gi-4940	325	5	summarized	summarize	VERB
gi-4940	325	6	as	as	SCONJ
gi-4940	325	7	follows	follow	VERB
gi-4940	325	8	:	:	PUNCT
gi-4940	326	1	1	1	X
gi-4940	326	2	.	.	X
gi-4940	326	3	the	the	DET
gi-4940	326	4	initial	initial	ADJ
gi-4940	326	5	phase	phase	NOUN
gi-4940	326	6	initialize	initialize	VERB
gi-4940	326	7	the	the	DET
gi-4940	326	8	empty	empty	ADJ
gi-4940	326	9	stack	stack	NOUN
gi-4940	326	10	s	s	PART
gi-4940	326	11	=	=	NOUN
gi-4940	326	12	∅	∅	NOUN
gi-4940	326	13	,	,	PUNCT
gi-4940	326	14	ωg	ωg	PROPN
gi-4940	326	15	=	=	PROPN
gi-4940	326	16	ω	ω	PROPN
gi-4940	326	17	and	and	CCONJ
gi-4940	326	18	push	push	NOUN
gi-4940	326	19	s	s	PROPN
gi-4940	326	20	←	←	PROPN
gi-4940	326	21	ω	ω	PROPN
gi-4940	326	22	.	.	PUNCT
gi-4940	327	1	set	set	VERB
gi-4940	327	2	the	the	DET
gi-4940	327	3	number	number	NOUN
gi-4940	327	4	of	of	ADP
gi-4940	327	5	splits	split	NOUN
gi-4940	327	6	to	to	ADP
gi-4940	327	7	s	s	PROPN
gi-4940	327	8	=	=	SYM
gi-4940	327	9	0	0	PROPN
gi-4940	327	10	.	.	PUNCT
gi-4940	328	1	geoinformatics	geoinformatic	NOUN
gi-4940	328	2	fce	fce	VERB
gi-4940	328	3	ctu	ctu	NOUN
gi-4940	328	4	17(2	17(2	NUM
gi-4940	328	5	)	)	PUNCT
gi-4940	328	6	,	,	PUNCT
gi-4940	328	7	2018	2018	NUM
gi-4940	328	8	41	41	NUM
gi-4940	328	9	t.	t.	NOUN
gi-4940	328	10	bayer	bayer	NOUN
gi-4940	328	11	:	:	PUNCT
gi-4940	328	12	plotting	plot	VERB
gi-4940	328	13	the	the	DET
gi-4940	328	14	map	map	NOUN
gi-4940	328	15	projection	projection	NOUN
gi-4940	328	16	graticule	graticule	NOUN
gi-4940	328	17	with	with	ADP
gi-4940	328	18	discontinuities	discontinuity	NOUN
gi-4940	328	19	algorithm	algorithm	NOUN
gi-4940	328	20	2	2	NUM
gi-4940	328	21	the	the	DET
gi-4940	328	22	construction	construction	NOUN
gi-4940	328	23	of	of	ADP
gi-4940	328	24	meridians	meridian	NOUN
gi-4940	328	25	.	.	PUNCT
gi-4940	329	1	1	1	NUM
gi-4940	329	2	:	:	PUNCT
gi-4940	329	3	function	function	VERB
gi-4940	329	4	meridians(lλ	meridians(lλ	PROPN
gi-4940	329	5	,	,	PUNCT
gi-4940	329	6	j	j	PROPN
gi-4940	329	7	,	,	PUNCT
gi-4940	329	8	ωϕ,j	ωϕ,j	X
gi-4940	329	9	,	,	PUNCT
gi-4940	329	10	ωλ	ωλ	PROPN
gi-4940	329	11	,	,	PUNCT
gi-4940	329	12	j	j	PROPN
gi-4940	329	13	,	,	PUNCT
gi-4940	329	14	∆λ	∆λ	PROPN
gi-4940	329	15	,	,	PUNCT
gi-4940	329	16	p	p	X
gi-4940	329	17	,	,	PUNCT
gi-4940	329	18	d	d	X
gi-4940	329	19	,	,	PUNCT
gi-4940	329	20	d	d	PROPN
gi-4940	329	21	,	,	PUNCT
gi-4940	329	22	ε	ε	PROPN
gi-4940	329	23	,	,	PUNCT
gi-4940	329	24	α	α	NOUN
gi-4940	329	25	)	)	PUNCT
gi-4940	329	26	2	2	NUM
gi-4940	329	27	:	:	PUNCT
gi-4940	329	28	λj	λj	PROPN
gi-4940	329	29	,	,	PUNCT
gi-4940	329	30	start	start	VERB
gi-4940	329	31	=	=	SYM
gi-4940	329	32	∆λ[1	∆λ[1	ADJ
gi-4940	329	33	+	+	NUM
gi-4940	329	34	floor	floor	NOUN
gi-4940	329	35	(	(	PUNCT
gi-4940	329	36	λj	λj	PROPN
gi-4940	329	37	,	,	PUNCT
gi-4940	329	38	∆λ	∆λ	PROPN
gi-4940	329	39	)	)	PUNCT
gi-4940	329	40	]	]	PUNCT
gi-4940	330	1	3	3	NUM
gi-4940	330	2	:	:	PUNCT
gi-4940	330	3	λj	λj	PROPN
gi-4940	330	4	,	,	PUNCT
gi-4940	330	5	end	end	NOUN
gi-4940	330	6	=	=	SYM
gi-4940	330	7	∆λ[ceil	∆λ[ceil	NOUN
gi-4940	330	8	(	(	PUNCT
gi-4940	330	9	λj	λj	PROPN
gi-4940	330	10	∆λ)−	∆λ)−	PROPN
gi-4940	330	11	1	1	NUM
gi-4940	330	12	]	]	SYM
gi-4940	330	13	4	4	NUM
gi-4940	330	14	:	:	PUNCT
gi-4940	330	15	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	330	16	,	,	PUNCT
gi-4940	330	17	j	j	PROPN
gi-4940	330	18	,	,	PUNCT
gi-4940	330	19	ωϕ,j	ωϕ,j	X
gi-4940	330	20	,	,	PUNCT
gi-4940	330	21	λj	λj	PROPN
gi-4940	330	22	,	,	PUNCT
gi-4940	330	23	start	start	VERB
gi-4940	330	24	,	,	PUNCT
gi-4940	330	25	p	p	X
gi-4940	330	26	,	,	PUNCT
gi-4940	330	27	d	d	X
gi-4940	330	28	,	,	PUNCT
gi-4940	330	29	d	d	PROPN
gi-4940	330	30	,	,	PUNCT
gi-4940	330	31	ε	ε	PROPN
gi-4940	330	32	,	,	PUNCT
gi-4940	330	33	α	α	NOUN
gi-4940	330	34	)	)	PUNCT
gi-4940	330	35	5	5	NUM
gi-4940	330	36	:	:	PUNCT
gi-4940	330	37	for	for	ADP
gi-4940	330	38	(	(	PUNCT
gi-4940	330	39	λ	λ	SYM
gi-4940	330	40	=	=	SYM
gi-4940	330	41	λj	λj	PROPN
gi-4940	330	42	,	,	PUNCT
gi-4940	330	43	start;λ	start;λ	NOUN
gi-4940	330	44	≤	≤	NUM
gi-4940	330	45	λj	λj	PROPN
gi-4940	330	46	,	,	PUNCT
gi-4940	330	47	end;λ	end;λ	PROPN
gi-4940	330	48	=	=	PUNCT
gi-4940	330	49	λ+	λ+	PUNCT
gi-4940	330	50	∆λ	∆λ	NOUN
gi-4940	330	51	)	)	PUNCT
gi-4940	330	52	do	do	VERB
gi-4940	330	53	6	6	NUM
gi-4940	330	54	:	:	PUNCT
gi-4940	330	55	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	330	56	,	,	PUNCT
gi-4940	330	57	j	j	PROPN
gi-4940	330	58	,	,	PUNCT
gi-4940	330	59	ωϕ,j	ωϕ,j	X
gi-4940	330	60	,	,	PUNCT
gi-4940	330	61	λ	λ	X
gi-4940	330	62	,	,	PUNCT
gi-4940	330	63	p	p	X
gi-4940	330	64	,	,	PUNCT
gi-4940	330	65	d	d	X
gi-4940	330	66	,	,	PUNCT
gi-4940	330	67	d	d	PROPN
gi-4940	330	68	,	,	PUNCT
gi-4940	330	69	ε	ε	PROPN
gi-4940	330	70	,	,	PUNCT
gi-4940	330	71	α	α	NOUN
gi-4940	330	72	)	)	PUNCT
gi-4940	330	73	7	7	NUM
gi-4940	330	74	:	:	PUNCT
gi-4940	330	75	if	if	SCONJ
gi-4940	330	76	(	(	PUNCT
gi-4940	330	77	λk	λk	PROPN
gi-4940	330	78	∈	∈	PROPN
gi-4940	330	79	ωλ	ωλ	PROPN
gi-4940	330	80	,	,	PUNCT
gi-4940	330	81	j	j	PROPN
gi-4940	330	82	)	)	PUNCT
gi-4940	330	83	then	then	ADV
gi-4940	330	84	8	8	NUM
gi-4940	330	85	:	:	PUNCT
gi-4940	330	86	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	330	87	,	,	PUNCT
gi-4940	330	88	j	j	PROPN
gi-4940	330	89	,	,	PUNCT
gi-4940	330	90	ωϕ,j	ωϕ,j	PUNCT
gi-4940	330	91	,	,	PUNCT
gi-4940	330	92	λ−	λ−	PROPN
gi-4940	330	93	ε	ε	PROPN
gi-4940	330	94	,	,	PUNCT
gi-4940	330	95	p	p	X
gi-4940	330	96	,	,	PUNCT
gi-4940	330	97	d	d	X
gi-4940	330	98	,	,	PUNCT
gi-4940	330	99	d	d	PROPN
gi-4940	330	100	,	,	PUNCT
gi-4940	330	101	ε	ε	PROPN
gi-4940	330	102	,	,	PUNCT
gi-4940	330	103	α	α	NOUN
gi-4940	330	104	)	)	PUNCT
gi-4940	330	105	9	9	NUM
gi-4940	330	106	:	:	PUNCT
gi-4940	330	107	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	330	108	,	,	PUNCT
gi-4940	330	109	j	j	PROPN
gi-4940	330	110	,	,	PUNCT
gi-4940	330	111	ωϕ,j	ωϕ,j	X
gi-4940	330	112	,	,	PUNCT
gi-4940	330	113	λ+	λ+	VERB
gi-4940	330	114	ε	ε	PROPN
gi-4940	330	115	,	,	PUNCT
gi-4940	330	116	p	p	X
gi-4940	330	117	,	,	PUNCT
gi-4940	330	118	d	d	X
gi-4940	330	119	,	,	PUNCT
gi-4940	330	120	d	d	PROPN
gi-4940	330	121	,	,	PUNCT
gi-4940	330	122	ε	ε	PROPN
gi-4940	330	123	,	,	PUNCT
gi-4940	330	124	α	α	NOUN
gi-4940	330	125	)	)	PUNCT
gi-4940	330	126	10	10	NUM
gi-4940	330	127	:	:	PUNCT
gi-4940	331	1	λk	λk	X
gi-4940	331	2	,	,	PUNCT
gi-4940	331	3	o	o	NOUN
gi-4940	331	4	=	=	PUNCT
gi-4940	331	5	(	(	PUNCT
gi-4940	331	6	λk	λk	ADP
gi-4940	331	7	>	>	X
gi-4940	331	8	0?λk	0?λk	NUM
gi-4940	331	9	−	−	PROPN
gi-4940	331	10	π	π	X
gi-4940	331	11	:	:	PUNCT
gi-4940	331	12	λk	λk	PROPN
gi-4940	332	1	+	+	NUM
gi-4940	332	2	π	π	X
gi-4940	332	3	)	)	PUNCT
gi-4940	332	4	11	11	NUM
gi-4940	332	5	:	:	PUNCT
gi-4940	332	6	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	332	7	,	,	PUNCT
gi-4940	332	8	j	j	PROPN
gi-4940	332	9	,	,	PUNCT
gi-4940	332	10	ωϕ,j	ωϕ,j	X
gi-4940	332	11	,	,	PUNCT
gi-4940	332	12	λk	λk	PROPN
gi-4940	332	13	,	,	PUNCT
gi-4940	332	14	o	o	NOUN
gi-4940	332	15	−	−	PROPN
gi-4940	332	16	ε	ε	PROPN
gi-4940	332	17	,	,	PUNCT
gi-4940	332	18	p	p	X
gi-4940	332	19	,	,	PUNCT
gi-4940	332	20	d	d	X
gi-4940	332	21	,	,	PUNCT
gi-4940	332	22	d	d	PROPN
gi-4940	332	23	,	,	PUNCT
gi-4940	332	24	ε	ε	PROPN
gi-4940	332	25	,	,	PUNCT
gi-4940	332	26	α	α	NOUN
gi-4940	332	27	)	)	PUNCT
gi-4940	332	28	12	12	NUM
gi-4940	332	29	:	:	PUNCT
gi-4940	332	30	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	332	31	,	,	PUNCT
gi-4940	332	32	j	j	PROPN
gi-4940	332	33	,	,	PUNCT
gi-4940	332	34	ωϕ,j	ωϕ,j	X
gi-4940	332	35	,	,	PUNCT
gi-4940	332	36	λk	λk	PROPN
gi-4940	332	37	,	,	PUNCT
gi-4940	332	38	o	o	PROPN
gi-4940	332	39	+	+	CCONJ
gi-4940	332	40	ε	ε	PROPN
gi-4940	332	41	,	,	PUNCT
gi-4940	332	42	p	p	X
gi-4940	332	43	,	,	PUNCT
gi-4940	332	44	d	d	X
gi-4940	332	45	,	,	PUNCT
gi-4940	332	46	d	d	PROPN
gi-4940	332	47	,	,	PUNCT
gi-4940	332	48	ε	ε	PROPN
gi-4940	332	49	,	,	PUNCT
gi-4940	332	50	α	α	NOUN
gi-4940	332	51	)	)	PUNCT
gi-4940	332	52	13	13	NUM
gi-4940	332	53	:	:	PUNCT
gi-4940	332	54	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	332	55	,	,	PUNCT
gi-4940	332	56	j	j	PROPN
gi-4940	332	57	,	,	PUNCT
gi-4940	332	58	ωϕ,j	ωϕ,j	X
gi-4940	332	59	,	,	PUNCT
gi-4940	332	60	λj	λj	PROPN
gi-4940	332	61	,	,	PUNCT
gi-4940	332	62	end	end	NOUN
gi-4940	332	63	,	,	PUNCT
gi-4940	332	64	p	p	X
gi-4940	332	65	,	,	PUNCT
gi-4940	332	66	d	d	X
gi-4940	332	67	,	,	PUNCT
gi-4940	332	68	d	d	PROPN
gi-4940	332	69	,	,	PUNCT
gi-4940	332	70	ε	ε	PROPN
gi-4940	332	71	,	,	PUNCT
gi-4940	332	72	α	α	NOUN
gi-4940	332	73	)	)	PUNCT
gi-4940	332	74	2	2	NUM
gi-4940	332	75	.	.	PUNCT
gi-4940	332	76	recursive	recursive	ADJ
gi-4940	332	77	steps	step	NOUN
gi-4940	332	78	repeat	repeat	VERB
gi-4940	332	79	the	the	DET
gi-4940	332	80	following	follow	VERB
gi-4940	332	81	steps	step	NOUN
gi-4940	332	82	until	until	SCONJ
gi-4940	332	83	s	s	NOUN
gi-4940	332	84	is	be	AUX
gi-4940	332	85	empty	empty	ADJ
gi-4940	332	86	:	:	PUNCT
gi-4940	332	87	(	(	PUNCT
gi-4940	332	88	a	a	X
gi-4940	332	89	)	)	PUNCT
gi-4940	332	90	pop	pop	NOUN
gi-4940	332	91	the	the	DET
gi-4940	332	92	actual	actual	ADJ
gi-4940	332	93	interval	interval	NOUN
gi-4940	332	94	ωj	ωj	PART
gi-4940	332	95	pop	pop	VERB
gi-4940	332	96	the	the	DET
gi-4940	332	97	actual	actual	ADJ
gi-4940	332	98	good	good	ADJ
gi-4940	332	99	interval	interval	NOUN
gi-4940	332	100	ωj	ωj	ADP
gi-4940	332	101	←	←	PROPN
gi-4940	332	102	s	s	PART
gi-4940	332	103	from	from	ADP
gi-4940	332	104	s	s	PROPN
gi-4940	332	105	,	,	PUNCT
gi-4940	332	106	where	where	SCONJ
gi-4940	332	107	ωg	ωg	AUX
gi-4940	332	108	j	j	PROPN
gi-4940	332	109	=	=	PUNCT
gi-4940	332	110	ωϕ,j	ωϕ,j	X
gi-4940	332	111	×	×	PROPN
gi-4940	332	112	ωλ	ωλ	PROPN
gi-4940	332	113	,	,	PUNCT
gi-4940	332	114	j	j	NOUN
gi-4940	332	115	,	,	PUNCT
gi-4940	332	116	and	and	CCONJ
gi-4940	332	117	ωϕ,j	ωϕ,j	PUNCT
gi-4940	332	118	=	=	PUNCT
gi-4940	333	1	[	[	X
gi-4940	333	2	ϕ	ϕ	X
gi-4940	333	3	j	j	PROPN
gi-4940	333	4	,	,	PUNCT
gi-4940	333	5	ϕj	ϕj	ADP
gi-4940	333	6	]	]	X
gi-4940	333	7	,	,	PUNCT
gi-4940	333	8	ωλ	ωλ	PROPN
gi-4940	333	9	,	,	PUNCT
gi-4940	333	10	j	j	PROPN
gi-4940	334	1	=	=	PUNCT
gi-4940	335	1	[	[	X
gi-4940	335	2	λj	λj	X
gi-4940	335	3	,	,	PUNCT
gi-4940	335	4	λj	λj	PROPN
gi-4940	335	5	]	]	X
gi-4940	335	6	.	.	PUNCT
gi-4940	336	1	(	(	PUNCT
gi-4940	336	2	b	b	X
gi-4940	336	3	)	)	PUNCT
gi-4940	336	4	create	create	VERB
gi-4940	336	5	the	the	DET
gi-4940	336	6	empty	empty	ADJ
gi-4940	336	7	lists	list	NOUN
gi-4940	336	8	create	create	VERB
gi-4940	336	9	new	new	ADJ
gi-4940	336	10	empty	empty	ADJ
gi-4940	336	11	lists	list	NOUN
gi-4940	337	1	lλ	lλ	VERB
gi-4940	337	2	,	,	PUNCT
gi-4940	337	3	j	j	NOUN
gi-4940	337	4	=	=	SYM
gi-4940	337	5	∅	∅	NOUN
gi-4940	337	6	,	,	PUNCT
gi-4940	337	7	lϕ,j	lϕ,j	PUNCT
gi-4940	337	8	=	=	NOUN
gi-4940	337	9	∅	∅	NOUN
gi-4940	337	10	storing	store	VERB
gi-4940	337	11	the	the	DET
gi-4940	337	12	polygonal	polygonal	ADJ
gi-4940	337	13	approximation	approximation	NOUN
gi-4940	337	14	of	of	ADP
gi-4940	337	15	the	the	DET
gi-4940	337	16	meridians	meridian	NOUN
gi-4940	337	17	and	and	CCONJ
gi-4940	337	18	parallels	parallel	NOUN
gi-4940	337	19	.	.	PUNCT
gi-4940	338	1	(	(	PUNCT
gi-4940	338	2	c	c	X
gi-4940	338	3	)	)	PUNCT
gi-4940	338	4	create	create	VERB
gi-4940	338	5	the	the	DET
gi-4940	338	6	intervals	interval	NOUN
gi-4940	338	7	for	for	ADP
gi-4940	338	8	feasible	feasible	ADJ
gi-4940	338	9	splitting	splitting	NOUN
gi-4940	338	10	initialize	initialize	NOUN
gi-4940	338	11	the	the	DET
gi-4940	338	12	newly	newly	ADV
gi-4940	338	13	created	create	VERB
gi-4940	338	14	intervalsωj,1	intervalsωj,1	NOUN
gi-4940	338	15	=	=	SYM
gi-4940	338	16	ωϕ,j,1×ωλ	ωϕ,j,1×ωλ	ADJ
gi-4940	338	17	,	,	PUNCT
gi-4940	338	18	j,1	j,1	NOUN
gi-4940	338	19	,	,	PUNCT
gi-4940	338	20	andωj,2	andωj,2	NOUN
gi-4940	338	21	=	=	SYM
gi-4940	338	22	ωϕ,j,2×ωλ	ωϕ,j,2×ωλ	NOUN
gi-4940	338	23	,	,	PUNCT
gi-4940	338	24	j,2	j,2	NOUN
gi-4940	338	25	,	,	PUNCT
gi-4940	338	26	as	as	ADP
gi-4940	338	27	ωj,1	ωj,1	NOUN
gi-4940	338	28	=	=	SYM
gi-4940	338	29	ωj	ωj	ADP
gi-4940	338	30	,	,	PUNCT
gi-4940	338	31	ωj,2	ωj,2	NOUN
gi-4940	338	32	=	=	SYM
gi-4940	338	33	ωj	ωj	NOUN
gi-4940	338	34	,	,	PUNCT
gi-4940	338	35	where	where	SCONJ
gi-4940	338	36	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	338	37	=	=	PUNCT
gi-4940	339	1	[	[	X
gi-4940	339	2	ϕ	ϕ	X
gi-4940	339	3	j,1	j,1	PROPN
gi-4940	339	4	,	,	PUNCT
gi-4940	339	5	ϕj,1	ϕj,1	NOUN
gi-4940	339	6	]	]	PUNCT
gi-4940	339	7	,	,	PUNCT
gi-4940	339	8	ωλ	ωλ	ADJ
gi-4940	339	9	,	,	PUNCT
gi-4940	339	10	j,1	j,1	X
gi-4940	339	11	=	=	PUNCT
gi-4940	340	1	[	[	X
gi-4940	340	2	λj,1	λj,1	PROPN
gi-4940	340	3	,	,	PUNCT
gi-4940	340	4	λj,1	λj,1	PROPN
gi-4940	340	5	]	]	PUNCT
gi-4940	340	6	,	,	PUNCT
gi-4940	340	7	and	and	CCONJ
gi-4940	340	8	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	340	9	=	=	PUNCT
gi-4940	341	1	[	[	X
gi-4940	341	2	ϕ	ϕ	X
gi-4940	341	3	j,2	j,2	NOUN
gi-4940	341	4	,	,	PUNCT
gi-4940	341	5	ϕj,2	ϕj,2	PROPN
gi-4940	341	6	]	]	PUNCT
gi-4940	341	7	,	,	PUNCT
gi-4940	341	8	ωλ	ωλ	ADJ
gi-4940	341	9	,	,	PUNCT
gi-4940	341	10	j,2	j,2	NOUN
gi-4940	341	11	=	=	PUNCT
gi-4940	342	1	[	[	X
gi-4940	342	2	λj,2	λj,2	NOUN
gi-4940	342	3	,	,	PUNCT
gi-4940	342	4	λj,2	λj,2	PROPN
gi-4940	342	5	]	]	PUNCT
gi-4940	342	6	used	use	VERB
gi-4940	342	7	for	for	ADP
gi-4940	342	8	feasible	feasible	ADJ
gi-4940	342	9	splitting	splitting	NOUN
gi-4940	342	10	of	of	ADP
gi-4940	342	11	ωg	ωg	PROPN
gi-4940	342	12	j	j	PROPN
gi-4940	342	13	.	.	PUNCT
gi-4940	343	1	set	set	VERB
gi-4940	343	2	the	the	DET
gi-4940	343	3	amount	amount	NOUN
gi-4940	343	4	of	of	ADP
gi-4940	343	5	newly	newly	ADV
gi-4940	343	6	created	create	VERB
gi-4940	343	7	intervals	interval	NOUN
gi-4940	343	8	as	as	ADP
gi-4940	343	9	k	k	PROPN
gi-4940	343	10	=	=	PROPN
gi-4940	343	11	0	0	PROPN
gi-4940	343	12	.	.	PUNCT
gi-4940	344	1	(	(	PUNCT
gi-4940	344	2	d	d	X
gi-4940	344	3	)	)	PUNCT
gi-4940	344	4	create	create	VERB
gi-4940	344	5	the	the	DET
gi-4940	344	6	temporary	temporary	ADJ
gi-4940	344	7	polygonal	polygonal	ADJ
gi-4940	344	8	approximation	approximation	NOUN
gi-4940	344	9	lϕ,j	lϕ,j	PUNCT
gi-4940	344	10	,	,	PUNCT
gi-4940	344	11	lλ	lλ	INTJ
gi-4940	344	12	,	,	PUNCT
gi-4940	344	13	j	j	PROPN
gi-4940	344	14	of	of	ADP
gi-4940	344	15	the	the	DET
gi-4940	344	16	graticule	graticule	NOUN
gi-4940	344	17	create	create	VERB
gi-4940	344	18	the	the	DET
gi-4940	344	19	temporary	temporary	ADJ
gi-4940	344	20	polygonal	polygonal	ADJ
gi-4940	344	21	approximation	approximation	NOUN
gi-4940	344	22	of	of	ADP
gi-4940	344	23	the	the	DET
gi-4940	344	24	meridians	meridian	NOUN
gi-4940	344	25	and	and	CCONJ
gi-4940	344	26	parallels	parallel	VERB
gi-4940	344	27	on	on	ADP
gi-4940	344	28	ωg	ωg	PART
gi-4940	344	29	j	j	PROPN
gi-4940	344	30	using	use	VERB
gi-4940	344	31	adaptive	adaptive	ADJ
gi-4940	344	32	sampling	sampling	NOUN
gi-4940	344	33	stored	store	VERB
gi-4940	344	34	in	in	ADP
gi-4940	344	35	lϕ,j	lϕ,j	PUNCT
gi-4940	344	36	,	,	PUNCT
gi-4940	344	37	lλ	lλ	INTJ
gi-4940	344	38	,	,	PUNCT
gi-4940	344	39	j	j	PROPN
gi-4940	344	40	.	.	PUNCT
gi-4940	345	1	(	(	PUNCT
gi-4940	345	2	e	e	X
gi-4940	345	3	)	)	PUNCT
gi-4940	345	4	copy	copy	VERB
gi-4940	345	5	the	the	DET
gi-4940	345	6	temporary	temporary	ADJ
gi-4940	345	7	polygonal	polygonal	ADJ
gi-4940	345	8	approximation	approximation	NOUN
gi-4940	345	9	if	if	SCONJ
gi-4940	345	10	no	no	DET
gi-4940	345	11	discontinuity	discontinuity	NOUN
gi-4940	345	12	appears	appear	VERB
gi-4940	345	13	,	,	PUNCT
gi-4940	345	14	add	add	VERB
gi-4940	345	15	lλ	lλ	PROPN
gi-4940	345	16	,	,	PUNCT
gi-4940	345	17	j	j	PROPN
gi-4940	345	18	tolλ	tolλ	NOUN
gi-4940	345	19	:	:	PUNCT
gi-4940	345	20	lλ	lλ	PROPN
gi-4940	345	21	←	←	PROPN
gi-4940	345	22	lλ	lλ	PROPN
gi-4940	345	23	,	,	PUNCT
gi-4940	345	24	j	j	PROPN
gi-4940	345	25	,	,	PUNCT
gi-4940	345	26	and	and	CCONJ
gi-4940	345	27	lϕ,j	lϕ,j	PUNCT
gi-4940	345	28	tolϕ	tolϕ	PROPN
gi-4940	345	29	:	:	PUNCT
gi-4940	345	30	lϕ	lϕ	PROPN
gi-4940	345	31	←	←	PROPN
gi-4940	345	32	lϕ,j	lϕ,j	X
gi-4940	345	33	,	,	PUNCT
gi-4940	345	34	and	and	CCONJ
gi-4940	345	35	go	go	VERB
gi-4940	345	36	to	to	PART
gi-4940	345	37	step	step	VERB
gi-4940	345	38	(	(	PUNCT
gi-4940	345	39	a	a	NOUN
gi-4940	345	40	)	)	PUNCT
gi-4940	345	41	.	.	PUNCT
gi-4940	346	1	otherwise	otherwise	ADV
gi-4940	346	2	,	,	PUNCT
gi-4940	346	3	c	c	PROPN
gi-4940	346	4	represents	represent	VERB
gi-4940	346	5	the	the	DET
gi-4940	346	6	discontinuity	discontinuity	NOUN
gi-4940	346	7	of	of	ADP
gi-4940	346	8	the	the	DET
gi-4940	346	9	given	give	VERB
gi-4940	346	10	type	type	NOUN
gi-4940	346	11	and	and	CCONJ
gi-4940	346	12	direction	direction	NOUN
gi-4940	346	13	detected	detect	VERB
gi-4940	346	14	.	.	PUNCT
gi-4940	347	1	the	the	DET
gi-4940	347	2	following	follow	VERB
gi-4940	347	3	cases	case	NOUN
gi-4940	347	4	,	,	PUNCT
gi-4940	347	5	when	when	SCONJ
gi-4940	347	6	c	c	NOUN
gi-4940	347	7	=	=	SYM
gi-4940	347	8	ϕi	ϕi	ADP
gi-4940	347	9	,	,	PUNCT
gi-4940	347	10	or	or	CCONJ
gi-4940	347	11	,	,	PUNCT
gi-4940	347	12	c	c	PROPN
gi-4940	347	13	=	=	SYM
gi-4940	347	14	λi	λi	PROPN
gi-4940	347	15	,	,	PUNCT
gi-4940	347	16	must	must	AUX
gi-4940	347	17	be	be	AUX
gi-4940	347	18	treated	treat	VERB
gi-4940	347	19	in	in	ADP
gi-4940	347	20	steps	step	NOUN
gi-4940	347	21	i	i	PROPN
gi-4940	347	22	-	-	PUNCT
gi-4940	347	23	iii	iii	NOUN
gi-4940	347	24	)	)	PUNCT
gi-4940	347	25	.	.	PUNCT
gi-4940	348	1	(	(	PUNCT
gi-4940	348	2	f	f	X
gi-4940	348	3	)	)	PUNCT
gi-4940	348	4	resolve	resolve	VERB
gi-4940	348	5	the	the	DET
gi-4940	348	6	singularities	singularity	NOUN
gi-4940	348	7	by	by	ADP
gi-4940	348	8	splitting	splitting	NOUN
gi-4940	348	9	ωϕ,j	ωϕ,j	X
gi-4940	348	10	,	,	PUNCT
gi-4940	348	11	ωλ	ωλ	PROPN
gi-4940	348	12	,	,	PUNCT
gi-4940	348	13	j	j	PROPN
gi-4940	348	14	geoinformatics	geoinformatic	NOUN
gi-4940	348	15	fce	fce	VERB
gi-4940	348	16	ctu	ctu	NOUN
gi-4940	348	17	17(2	17(2	NUM
gi-4940	348	18	)	)	PUNCT
gi-4940	348	19	,	,	PUNCT
gi-4940	348	20	2018	2018	NUM
gi-4940	348	21	42	42	NUM
gi-4940	348	22	t.	t.	NOUN
gi-4940	348	23	bayer	bayer	NOUN
gi-4940	348	24	:	:	PUNCT
gi-4940	348	25	plotting	plot	VERB
gi-4940	348	26	the	the	DET
gi-4940	348	27	map	map	NOUN
gi-4940	348	28	projection	projection	NOUN
gi-4940	348	29	graticule	graticule	NOUN
gi-4940	348	30	with	with	ADP
gi-4940	348	31	discontinuities	discontinuity	NOUN
gi-4940	348	32	depending	depend	VERB
gi-4940	348	33	on	on	ADP
gi-4940	348	34	the	the	DET
gi-4940	348	35	singularity	singularity	NOUN
gi-4940	348	36	c	c	NOUN
gi-4940	348	37	direction	direction	NOUN
gi-4940	348	38	,	,	PUNCT
gi-4940	348	39	do	do	VERB
gi-4940	348	40	the	the	DET
gi-4940	348	41	following	follow	VERB
gi-4940	348	42	steps	step	NOUN
gi-4940	348	43	:	:	PUNCT
gi-4940	348	44	i.	i.	NOUN
gi-4940	348	45	if	if	SCONJ
gi-4940	348	46	c	c	PROPN
gi-4940	348	47	=	=	SYM
gi-4940	348	48	ϕi	ϕi	PROPN
gi-4940	348	49	,	,	PUNCT
gi-4940	348	50	then	then	ADV
gi-4940	348	51	ωϕ,j	ωϕ,j	PUNCT
gi-4940	348	52	needs	need	VERB
gi-4940	348	53	to	to	PART
gi-4940	348	54	be	be	AUX
gi-4940	348	55	split	split	VERB
gi-4940	348	56	.	.	PUNCT
gi-4940	349	1	call	call	VERB
gi-4940	349	2	the	the	DET
gi-4940	349	3	function	function	NOUN
gi-4940	349	4	processint	processint	NOUN
gi-4940	349	5	(	(	PUNCT
gi-4940	349	6	)	)	PUNCT
gi-4940	349	7	with	with	ADP
gi-4940	349	8	parameters	parameter	NOUN
gi-4940	349	9	:	:	PUNCT
gi-4940	349	10	ωϕ,j	ωϕ,j	X
gi-4940	349	11	,	,	PUNCT
gi-4940	349	12	c	c	X
gi-4940	349	13	,	,	PUNCT
gi-4940	349	14	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	349	15	,	,	PUNCT
gi-4940	349	16	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	349	17	,	,	PUNCT
gi-4940	349	18	k	k	PROPN
gi-4940	349	19	,	,	PUNCT
gi-4940	349	20	s	s	PROPN
gi-4940	349	21	,	,	PUNCT
gi-4940	349	22	ε	ε	PROPN
gi-4940	349	23	.	.	PUNCT
gi-4940	350	1	the	the	DET
gi-4940	350	2	subintervals	subinterval	NOUN
gi-4940	350	3	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	350	4	,	,	PUNCT
gi-4940	350	5	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	350	6	are	be	AUX
gi-4940	350	7	passing	pass	VERB
gi-4940	350	8	by	by	ADP
gi-4940	350	9	reference	reference	NOUN
gi-4940	350	10	.	.	PUNCT
gi-4940	351	1	ii	ii	PROPN
gi-4940	351	2	.	.	PUNCT
gi-4940	352	1	if	if	SCONJ
gi-4940	352	2	c	c	PROPN
gi-4940	352	3	=	=	SYM
gi-4940	352	4	λi	λi	PROPN
gi-4940	352	5	,	,	PUNCT
gi-4940	352	6	then	then	ADV
gi-4940	352	7	ωλ	ωλ	ADJ
gi-4940	352	8	,	,	PUNCT
gi-4940	352	9	j	j	PROPN
gi-4940	352	10	needs	need	VERB
gi-4940	352	11	to	to	PART
gi-4940	352	12	be	be	AUX
gi-4940	352	13	split	split	VERB
gi-4940	352	14	.	.	PUNCT
gi-4940	353	1	call	call	VERB
gi-4940	353	2	the	the	DET
gi-4940	353	3	function	function	NOUN
gi-4940	353	4	processint	processint	NOUN
gi-4940	353	5	(	(	PUNCT
gi-4940	353	6	)	)	PUNCT
gi-4940	353	7	with	with	ADP
gi-4940	353	8	parameters	parameter	NOUN
gi-4940	353	9	:	:	PUNCT
gi-4940	353	10	ωλ	ωλ	ADJ
gi-4940	353	11	,	,	PUNCT
gi-4940	353	12	j	j	PROPN
gi-4940	353	13	,	,	PUNCT
gi-4940	353	14	c	c	X
gi-4940	353	15	,	,	PUNCT
gi-4940	353	16	ωλ	ωλ	ADJ
gi-4940	353	17	,	,	PUNCT
gi-4940	353	18	j,1	j,1	NOUN
gi-4940	353	19	,	,	PUNCT
gi-4940	353	20	ωλ	ωλ	ADJ
gi-4940	353	21	,	,	PUNCT
gi-4940	353	22	j,2	j,2	NOUN
gi-4940	353	23	,	,	PUNCT
gi-4940	353	24	k	k	PROPN
gi-4940	353	25	,	,	PUNCT
gi-4940	353	26	s	s	PROPN
gi-4940	353	27	,	,	PUNCT
gi-4940	353	28	ε	ε	PROPN
gi-4940	353	29	.	.	PUNCT
gi-4940	354	1	the	the	DET
gi-4940	354	2	subintervals	subinterval	NOUN
gi-4940	354	3	ωλ	ωλ	VERB
gi-4940	354	4	,	,	PUNCT
gi-4940	354	5	j,1	j,1	NOUN
gi-4940	354	6	,	,	PUNCT
gi-4940	354	7	ωλ	ωλ	VERB
gi-4940	354	8	,	,	PUNCT
gi-4940	354	9	j,2	j,2	NOUN
gi-4940	354	10	are	be	AUX
gi-4940	354	11	passing	pass	VERB
gi-4940	354	12	by	by	ADP
gi-4940	354	13	reference	reference	NOUN
gi-4940	354	14	.	.	PUNCT
gi-4940	355	1	iii	iii	X
gi-4940	355	2	.	.	PUNCT
gi-4940	356	1	if	if	SCONJ
gi-4940	356	2	c	c	PROPN
gi-4940	356	3	=	=	PUNCT
gi-4940	356	4	ϕi	ϕi	ADP
gi-4940	356	5	∨	∨	NUM
gi-4940	356	6	c	c	X
gi-4940	356	7	=	=	SYM
gi-4940	356	8	λi	λi	PROPN
gi-4940	356	9	,	,	PUNCT
gi-4940	356	10	do	do	VERB
gi-4940	356	11	the	the	DET
gi-4940	356	12	following	follow	VERB
gi-4940	356	13	steps	step	NOUN
gi-4940	356	14	.	.	PUNCT
gi-4940	357	1	if	if	SCONJ
gi-4940	357	2	s	s	X
gi-4940	357	3	>	>	X
gi-4940	357	4	s	s	PROPN
gi-4940	357	5	,	,	PUNCT
gi-4940	357	6	the	the	DET
gi-4940	357	7	maximum	maximum	ADJ
gi-4940	357	8	allowed	allow	VERB
gi-4940	357	9	recursion	recursion	NOUN
gi-4940	357	10	depth	depth	NOUN
gi-4940	357	11	is	be	AUX
gi-4940	357	12	exceeded	exceed	VERB
gi-4940	357	13	without	without	ADP
gi-4940	357	14	a	a	DET
gi-4940	357	15	reasonable	reasonable	ADJ
gi-4940	357	16	solution	solution	NOUN
gi-4940	357	17	,	,	PUNCT
gi-4940	357	18	clear	clear	ADJ
gi-4940	357	19	the	the	DET
gi-4940	357	20	polygonal	polygonal	ADJ
gi-4940	357	21	approximations	approximation	NOUN
gi-4940	357	22	lϕ	lϕ	ADP
gi-4940	357	23	,	,	PUNCT
gi-4940	357	24	lλ	lλ	INTJ
gi-4940	357	25	.	.	PUNCT
gi-4940	358	1	otherwise	otherwise	ADV
gi-4940	358	2	,	,	PUNCT
gi-4940	358	3	if	if	SCONJ
gi-4940	358	4	k	k	PROPN
gi-4940	358	5	>	>	X
gi-4940	358	6	0	0	PROPN
gi-4940	358	7	,	,	PUNCT
gi-4940	358	8	at	at	ADV
gi-4940	358	9	least	least	ADJ
gi-4940	358	10	one	one	NUM
gi-4940	358	11	new	new	ADJ
gi-4940	358	12	interval	interval	NOUN
gi-4940	358	13	needs	need	VERB
gi-4940	358	14	to	to	PART
gi-4940	358	15	be	be	AUX
gi-4940	358	16	created	create	VERB
gi-4940	358	17	;	;	PUNCT
gi-4940	358	18	push	push	VERB
gi-4940	358	19	ωj,1	ωj,1	NOUN
gi-4940	358	20	to	to	ADP
gi-4940	358	21	the	the	DET
gi-4940	358	22	stack	stack	NOUN
gi-4940	358	23	:	:	PUNCT
gi-4940	358	24	s	s	PART
gi-4940	358	25	←	←	PROPN
gi-4940	358	26	ωj,1	ωj,1	NOUN
gi-4940	358	27	.	.	PUNCT
gi-4940	359	1	if	if	SCONJ
gi-4940	359	2	k	k	PROPN
gi-4940	359	3	>	>	X
gi-4940	359	4	1	1	NUM
gi-4940	359	5	,	,	PUNCT
gi-4940	359	6	push	push	VERB
gi-4940	359	7	the	the	DET
gi-4940	359	8	second	second	ADJ
gi-4940	359	9	interval	interval	NOUN
gi-4940	359	10	ωj,2	ωj,2	NOUN
gi-4940	359	11	to	to	ADP
gi-4940	359	12	the	the	DET
gi-4940	359	13	stack	stack	NOUN
gi-4940	359	14	:	:	PUNCT
gi-4940	359	15	s	s	PART
gi-4940	359	16	←	←	PROPN
gi-4940	359	17	ωj,2	ωj,2	NOUN
gi-4940	359	18	.	.	PUNCT
gi-4940	360	1	for	for	ADP
gi-4940	360	2	the	the	DET
gi-4940	360	3	implementation	implementation	NOUN
gi-4940	360	4	,	,	PUNCT
gi-4940	360	5	see	see	VERB
gi-4940	360	6	alg	alg	PROPN
gi-4940	360	7	.	.	PUNCT
gi-4940	361	1	1	1	X
gi-4940	361	2	.	.	PUNCT
gi-4940	362	1	its	its	PRON
gi-4940	362	2	design	design	NOUN
gi-4940	362	3	is	be	AUX
gi-4940	362	4	robust	robust	ADJ
gi-4940	362	5	against	against	ADP
gi-4940	362	6	common	common	ADJ
gi-4940	362	7	numerical	numerical	ADJ
gi-4940	362	8	failures	failure	NOUN
gi-4940	362	9	.	.	PUNCT
gi-4940	363	1	the	the	DET
gi-4940	363	2	singularity	singularity	NOUN
gi-4940	363	3	value	value	NOUN
gi-4940	363	4	c	c	NOUN
gi-4940	363	5	is	be	AUX
gi-4940	363	6	stored	store	VERB
gi-4940	363	7	in	in	ADP
gi-4940	363	8	the	the	DET
gi-4940	363	9	thrown	throw	VERB
gi-4940	363	10	exceptions	exception	NOUN
gi-4940	363	11	singularitylaterror	singularitylaterror	NOUN
gi-4940	363	12	,	,	PUNCT
gi-4940	363	13	singularitylonerror	singularitylonerror	NOUN
gi-4940	363	14	,	,	PUNCT
gi-4940	363	15	which	which	PRON
gi-4940	363	16	are	be	AUX
gi-4940	363	17	derived	derive	VERB
gi-4940	363	18	from	from	ADP
gi-4940	363	19	the	the	DET
gi-4940	363	20	base	base	NOUN
gi-4940	363	21	class	class	NOUN
gi-4940	363	22	singularityerror	singularityerror	NOUN
gi-4940	363	23	.	.	PUNCT
gi-4940	364	1	the	the	DET
gi-4940	364	2	splitting	splitting	NOUN
gi-4940	364	3	procedure	procedure	NOUN
gi-4940	364	4	is	be	AUX
gi-4940	364	5	realized	realize	VERB
gi-4940	364	6	in	in	ADP
gi-4940	364	7	accordance	accordance	NOUN
gi-4940	364	8	with	with	ADP
gi-4940	364	9	the	the	DET
gi-4940	364	10	singularity	singularity	NOUN
gi-4940	364	11	direction	direction	NOUN
gi-4940	364	12	.	.	PUNCT
gi-4940	365	1	generate	generate	VERB
gi-4940	365	2	meridians	meridian	NOUN
gi-4940	365	3	.	.	PUNCT
gi-4940	366	1	the	the	DET
gi-4940	366	2	procedure	procedure	NOUN
gi-4940	366	3	creates	create	VERB
gi-4940	366	4	all	all	DET
gi-4940	366	5	meridians	meridian	NOUN
gi-4940	366	6	inside	inside	ADP
gi-4940	366	7	the	the	DET
gi-4940	366	8	given	give	VERB
gi-4940	366	9	interval	interval	NOUN
gi-4940	366	10	ωj	ωj	ADP
gi-4940	366	11	=	=	SYM
gi-4940	366	12	ωϕ,j	ωϕ,j	SYM
gi-4940	366	13	×	×	PROPN
gi-4940	366	14	ωλ	ωλ	PROPN
gi-4940	366	15	,	,	PUNCT
gi-4940	366	16	j	j	PROPN
gi-4940	366	17	,	,	PUNCT
gi-4940	366	18	where	where	SCONJ
gi-4940	366	19	ωϕ,j	ωϕ,j	X
gi-4940	366	20	=	=	PUNCT
gi-4940	367	1	[	[	X
gi-4940	367	2	ϕ	ϕ	X
gi-4940	367	3	j	j	PROPN
gi-4940	367	4	,	,	PUNCT
gi-4940	367	5	ϕj	ϕj	ADP
gi-4940	367	6	]	]	X
gi-4940	367	7	,	,	PUNCT
gi-4940	367	8	ωλ	ωλ	PROPN
gi-4940	367	9	,	,	PUNCT
gi-4940	367	10	j	j	PROPN
gi-4940	368	1	=	=	PUNCT
gi-4940	369	1	[	[	X
gi-4940	369	2	λj	λj	X
gi-4940	369	3	,	,	PUNCT
gi-4940	369	4	λj	λj	PROPN
gi-4940	369	5	]	]	X
gi-4940	369	6	.	.	PUNCT
gi-4940	370	1	initially	initially	ADV
gi-4940	370	2	,	,	PUNCT
gi-4940	370	3	the	the	DET
gi-4940	370	4	bounding	bounding	NOUN
gi-4940	370	5	meridians	meridian	NOUN
gi-4940	370	6	m(λj	m(λj	NOUN
gi-4940	370	7	)	)	PUNCT
gi-4940	370	8	,	,	PUNCT
gi-4940	370	9	and	and	CCONJ
gi-4940	370	10	m(λj	m(λj	NOUN
gi-4940	370	11	)	)	PUNCT
gi-4940	370	12	are	be	AUX
gi-4940	370	13	created	create	VERB
gi-4940	370	14	.	.	PUNCT
gi-4940	371	1	to	to	PART
gi-4940	371	2	find	find	VERB
gi-4940	371	3	the	the	DET
gi-4940	371	4	longitude	longitude	ADJ
gi-4940	371	5	λstart	λstart	NOUN
gi-4940	371	6	of	of	ADP
gi-4940	371	7	the	the	DET
gi-4940	371	8	first	first	ADJ
gi-4940	371	9	meridian	meridian	PROPN
gi-4940	371	10	m(λstart	m(λstart	PROPN
gi-4940	371	11	)	)	PUNCT
gi-4940	371	12	,	,	PUNCT
gi-4940	371	13	which	which	PRON
gi-4940	371	14	is	be	AUX
gi-4940	371	15	the	the	DET
gi-4940	371	16	smallest	small	ADJ
gi-4940	371	17	multiplier	multiplier	NOUN
gi-4940	371	18	of	of	ADP
gi-4940	371	19	∆λ	∆λ	PROPN
gi-4940	371	20	higher	high	ADJ
gi-4940	371	21	than	than	ADP
gi-4940	371	22	λj	λj	PROPN
gi-4940	371	23	,	,	PUNCT
gi-4940	371	24	and	and	CCONJ
gi-4940	371	25	the	the	DET
gi-4940	371	26	last	last	ADJ
gi-4940	371	27	meridian	meridian	PROPN
gi-4940	371	28	m(λend	m(λend	PROPN
gi-4940	371	29	)	)	PUNCT
gi-4940	371	30	,	,	PUNCT
gi-4940	371	31	which	which	PRON
gi-4940	371	32	is	be	AUX
gi-4940	371	33	the	the	DET
gi-4940	371	34	largest	large	ADJ
gi-4940	371	35	multiplier	multiplier	NOUN
gi-4940	371	36	of	of	ADP
gi-4940	371	37	∆λ	∆λ	PROPN
gi-4940	371	38	lower	low	ADJ
gi-4940	371	39	than	than	ADP
gi-4940	371	40	λj	λj	PROPN
gi-4940	371	41	,	,	PUNCT
gi-4940	371	42	use	use	VERB
gi-4940	371	43	λj	λj	PROPN
gi-4940	371	44	,	,	PUNCT
gi-4940	371	45	start	start	VERB
gi-4940	371	46	=	=	SYM
gi-4940	371	47	∆λ[1	∆λ[1	ADJ
gi-4940	371	48	+	+	NUM
gi-4940	371	49	floor	floor	NOUN
gi-4940	371	50	(	(	PUNCT
gi-4940	371	51	λj	λj	PROPN
gi-4940	371	52	,	,	PUNCT
gi-4940	371	53	∆λ	∆λ	PROPN
gi-4940	371	54	)	)	PUNCT
gi-4940	371	55	]	]	PUNCT
gi-4940	371	56	,	,	PUNCT
gi-4940	371	57	λj	λj	PROPN
gi-4940	371	58	,	,	PUNCT
gi-4940	371	59	end	end	NOUN
gi-4940	371	60	=	=	SYM
gi-4940	371	61	∆λ[ceil	∆λ[ceil	NOUN
gi-4940	371	62	(	(	PUNCT
gi-4940	371	63	λj∆λ)−	λj∆λ)−	NOUN
gi-4940	371	64	1	1	NUM
gi-4940	371	65	]	]	PUNCT
gi-4940	371	66	.	.	PUNCT
gi-4940	372	1	other	other	ADJ
gi-4940	372	2	meridians	meridian	NOUN
gi-4940	372	3	m(λj	m(λj	PROPN
gi-4940	372	4	,	,	PUNCT
gi-4940	372	5	i	i	PRON
gi-4940	372	6	)	)	PUNCT
gi-4940	372	7	are	be	AUX
gi-4940	372	8	generated	generate	VERB
gi-4940	372	9	inside	inside	ADP
gi-4940	372	10	the	the	DET
gi-4940	372	11	interval	interval	NOUN
gi-4940	373	1	[	[	X
gi-4940	373	2	λstart	λstart	NOUN
gi-4940	373	3	,	,	PUNCT
gi-4940	373	4	λend	λend	NOUN
gi-4940	373	5	]	]	PUNCT
gi-4940	373	6	so	so	SCONJ
gi-4940	373	7	that	that	SCONJ
gi-4940	373	8	λj	λj	PROPN
gi-4940	373	9	=	=	SYM
gi-4940	373	10	λj	λj	PROPN
gi-4940	373	11	,	,	PUNCT
gi-4940	373	12	start	start	VERB
gi-4940	373	13	+	+	CCONJ
gi-4940	373	14	i∆λ	i∆λ	NOUN
gi-4940	373	15	,	,	PUNCT
gi-4940	373	16	λstart	λstart	NOUN
gi-4940	373	17	<	<	X
gi-4940	373	18	λ	λ	X
gi-4940	373	19	<	<	X
gi-4940	373	20	λend	λend	NOUN
gi-4940	373	21	.	.	PUNCT
gi-4940	374	1	due	due	ADP
gi-4940	374	2	to	to	ADP
gi-4940	374	3	possible	possible	ADJ
gi-4940	374	4	discontinuities	discontinuity	NOUN
gi-4940	374	5	,	,	PUNCT
gi-4940	374	6	the	the	DET
gi-4940	374	7	meridian	meridian	PROPN
gi-4940	374	8	consists	consist	VERB
gi-4940	374	9	of	of	ADP
gi-4940	374	10	several	several	ADJ
gi-4940	374	11	parts	part	NOUN
gi-4940	374	12	.	.	PUNCT
gi-4940	375	1	if	if	SCONJ
gi-4940	375	2	a	a	DET
gi-4940	375	3	discontinuity	discontinuity	NOUN
gi-4940	375	4	at	at	ADP
gi-4940	375	5	c	c	NOUN
gi-4940	375	6	=	=	PUNCT
gi-4940	375	7	ϕj	ϕj	PROPN
gi-4940	375	8	is	be	AUX
gi-4940	375	9	found	find	VERB
gi-4940	375	10	,	,	PUNCT
gi-4940	375	11	the	the	DET
gi-4940	375	12	meridian	meridian	PROPN
gi-4940	375	13	needs	need	VERB
gi-4940	375	14	to	to	PART
gi-4940	375	15	be	be	AUX
gi-4940	375	16	split	split	VERB
gi-4940	375	17	at	at	ADP
gi-4940	375	18	c.	c.	PROPN
gi-4940	375	19	if	if	SCONJ
gi-4940	375	20	a	a	DET
gi-4940	375	21	discontinuity	discontinuity	NOUN
gi-4940	375	22	at	at	ADP
gi-4940	375	23	c	c	NOUN
gi-4940	375	24	=	=	PUNCT
gi-4940	375	25	λj	λj	PROPN
gi-4940	375	26	is	be	AUX
gi-4940	375	27	detected	detect	VERB
gi-4940	375	28	,	,	PUNCT
gi-4940	375	29	a	a	DET
gi-4940	375	30	meridian	meridian	PROPN
gi-4940	375	31	needs	need	VERB
gi-4940	375	32	to	to	PART
gi-4940	375	33	be	be	AUX
gi-4940	375	34	shifted	shift	VERB
gi-4940	375	35	.	.	PUNCT
gi-4940	376	1	this	this	PRON
gi-4940	376	2	is	be	AUX
gi-4940	376	3	achieved	achieve	VERB
gi-4940	376	4	by	by	ADP
gi-4940	376	5	splitting	splitting	NOUN
gi-4940	376	6	ωj	ωj	ADP
gi-4940	376	7	at	at	ADP
gi-4940	376	8	c	c	NOUN
gi-4940	376	9	=	=	SYM
gi-4940	376	10	ϕj	ϕj	PROPN
gi-4940	376	11	,	,	PUNCT
gi-4940	376	12	or	or	CCONJ
gi-4940	376	13	,	,	PUNCT
gi-4940	376	14	at	at	ADP
gi-4940	376	15	c	c	NOUN
gi-4940	376	16	=	=	SYM
gi-4940	376	17	λj	λj	PROPN
gi-4940	376	18	with	with	ADP
gi-4940	376	19	the	the	DET
gi-4940	376	20	additional	additional	ADJ
gi-4940	376	21	shift	shift	NOUN
gi-4940	376	22	ε	ε	PROPN
gi-4940	376	23	.	.	PUNCT
gi-4940	377	1	otherwise	otherwise	ADV
gi-4940	377	2	,	,	PUNCT
gi-4940	377	3	a	a	DET
gi-4940	377	4	current	current	ADJ
gi-4940	377	5	meridian	meridian	NOUN
gi-4940	377	6	m(λj	m(λj	PROPN
gi-4940	377	7	)	)	PUNCT
gi-4940	377	8	is	be	AUX
gi-4940	377	9	constructed	construct	VERB
gi-4940	377	10	.	.	PUNCT
gi-4940	378	1	finally	finally	ADV
gi-4940	378	2	,	,	PUNCT
gi-4940	378	3	the	the	DET
gi-4940	378	4	meridians	meridian	NOUN
gi-4940	378	5	passing	pass	VERB
gi-4940	378	6	along	along	ADP
gi-4940	378	7	the	the	DET
gi-4940	378	8	pole	pole	NOUN
gi-4940	378	9	m(λk	m(λk	PROPN
gi-4940	378	10	±	±	NUM
gi-4940	378	11	ε	ε	PROPN
gi-4940	378	12	)	)	PUNCT
gi-4940	378	13	and	and	CCONJ
gi-4940	378	14	the	the	DET
gi-4940	378	15	opposite	opposite	ADJ
gi-4940	378	16	meridians	meridian	NOUN
gi-4940	378	17	m(λk	m(λk	NOUN
gi-4940	378	18	±	±	NUM
gi-4940	379	1	π	π	X
gi-4940	379	2	∓	∓	PROPN
gi-4940	379	3	ε	ε	PROPN
gi-4940	379	4	)	)	PUNCT
gi-4940	380	1	,	,	PUNCT
gi-4940	380	2	forλk	forλk	PROPN
gi-4940	380	3	≶	≶	PROPN
gi-4940	380	4	0	0	NUM
gi-4940	380	5	are	be	AUX
gi-4940	380	6	added	add	VERB
gi-4940	380	7	.	.	PUNCT
gi-4940	381	1	the	the	DET
gi-4940	381	2	procedure	procedure	NOUN
gi-4940	381	3	is	be	AUX
gi-4940	381	4	summarized	summarize	VERB
gi-4940	381	5	in	in	ADP
gi-4940	381	6	alg	alg	PROPN
gi-4940	381	7	.	.	PUNCT
gi-4940	382	1	2	2	X
gi-4940	382	2	.	.	X
gi-4940	382	3	generate	generate	NOUN
gi-4940	382	4	parallels	parallel	NOUN
gi-4940	382	5	.	.	PUNCT
gi-4940	383	1	the	the	DET
gi-4940	383	2	procedure	procedure	NOUN
gi-4940	383	3	generates	generate	VERB
gi-4940	383	4	all	all	DET
gi-4940	383	5	parallels	parallel	NOUN
gi-4940	383	6	inside	inside	ADP
gi-4940	383	7	the	the	DET
gi-4940	383	8	interval	interval	NOUN
gi-4940	383	9	ωj	ωj	ADP
gi-4940	383	10	=	=	SYM
gi-4940	383	11	ωϕ,j	ωϕ,j	SYM
gi-4940	383	12	×	×	PROPN
gi-4940	383	13	ωλ	ωλ	PROPN
gi-4940	383	14	,	,	PUNCT
gi-4940	383	15	j	j	PROPN
gi-4940	383	16	,	,	PUNCT
gi-4940	383	17	where	where	SCONJ
gi-4940	383	18	ωϕ,j	ωϕ,j	X
gi-4940	383	19	=	=	PUNCT
gi-4940	384	1	[	[	X
gi-4940	384	2	ϕ	ϕ	X
gi-4940	384	3	j	j	PROPN
gi-4940	384	4	,	,	PUNCT
gi-4940	384	5	ϕj	ϕj	ADP
gi-4940	384	6	]	]	X
gi-4940	384	7	,	,	PUNCT
gi-4940	384	8	ωλ	ωλ	PROPN
gi-4940	384	9	,	,	PUNCT
gi-4940	384	10	j	j	PROPN
gi-4940	385	1	=	=	PUNCT
gi-4940	386	1	[	[	X
gi-4940	386	2	λj	λj	X
gi-4940	386	3	,	,	PUNCT
gi-4940	386	4	λj	λj	PROPN
gi-4940	386	5	]	]	X
gi-4940	386	6	.	.	PUNCT
gi-4940	387	1	initially	initially	ADV
gi-4940	387	2	,	,	PUNCT
gi-4940	387	3	the	the	DET
gi-4940	387	4	bounding	bounding	NOUN
gi-4940	387	5	parallels	parallel	VERB
gi-4940	387	6	p(ϕ	p(ϕ	PROPN
gi-4940	387	7	j	j	PROPN
gi-4940	387	8	)	)	PUNCT
gi-4940	387	9	,	,	PUNCT
gi-4940	387	10	and	and	CCONJ
gi-4940	387	11	p(ϕj	p(ϕj	NOUN
gi-4940	387	12	)	)	PUNCT
gi-4940	387	13	are	be	AUX
gi-4940	387	14	created	create	VERB
gi-4940	387	15	.	.	PUNCT
gi-4940	388	1	the	the	DET
gi-4940	388	2	latitude	latitude	NOUN
gi-4940	388	3	ϕstart	ϕstart	NOUN
gi-4940	388	4	of	of	ADP
gi-4940	388	5	the	the	DET
gi-4940	388	6	first	first	ADJ
gi-4940	388	7	parallel	parallel	ADJ
gi-4940	388	8	p(ϕstart	p(ϕstart	NOUN
gi-4940	388	9	)	)	PUNCT
gi-4940	388	10	is	be	AUX
gi-4940	388	11	the	the	DET
gi-4940	388	12	smallest	small	ADJ
gi-4940	388	13	multiplier	multiplier	NOUN
gi-4940	388	14	of	of	ADP
gi-4940	388	15	∆ϕ	∆ϕ	NOUN
gi-4940	388	16	higher	high	ADJ
gi-4940	388	17	than	than	ADP
gi-4940	388	18	ϕ	ϕ	PROPN
gi-4940	388	19	j	j	PROPN
gi-4940	388	20	,	,	PUNCT
gi-4940	388	21	the	the	DET
gi-4940	388	22	last	last	ADJ
gi-4940	388	23	parallel	parallel	ADJ
gi-4940	388	24	p(ϕend	p(ϕend	NOUN
gi-4940	388	25	)	)	PUNCT
gi-4940	388	26	is	be	AUX
gi-4940	388	27	the	the	DET
gi-4940	388	28	largest	large	ADJ
gi-4940	388	29	multiplier	multiplier	NOUN
gi-4940	388	30	of	of	ADP
gi-4940	388	31	∆ϕ	∆ϕ	NOUN
gi-4940	388	32	lower	low	ADJ
gi-4940	388	33	than	than	ADP
gi-4940	388	34	ϕj	ϕj	PROPN
gi-4940	388	35	.	.	PUNCT
gi-4940	389	1	other	other	ADJ
gi-4940	389	2	parallels	parallel	VERB
gi-4940	389	3	p(ϕj	p(ϕj	NOUN
gi-4940	389	4	,	,	PUNCT
gi-4940	389	5	i	i	PRON
gi-4940	389	6	)	)	PUNCT
gi-4940	389	7	are	be	AUX
gi-4940	389	8	generated	generate	VERB
gi-4940	389	9	inside	inside	ADP
gi-4940	389	10	the	the	DET
gi-4940	389	11	interval	interval	NOUN
gi-4940	390	1	[	[	X
gi-4940	390	2	ϕstart	ϕstart	NOUN
gi-4940	390	3	,	,	PUNCT
gi-4940	390	4	ϕend	ϕend	VERB
gi-4940	390	5	]	]	X
gi-4940	390	6	so	so	SCONJ
gi-4940	390	7	that	that	SCONJ
gi-4940	390	8	ϕj	ϕj	ADP
gi-4940	390	9	=	=	SYM
gi-4940	390	10	ϕstart	ϕstart	NOUN
gi-4940	390	11	+	+	CCONJ
gi-4940	390	12	i∆ϕ	i∆ϕ	ADJ
gi-4940	390	13	,	,	PUNCT
gi-4940	390	14	ϕstart	ϕstart	NOUN
gi-4940	390	15	<	<	X
gi-4940	390	16	ϕ	ϕ	X
gi-4940	390	17	<	<	X
gi-4940	390	18	ϕend	ϕend	NOUN
gi-4940	390	19	.	.	PUNCT
gi-4940	391	1	if	if	SCONJ
gi-4940	391	2	a	a	DET
gi-4940	391	3	discontinuity	discontinuity	NOUN
gi-4940	391	4	at	at	ADP
gi-4940	391	5	c	c	NOUN
gi-4940	391	6	=	=	PUNCT
gi-4940	391	7	λj	λj	PROPN
gi-4940	391	8	is	be	AUX
gi-4940	391	9	found	find	VERB
gi-4940	391	10	,	,	PUNCT
gi-4940	391	11	the	the	DET
gi-4940	391	12	parallel	parallel	ADJ
gi-4940	391	13	needs	need	VERB
gi-4940	391	14	to	to	PART
gi-4940	391	15	be	be	AUX
gi-4940	391	16	split	split	VERB
gi-4940	391	17	at	at	ADP
gi-4940	391	18	c.	c.	PROPN
gi-4940	391	19	if	if	SCONJ
gi-4940	391	20	a	a	DET
gi-4940	391	21	discontinuity	discontinuity	NOUN
gi-4940	391	22	at	at	ADP
gi-4940	391	23	c	c	NOUN
gi-4940	391	24	=	=	PUNCT
gi-4940	391	25	ϕj	ϕj	PROPN
gi-4940	391	26	is	be	AUX
gi-4940	391	27	detected	detect	VERB
gi-4940	391	28	,	,	PUNCT
gi-4940	391	29	the	the	DET
gi-4940	391	30	parallel	parallel	ADJ
gi-4940	391	31	needs	need	NOUN
gi-4940	391	32	to	to	PART
gi-4940	391	33	be	be	AUX
gi-4940	391	34	shifted	shift	VERB
gi-4940	391	35	.	.	PUNCT
gi-4940	392	1	this	this	PRON
gi-4940	392	2	is	be	AUX
gi-4940	392	3	achieved	achieve	VERB
gi-4940	392	4	by	by	ADP
gi-4940	392	5	splitting	splitting	NOUN
gi-4940	392	6	ωj	ωj	ADP
gi-4940	392	7	at	at	ADP
gi-4940	392	8	c	c	NOUN
gi-4940	392	9	=	=	SYM
gi-4940	392	10	ϕj	ϕj	PROPN
gi-4940	392	11	,	,	PUNCT
gi-4940	392	12	or	or	CCONJ
gi-4940	392	13	,	,	PUNCT
gi-4940	392	14	at	at	ADP
gi-4940	392	15	c	c	X
gi-4940	392	16	=	=	SYM
gi-4940	392	17	λj	λj	PROPN
gi-4940	392	18	.	.	PUNCT
gi-4940	393	1	otherwise	otherwise	ADV
gi-4940	393	2	,	,	PUNCT
gi-4940	393	3	a	a	DET
gi-4940	393	4	current	current	ADJ
gi-4940	393	5	parallel	parallel	ADJ
gi-4940	393	6	p(ϕj	p(ϕj	NOUN
gi-4940	393	7	)	)	PUNCT
gi-4940	393	8	is	be	AUX
gi-4940	393	9	constructed	construct	VERB
gi-4940	393	10	.	.	PUNCT
gi-4940	394	1	the	the	DET
gi-4940	394	2	procedure	procedure	NOUN
gi-4940	394	3	is	be	AUX
gi-4940	394	4	summarized	summarize	VERB
gi-4940	394	5	in	in	ADP
gi-4940	394	6	alg	alg	PROPN
gi-4940	394	7	.	.	PUNCT
gi-4940	395	1	3	3	X
gi-4940	395	2	.	.	X
gi-4940	395	3	generate	generate	VERB
gi-4940	395	4	a	a	DET
gi-4940	395	5	meridian	meridian	NOUN
gi-4940	395	6	.	.	PUNCT
gi-4940	396	1	combined	combine	VERB
gi-4940	396	2	sampling	sampling	NOUN
gi-4940	396	3	provides	provide	VERB
gi-4940	396	4	a	a	DET
gi-4940	396	5	polynomial	polynomial	ADJ
gi-4940	396	6	approximation	approximation	NOUN
gi-4940	396	7	of	of	ADP
gi-4940	396	8	the	the	DET
gi-4940	396	9	meridianm(λ	meridianm(λ	NOUN
gi-4940	396	10	)	)	PUNCT
gi-4940	396	11	by	by	ADP
gi-4940	396	12	the	the	DET
gi-4940	396	13	refinement	refinement	NOUN
gi-4940	396	14	α	α	PROPN
gi-4940	396	15	and	and	CCONJ
gi-4940	396	16	the	the	DET
gi-4940	396	17	recursion	recursion	NOUN
gi-4940	396	18	depth	depth	NOUN
gi-4940	396	19	d	d	NOUN
gi-4940	396	20	over	over	ADP
gi-4940	396	21	the	the	DET
gi-4940	396	22	interval	interval	NOUN
gi-4940	396	23	ωϕ,j	ωϕ,j	PUNCT
gi-4940	396	24	=	=	PUNCT
gi-4940	397	1	[	[	X
gi-4940	397	2	ϕ	ϕ	X
gi-4940	397	3	j	j	PROPN
gi-4940	397	4	,	,	PUNCT
gi-4940	397	5	ϕj	ϕj	PROPN
gi-4940	397	6	]	]	PUNCT
gi-4940	397	7	.	.	PUNCT
gi-4940	398	1	geoinformatics	geoinformatic	NOUN
gi-4940	398	2	fce	fce	VERB
gi-4940	398	3	ctu	ctu	NOUN
gi-4940	398	4	17(2	17(2	NUM
gi-4940	398	5	)	)	PUNCT
gi-4940	398	6	,	,	PUNCT
gi-4940	398	7	2018	2018	NUM
gi-4940	398	8	43	43	NUM
gi-4940	398	9	t.	t.	NOUN
gi-4940	398	10	bayer	bayer	PROPN
gi-4940	398	11	:	:	PUNCT
gi-4940	398	12	plotting	plot	VERB
gi-4940	398	13	the	the	DET
gi-4940	398	14	map	map	NOUN
gi-4940	398	15	projection	projection	NOUN
gi-4940	398	16	graticule	graticule	NOUN
gi-4940	398	17	with	with	ADP
gi-4940	398	18	discontinuities	discontinuity	NOUN
gi-4940	398	19	algorithm	algorithm	NOUN
gi-4940	398	20	3	3	NUM
gi-4940	398	21	the	the	DET
gi-4940	398	22	construction	construction	NOUN
gi-4940	398	23	of	of	ADP
gi-4940	398	24	parallels	parallel	NOUN
gi-4940	398	25	.	.	PUNCT
gi-4940	399	1	1	1	NUM
gi-4940	399	2	:	:	PUNCT
gi-4940	399	3	function	function	NOUN
gi-4940	399	4	parallels(lλ	parallels(lλ	PROPN
gi-4940	399	5	,	,	PUNCT
gi-4940	399	6	j	j	PROPN
gi-4940	399	7	,	,	PUNCT
gi-4940	399	8	ωϕ,j	ωϕ,j	X
gi-4940	399	9	,	,	PUNCT
gi-4940	399	10	ωλ	ωλ	PROPN
gi-4940	399	11	,	,	PUNCT
gi-4940	399	12	j	j	PROPN
gi-4940	399	13	,	,	PUNCT
gi-4940	399	14	∆ϕ,p	∆ϕ,p	NOUN
gi-4940	399	15	,	,	PUNCT
gi-4940	399	16	d	d	NOUN
gi-4940	399	17	,	,	PUNCT
gi-4940	399	18	d	d	PROPN
gi-4940	399	19	,	,	PUNCT
gi-4940	399	20	ε	ε	PROPN
gi-4940	399	21	,	,	PUNCT
gi-4940	399	22	α	α	NOUN
gi-4940	399	23	)	)	PUNCT
gi-4940	399	24	2	2	NUM
gi-4940	399	25	:	:	PUNCT
gi-4940	399	26	ϕj	ϕj	VERB
gi-4940	399	27	,	,	PUNCT
gi-4940	399	28	start	start	VERB
gi-4940	399	29	=	=	PUNCT
gi-4940	399	30	∆ϕ[1	∆ϕ[1	ADJ
gi-4940	399	31	+	+	SYM
gi-4940	399	32	floor	floor	NOUN
gi-4940	399	33	(	(	PUNCT
gi-4940	399	34	ϕ	ϕ	PROPN
gi-4940	399	35	j	j	PROPN
gi-4940	399	36	,	,	PUNCT
gi-4940	399	37	∆ϕ	∆ϕ	PROPN
gi-4940	399	38	)	)	PUNCT
gi-4940	399	39	]	]	PUNCT
gi-4940	400	1	3	3	X
gi-4940	400	2	:	:	PUNCT
gi-4940	400	3	ϕj	ϕj	NOUN
gi-4940	400	4	,	,	PUNCT
gi-4940	400	5	end	end	NOUN
gi-4940	400	6	=	=	SYM
gi-4940	400	7	∆ϕ[ceil	∆ϕ[ceil	NOUN
gi-4940	400	8	(	(	PUNCT
gi-4940	400	9	ϕj	ϕj	ADP
gi-4940	400	10	∆ϕ)−	∆ϕ)−	PROPN
gi-4940	400	11	1	1	NUM
gi-4940	400	12	]	]	SYM
gi-4940	400	13	4	4	NUM
gi-4940	400	14	:	:	PUNCT
gi-4940	400	15	parallelpart(lϕ,j	parallelpart(lϕ,j	NOUN
gi-4940	400	16	,	,	PUNCT
gi-4940	400	17	ωϕ,j	ωϕ,j	X
gi-4940	400	18	,	,	PUNCT
gi-4940	400	19	ϕj	ϕj	INTJ
gi-4940	400	20	,	,	PUNCT
gi-4940	400	21	start	start	VERB
gi-4940	400	22	,	,	PUNCT
gi-4940	400	23	p	p	X
gi-4940	400	24	,	,	PUNCT
gi-4940	400	25	d	d	X
gi-4940	400	26	,	,	PUNCT
gi-4940	400	27	d	d	PROPN
gi-4940	400	28	,	,	PUNCT
gi-4940	400	29	ε	ε	PROPN
gi-4940	400	30	,	,	PUNCT
gi-4940	400	31	α	α	NOUN
gi-4940	400	32	)	)	PUNCT
gi-4940	400	33	5	5	NUM
gi-4940	400	34	:	:	PUNCT
gi-4940	400	35	for	for	ADP
gi-4940	400	36	(	(	PUNCT
gi-4940	400	37	ϕ	ϕ	NOUN
gi-4940	400	38	=	=	SYM
gi-4940	400	39	ϕj	ϕj	PROPN
gi-4940	400	40	,	,	PUNCT
gi-4940	400	41	start;ϕ	start;ϕ	NOUN
gi-4940	400	42	≤	≤	NUM
gi-4940	400	43	ϕj	ϕj	NOUN
gi-4940	400	44	,	,	PUNCT
gi-4940	400	45	end;ϕ	end;ϕ	PROPN
gi-4940	400	46	=	=	PRON
gi-4940	400	47	ϕ+	ϕ+	PUNCT
gi-4940	400	48	∆ϕ	∆ϕ	PROPN
gi-4940	400	49	)	)	PUNCT
gi-4940	400	50	do	do	VERB
gi-4940	400	51	6	6	NUM
gi-4940	400	52	:	:	PUNCT
gi-4940	400	53	parallelpart(lϕ,j	parallelpart(lϕ,j	PROPN
gi-4940	400	54	,	,	PUNCT
gi-4940	400	55	ωϕ,j	ωϕ,j	X
gi-4940	400	56	,	,	PUNCT
gi-4940	400	57	ϕ,p	ϕ,p	PROPN
gi-4940	400	58	,	,	PUNCT
gi-4940	400	59	d	d	NOUN
gi-4940	400	60	,	,	PUNCT
gi-4940	400	61	d	d	PROPN
gi-4940	400	62	,	,	PUNCT
gi-4940	400	63	ε	ε	PROPN
gi-4940	400	64	,	,	PUNCT
gi-4940	400	65	α	α	NOUN
gi-4940	400	66	)	)	PUNCT
gi-4940	400	67	7	7	NUM
gi-4940	400	68	:	:	PUNCT
gi-4940	400	69	parallelpart(lϕ,j	parallelpart(lϕ,j	NOUN
gi-4940	400	70	,	,	PUNCT
gi-4940	400	71	ωϕ,j	ωϕ,j	X
gi-4940	400	72	,	,	PUNCT
gi-4940	400	73	ϕj	ϕj	INTJ
gi-4940	400	74	,	,	PUNCT
gi-4940	400	75	end	end	NOUN
gi-4940	400	76	,	,	PUNCT
gi-4940	400	77	p	p	X
gi-4940	400	78	,	,	PUNCT
gi-4940	400	79	d	d	X
gi-4940	400	80	,	,	PUNCT
gi-4940	400	81	d	d	PROPN
gi-4940	400	82	,	,	PUNCT
gi-4940	400	83	ε	ε	PROPN
gi-4940	400	84	,	,	PUNCT
gi-4940	400	85	α	α	NOUN
gi-4940	400	86	)	)	PUNCT
gi-4940	400	87	suppose	suppose	VERB
gi-4940	400	88	m′(λ′0	m′(λ′0	PROPN
gi-4940	400	89	)	)	PUNCT
gi-4940	400	90	to	to	PART
gi-4940	400	91	be	be	AUX
gi-4940	400	92	the	the	DET
gi-4940	400	93	central	central	PROPN
gi-4940	400	94	meridian	meridian	PROPN
gi-4940	400	95	.	.	PUNCT
gi-4940	401	1	the	the	DET
gi-4940	401	2	polygonal	polygonal	ADJ
gi-4940	401	3	approximation	approximation	NOUN
gi-4940	401	4	consists	consist	VERB
gi-4940	401	5	of	of	ADP
gi-4940	401	6	two	two	NUM
gi-4940	401	7	steps	step	NOUN
gi-4940	401	8	:	:	PUNCT
gi-4940	402	1	1	1	X
gi-4940	402	2	.	.	PUNCT
gi-4940	402	3	the	the	DET
gi-4940	402	4	partition	partition	NOUN
gi-4940	402	5	of	of	ADP
gi-4940	402	6	m(λ	m(λ	PROPN
gi-4940	402	7	)	)	PUNCT
gi-4940	402	8	to	to	ADP
gi-4940	402	9	the	the	DET
gi-4940	402	10	fragments	fragment	NOUN
gi-4940	402	11	.	.	PUNCT
gi-4940	403	1	depending	depend	VERB
gi-4940	403	2	on	on	ADP
gi-4940	403	3	the	the	DET
gi-4940	403	4	position	position	NOUN
gi-4940	403	5	of	of	ADP
gi-4940	403	6	the	the	DET
gi-4940	403	7	pole	pole	NOUN
gi-4940	403	8	k	k	PROPN
gi-4940	404	1	=	=	PUNCT
gi-4940	405	1	[	[	X
gi-4940	405	2	ϕk	ϕk	X
gi-4940	405	3	,	,	PUNCT
gi-4940	405	4	λk	λk	X
gi-4940	405	5	]	]	PUNCT
gi-4940	405	6	and	and	CCONJ
gi-4940	405	7	the	the	DET
gi-4940	405	8	central	central	ADJ
gi-4940	405	9	meridian	meridian	PROPN
gi-4940	405	10	m′(λ′0	m′(λ′0	PROPN
gi-4940	405	11	)	)	PUNCT
gi-4940	405	12	,	,	PUNCT
gi-4940	405	13	the	the	DET
gi-4940	405	14	original	original	ADJ
gi-4940	405	15	interval	interval	NOUN
gi-4940	405	16	ωϕ,j	ωϕ,j	PUNCT
gi-4940	405	17	of	of	ADP
gi-4940	405	18	the	the	DET
gi-4940	405	19	meridian	meridian	PROPN
gi-4940	405	20	m(λ	m(λ	PROPN
gi-4940	405	21	)	)	PUNCT
gi-4940	405	22	needs	need	VERB
gi-4940	405	23	to	to	PART
gi-4940	405	24	be	be	AUX
gi-4940	405	25	split	split	VERB
gi-4940	405	26	along	along	ADP
gi-4940	405	27	the	the	DET
gi-4940	405	28	intersection	intersection	NOUN
gi-4940	405	29	point	point	NOUN
gi-4940	405	30	m3	m3	PROPN
gi-4940	405	31	=	=	PUNCT
gi-4940	406	1	[	[	X
gi-4940	406	2	ϕ3	ϕ3	NOUN
gi-4940	406	3	,	,	PUNCT
gi-4940	406	4	λ	λ	X
gi-4940	406	5	]	]	X
gi-4940	406	6	.	.	PUNCT
gi-4940	407	1	if	if	SCONJ
gi-4940	407	2	λ′0	λ′0	PROPN
gi-4940	407	3	=	=	SYM
gi-4940	407	4	0	0	PROPN
gi-4940	408	1	the	the	DET
gi-4940	408	2	meridians	meridian	NOUN
gi-4940	408	3	m′(0	m′(0	NOUN
gi-4940	408	4	)	)	PUNCT
gi-4940	408	5	and	and	CCONJ
gi-4940	408	6	m(λ	m(λ	PROPN
gi-4940	408	7	)	)	PUNCT
gi-4940	408	8	have	have	VERB
gi-4940	408	9	just	just	ADV
gi-4940	408	10	two	two	NUM
gi-4940	408	11	intersections	intersection	NOUN
gi-4940	408	12	m3	m3	NOUN
gi-4940	408	13	=	=	PUNCT
gi-4940	409	1	[	[	X
gi-4940	409	2	π/2	π/2	NUM
gi-4940	409	3	,	,	PUNCT
gi-4940	409	4	·	·	PUNCT
gi-4940	409	5	]	]	X
gi-4940	409	6	≡	≡	PROPN
gi-4940	409	7	a	a	X
gi-4940	409	8	,	,	PUNCT
gi-4940	409	9	m4	m4	PROPN
gi-4940	409	10	=	=	PUNCT
gi-4940	410	1	[	[	X
gi-4940	410	2	−π/2	−π/2	PROPN
gi-4940	410	3	,	,	PUNCT
gi-4940	410	4	·	·	PUNCT
gi-4940	410	5	]	]	PUNCT
gi-4940	410	6	≡	≡	PROPN
gi-4940	410	7	b	b	PROPN
gi-4940	410	8	at	at	ADP
gi-4940	410	9	poles	poles	PROPN
gi-4940	410	10	a	a	PRON
gi-4940	410	11	,	,	PUNCT
gi-4940	410	12	b	b	X
gi-4940	410	13	(	(	PUNCT
gi-4940	410	14	this	this	DET
gi-4940	410	15	case	case	NOUN
gi-4940	410	16	is	be	AUX
gi-4940	410	17	not	not	PART
gi-4940	410	18	important	important	ADJ
gi-4940	410	19	for	for	ADP
gi-4940	410	20	the	the	DET
gi-4940	410	21	algorithm	algorithm	NOUN
gi-4940	410	22	)	)	PUNCT
gi-4940	410	23	.	.	PUNCT
gi-4940	411	1	otherwise	otherwise	ADV
gi-4940	411	2	,	,	PUNCT
gi-4940	411	3	the	the	DET
gi-4940	411	4	solution	solution	NOUN
gi-4940	411	5	m3	m3	PROPN
gi-4940	411	6	=	=	PUNCT
gi-4940	412	1	[	[	X
gi-4940	412	2	ϕ3	ϕ3	NOUN
gi-4940	412	3	,	,	PUNCT
gi-4940	412	4	λ3	λ3	PROPN
gi-4940	412	5	]	]	PUNCT
gi-4940	412	6	found	find	VERB
gi-4940	412	7	from	from	ADP
gi-4940	412	8	the	the	DET
gi-4940	412	9	intersection	intersection	NOUN
gi-4940	412	10	of	of	ADP
gi-4940	412	11	two	two	NUM
gi-4940	412	12	planes	plane	NOUN
gi-4940	412	13	(	(	PUNCT
gi-4940	412	14	see	see	VERB
gi-4940	412	15	sec	sec	PROPN
gi-4940	412	16	.	.	PROPN
gi-4940	412	17	3.2	3.2	NUM
gi-4940	412	18	)	)	PUNCT
gi-4940	412	19	holds	hold	VERB
gi-4940	412	20	ϕ3	ϕ3	PROPN
gi-4940	412	21	∈	∈	PROPN
gi-4940	412	22	[	[	X
gi-4940	412	23	ϕ	ϕ	X
gi-4940	412	24	j	j	PROPN
gi-4940	412	25	+	+	CCONJ
gi-4940	412	26	ε	ε	PROPN
gi-4940	412	27	,	,	PUNCT
gi-4940	412	28	ϕj	ϕj	ADP
gi-4940	412	29	−	−	PUNCT
gi-4940	412	30	ε	ε	PROPN
gi-4940	412	31	]	]	X
gi-4940	412	32	∧	∧	PROPN
gi-4940	412	33	(	(	PUNCT
gi-4940	412	34	|λ3	|λ3	NOUN
gi-4940	412	35	−	−	PROPN
gi-4940	412	36	λ|	λ|	PROPN
gi-4940	412	37	<	<	X
gi-4940	412	38	ε	ε	PROPN
gi-4940	412	39	)	)	PUNCT
gi-4940	412	40	.	.	PUNCT
gi-4940	413	1	if	if	SCONJ
gi-4940	413	2	an	an	DET
gi-4940	413	3	intersection	intersection	NOUN
gi-4940	413	4	m3	m3	PROPN
gi-4940	413	5	is	be	AUX
gi-4940	413	6	found	find	VERB
gi-4940	413	7	,	,	PUNCT
gi-4940	413	8	the	the	DET
gi-4940	413	9	splitting	splitting	NOUN
gi-4940	413	10	procedure	procedure	NOUN
gi-4940	413	11	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	413	12	=	=	PUNCT
gi-4940	414	1	[	[	X
gi-4940	414	2	ϕ	ϕ	X
gi-4940	414	3	j	j	PROPN
gi-4940	414	4	,	,	PUNCT
gi-4940	414	5	ϕ3	ϕ3	PROPN
gi-4940	414	6	−	−	PROPN
gi-4940	414	7	ε	ε	PROPN
gi-4940	414	8	]	]	X
gi-4940	414	9	,	,	PUNCT
gi-4940	414	10	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	414	11	=	=	PUNCT
gi-4940	415	1	[	[	X
gi-4940	415	2	ϕ3	ϕ3	PROPN
gi-4940	415	3	+	+	CCONJ
gi-4940	415	4	ε	ε	PROPN
gi-4940	415	5	,	,	PUNCT
gi-4940	415	6	ϕj	ϕj	ADP
gi-4940	415	7	]	]	PUNCT
gi-4940	415	8	,	,	PUNCT
gi-4940	415	9	is	be	AUX
gi-4940	415	10	undertaken	undertake	VERB
gi-4940	415	11	;	;	PUNCT
gi-4940	415	12	see	see	VERB
gi-4940	415	13	fig	fig	NOUN
gi-4940	415	14	.	.	PUNCT
gi-4940	416	1	3.4	3.4	NUM
gi-4940	416	2	and	and	CCONJ
gi-4940	416	3	alg	alg	PROPN
gi-4940	416	4	.	.	PROPN
gi-4940	417	1	4	4	NUM
gi-4940	417	2	.	.	X
gi-4940	417	3	2	2	NUM
gi-4940	417	4	.	.	X
gi-4940	417	5	a	a	DET
gi-4940	417	6	combined	combine	VERB
gi-4940	417	7	sampling	sampling	NOUN
gi-4940	417	8	of	of	ADP
gi-4940	417	9	the	the	DET
gi-4940	417	10	fragments	fragment	NOUN
gi-4940	417	11	.	.	PUNCT
gi-4940	418	1	the	the	DET
gi-4940	418	2	sampling	sample	VERB
gi-4940	418	3	methods	method	NOUN
gi-4940	418	4	will	will	AUX
gi-4940	418	5	be	be	AUX
gi-4940	418	6	discussed	discuss	VERB
gi-4940	418	7	in	in	ADP
gi-4940	418	8	sec	sec	PROPN
gi-4940	418	9	.	.	PROPN
gi-4940	419	1	4.2	4.2	NUM
gi-4940	419	2	.	.	PUNCT
gi-4940	419	3	generate	generate	VERB
gi-4940	419	4	a	a	DET
gi-4940	419	5	parallel	parallel	NOUN
gi-4940	419	6	.	.	PUNCT
gi-4940	420	1	the	the	DET
gi-4940	420	2	parallel	parallel	ADJ
gi-4940	420	3	p(ϕ	p(ϕ	NOUN
gi-4940	420	4	)	)	PUNCT
gi-4940	420	5	is	be	AUX
gi-4940	420	6	intersected	intersect	VERB
gi-4940	420	7	by	by	ADP
gi-4940	420	8	the	the	DET
gi-4940	420	9	meridianm′(λ′0	meridianm′(λ′0	PROPN
gi-4940	420	10	)	)	PUNCT
gi-4940	420	11	in	in	ADP
gi-4940	420	12	at	at	ADP
gi-4940	420	13	most	most	ADV
gi-4940	420	14	two	two	NUM
gi-4940	420	15	points	point	NOUN
gi-4940	420	16	.	.	PUNCT
gi-4940	421	1	the	the	DET
gi-4940	421	2	original	original	ADJ
gi-4940	421	3	interval	interval	NOUN
gi-4940	421	4	ωλ	ωλ	VERB
gi-4940	421	5	,	,	PUNCT
gi-4940	421	6	j	j	PROPN
gi-4940	421	7	needs	need	VERB
gi-4940	421	8	to	to	PART
gi-4940	421	9	be	be	AUX
gi-4940	421	10	split	split	VERB
gi-4940	421	11	along	along	ADP
gi-4940	421	12	the	the	DET
gi-4940	421	13	intersection	intersection	NOUN
gi-4940	421	14	pointsm1	pointsm1	NOUN
gi-4940	421	15	=	=	PUNCT
gi-4940	422	1	[	[	X
gi-4940	422	2	ϕ1	ϕ1	NOUN
gi-4940	422	3	,	,	PUNCT
gi-4940	422	4	λ1	λ1	PROPN
gi-4940	422	5	]	]	PUNCT
gi-4940	422	6	,	,	PUNCT
gi-4940	422	7	m2	m2	PROPN
gi-4940	422	8	=	=	PUNCT
gi-4940	423	1	[	[	X
gi-4940	423	2	ϕ2	ϕ2	ADV
gi-4940	423	3	,	,	PUNCT
gi-4940	423	4	λ2	λ2	PROPN
gi-4940	423	5	]	]	PUNCT
gi-4940	423	6	;	;	PUNCT
gi-4940	423	7	the	the	DET
gi-4940	423	8	solution	solution	NOUN
gi-4940	423	9	is	be	AUX
gi-4940	423	10	found	find	VERB
gi-4940	423	11	from	from	ADP
gi-4940	423	12	the	the	DET
gi-4940	423	13	intersection	intersection	NOUN
gi-4940	423	14	of	of	ADP
gi-4940	423	15	two	two	NUM
gi-4940	423	16	planes	plane	NOUN
gi-4940	423	17	(	(	PUNCT
gi-4940	423	18	see	see	VERB
gi-4940	423	19	sec	sec	PROPN
gi-4940	423	20	.	.	PROPN
gi-4940	423	21	3.2	3.2	NUM
gi-4940	423	22	)	)	PUNCT
gi-4940	423	23	.	.	PUNCT
gi-4940	424	1	in	in	ADP
gi-4940	424	2	general	general	ADJ
gi-4940	424	3	,	,	PUNCT
gi-4940	424	4	the	the	DET
gi-4940	424	5	following	follow	VERB
gi-4940	424	6	cases	case	NOUN
gi-4940	424	7	are	be	AUX
gi-4940	424	8	solved	solve	VERB
gi-4940	424	9	:	:	PUNCT
gi-4940	424	10	•	•	ADP
gi-4940	424	11	if	if	SCONJ
gi-4940	424	12	m1	m1	PROPN
gi-4940	424	13	∈	∈	PROPN
gi-4940	424	14	ωλ	ωλ	VERB
gi-4940	424	15	,	,	PUNCT
gi-4940	424	16	j	j	PROPN
gi-4940	424	17	,	,	PUNCT
gi-4940	424	18	than	than	ADP
gi-4940	424	19	λ1	λ1	PROPN
gi-4940	424	20	∈	∈	PROPN
gi-4940	425	1	[	[	X
gi-4940	425	2	λj	λj	X
gi-4940	425	3	+	+	NUM
gi-4940	425	4	ε	ε	PROPN
gi-4940	425	5	,	,	PUNCT
gi-4940	425	6	λj	λj	PROPN
gi-4940	425	7	−	−	PROPN
gi-4940	425	8	ε	ε	PROPN
gi-4940	425	9	]	]	PUNCT
gi-4940	425	10	and	and	CCONJ
gi-4940	425	11	ωλ	ωλ	ADJ
gi-4940	425	12	,	,	PUNCT
gi-4940	425	13	j	j	PROPN
gi-4940	425	14	is	be	AUX
gi-4940	425	15	split	split	VERB
gi-4940	425	16	to	to	PART
gi-4940	425	17	ωλ	ωλ	VERB
gi-4940	425	18	,	,	PUNCT
gi-4940	425	19	j,1	j,1	X
gi-4940	425	20	=	=	PUNCT
gi-4940	426	1	[	[	X
gi-4940	426	2	λj	λj	X
gi-4940	426	3	,	,	PUNCT
gi-4940	426	4	λ1	λ1	PROPN
gi-4940	426	5	−	−	PROPN
gi-4940	426	6	ε	ε	PROPN
gi-4940	426	7	]	]	PUNCT
gi-4940	426	8	,	,	PUNCT
gi-4940	426	9	ωλ	ωλ	ADJ
gi-4940	426	10	,	,	PUNCT
gi-4940	426	11	j,2	j,2	NOUN
gi-4940	426	12	=	=	PUNCT
gi-4940	427	1	[	[	X
gi-4940	427	2	λ1	λ1	X
gi-4940	427	3	+	+	CCONJ
gi-4940	427	4	ε	ε	PROPN
gi-4940	427	5	,	,	PUNCT
gi-4940	427	6	λj	λj	X
gi-4940	427	7	]	]	X
gi-4940	427	8	.	.	PUNCT
gi-4940	428	1	•	•	INTJ
gi-4940	428	2	if	if	SCONJ
gi-4940	428	3	m2	m2	PROPN
gi-4940	428	4	∈	∈	PROPN
gi-4940	428	5	ωλ	ωλ	VERB
gi-4940	428	6	,	,	PUNCT
gi-4940	428	7	j	j	PROPN
gi-4940	428	8	,	,	PUNCT
gi-4940	428	9	than	than	ADP
gi-4940	428	10	λ2	λ2	PROPN
gi-4940	428	11	∈	∈	PROPN
gi-4940	429	1	[	[	X
gi-4940	429	2	λj	λj	X
gi-4940	429	3	+	+	NUM
gi-4940	429	4	ε	ε	PROPN
gi-4940	429	5	,	,	PUNCT
gi-4940	429	6	λj	λj	PROPN
gi-4940	429	7	−	−	PROPN
gi-4940	429	8	ε	ε	PROPN
gi-4940	429	9	]	]	PUNCT
gi-4940	429	10	and	and	CCONJ
gi-4940	429	11	ωλ	ωλ	ADJ
gi-4940	429	12	,	,	PUNCT
gi-4940	429	13	j	j	PROPN
gi-4940	429	14	is	be	AUX
gi-4940	429	15	split	split	VERB
gi-4940	429	16	to	to	PART
gi-4940	429	17	ωλ	ωλ	VERB
gi-4940	429	18	,	,	PUNCT
gi-4940	429	19	j,1	j,1	X
gi-4940	430	1	=	=	PUNCT
gi-4940	431	1	[	[	X
gi-4940	431	2	λj	λj	INTJ
gi-4940	431	3	,	,	PUNCT
gi-4940	431	4	λ2	λ2	PROPN
gi-4940	431	5	−	−	PROPN
gi-4940	431	6	ε	ε	PROPN
gi-4940	431	7	]	]	PUNCT
gi-4940	431	8	,	,	PUNCT
gi-4940	431	9	ωλ	ωλ	ADJ
gi-4940	431	10	,	,	PUNCT
gi-4940	431	11	j,2	j,2	NOUN
gi-4940	431	12	=	=	PUNCT
gi-4940	432	1	[	[	X
gi-4940	432	2	λ2	λ2	X
gi-4940	432	3	+	+	CCONJ
gi-4940	432	4	ε	ε	PROPN
gi-4940	432	5	,	,	PUNCT
gi-4940	432	6	λj	λj	X
gi-4940	432	7	]	]	X
gi-4940	432	8	.	.	PUNCT
gi-4940	433	1	•	•	INTJ
gi-4940	433	2	if	if	SCONJ
gi-4940	433	3	m1	m1	PROPN
gi-4940	433	4	∈	∈	PROPN
gi-4940	433	5	ωλ	ωλ	VERB
gi-4940	433	6	,	,	PUNCT
gi-4940	433	7	j	j	PROPN
gi-4940	433	8	∧m1	∧m1	PROPN
gi-4940	433	9	∈	∈	PROPN
gi-4940	433	10	ωλ	ωλ	VERB
gi-4940	433	11	,	,	PUNCT
gi-4940	433	12	j	j	PROPN
gi-4940	433	13	,	,	PUNCT
gi-4940	433	14	than	than	ADP
gi-4940	433	15	ωλ	ωλ	ADJ
gi-4940	433	16	,	,	PUNCT
gi-4940	433	17	j	j	PROPN
gi-4940	433	18	is	be	AUX
gi-4940	433	19	split	split	VERB
gi-4940	433	20	to	to	PART
gi-4940	433	21	ωλ	ωλ	VERB
gi-4940	433	22	,	,	PUNCT
gi-4940	433	23	j,1	j,1	X
gi-4940	433	24	=	=	PUNCT
gi-4940	434	1	[	[	X
gi-4940	434	2	λj	λj	X
gi-4940	434	3	,	,	PUNCT
gi-4940	434	4	λ1	λ1	PROPN
gi-4940	434	5	−	−	PROPN
gi-4940	434	6	ε	ε	PROPN
gi-4940	434	7	]	]	PUNCT
gi-4940	434	8	,	,	PUNCT
gi-4940	434	9	ωλ	ωλ	ADJ
gi-4940	434	10	,	,	PUNCT
gi-4940	434	11	j,2	j,2	NOUN
gi-4940	434	12	=	=	PUNCT
gi-4940	435	1	[	[	X
gi-4940	435	2	λ1	λ1	X
gi-4940	435	3	+	+	CCONJ
gi-4940	435	4	ε	ε	PROPN
gi-4940	435	5	,	,	PUNCT
gi-4940	435	6	λ2	λ2	PROPN
gi-4940	435	7	−	−	PROPN
gi-4940	435	8	ε	ε	PROPN
gi-4940	435	9	]	]	PUNCT
gi-4940	435	10	,	,	PUNCT
gi-4940	435	11	ωλ	ωλ	VERB
gi-4940	435	12	,	,	PUNCT
gi-4940	435	13	j,3	j,3	NOUN
gi-4940	435	14	=	=	PUNCT
gi-4940	436	1	[	[	X
gi-4940	436	2	λ2	λ2	X
gi-4940	436	3	+	+	CCONJ
gi-4940	436	4	ε	ε	PROPN
gi-4940	436	5	,	,	PUNCT
gi-4940	436	6	λj	λj	X
gi-4940	436	7	]	]	X
gi-4940	436	8	.	.	PUNCT
gi-4940	437	1	for	for	ADP
gi-4940	437	2	practical	practical	ADJ
gi-4940	437	3	computation	computation	NOUN
gi-4940	437	4	,	,	PUNCT
gi-4940	437	5	the	the	DET
gi-4940	437	6	coordinates	coordinate	NOUN
gi-4940	437	7	are	be	AUX
gi-4940	437	8	sorted	sort	VERB
gi-4940	437	9	so	so	SCONJ
gi-4940	437	10	that	that	SCONJ
gi-4940	437	11	λ1	λ1	ADJ
gi-4940	437	12	≤	≤	ADJ
gi-4940	437	13	λ2	λ2	NOUN
gi-4940	437	14	;	;	PUNCT
gi-4940	437	15	see	see	VERB
gi-4940	437	16	alg	alg	PROPN
gi-4940	437	17	.	.	PUNCT
gi-4940	438	1	5	5	NUM
gi-4940	438	2	.	.	X
gi-4940	438	3	geoinformatics	geoinformatic	NOUN
gi-4940	438	4	fce	fce	VERB
gi-4940	438	5	ctu	ctu	NOUN
gi-4940	438	6	17(2	17(2	NUM
gi-4940	438	7	)	)	PUNCT
gi-4940	438	8	,	,	PUNCT
gi-4940	438	9	2018	2018	NUM
gi-4940	438	10	44	44	NUM
gi-4940	438	11	t.	t.	NOUN
gi-4940	438	12	bayer	bayer	PROPN
gi-4940	438	13	:	:	PUNCT
gi-4940	438	14	plotting	plot	VERB
gi-4940	438	15	the	the	DET
gi-4940	438	16	map	map	NOUN
gi-4940	438	17	projection	projection	NOUN
gi-4940	438	18	graticule	graticule	NOUN
gi-4940	438	19	with	with	ADP
gi-4940	438	20	discontinuities	discontinuity	NOUN
gi-4940	438	21	algorithm	algorithm	NOUN
gi-4940	438	22	4	4	NUM
gi-4940	438	23	the	the	DET
gi-4940	438	24	construction	construction	NOUN
gi-4940	438	25	of	of	ADP
gi-4940	438	26	a	a	DET
gi-4940	438	27	meridian	meridian	NOUN
gi-4940	438	28	from	from	ADP
gi-4940	438	29	the	the	DET
gi-4940	438	30	fragments	fragment	NOUN
gi-4940	438	31	.	.	PUNCT
gi-4940	439	1	1	1	NUM
gi-4940	439	2	:	:	PUNCT
gi-4940	439	3	function	function	NOUN
gi-4940	439	4	meridianpart(lλ	meridianpart(lλ	PROPN
gi-4940	439	5	,	,	PUNCT
gi-4940	439	6	j	j	PROPN
gi-4940	439	7	,	,	PUNCT
gi-4940	439	8	k	k	PROPN
gi-4940	439	9	,	,	PUNCT
gi-4940	439	10	ωϕ,j	ωϕ,j	X
gi-4940	439	11	,	,	PUNCT
gi-4940	439	12	λ	λ	X
gi-4940	439	13	,	,	PUNCT
gi-4940	439	14	p	p	X
gi-4940	439	15	,	,	PUNCT
gi-4940	439	16	d	d	X
gi-4940	439	17	,	,	PUNCT
gi-4940	439	18	d	d	PROPN
gi-4940	439	19	,	,	PUNCT
gi-4940	439	20	ε	ε	PROPN
gi-4940	439	21	,	,	PUNCT
gi-4940	439	22	α	α	NOUN
gi-4940	439	23	)	)	PUNCT
gi-4940	439	24	2	2	NUM
gi-4940	439	25	:	:	PUNCT
gi-4940	439	26	〈	〈	PROPN
gi-4940	439	27	m1	m1	PROPN
gi-4940	439	28	3	3	NUM
gi-4940	439	29	,	,	PUNCT
gi-4940	439	30	m	m	PROPN
gi-4940	439	31	2	2	NUM
gi-4940	439	32	3	3	NUM
gi-4940	439	33	〉	〉	NOUN
gi-4940	439	34	=	=	PUNCT
gi-4940	439	35	m(λ)×m′(ϕ′	m(λ)×m′(ϕ′	X
gi-4940	439	36	,	,	PUNCT
gi-4940	439	37	λ′0	λ′0	PROPN
gi-4940	439	38	)	)	PUNCT
gi-4940	440	1	3	3	NUM
gi-4940	440	2	:	:	PUNCT
gi-4940	440	3	lλ	lλ	ADJ
gi-4940	440	4	,	,	PUNCT
gi-4940	440	5	j,1	j,1	PROPN
gi-4940	440	6	=	=	SYM
gi-4940	440	7	∅	∅	NOUN
gi-4940	440	8	,	,	PUNCT
gi-4940	440	9	lλ	lλ	NOUN
gi-4940	440	10	,	,	PUNCT
gi-4940	440	11	j,2	j,2	NOUN
gi-4940	440	12	=	=	SYM
gi-4940	440	13	∅	∅	NOUN
gi-4940	440	14	4	4	NUM
gi-4940	440	15	:	:	PUNCT
gi-4940	440	16	if	if	SCONJ
gi-4940	440	17	(	(	PUNCT
gi-4940	440	18	ϕ1	ϕ1	NOUN
gi-4940	440	19	3	3	NUM
gi-4940	440	20	>	>	X
gi-4940	440	21	ϕ	ϕ	PROPN
gi-4940	440	22	j	j	PROPN
gi-4940	440	23	+	+	CCONJ
gi-4940	440	24	ε	ε	PROPN
gi-4940	440	25	)	)	PUNCT
gi-4940	440	26	∧	∧	PROPN
gi-4940	440	27	(	(	PUNCT
gi-4940	440	28	ϕ1	ϕ1	PROPN
gi-4940	440	29	3	3	NUM
gi-4940	440	30	<	<	X
gi-4940	440	31	ϕj	ϕj	PROPN
gi-4940	440	32	−	−	PROPN
gi-4940	440	33	ε	ε	PROPN
gi-4940	440	34	)	)	PUNCT
gi-4940	440	35	∧	∧	PROPN
gi-4940	440	36	(	(	PUNCT
gi-4940	440	37	∣∣λ1	∣∣λ1	NOUN
gi-4940	440	38	3	3	NUM
gi-4940	440	39	−	−	NOUN
gi-4940	440	40	λ	λ	X
gi-4940	440	41	∣∣	∣∣	X
gi-4940	440	42	<	<	X
gi-4940	440	43	ε	ε	PROPN
gi-4940	440	44	)	)	PUNCT
gi-4940	440	45	then	then	ADV
gi-4940	440	46	5	5	NUM
gi-4940	440	47	:	:	PUNCT
gi-4940	440	48	ϕj,1	ϕj,1	NOUN
gi-4940	440	49	=	=	PUNCT
gi-4940	440	50	ϕ1	ϕ1	VERB
gi-4940	440	51	3	3	NUM
gi-4940	440	52	−	−	NOUN
gi-4940	440	53	ε	ε	PROPN
gi-4940	440	54	,	,	PUNCT
gi-4940	440	55	ϕj,2	ϕj,2	PROPN
gi-4940	440	56	=	=	PUNCT
gi-4940	440	57	ϕ1	ϕ1	NOUN
gi-4940	440	58	3	3	NUM
gi-4940	440	59	+	+	CCONJ
gi-4940	440	60	ε	ε	PROPN
gi-4940	440	61	6	6	NUM
gi-4940	440	62	:	:	PUNCT
gi-4940	440	63	csmerinit(p	csmerinit(p	PROPN
gi-4940	440	64	,	,	PUNCT
gi-4940	440	65	lλ	lλ	INTJ
gi-4940	440	66	,	,	PUNCT
gi-4940	440	67	j,1	j,1	PROPN
gi-4940	440	68	,	,	PUNCT
gi-4940	440	69	ϕj	ϕj	INTJ
gi-4940	440	70	,	,	PUNCT
gi-4940	440	71	ϕj,1	ϕj,1	PROPN
gi-4940	440	72	,	,	PUNCT
gi-4940	440	73	λ	λ	PROPN
gi-4940	440	74	,	,	PUNCT
gi-4940	440	75	d	d	NOUN
gi-4940	440	76	,	,	PUNCT
gi-4940	440	77	d	d	PROPN
gi-4940	440	78	,	,	PUNCT
gi-4940	440	79	ε	ε	PROPN
gi-4940	440	80	,	,	PUNCT
gi-4940	440	81	α	α	NOUN
gi-4940	440	82	)	)	PUNCT
gi-4940	440	83	7	7	NUM
gi-4940	440	84	:	:	PUNCT
gi-4940	440	85	lλ	lλ	PROPN
gi-4940	440	86	,	,	PUNCT
gi-4940	440	87	j	j	PROPN
gi-4940	440	88	←	←	PROPN
gi-4940	440	89	lλ	lλ	PROPN
gi-4940	440	90	,	,	PUNCT
gi-4940	440	91	j1	j1	PROPN
gi-4940	440	92	8	8	NUM
gi-4940	440	93	:	:	PUNCT
gi-4940	440	94	csmerinit(p	csmerinit(p	PROPN
gi-4940	440	95	,	,	PUNCT
gi-4940	440	96	lλ	lλ	NOUN
gi-4940	440	97	,	,	PUNCT
gi-4940	440	98	j,2	j,2	NOUN
gi-4940	440	99	,	,	PUNCT
gi-4940	440	100	ϕj,2	ϕj,2	PROPN
gi-4940	440	101	,	,	PUNCT
gi-4940	440	102	ϕj	ϕj	INTJ
gi-4940	440	103	,	,	PUNCT
gi-4940	440	104	λ	λ	PROPN
gi-4940	440	105	,	,	PUNCT
gi-4940	440	106	d	d	NOUN
gi-4940	440	107	,	,	PUNCT
gi-4940	440	108	d	d	PROPN
gi-4940	440	109	,	,	PUNCT
gi-4940	440	110	ε	ε	PROPN
gi-4940	440	111	,	,	PUNCT
gi-4940	440	112	α	α	NOUN
gi-4940	440	113	)	)	PUNCT
gi-4940	440	114	9	9	NUM
gi-4940	440	115	:	:	PUNCT
gi-4940	440	116	lλ	lλ	PROPN
gi-4940	440	117	,	,	PUNCT
gi-4940	440	118	j	j	PROPN
gi-4940	440	119	←	←	PROPN
gi-4940	440	120	lλ	lλ	PROPN
gi-4940	440	121	,	,	PUNCT
gi-4940	440	122	j2	j2	PROPN
gi-4940	440	123	10	10	NUM
gi-4940	440	124	:	:	PUNCT
gi-4940	440	125	else	else	ADV
gi-4940	440	126	if	if	SCONJ
gi-4940	440	127	(	(	PUNCT
gi-4940	440	128	ϕ2	ϕ2	ADV
gi-4940	440	129	3	3	NUM
gi-4940	440	130	>	>	X
gi-4940	440	131	ϕ	ϕ	PROPN
gi-4940	440	132	j	j	PROPN
gi-4940	440	133	+	+	CCONJ
gi-4940	440	134	ε	ε	PROPN
gi-4940	440	135	)	)	PUNCT
gi-4940	440	136	∧	∧	NOUN
gi-4940	440	137	(	(	PUNCT
gi-4940	440	138	ϕ2	ϕ2	ADV
gi-4940	440	139	3	3	NUM
gi-4940	440	140	<	<	X
gi-4940	440	141	ϕj	ϕj	PROPN
gi-4940	440	142	−	−	PROPN
gi-4940	440	143	ε	ε	PROPN
gi-4940	440	144	)	)	PUNCT
gi-4940	440	145	∧	∧	PROPN
gi-4940	440	146	(	(	PUNCT
gi-4940	440	147	∣∣λ2	∣∣λ2	ADJ
gi-4940	440	148	3	3	NUM
gi-4940	440	149	−	−	PROPN
gi-4940	440	150	λ	λ	X
gi-4940	440	151	∣∣	∣∣	X
gi-4940	440	152	<	<	X
gi-4940	440	153	ε	ε	PROPN
gi-4940	440	154	)	)	PUNCT
gi-4940	441	1	then	then	ADV
gi-4940	441	2	11	11	NUM
gi-4940	441	3	:	:	PUNCT
gi-4940	441	4	ϕj,1	ϕj,1	NOUN
gi-4940	441	5	=	=	PUNCT
gi-4940	442	1	ϕ2	ϕ2	ADV
gi-4940	442	2	3	3	NUM
gi-4940	442	3	−	−	NOUN
gi-4940	442	4	ε	ε	PROPN
gi-4940	442	5	,	,	PUNCT
gi-4940	442	6	ϕj,2	ϕj,2	PROPN
gi-4940	442	7	=	=	PUNCT
gi-4940	442	8	ϕ2	ϕ2	ADV
gi-4940	442	9	3	3	NUM
gi-4940	442	10	+	+	CCONJ
gi-4940	442	11	ε	ε	PROPN
gi-4940	442	12	12	12	NUM
gi-4940	442	13	:	:	PUNCT
gi-4940	442	14	csmerinit(p	csmerinit(p	PROPN
gi-4940	442	15	,	,	PUNCT
gi-4940	442	16	lλ	lλ	INTJ
gi-4940	442	17	,	,	PUNCT
gi-4940	442	18	j,1	j,1	PROPN
gi-4940	442	19	,	,	PUNCT
gi-4940	442	20	ϕj	ϕj	INTJ
gi-4940	442	21	,	,	PUNCT
gi-4940	442	22	ϕj,1	ϕj,1	PROPN
gi-4940	442	23	,	,	PUNCT
gi-4940	442	24	λ	λ	PROPN
gi-4940	442	25	,	,	PUNCT
gi-4940	442	26	d	d	NOUN
gi-4940	442	27	,	,	PUNCT
gi-4940	442	28	d	d	PROPN
gi-4940	442	29	,	,	PUNCT
gi-4940	442	30	ε	ε	PROPN
gi-4940	442	31	,	,	PUNCT
gi-4940	442	32	α	α	NOUN
gi-4940	442	33	)	)	PUNCT
gi-4940	442	34	13	13	NUM
gi-4940	442	35	:	:	PUNCT
gi-4940	442	36	lλ	lλ	PROPN
gi-4940	442	37	,	,	PUNCT
gi-4940	442	38	j	j	PROPN
gi-4940	442	39	←	←	PROPN
gi-4940	442	40	lλ	lλ	PROPN
gi-4940	442	41	,	,	PUNCT
gi-4940	442	42	j1	j1	PROPN
gi-4940	442	43	14	14	NUM
gi-4940	442	44	:	:	PUNCT
gi-4940	442	45	csmerinit(p	csmerinit(p	PROPN
gi-4940	442	46	,	,	PUNCT
gi-4940	442	47	lλ	lλ	NOUN
gi-4940	442	48	,	,	PUNCT
gi-4940	442	49	j,2	j,2	NOUN
gi-4940	442	50	,	,	PUNCT
gi-4940	442	51	ϕj,2	ϕj,2	PROPN
gi-4940	442	52	,	,	PUNCT
gi-4940	442	53	ϕj	ϕj	INTJ
gi-4940	442	54	,	,	PUNCT
gi-4940	442	55	λ	λ	PROPN
gi-4940	442	56	,	,	PUNCT
gi-4940	442	57	d	d	NOUN
gi-4940	442	58	,	,	PUNCT
gi-4940	442	59	d	d	PROPN
gi-4940	442	60	,	,	PUNCT
gi-4940	442	61	ε	ε	PROPN
gi-4940	442	62	,	,	PUNCT
gi-4940	442	63	α	α	NOUN
gi-4940	442	64	)	)	PUNCT
gi-4940	442	65	15	15	NUM
gi-4940	442	66	:	:	PUNCT
gi-4940	442	67	lλ	lλ	PROPN
gi-4940	442	68	,	,	PUNCT
gi-4940	442	69	j	j	PROPN
gi-4940	442	70	←	←	PROPN
gi-4940	442	71	lλ	lλ	PROPN
gi-4940	442	72	,	,	PUNCT
gi-4940	442	73	j2	j2	PROPN
gi-4940	442	74	4.2	4.2	NUM
gi-4940	442	75	.	.	PUNCT
gi-4940	443	1	combined	combined	ADJ
gi-4940	443	2	sampling	sampling	NOUN
gi-4940	443	3	of	of	ADP
gi-4940	443	4	meridian	meridian	NOUN
gi-4940	443	5	and	and	CCONJ
gi-4940	443	6	parallel	parallel	ADJ
gi-4940	443	7	fragments	fragment	NOUN
gi-4940	443	8	three	three	NUM
gi-4940	443	9	sampling	sample	VERB
gi-4940	443	10	techniques	technique	NOUN
gi-4940	443	11	denoted	denote	VERB
gi-4940	443	12	as	as	ADP
gi-4940	443	13	s1	s1	NOUN
gi-4940	443	14	,	,	PUNCT
gi-4940	443	15	s2	s2	PROPN
gi-4940	443	16	,	,	PUNCT
gi-4940	443	17	s3	s3	PROPN
gi-4940	443	18	representing	represent	VERB
gi-4940	443	19	a	a	DET
gi-4940	443	20	natural	natural	ADJ
gi-4940	443	21	extension	extension	NOUN
gi-4940	443	22	of	of	ADP
gi-4940	443	23	the	the	DET
gi-4940	443	24	sampling	sample	VERB
gi-4940	443	25	methods	method	NOUN
gi-4940	443	26	described	describe	VERB
gi-4940	443	27	in	in	ADP
gi-4940	443	28	[	[	X
gi-4940	443	29	5	5	NUM
gi-4940	443	30	]	]	PUNCT
gi-4940	443	31	will	will	AUX
gi-4940	443	32	be	be	AUX
gi-4940	443	33	illustrated	illustrate	VERB
gi-4940	443	34	on	on	ADP
gi-4940	443	35	the	the	DET
gi-4940	443	36	meridian	meridian	PROPN
gi-4940	443	37	/	/	SYM
gi-4940	443	38	parallel	parallel	NOUN
gi-4940	443	39	approximation	approximation	NOUN
gi-4940	443	40	.	.	PUNCT
gi-4940	444	1	sampling	sample	VERB
gi-4940	444	2	method	method	NOUN
gi-4940	444	3	s1	s1	NOUN
gi-4940	444	4	.	.	PUNCT
gi-4940	445	1	it	it	PRON
gi-4940	445	2	provides	provide	VERB
gi-4940	445	3	a	a	DET
gi-4940	445	4	polynomial	polynomial	ADJ
gi-4940	445	5	approximation	approximation	NOUN
gi-4940	445	6	of	of	ADP
gi-4940	445	7	the	the	DET
gi-4940	445	8	meridian	meridian	PROPN
gi-4940	445	9	m(λ	m(λ	PROPN
gi-4940	445	10	)	)	PUNCT
gi-4940	445	11	by	by	ADP
gi-4940	445	12	the	the	DET
gi-4940	445	13	refinement	refinement	NOUN
gi-4940	445	14	criteria	criterion	NOUN
gi-4940	445	15	α	α	PROPN
gi-4940	445	16	and	and	CCONJ
gi-4940	445	17	the	the	DET
gi-4940	445	18	recursion	recursion	NOUN
gi-4940	445	19	depth	depth	NOUN
gi-4940	445	20	d.	d.	NOUN
gi-4940	445	21	both	both	DET
gi-4940	445	22	ωϕ,j,1,ωϕ,j,2	ωϕ,j,1,ωϕ,j,2	PROPN
gi-4940	445	23	are	be	AUX
gi-4940	445	24	partitioned	partition	VERB
gi-4940	445	25	into	into	ADP
gi-4940	445	26	four	four	NUM
gi-4940	445	27	disjoint	disjoint	ADJ
gi-4940	445	28	subintervals	subinterval	NOUN
gi-4940	445	29	with	with	ADP
gi-4940	445	30	the	the	DET
gi-4940	445	31	randomly	randomly	ADV
gi-4940	445	32	shifting	shift	VERB
gi-4940	445	33	borders	border	NOUN
gi-4940	445	34	.	.	PUNCT
gi-4940	446	1	1	1	X
gi-4940	446	2	.	.	X
gi-4940	446	3	the	the	DET
gi-4940	446	4	initial	initial	ADJ
gi-4940	446	5	phase	phase	NOUN
gi-4940	446	6	let	let	VERB
gi-4940	446	7	lλ	lλ	PROPN
gi-4940	446	8	,	,	PUNCT
gi-4940	446	9	j	j	PROPN
gi-4940	446	10	,	,	PUNCT
gi-4940	446	11	k	k	NOUN
gi-4940	447	1	=	=	NOUN
gi-4940	447	2	∅	∅	NOUN
gi-4940	447	3	be	be	VERB
gi-4940	447	4	the	the	DET
gi-4940	447	5	empty	empty	ADJ
gi-4940	447	6	set	set	NOUN
gi-4940	447	7	.	.	PUNCT
gi-4940	448	1	compute	compute	NOUN
gi-4940	448	2	xa	xa	PROPN
gi-4940	449	1	=	=	PROPN
gi-4940	449	2	f	f	PROPN
gi-4940	449	3	(	(	PUNCT
gi-4940	449	4	a	a	PRON
gi-4940	449	5	,	,	PUNCT
gi-4940	449	6	λ	λ	NOUN
gi-4940	449	7	)	)	PUNCT
gi-4940	449	8	,	,	PUNCT
gi-4940	449	9	ya	ya	PROPN
gi-4940	449	10	=	=	SYM
gi-4940	449	11	g(a	g(a	PROPN
gi-4940	449	12	,	,	PUNCT
gi-4940	449	13	λ	λ	PROPN
gi-4940	449	14	)	)	PUNCT
gi-4940	449	15	and	and	CCONJ
gi-4940	449	16	xb	xb	X
gi-4940	449	17	=	=	SYM
gi-4940	449	18	f	f	PROPN
gi-4940	449	19	(	(	PUNCT
gi-4940	449	20	b	b	PROPN
gi-4940	449	21	,	,	PUNCT
gi-4940	449	22	λ	λ	NOUN
gi-4940	449	23	)	)	PUNCT
gi-4940	449	24	,	,	PUNCT
gi-4940	449	25	yb	yb	PROPN
gi-4940	449	26	=	=	SYM
gi-4940	449	27	g(b	g(b	PROPN
gi-4940	449	28	,	,	PUNCT
gi-4940	449	29	λ	λ	PROPN
gi-4940	449	30	)	)	PUNCT
gi-4940	449	31	,	,	PUNCT
gi-4940	449	32	where	where	SCONJ
gi-4940	449	33	pa	pa	PROPN
gi-4940	449	34	=	=	PROPN
gi-4940	450	1	[	[	X
gi-4940	450	2	xa	xa	PROPN
gi-4940	450	3	,	,	PUNCT
gi-4940	450	4	ya	ya	PROPN
gi-4940	450	5	]	]	PUNCT
gi-4940	450	6	and	and	CCONJ
gi-4940	450	7	pb	pb	ADP
gi-4940	450	8	=	=	PUNCT
gi-4940	451	1	[	[	X
gi-4940	451	2	xb	xb	X
gi-4940	451	3	,	,	PUNCT
gi-4940	451	4	yb	yb	PROPN
gi-4940	451	5	]	]	PUNCT
gi-4940	451	6	.	.	PUNCT
gi-4940	452	1	if	if	SCONJ
gi-4940	452	2	a	a	DET
gi-4940	452	3	singularity	singularity	NOUN
gi-4940	452	4	in	in	ADP
gi-4940	452	5	a	a	DET
gi-4940	452	6	or	or	CCONJ
gi-4940	452	7	b	b	NOUN
gi-4940	452	8	is	be	AUX
gi-4940	452	9	detected	detect	VERB
gi-4940	452	10	,	,	PUNCT
gi-4940	452	11	throw	throw	VERB
gi-4940	452	12	an	an	DET
gi-4940	452	13	exception	exception	NOUN
gi-4940	452	14	.	.	PUNCT
gi-4940	453	1	add	add	VERB
gi-4940	453	2	the	the	DET
gi-4940	453	3	initial	initial	ADJ
gi-4940	453	4	vertex	vertex	NOUN
gi-4940	453	5	to	to	ADP
gi-4940	453	6	lλ	lλ	VERB
gi-4940	453	7	,	,	PUNCT
gi-4940	453	8	j	j	PROPN
gi-4940	453	9	,	,	PUNCT
gi-4940	453	10	k	k	NOUN
gi-4940	453	11	:	:	PUNCT
gi-4940	453	12	lλ	lλ	PROPN
gi-4940	453	13	,	,	PUNCT
gi-4940	453	14	j	j	PROPN
gi-4940	453	15	,	,	PUNCT
gi-4940	453	16	k	k	PROPN
gi-4940	453	17	←	←	PROPN
gi-4940	453	18	pa	pa	PROPN
gi-4940	453	19	,	,	PUNCT
gi-4940	453	20	where	where	SCONJ
gi-4940	453	21	pa	pa	PROPN
gi-4940	453	22	=	=	SYM
gi-4940	453	23	(	(	PUNCT
gi-4940	453	24	xa	xa	PROPN
gi-4940	453	25	,	,	PUNCT
gi-4940	453	26	ya	ya	PROPN
gi-4940	453	27	)	)	PUNCT
gi-4940	453	28	.	.	PUNCT
gi-4940	454	1	set	set	VERB
gi-4940	454	2	the	the	DET
gi-4940	454	3	recursion	recursion	NOUN
gi-4940	454	4	depth	depth	NOUN
gi-4940	454	5	d	d	X
gi-4940	454	6	=	=	SYM
gi-4940	454	7	1	1	X
gi-4940	454	8	.	.	PUNCT
gi-4940	455	1	the	the	DET
gi-4940	455	2	procedure	procedure	NOUN
gi-4940	455	3	is	be	AUX
gi-4940	455	4	summarized	summarize	VERB
gi-4940	455	5	in	in	ADP
gi-4940	455	6	alg	alg	PROPN
gi-4940	455	7	.	.	PROPN
gi-4940	456	1	6	6	NUM
gi-4940	456	2	.	.	NOUN
gi-4940	456	3	2	2	NUM
gi-4940	456	4	.	.	X
gi-4940	457	1	the	the	DET
gi-4940	457	2	recursive	recursive	ADJ
gi-4940	457	3	procedure	procedure	NOUN
gi-4940	457	4	enter	enter	VERB
gi-4940	457	5	the	the	DET
gi-4940	457	6	recursive	recursive	ADJ
gi-4940	457	7	procedure	procedure	NOUN
gi-4940	457	8	and	and	CCONJ
gi-4940	457	9	do	do	VERB
gi-4940	457	10	the	the	DET
gi-4940	457	11	following	follow	VERB
gi-4940	457	12	substeps	substep	NOUN
gi-4940	457	13	:	:	PUNCT
gi-4940	457	14	(	(	PUNCT
gi-4940	457	15	a	a	X
gi-4940	457	16	)	)	PUNCT
gi-4940	457	17	if	if	SCONJ
gi-4940	457	18	d	d	PROPN
gi-4940	457	19	>	>	X
gi-4940	457	20	d	d	PROPN
gi-4940	457	21	or	or	CCONJ
gi-4940	457	22	b−	b−	PRON
gi-4940	457	23	a	a	DET
gi-4940	457	24	<	<	X
gi-4940	457	25	ε	ε	PROPN
gi-4940	457	26	,	,	PUNCT
gi-4940	457	27	stop	stop	VERB
gi-4940	457	28	the	the	DET
gi-4940	457	29	recursive	recursive	ADJ
gi-4940	457	30	procedure	procedure	NOUN
gi-4940	457	31	and	and	CCONJ
gi-4940	457	32	go	go	VERB
gi-4940	457	33	to	to	PART
gi-4940	457	34	step	step	VERB
gi-4940	457	35	3	3	NUM
gi-4940	457	36	.	.	PUNCT
gi-4940	458	1	(	(	PUNCT
gi-4940	458	2	b	b	X
gi-4940	458	3	)	)	PUNCT
gi-4940	458	4	for	for	ADP
gi-4940	458	5	a	a	DET
gi-4940	458	6	given	give	VERB
gi-4940	458	7	ωϕ,j	ωϕ,j	NOUN
gi-4940	458	8	,	,	PUNCT
gi-4940	458	9	k	k	PROPN
gi-4940	459	1	=	=	PUNCT
gi-4940	460	1	[	[	X
gi-4940	460	2	a	a	X
gi-4940	460	3	,	,	PUNCT
gi-4940	460	4	b	b	NOUN
gi-4940	460	5	]	]	X
gi-4940	460	6	,	,	PUNCT
gi-4940	460	7	the	the	DET
gi-4940	460	8	interval	interval	NOUN
gi-4940	460	9	is	be	AUX
gi-4940	460	10	split	split	VERB
gi-4940	460	11	by	by	ADP
gi-4940	460	12	three	three	NUM
gi-4940	460	13	points	point	NOUN
gi-4940	460	14	ϕ1	ϕ1	NOUN
gi-4940	460	15	=	=	SYM
gi-4940	460	16	a+	a+	PUNCT
gi-4940	460	17	1	1	NUM
gi-4940	460	18	2r1(b−	2r1(b−	NUM
gi-4940	460	19	a	a	NOUN
gi-4940	460	20	)	)	PUNCT
gi-4940	460	21	,	,	PUNCT
gi-4940	460	22	ϕ2	ϕ2	ADV
gi-4940	460	23	=	=	SYM
gi-4940	460	24	a+	a+	PUNCT
gi-4940	460	25	r2(b−	r2(b−	X
gi-4940	460	26	a	a	PRON
gi-4940	460	27	)	)	PUNCT
gi-4940	460	28	,	,	PUNCT
gi-4940	460	29	ϕ3	ϕ3	PROPN
gi-4940	460	30	=	=	SYM
gi-4940	460	31	a+	a+	PUNCT
gi-4940	460	32	3	3	NUM
gi-4940	460	33	2r3(b−	2r3(b−	NUM
gi-4940	460	34	a	a	NOUN
gi-4940	460	35	)	)	PUNCT
gi-4940	460	36	,	,	PUNCT
gi-4940	460	37	into	into	ADP
gi-4940	460	38	the	the	DET
gi-4940	460	39	approximate	approximate	ADJ
gi-4940	460	40	quarters	quarter	NOUN
gi-4940	460	41	ωϕ,j	ωϕ,j	X
gi-4940	460	42	,	,	PUNCT
gi-4940	460	43	k,1	k,1	PROPN
gi-4940	460	44	=	=	PUNCT
gi-4940	461	1	[	[	X
gi-4940	461	2	a	a	DET
gi-4940	461	3	,	,	PUNCT
gi-4940	461	4	ϕ1	ϕ1	NOUN
gi-4940	461	5	]	]	PUNCT
gi-4940	461	6	,	,	PUNCT
gi-4940	461	7	ωϕ,j	ωϕ,j	X
gi-4940	461	8	,	,	PUNCT
gi-4940	461	9	k,2	k,2	X
gi-4940	461	10	=	=	PUNCT
gi-4940	462	1	[	[	X
gi-4940	462	2	ϕ1	ϕ1	NOUN
gi-4940	462	3	,	,	PUNCT
gi-4940	462	4	ϕ2	ϕ2	ADV
gi-4940	462	5	]	]	PUNCT
gi-4940	462	6	ωϕ,j	ωϕ,j	X
gi-4940	462	7	,	,	PUNCT
gi-4940	462	8	k,3	k,3	X
gi-4940	462	9	=	=	PUNCT
gi-4940	463	1	[	[	X
gi-4940	463	2	ϕ2	ϕ2	ADV
gi-4940	463	3	,	,	PUNCT
gi-4940	463	4	ϕ3	ϕ3	PROPN
gi-4940	463	5	]	]	PUNCT
gi-4940	463	6	,	,	PUNCT
gi-4940	463	7	ωϕ,j	ωϕ,j	X
gi-4940	463	8	,	,	PUNCT
gi-4940	463	9	k,4	k,4	X
gi-4940	463	10	=	=	PUNCT
gi-4940	464	1	[	[	X
gi-4940	464	2	ϕ3	ϕ3	PROPN
gi-4940	464	3	,	,	PUNCT
gi-4940	464	4	b	b	NOUN
gi-4940	464	5	]	]	X
gi-4940	464	6	,	,	PUNCT
gi-4940	464	7	where	where	SCONJ
gi-4940	464	8	r1	r1	PROPN
gi-4940	464	9	,	,	PUNCT
gi-4940	464	10	r2	r2	PROPN
gi-4940	464	11	,	,	PUNCT
gi-4940	464	12	r3	r3	PROPN
gi-4940	464	13	are	be	AUX
gi-4940	464	14	the	the	DET
gi-4940	464	15	random	random	ADJ
gi-4940	464	16	numbers	number	NOUN
gi-4940	464	17	inside	inside	ADP
gi-4940	464	18	the	the	DET
gi-4940	464	19	interval	interval	NOUN
gi-4940	464	20	[	[	X
gi-4940	464	21	0.45	0.45	NUM
gi-4940	464	22	,	,	PUNCT
gi-4940	464	23	0.55	0.55	NUM
gi-4940	464	24	]	]	PUNCT
gi-4940	464	25	.	.	PUNCT
gi-4940	465	1	geoinformatics	geoinformatic	NOUN
gi-4940	465	2	fce	fce	VERB
gi-4940	465	3	ctu	ctu	NOUN
gi-4940	465	4	17(2	17(2	NUM
gi-4940	465	5	)	)	PUNCT
gi-4940	465	6	,	,	PUNCT
gi-4940	465	7	2018	2018	NUM
gi-4940	465	8	45	45	NUM
gi-4940	465	9	t.	t.	NOUN
gi-4940	465	10	bayer	bayer	NOUN
gi-4940	465	11	:	:	PUNCT
gi-4940	465	12	plotting	plot	VERB
gi-4940	465	13	the	the	DET
gi-4940	465	14	map	map	NOUN
gi-4940	465	15	projection	projection	NOUN
gi-4940	465	16	graticule	graticule	NOUN
gi-4940	465	17	with	with	ADP
gi-4940	465	18	discontinuities	discontinuity	NOUN
gi-4940	465	19	algorithm	algorithm	NOUN
gi-4940	465	20	5	5	NUM
gi-4940	465	21	the	the	DET
gi-4940	465	22	construction	construction	NOUN
gi-4940	465	23	of	of	ADP
gi-4940	465	24	a	a	DET
gi-4940	465	25	parallel	parallel	NOUN
gi-4940	465	26	from	from	ADP
gi-4940	465	27	the	the	DET
gi-4940	465	28	fragments	fragment	NOUN
gi-4940	465	29	.	.	PUNCT
gi-4940	466	1	1	1	NUM
gi-4940	466	2	:	:	PUNCT
gi-4940	466	3	function	function	NOUN
gi-4940	466	4	parallelpart(lϕ,j	parallelpart(lϕ,j	PROPN
gi-4940	466	5	,	,	PUNCT
gi-4940	466	6	k	k	PROPN
gi-4940	466	7	,	,	PUNCT
gi-4940	466	8	ωλ	ωλ	PROPN
gi-4940	466	9	,	,	PUNCT
gi-4940	466	10	j	j	PROPN
gi-4940	466	11	,	,	PUNCT
gi-4940	466	12	ϕ,p	ϕ,p	PROPN
gi-4940	466	13	,	,	PUNCT
gi-4940	466	14	d	d	NOUN
gi-4940	466	15	,	,	PUNCT
gi-4940	466	16	d	d	PROPN
gi-4940	466	17	,	,	PUNCT
gi-4940	466	18	ε	ε	PROPN
gi-4940	466	19	,	,	PUNCT
gi-4940	466	20	α	α	NOUN
gi-4940	466	21	)	)	PUNCT
gi-4940	466	22	2	2	NUM
gi-4940	466	23	:	:	PUNCT
gi-4940	466	24	〈	〈	PROPN
gi-4940	466	25	m1,m2	m1,m2	PROPN
gi-4940	466	26	〉	〉	PROPN
gi-4940	466	27	=	=	SYM
gi-4940	466	28	p(ϕ)×m′(ϕ′	p(ϕ)×m′(ϕ′	NUM
gi-4940	466	29	,	,	PUNCT
gi-4940	466	30	λ′0	λ′0	PROPN
gi-4940	466	31	)	)	PUNCT
gi-4940	466	32	3	3	NUM
gi-4940	466	33	:	:	PUNCT
gi-4940	466	34	lϕ,j,1	lϕ,j,1	PROPN
gi-4940	466	35	=	=	PUNCT
gi-4940	466	36	∅	∅	NOUN
gi-4940	466	37	,	,	PUNCT
gi-4940	466	38	lϕ,j,2	lϕ,j,2	PROPN
gi-4940	466	39	=	=	SYM
gi-4940	466	40	∅	∅	NOUN
gi-4940	466	41	,	,	PUNCT
gi-4940	466	42	lϕ,j,3	lϕ,j,3	PROPN
gi-4940	466	43	=	=	SYM
gi-4940	466	44	∅	∅	NOUN
gi-4940	466	45	4	4	NUM
gi-4940	466	46	:	:	PUNCT
gi-4940	466	47	if	if	SCONJ
gi-4940	466	48	(	(	PUNCT
gi-4940	466	49	λ1	λ1	INTJ
gi-4940	466	50	>	>	X
gi-4940	466	51	λj	λj	PROPN
gi-4940	466	52	+	+	CCONJ
gi-4940	466	53	ε	ε	PROPN
gi-4940	466	54	)	)	PUNCT
gi-4940	466	55	∧	∧	PROPN
gi-4940	466	56	(	(	PUNCT
gi-4940	466	57	λ1	λ1	X
gi-4940	466	58	<	<	X
gi-4940	466	59	λj	λj	X
gi-4940	466	60	−	−	PUNCT
gi-4940	466	61	ε	ε	PROPN
gi-4940	466	62	)	)	PUNCT
gi-4940	466	63	∧	∧	PROPN
gi-4940	466	64	(	(	PUNCT
gi-4940	466	65	λ2	λ2	X
gi-4940	466	66	>	>	X
gi-4940	466	67	λj	λj	PROPN
gi-4940	466	68	+	+	CCONJ
gi-4940	466	69	ε	ε	PROPN
gi-4940	466	70	)	)	PUNCT
gi-4940	466	71	∧	∧	PROPN
gi-4940	466	72	(	(	PUNCT
gi-4940	466	73	λ2	λ2	NOUN
gi-4940	466	74	<	<	X
gi-4940	466	75	λj	λj	X
gi-4940	466	76	−	−	PROPN
gi-4940	466	77	ε	ε	PROPN
gi-4940	466	78	)	)	PUNCT
gi-4940	466	79	then	then	ADV
gi-4940	466	80	5	5	NUM
gi-4940	466	81	:	:	PUNCT
gi-4940	466	82	λ1,2	λ1,2	PROPN
gi-4940	466	83	=	=	SYM
gi-4940	466	84	min(λ1	min(λ1	PROPN
gi-4940	466	85	,	,	PUNCT
gi-4940	466	86	λ2	λ2	PROPN
gi-4940	466	87	)	)	PUNCT
gi-4940	466	88	,	,	PUNCT
gi-4940	467	1	λ1,2	λ1,2	PROPN
gi-4940	467	2	=	=	SYM
gi-4940	467	3	max(λ1	max(λ1	NOUN
gi-4940	467	4	,	,	PUNCT
gi-4940	467	5	λ2	λ2	NOUN
gi-4940	467	6	)	)	PUNCT
gi-4940	467	7	6	6	NUM
gi-4940	467	8	:	:	PUNCT
gi-4940	467	9	λj,1	λj,1	PROPN
gi-4940	467	10	=	=	PUNCT
gi-4940	467	11	λ1,2	λ1,2	ADJ
gi-4940	467	12	−	−	PROPN
gi-4940	467	13	ε	ε	PROPN
gi-4940	467	14	,	,	PUNCT
gi-4940	467	15	λj,2	λj,2	PROPN
gi-4940	467	16	=	=	SYM
gi-4940	468	1	λ1,2	λ1,2	PROPN
gi-4940	468	2	+	+	CCONJ
gi-4940	468	3	ε	ε	PROPN
gi-4940	468	4	,	,	PUNCT
gi-4940	468	5	λj,2	λj,2	PROPN
gi-4940	468	6	=	=	PUNCT
gi-4940	469	1	λ1,2	λ1,2	ADJ
gi-4940	469	2	−	−	PROPN
gi-4940	469	3	ε	ε	PROPN
gi-4940	469	4	,	,	PUNCT
gi-4940	469	5	λj,2	λj,2	PROPN
gi-4940	469	6	=	=	SYM
gi-4940	470	1	λ1,2	λ1,2	PROPN
gi-4940	470	2	+	+	CCONJ
gi-4940	470	3	ε	ε	PROPN
gi-4940	470	4	7	7	NUM
gi-4940	470	5	:	:	PUNCT
gi-4940	470	6	csparinit(p	csparinit(p	NOUN
gi-4940	470	7	,	,	PUNCT
gi-4940	470	8	lϕ,j,1	lϕ,j,1	PROPN
gi-4940	470	9	,	,	PUNCT
gi-4940	470	10	λj	λj	INTJ
gi-4940	470	11	,	,	PUNCT
gi-4940	470	12	λj,1	λj,1	PROPN
gi-4940	470	13	,	,	PUNCT
gi-4940	470	14	ϕ	ϕ	NOUN
gi-4940	470	15	,	,	PUNCT
gi-4940	470	16	d	d	NOUN
gi-4940	470	17	,	,	PUNCT
gi-4940	470	18	d	d	PROPN
gi-4940	470	19	,	,	PUNCT
gi-4940	470	20	ε	ε	PROPN
gi-4940	470	21	,	,	PUNCT
gi-4940	470	22	α	α	NOUN
gi-4940	470	23	)	)	PUNCT
gi-4940	470	24	8	8	NUM
gi-4940	470	25	:	:	PUNCT
gi-4940	470	26	lϕ,j	lϕ,j	PUNCT
gi-4940	470	27	←	←	PROPN
gi-4940	470	28	lϕ,j1	lϕ,j1	PROPN
gi-4940	470	29	9	9	NUM
gi-4940	470	30	:	:	PUNCT
gi-4940	470	31	csparinit(p	csparinit(p	NOUN
gi-4940	470	32	,	,	PUNCT
gi-4940	470	33	lϕ,j,2	lϕ,j,2	PROPN
gi-4940	470	34	,	,	PUNCT
gi-4940	470	35	λj,2	λj,2	NOUN
gi-4940	470	36	,	,	PUNCT
gi-4940	470	37	λj,2	λj,2	PROPN
gi-4940	470	38	,	,	PUNCT
gi-4940	470	39	ϕ	ϕ	NOUN
gi-4940	470	40	,	,	PUNCT
gi-4940	470	41	d	d	NOUN
gi-4940	470	42	,	,	PUNCT
gi-4940	470	43	d	d	PROPN
gi-4940	470	44	,	,	PUNCT
gi-4940	470	45	ε	ε	PROPN
gi-4940	470	46	,	,	PUNCT
gi-4940	470	47	α	α	NOUN
gi-4940	470	48	)	)	PUNCT
gi-4940	470	49	10	10	NUM
gi-4940	470	50	:	:	PUNCT
gi-4940	470	51	lϕ,j	lϕ,j	X
gi-4940	470	52	←	←	PROPN
gi-4940	470	53	lϕ,j2	lϕ,j2	PROPN
gi-4940	470	54	11	11	NUM
gi-4940	470	55	:	:	PUNCT
gi-4940	470	56	csparinit(p	csparinit(p	NOUN
gi-4940	470	57	,	,	PUNCT
gi-4940	470	58	lϕ,j,3	lϕ,j,3	PROPN
gi-4940	470	59	,	,	PUNCT
gi-4940	470	60	λj,3	λj,3	PROPN
gi-4940	470	61	,	,	PUNCT
gi-4940	470	62	λj	λj	PROPN
gi-4940	470	63	,	,	PUNCT
gi-4940	470	64	ϕ	ϕ	PROPN
gi-4940	470	65	,	,	PUNCT
gi-4940	470	66	d	d	NOUN
gi-4940	470	67	,	,	PUNCT
gi-4940	470	68	d	d	PROPN
gi-4940	470	69	,	,	PUNCT
gi-4940	470	70	ε	ε	PROPN
gi-4940	470	71	,	,	PUNCT
gi-4940	470	72	α	α	NOUN
gi-4940	470	73	)	)	PUNCT
gi-4940	470	74	12	12	NUM
gi-4940	470	75	:	:	PUNCT
gi-4940	470	76	lϕ,j	lϕ,j	PUNCT
gi-4940	470	77	←	←	PROPN
gi-4940	470	78	lϕ,j3	lϕ,j3	PROPN
gi-4940	470	79	13	13	NUM
gi-4940	470	80	:	:	PUNCT
gi-4940	470	81	else	else	ADV
gi-4940	471	1	if	if	SCONJ
gi-4940	471	2	(	(	PUNCT
gi-4940	471	3	λ1	λ1	INTJ
gi-4940	471	4	>	>	X
gi-4940	471	5	λj	λj	PROPN
gi-4940	471	6	+	+	CCONJ
gi-4940	471	7	ε	ε	PROPN
gi-4940	471	8	)	)	PUNCT
gi-4940	471	9	∧	∧	PROPN
gi-4940	471	10	(	(	PUNCT
gi-4940	471	11	λ1	λ1	X
gi-4940	471	12	<	<	X
gi-4940	471	13	λj	λj	X
gi-4940	471	14	−	−	PROPN
gi-4940	471	15	ε	ε	PROPN
gi-4940	471	16	)	)	PUNCT
gi-4940	471	17	then	then	ADV
gi-4940	471	18	14	14	NUM
gi-4940	471	19	:	:	PUNCT
gi-4940	471	20	λj,1	λj,1	PROPN
gi-4940	471	21	=	=	PROPN
gi-4940	471	22	λ1	λ1	PROPN
gi-4940	471	23	−	−	PROPN
gi-4940	471	24	ε	ε	PROPN
gi-4940	471	25	,	,	PUNCT
gi-4940	471	26	λj,2	λj,2	PROPN
gi-4940	471	27	=	=	SYM
gi-4940	471	28	λ1	λ1	PROPN
gi-4940	471	29	+	+	CCONJ
gi-4940	471	30	ε	ε	PROPN
gi-4940	471	31	15	15	NUM
gi-4940	471	32	:	:	PUNCT
gi-4940	471	33	csparinit(p	csparinit(p	NOUN
gi-4940	471	34	,	,	PUNCT
gi-4940	471	35	lϕ,j,1	lϕ,j,1	PROPN
gi-4940	471	36	,	,	PUNCT
gi-4940	471	37	λj	λj	INTJ
gi-4940	471	38	,	,	PUNCT
gi-4940	471	39	λj,1	λj,1	PROPN
gi-4940	471	40	,	,	PUNCT
gi-4940	471	41	ϕ	ϕ	NOUN
gi-4940	471	42	,	,	PUNCT
gi-4940	471	43	d	d	NOUN
gi-4940	471	44	,	,	PUNCT
gi-4940	471	45	d	d	PROPN
gi-4940	471	46	,	,	PUNCT
gi-4940	471	47	ε	ε	PROPN
gi-4940	471	48	,	,	PUNCT
gi-4940	471	49	α	α	NOUN
gi-4940	471	50	)	)	PUNCT
gi-4940	471	51	16	16	NUM
gi-4940	471	52	:	:	PUNCT
gi-4940	471	53	lϕ,j	lϕ,j	PUNCT
gi-4940	471	54	←	←	PROPN
gi-4940	471	55	lϕ,j1	lϕ,j1	PROPN
gi-4940	471	56	17	17	NUM
gi-4940	471	57	:	:	PUNCT
gi-4940	471	58	csparinit(p	csparinit(p	NOUN
gi-4940	471	59	,	,	PUNCT
gi-4940	471	60	lϕ,j,2	lϕ,j,2	PROPN
gi-4940	471	61	,	,	PUNCT
gi-4940	471	62	λj2	λj2	INTJ
gi-4940	471	63	,	,	PUNCT
gi-4940	471	64	λj	λj	PROPN
gi-4940	471	65	,	,	PUNCT
gi-4940	471	66	ϕ	ϕ	PROPN
gi-4940	471	67	,	,	PUNCT
gi-4940	471	68	d	d	NOUN
gi-4940	471	69	,	,	PUNCT
gi-4940	471	70	d	d	PROPN
gi-4940	471	71	,	,	PUNCT
gi-4940	471	72	ε	ε	PROPN
gi-4940	471	73	,	,	PUNCT
gi-4940	471	74	α	α	NOUN
gi-4940	471	75	)	)	PUNCT
gi-4940	471	76	18	18	NUM
gi-4940	471	77	:	:	PUNCT
gi-4940	471	78	lϕ,j	lϕ,j	X
gi-4940	471	79	←	←	PROPN
gi-4940	471	80	lϕ,j2	lϕ,j2	PROPN
gi-4940	471	81	19	19	NUM
gi-4940	471	82	:	:	PUNCT
gi-4940	471	83	else	else	ADV
gi-4940	471	84	if	if	SCONJ
gi-4940	471	85	(	(	PUNCT
gi-4940	471	86	λ2	λ2	NOUN
gi-4940	471	87	>	>	X
gi-4940	471	88	λj	λj	PROPN
gi-4940	471	89	+	+	CCONJ
gi-4940	471	90	ε	ε	PROPN
gi-4940	471	91	)	)	PUNCT
gi-4940	471	92	∧	∧	PROPN
gi-4940	471	93	(	(	PUNCT
gi-4940	471	94	λ2	λ2	NOUN
gi-4940	471	95	<	<	X
gi-4940	471	96	λj	λj	X
gi-4940	471	97	−	−	PROPN
gi-4940	471	98	ε	ε	PROPN
gi-4940	471	99	)	)	PUNCT
gi-4940	471	100	then	then	ADV
gi-4940	471	101	20	20	NUM
gi-4940	471	102	:	:	PUNCT
gi-4940	471	103	λj,1	λj,1	PROPN
gi-4940	471	104	=	=	SYM
gi-4940	471	105	λ2	λ2	PROPN
gi-4940	471	106	−	−	PROPN
gi-4940	471	107	ε	ε	PROPN
gi-4940	471	108	,	,	PUNCT
gi-4940	471	109	λj,2	λj,2	PROPN
gi-4940	471	110	=	=	SYM
gi-4940	472	1	λ2	λ2	PROPN
gi-4940	472	2	+	+	CCONJ
gi-4940	472	3	ε	ε	PROPN
gi-4940	472	4	21	21	NUM
gi-4940	472	5	:	:	PUNCT
gi-4940	472	6	csparinit(p	csparinit(p	NOUN
gi-4940	472	7	,	,	PUNCT
gi-4940	472	8	lϕ,j,1	lϕ,j,1	PROPN
gi-4940	472	9	,	,	PUNCT
gi-4940	472	10	λj	λj	INTJ
gi-4940	472	11	,	,	PUNCT
gi-4940	472	12	λj,1	λj,1	PROPN
gi-4940	472	13	,	,	PUNCT
gi-4940	472	14	ϕ	ϕ	NOUN
gi-4940	472	15	,	,	PUNCT
gi-4940	472	16	d	d	NOUN
gi-4940	472	17	,	,	PUNCT
gi-4940	472	18	d	d	PROPN
gi-4940	472	19	,	,	PUNCT
gi-4940	472	20	ε	ε	PROPN
gi-4940	472	21	,	,	PUNCT
gi-4940	472	22	α	α	NOUN
gi-4940	472	23	)	)	PUNCT
gi-4940	472	24	22	22	NUM
gi-4940	472	25	:	:	PUNCT
gi-4940	472	26	lϕ,j	lϕ,j	PUNCT
gi-4940	472	27	←	←	PROPN
gi-4940	472	28	lϕ,j1	lϕ,j1	PROPN
gi-4940	472	29	23	23	NUM
gi-4940	472	30	:	:	PUNCT
gi-4940	472	31	csparinit(p	csparinit(p	NOUN
gi-4940	472	32	,	,	PUNCT
gi-4940	472	33	lϕ,j,2	lϕ,j,2	PROPN
gi-4940	472	34	,	,	PUNCT
gi-4940	472	35	λj2	λj2	INTJ
gi-4940	472	36	,	,	PUNCT
gi-4940	472	37	λj	λj	PROPN
gi-4940	472	38	,	,	PUNCT
gi-4940	472	39	ϕ	ϕ	PROPN
gi-4940	472	40	,	,	PUNCT
gi-4940	472	41	d	d	NOUN
gi-4940	472	42	,	,	PUNCT
gi-4940	472	43	d	d	PROPN
gi-4940	472	44	,	,	PUNCT
gi-4940	472	45	ε	ε	PROPN
gi-4940	472	46	,	,	PUNCT
gi-4940	472	47	α	α	NOUN
gi-4940	472	48	)	)	PUNCT
gi-4940	472	49	24	24	NUM
gi-4940	472	50	:	:	PUNCT
gi-4940	472	51	lϕ,j	lϕ,j	X
gi-4940	472	52	←	←	PROPN
gi-4940	472	53	lϕ,j2	lϕ,j2	PROPN
gi-4940	472	54	(	(	PUNCT
gi-4940	472	55	c	c	X
gi-4940	472	56	)	)	PUNCT
gi-4940	472	57	if	if	SCONJ
gi-4940	472	58	a	a	DET
gi-4940	472	59	singularity	singularity	NOUN
gi-4940	472	60	in	in	ADP
gi-4940	472	61	[	[	X
gi-4940	472	62	ϕ1	ϕ1	NOUN
gi-4940	472	63	,	,	PUNCT
gi-4940	472	64	λ	λ	X
gi-4940	472	65	]	]	X
gi-4940	472	66	,	,	PUNCT
gi-4940	473	1	[	[	X
gi-4940	473	2	ϕ2	ϕ2	ADV
gi-4940	473	3	,	,	PUNCT
gi-4940	473	4	λ	λ	NOUN
gi-4940	473	5	]	]	X
gi-4940	473	6	,	,	PUNCT
gi-4940	473	7	or	or	CCONJ
gi-4940	473	8	[	[	X
gi-4940	473	9	ϕ3	ϕ3	NOUN
gi-4940	473	10	,	,	PUNCT
gi-4940	473	11	λ	λ	X
gi-4940	473	12	]	]	X
gi-4940	473	13	occurs	occur	VERB
gi-4940	473	14	,	,	PUNCT
gi-4940	473	15	throw	throw	VERB
gi-4940	473	16	a	a	DET
gi-4940	473	17	new	new	ADJ
gi-4940	473	18	exception	exception	NOUN
gi-4940	473	19	according	accord	VERB
gi-4940	473	20	to	to	ADP
gi-4940	473	21	the	the	DET
gi-4940	473	22	discontinuity	discontinuity	NOUN
gi-4940	473	23	direction	direction	NOUN
gi-4940	473	24	.	.	PUNCT
gi-4940	474	1	(	(	PUNCT
gi-4940	474	2	d	d	X
gi-4940	474	3	)	)	PUNCT
gi-4940	474	4	otherwise	otherwise	ADV
gi-4940	474	5	,	,	PUNCT
gi-4940	474	6	evaluate	evaluate	VERB
gi-4940	474	7	the	the	DET
gi-4940	474	8	function	function	NOUN
gi-4940	474	9	values	value	NOUN
gi-4940	475	1	x1	x1	NOUN
gi-4940	475	2	=	=	SYM
gi-4940	475	3	f	f	PROPN
gi-4940	475	4	(	(	PUNCT
gi-4940	475	5	ϕ1	ϕ1	PROPN
gi-4940	475	6	,	,	PUNCT
gi-4940	475	7	λ	λ	NOUN
gi-4940	475	8	)	)	PUNCT
gi-4940	475	9	,	,	PUNCT
gi-4940	475	10	y1	y1	NOUN
gi-4940	475	11	=	=	PUNCT
gi-4940	475	12	g(ϕ1	g(ϕ1	NOUN
gi-4940	475	13	,	,	PUNCT
gi-4940	475	14	λ	λ	NOUN
gi-4940	475	15	)	)	PUNCT
gi-4940	475	16	,	,	PUNCT
gi-4940	475	17	x2	x2	PROPN
gi-4940	476	1	=	=	SYM
gi-4940	476	2	f	f	PROPN
gi-4940	476	3	(	(	PUNCT
gi-4940	476	4	ϕ2	ϕ2	ADV
gi-4940	476	5	,	,	PUNCT
gi-4940	476	6	λ	λ	NOUN
gi-4940	476	7	)	)	PUNCT
gi-4940	476	8	,	,	PUNCT
gi-4940	476	9	y2	y2	NOUN
gi-4940	476	10	=	=	SYM
gi-4940	476	11	g(ϕ2	g(ϕ2	NOUN
gi-4940	476	12	,	,	PUNCT
gi-4940	476	13	λ	λ	PROPN
gi-4940	476	14	)	)	PUNCT
gi-4940	476	15	,	,	PUNCT
gi-4940	476	16	x3	x3	NOUN
gi-4940	476	17	=	=	SYM
gi-4940	477	1	f	f	PROPN
gi-4940	477	2	(	(	PUNCT
gi-4940	477	3	ϕ3	ϕ3	PROPN
gi-4940	477	4	,	,	PUNCT
gi-4940	477	5	λ	λ	NOUN
gi-4940	477	6	)	)	PUNCT
gi-4940	477	7	,	,	PUNCT
gi-4940	477	8	y3	y3	NOUN
gi-4940	477	9	=	=	SYM
gi-4940	477	10	g(ϕ3	g(ϕ3	PROPN
gi-4940	477	11	,	,	PUNCT
gi-4940	477	12	λ	λ	PROPN
gi-4940	477	13	)	)	PUNCT
gi-4940	477	14	,	,	PUNCT
gi-4940	477	15	at	at	ADP
gi-4940	477	16	new	new	ADJ
gi-4940	477	17	vertices	vertex	NOUN
gi-4940	477	18	p1	p1	NOUN
gi-4940	477	19	,	,	PUNCT
gi-4940	477	20	p2	p2	NOUN
gi-4940	477	21	,	,	PUNCT
gi-4940	477	22	p3	p3	PROPN
gi-4940	477	23	.	.	PUNCT
gi-4940	478	1	(	(	PUNCT
gi-4940	478	2	e	e	NOUN
gi-4940	478	3	)	)	PUNCT
gi-4940	478	4	for	for	ADP
gi-4940	478	5	d	d	PROPN
gi-4940	478	6	≤	≤	PROPN
gi-4940	478	7	d	d	X
gi-4940	478	8	,	,	PUNCT
gi-4940	478	9	this	this	DET
gi-4940	478	10	step	step	NOUN
gi-4940	478	11	begins	begin	VERB
gi-4940	478	12	with	with	ADP
gi-4940	478	13	uniform	uniform	ADJ
gi-4940	478	14	sampling	sampling	NOUN
gi-4940	478	15	of	of	ADP
gi-4940	478	16	the	the	DET
gi-4940	478	17	meridian	meridian	PROPN
gi-4940	478	18	points	point	NOUN
gi-4940	478	19	.	.	PUNCT
gi-4940	479	1	if	if	SCONJ
gi-4940	479	2	d	d	PROPN
gi-4940	479	3	>	>	X
gi-4940	479	4	d	d	PROPN
gi-4940	479	5	,	,	PUNCT
gi-4940	479	6	it	it	PRON
gi-4940	479	7	transforms	transform	VERB
gi-4940	479	8	to	to	ADP
gi-4940	479	9	the	the	DET
gi-4940	479	10	adaptive	adaptive	ADJ
gi-4940	479	11	method	method	NOUN
gi-4940	479	12	.	.	PUNCT
gi-4940	480	1	check	check	VERB
gi-4940	480	2	the	the	DET
gi-4940	480	3	refinement	refinement	NOUN
gi-4940	480	4	criteria	criterion	NOUN
gi-4940	480	5	α1	α1	PROPN
gi-4940	480	6	=	=	SYM
gi-4940	480	7	α(pa	α(pa	NUM
gi-4940	480	8	,	,	PUNCT
gi-4940	480	9	p1	p1	NOUN
gi-4940	480	10	,	,	PUNCT
gi-4940	480	11	p2	p2	NOUN
gi-4940	480	12	)	)	PUNCT
gi-4940	480	13	,	,	PUNCT
gi-4940	480	14	α2	α2	PROPN
gi-4940	480	15	=	=	SYM
gi-4940	480	16	α(p1	α(p1	NOUN
gi-4940	480	17	,	,	PUNCT
gi-4940	480	18	p2	p2	NOUN
gi-4940	480	19	,	,	PUNCT
gi-4940	480	20	p3	p3	PROPN
gi-4940	480	21	)	)	PUNCT
gi-4940	480	22	,	,	PUNCT
gi-4940	480	23	α3	α3	NOUN
gi-4940	480	24	=	=	SYM
gi-4940	480	25	α(p2	α(p2	ADJ
gi-4940	480	26	,	,	PUNCT
gi-4940	480	27	p3	p3	PROPN
gi-4940	480	28	,	,	PUNCT
gi-4940	480	29	pb	pb	PROPN
gi-4940	480	30	)	)	PUNCT
gi-4940	480	31	,	,	PUNCT
gi-4940	480	32	and	and	CCONJ
gi-4940	480	33	the	the	DET
gi-4940	480	34	recursive	recursive	ADJ
gi-4940	480	35	depth	depth	NOUN
gi-4940	480	36	d.	d.	NOUN
gi-4940	480	37	when	when	SCONJ
gi-4940	480	38	the	the	DET
gi-4940	480	39	meridian	meridian	PROPN
gi-4940	480	40	is	be	AUX
gi-4940	480	41	not	not	PART
gi-4940	480	42	sufficiently	sufficiently	ADV
gi-4940	480	43	smooth	smooth	ADJ
gi-4940	480	44	,	,	PUNCT
gi-4940	480	45	or	or	CCONJ
gi-4940	481	1	d	d	X
gi-4940	481	2	≤	≤	NUM
gi-4940	481	3	d	d	X
gi-4940	481	4	,	,	PUNCT
gi-4940	481	5	it	it	PRON
gi-4940	481	6	needs	need	VERB
gi-4940	481	7	to	to	PART
gi-4940	481	8	be	be	AUX
gi-4940	481	9	refined	refine	VERB
gi-4940	481	10	.	.	PUNCT
gi-4940	482	1	hence	hence	ADV
gi-4940	482	2	,	,	PUNCT
gi-4940	482	3	the	the	DET
gi-4940	482	4	recursive	recursive	ADJ
gi-4940	482	5	subdivision	subdivision	NOUN
gi-4940	482	6	is	be	AUX
gi-4940	482	7	necessary	necessary	ADJ
gi-4940	482	8	.	.	PUNCT
gi-4940	483	1	(	(	PUNCT
gi-4940	483	2	f	f	X
gi-4940	483	3	)	)	PUNCT
gi-4940	483	4	if	if	SCONJ
gi-4940	483	5	α1	α1	PROPN
gi-4940	483	6	>	>	X
gi-4940	483	7	α	α	PROPN
gi-4940	483	8	,	,	PUNCT
gi-4940	483	9	call	call	VERB
gi-4940	483	10	the	the	DET
gi-4940	483	11	recursive	recursive	ADJ
gi-4940	483	12	procedure	procedure	NOUN
gi-4940	483	13	with	with	ADP
gi-4940	483	14	the	the	DET
gi-4940	483	15	increased	increase	VERB
gi-4940	483	16	depth	depth	NOUN
gi-4940	483	17	d	d	X
gi-4940	483	18	=	=	SYM
gi-4940	483	19	d+	d+	PUNCT
gi-4940	483	20	1	1	NUM
gi-4940	483	21	for	for	ADP
gi-4940	483	22	the	the	DET
gi-4940	483	23	interval	interval	NOUN
gi-4940	483	24	[	[	X
gi-4940	483	25	a	a	X
gi-4940	483	26	,	,	PUNCT
gi-4940	483	27	ϕ1	ϕ1	NOUN
gi-4940	483	28	]	]	PUNCT
gi-4940	483	29	.	.	PUNCT
gi-4940	484	1	(	(	PUNCT
gi-4940	484	2	g	g	NOUN
gi-4940	484	3	)	)	PUNCT
gi-4940	484	4	add	add	VERB
gi-4940	484	5	the	the	DET
gi-4940	484	6	new	new	ADJ
gi-4940	484	7	point	point	NOUN
gi-4940	484	8	p1	p1	NOUN
gi-4940	484	9	to	to	ADP
gi-4940	484	10	the	the	DET
gi-4940	484	11	polynomial	polynomial	ADJ
gi-4940	484	12	approximation	approximation	NOUN
gi-4940	484	13	of	of	ADP
gi-4940	484	14	m̃(λ	m̃(λ	PROPN
gi-4940	484	15	)	)	PUNCT
gi-4940	484	16	:	:	PUNCT
gi-4940	485	1	lλ	lλ	INTJ
gi-4940	485	2	,	,	PUNCT
gi-4940	485	3	j	j	PROPN
gi-4940	485	4	,	,	PUNCT
gi-4940	485	5	k	k	PROPN
gi-4940	485	6	←	←	PROPN
gi-4940	485	7	p1	p1	PROPN
gi-4940	485	8	.	.	PUNCT
gi-4940	486	1	(	(	PUNCT
gi-4940	486	2	h	h	NOUN
gi-4940	486	3	)	)	PUNCT
gi-4940	486	4	if	if	SCONJ
gi-4940	486	5	α1	α1	PROPN
gi-4940	486	6	>	>	X
gi-4940	486	7	α∨α2	α∨α2	PROPN
gi-4940	486	8	>	>	X
gi-4940	486	9	α	α	X
gi-4940	486	10	,	,	PUNCT
gi-4940	486	11	call	call	VERB
gi-4940	486	12	the	the	DET
gi-4940	486	13	recursive	recursive	ADJ
gi-4940	486	14	procedure	procedure	NOUN
gi-4940	486	15	with	with	ADP
gi-4940	486	16	the	the	DET
gi-4940	486	17	increased	increase	VERB
gi-4940	486	18	depth	depth	NOUN
gi-4940	486	19	d	d	NOUN
gi-4940	486	20	=	=	SYM
gi-4940	486	21	d+1	d+1	PROPN
gi-4940	486	22	for	for	ADP
gi-4940	486	23	the	the	DET
gi-4940	486	24	interval	interval	NOUN
gi-4940	486	25	[	[	X
gi-4940	486	26	ϕ1	ϕ1	NOUN
gi-4940	486	27	,	,	PUNCT
gi-4940	486	28	ϕ2	ϕ2	ADV
gi-4940	486	29	]	]	PUNCT
gi-4940	486	30	.	.	PUNCT
gi-4940	487	1	(	(	PUNCT
gi-4940	487	2	i	i	NOUN
gi-4940	487	3	)	)	PUNCT
gi-4940	487	4	add	add	VERB
gi-4940	487	5	the	the	DET
gi-4940	487	6	new	new	ADJ
gi-4940	487	7	point	point	NOUN
gi-4940	487	8	p2	p2	NOUN
gi-4940	487	9	to	to	ADP
gi-4940	487	10	the	the	DET
gi-4940	487	11	polynomial	polynomial	ADJ
gi-4940	487	12	approximation	approximation	NOUN
gi-4940	487	13	of	of	ADP
gi-4940	487	14	m̃(λ	m̃(λ	PROPN
gi-4940	487	15	)	)	PUNCT
gi-4940	487	16	:	:	PUNCT
gi-4940	488	1	lλ	lλ	INTJ
gi-4940	488	2	,	,	PUNCT
gi-4940	488	3	j	j	PROPN
gi-4940	488	4	,	,	PUNCT
gi-4940	488	5	k	k	PROPN
gi-4940	488	6	←	←	PROPN
gi-4940	488	7	p2	p2	PROPN
gi-4940	488	8	.	.	PUNCT
gi-4940	489	1	geoinformatics	geoinformatic	NOUN
gi-4940	489	2	fce	fce	VERB
gi-4940	489	3	ctu	ctu	NOUN
gi-4940	489	4	17(2	17(2	NUM
gi-4940	489	5	)	)	PUNCT
gi-4940	489	6	,	,	PUNCT
gi-4940	489	7	2018	2018	NUM
gi-4940	489	8	46	46	NUM
gi-4940	489	9	t.	t.	NOUN
gi-4940	489	10	bayer	bayer	PROPN
gi-4940	489	11	:	:	PUNCT
gi-4940	489	12	plotting	plot	VERB
gi-4940	489	13	the	the	DET
gi-4940	489	14	map	map	NOUN
gi-4940	489	15	projection	projection	NOUN
gi-4940	489	16	graticule	graticule	NOUN
gi-4940	489	17	with	with	ADP
gi-4940	489	18	discontinuities	discontinuity	NOUN
gi-4940	489	19	algorithm	algorithm	NOUN
gi-4940	489	20	6	6	NUM
gi-4940	489	21	combined	combine	VERB
gi-4940	489	22	sampling	sampling	NOUN
gi-4940	489	23	of	of	ADP
gi-4940	489	24	the	the	DET
gi-4940	489	25	meridian	meridian	PROPN
gi-4940	489	26	,	,	PUNCT
gi-4940	489	27	the	the	DET
gi-4940	489	28	initial	initial	ADJ
gi-4940	489	29	phase	phase	NOUN
gi-4940	489	30	.	.	PUNCT
gi-4940	490	1	1	1	NUM
gi-4940	490	2	:	:	PUNCT
gi-4940	490	3	function	function	NOUN
gi-4940	490	4	csmerinit(p	csmerinit(p	PROPN
gi-4940	490	5	,	,	PUNCT
gi-4940	490	6	lλ	lλ	INTJ
gi-4940	490	7	,	,	PUNCT
gi-4940	490	8	j	j	PROPN
gi-4940	490	9	,	,	PUNCT
gi-4940	490	10	k	k	PROPN
gi-4940	490	11	,	,	PUNCT
gi-4940	490	12	a	a	DET
gi-4940	490	13	,	,	PUNCT
gi-4940	490	14	b	b	NOUN
gi-4940	490	15	,	,	PUNCT
gi-4940	490	16	λ	λ	PROPN
gi-4940	490	17	,	,	PUNCT
gi-4940	490	18	d	d	NOUN
gi-4940	490	19	,	,	PUNCT
gi-4940	490	20	d	d	NOUN
gi-4940	490	21	,	,	PUNCT
gi-4940	490	22	d	d	PROPN
gi-4940	490	23	,	,	PUNCT
gi-4940	490	24	ε	ε	PROPN
gi-4940	490	25	,	,	PUNCT
gi-4940	490	26	α	α	NOUN
gi-4940	490	27	)	)	PUNCT
gi-4940	490	28	2	2	NUM
gi-4940	490	29	:	:	PUNCT
gi-4940	490	30	lλ	lλ	PROPN
gi-4940	490	31	,	,	PUNCT
gi-4940	490	32	j	j	PROPN
gi-4940	490	33	,	,	PUNCT
gi-4940	490	34	k	k	NOUN
gi-4940	490	35	=	=	NOUN
gi-4940	490	36	∅	∅	NOUN
gi-4940	490	37	3	3	NUM
gi-4940	490	38	:	:	PUNCT
gi-4940	490	39	if	if	SCONJ
gi-4940	490	40	discontinuity	discontinuity	NOUN
gi-4940	490	41	in	in	ADP
gi-4940	490	42	(	(	PUNCT
gi-4940	490	43	a	a	PRON
gi-4940	490	44	,	,	PUNCT
gi-4940	490	45	λ	λ	NOUN
gi-4940	490	46	)	)	PUNCT
gi-4940	490	47	in	in	ADP
gi-4940	490	48	ϕ	ϕ	NOUN
gi-4940	490	49	direction	direction	NOUN
gi-4940	490	50	then	then	ADV
gi-4940	490	51	4	4	NUM
gi-4940	490	52	:	:	PUNCT
gi-4940	490	53	throw	throw	VERB
gi-4940	490	54	latsingularityexception	latsingularityexception	NOUN
gi-4940	490	55	(	(	PUNCT
gi-4940	490	56	a	a	X
gi-4940	490	57	)	)	PUNCT
gi-4940	490	58	5	5	NUM
gi-4940	490	59	:	:	PUNCT
gi-4940	490	60	if	if	SCONJ
gi-4940	490	61	discontinuity	discontinuity	NOUN
gi-4940	490	62	in	in	ADP
gi-4940	490	63	(	(	PUNCT
gi-4940	490	64	a	a	PRON
gi-4940	490	65	,	,	PUNCT
gi-4940	490	66	λ	λ	NOUN
gi-4940	490	67	)	)	PUNCT
gi-4940	490	68	in	in	ADP
gi-4940	490	69	λ	λ	PROPN
gi-4940	490	70	direction	direction	NOUN
gi-4940	490	71	then	then	ADV
gi-4940	490	72	6	6	NUM
gi-4940	490	73	:	:	PUNCT
gi-4940	490	74	throw	throw	VERB
gi-4940	490	75	lonsingularityexception	lonsingularityexception	NOUN
gi-4940	490	76	(	(	PUNCT
gi-4940	490	77	λ	λ	X
gi-4940	490	78	)	)	PUNCT
gi-4940	490	79	7	7	NUM
gi-4940	490	80	:	:	PUNCT
gi-4940	490	81	if	if	SCONJ
gi-4940	490	82	discontinuity	discontinuity	NOUN
gi-4940	490	83	in	in	ADP
gi-4940	490	84	(	(	PUNCT
gi-4940	490	85	b	b	NOUN
gi-4940	490	86	,	,	PUNCT
gi-4940	490	87	λ	λ	NOUN
gi-4940	490	88	)	)	PUNCT
gi-4940	490	89	in	in	ADP
gi-4940	490	90	ϕ	ϕ	NOUN
gi-4940	490	91	direction	direction	NOUN
gi-4940	490	92	then	then	ADV
gi-4940	490	93	8	8	NUM
gi-4940	490	94	:	:	PUNCT
gi-4940	490	95	throw	throw	VERB
gi-4940	490	96	latsingularityexception	latsingularityexception	NOUN
gi-4940	490	97	(	(	PUNCT
gi-4940	490	98	b	b	NOUN
gi-4940	490	99	)	)	PUNCT
gi-4940	490	100	9	9	NUM
gi-4940	490	101	:	:	PUNCT
gi-4940	490	102	if	if	SCONJ
gi-4940	490	103	discontinuity	discontinuity	NOUN
gi-4940	490	104	in	in	ADP
gi-4940	490	105	(	(	PUNCT
gi-4940	490	106	b	b	NOUN
gi-4940	490	107	,	,	PUNCT
gi-4940	490	108	λ	λ	NOUN
gi-4940	490	109	)	)	PUNCT
gi-4940	490	110	in	in	ADP
gi-4940	490	111	λ	λ	PROPN
gi-4940	490	112	direction	direction	NOUN
gi-4940	490	113	then	then	ADV
gi-4940	490	114	10	10	NUM
gi-4940	490	115	:	:	PUNCT
gi-4940	490	116	throw	throw	VERB
gi-4940	490	117	lonsingularityexception	lonsingularityexception	NOUN
gi-4940	490	118	(	(	PUNCT
gi-4940	490	119	λ	λ	NOUN
gi-4940	490	120	)	)	PUNCT
gi-4940	490	121	11	11	NUM
gi-4940	490	122	:	:	PUNCT
gi-4940	491	1	xa	xa	PROPN
gi-4940	491	2	=	=	SYM
gi-4940	491	3	f	f	PROPN
gi-4940	491	4	(	(	PUNCT
gi-4940	491	5	a	a	PRON
gi-4940	491	6	,	,	PUNCT
gi-4940	491	7	λ	λ	NOUN
gi-4940	491	8	)	)	PUNCT
gi-4940	491	9	,	,	PUNCT
gi-4940	491	10	ya	ya	PROPN
gi-4940	491	11	=	=	SYM
gi-4940	491	12	g(a	g(a	PROPN
gi-4940	491	13	,	,	PUNCT
gi-4940	491	14	λ	λ	PROPN
gi-4940	491	15	)	)	PUNCT
gi-4940	491	16	12	12	NUM
gi-4940	491	17	:	:	PUNCT
gi-4940	491	18	lλ	lλ	PROPN
gi-4940	491	19	,	,	PUNCT
gi-4940	491	20	j	j	PROPN
gi-4940	491	21	,	,	PUNCT
gi-4940	491	22	k	k	PROPN
gi-4940	491	23	←	←	PROPN
gi-4940	491	24	point(xa	point(xa	PROPN
gi-4940	491	25	,	,	PUNCT
gi-4940	491	26	ya	ya	PROPN
gi-4940	491	27	)	)	PUNCT
gi-4940	491	28	13	13	NUM
gi-4940	491	29	:	:	PUNCT
gi-4940	491	30	csmer(p	csmer(p	PROPN
gi-4940	491	31	,	,	PUNCT
gi-4940	491	32	lλ	lλ	INTJ
gi-4940	491	33	,	,	PUNCT
gi-4940	491	34	j	j	PROPN
gi-4940	491	35	,	,	PUNCT
gi-4940	491	36	k	k	PROPN
gi-4940	491	37	,	,	PUNCT
gi-4940	491	38	a	a	DET
gi-4940	491	39	,	,	PUNCT
gi-4940	491	40	b	b	PROPN
gi-4940	491	41	,	,	PUNCT
gi-4940	491	42	xa	xa	PROPN
gi-4940	491	43	,	,	PUNCT
gi-4940	491	44	ya	ya	PROPN
gi-4940	491	45	,	,	PUNCT
gi-4940	491	46	xb	xb	PROPN
gi-4940	491	47	,	,	PUNCT
gi-4940	491	48	yb	yb	PROPN
gi-4940	491	49	,	,	PUNCT
gi-4940	491	50	d	d	PROPN
gi-4940	491	51	,	,	PUNCT
gi-4940	491	52	d	d	NOUN
gi-4940	491	53	,	,	PUNCT
gi-4940	491	54	d	d	PROPN
gi-4940	491	55	,	,	PUNCT
gi-4940	491	56	ε	ε	PROPN
gi-4940	491	57	,	,	PUNCT
gi-4940	491	58	α	α	NOUN
gi-4940	491	59	)	)	PUNCT
gi-4940	491	60	14	14	NUM
gi-4940	491	61	:	:	PUNCT
gi-4940	491	62	xb	xb	X
gi-4940	491	63	=	=	PUNCT
gi-4940	491	64	f	f	PROPN
gi-4940	491	65	(	(	PUNCT
gi-4940	491	66	b	b	PROPN
gi-4940	491	67	,	,	PUNCT
gi-4940	491	68	λ	λ	NOUN
gi-4940	491	69	)	)	PUNCT
gi-4940	491	70	,	,	PUNCT
gi-4940	491	71	yb	yb	PROPN
gi-4940	491	72	=	=	SYM
gi-4940	491	73	g(b	g(b	PROPN
gi-4940	491	74	,	,	PUNCT
gi-4940	491	75	λ	λ	NOUN
gi-4940	491	76	)	)	PUNCT
gi-4940	491	77	15	15	NUM
gi-4940	491	78	:	:	PUNCT
gi-4940	491	79	lλ	lλ	PROPN
gi-4940	491	80	,	,	PUNCT
gi-4940	491	81	j	j	PROPN
gi-4940	491	82	,	,	PUNCT
gi-4940	491	83	k	k	PROPN
gi-4940	491	84	←	←	PROPN
gi-4940	491	85	point(xb	point(xb	PROPN
gi-4940	491	86	,	,	PUNCT
gi-4940	491	87	yb	yb	PROPN
gi-4940	491	88	)	)	PUNCT
gi-4940	491	89	(	(	PUNCT
gi-4940	491	90	j	j	NOUN
gi-4940	491	91	)	)	PUNCT
gi-4940	491	92	if	if	SCONJ
gi-4940	491	93	α2	α2	PROPN
gi-4940	491	94	>	>	X
gi-4940	491	95	α∨α3	α∨α3	PUNCT
gi-4940	491	96	>	>	PUNCT
gi-4940	491	97	α	α	X
gi-4940	491	98	,	,	PUNCT
gi-4940	491	99	call	call	VERB
gi-4940	491	100	the	the	DET
gi-4940	491	101	recursive	recursive	ADJ
gi-4940	491	102	procedure	procedure	NOUN
gi-4940	491	103	with	with	ADP
gi-4940	491	104	the	the	DET
gi-4940	491	105	increased	increase	VERB
gi-4940	491	106	depth	depth	NOUN
gi-4940	491	107	d	d	NOUN
gi-4940	491	108	=	=	SYM
gi-4940	491	109	d+1	d+1	PROPN
gi-4940	491	110	for	for	ADP
gi-4940	491	111	the	the	DET
gi-4940	491	112	interval	interval	NOUN
gi-4940	491	113	[	[	X
gi-4940	491	114	ϕ2	ϕ2	ADV
gi-4940	491	115	,	,	PUNCT
gi-4940	491	116	x3	x3	ADJ
gi-4940	491	117	]	]	PUNCT
gi-4940	491	118	.	.	PUNCT
gi-4940	492	1	(	(	PUNCT
gi-4940	492	2	k	k	X
gi-4940	492	3	)	)	PUNCT
gi-4940	492	4	add	add	VERB
gi-4940	492	5	the	the	DET
gi-4940	492	6	new	new	ADJ
gi-4940	492	7	point	point	NOUN
gi-4940	492	8	p3	p3	PROPN
gi-4940	492	9	to	to	ADP
gi-4940	492	10	the	the	DET
gi-4940	492	11	polynomial	polynomial	ADJ
gi-4940	492	12	approximation	approximation	NOUN
gi-4940	492	13	of	of	ADP
gi-4940	492	14	m̃(λ	m̃(λ	PROPN
gi-4940	492	15	)	)	PUNCT
gi-4940	492	16	:	:	PUNCT
gi-4940	493	1	lλ	lλ	INTJ
gi-4940	493	2	,	,	PUNCT
gi-4940	493	3	j	j	PROPN
gi-4940	493	4	,	,	PUNCT
gi-4940	493	5	k	k	PROPN
gi-4940	493	6	←	←	PROPN
gi-4940	493	7	p3	p3	PROPN
gi-4940	493	8	.	.	PUNCT
gi-4940	494	1	(	(	PUNCT
gi-4940	494	2	l	l	NOUN
gi-4940	494	3	)	)	PUNCT
gi-4940	494	4	if	if	SCONJ
gi-4940	494	5	α3	α3	PROPN
gi-4940	494	6	>	>	X
gi-4940	494	7	α	α	PROPN
gi-4940	494	8	,	,	PUNCT
gi-4940	494	9	call	call	VERB
gi-4940	494	10	the	the	DET
gi-4940	494	11	recursive	recursive	ADJ
gi-4940	494	12	procedure	procedure	NOUN
gi-4940	494	13	for	for	ADP
gi-4940	494	14	the	the	DET
gi-4940	494	15	interval	interval	NOUN
gi-4940	494	16	[	[	X
gi-4940	494	17	ϕ3	ϕ3	PROPN
gi-4940	494	18	,	,	PUNCT
gi-4940	494	19	b	b	NOUN
gi-4940	494	20	]	]	X
gi-4940	494	21	.	.	PUNCT
gi-4940	495	1	3	3	X
gi-4940	495	2	.	.	X
gi-4940	495	3	add	add	VERB
gi-4940	495	4	the	the	DET
gi-4940	495	5	last	last	ADJ
gi-4940	495	6	point	point	NOUN
gi-4940	495	7	add	add	VERB
gi-4940	495	8	the	the	DET
gi-4940	495	9	last	last	ADJ
gi-4940	495	10	point	point	NOUN
gi-4940	495	11	pb	pb	ADP
gi-4940	495	12	to	to	ADP
gi-4940	495	13	the	the	DET
gi-4940	495	14	polynomial	polynomial	ADJ
gi-4940	495	15	approximation	approximation	NOUN
gi-4940	495	16	of	of	ADP
gi-4940	495	17	m̃(λ	m̃(λ	PROPN
gi-4940	495	18	)	)	PUNCT
gi-4940	495	19	:	:	PUNCT
gi-4940	496	1	lλ	lλ	INTJ
gi-4940	496	2	,	,	PUNCT
gi-4940	496	3	j	j	PROPN
gi-4940	496	4	,	,	PUNCT
gi-4940	496	5	k	k	PROPN
gi-4940	496	6	←	←	PROPN
gi-4940	496	7	pb	pb	X
gi-4940	496	8	and	and	CCONJ
gi-4940	496	9	finish	finish	VERB
gi-4940	496	10	the	the	DET
gi-4940	496	11	adaptive	adaptive	ADJ
gi-4940	496	12	sampling	sample	VERB
gi-4940	496	13	procedure	procedure	NOUN
gi-4940	496	14	.	.	PUNCT
gi-4940	497	1	the	the	DET
gi-4940	497	2	procedure	procedure	NOUN
gi-4940	497	3	is	be	AUX
gi-4940	497	4	summarized	summarize	VERB
gi-4940	497	5	in	in	ADP
gi-4940	497	6	alg	alg	PROPN
gi-4940	497	7	.	.	PUNCT
gi-4940	498	1	7	7	X
gi-4940	498	2	.	.	X
gi-4940	498	3	unfortunately	unfortunately	ADV
gi-4940	498	4	,	,	PUNCT
gi-4940	498	5	this	this	DET
gi-4940	498	6	technique	technique	NOUN
gi-4940	498	7	does	do	AUX
gi-4940	498	8	not	not	PART
gi-4940	498	9	involve	involve	VERB
gi-4940	498	10	the	the	DET
gi-4940	498	11	angles	angle	NOUN
gi-4940	498	12	α	α	NOUN
gi-4940	498	13	between	between	ADP
gi-4940	498	14	the	the	DET
gi-4940	498	15	adjacent	adjacent	ADJ
gi-4940	498	16	segments	segment	NOUN
gi-4940	498	17	from	from	ADP
gi-4940	498	18	the	the	DET
gi-4940	498	19	previous	previous	ADJ
gi-4940	498	20	iteration	iteration	NOUN
gi-4940	498	21	.	.	PUNCT
gi-4940	499	1	while	while	SCONJ
gi-4940	499	2	the	the	DET
gi-4940	499	3	newly	newly	ADV
gi-4940	499	4	created	create	VERB
gi-4940	499	5	segments	segment	NOUN
gi-4940	499	6	of	of	ADP
gi-4940	499	7	the	the	DET
gi-4940	499	8	polygonal	polygonal	ADJ
gi-4940	499	9	approximation	approximation	NOUN
gi-4940	499	10	of	of	ADP
gi-4940	499	11	m(λ	m(λ	PROPN
gi-4940	499	12	)	)	PUNCT
gi-4940	499	13	can	can	AUX
gi-4940	499	14	fulfill	fulfill	VERB
gi-4940	499	15	the	the	DET
gi-4940	499	16	condition	condition	NOUN
gi-4940	499	17	of	of	ADP
gi-4940	499	18	αi	αi	NOUN
gi-4940	499	19	≤	≤	NUM
gi-4940	499	20	α	α	NOUN
gi-4940	499	21	,	,	PUNCT
gi-4940	499	22	their	their	PRON
gi-4940	499	23	joining	join	VERB
gi-4940	499	24	to	to	ADP
gi-4940	499	25	the	the	DET
gi-4940	499	26	previous	previous	ADJ
gi-4940	499	27	/	/	SYM
gi-4940	499	28	next	next	ADJ
gi-4940	499	29	segments	segment	NOUN
gi-4940	499	30	may	may	AUX
gi-4940	499	31	not	not	PART
gi-4940	499	32	hold	hold	VERB
gi-4940	499	33	this	this	DET
gi-4940	499	34	requirement	requirement	NOUN
gi-4940	499	35	.	.	PUNCT
gi-4940	500	1	in	in	ADP
gi-4940	500	2	general	general	ADJ
gi-4940	500	3	,	,	PUNCT
gi-4940	500	4	this	this	DET
gi-4940	500	5	issue	issue	NOUN
gi-4940	500	6	affects	affect	VERB
gi-4940	500	7	curves	curve	NOUN
gi-4940	500	8	of	of	ADP
gi-4940	500	9	the	the	DET
gi-4940	500	10	complex	complex	ADJ
gi-4940	500	11	shape	shape	NOUN
gi-4940	500	12	,	,	PUNCT
gi-4940	500	13	where	where	SCONJ
gi-4940	500	14	the	the	DET
gi-4940	500	15	average	average	ADJ
gi-4940	500	16	maximum	maximum	ADJ
gi-4940	500	17	value	value	NOUN
gi-4940	500	18	αi	αi	NOUN
gi-4940	500	19	.=	.=	PUNCT
gi-4940	501	1	1.25α	1.25α	NUM
gi-4940	501	2	.	.	PUNCT
gi-4940	501	3	sampling	sample	VERB
gi-4940	501	4	method	method	NOUN
gi-4940	501	5	s2	s2	PROPN
gi-4940	501	6	.	.	PUNCT
gi-4940	502	1	the	the	DET
gi-4940	502	2	first	first	ADJ
gi-4940	502	3	improvement	improvement	NOUN
gi-4940	502	4	is	be	AUX
gi-4940	502	5	represented	represent	VERB
gi-4940	502	6	by	by	ADP
gi-4940	502	7	the	the	DET
gi-4940	502	8	refinement	refinement	NOUN
gi-4940	502	9	of	of	ADP
gi-4940	502	10	the	the	DET
gi-4940	502	11	recursive	recursive	ADJ
gi-4940	502	12	condition	condition	NOUN
gi-4940	502	13	.	.	PUNCT
gi-4940	503	1	the	the	DET
gi-4940	503	2	original	original	ADJ
gi-4940	503	3	conditions	condition	NOUN
gi-4940	503	4	α1	α1	PROPN
gi-4940	503	5	>	>	X
gi-4940	503	6	α	α	PROPN
gi-4940	503	7	,	,	PUNCT
gi-4940	503	8	α1	α1	PROPN
gi-4940	503	9	>	>	X
gi-4940	503	10	α	α	PROPN
gi-4940	503	11	∨	∨	VERB
gi-4940	503	12	α2	α2	PROPN
gi-4940	503	13	>	>	X
gi-4940	504	1	α	α	PROPN
gi-4940	504	2	,	,	PUNCT
gi-4940	504	3	α2	α2	PROPN
gi-4940	504	4	>	>	X
gi-4940	504	5	α	α	PROPN
gi-4940	504	6	∨	∨	NUM
gi-4940	504	7	α3	α3	PROPN
gi-4940	504	8	>	>	X
gi-4940	504	9	α	α	PROPN
gi-4940	504	10	,	,	PUNCT
gi-4940	504	11	and	and	CCONJ
gi-4940	504	12	α3	α3	NOUN
gi-4940	504	13	>	>	X
gi-4940	504	14	α	α	PROPN
gi-4940	504	15	,	,	PUNCT
gi-4940	504	16	are	be	AUX
gi-4940	504	17	replaced	replace	VERB
gi-4940	504	18	with	with	ADP
gi-4940	504	19	the	the	DET
gi-4940	504	20	new	new	ADJ
gi-4940	504	21	α1	α1	PROPN
gi-4940	504	22	>	>	X
gi-4940	504	23	α	α	PROPN
gi-4940	504	24	∨	∨	VERB
gi-4940	504	25	α2	α2	PROPN
gi-4940	504	26	>	>	PUNCT
gi-4940	505	1	α	α	PROPN
gi-4940	505	2	∨	∨	NUM
gi-4940	505	3	α3	α3	PROPN
gi-4940	505	4	>	>	X
gi-4940	505	5	α	α	PROPN
gi-4940	505	6	,	,	PUNCT
gi-4940	505	7	(	(	PUNCT
gi-4940	505	8	4.1	4.1	NUM
gi-4940	505	9	)	)	PUNCT
gi-4940	505	10	identical	identical	ADJ
gi-4940	505	11	for	for	ADP
gi-4940	505	12	all	all	DET
gi-4940	505	13	recursive	recursive	ADJ
gi-4940	505	14	calls	call	NOUN
gi-4940	505	15	.	.	PUNCT
gi-4940	506	1	this	this	DET
gi-4940	506	2	approach	approach	NOUN
gi-4940	506	3	brings	bring	VERB
gi-4940	506	4	a	a	DET
gi-4940	506	5	slightly	slightly	ADV
gi-4940	506	6	increased	increase	VERB
gi-4940	506	7	amount	amount	NOUN
gi-4940	506	8	of	of	ADP
gi-4940	506	9	the	the	DET
gi-4940	506	10	recursive	recursive	ADJ
gi-4940	506	11	calls	call	NOUN
gi-4940	506	12	,	,	PUNCT
gi-4940	506	13	while	while	SCONJ
gi-4940	506	14	the	the	DET
gi-4940	506	15	average	average	ADJ
gi-4940	506	16	maximum	maximum	ADJ
gi-4940	506	17	value	value	NOUN
gi-4940	506	18	falls	fall	VERB
gi-4940	506	19	to	to	ADP
gi-4940	506	20	αi	αi	PROPN
gi-4940	506	21	.=	.=	PUNCT
gi-4940	507	1	1.15α	1.15α	NUM
gi-4940	507	2	.	.	PUNCT
gi-4940	508	1	in	in	ADP
gi-4940	508	2	most	most	ADJ
gi-4940	508	3	situations	situation	NOUN
gi-4940	508	4	,	,	PUNCT
gi-4940	508	5	this	this	DET
gi-4940	508	6	issue	issue	NOUN
gi-4940	508	7	does	do	AUX
gi-4940	508	8	not	not	PART
gi-4940	508	9	significantly	significantly	ADV
gi-4940	508	10	affect	affect	VERB
gi-4940	508	11	the	the	DET
gi-4940	508	12	smoothness	smoothness	NOUN
gi-4940	508	13	of	of	ADP
gi-4940	508	14	the	the	DET
gi-4940	508	15	polynomial	polynomial	ADJ
gi-4940	508	16	approximation	approximation	NOUN
gi-4940	508	17	and	and	CCONJ
gi-4940	508	18	its	its	PRON
gi-4940	508	19	perception	perception	NOUN
gi-4940	508	20	by	by	ADP
gi-4940	508	21	the	the	DET
gi-4940	508	22	user	user	NOUN
gi-4940	508	23	.	.	PUNCT
gi-4940	509	1	however	however	ADV
gi-4940	509	2	,	,	PUNCT
gi-4940	509	3	exceeding	exceed	VERB
gi-4940	509	4	the	the	DET
gi-4940	509	5	threshold	threshold	NOUN
gi-4940	509	6	may	may	AUX
gi-4940	509	7	not	not	PART
gi-4940	509	8	always	always	ADV
gi-4940	509	9	be	be	AUX
gi-4940	509	10	acceptable	acceptable	ADJ
gi-4940	509	11	.	.	PUNCT
gi-4940	510	1	sampling	sample	VERB
gi-4940	510	2	method	method	NOUN
gi-4940	510	3	s3	s3	PROPN
gi-4940	510	4	.	.	PUNCT
gi-4940	511	1	unlike	unlike	ADP
gi-4940	511	2	s1	s1	NOUN
gi-4940	511	3	,	,	PUNCT
gi-4940	511	4	s2	s2	PROPN
gi-4940	511	5	,	,	PUNCT
gi-4940	511	6	the	the	DET
gi-4940	511	7	improved	improved	ADJ
gi-4940	511	8	sampling	sampling	NOUN
gi-4940	511	9	method	method	NOUN
gi-4940	511	10	s3	s3	PROPN
gi-4940	511	11	takes	take	VERB
gi-4940	511	12	into	into	ADP
gi-4940	511	13	account	account	NOUN
gi-4940	511	14	angles	angle	NOUN
gi-4940	511	15	between	between	ADP
gi-4940	511	16	the	the	DET
gi-4940	511	17	newly	newly	ADV
gi-4940	511	18	created	create	VERB
gi-4940	511	19	and	and	CCONJ
gi-4940	511	20	adjacent	adjacent	ADJ
gi-4940	511	21	segments	segment	NOUN
gi-4940	511	22	from	from	ADP
gi-4940	511	23	the	the	DET
gi-4940	511	24	previous	previous	ADJ
gi-4940	511	25	iteration	iteration	NOUN
gi-4940	511	26	.	.	PUNCT
gi-4940	512	1	geoinformatics	geoinformatic	NOUN
gi-4940	512	2	fce	fce	VERB
gi-4940	512	3	ctu	ctu	NOUN
gi-4940	512	4	17(2	17(2	NUM
gi-4940	512	5	)	)	PUNCT
gi-4940	512	6	,	,	PUNCT
gi-4940	513	1	2018	2018	NUM
gi-4940	513	2	47	47	NUM
gi-4940	513	3	t.	t.	NOUN
gi-4940	513	4	bayer	bayer	PROPN
gi-4940	513	5	:	:	PUNCT
gi-4940	513	6	plotting	plot	VERB
gi-4940	513	7	the	the	DET
gi-4940	513	8	map	map	NOUN
gi-4940	513	9	projection	projection	NOUN
gi-4940	513	10	graticule	graticule	NOUN
gi-4940	513	11	with	with	ADP
gi-4940	513	12	discontinuities	discontinuity	NOUN
gi-4940	513	13	algorithm	algorithm	NOUN
gi-4940	513	14	7	7	NUM
gi-4940	513	15	combined	combine	VERB
gi-4940	513	16	sampling	sampling	NOUN
gi-4940	513	17	of	of	ADP
gi-4940	513	18	the	the	DET
gi-4940	513	19	meridian	meridian	PROPN
gi-4940	513	20	points	point	NOUN
gi-4940	513	21	,	,	PUNCT
gi-4940	513	22	the	the	DET
gi-4940	513	23	recursive	recursive	ADJ
gi-4940	513	24	phase	phase	NOUN
gi-4940	513	25	,	,	PUNCT
gi-4940	513	26	method	method	NOUN
gi-4940	513	27	s1	s1	NOUN
gi-4940	513	28	.	.	PUNCT
gi-4940	514	1	1	1	NUM
gi-4940	514	2	:	:	PUNCT
gi-4940	514	3	function	function	NOUN
gi-4940	514	4	csmer(p	csmer(p	PROPN
gi-4940	514	5	,	,	PUNCT
gi-4940	514	6	lλ	lλ	INTJ
gi-4940	514	7	,	,	PUNCT
gi-4940	514	8	j	j	PROPN
gi-4940	514	9	,	,	PUNCT
gi-4940	514	10	k	k	PROPN
gi-4940	514	11	,	,	PUNCT
gi-4940	514	12	a	a	DET
gi-4940	514	13	,	,	PUNCT
gi-4940	514	14	b	b	PROPN
gi-4940	514	15	,	,	PUNCT
gi-4940	514	16	xa	xa	PROPN
gi-4940	514	17	,	,	PUNCT
gi-4940	514	18	ya	ya	PROPN
gi-4940	514	19	,	,	PUNCT
gi-4940	514	20	xb	xb	PROPN
gi-4940	514	21	,	,	PUNCT
gi-4940	514	22	yb	yb	PROPN
gi-4940	514	23	,	,	PUNCT
gi-4940	514	24	d	d	PROPN
gi-4940	514	25	,	,	PUNCT
gi-4940	514	26	d	d	NOUN
gi-4940	514	27	,	,	PUNCT
gi-4940	514	28	d	d	PROPN
gi-4940	514	29	,	,	PUNCT
gi-4940	514	30	ε	ε	PROPN
gi-4940	514	31	,	,	PUNCT
gi-4940	514	32	α	α	NOUN
gi-4940	514	33	)	)	PUNCT
gi-4940	514	34	)	)	PUNCT
gi-4940	515	1	2	2	NUM
gi-4940	515	2	:	:	PUNCT
gi-4940	515	3	if	if	SCONJ
gi-4940	515	4	(	(	PUNCT
gi-4940	515	5	d	d	X
gi-4940	515	6	>	>	X
gi-4940	515	7	d	d	PROPN
gi-4940	515	8	)	)	PUNCT
gi-4940	515	9	∨	∨	PROPN
gi-4940	515	10	(	(	PUNCT
gi-4940	515	11	b−	b−	PROPN
gi-4940	515	12	a	a	DET
gi-4940	515	13	<	<	X
gi-4940	515	14	ε	ε	PROPN
gi-4940	515	15	)	)	PUNCT
gi-4940	515	16	then	then	ADV
gi-4940	515	17	3	3	NUM
gi-4940	515	18	:	:	PUNCT
gi-4940	515	19	return	return	VERB
gi-4940	515	20	4	4	NUM
gi-4940	515	21	:	:	PUNCT
gi-4940	515	22	r1	r1	PROPN
gi-4940	515	23	=	=	PUNCT
gi-4940	515	24	rand(0.45	rand(0.45	NOUN
gi-4940	515	25	,	,	PUNCT
gi-4940	515	26	0.55	0.55	NUM
gi-4940	515	27	)	)	PUNCT
gi-4940	515	28	,	,	PUNCT
gi-4940	515	29	r2	r2	PROPN
gi-4940	515	30	=	=	SYM
gi-4940	515	31	rand(0.45	rand(0.45	NOUN
gi-4940	515	32	,	,	PUNCT
gi-4940	515	33	0.55	0.55	NUM
gi-4940	515	34	)	)	PUNCT
gi-4940	515	35	,	,	PUNCT
gi-4940	515	36	r3	r3	PROPN
gi-4940	515	37	=	=	SYM
gi-4940	515	38	rand(0.45	rand(0.45	PROPN
gi-4940	515	39	,	,	PUNCT
gi-4940	515	40	0.55	0.55	NUM
gi-4940	515	41	)	)	PUNCT
gi-4940	515	42	5	5	NUM
gi-4940	515	43	:	:	PUNCT
gi-4940	515	44	ϕ1	ϕ1	NOUN
gi-4940	515	45	=	=	SYM
gi-4940	515	46	a+	a+	PUNCT
gi-4940	515	47	1	1	NUM
gi-4940	515	48	2r1(b−	2r1(b−	NUM
gi-4940	515	49	a	a	NOUN
gi-4940	515	50	)	)	PUNCT
gi-4940	515	51	,	,	PUNCT
gi-4940	515	52	ϕ2	ϕ2	ADV
gi-4940	515	53	=	=	SYM
gi-4940	515	54	a+	a+	PUNCT
gi-4940	515	55	r2(b−	r2(b−	X
gi-4940	515	56	a	a	PRON
gi-4940	515	57	)	)	PUNCT
gi-4940	515	58	,	,	PUNCT
gi-4940	515	59	ϕ3	ϕ3	PROPN
gi-4940	515	60	=	=	SYM
gi-4940	515	61	a+	a+	PUNCT
gi-4940	515	62	3	3	NUM
gi-4940	515	63	2r3(b−	2r3(b−	NUM
gi-4940	515	64	a	a	NOUN
gi-4940	515	65	)	)	PUNCT
gi-4940	515	66	6	6	NUM
gi-4940	515	67	:	:	PUNCT
gi-4940	515	68	if	if	SCONJ
gi-4940	515	69	discontinuity	discontinuity	NOUN
gi-4940	515	70	in	in	ADP
gi-4940	515	71	(	(	PUNCT
gi-4940	515	72	ϕi	ϕi	ADP
gi-4940	515	73	,	,	PUNCT
gi-4940	515	74	λ)i	λ)i	ADJ
gi-4940	515	75	in	in	ADP
gi-4940	515	76	ϕ	ϕ	PROPN
gi-4940	515	77	direction	direction	NOUN
gi-4940	515	78	then	then	ADV
gi-4940	515	79	7	7	NUM
gi-4940	515	80	:	:	PUNCT
gi-4940	515	81	throw	throw	VERB
gi-4940	515	82	latsingularityexception	latsingularityexception	NOUN
gi-4940	515	83	(	(	PUNCT
gi-4940	515	84	ϕi	ϕi	PROPN
gi-4940	515	85	)	)	PUNCT
gi-4940	515	86	,	,	PUNCT
gi-4940	515	87	i	i	PRON
gi-4940	515	88	=	=	NOUN
gi-4940	515	89	1	1	NUM
gi-4940	515	90	,	,	PUNCT
gi-4940	515	91	2	2	NUM
gi-4940	515	92	,	,	PUNCT
gi-4940	515	93	3	3	NUM
gi-4940	515	94	8	8	NUM
gi-4940	515	95	:	:	PUNCT
gi-4940	515	96	if	if	SCONJ
gi-4940	515	97	discontinuity	discontinuity	NOUN
gi-4940	515	98	in	in	ADP
gi-4940	515	99	(	(	PUNCT
gi-4940	515	100	ϕi	ϕi	ADP
gi-4940	515	101	,	,	PUNCT
gi-4940	515	102	λ)i	λ)i	ADJ
gi-4940	515	103	in	in	ADP
gi-4940	515	104	λ	λ	PROPN
gi-4940	515	105	direction	direction	NOUN
gi-4940	515	106	then	then	ADV
gi-4940	515	107	9	9	NUM
gi-4940	515	108	:	:	PUNCT
gi-4940	515	109	throw	throw	VERB
gi-4940	515	110	lonsingularityexception	lonsingularityexception	NOUN
gi-4940	515	111	(	(	PUNCT
gi-4940	515	112	λ	λ	NOUN
gi-4940	515	113	)	)	PUNCT
gi-4940	515	114	,	,	PUNCT
gi-4940	515	115	i	i	PRON
gi-4940	515	116	=	=	NOUN
gi-4940	515	117	1	1	NUM
gi-4940	515	118	,	,	PUNCT
gi-4940	515	119	2	2	NUM
gi-4940	515	120	,	,	PUNCT
gi-4940	515	121	3	3	NUM
gi-4940	515	122	10	10	NUM
gi-4940	515	123	:	:	PUNCT
gi-4940	515	124	xi	xi	X
gi-4940	515	125	=	=	SYM
gi-4940	515	126	f	f	PROPN
gi-4940	515	127	(	(	PUNCT
gi-4940	515	128	ϕi	ϕi	PROPN
gi-4940	515	129	,	,	PUNCT
gi-4940	515	130	λ	λ	NOUN
gi-4940	515	131	)	)	PUNCT
gi-4940	515	132	,	,	PUNCT
gi-4940	515	133	yi	yi	NOUN
gi-4940	515	134	=	=	PUNCT
gi-4940	515	135	g(ϕi	g(ϕi	PROPN
gi-4940	515	136	,	,	PUNCT
gi-4940	515	137	λ	λ	NOUN
gi-4940	515	138	)	)	PUNCT
gi-4940	515	139	,	,	PUNCT
gi-4940	515	140	i	i	PRON
gi-4940	515	141	=	=	NOUN
gi-4940	515	142	1	1	NUM
gi-4940	515	143	,	,	PUNCT
gi-4940	515	144	2	2	NUM
gi-4940	515	145	,	,	PUNCT
gi-4940	515	146	3	3	NUM
gi-4940	515	147	11	11	NUM
gi-4940	515	148	:	:	PUNCT
gi-4940	515	149	pa	pa	PROPN
gi-4940	515	150	=	=	PROPN
gi-4940	515	151	point(xa	point(xa	PROPN
gi-4940	515	152	,	,	PUNCT
gi-4940	515	153	ya	ya	PROPN
gi-4940	515	154	)	)	PUNCT
gi-4940	515	155	,	,	PUNCT
gi-4940	515	156	pb	pb	ADP
gi-4940	515	157	=	=	PROPN
gi-4940	515	158	point(xb	point(xb	PROPN
gi-4940	515	159	,	,	PUNCT
gi-4940	515	160	yb	yb	PROPN
gi-4940	515	161	)	)	PUNCT
gi-4940	515	162	,	,	PUNCT
gi-4940	515	163	pi	pi	NOUN
gi-4940	515	164	=	=	SYM
gi-4940	515	165	point(xi	point(xi	PROPN
gi-4940	515	166	,	,	PUNCT
gi-4940	515	167	yi	yi	PROPN
gi-4940	515	168	)	)	PUNCT
gi-4940	515	169	,	,	PUNCT
gi-4940	515	170	i	i	PRON
gi-4940	515	171	=	=	NOUN
gi-4940	515	172	1	1	NUM
gi-4940	515	173	,	,	PUNCT
gi-4940	515	174	2	2	NUM
gi-4940	515	175	,	,	PUNCT
gi-4940	515	176	3	3	NUM
gi-4940	515	177	12	12	NUM
gi-4940	515	178	:	:	PUNCT
gi-4940	515	179	α1	α1	PROPN
gi-4940	515	180	=	=	SYM
gi-4940	515	181	α(pa	α(pa	NOUN
gi-4940	515	182	,	,	PUNCT
gi-4940	515	183	p1	p1	NOUN
gi-4940	515	184	,	,	PUNCT
gi-4940	515	185	p2	p2	NOUN
gi-4940	515	186	)	)	PUNCT
gi-4940	515	187	,	,	PUNCT
gi-4940	515	188	α2	α2	PROPN
gi-4940	515	189	=	=	SYM
gi-4940	515	190	α(p1	α(p1	NOUN
gi-4940	515	191	,	,	PUNCT
gi-4940	515	192	p2	p2	NOUN
gi-4940	515	193	,	,	PUNCT
gi-4940	515	194	p3	p3	PROPN
gi-4940	515	195	)	)	PUNCT
gi-4940	515	196	,	,	PUNCT
gi-4940	515	197	α3	α3	NOUN
gi-4940	515	198	=	=	SYM
gi-4940	515	199	α(p2	α(p2	ADJ
gi-4940	515	200	,	,	PUNCT
gi-4940	515	201	p3	p3	PROPN
gi-4940	515	202	,	,	PUNCT
gi-4940	515	203	pb	pb	ADP
gi-4940	515	204	)	)	PUNCT
gi-4940	515	205	13	13	NUM
gi-4940	515	206	:	:	PUNCT
gi-4940	515	207	if	if	SCONJ
gi-4940	515	208	(	(	PUNCT
gi-4940	515	209	α1	α1	PROPN
gi-4940	515	210	>	>	X
gi-4940	515	211	α	α	PROPN
gi-4940	515	212	)	)	PUNCT
gi-4940	515	213	∨	∨	PROPN
gi-4940	515	214	(	(	PUNCT
gi-4940	515	215	d	d	X
gi-4940	515	216	<	<	X
gi-4940	515	217	=	=	SYM
gi-4940	515	218	d	d	NOUN
gi-4940	515	219	)	)	PUNCT
gi-4940	515	220	then	then	ADV
gi-4940	515	221	14	14	NUM
gi-4940	515	222	:	:	PUNCT
gi-4940	515	223	csmer(p	csmer(p	PROPN
gi-4940	515	224	,	,	PUNCT
gi-4940	515	225	lλ	lλ	INTJ
gi-4940	515	226	,	,	PUNCT
gi-4940	515	227	j	j	PROPN
gi-4940	515	228	,	,	PUNCT
gi-4940	515	229	k	k	PROPN
gi-4940	515	230	,	,	PUNCT
gi-4940	515	231	a	a	PRON
gi-4940	515	232	,	,	PUNCT
gi-4940	515	233	ϕ1	ϕ1	PROPN
gi-4940	515	234	,	,	PUNCT
gi-4940	515	235	xa	xa	PROPN
gi-4940	515	236	,	,	PUNCT
gi-4940	515	237	ya	ya	PROPN
gi-4940	515	238	,	,	PUNCT
gi-4940	515	239	x1	x1	PROPN
gi-4940	515	240	,	,	PUNCT
gi-4940	515	241	y1	y1	NOUN
gi-4940	515	242	,	,	PUNCT
gi-4940	515	243	d+	d+	X
gi-4940	515	244	1	1	NUM
gi-4940	515	245	,	,	PUNCT
gi-4940	515	246	d	d	NOUN
gi-4940	515	247	,	,	PUNCT
gi-4940	515	248	d	d	PROPN
gi-4940	515	249	,	,	PUNCT
gi-4940	515	250	α	α	NOUN
gi-4940	515	251	)	)	PUNCT
gi-4940	515	252	;	;	PUNCT
gi-4940	515	253	15	15	NUM
gi-4940	515	254	:	:	PUNCT
gi-4940	515	255	lλ	lλ	PROPN
gi-4940	515	256	,	,	PUNCT
gi-4940	515	257	j	j	PROPN
gi-4940	515	258	,	,	PUNCT
gi-4940	515	259	k	k	PROPN
gi-4940	515	260	←	←	PROPN
gi-4940	515	261	point(x1	point(x1	PROPN
gi-4940	515	262	,	,	PUNCT
gi-4940	515	263	y1	y1	NOUN
gi-4940	515	264	)	)	PUNCT
gi-4940	515	265	16	16	NUM
gi-4940	515	266	:	:	PUNCT
gi-4940	515	267	if	if	SCONJ
gi-4940	515	268	(	(	PUNCT
gi-4940	515	269	α1	α1	PROPN
gi-4940	515	270	>	>	X
gi-4940	515	271	α	α	PROPN
gi-4940	515	272	)	)	PUNCT
gi-4940	515	273	∨	∨	PROPN
gi-4940	515	274	(	(	PUNCT
gi-4940	515	275	α2	α2	NOUN
gi-4940	515	276	>	>	X
gi-4940	515	277	α	α	PROPN
gi-4940	515	278	)	)	PUNCT
gi-4940	515	279	∨	∨	PROPN
gi-4940	515	280	(	(	PUNCT
gi-4940	515	281	d	d	X
gi-4940	515	282	<	<	X
gi-4940	515	283	=	=	SYM
gi-4940	515	284	d	d	NOUN
gi-4940	515	285	)	)	PUNCT
gi-4940	515	286	then	then	ADV
gi-4940	515	287	17	17	NUM
gi-4940	515	288	:	:	PUNCT
gi-4940	516	1	csmer(p	csmer(p	NOUN
gi-4940	516	2	,	,	PUNCT
gi-4940	516	3	lλ	lλ	INTJ
gi-4940	516	4	,	,	PUNCT
gi-4940	516	5	j	j	PROPN
gi-4940	516	6	,	,	PUNCT
gi-4940	516	7	k	k	PROPN
gi-4940	516	8	,	,	PUNCT
gi-4940	516	9	ϕ1	ϕ1	NOUN
gi-4940	516	10	,	,	PUNCT
gi-4940	516	11	ϕ2	ϕ2	ADV
gi-4940	516	12	,	,	PUNCT
gi-4940	516	13	x1	x1	PROPN
gi-4940	516	14	,	,	PUNCT
gi-4940	516	15	y1	y1	PROPN
gi-4940	516	16	,	,	PUNCT
gi-4940	516	17	x2	x2	PROPN
gi-4940	516	18	,	,	PUNCT
gi-4940	516	19	y2	y2	PROPN
gi-4940	516	20	,	,	PUNCT
gi-4940	516	21	d+	d+	X
gi-4940	516	22	1	1	NUM
gi-4940	516	23	,	,	PUNCT
gi-4940	516	24	d	d	NOUN
gi-4940	516	25	,	,	PUNCT
gi-4940	516	26	d	d	PROPN
gi-4940	516	27	,	,	PUNCT
gi-4940	516	28	α	α	NOUN
gi-4940	516	29	)	)	PUNCT
gi-4940	516	30	;	;	PUNCT
gi-4940	516	31	18	18	NUM
gi-4940	516	32	:	:	PUNCT
gi-4940	516	33	lλ	lλ	PROPN
gi-4940	516	34	,	,	PUNCT
gi-4940	516	35	j	j	PROPN
gi-4940	516	36	,	,	PUNCT
gi-4940	516	37	k	k	PROPN
gi-4940	516	38	←	←	PROPN
gi-4940	516	39	point(x2	point(x2	PROPN
gi-4940	516	40	,	,	PUNCT
gi-4940	516	41	y2	y2	PROPN
gi-4940	516	42	)	)	PUNCT
gi-4940	516	43	19	19	NUM
gi-4940	516	44	:	:	PUNCT
gi-4940	516	45	if	if	SCONJ
gi-4940	516	46	(	(	PUNCT
gi-4940	516	47	α2	α2	ADJ
gi-4940	516	48	>	>	X
gi-4940	516	49	α	α	X
gi-4940	516	50	)	)	PUNCT
gi-4940	516	51	∨	∨	PROPN
gi-4940	516	52	(	(	PUNCT
gi-4940	516	53	α3	α3	NOUN
gi-4940	516	54	>	>	NOUN
gi-4940	516	55	α	α	PROPN
gi-4940	516	56	)	)	PUNCT
gi-4940	516	57	∨	∨	PROPN
gi-4940	516	58	(	(	PUNCT
gi-4940	516	59	d	d	X
gi-4940	516	60	<	<	X
gi-4940	516	61	=	=	SYM
gi-4940	516	62	d	d	NOUN
gi-4940	516	63	)	)	PUNCT
gi-4940	516	64	then	then	ADV
gi-4940	516	65	20	20	NUM
gi-4940	516	66	:	:	PUNCT
gi-4940	516	67	csmer(p	csmer(p	NOUN
gi-4940	516	68	,	,	PUNCT
gi-4940	516	69	lλ	lλ	INTJ
gi-4940	516	70	,	,	PUNCT
gi-4940	516	71	j	j	PROPN
gi-4940	516	72	,	,	PUNCT
gi-4940	516	73	k	k	PROPN
gi-4940	516	74	,	,	PUNCT
gi-4940	516	75	ϕ2	ϕ2	ADV
gi-4940	516	76	,	,	PUNCT
gi-4940	516	77	ϕ3	ϕ3	PROPN
gi-4940	516	78	,	,	PUNCT
gi-4940	516	79	x2	x2	PROPN
gi-4940	516	80	,	,	PUNCT
gi-4940	516	81	y2	y2	PROPN
gi-4940	516	82	,	,	PUNCT
gi-4940	516	83	x3	x3	ADJ
gi-4940	516	84	,	,	PUNCT
gi-4940	516	85	y3	y3	NOUN
gi-4940	516	86	,	,	PUNCT
gi-4940	516	87	d+	d+	PUNCT
gi-4940	516	88	1	1	NUM
gi-4940	516	89	,	,	PUNCT
gi-4940	516	90	d	d	NOUN
gi-4940	516	91	,	,	PUNCT
gi-4940	516	92	d	d	PROPN
gi-4940	516	93	,	,	PUNCT
gi-4940	516	94	α	α	NOUN
gi-4940	516	95	)	)	PUNCT
gi-4940	516	96	;	;	PUNCT
gi-4940	516	97	21	21	NUM
gi-4940	516	98	:	:	PUNCT
gi-4940	516	99	lλ	lλ	PROPN
gi-4940	516	100	,	,	PUNCT
gi-4940	516	101	j	j	PROPN
gi-4940	516	102	,	,	PUNCT
gi-4940	516	103	k	k	PROPN
gi-4940	516	104	←	←	PROPN
gi-4940	516	105	point(x3	point(x3	PROPN
gi-4940	516	106	,	,	PUNCT
gi-4940	516	107	y3	y3	PROPN
gi-4940	516	108	)	)	PUNCT
gi-4940	516	109	22	22	NUM
gi-4940	516	110	:	:	PUNCT
gi-4940	516	111	if	if	SCONJ
gi-4940	516	112	(	(	PUNCT
gi-4940	516	113	α3	α3	INTJ
gi-4940	516	114	>	>	X
gi-4940	516	115	α	α	PROPN
gi-4940	516	116	)	)	PUNCT
gi-4940	516	117	∨	∨	PROPN
gi-4940	516	118	(	(	PUNCT
gi-4940	516	119	d	d	X
gi-4940	516	120	<	<	X
gi-4940	516	121	=	=	SYM
gi-4940	516	122	d	d	NOUN
gi-4940	516	123	)	)	PUNCT
gi-4940	516	124	then	then	ADV
gi-4940	516	125	23	23	NUM
gi-4940	516	126	:	:	PUNCT
gi-4940	516	127	csmer(p	csmer(p	NOUN
gi-4940	516	128	,	,	PUNCT
gi-4940	516	129	lλ	lλ	INTJ
gi-4940	516	130	,	,	PUNCT
gi-4940	516	131	j	j	PROPN
gi-4940	516	132	,	,	PUNCT
gi-4940	516	133	k	k	PROPN
gi-4940	516	134	,	,	PUNCT
gi-4940	516	135	ϕ3	ϕ3	PROPN
gi-4940	516	136	,	,	PUNCT
gi-4940	516	137	b	b	NOUN
gi-4940	516	138	,	,	PUNCT
gi-4940	516	139	x3	x3	ADJ
gi-4940	516	140	,	,	PUNCT
gi-4940	516	141	y3	y3	PROPN
gi-4940	516	142	,	,	PUNCT
gi-4940	516	143	xb	xb	PROPN
gi-4940	516	144	,	,	PUNCT
gi-4940	516	145	yb	yb	PROPN
gi-4940	516	146	,	,	PUNCT
gi-4940	516	147	d+	d+	PUNCT
gi-4940	516	148	1	1	NUM
gi-4940	516	149	,	,	PUNCT
gi-4940	516	150	d	d	NOUN
gi-4940	516	151	,	,	PUNCT
gi-4940	516	152	d	d	PROPN
gi-4940	516	153	,	,	PUNCT
gi-4940	516	154	α	α	NOUN
gi-4940	516	155	)	)	PUNCT
gi-4940	516	156	;	;	PUNCT
gi-4940	516	157	for	for	ADP
gi-4940	516	158	a	a	DET
gi-4940	516	159	given	give	VERB
gi-4940	516	160	ωϕ,j	ωϕ,j	NOUN
gi-4940	516	161	,	,	PUNCT
gi-4940	516	162	k	k	PROPN
gi-4940	516	163	=	=	PUNCT
gi-4940	517	1	[	[	X
gi-4940	517	2	ak	ak	PROPN
gi-4940	517	3	,	,	PUNCT
gi-4940	517	4	bk	bk	PROPN
gi-4940	517	5	]	]	PUNCT
gi-4940	517	6	,	,	PUNCT
gi-4940	517	7	its	its	PRON
gi-4940	517	8	predecessor	predecessor	NOUN
gi-4940	517	9	ωϕ,j	ωϕ,j	PART
gi-4940	517	10	,	,	PUNCT
gi-4940	517	11	k−1	k−1	PROPN
gi-4940	517	12	=	=	PUNCT
gi-4940	518	1	[	[	X
gi-4940	518	2	ak−1	ak−1	ADJ
gi-4940	518	3	,	,	PUNCT
gi-4940	518	4	bk−1	bk−1	NOUN
gi-4940	518	5	]	]	PUNCT
gi-4940	518	6	and	and	CCONJ
gi-4940	518	7	successor	successor	NOUN
gi-4940	518	8	ωϕ,j	ωϕ,j	PART
gi-4940	518	9	,	,	PUNCT
gi-4940	518	10	k+1	k+1	X
gi-4940	518	11	=	=	PUNCT
gi-4940	519	1	[	[	X
gi-4940	519	2	ak+1	ak+1	NOUN
gi-4940	519	3	,	,	PUNCT
gi-4940	519	4	bk+1	bk+1	NOUN
gi-4940	519	5	]	]	PUNCT
gi-4940	519	6	are	be	AUX
gi-4940	519	7	ωϕ,j	ωϕ,j	X
gi-4940	519	8	,	,	PUNCT
gi-4940	519	9	k−1	k−1	PROPN
gi-4940	519	10	=	=	SYM
gi-4940	519	11	pred(ωϕ,j	pred(ωϕ,j	PROPN
gi-4940	519	12	,	,	PUNCT
gi-4940	519	13	k	k	NOUN
gi-4940	519	14	)	)	PUNCT
gi-4940	519	15	,	,	PUNCT
gi-4940	519	16	ωϕ,j	ωϕ,j	X
gi-4940	519	17	,	,	PUNCT
gi-4940	519	18	k+1	k+1	X
gi-4940	519	19	=	=	SYM
gi-4940	519	20	succ(ωϕ,j	succ(ωϕ,j	PROPN
gi-4940	519	21	,	,	PUNCT
gi-4940	519	22	k	k	NOUN
gi-4940	519	23	)	)	PUNCT
gi-4940	519	24	,	,	PUNCT
gi-4940	519	25	where	where	SCONJ
gi-4940	519	26	bk−1	bk−1	ADJ
gi-4940	519	27	=	=	SYM
gi-4940	519	28	ak	ak	PROPN
gi-4940	519	29	,	,	PUNCT
gi-4940	519	30	ak+1	ak+1	VERB
gi-4940	519	31	=	=	PUNCT
gi-4940	519	32	bk	bk	NOUN
gi-4940	519	33	.	.	PUNCT
gi-4940	520	1	analogously	analogously	ADV
gi-4940	520	2	,	,	PUNCT
gi-4940	520	3	for	for	ADP
gi-4940	520	4	the	the	DET
gi-4940	520	5	polygonal	polygonal	ADJ
gi-4940	520	6	approximation	approximation	NOUN
gi-4940	520	7	of	of	ADP
gi-4940	520	8	ωϕ,j	ωϕ,j	PROPN
gi-4940	520	9	,	,	PUNCT
gi-4940	520	10	k	k	PROPN
gi-4940	520	11	bounds	bound	NOUN
gi-4940	520	12	are	be	AUX
gi-4940	520	13	pa	pa	PROPN
gi-4940	520	14	,	,	PUNCT
gi-4940	520	15	k−1	k−1	PROPN
gi-4940	520	16	=	=	SYM
gi-4940	520	17	pred(pa	pred(pa	PROPN
gi-4940	520	18	,	,	PUNCT
gi-4940	520	19	k	k	NOUN
gi-4940	520	20	)	)	PUNCT
gi-4940	520	21	,	,	PUNCT
gi-4940	520	22	pb	pb	PROPN
gi-4940	520	23	,	,	PUNCT
gi-4940	520	24	k+1	k+1	X
gi-4940	520	25	=	=	SYM
gi-4940	520	26	succ(pb	succ(pb	PROPN
gi-4940	520	27	,	,	PUNCT
gi-4940	520	28	k	k	PROPN
gi-4940	520	29	)	)	PUNCT
gi-4940	520	30	,	,	PUNCT
gi-4940	521	1	where	where	SCONJ
gi-4940	521	2	pa	pa	PROPN
gi-4940	521	3	,	,	PUNCT
gi-4940	521	4	k−1	k−1	PROPN
gi-4940	521	5	=	=	PUNCT
gi-4940	522	1	[	[	X
gi-4940	522	2	xa	xa	PROPN
gi-4940	522	3	,	,	PUNCT
gi-4940	522	4	k−1	k−1	PROPN
gi-4940	522	5	,	,	PUNCT
gi-4940	522	6	ya	ya	PROPN
gi-4940	522	7	,	,	PUNCT
gi-4940	522	8	k−1	k−1	PROPN
gi-4940	522	9	]	]	PUNCT
gi-4940	522	10	,	,	PUNCT
gi-4940	522	11	pa	pa	PROPN
gi-4940	522	12	,	,	PUNCT
gi-4940	522	13	k	k	PROPN
gi-4940	523	1	=	=	PUNCT
gi-4940	524	1	[	[	X
gi-4940	524	2	xa	xa	PROPN
gi-4940	524	3	,	,	PUNCT
gi-4940	524	4	k	k	PROPN
gi-4940	524	5	,	,	PUNCT
gi-4940	524	6	ya	ya	PROPN
gi-4940	524	7	,	,	PUNCT
gi-4940	524	8	k	k	PROPN
gi-4940	524	9	]	]	X
gi-4940	524	10	≡	≡	PROPN
gi-4940	524	11	pb	pb	PROPN
gi-4940	524	12	,	,	PUNCT
gi-4940	524	13	k−1	k−1	PROPN
gi-4940	524	14	,	,	PUNCT
gi-4940	524	15	pb	pb	PROPN
gi-4940	524	16	,	,	PUNCT
gi-4940	524	17	k	k	PROPN
gi-4940	524	18	=	=	PUNCT
gi-4940	525	1	[	[	X
gi-4940	525	2	xb	xb	X
gi-4940	525	3	,	,	PUNCT
gi-4940	525	4	k	k	PROPN
gi-4940	525	5	,	,	PUNCT
gi-4940	525	6	yb	yb	PROPN
gi-4940	525	7	,	,	PUNCT
gi-4940	525	8	k	k	PROPN
gi-4940	525	9	]	]	X
gi-4940	525	10	≡	≡	PROPN
gi-4940	525	11	pa	pa	PROPN
gi-4940	525	12	,	,	PUNCT
gi-4940	525	13	k+1	k+1	PROPN
gi-4940	525	14	,	,	PUNCT
gi-4940	525	15	pb	pb	PROPN
gi-4940	525	16	,	,	PUNCT
gi-4940	525	17	k+1	k+1	X
gi-4940	525	18	=	=	X
gi-4940	526	1	[	[	X
gi-4940	526	2	xb	xb	X
gi-4940	526	3	,	,	PUNCT
gi-4940	526	4	k+1	k+1	PROPN
gi-4940	526	5	,	,	PUNCT
gi-4940	526	6	yb	yb	PROPN
gi-4940	526	7	,	,	PUNCT
gi-4940	526	8	k+1	k+1	X
gi-4940	526	9	]	]	X
gi-4940	526	10	,	,	PUNCT
gi-4940	526	11	and	and	CCONJ
gi-4940	526	12	xa	xa	PROPN
gi-4940	526	13	,	,	PUNCT
gi-4940	526	14	k−1	k−1	PROPN
gi-4940	526	15	=	=	SYM
gi-4940	526	16	f	f	PROPN
gi-4940	526	17	(	(	PUNCT
gi-4940	526	18	ak−1	ak−1	PROPN
gi-4940	526	19	,	,	PUNCT
gi-4940	526	20	λ	λ	NOUN
gi-4940	526	21	)	)	PUNCT
gi-4940	526	22	,	,	PUNCT
gi-4940	526	23	xa	xa	PROPN
gi-4940	526	24	,	,	PUNCT
gi-4940	526	25	k	k	PROPN
gi-4940	526	26	=	=	SYM
gi-4940	526	27	f	f	PROPN
gi-4940	526	28	(	(	PUNCT
gi-4940	526	29	ak	ak	PROPN
gi-4940	526	30	,	,	PUNCT
gi-4940	526	31	λ	λ	PROPN
gi-4940	526	32	)	)	PUNCT
gi-4940	526	33	,	,	PUNCT
gi-4940	526	34	xb	xb	PROPN
gi-4940	526	35	,	,	PUNCT
gi-4940	526	36	k	k	PROPN
gi-4940	526	37	=	=	SYM
gi-4940	526	38	f	f	PROPN
gi-4940	526	39	(	(	PUNCT
gi-4940	526	40	bk	bk	PROPN
gi-4940	526	41	,	,	PUNCT
gi-4940	526	42	λ	λ	NOUN
gi-4940	526	43	)	)	PUNCT
gi-4940	526	44	,	,	PUNCT
gi-4940	526	45	xb	xb	PROPN
gi-4940	526	46	,	,	PUNCT
gi-4940	526	47	k+1	k+1	X
gi-4940	526	48	=	=	SYM
gi-4940	526	49	f	f	PROPN
gi-4940	526	50	(	(	PUNCT
gi-4940	526	51	bk+1	bk+1	NOUN
gi-4940	526	52	,	,	PUNCT
gi-4940	526	53	λ	λ	NOUN
gi-4940	526	54	)	)	PUNCT
gi-4940	526	55	;	;	PUNCT
gi-4940	526	56	see	see	VERB
gi-4940	526	57	fig	fig	NOUN
gi-4940	526	58	.	.	PUNCT
gi-4940	527	1	4.2	4.2	NUM
gi-4940	527	2	the	the	DET
gi-4940	527	3	approximate	approximate	ADJ
gi-4940	527	4	quarters	quarter	NOUN
gi-4940	527	5	of	of	ADP
gi-4940	527	6	ωϕ,j	ωϕ,j	PROPN
gi-4940	527	7	,	,	PUNCT
gi-4940	527	8	k	k	PROPN
gi-4940	527	9	denoted	denote	VERB
gi-4940	527	10	as	as	ADP
gi-4940	527	11	ωϕ,j	ωϕ,j	X
gi-4940	527	12	,	,	PUNCT
gi-4940	527	13	k	k	PROPN
gi-4940	527	14	,	,	PUNCT
gi-4940	527	15	l	l	NOUN
gi-4940	527	16	,	,	PUNCT
gi-4940	527	17	l	l	NOUN
gi-4940	527	18	=	=	SYM
gi-4940	527	19	1	1	NUM
gi-4940	527	20	,	,	PUNCT
gi-4940	527	21	...	...	PUNCT
gi-4940	527	22	,	,	PUNCT
gi-4940	527	23	4	4	NUM
gi-4940	527	24	,	,	PUNCT
gi-4940	527	25	have	have	VERB
gi-4940	527	26	the	the	DET
gi-4940	527	27	form	form	NOUN
gi-4940	527	28	of	of	ADP
gi-4940	527	29	ωϕ,j	ωϕ,j	X
gi-4940	527	30	,	,	PUNCT
gi-4940	527	31	k,1	k,1	PROPN
gi-4940	527	32	=	=	PUNCT
gi-4940	528	1	[	[	X
gi-4940	528	2	ak	ak	PROPN
gi-4940	528	3	,	,	PUNCT
gi-4940	528	4	ϕ1,k	ϕ1,k	PROPN
gi-4940	528	5	]	]	X
gi-4940	528	6	,	,	PUNCT
gi-4940	528	7	ωϕ,j	ωϕ,j	X
gi-4940	528	8	,	,	PUNCT
gi-4940	528	9	k,2	k,2	X
gi-4940	528	10	=	=	X
gi-4940	529	1	[	[	X
gi-4940	529	2	ϕ1,k	ϕ1,k	PROPN
gi-4940	529	3	,	,	PUNCT
gi-4940	529	4	ϕ2,k	ϕ2,k	PROPN
gi-4940	529	5	]	]	PUNCT
gi-4940	529	6	ωϕ,j	ωϕ,j	X
gi-4940	529	7	,	,	PUNCT
gi-4940	529	8	k,3	k,3	X
gi-4940	529	9	=	=	PUNCT
gi-4940	530	1	[	[	X
gi-4940	530	2	ϕ2,k	ϕ2,k	PROPN
gi-4940	530	3	,	,	PUNCT
gi-4940	530	4	ϕ3,k	ϕ3,k	PROPN
gi-4940	530	5	]	]	X
gi-4940	530	6	,	,	PUNCT
gi-4940	530	7	ωϕ,j	ωϕ,j	X
gi-4940	530	8	,	,	PUNCT
gi-4940	530	9	k,4	k,4	X
gi-4940	530	10	=	=	PUNCT
gi-4940	531	1	[	[	X
gi-4940	531	2	ϕ3,k	ϕ3,k	PROPN
gi-4940	531	3	,	,	PUNCT
gi-4940	531	4	bk	bk	ADP
gi-4940	531	5	]	]	PUNCT
gi-4940	531	6	,	,	PUNCT
gi-4940	531	7	the	the	DET
gi-4940	531	8	idea	idea	NOUN
gi-4940	531	9	of	of	ADP
gi-4940	531	10	modification	modification	NOUN
gi-4940	531	11	is	be	AUX
gi-4940	531	12	straightforward	straightforward	ADJ
gi-4940	531	13	,	,	PUNCT
gi-4940	531	14	an	an	DET
gi-4940	531	15	information	information	NOUN
gi-4940	531	16	about	about	ADP
gi-4940	531	17	previous	previous	ADJ
gi-4940	531	18	and	and	CCONJ
gi-4940	531	19	subsequent	subsequent	ADJ
gi-4940	531	20	quarters	quarter	NOUN
gi-4940	531	21	of	of	ADP
gi-4940	531	22	ωϕ,j	ωϕ,j	X
gi-4940	531	23	,	,	PUNCT
gi-4940	531	24	k	k	PROPN
gi-4940	531	25	,	,	PUNCT
gi-4940	531	26	l	l	NOUN
gi-4940	531	27	is	be	AUX
gi-4940	531	28	stored	store	VERB
gi-4940	531	29	ωϕ,j	ωϕ,j	X
gi-4940	531	30	,	,	PUNCT
gi-4940	531	31	k	k	PROPN
gi-4940	531	32	,	,	PUNCT
gi-4940	531	33	l−1	l−1	PROPN
gi-4940	531	34	=	=	SYM
gi-4940	531	35	pred(ωϕ,j	pred(ωϕ,j	PROPN
gi-4940	531	36	,	,	PUNCT
gi-4940	531	37	k	k	PROPN
gi-4940	531	38	,	,	PUNCT
gi-4940	531	39	l	l	NOUN
gi-4940	531	40	)	)	PUNCT
gi-4940	531	41	,	,	PUNCT
gi-4940	531	42	ωϕ,j	ωϕ,j	X
gi-4940	531	43	,	,	PUNCT
gi-4940	531	44	k	k	PROPN
gi-4940	531	45	,	,	PUNCT
gi-4940	531	46	l+1	l+1	X
gi-4940	531	47	=	=	SYM
gi-4940	531	48	succ(ωϕ,j	succ(ωϕ,j	PROPN
gi-4940	531	49	,	,	PUNCT
gi-4940	531	50	k	k	NOUN
gi-4940	531	51	,	,	PUNCT
gi-4940	531	52	l	l	NOUN
gi-4940	531	53	)	)	PUNCT
gi-4940	531	54	.	.	PUNCT
gi-4940	532	1	while	while	SCONJ
gi-4940	532	2	the	the	DET
gi-4940	532	3	first	first	ADJ
gi-4940	532	4	quarter	quarter	NOUN
gi-4940	532	5	lacks	lack	VERB
gi-4940	532	6	its	its	PRON
gi-4940	532	7	predecessor	predecessor	NOUN
gi-4940	532	8	,	,	PUNCT
gi-4940	532	9	the	the	DET
gi-4940	532	10	last	last	ADJ
gi-4940	532	11	quarter	quarter	NOUN
gi-4940	532	12	lacks	lack	VERB
gi-4940	532	13	the	the	DET
gi-4940	532	14	successor	successor	NOUN
gi-4940	532	15	.	.	PUNCT
gi-4940	533	1	for	for	ADP
gi-4940	533	2	a	a	DET
gi-4940	533	3	current	current	ADJ
gi-4940	533	4	recursive	recursive	ADJ
gi-4940	533	5	depth	depth	NOUN
gi-4940	533	6	d	d	NOUN
gi-4940	533	7	,	,	PUNCT
gi-4940	533	8	the	the	DET
gi-4940	533	9	segment	segment	NOUN
gi-4940	533	10	(	(	PUNCT
gi-4940	533	11	pa	pa	PROPN
gi-4940	533	12	,	,	PUNCT
gi-4940	533	13	k	k	PROPN
gi-4940	533	14	,	,	PUNCT
gi-4940	533	15	pb	pb	PROPN
gi-4940	533	16	,	,	PUNCT
gi-4940	533	17	k	k	NOUN
gi-4940	533	18	)	)	PUNCT
gi-4940	533	19	of	of	ADP
gi-4940	533	20	the	the	DET
gi-4940	533	21	polygonal	polygonal	ADJ
gi-4940	533	22	approximation	approximation	NOUN
gi-4940	533	23	is	be	AUX
gi-4940	533	24	split	split	VERB
gi-4940	533	25	to	to	ADP
gi-4940	533	26	the	the	DET
gi-4940	533	27	quarters	quarter	NOUN
gi-4940	533	28	,	,	PUNCT
gi-4940	533	29	where	where	SCONJ
gi-4940	533	30	p1,k	p1,k	PROPN
gi-4940	533	31	,	,	PUNCT
gi-4940	533	32	p2,k	p2,k	PROPN
gi-4940	533	33	,	,	PUNCT
gi-4940	533	34	p3,k	p3,k	PROPN
gi-4940	533	35	are	be	AUX
gi-4940	533	36	the	the	DET
gi-4940	533	37	newly	newly	ADV
gi-4940	533	38	created	create	VERB
gi-4940	533	39	vertices	vertex	NOUN
gi-4940	533	40	at	at	ADP
gi-4940	533	41	the	the	DET
gi-4940	533	42	recursive	recursive	ADJ
gi-4940	533	43	depth	depth	NOUN
gi-4940	533	44	d+	d+	NOUN
gi-4940	533	45	1	1	NUM
gi-4940	533	46	representing	represent	VERB
gi-4940	533	47	the	the	DET
gi-4940	533	48	“	"	PUNCT
gi-4940	533	49	projected	project	VERB
gi-4940	533	50	bounds	bound	NOUN
gi-4940	533	51	”	"	PUNCT
gi-4940	533	52	of	of	ADP
gi-4940	533	53	newly	newly	ADV
gi-4940	533	54	created	create	VERB
gi-4940	533	55	intervals	interval	NOUN
gi-4940	533	56	ωϕ,j	ωϕ,j	X
gi-4940	533	57	,	,	PUNCT
gi-4940	533	58	k,1,	k,1,	PROPN
gi-4940	533	59	...	...	PUNCT
gi-4940	533	60	,ωϕ,j	,ωϕ,j	PUNCT
gi-4940	533	61	,	,	PUNCT
gi-4940	533	62	k,4	k,4	PROPN
gi-4940	533	63	.	.	PUNCT
gi-4940	534	1	unlike	unlike	ADP
gi-4940	534	2	s1	s1	NOUN
gi-4940	534	3	,	,	PUNCT
gi-4940	534	4	s2	s2	PROPN
gi-4940	534	5	,	,	PUNCT
gi-4940	534	6	the	the	DET
gi-4940	534	7	angles	angle	NOUN
gi-4940	534	8	αi	αi	NOUN
gi-4940	534	9	are	be	AUX
gi-4940	534	10	measured	measure	VERB
gi-4940	534	11	not	not	PART
gi-4940	534	12	only	only	ADV
gi-4940	534	13	between	between	ADP
gi-4940	534	14	the	the	DET
gi-4940	534	15	newly	newly	ADV
gi-4940	534	16	created	create	VERB
gi-4940	534	17	segments	segment	NOUN
gi-4940	534	18	geoinformatics	geoinformatic	NOUN
gi-4940	534	19	fce	fce	VERB
gi-4940	534	20	ctu	ctu	NOUN
gi-4940	534	21	17(2	17(2	NUM
gi-4940	534	22	)	)	PUNCT
gi-4940	534	23	,	,	PUNCT
gi-4940	534	24	2018	2018	NUM
gi-4940	534	25	48	48	NUM
gi-4940	534	26	t.	t.	NOUN
gi-4940	534	27	bayer	bayer	PROPN
gi-4940	534	28	:	:	PUNCT
gi-4940	534	29	plotting	plot	VERB
gi-4940	534	30	the	the	DET
gi-4940	534	31	map	map	NOUN
gi-4940	534	32	projection	projection	NOUN
gi-4940	534	33	graticule	graticule	NOUN
gi-4940	534	34	with	with	ADP
gi-4940	534	35	discontinuities	discontinuity	NOUN
gi-4940	534	36	p	p	VERB
gi-4940	534	37	a,1	a,1	NOUN
gi-4940	534	38	p	p	NOUN
gi-4940	534	39	b,1	b,1	ADP
gi-4940	534	40	m(l	m(l	PROPN
gi-4940	534	41	)	)	PUNCT
gi-4940	535	1	p	p	NOUN
gi-4940	535	2	a,1	a,1	NOUN
gi-4940	535	3	p	p	NOUN
gi-4940	535	4	b,1	b,1	NOUN
gi-4940	535	5	=	=	SYM
gi-4940	535	6	p	p	NOUN
gi-4940	535	7	a,2	a,2	X
gi-4940	535	8	p	p	PROPN
gi-4940	535	9	1,1	1,1	NUM
gi-4940	535	10	p	p	NOUN
gi-4940	535	11	2,1	2,1	NUM
gi-4940	535	12	p	p	NOUN
gi-4940	535	13	3,1	3,1	NUM
gi-4940	535	14	p	p	NOUN
gi-4940	535	15	1,1	1,1	NUM
gi-4940	535	16	p	p	NOUN
gi-4940	535	17	2,1	2,1	NUM
gi-4940	535	18	p	p	NOUN
gi-4940	535	19	3,1	3,1	NUM
gi-4940	535	20	p	p	NOUN
gi-4940	535	21	1,2	1,2	NUM
gi-4940	535	22	p	p	NOUN
gi-4940	535	23	2,2	2,2	NUM
gi-4940	535	24	p	p	NOUN
gi-4940	535	25	3,2	3,2	NUM
gi-4940	535	26	p	p	NOUN
gi-4940	535	27	1,3	1,3	NUM
gi-4940	535	28	p	p	NOUN
gi-4940	535	29	2,3	2,3	NUM
gi-4940	535	30	p	p	NOUN
gi-4940	535	31	3,3	3,3	NUM
gi-4940	535	32	m(l	m(l	NOUN
gi-4940	535	33	)	)	PUNCT
gi-4940	535	34	m(l	m(l	NOUN
gi-4940	535	35	)	)	PUNCT
gi-4940	535	36	m(l	m(l	NOUN
gi-4940	535	37	)	)	PUNCT
gi-4940	535	38	p	p	NOUN
gi-4940	535	39	3,1	3,1	NUM
gi-4940	536	1	p	p	NOUN
gi-4940	536	2	1,3	1,3	NUM
gi-4940	536	3	p	p	NOUN
gi-4940	536	4	a,1	a,1	NOUN
gi-4940	536	5	p	p	NOUN
gi-4940	536	6	b,4	b,4	NOUN
gi-4940	536	7	p	p	NOUN
gi-4940	536	8	3,2	3,2	NUM
gi-4940	536	9	p	p	NOUN
gi-4940	536	10	1,4	1,4	NUM
gi-4940	536	11	p	p	NOUN
gi-4940	536	12	a,1	a,1	NOUN
gi-4940	536	13	p	p	NOUN
gi-4940	536	14	b,1	b,1	NOUN
gi-4940	537	1	=	=	SYM
gi-4940	537	2	p	p	NOUN
gi-4940	537	3	a,2	a,2	X
gi-4940	537	4	p	p	NOUN
gi-4940	537	5	b,2	b,2	VERB
gi-4940	537	6	=	=	PROPN
gi-4940	537	7	p	p	NOUN
gi-4940	537	8	a,3	a,3	NOUN
gi-4940	537	9	p	p	NOUN
gi-4940	537	10	b,3	b,3	NOUN
gi-4940	538	1	=	=	SYM
gi-4940	538	2	p	p	X
gi-4940	538	3	a,4	a,4	NOUN
gi-4940	538	4	p	p	NOUN
gi-4940	538	5	b,1	b,1	NOUN
gi-4940	539	1	=	=	SYM
gi-4940	539	2	p	p	NOUN
gi-4940	539	3	a,2	a,2	X
gi-4940	539	4	p	p	NOUN
gi-4940	539	5	b,2	b,2	VERB
gi-4940	539	6	=	=	PROPN
gi-4940	539	7	p	p	NOUN
gi-4940	539	8	a,3	a,3	NOUN
gi-4940	539	9	p	p	NOUN
gi-4940	539	10	b,3	b,3	NOUN
gi-4940	540	1	=	=	SYM
gi-4940	540	2	p	p	X
gi-4940	540	3	a,4	a,4	NOUN
gi-4940	540	4	p	p	NOUN
gi-4940	540	5	b,4	b,4	PROPN
gi-4940	540	6	p	p	NOUN
gi-4940	540	7	b,4	b,4	NOUN
gi-4940	540	8	p	p	NOUN
gi-4940	540	9	b,2	b,2	VERB
gi-4940	540	10	=	=	NOUN
gi-4940	540	11	p	p	NOUN
gi-4940	540	12	a,3	a,3	NOUN
gi-4940	540	13	p	p	NOUN
gi-4940	540	14	b,3	b,3	NOUN
gi-4940	541	1	=	=	SYM
gi-4940	541	2	p	p	NOUN
gi-4940	541	3	a,4	a,4	NOUN
gi-4940	541	4	p	p	NOUN
gi-4940	541	5	1,2	1,2	NUM
gi-4940	541	6	figure	figure	NOUN
gi-4940	541	7	4.2	4.2	NUM
gi-4940	541	8	:	:	PUNCT
gi-4940	541	9	illustration	illustration	NOUN
gi-4940	541	10	of	of	ADP
gi-4940	541	11	the	the	DET
gi-4940	541	12	combined	combine	VERB
gi-4940	541	13	sampling	sampling	NOUN
gi-4940	541	14	method	method	NOUN
gi-4940	541	15	s3	s3	PROPN
gi-4940	541	16	for	for	ADP
gi-4940	541	17	the	the	DET
gi-4940	541	18	meridian	meridian	PROPN
gi-4940	541	19	m(λ	m(λ	PROPN
gi-4940	541	20	)	)	PUNCT
gi-4940	541	21	.	.	PUNCT
gi-4940	542	1	α1	α1	PROPN
gi-4940	542	2	=	=	SYM
gi-4940	542	3	α(pa	α(pa	NOUN
gi-4940	542	4	,	,	PUNCT
gi-4940	542	5	k	k	PROPN
gi-4940	542	6	,	,	PUNCT
gi-4940	542	7	p1,k	p1,k	PROPN
gi-4940	542	8	,	,	PUNCT
gi-4940	542	9	p2,k	p2,k	PROPN
gi-4940	542	10	)	)	PUNCT
gi-4940	542	11	,	,	PUNCT
gi-4940	542	12	α2	α2	PROPN
gi-4940	542	13	=	=	SYM
gi-4940	542	14	α(p1,k	α(p1,k	PROPN
gi-4940	542	15	,	,	PUNCT
gi-4940	542	16	p2,k	p2,k	PROPN
gi-4940	542	17	,	,	PUNCT
gi-4940	542	18	p3,k	p3,k	PROPN
gi-4940	542	19	)	)	PUNCT
gi-4940	542	20	,	,	PUNCT
gi-4940	542	21	α3	α3	PROPN
gi-4940	542	22	=	=	SYM
gi-4940	542	23	α(p2,k	α(p2,k	PROPN
gi-4940	542	24	,	,	PUNCT
gi-4940	542	25	p3,k	p3,k	PROPN
gi-4940	542	26	,	,	PUNCT
gi-4940	542	27	pb	pb	ADP
gi-4940	542	28	,	,	PUNCT
gi-4940	542	29	k	k	NOUN
gi-4940	542	30	)	)	PUNCT
gi-4940	542	31	,	,	PUNCT
gi-4940	542	32	in	in	ADP
gi-4940	542	33	the	the	DET
gi-4940	542	34	recursive	recursive	ADJ
gi-4940	542	35	depth	depth	NOUN
gi-4940	542	36	d+	d+	PUNCT
gi-4940	542	37	1	1	NUM
gi-4940	542	38	,	,	PUNCT
gi-4940	542	39	but	but	CCONJ
gi-4940	542	40	also	also	ADV
gi-4940	542	41	between	between	ADP
gi-4940	542	42	the	the	DET
gi-4940	542	43	adjacent	adjacent	ADJ
gi-4940	542	44	segments	segment	NOUN
gi-4940	542	45	α0	α0	PROPN
gi-4940	542	46	=	=	SYM
gi-4940	542	47	α(p3,k−1	α(p3,k−1	PROPN
gi-4940	542	48	,	,	PUNCT
gi-4940	542	49	pa	pa	PROPN
gi-4940	542	50	,	,	PUNCT
gi-4940	542	51	k	k	PROPN
gi-4940	542	52	,	,	PUNCT
gi-4940	542	53	p1,k	p1,k	PROPN
gi-4940	542	54	)	)	PUNCT
gi-4940	542	55	,	,	PUNCT
gi-4940	542	56	α4	α4	NOUN
gi-4940	542	57	=	=	SYM
gi-4940	542	58	α(p3,k	α(p3,k	PROPN
gi-4940	542	59	,	,	PUNCT
gi-4940	542	60	pb	pb	PROPN
gi-4940	542	61	,	,	PUNCT
gi-4940	542	62	k	k	NOUN
gi-4940	542	63	,	,	PUNCT
gi-4940	542	64	p1,k+1	p1,k+1	PROPN
gi-4940	542	65	)	)	PUNCT
gi-4940	542	66	,	,	PUNCT
gi-4940	542	67	where	where	SCONJ
gi-4940	542	68	p3,k−1	p3,k−1	PROPN
gi-4940	542	69	is	be	AUX
gi-4940	542	70	the	the	DET
gi-4940	542	71	projected	project	VERB
gi-4940	542	72	lower	lower	ADV
gi-4940	542	73	bound	bind	VERB
gi-4940	542	74	of	of	ADP
gi-4940	542	75	ωϕ,j	ωϕ,j	X
gi-4940	542	76	,	,	PUNCT
gi-4940	542	77	k−1,4	k−1,4	PROPN
gi-4940	542	78	(	(	PUNCT
gi-4940	542	79	a	a	DET
gi-4940	542	80	projected	project	VERB
gi-4940	542	81	third	third	ADJ
gi-4940	542	82	quarter	quarter	NOUN
gi-4940	542	83	of	of	ADP
gi-4940	542	84	the	the	DET
gi-4940	542	85	interval	interval	NOUN
gi-4940	542	86	ωϕ,j	ωϕ,j	PUNCT
gi-4940	542	87	,	,	PUNCT
gi-4940	542	88	k−1	k−1	PROPN
gi-4940	542	89	previous	previous	ADJ
gi-4940	542	90	to	to	ADP
gi-4940	542	91	ωϕ,j	ωϕ,j	X
gi-4940	542	92	,	,	PUNCT
gi-4940	542	93	k	k	NOUN
gi-4940	542	94	)	)	PUNCT
gi-4940	542	95	with	with	ADP
gi-4940	542	96	the	the	DET
gi-4940	542	97	latitude	latitude	NOUN
gi-4940	542	98	ϕ3,k−1	ϕ3,k−1	PROPN
gi-4940	542	99	=	=	SYM
gi-4940	542	100	ak	ak	PROPN
gi-4940	542	101	+	+	PROPN
gi-4940	542	102	1	1	NUM
gi-4940	542	103	2r0(ak−1	2r0(ak−1	PROPN
gi-4940	542	104	−	−	PROPN
gi-4940	542	105	ak	ak	PROPN
gi-4940	542	106	)	)	PUNCT
gi-4940	542	107	,	,	PUNCT
gi-4940	542	108	p1,k+1	p1,k+1	PROPN
gi-4940	542	109	is	be	AUX
gi-4940	542	110	the	the	DET
gi-4940	542	111	projected	project	VERB
gi-4940	542	112	first	first	ADJ
gi-4940	542	113	-	-	PUNCT
gi-4940	542	114	quarter	quarter	NOUN
gi-4940	542	115	ωϕ,j	ωϕ,j	NOUN
gi-4940	542	116	,	,	PUNCT
gi-4940	542	117	k+1,1	k+1,1	NOUN
gi-4940	542	118	of	of	ADP
gi-4940	542	119	the	the	DET
gi-4940	542	120	next	next	ADJ
gi-4940	542	121	interval	interval	NOUN
gi-4940	542	122	ωϕ,j	ωϕ,j	PUNCT
gi-4940	542	123	,	,	PUNCT
gi-4940	542	124	k+1	k+1	X
gi-4940	542	125	with	with	ADP
gi-4940	542	126	the	the	DET
gi-4940	542	127	latitude	latitude	NOUN
gi-4940	542	128	ϕ1,k+1	ϕ1,k+1	PUNCT
gi-4940	543	1	=	=	PUNCT
gi-4940	543	2	bk	bk	PROPN
gi-4940	543	3	+	+	NOUN
gi-4940	543	4	1	1	NUM
gi-4940	543	5	2r4(bk+1	2r4(bk+1	NUM
gi-4940	543	6	−	−	NOUN
gi-4940	543	7	bk	bk	NOUN
gi-4940	543	8	)	)	PUNCT
gi-4940	543	9	,	,	PUNCT
gi-4940	543	10	and	and	CCONJ
gi-4940	543	11	r0	r0	NOUN
gi-4940	543	12	,	,	PUNCT
gi-4940	543	13	r4	r4	PROPN
gi-4940	543	14	are	be	AUX
gi-4940	543	15	the	the	DET
gi-4940	543	16	random	random	ADJ
gi-4940	543	17	numbers	number	NOUN
gi-4940	543	18	generated	generate	VERB
gi-4940	543	19	according	accord	VERB
gi-4940	543	20	to	to	ADP
gi-4940	543	21	the	the	DET
gi-4940	543	22	principles	principle	NOUN
gi-4940	543	23	mentioned	mention	VERB
gi-4940	543	24	above	above	ADV
gi-4940	543	25	.	.	PUNCT
gi-4940	544	1	the	the	DET
gi-4940	544	2	modified	modify	VERB
gi-4940	544	3	condition	condition	NOUN
gi-4940	544	4	for	for	ADP
gi-4940	544	5	the	the	DET
gi-4940	544	6	recursive	recursive	ADJ
gi-4940	544	7	call	call	NOUN
gi-4940	544	8	has	have	VERB
gi-4940	544	9	the	the	DET
gi-4940	544	10	form	form	NOUN
gi-4940	544	11	of	of	ADP
gi-4940	544	12	α0	α0	PROPN
gi-4940	544	13	>	>	PUNCT
gi-4940	544	14	α	α	PROPN
gi-4940	544	15	∨	∨	PROPN
gi-4940	544	16	α1	α1	PROPN
gi-4940	544	17	>	>	X
gi-4940	544	18	α	α	PROPN
gi-4940	544	19	∨	∨	VERB
gi-4940	544	20	α2	α2	PROPN
gi-4940	544	21	>	>	PUNCT
gi-4940	545	1	α	α	PROPN
gi-4940	545	2	∨	∨	NUM
gi-4940	545	3	α3	α3	PROPN
gi-4940	545	4	>	>	X
gi-4940	545	5	α	α	PROPN
gi-4940	545	6	∨	∨	NUM
gi-4940	545	7	α4	α4	PROPN
gi-4940	545	8	>	>	X
gi-4940	545	9	α	α	X
gi-4940	545	10	.	.	PUNCT
gi-4940	546	1	(	(	PUNCT
gi-4940	546	2	4.2	4.2	NUM
gi-4940	546	3	)	)	PUNCT
gi-4940	546	4	in	in	ADP
gi-4940	546	5	general	general	ADJ
gi-4940	546	6	,	,	PUNCT
gi-4940	546	7	the	the	DET
gi-4940	546	8	improved	improved	ADJ
gi-4940	546	9	performance	performance	NOUN
gi-4940	546	10	of	of	ADP
gi-4940	546	11	s3	s3	PROPN
gi-4940	546	12	occurs	occur	VERB
gi-4940	546	13	only	only	ADV
gi-4940	546	14	in	in	ADP
gi-4940	546	15	specific	specific	ADJ
gi-4940	546	16	situations	situation	NOUN
gi-4940	546	17	when	when	SCONJ
gi-4940	546	18	the	the	DET
gi-4940	546	19	sampled	sample	VERB
gi-4940	546	20	function	function	NOUN
gi-4940	546	21	has	have	VERB
gi-4940	546	22	a	a	DET
gi-4940	546	23	complex	complex	ADJ
gi-4940	546	24	shape	shape	NOUN
gi-4940	546	25	(	(	PUNCT
gi-4940	546	26	meridians	meridian	NOUN
gi-4940	546	27	of	of	ADP
gi-4940	546	28	bonne	bonne	PROPN
gi-4940	546	29	projections	projection	NOUN
gi-4940	546	30	)	)	PUNCT
gi-4940	546	31	.	.	PUNCT
gi-4940	547	1	however	however	ADV
gi-4940	547	2	,	,	PUNCT
gi-4940	547	3	the	the	DET
gi-4940	547	4	significant	significant	ADJ
gi-4940	547	5	disadvantage	disadvantage	NOUN
gi-4940	547	6	is	be	AUX
gi-4940	547	7	represented	represent	VERB
gi-4940	547	8	by	by	ADP
gi-4940	547	9	the	the	DET
gi-4940	547	10	increased	increase	VERB
gi-4940	547	11	amount	amount	NOUN
gi-4940	547	12	of	of	ADP
gi-4940	547	13	sampled	sample	VERB
gi-4940	547	14	points	point	NOUN
gi-4940	547	15	in	in	ADP
gi-4940	547	16	the	the	DET
gi-4940	547	17	highly	highly	ADV
gi-4940	547	18	curved	curved	ADJ
gi-4940	547	19	areas	area	NOUN
gi-4940	547	20	.	.	PUNCT
gi-4940	548	1	the	the	DET
gi-4940	548	2	recursive	recursive	ADJ
gi-4940	548	3	step	step	NOUN
gi-4940	548	4	has	have	VERB
gi-4940	548	5	a	a	DET
gi-4940	548	6	slightly	slightly	ADV
gi-4940	548	7	different	different	ADJ
gi-4940	548	8	form	form	NOUN
gi-4940	548	9	:	:	PUNCT
gi-4940	549	1	1	1	X
gi-4940	549	2	.	.	X
gi-4940	549	3	if	if	SCONJ
gi-4940	549	4	d	d	PROPN
gi-4940	549	5	>	>	X
gi-4940	549	6	d	d	PROPN
gi-4940	549	7	or	or	CCONJ
gi-4940	549	8	bk	bk	PROPN
gi-4940	549	9	−	−	PROPN
gi-4940	549	10	ak	ak	PROPN
gi-4940	549	11	<	<	X
gi-4940	549	12	ε	ε	PROPN
gi-4940	549	13	,	,	PUNCT
gi-4940	549	14	stop	stop	VERB
gi-4940	549	15	the	the	DET
gi-4940	549	16	recursive	recursive	ADJ
gi-4940	549	17	procedure	procedure	NOUN
gi-4940	549	18	and	and	CCONJ
gi-4940	549	19	go	go	VERB
gi-4940	549	20	to	to	PART
gi-4940	549	21	step	step	VERB
gi-4940	549	22	3	3	NUM
gi-4940	549	23	.	.	NOUN
gi-4940	549	24	2	2	NUM
gi-4940	549	25	.	.	X
gi-4940	549	26	for	for	ADP
gi-4940	549	27	a	a	DET
gi-4940	549	28	given	give	VERB
gi-4940	549	29	ωϕ,j	ωϕ,j	NOUN
gi-4940	549	30	,	,	PUNCT
gi-4940	549	31	k	k	PROPN
gi-4940	549	32	=	=	PUNCT
gi-4940	550	1	[	[	X
gi-4940	550	2	ak	ak	PROPN
gi-4940	550	3	,	,	PUNCT
gi-4940	550	4	bk	bk	PROPN
gi-4940	550	5	]	]	PUNCT
gi-4940	550	6	,	,	PUNCT
gi-4940	550	7	its	its	PRON
gi-4940	550	8	predecessor	predecessor	NOUN
gi-4940	550	9	ωϕ,j	ωϕ,j	PART
gi-4940	550	10	,	,	PUNCT
gi-4940	550	11	k−1	k−1	PROPN
gi-4940	550	12	=	=	PUNCT
gi-4940	551	1	[	[	X
gi-4940	551	2	ak−1	ak−1	ADJ
gi-4940	551	3	,	,	PUNCT
gi-4940	551	4	bk−1	bk−1	NOUN
gi-4940	551	5	]	]	X
gi-4940	551	6	,	,	PUNCT
gi-4940	551	7	and	and	CCONJ
gi-4940	551	8	successor	successor	NOUN
gi-4940	551	9	ωϕ,j	ωϕ,j	PART
gi-4940	551	10	,	,	PUNCT
gi-4940	551	11	k+1	k+1	X
gi-4940	551	12	=	=	PUNCT
gi-4940	552	1	[	[	X
gi-4940	552	2	ak+1	ak+1	NOUN
gi-4940	552	3	,	,	PUNCT
gi-4940	552	4	bk+1	bk+1	NOUN
gi-4940	552	5	]	]	PUNCT
gi-4940	552	6	,	,	PUNCT
gi-4940	552	7	the	the	DET
gi-4940	552	8	interval	interval	NOUN
gi-4940	552	9	is	be	AUX
gi-4940	552	10	split	split	VERB
gi-4940	552	11	by	by	ADP
gi-4940	552	12	three	three	NUM
gi-4940	552	13	points	point	NOUN
gi-4940	552	14	,	,	PUNCT
gi-4940	552	15	the	the	DET
gi-4940	552	16	positions	position	NOUN
gi-4940	552	17	are	be	AUX
gi-4940	552	18	close	close	ADJ
gi-4940	552	19	to	to	ADP
gi-4940	552	20	the	the	DET
gi-4940	552	21	quarters	quarter	NOUN
gi-4940	552	22	of	of	ADP
gi-4940	552	23	the	the	DET
gi-4940	552	24	interval	interval	NOUN
gi-4940	552	25	ϕ1,k	ϕ1,k	PROPN
gi-4940	552	26	=	=	PROPN
gi-4940	552	27	ak	ak	PROPN
gi-4940	553	1	+	+	PROPN
gi-4940	553	2	1	1	NUM
gi-4940	553	3	2r1(bk	2r1(bk	NUM
gi-4940	553	4	−	−	PROPN
gi-4940	553	5	ak	ak	PROPN
gi-4940	553	6	)	)	PUNCT
gi-4940	553	7	,	,	PUNCT
gi-4940	553	8	ϕ2,k	ϕ2,k	PROPN
gi-4940	553	9	=	=	SYM
gi-4940	553	10	ak	ak	PROPN
gi-4940	553	11	+	+	CCONJ
gi-4940	553	12	r2(bk	r2(bk	PROPN
gi-4940	553	13	−	−	PROPN
gi-4940	553	14	ak	ak	PROPN
gi-4940	553	15	)	)	PUNCT
gi-4940	553	16	,	,	PUNCT
gi-4940	553	17	ϕ3,k	ϕ3,k	PROPN
gi-4940	553	18	=	=	PROPN
gi-4940	553	19	ak	ak	PROPN
gi-4940	554	1	+	+	CCONJ
gi-4940	554	2	3	3	NUM
gi-4940	554	3	2r3(bk	2r3(bk	NUM
gi-4940	554	4	−	−	PROPN
gi-4940	554	5	ak	ak	PROPN
gi-4940	554	6	)	)	PUNCT
gi-4940	554	7	.	.	PUNCT
gi-4940	555	1	geoinformatics	geoinformatic	NOUN
gi-4940	555	2	fce	fce	VERB
gi-4940	555	3	ctu	ctu	NOUN
gi-4940	555	4	17(2	17(2	NUM
gi-4940	555	5	)	)	PUNCT
gi-4940	555	6	,	,	PUNCT
gi-4940	555	7	2018	2018	NUM
gi-4940	555	8	49	49	NUM
gi-4940	555	9	t.	t.	NOUN
gi-4940	555	10	bayer	bayer	PROPN
gi-4940	555	11	:	:	PUNCT
gi-4940	555	12	plotting	plot	VERB
gi-4940	555	13	the	the	DET
gi-4940	555	14	map	map	NOUN
gi-4940	555	15	projection	projection	NOUN
gi-4940	555	16	graticule	graticule	NOUN
gi-4940	555	17	with	with	ADP
gi-4940	555	18	discontinuities	discontinuity	NOUN
gi-4940	555	19	algorithm	algorithm	NOUN
gi-4940	555	20	8	8	NUM
gi-4940	555	21	combined	combine	VERB
gi-4940	555	22	sampling	sampling	NOUN
gi-4940	555	23	of	of	ADP
gi-4940	555	24	the	the	DET
gi-4940	555	25	meridian	meridian	PROPN
gi-4940	555	26	points	point	NOUN
gi-4940	555	27	,	,	PUNCT
gi-4940	555	28	the	the	DET
gi-4940	555	29	recursive	recursive	ADJ
gi-4940	555	30	phase	phase	NOUN
gi-4940	555	31	,	,	PUNCT
gi-4940	555	32	method	method	NOUN
gi-4940	555	33	s3	s3	PROPN
gi-4940	555	34	.	.	PROPN
gi-4940	556	1	1	1	NUM
gi-4940	556	2	:	:	PUNCT
gi-4940	556	3	function	function	NOUN
gi-4940	556	4	csmer(p	csmer(p	PROPN
gi-4940	556	5	,	,	PUNCT
gi-4940	556	6	lλ	lλ	INTJ
gi-4940	556	7	,	,	PUNCT
gi-4940	556	8	j	j	PROPN
gi-4940	556	9	,	,	PUNCT
gi-4940	556	10	k	k	PROPN
gi-4940	556	11	,	,	PUNCT
gi-4940	556	12	ak	ak	PROPN
gi-4940	556	13	,	,	PUNCT
gi-4940	556	14	bk	bk	PROPN
gi-4940	556	15	,	,	PUNCT
gi-4940	556	16	ak−1	ak−1	ADJ
gi-4940	556	17	,	,	PUNCT
gi-4940	556	18	bk+1	bk+1	NOUN
gi-4940	556	19	,	,	PUNCT
gi-4940	556	20	xa	xa	PROPN
gi-4940	556	21	,	,	PUNCT
gi-4940	556	22	ya	ya	PROPN
gi-4940	556	23	,	,	PUNCT
gi-4940	556	24	xb	xb	PROPN
gi-4940	556	25	,	,	PUNCT
gi-4940	556	26	yb	yb	PROPN
gi-4940	556	27	,	,	PUNCT
gi-4940	556	28	d	d	PROPN
gi-4940	556	29	,	,	PUNCT
gi-4940	556	30	d	d	NOUN
gi-4940	556	31	,	,	PUNCT
gi-4940	556	32	d	d	PROPN
gi-4940	556	33	,	,	PUNCT
gi-4940	556	34	ε	ε	PROPN
gi-4940	556	35	,	,	PUNCT
gi-4940	556	36	α	α	NOUN
gi-4940	556	37	)	)	PUNCT
gi-4940	556	38	)	)	PUNCT
gi-4940	557	1	2	2	NUM
gi-4940	557	2	:	:	PUNCT
gi-4940	557	3	if	if	SCONJ
gi-4940	557	4	(	(	PUNCT
gi-4940	557	5	d	d	X
gi-4940	557	6	>	>	X
gi-4940	557	7	d	d	PROPN
gi-4940	557	8	)	)	PUNCT
gi-4940	557	9	∨	∨	PROPN
gi-4940	557	10	(	(	PUNCT
gi-4940	557	11	bk	bk	PROPN
gi-4940	557	12	−	−	PROPN
gi-4940	557	13	ak	ak	PROPN
gi-4940	557	14	<	<	X
gi-4940	557	15	ε	ε	PROPN
gi-4940	557	16	)	)	PUNCT
gi-4940	557	17	then	then	ADV
gi-4940	557	18	3	3	NUM
gi-4940	557	19	:	:	PUNCT
gi-4940	557	20	return	return	VERB
gi-4940	557	21	4	4	NUM
gi-4940	557	22	:	:	PUNCT
gi-4940	557	23	ri	ri	PROPN
gi-4940	557	24	=	=	PUNCT
gi-4940	557	25	rand(0.45	rand(0.45	NOUN
gi-4940	557	26	,	,	PUNCT
gi-4940	557	27	0.55	0.55	NUM
gi-4940	557	28	)	)	PUNCT
gi-4940	557	29	,	,	PUNCT
gi-4940	557	30	i	i	PRON
gi-4940	557	31	=	=	NOUN
gi-4940	557	32	0	0	NUM
gi-4940	557	33	,	,	PUNCT
gi-4940	557	34	...	...	PUNCT
gi-4940	557	35	,	,	PUNCT
gi-4940	557	36	4	4	NUM
gi-4940	557	37	5	5	NUM
gi-4940	557	38	:	:	PUNCT
gi-4940	557	39	ϕ1,k	ϕ1,k	PROPN
gi-4940	557	40	=	=	PROPN
gi-4940	557	41	ak	ak	PROPN
gi-4940	557	42	+	+	PROPN
gi-4940	558	1	1	1	NUM
gi-4940	558	2	2r1(bk	2r1(bk	NUM
gi-4940	558	3	−	−	PROPN
gi-4940	558	4	ak	ak	PROPN
gi-4940	558	5	)	)	PUNCT
gi-4940	558	6	,	,	PUNCT
gi-4940	559	1	ϕ2,k	ϕ2,k	PROPN
gi-4940	559	2	=	=	PRON
gi-4940	559	3	a+	a+	PUNCT
gi-4940	559	4	r2(bk	r2(bk	PROPN
gi-4940	559	5	−	−	PROPN
gi-4940	559	6	a	a	X
gi-4940	559	7	)	)	PUNCT
gi-4940	559	8	,	,	PUNCT
gi-4940	559	9	ϕ3,k	ϕ3,k	PROPN
gi-4940	559	10	=	=	PUNCT
gi-4940	559	11	a+	a+	PUNCT
gi-4940	559	12	3	3	NUM
gi-4940	559	13	2r3(bk	2r3(bk	NUM
gi-4940	559	14	−	−	PROPN
gi-4940	559	15	ak	ak	PROPN
gi-4940	559	16	)	)	PUNCT
gi-4940	559	17	6	6	NUM
gi-4940	559	18	:	:	PUNCT
gi-4940	559	19	ϕ3,k−1	ϕ3,k−1	PROPN
gi-4940	559	20	=	=	SYM
gi-4940	559	21	ak	ak	PROPN
gi-4940	559	22	+	+	CCONJ
gi-4940	559	23	1	1	NUM
gi-4940	559	24	2r1(bk−1	2r1(bk−1	PROPN
gi-4940	559	25	−	−	PROPN
gi-4940	559	26	ak	ak	PROPN
gi-4940	559	27	)	)	PUNCT
gi-4940	559	28	,	,	PUNCT
gi-4940	559	29	ϕ1,k+1	ϕ1,k+1	PUNCT
gi-4940	560	1	=	=	VERB
gi-4940	560	2	bk	bk	PROPN
gi-4940	560	3	+	+	NOUN
gi-4940	560	4	r4(bk+1	r4(bk+1	NOUN
gi-4940	560	5	−	−	PROPN
gi-4940	560	6	bk	bk	NOUN
gi-4940	560	7	)	)	PUNCT
gi-4940	560	8	7	7	NUM
gi-4940	560	9	:	:	PUNCT
gi-4940	560	10	if	if	SCONJ
gi-4940	560	11	discontinuity	discontinuity	NOUN
gi-4940	560	12	in	in	ADP
gi-4940	560	13	(	(	PUNCT
gi-4940	560	14	ϕi	ϕi	ADP
gi-4940	560	15	,	,	PUNCT
gi-4940	560	16	k	k	NOUN
gi-4940	560	17	,	,	PUNCT
gi-4940	560	18	λ	λ	NOUN
gi-4940	560	19	)	)	PUNCT
gi-4940	560	20	in	in	ADP
gi-4940	560	21	ϕ	ϕ	NOUN
gi-4940	560	22	direction	direction	NOUN
gi-4940	560	23	then	then	ADV
gi-4940	560	24	8	8	NUM
gi-4940	560	25	:	:	PUNCT
gi-4940	560	26	throw	throw	VERB
gi-4940	560	27	latsingularityexception	latsingularityexception	NOUN
gi-4940	560	28	(	(	PUNCT
gi-4940	560	29	ϕi	ϕi	ADP
gi-4940	560	30	,	,	PUNCT
gi-4940	560	31	k	k	NOUN
gi-4940	560	32	)	)	PUNCT
gi-4940	560	33	,	,	PUNCT
gi-4940	560	34	i	i	PRON
gi-4940	560	35	=	=	NOUN
gi-4940	560	36	1	1	NUM
gi-4940	560	37	,	,	PUNCT
gi-4940	560	38	2	2	NUM
gi-4940	560	39	,	,	PUNCT
gi-4940	560	40	3	3	NUM
gi-4940	560	41	9	9	NUM
gi-4940	560	42	:	:	PUNCT
gi-4940	560	43	if	if	SCONJ
gi-4940	560	44	discontinuity	discontinuity	NOUN
gi-4940	560	45	in	in	ADP
gi-4940	560	46	(	(	PUNCT
gi-4940	560	47	ϕi	ϕi	ADP
gi-4940	560	48	,	,	PUNCT
gi-4940	560	49	k	k	NOUN
gi-4940	560	50	,	,	PUNCT
gi-4940	560	51	λ	λ	NOUN
gi-4940	560	52	)	)	PUNCT
gi-4940	560	53	in	in	ADP
gi-4940	560	54	λ	λ	PROPN
gi-4940	560	55	direction	direction	NOUN
gi-4940	560	56	then	then	ADV
gi-4940	560	57	10	10	NUM
gi-4940	560	58	:	:	PUNCT
gi-4940	560	59	throw	throw	VERB
gi-4940	560	60	lonsingularityexception	lonsingularityexception	NOUN
gi-4940	560	61	(	(	PUNCT
gi-4940	560	62	λ	λ	NOUN
gi-4940	560	63	)	)	PUNCT
gi-4940	560	64	,	,	PUNCT
gi-4940	560	65	i	i	PRON
gi-4940	560	66	=	=	NOUN
gi-4940	560	67	1	1	NUM
gi-4940	560	68	,	,	PUNCT
gi-4940	560	69	2	2	NUM
gi-4940	560	70	,	,	PUNCT
gi-4940	560	71	3	3	NUM
gi-4940	560	72	11	11	NUM
gi-4940	560	73	:	:	PUNCT
gi-4940	561	1	x3,k−1	x3,k−1	X
gi-4940	561	2	=	=	SYM
gi-4940	561	3	f	f	PROPN
gi-4940	561	4	(	(	PUNCT
gi-4940	561	5	ϕ3,k−1	ϕ3,k−1	ADJ
gi-4940	561	6	,	,	PUNCT
gi-4940	561	7	λ	λ	NOUN
gi-4940	561	8	)	)	PUNCT
gi-4940	561	9	,	,	PUNCT
gi-4940	561	10	y3,k−1	y3,k−1	NOUN
gi-4940	561	11	=	=	SYM
gi-4940	561	12	g(ϕ3,k−1	g(ϕ3,k−1	NOUN
gi-4940	561	13	,	,	PUNCT
gi-4940	561	14	λ	λ	NOUN
gi-4940	561	15	)	)	PUNCT
gi-4940	561	16	12	12	NUM
gi-4940	561	17	:	:	PUNCT
gi-4940	561	18	xi	xi	PROPN
gi-4940	561	19	,	,	PUNCT
gi-4940	561	20	k	k	PROPN
gi-4940	561	21	=	=	SYM
gi-4940	561	22	f	f	PROPN
gi-4940	561	23	(	(	PUNCT
gi-4940	561	24	ϕi	ϕi	ADP
gi-4940	561	25	,	,	PUNCT
gi-4940	561	26	k	k	NOUN
gi-4940	561	27	,	,	PUNCT
gi-4940	561	28	λ	λ	NOUN
gi-4940	561	29	)	)	PUNCT
gi-4940	561	30	,	,	PUNCT
gi-4940	561	31	yi	yi	PROPN
gi-4940	561	32	,	,	PUNCT
gi-4940	561	33	k	k	NOUN
gi-4940	561	34	=	=	PUNCT
gi-4940	561	35	g(ϕi	g(ϕi	PROPN
gi-4940	561	36	,	,	PUNCT
gi-4940	561	37	k	k	NOUN
gi-4940	561	38	,	,	PUNCT
gi-4940	561	39	λ	λ	PROPN
gi-4940	561	40	)	)	PUNCT
gi-4940	561	41	,	,	PUNCT
gi-4940	561	42	i	i	PRON
gi-4940	561	43	=	=	NOUN
gi-4940	561	44	1	1	NUM
gi-4940	561	45	,	,	PUNCT
gi-4940	561	46	2	2	NUM
gi-4940	561	47	,	,	PUNCT
gi-4940	561	48	3	3	NUM
gi-4940	561	49	13	13	NUM
gi-4940	561	50	:	:	PUNCT
gi-4940	561	51	x1,k+1	x1,k+1	PUNCT
gi-4940	562	1	=	=	SYM
gi-4940	562	2	f	f	PROPN
gi-4940	562	3	(	(	PUNCT
gi-4940	562	4	ϕ1,k+1	ϕ1,k+1	PROPN
gi-4940	562	5	,	,	PUNCT
gi-4940	562	6	λ	λ	NOUN
gi-4940	562	7	)	)	PUNCT
gi-4940	562	8	,	,	PUNCT
gi-4940	562	9	y1,k+1	y1,k+1	PROPN
gi-4940	562	10	=	=	PUNCT
gi-4940	562	11	g(ϕ1,k+1	g(ϕ1,k+1	PROPN
gi-4940	562	12	,	,	PUNCT
gi-4940	562	13	λ	λ	NOUN
gi-4940	562	14	)	)	PUNCT
gi-4940	562	15	14	14	NUM
gi-4940	562	16	:	:	PUNCT
gi-4940	562	17	pa	pa	PROPN
gi-4940	562	18	,	,	PUNCT
gi-4940	562	19	k	k	PROPN
gi-4940	562	20	=	=	SYM
gi-4940	562	21	point(xa	point(xa	PROPN
gi-4940	562	22	,	,	PUNCT
gi-4940	562	23	k	k	PROPN
gi-4940	562	24	,	,	PUNCT
gi-4940	562	25	ya	ya	PROPN
gi-4940	562	26	,	,	PUNCT
gi-4940	562	27	k	k	PROPN
gi-4940	562	28	)	)	PUNCT
gi-4940	562	29	,	,	PUNCT
gi-4940	562	30	pb	pb	PROPN
gi-4940	562	31	,	,	PUNCT
gi-4940	562	32	k	k	PROPN
gi-4940	562	33	=	=	PUNCT
gi-4940	562	34	point(xb	point(xb	PROPN
gi-4940	562	35	,	,	PUNCT
gi-4940	562	36	k	k	PROPN
gi-4940	562	37	,	,	PUNCT
gi-4940	562	38	yb	yb	PROPN
gi-4940	562	39	,	,	PUNCT
gi-4940	562	40	k	k	PROPN
gi-4940	562	41	)	)	PUNCT
gi-4940	562	42	15	15	NUM
gi-4940	562	43	:	:	PUNCT
gi-4940	562	44	pi	pi	NOUN
gi-4940	562	45	,	,	PUNCT
gi-4940	562	46	k	k	PROPN
gi-4940	562	47	=	=	SYM
gi-4940	562	48	point(xi	point(xi	PROPN
gi-4940	562	49	,	,	PUNCT
gi-4940	562	50	k	k	PROPN
gi-4940	562	51	,	,	PUNCT
gi-4940	562	52	yi	yi	PROPN
gi-4940	562	53	,	,	PUNCT
gi-4940	562	54	k	k	PROPN
gi-4940	562	55	)	)	PUNCT
gi-4940	562	56	,	,	PUNCT
gi-4940	562	57	i	i	PRON
gi-4940	562	58	=	=	NOUN
gi-4940	562	59	1	1	NUM
gi-4940	562	60	,	,	PUNCT
gi-4940	562	61	2	2	NUM
gi-4940	562	62	,	,	PUNCT
gi-4940	562	63	3	3	NUM
gi-4940	562	64	16	16	NUM
gi-4940	562	65	:	:	PUNCT
gi-4940	562	66	p3,k−1	p3,k−1	NOUN
gi-4940	562	67	=	=	PUNCT
gi-4940	562	68	point(x3,k−1	point(x3,k−1	NOUN
gi-4940	562	69	,	,	PUNCT
gi-4940	562	70	y3,k−1	y3,k−1	NOUN
gi-4940	562	71	)	)	PUNCT
gi-4940	562	72	,	,	PUNCT
gi-4940	562	73	p1,k+1	p1,k+1	PROPN
gi-4940	562	74	=	=	SYM
gi-4940	562	75	point(x1,k+1	point(x1,k+1	PROPN
gi-4940	562	76	,	,	PUNCT
gi-4940	562	77	y1,k+1	y1,k+1	PROPN
gi-4940	562	78	)	)	PUNCT
gi-4940	562	79	17	17	NUM
gi-4940	562	80	:	:	PUNCT
gi-4940	562	81	α1	α1	PROPN
gi-4940	562	82	=	=	SYM
gi-4940	562	83	α(pa	α(pa	NOUN
gi-4940	562	84	,	,	PUNCT
gi-4940	562	85	k	k	PROPN
gi-4940	562	86	,	,	PUNCT
gi-4940	562	87	p1,k	p1,k	PROPN
gi-4940	562	88	,	,	PUNCT
gi-4940	562	89	p2,k	p2,k	PROPN
gi-4940	562	90	)	)	PUNCT
gi-4940	562	91	,	,	PUNCT
gi-4940	562	92	α2	α2	PROPN
gi-4940	562	93	=	=	SYM
gi-4940	562	94	α(p1,k	α(p1,k	PROPN
gi-4940	562	95	,	,	PUNCT
gi-4940	562	96	p2,k	p2,k	PROPN
gi-4940	562	97	,	,	PUNCT
gi-4940	562	98	p3,k	p3,k	PROPN
gi-4940	562	99	)	)	PUNCT
gi-4940	562	100	,	,	PUNCT
gi-4940	562	101	α3	α3	PROPN
gi-4940	562	102	=	=	SYM
gi-4940	562	103	α(p2,k	α(p2,k	PROPN
gi-4940	562	104	,	,	PUNCT
gi-4940	562	105	p3,k	p3,k	PROPN
gi-4940	562	106	,	,	PUNCT
gi-4940	562	107	pb	pb	ADP
gi-4940	562	108	,	,	PUNCT
gi-4940	562	109	k	k	NOUN
gi-4940	562	110	)	)	PUNCT
gi-4940	562	111	18	18	NUM
gi-4940	562	112	:	:	PUNCT
gi-4940	562	113	α0	α0	PROPN
gi-4940	562	114	=	=	SYM
gi-4940	562	115	α(p3,k−1	α(p3,k−1	PROPN
gi-4940	562	116	,	,	PUNCT
gi-4940	562	117	pa	pa	PROPN
gi-4940	562	118	,	,	PUNCT
gi-4940	562	119	k	k	PROPN
gi-4940	562	120	,	,	PUNCT
gi-4940	562	121	p1,k	p1,k	PROPN
gi-4940	562	122	)	)	PUNCT
gi-4940	562	123	,	,	PUNCT
gi-4940	562	124	α4	α4	NOUN
gi-4940	562	125	=	=	SYM
gi-4940	562	126	α(p3,k	α(p3,k	PROPN
gi-4940	562	127	,	,	PUNCT
gi-4940	562	128	pb	pb	PROPN
gi-4940	562	129	,	,	PUNCT
gi-4940	562	130	k	k	PROPN
gi-4940	562	131	,	,	PUNCT
gi-4940	562	132	p1,k+1	p1,k+1	PROPN
gi-4940	562	133	)	)	PUNCT
gi-4940	562	134	19	19	NUM
gi-4940	562	135	:	:	PUNCT
gi-4940	562	136	if	if	SCONJ
gi-4940	562	137	(	(	PUNCT
gi-4940	562	138	α0	α0	ADJ
gi-4940	562	139	>	>	X
gi-4940	562	140	α	α	NOUN
gi-4940	562	141	)	)	PUNCT
gi-4940	562	142	∨	∨	PROPN
gi-4940	562	143	(	(	PUNCT
gi-4940	562	144	α1	α1	PROPN
gi-4940	562	145	>	>	X
gi-4940	562	146	α	α	PROPN
gi-4940	562	147	)	)	PUNCT
gi-4940	562	148	∨	∨	PROPN
gi-4940	562	149	(	(	PUNCT
gi-4940	562	150	α2	α2	NOUN
gi-4940	562	151	>	>	X
gi-4940	562	152	α	α	PROPN
gi-4940	562	153	)	)	PUNCT
gi-4940	562	154	∨	∨	PROPN
gi-4940	562	155	(	(	PUNCT
gi-4940	562	156	α3	α3	NOUN
gi-4940	562	157	>	>	NOUN
gi-4940	562	158	α	α	PROPN
gi-4940	562	159	)	)	PUNCT
gi-4940	562	160	∨	∨	PROPN
gi-4940	562	161	(	(	PUNCT
gi-4940	562	162	α4	α4	NOUN
gi-4940	562	163	>	>	X
gi-4940	562	164	α	α	PROPN
gi-4940	562	165	)	)	PUNCT
gi-4940	562	166	∨	∨	PROPN
gi-4940	562	167	(	(	PUNCT
gi-4940	562	168	d	d	X
gi-4940	562	169	<	<	X
gi-4940	562	170	=	=	ADJ
gi-4940	562	171	d	d	NOUN
gi-4940	562	172	)	)	PUNCT
gi-4940	562	173	)	)	PUNCT
gi-4940	563	1	then	then	ADV
gi-4940	563	2	20	20	NUM
gi-4940	563	3	:	:	PUNCT
gi-4940	563	4	csmer(p	csmer(p	NOUN
gi-4940	563	5	,	,	PUNCT
gi-4940	563	6	lλ	lλ	INTJ
gi-4940	563	7	,	,	PUNCT
gi-4940	563	8	j	j	PROPN
gi-4940	563	9	,	,	PUNCT
gi-4940	563	10	k	k	PROPN
gi-4940	563	11	,	,	PUNCT
gi-4940	563	12	ak	ak	PROPN
gi-4940	563	13	,	,	PUNCT
gi-4940	563	14	ϕ1,k	ϕ1,k	PROPN
gi-4940	563	15	,	,	PUNCT
gi-4940	563	16	ϕ3,k−1	ϕ3,k−1	PROPN
gi-4940	563	17	,	,	PUNCT
gi-4940	563	18	ϕ2,k	ϕ2,k	PROPN
gi-4940	563	19	,	,	PUNCT
gi-4940	563	20	xa	xa	PROPN
gi-4940	563	21	,	,	PUNCT
gi-4940	563	22	k	k	PROPN
gi-4940	563	23	,	,	PUNCT
gi-4940	563	24	ya	ya	PROPN
gi-4940	563	25	,	,	PUNCT
gi-4940	563	26	k	k	PROPN
gi-4940	563	27	,	,	PUNCT
gi-4940	563	28	x1,k	x1,k	PROPN
gi-4940	563	29	,	,	PUNCT
gi-4940	563	30	y1,k	y1,k	PROPN
gi-4940	563	31	,	,	PUNCT
gi-4940	563	32	d+	d+	PUNCT
gi-4940	563	33	1	1	NUM
gi-4940	563	34	,	,	PUNCT
gi-4940	563	35	d	d	NOUN
gi-4940	563	36	,	,	PUNCT
gi-4940	563	37	d	d	PROPN
gi-4940	563	38	,	,	PUNCT
gi-4940	563	39	α	α	NOUN
gi-4940	563	40	)	)	PUNCT
gi-4940	563	41	21	21	NUM
gi-4940	563	42	:	:	PUNCT
gi-4940	563	43	lλ	lλ	PROPN
gi-4940	563	44	,	,	PUNCT
gi-4940	563	45	j	j	PROPN
gi-4940	563	46	,	,	PUNCT
gi-4940	563	47	k	k	PROPN
gi-4940	563	48	←	←	PROPN
gi-4940	563	49	point(x1,k	point(x1,k	PROPN
gi-4940	563	50	,	,	PUNCT
gi-4940	563	51	y1,k	y1,k	PROPN
gi-4940	563	52	)	)	PUNCT
gi-4940	563	53	22	22	NUM
gi-4940	563	54	:	:	PUNCT
gi-4940	563	55	if	if	SCONJ
gi-4940	563	56	(	(	PUNCT
gi-4940	563	57	α0	α0	ADJ
gi-4940	563	58	>	>	X
gi-4940	563	59	α	α	NOUN
gi-4940	563	60	)	)	PUNCT
gi-4940	563	61	∨	∨	PROPN
gi-4940	563	62	(	(	PUNCT
gi-4940	563	63	α1	α1	PROPN
gi-4940	563	64	>	>	X
gi-4940	563	65	α	α	PROPN
gi-4940	563	66	)	)	PUNCT
gi-4940	563	67	∨	∨	PROPN
gi-4940	563	68	(	(	PUNCT
gi-4940	563	69	α2	α2	NOUN
gi-4940	563	70	>	>	X
gi-4940	563	71	α	α	PROPN
gi-4940	563	72	)	)	PUNCT
gi-4940	563	73	∨	∨	PROPN
gi-4940	563	74	(	(	PUNCT
gi-4940	563	75	α3	α3	NOUN
gi-4940	563	76	>	>	NOUN
gi-4940	563	77	α	α	PROPN
gi-4940	563	78	)	)	PUNCT
gi-4940	563	79	∨	∨	PROPN
gi-4940	563	80	(	(	PUNCT
gi-4940	563	81	α4	α4	NOUN
gi-4940	563	82	>	>	X
gi-4940	563	83	α	α	PROPN
gi-4940	563	84	)	)	PUNCT
gi-4940	563	85	∨	∨	PROPN
gi-4940	563	86	(	(	PUNCT
gi-4940	563	87	d	d	X
gi-4940	563	88	<	<	X
gi-4940	563	89	=	=	SYM
gi-4940	563	90	d	d	NOUN
gi-4940	563	91	)	)	PUNCT
gi-4940	563	92	then	then	ADV
gi-4940	563	93	23	23	NUM
gi-4940	563	94	:	:	PUNCT
gi-4940	563	95	csmer(p	csmer(p	NOUN
gi-4940	563	96	,	,	PUNCT
gi-4940	563	97	lλ	lλ	INTJ
gi-4940	563	98	,	,	PUNCT
gi-4940	563	99	j	j	PROPN
gi-4940	563	100	,	,	PUNCT
gi-4940	563	101	k	k	PROPN
gi-4940	563	102	,	,	PUNCT
gi-4940	563	103	ϕ1,k	ϕ1,k	PROPN
gi-4940	563	104	,	,	PUNCT
gi-4940	563	105	ϕ2,k	ϕ2,k	PROPN
gi-4940	563	106	,	,	PUNCT
gi-4940	563	107	ϕa	ϕa	NOUN
gi-4940	563	108	,	,	PUNCT
gi-4940	563	109	k	k	PROPN
gi-4940	563	110	,	,	PUNCT
gi-4940	563	111	ϕ3,k	ϕ3,k	PROPN
gi-4940	563	112	,	,	PUNCT
gi-4940	563	113	x1,k	x1,k	PROPN
gi-4940	563	114	,	,	PUNCT
gi-4940	563	115	y1,k	y1,k	PROPN
gi-4940	563	116	,	,	PUNCT
gi-4940	563	117	x2,k	x2,k	PROPN
gi-4940	563	118	,	,	PUNCT
gi-4940	563	119	y2,k	y2,k	PROPN
gi-4940	563	120	,	,	PUNCT
gi-4940	563	121	d+	d+	PUNCT
gi-4940	563	122	1	1	NUM
gi-4940	563	123	,	,	PUNCT
gi-4940	563	124	d	d	NOUN
gi-4940	563	125	,	,	PUNCT
gi-4940	563	126	d	d	PROPN
gi-4940	563	127	,	,	PUNCT
gi-4940	563	128	α	α	NOUN
gi-4940	563	129	)	)	PUNCT
gi-4940	563	130	24	24	NUM
gi-4940	563	131	:	:	PUNCT
gi-4940	563	132	lλ	lλ	PROPN
gi-4940	563	133	,	,	PUNCT
gi-4940	563	134	j	j	PROPN
gi-4940	563	135	,	,	PUNCT
gi-4940	563	136	k	k	PROPN
gi-4940	563	137	←	←	PROPN
gi-4940	563	138	point(x2,k	point(x2,k	PROPN
gi-4940	563	139	,	,	PUNCT
gi-4940	563	140	y2,k	y2,k	PROPN
gi-4940	563	141	)	)	PUNCT
gi-4940	563	142	25	25	NUM
gi-4940	563	143	:	:	PUNCT
gi-4940	563	144	if	if	SCONJ
gi-4940	563	145	(	(	PUNCT
gi-4940	563	146	α0	α0	ADJ
gi-4940	563	147	>	>	X
gi-4940	563	148	α	α	NOUN
gi-4940	563	149	)	)	PUNCT
gi-4940	563	150	∨	∨	PROPN
gi-4940	563	151	(	(	PUNCT
gi-4940	563	152	α1	α1	PROPN
gi-4940	563	153	>	>	X
gi-4940	563	154	α	α	PROPN
gi-4940	563	155	)	)	PUNCT
gi-4940	563	156	∨	∨	PROPN
gi-4940	563	157	(	(	PUNCT
gi-4940	563	158	α2	α2	NOUN
gi-4940	563	159	>	>	X
gi-4940	563	160	α	α	PROPN
gi-4940	563	161	)	)	PUNCT
gi-4940	563	162	∨	∨	PROPN
gi-4940	563	163	(	(	PUNCT
gi-4940	563	164	α3	α3	NOUN
gi-4940	563	165	>	>	NOUN
gi-4940	563	166	α	α	PROPN
gi-4940	563	167	)	)	PUNCT
gi-4940	563	168	∨	∨	PROPN
gi-4940	563	169	(	(	PUNCT
gi-4940	563	170	α4	α4	NOUN
gi-4940	563	171	>	>	X
gi-4940	563	172	α	α	PROPN
gi-4940	563	173	)	)	PUNCT
gi-4940	563	174	∨	∨	PROPN
gi-4940	563	175	(	(	PUNCT
gi-4940	563	176	d	d	X
gi-4940	563	177	<	<	X
gi-4940	563	178	=	=	SYM
gi-4940	563	179	d	d	NOUN
gi-4940	563	180	)	)	PUNCT
gi-4940	563	181	then	then	ADV
gi-4940	563	182	26	26	NUM
gi-4940	563	183	:	:	PUNCT
gi-4940	563	184	csmer(p	csmer(p	PROPN
gi-4940	563	185	,	,	PUNCT
gi-4940	563	186	lλ	lλ	INTJ
gi-4940	563	187	,	,	PUNCT
gi-4940	563	188	j	j	PROPN
gi-4940	563	189	,	,	PUNCT
gi-4940	563	190	k	k	PROPN
gi-4940	563	191	,	,	PUNCT
gi-4940	563	192	ϕ2,k	ϕ2,k	PROPN
gi-4940	563	193	,	,	PUNCT
gi-4940	563	194	ϕ3,k	ϕ3,k	PROPN
gi-4940	563	195	,	,	PUNCT
gi-4940	563	196	ϕ1,k	ϕ1,k	PROPN
gi-4940	563	197	,	,	PUNCT
gi-4940	563	198	bk	bk	PROPN
gi-4940	563	199	,	,	PUNCT
gi-4940	563	200	x2,k	x2,k	PROPN
gi-4940	563	201	,	,	PUNCT
gi-4940	563	202	y2,k	y2,k	PROPN
gi-4940	563	203	,	,	PUNCT
gi-4940	563	204	x3,k	x3,k	PROPN
gi-4940	563	205	,	,	PUNCT
gi-4940	563	206	y3,k	y3,k	PROPN
gi-4940	563	207	,	,	PUNCT
gi-4940	563	208	d+	d+	PUNCT
gi-4940	563	209	1	1	NUM
gi-4940	563	210	,	,	PUNCT
gi-4940	563	211	d	d	NOUN
gi-4940	563	212	,	,	PUNCT
gi-4940	563	213	d	d	PROPN
gi-4940	563	214	,	,	PUNCT
gi-4940	563	215	α	α	NOUN
gi-4940	563	216	)	)	PUNCT
gi-4940	563	217	27	27	NUM
gi-4940	563	218	:	:	PUNCT
gi-4940	563	219	lλ	lλ	PROPN
gi-4940	563	220	,	,	PUNCT
gi-4940	563	221	j	j	PROPN
gi-4940	563	222	,	,	PUNCT
gi-4940	563	223	k	k	PROPN
gi-4940	563	224	←	←	PROPN
gi-4940	563	225	point(x3,k	point(x3,k	PROPN
gi-4940	563	226	,	,	PUNCT
gi-4940	563	227	y3,k	y3,k	PROPN
gi-4940	563	228	)	)	PUNCT
gi-4940	563	229	28	28	NUM
gi-4940	563	230	:	:	PUNCT
gi-4940	563	231	if	if	SCONJ
gi-4940	563	232	(	(	PUNCT
gi-4940	563	233	α0	α0	ADJ
gi-4940	563	234	>	>	X
gi-4940	563	235	α	α	NOUN
gi-4940	563	236	)	)	PUNCT
gi-4940	563	237	∨	∨	PROPN
gi-4940	563	238	(	(	PUNCT
gi-4940	563	239	α1	α1	PROPN
gi-4940	563	240	>	>	X
gi-4940	563	241	α	α	PROPN
gi-4940	563	242	)	)	PUNCT
gi-4940	563	243	∨	∨	PROPN
gi-4940	563	244	(	(	PUNCT
gi-4940	563	245	α2	α2	NOUN
gi-4940	563	246	>	>	X
gi-4940	563	247	α	α	PROPN
gi-4940	563	248	)	)	PUNCT
gi-4940	563	249	∨	∨	PROPN
gi-4940	563	250	(	(	PUNCT
gi-4940	563	251	α3	α3	NOUN
gi-4940	563	252	>	>	NOUN
gi-4940	563	253	α	α	PROPN
gi-4940	563	254	)	)	PUNCT
gi-4940	563	255	∨	∨	PROPN
gi-4940	563	256	(	(	PUNCT
gi-4940	563	257	α4	α4	NOUN
gi-4940	563	258	>	>	X
gi-4940	563	259	α	α	PROPN
gi-4940	563	260	)	)	PUNCT
gi-4940	563	261	∨	∨	PROPN
gi-4940	563	262	(	(	PUNCT
gi-4940	563	263	d	d	X
gi-4940	563	264	<	<	X
gi-4940	563	265	=	=	SYM
gi-4940	563	266	d	d	NOUN
gi-4940	563	267	)	)	PUNCT
gi-4940	563	268	then	then	ADV
gi-4940	563	269	29	29	NUM
gi-4940	563	270	:	:	PUNCT
gi-4940	563	271	csmer(p	csmer(p	NOUN
gi-4940	563	272	,	,	PUNCT
gi-4940	563	273	lλ	lλ	INTJ
gi-4940	563	274	,	,	PUNCT
gi-4940	563	275	j	j	PROPN
gi-4940	563	276	,	,	PUNCT
gi-4940	563	277	k	k	PROPN
gi-4940	563	278	,	,	PUNCT
gi-4940	563	279	ϕ3,k	ϕ3,k	PROPN
gi-4940	563	280	,	,	PUNCT
gi-4940	563	281	bk	bk	PROPN
gi-4940	563	282	,	,	PUNCT
gi-4940	563	283	ϕ2,k	ϕ2,k	PROPN
gi-4940	563	284	,	,	PUNCT
gi-4940	563	285	ϕ1,k+1	ϕ1,k+1	X
gi-4940	563	286	,	,	PUNCT
gi-4940	563	287	x3,k	x3,k	PROPN
gi-4940	563	288	,	,	PUNCT
gi-4940	563	289	y3,k	y3,k	PROPN
gi-4940	563	290	,	,	PUNCT
gi-4940	563	291	xb	xb	PROPN
gi-4940	563	292	,	,	PUNCT
gi-4940	563	293	k	k	PROPN
gi-4940	563	294	,	,	PUNCT
gi-4940	563	295	yb	yb	PROPN
gi-4940	563	296	,	,	PUNCT
gi-4940	563	297	k	k	PROPN
gi-4940	563	298	,	,	PUNCT
gi-4940	563	299	d+	d+	PUNCT
gi-4940	563	300	1	1	NUM
gi-4940	563	301	,	,	PUNCT
gi-4940	563	302	d	d	NOUN
gi-4940	563	303	,	,	PUNCT
gi-4940	563	304	d	d	PROPN
gi-4940	563	305	,	,	PUNCT
gi-4940	563	306	α	α	NOUN
gi-4940	563	307	)	)	PUNCT
gi-4940	563	308	subsequently	subsequently	ADV
gi-4940	563	309	,	,	PUNCT
gi-4940	563	310	the	the	DET
gi-4940	563	311	third	third	ADJ
gi-4940	563	312	quarter	quarter	NOUN
gi-4940	563	313	ϕ3,k−1	ϕ3,k−1	ADV
gi-4940	563	314	of	of	ADP
gi-4940	563	315	the	the	DET
gi-4940	563	316	previous	previous	ADJ
gi-4940	563	317	interval	interval	NOUN
gi-4940	563	318	ωϕ,j	ωϕ,j	X
gi-4940	563	319	,	,	PUNCT
gi-4940	563	320	k−1	k−1	PROPN
gi-4940	563	321	representing	represent	VERB
gi-4940	563	322	the	the	DET
gi-4940	563	323	lower	low	ADJ
gi-4940	563	324	bound	bind	VERB
gi-4940	563	325	of	of	ADP
gi-4940	563	326	ωϕ,j	ωϕ,j	X
gi-4940	563	327	,	,	PUNCT
gi-4940	563	328	k−1,4	k−1,4	PROPN
gi-4940	563	329	and	and	CCONJ
gi-4940	563	330	the	the	DET
gi-4940	563	331	first	first	ADJ
gi-4940	563	332	quarter	quarter	NOUN
gi-4940	563	333	ϕ1,k+1	ϕ1,k+1	ADP
gi-4940	563	334	of	of	ADP
gi-4940	563	335	the	the	DET
gi-4940	563	336	next	next	ADJ
gi-4940	563	337	intervals	interval	NOUN
gi-4940	563	338	ωϕ,j	ωϕ,j	PRON
gi-4940	563	339	,	,	PUNCT
gi-4940	563	340	k+1	k+1	X
gi-4940	563	341	representing	represent	VERB
gi-4940	563	342	the	the	DET
gi-4940	563	343	upper	upper	ADJ
gi-4940	563	344	bound	bound	NOUN
gi-4940	563	345	of	of	ADP
gi-4940	563	346	ωϕ,j	ωϕ,j	X
gi-4940	563	347	,	,	PUNCT
gi-4940	563	348	k+1,1	k+1,1	PROPN
gi-4940	563	349	,	,	PUNCT
gi-4940	563	350	are	be	AUX
gi-4940	563	351	evaluated	evaluate	VERB
gi-4940	563	352	.	.	PUNCT
gi-4940	564	1	(	(	PUNCT
gi-4940	564	2	a	a	X
gi-4940	564	3	)	)	PUNCT
gi-4940	564	4	if	if	SCONJ
gi-4940	564	5	a	a	DET
gi-4940	564	6	singularity	singularity	NOUN
gi-4940	564	7	in	in	ADP
gi-4940	564	8	[	[	X
gi-4940	564	9	ϕ3,k−1	ϕ3,k−1	ADJ
gi-4940	564	10	,	,	PUNCT
gi-4940	564	11	λ	λ	NOUN
gi-4940	564	12	]	]	X
gi-4940	564	13	,	,	PUNCT
gi-4940	564	14	[	[	X
gi-4940	564	15	ϕ1,k	ϕ1,k	PROPN
gi-4940	564	16	,	,	PUNCT
gi-4940	564	17	λ	λ	PROPN
gi-4940	564	18	]	]	X
gi-4940	564	19	,	,	PUNCT
gi-4940	564	20	[	[	X
gi-4940	564	21	ϕ2,k	ϕ2,k	PROPN
gi-4940	564	22	,	,	PUNCT
gi-4940	564	23	λ	λ	X
gi-4940	564	24	]	]	X
gi-4940	564	25	,	,	PUNCT
gi-4940	564	26	[	[	X
gi-4940	564	27	ϕ3,k	ϕ3,k	PROPN
gi-4940	564	28	,	,	PUNCT
gi-4940	564	29	λ	λ	X
gi-4940	564	30	]	]	X
gi-4940	564	31	,	,	PUNCT
gi-4940	564	32	or	or	CCONJ
gi-4940	564	33	[	[	X
gi-4940	564	34	ϕ1,k+1	ϕ1,k+1	X
gi-4940	564	35	,	,	PUNCT
gi-4940	564	36	λ	λ	X
gi-4940	564	37	]	]	X
gi-4940	564	38	occurs	occur	VERB
gi-4940	564	39	,	,	PUNCT
gi-4940	564	40	throw	throw	VERB
gi-4940	564	41	a	a	DET
gi-4940	564	42	new	new	ADJ
gi-4940	564	43	exception	exception	NOUN
gi-4940	564	44	according	accord	VERB
gi-4940	564	45	to	to	ADP
gi-4940	564	46	the	the	DET
gi-4940	564	47	discontinuity	discontinuity	NOUN
gi-4940	564	48	direction	direction	NOUN
gi-4940	564	49	.	.	PUNCT
gi-4940	565	1	(	(	PUNCT
gi-4940	565	2	b	b	X
gi-4940	565	3	)	)	PUNCT
gi-4940	565	4	otherwise	otherwise	ADV
gi-4940	565	5	,	,	PUNCT
gi-4940	565	6	evaluate	evaluate	VERB
gi-4940	565	7	the	the	DET
gi-4940	565	8	function	function	NOUN
gi-4940	565	9	values	value	NOUN
gi-4940	565	10	x3,k−1	x3,k−1	X
gi-4940	566	1	=	=	SYM
gi-4940	566	2	f	f	PROPN
gi-4940	566	3	(	(	PUNCT
gi-4940	566	4	ϕ3,k−1	ϕ3,k−1	ADJ
gi-4940	566	5	,	,	PUNCT
gi-4940	566	6	λ	λ	NOUN
gi-4940	566	7	)	)	PUNCT
gi-4940	566	8	,	,	PUNCT
gi-4940	566	9	y3,k−1	y3,k−1	NOUN
gi-4940	566	10	=	=	SYM
gi-4940	566	11	g(ϕ3,k−1	g(ϕ3,k−1	PROPN
gi-4940	566	12	,	,	PUNCT
gi-4940	566	13	λ	λ	NOUN
gi-4940	566	14	)	)	PUNCT
gi-4940	566	15	,	,	PUNCT
gi-4940	566	16	x1,k	x1,k	PROPN
gi-4940	567	1	=	=	SYM
gi-4940	567	2	f	f	PROPN
gi-4940	567	3	(	(	PUNCT
gi-4940	567	4	ϕ1,k	ϕ1,k	PROPN
gi-4940	567	5	,	,	PUNCT
gi-4940	567	6	λ	λ	PROPN
gi-4940	567	7	)	)	PUNCT
gi-4940	567	8	,	,	PUNCT
gi-4940	567	9	y1,k	y1,k	PROPN
gi-4940	567	10	=	=	SYM
gi-4940	567	11	g(ϕ1,k	g(ϕ1,k	PROPN
gi-4940	567	12	,	,	PUNCT
gi-4940	567	13	λ	λ	PROPN
gi-4940	567	14	)	)	PUNCT
gi-4940	567	15	,	,	PUNCT
gi-4940	567	16	x2,k	x2,k	PROPN
gi-4940	568	1	=	=	SYM
gi-4940	569	1	f	f	PROPN
gi-4940	569	2	(	(	PUNCT
gi-4940	569	3	ϕ2,k	ϕ2,k	PROPN
gi-4940	569	4	,	,	PUNCT
gi-4940	569	5	λ	λ	NOUN
gi-4940	569	6	)	)	PUNCT
gi-4940	569	7	,	,	PUNCT
gi-4940	569	8	y2,k	y2,k	PROPN
gi-4940	569	9	=	=	SYM
gi-4940	569	10	g(ϕ2	g(ϕ2	NOUN
gi-4940	569	11	,	,	PUNCT
gi-4940	569	12	λ	λ	PROPN
gi-4940	569	13	)	)	PUNCT
gi-4940	569	14	,	,	PUNCT
gi-4940	569	15	x3,k	x3,k	PROPN
gi-4940	570	1	=	=	SYM
gi-4940	570	2	f	f	PROPN
gi-4940	570	3	(	(	PUNCT
gi-4940	570	4	ϕ3,k	ϕ3,k	PROPN
gi-4940	570	5	,	,	PUNCT
gi-4940	570	6	λ	λ	PROPN
gi-4940	570	7	)	)	PUNCT
gi-4940	570	8	,	,	PUNCT
gi-4940	570	9	y3,k	y3,k	PROPN
gi-4940	570	10	=	=	SYM
gi-4940	570	11	g(ϕ3,k	g(ϕ3,k	NOUN
gi-4940	570	12	,	,	PUNCT
gi-4940	570	13	λ	λ	PROPN
gi-4940	570	14	)	)	PUNCT
gi-4940	570	15	,	,	PUNCT
gi-4940	570	16	x1,k+1	x1,k+1	PUNCT
gi-4940	571	1	=	=	SYM
gi-4940	571	2	f	f	PROPN
gi-4940	571	3	(	(	PUNCT
gi-4940	571	4	ϕ1,k+1	ϕ1,k+1	PROPN
gi-4940	571	5	,	,	PUNCT
gi-4940	571	6	λ	λ	NOUN
gi-4940	571	7	)	)	PUNCT
gi-4940	571	8	,	,	PUNCT
gi-4940	571	9	y1,k+1	y1,k+1	PROPN
gi-4940	571	10	=	=	PUNCT
gi-4940	571	11	g(ϕ1,k+1	g(ϕ1,k+1	PROPN
gi-4940	571	12	,	,	PUNCT
gi-4940	571	13	λ	λ	NOUN
gi-4940	571	14	)	)	PUNCT
gi-4940	571	15	,	,	PUNCT
gi-4940	571	16	at	at	ADP
gi-4940	571	17	new	new	ADJ
gi-4940	571	18	vertices	vertex	NOUN
gi-4940	571	19	p1,k	p1,k	PROPN
gi-4940	571	20	,	,	PUNCT
gi-4940	571	21	p2,k	p2,k	PROPN
gi-4940	571	22	,	,	PUNCT
gi-4940	571	23	p3,k	p3,k	PROPN
gi-4940	571	24	and	and	CCONJ
gi-4940	571	25	the	the	DET
gi-4940	571	26	supplementary	supplementary	ADJ
gi-4940	571	27	vertices	vertex	NOUN
gi-4940	571	28	p3,k−1	p3,k−1	NOUN
gi-4940	571	29	,	,	PUNCT
gi-4940	571	30	p1,k+1	p1,k+1	PROPN
gi-4940	571	31	.	.	PUNCT
gi-4940	571	32	(	(	PUNCT
gi-4940	571	33	c	c	X
gi-4940	571	34	)	)	PUNCT
gi-4940	571	35	for	for	ADP
gi-4940	571	36	d	d	PROPN
gi-4940	571	37	≤	≤	PROPN
gi-4940	571	38	d	d	X
gi-4940	571	39	,	,	PUNCT
gi-4940	571	40	this	this	DET
gi-4940	571	41	step	step	NOUN
gi-4940	571	42	begins	begin	VERB
gi-4940	571	43	with	with	ADP
gi-4940	571	44	uniform	uniform	ADJ
gi-4940	571	45	sampling	sampling	NOUN
gi-4940	571	46	of	of	ADP
gi-4940	571	47	the	the	DET
gi-4940	571	48	meridian	meridian	PROPN
gi-4940	571	49	points	point	NOUN
gi-4940	571	50	.	.	PUNCT
gi-4940	572	1	if	if	SCONJ
gi-4940	572	2	d	d	PROPN
gi-4940	572	3	>	>	X
gi-4940	572	4	d	d	PROPN
gi-4940	572	5	,	,	PUNCT
gi-4940	572	6	it	it	PRON
gi-4940	572	7	transforms	transform	VERB
gi-4940	572	8	to	to	ADP
gi-4940	572	9	the	the	DET
gi-4940	572	10	adaptive	adaptive	ADJ
gi-4940	572	11	method	method	NOUN
gi-4940	572	12	.	.	PUNCT
gi-4940	573	1	check	check	VERB
gi-4940	573	2	the	the	DET
gi-4940	573	3	refinement	refinement	NOUN
gi-4940	573	4	criteria	criterion	NOUN
gi-4940	573	5	α0	α0	PROPN
gi-4940	573	6	=	=	SYM
gi-4940	573	7	α(p3,k−1	α(p3,k−1	PROPN
gi-4940	573	8	,	,	PUNCT
gi-4940	573	9	pa	pa	PROPN
gi-4940	573	10	,	,	PUNCT
gi-4940	573	11	k	k	PROPN
gi-4940	573	12	,	,	PUNCT
gi-4940	573	13	p1,k	p1,k	PROPN
gi-4940	573	14	)	)	PUNCT
gi-4940	573	15	,	,	PUNCT
gi-4940	573	16	α1	α1	PROPN
gi-4940	573	17	=	=	SYM
gi-4940	573	18	α(pa	α(pa	NOUN
gi-4940	573	19	,	,	PUNCT
gi-4940	573	20	k	k	PROPN
gi-4940	573	21	,	,	PUNCT
gi-4940	573	22	p1,k	p1,k	PROPN
gi-4940	573	23	,	,	PUNCT
gi-4940	573	24	p2,k	p2,k	PROPN
gi-4940	573	25	)	)	PUNCT
gi-4940	573	26	,	,	PUNCT
gi-4940	573	27	α2	α2	PROPN
gi-4940	573	28	=	=	SYM
gi-4940	573	29	α(p1,k	α(p1,k	PROPN
gi-4940	573	30	,	,	PUNCT
gi-4940	573	31	p2,k	p2,k	PROPN
gi-4940	573	32	,	,	PUNCT
gi-4940	573	33	p3,k	p3,k	PROPN
gi-4940	573	34	)	)	PUNCT
gi-4940	573	35	,	,	PUNCT
gi-4940	573	36	α3	α3	NOUN
gi-4940	573	37	=	=	NOUN
gi-4940	573	38	geoinformatics	geoinformatic	NOUN
gi-4940	573	39	fce	fce	VERB
gi-4940	573	40	ctu	ctu	NOUN
gi-4940	573	41	17(2	17(2	NUM
gi-4940	573	42	)	)	PUNCT
gi-4940	573	43	,	,	PUNCT
gi-4940	573	44	2018	2018	NUM
gi-4940	573	45	50	50	NUM
gi-4940	573	46	t.	t.	NOUN
gi-4940	573	47	bayer	bayer	NOUN
gi-4940	573	48	:	:	PUNCT
gi-4940	573	49	plotting	plot	VERB
gi-4940	573	50	the	the	DET
gi-4940	573	51	map	map	NOUN
gi-4940	573	52	projection	projection	NOUN
gi-4940	573	53	graticule	graticule	NOUN
gi-4940	573	54	with	with	ADP
gi-4940	573	55	discontinuities	discontinuity	NOUN
gi-4940	573	56	figure	figure	VERB
gi-4940	573	57	4.3	4.3	NUM
gi-4940	573	58	:	:	PUNCT
gi-4940	573	59	the	the	DET
gi-4940	573	60	discontinuity	discontinuity	NOUN
gi-4940	573	61	treatment	treatment	NOUN
gi-4940	573	62	without	without	ADP
gi-4940	573	63	its	its	PRON
gi-4940	573	64	classification	classification	NOUN
gi-4940	573	65	using	use	VERB
gi-4940	573	66	the	the	DET
gi-4940	573	67	proposed	propose	VERB
gi-4940	573	68	algorithm	algorithm	NOUN
gi-4940	573	69	in	in	ADP
gi-4940	573	70	polyconic	polyconic	ADJ
gi-4940	573	71	projection	projection	NOUN
gi-4940	573	72	;	;	PUNCT
gi-4940	573	73	the	the	DET
gi-4940	573	74	doubled	double	VERB
gi-4940	573	75	equator	equator	NOUN
gi-4940	573	76	is	be	AUX
gi-4940	573	77	visible	visible	ADJ
gi-4940	573	78	under	under	ADP
gi-4940	573	79	magnification	magnification	NOUN
gi-4940	573	80	.	.	PUNCT
gi-4940	574	1	α(p2,k	α(p2,k	PROPN
gi-4940	574	2	,	,	PUNCT
gi-4940	574	3	p3,k	p3,k	PROPN
gi-4940	574	4	,	,	PUNCT
gi-4940	574	5	pb	pb	ADP
gi-4940	574	6	,	,	PUNCT
gi-4940	574	7	k	k	NOUN
gi-4940	574	8	)	)	PUNCT
gi-4940	574	9	,	,	PUNCT
gi-4940	574	10	α4	α4	NOUN
gi-4940	574	11	=	=	SYM
gi-4940	574	12	α(p3,k	α(p3,k	PROPN
gi-4940	574	13	,	,	PUNCT
gi-4940	574	14	pb	pb	PROPN
gi-4940	574	15	,	,	PUNCT
gi-4940	574	16	k	k	NOUN
gi-4940	574	17	,	,	PUNCT
gi-4940	574	18	p1,k+1	p1,k+1	PROPN
gi-4940	574	19	)	)	PUNCT
gi-4940	574	20	,	,	PUNCT
gi-4940	574	21	and	and	CCONJ
gi-4940	574	22	the	the	DET
gi-4940	574	23	recursive	recursive	ADJ
gi-4940	574	24	depth	depth	NOUN
gi-4940	574	25	d.	d.	NOUN
gi-4940	574	26	when	when	SCONJ
gi-4940	574	27	a	a	DET
gi-4940	574	28	meridian	meridian	NOUN
gi-4940	574	29	is	be	AUX
gi-4940	574	30	not	not	PART
gi-4940	574	31	sufficiently	sufficiently	ADV
gi-4940	574	32	smooth	smooth	ADJ
gi-4940	574	33	,	,	PUNCT
gi-4940	574	34	or	or	CCONJ
gi-4940	574	35	d	d	X
gi-4940	574	36	≤	≤	NUM
gi-4940	575	1	d	d	X
gi-4940	575	2	,	,	PUNCT
gi-4940	575	3	it	it	PRON
gi-4940	575	4	needs	need	VERB
gi-4940	575	5	to	to	PART
gi-4940	575	6	be	be	AUX
gi-4940	575	7	refined	refine	VERB
gi-4940	575	8	;	;	PUNCT
gi-4940	575	9	the	the	DET
gi-4940	575	10	recursive	recursive	ADJ
gi-4940	575	11	subdivision	subdivision	NOUN
gi-4940	575	12	is	be	AUX
gi-4940	575	13	necessary	necessary	ADJ
gi-4940	575	14	.	.	PUNCT
gi-4940	576	1	(	(	PUNCT
gi-4940	576	2	d	d	X
gi-4940	576	3	)	)	PUNCT
gi-4940	576	4	if	if	SCONJ
gi-4940	576	5	the	the	DET
gi-4940	576	6	condition	condition	NOUN
gi-4940	576	7	given	give	VERB
gi-4940	576	8	by	by	ADP
gi-4940	576	9	eq	eq	PROPN
gi-4940	576	10	.	.	PROPN
gi-4940	576	11	4.2	4.2	NUM
gi-4940	576	12	is	be	AUX
gi-4940	576	13	held	hold	VERB
gi-4940	576	14	,	,	PUNCT
gi-4940	576	15	call	call	VERB
gi-4940	576	16	the	the	DET
gi-4940	576	17	recursive	recursive	ADJ
gi-4940	576	18	procedure	procedure	NOUN
gi-4940	576	19	with	with	ADP
gi-4940	576	20	the	the	DET
gi-4940	576	21	increased	increase	VERB
gi-4940	576	22	depth	depth	NOUN
gi-4940	577	1	d	d	NOUN
gi-4940	577	2	=	=	SYM
gi-4940	577	3	d	d	PROPN
gi-4940	577	4	+	+	NOUN
gi-4940	577	5	1	1	NUM
gi-4940	577	6	for	for	ADP
gi-4940	577	7	the	the	DET
gi-4940	577	8	interval	interval	NOUN
gi-4940	577	9	ωϕ,j	ωϕ,j	X
gi-4940	577	10	,	,	PUNCT
gi-4940	577	11	k,1	k,1	PROPN
gi-4940	577	12	=	=	PUNCT
gi-4940	578	1	[	[	X
gi-4940	578	2	ak	ak	PROPN
gi-4940	578	3	,	,	PUNCT
gi-4940	578	4	ϕ1,k	ϕ1,k	PROPN
gi-4940	578	5	]	]	X
gi-4940	578	6	,	,	PUNCT
gi-4940	578	7	its	its	PRON
gi-4940	578	8	predecessor	predecessor	NOUN
gi-4940	578	9	ωϕ,j	ωϕ,j	X
gi-4940	578	10	,	,	PUNCT
gi-4940	578	11	k−1,4	k−1,4	PROPN
gi-4940	578	12	=	=	SYM
gi-4940	579	1	[	[	X
gi-4940	579	2	ϕ3,k−1	ϕ3,k−1	ADJ
gi-4940	579	3	,	,	PUNCT
gi-4940	579	4	ak	ak	PROPN
gi-4940	579	5	]	]	X
gi-4940	579	6	,	,	PUNCT
gi-4940	579	7	and	and	CCONJ
gi-4940	579	8	successor	successor	NOUN
gi-4940	579	9	ωϕ,j	ωϕ,j	X
gi-4940	579	10	,	,	PUNCT
gi-4940	579	11	k,2	k,2	X
gi-4940	579	12	=	=	X
gi-4940	580	1	[	[	X
gi-4940	580	2	ϕ1,k	ϕ1,k	PROPN
gi-4940	580	3	,	,	PUNCT
gi-4940	580	4	ϕ2,k	ϕ2,k	PROPN
gi-4940	580	5	]	]	PUNCT
gi-4940	580	6	.	.	PUNCT
gi-4940	581	1	(	(	PUNCT
gi-4940	581	2	e	e	X
gi-4940	581	3	)	)	PUNCT
gi-4940	581	4	add	add	VERB
gi-4940	581	5	the	the	DET
gi-4940	581	6	new	new	ADJ
gi-4940	581	7	point	point	NOUN
gi-4940	581	8	p1,k	p1,k	PROPN
gi-4940	581	9	to	to	ADP
gi-4940	581	10	the	the	DET
gi-4940	581	11	polynomial	polynomial	ADJ
gi-4940	581	12	approximation	approximation	NOUN
gi-4940	581	13	of	of	ADP
gi-4940	581	14	m̃(λ	m̃(λ	PROPN
gi-4940	581	15	)	)	PUNCT
gi-4940	581	16	:	:	PUNCT
gi-4940	582	1	lλ	lλ	INTJ
gi-4940	582	2	,	,	PUNCT
gi-4940	582	3	j	j	PROPN
gi-4940	582	4	,	,	PUNCT
gi-4940	582	5	k	k	PROPN
gi-4940	582	6	←	←	PROPN
gi-4940	582	7	p1,k	p1,k	PROPN
gi-4940	582	8	.	.	PUNCT
gi-4940	583	1	(	(	PUNCT
gi-4940	583	2	f	f	X
gi-4940	583	3	)	)	PUNCT
gi-4940	583	4	if	if	SCONJ
gi-4940	583	5	the	the	DET
gi-4940	583	6	condition	condition	NOUN
gi-4940	583	7	given	give	VERB
gi-4940	583	8	by	by	ADP
gi-4940	583	9	eq	eq	PROPN
gi-4940	583	10	.	.	PROPN
gi-4940	583	11	4.2	4.2	NUM
gi-4940	583	12	is	be	AUX
gi-4940	583	13	held	hold	VERB
gi-4940	583	14	,	,	PUNCT
gi-4940	583	15	call	call	VERB
gi-4940	583	16	the	the	DET
gi-4940	583	17	recursive	recursive	ADJ
gi-4940	583	18	procedure	procedure	NOUN
gi-4940	583	19	with	with	ADP
gi-4940	583	20	the	the	DET
gi-4940	583	21	increased	increase	VERB
gi-4940	583	22	depth	depth	NOUN
gi-4940	584	1	d	d	NOUN
gi-4940	584	2	=	=	SYM
gi-4940	584	3	d	d	PROPN
gi-4940	584	4	+	+	NOUN
gi-4940	584	5	1	1	NUM
gi-4940	584	6	for	for	ADP
gi-4940	584	7	the	the	DET
gi-4940	584	8	interval	interval	NOUN
gi-4940	584	9	ωϕ,j	ωϕ,j	X
gi-4940	584	10	,	,	PUNCT
gi-4940	584	11	k,2	k,2	X
gi-4940	584	12	=	=	X
gi-4940	585	1	[	[	X
gi-4940	585	2	ϕ1,k	ϕ1,k	PROPN
gi-4940	585	3	,	,	PUNCT
gi-4940	585	4	ϕ2,k	ϕ2,k	PROPN
gi-4940	585	5	]	]	PUNCT
gi-4940	585	6	,	,	PUNCT
gi-4940	585	7	its	its	PRON
gi-4940	585	8	predecessor	predecessor	NOUN
gi-4940	585	9	ωϕ,j	ωϕ,j	PART
gi-4940	585	10	,	,	PUNCT
gi-4940	585	11	k,1	k,1	PROPN
gi-4940	585	12	=	=	PUNCT
gi-4940	585	13	[	[	X
gi-4940	585	14	ak	ak	PROPN
gi-4940	585	15	,	,	PUNCT
gi-4940	585	16	ϕ1,k	ϕ1,k	PROPN
gi-4940	585	17	]	]	X
gi-4940	585	18	,	,	PUNCT
gi-4940	585	19	and	and	CCONJ
gi-4940	585	20	successor	successor	NOUN
gi-4940	585	21	ωϕ,j	ωϕ,j	X
gi-4940	585	22	,	,	PUNCT
gi-4940	585	23	k,3	k,3	X
gi-4940	585	24	=	=	PUNCT
gi-4940	586	1	[	[	X
gi-4940	586	2	ϕ2,k	ϕ2,k	PROPN
gi-4940	586	3	,	,	PUNCT
gi-4940	586	4	ϕ3,k	ϕ3,k	PROPN
gi-4940	586	5	]	]	PUNCT
gi-4940	586	6	.	.	PUNCT
gi-4940	587	1	(	(	PUNCT
gi-4940	587	2	g	g	NOUN
gi-4940	587	3	)	)	PUNCT
gi-4940	587	4	add	add	VERB
gi-4940	587	5	the	the	DET
gi-4940	587	6	new	new	ADJ
gi-4940	587	7	point	point	NOUN
gi-4940	587	8	p2,k	p2,k	PROPN
gi-4940	587	9	to	to	ADP
gi-4940	587	10	the	the	DET
gi-4940	587	11	polynomial	polynomial	ADJ
gi-4940	587	12	approximation	approximation	NOUN
gi-4940	587	13	of	of	ADP
gi-4940	587	14	m̃(λ	m̃(λ	PROPN
gi-4940	587	15	)	)	PUNCT
gi-4940	587	16	:	:	PUNCT
gi-4940	588	1	lλ	lλ	INTJ
gi-4940	588	2	,	,	PUNCT
gi-4940	588	3	j	j	PROPN
gi-4940	588	4	,	,	PUNCT
gi-4940	588	5	k	k	PROPN
gi-4940	588	6	←	←	PROPN
gi-4940	588	7	p2,k	p2,k	PROPN
gi-4940	588	8	.	.	PUNCT
gi-4940	589	1	(	(	PUNCT
gi-4940	589	2	h	h	NOUN
gi-4940	589	3	)	)	PUNCT
gi-4940	589	4	if	if	SCONJ
gi-4940	589	5	the	the	DET
gi-4940	589	6	condition	condition	NOUN
gi-4940	589	7	given	give	VERB
gi-4940	589	8	by	by	ADP
gi-4940	589	9	eq	eq	PROPN
gi-4940	589	10	.	.	PROPN
gi-4940	589	11	4.2	4.2	NUM
gi-4940	589	12	is	be	AUX
gi-4940	589	13	held	hold	VERB
gi-4940	589	14	,	,	PUNCT
gi-4940	589	15	call	call	VERB
gi-4940	589	16	the	the	DET
gi-4940	589	17	recursive	recursive	ADJ
gi-4940	589	18	procedure	procedure	NOUN
gi-4940	589	19	with	with	ADP
gi-4940	589	20	the	the	DET
gi-4940	589	21	increased	increase	VERB
gi-4940	589	22	depth	depth	NOUN
gi-4940	590	1	d	d	NOUN
gi-4940	590	2	=	=	SYM
gi-4940	590	3	d	d	PROPN
gi-4940	590	4	+	+	NOUN
gi-4940	590	5	1	1	NUM
gi-4940	590	6	for	for	ADP
gi-4940	590	7	the	the	DET
gi-4940	590	8	interval	interval	NOUN
gi-4940	590	9	ωϕ,j	ωϕ,j	X
gi-4940	590	10	,	,	PUNCT
gi-4940	590	11	k,3	k,3	X
gi-4940	590	12	=	=	PUNCT
gi-4940	591	1	[	[	X
gi-4940	591	2	ϕ2,k	ϕ2,k	PROPN
gi-4940	591	3	,	,	PUNCT
gi-4940	591	4	ϕ3,k	ϕ3,k	PROPN
gi-4940	591	5	]	]	X
gi-4940	591	6	,	,	PUNCT
gi-4940	591	7	its	its	PRON
gi-4940	591	8	predecessor	predecessor	NOUN
gi-4940	591	9	ωϕ,j	ωϕ,j	X
gi-4940	591	10	,	,	PUNCT
gi-4940	591	11	k,2	k,2	X
gi-4940	591	12	=	=	X
gi-4940	592	1	[	[	X
gi-4940	592	2	ϕ1,k	ϕ1,k	PROPN
gi-4940	592	3	,	,	PUNCT
gi-4940	592	4	ϕ2,k	ϕ2,k	PROPN
gi-4940	592	5	]	]	X
gi-4940	592	6	,	,	PUNCT
gi-4940	592	7	and	and	CCONJ
gi-4940	592	8	successor	successor	NOUN
gi-4940	592	9	ωϕ,j	ωϕ,j	X
gi-4940	592	10	,	,	PUNCT
gi-4940	592	11	k,4	k,4	X
gi-4940	592	12	=	=	PUNCT
gi-4940	593	1	[	[	X
gi-4940	593	2	ϕ3,k	ϕ3,k	PROPN
gi-4940	593	3	,	,	PUNCT
gi-4940	593	4	bk	bk	ADP
gi-4940	593	5	]	]	PUNCT
gi-4940	593	6	.	.	PUNCT
gi-4940	594	1	(	(	PUNCT
gi-4940	594	2	i	i	NOUN
gi-4940	594	3	)	)	PUNCT
gi-4940	594	4	add	add	VERB
gi-4940	594	5	the	the	DET
gi-4940	594	6	new	new	ADJ
gi-4940	594	7	point	point	NOUN
gi-4940	594	8	p3,k	p3,k	PROPN
gi-4940	594	9	to	to	ADP
gi-4940	594	10	the	the	DET
gi-4940	594	11	polynomial	polynomial	ADJ
gi-4940	594	12	approximation	approximation	NOUN
gi-4940	594	13	of	of	ADP
gi-4940	594	14	m̃(λ	m̃(λ	PROPN
gi-4940	594	15	)	)	PUNCT
gi-4940	594	16	:	:	PUNCT
gi-4940	595	1	lλ	lλ	INTJ
gi-4940	595	2	,	,	PUNCT
gi-4940	595	3	j	j	PROPN
gi-4940	595	4	,	,	PUNCT
gi-4940	595	5	k	k	PROPN
gi-4940	595	6	←	←	PROPN
gi-4940	595	7	p3,k	p3,k	PROPN
gi-4940	595	8	.	.	PUNCT
gi-4940	596	1	(	(	PUNCT
gi-4940	596	2	j	j	NOUN
gi-4940	596	3	)	)	PUNCT
gi-4940	596	4	if	if	SCONJ
gi-4940	596	5	the	the	DET
gi-4940	596	6	condition	condition	NOUN
gi-4940	596	7	given	give	VERB
gi-4940	596	8	by	by	ADP
gi-4940	596	9	eq	eq	PROPN
gi-4940	596	10	.	.	PROPN
gi-4940	596	11	4.2	4.2	NUM
gi-4940	596	12	is	be	AUX
gi-4940	596	13	held	hold	VERB
gi-4940	596	14	,	,	PUNCT
gi-4940	596	15	call	call	VERB
gi-4940	596	16	the	the	DET
gi-4940	596	17	recursive	recursive	ADJ
gi-4940	596	18	procedure	procedure	NOUN
gi-4940	596	19	for	for	ADP
gi-4940	596	20	the	the	DET
gi-4940	596	21	last	last	ADJ
gi-4940	596	22	interval	interval	NOUN
gi-4940	596	23	ωϕ,j	ωϕ,j	X
gi-4940	596	24	,	,	PUNCT
gi-4940	596	25	k,4	k,4	X
gi-4940	596	26	=	=	PUNCT
gi-4940	597	1	[	[	X
gi-4940	597	2	ϕ3,k	ϕ3,k	PROPN
gi-4940	597	3	,	,	PUNCT
gi-4940	597	4	bk	bk	ADP
gi-4940	597	5	]	]	PUNCT
gi-4940	597	6	,	,	PUNCT
gi-4940	597	7	its	its	PRON
gi-4940	597	8	predecessor	predecessor	NOUN
gi-4940	597	9	ωϕ,j	ωϕ,j	X
gi-4940	597	10	,	,	PUNCT
gi-4940	597	11	k,3	k,3	X
gi-4940	597	12	=	=	PUNCT
gi-4940	598	1	[	[	X
gi-4940	598	2	ϕ2,k	ϕ2,k	PROPN
gi-4940	598	3	,	,	PUNCT
gi-4940	598	4	ϕ3,k	ϕ3,k	PROPN
gi-4940	598	5	]	]	X
gi-4940	598	6	,	,	PUNCT
gi-4940	598	7	and	and	CCONJ
gi-4940	598	8	successor	successor	NOUN
gi-4940	598	9	ωϕ,j	ωϕ,j	X
gi-4940	598	10	,	,	PUNCT
gi-4940	598	11	k+1,1	k+1,1	NOUN
gi-4940	598	12	=	=	PUNCT
gi-4940	599	1	[	[	X
gi-4940	599	2	bk	bk	ADP
gi-4940	599	3	,	,	PUNCT
gi-4940	599	4	ϕ1,l+1	ϕ1,l+1	PROPN
gi-4940	599	5	]	]	X
gi-4940	599	6	.	.	PUNCT
gi-4940	600	1	the	the	DET
gi-4940	600	2	procedure	procedure	NOUN
gi-4940	600	3	is	be	AUX
gi-4940	600	4	summarized	summarize	VERB
gi-4940	600	5	in	in	ADP
gi-4940	600	6	alg	alg	PROPN
gi-4940	600	7	.	.	PROPN
gi-4940	601	1	8	8	NUM
gi-4940	601	2	.	.	PUNCT
gi-4940	602	1	a	a	DET
gi-4940	602	2	combined	combine	VERB
gi-4940	602	3	sampling	sampling	NOUN
gi-4940	602	4	of	of	ADP
gi-4940	602	5	the	the	DET
gi-4940	602	6	parallel	parallel	NOUN
gi-4940	602	7	.	.	PUNCT
gi-4940	603	1	analogously	analogously	ADV
gi-4940	603	2	,	,	PUNCT
gi-4940	603	3	the	the	DET
gi-4940	603	4	parallel	parallel	ADJ
gi-4940	603	5	p(ϕ	p(ϕ	NOUN
gi-4940	603	6	)	)	PUNCT
gi-4940	603	7	is	be	AUX
gi-4940	603	8	sampled	sample	VERB
gi-4940	603	9	over	over	ADP
gi-4940	603	10	the	the	DET
gi-4940	603	11	interval	interval	NOUN
gi-4940	603	12	ωλ	ωλ	VERB
gi-4940	603	13	,	,	PUNCT
gi-4940	603	14	j	j	PROPN
gi-4940	604	1	=	=	PUNCT
gi-4940	605	1	[	[	X
gi-4940	605	2	λj	λj	X
gi-4940	605	3	,	,	PUNCT
gi-4940	605	4	λj	λj	PROPN
gi-4940	605	5	]	]	X
gi-4940	605	6	.	.	PUNCT
gi-4940	606	1	the	the	DET
gi-4940	606	2	polygonal	polygonal	ADJ
gi-4940	606	3	approximation	approximation	NOUN
gi-4940	606	4	consists	consist	VERB
gi-4940	606	5	of	of	ADP
gi-4940	606	6	two	two	NUM
gi-4940	606	7	steps	step	NOUN
gi-4940	606	8	:	:	PUNCT
gi-4940	606	9	a	a	DET
gi-4940	606	10	partition	partition	NOUN
gi-4940	606	11	of	of	ADP
gi-4940	606	12	p(ϕ	p(ϕ	NOUN
gi-4940	606	13	)	)	PUNCT
gi-4940	606	14	to	to	ADP
gi-4940	606	15	the	the	DET
gi-4940	606	16	fragments	fragment	NOUN
gi-4940	606	17	and	and	CCONJ
gi-4940	606	18	combined	combined	ADJ
gi-4940	606	19	sampling	sampling	NOUN
gi-4940	606	20	of	of	ADP
gi-4940	606	21	the	the	DET
gi-4940	606	22	fragments	fragment	NOUN
gi-4940	606	23	.	.	PUNCT
gi-4940	607	1	each	each	DET
gi-4940	607	2	parallel	parallel	ADJ
gi-4940	607	3	fragment	fragment	NOUN
gi-4940	607	4	needs	need	VERB
gi-4940	607	5	to	to	PART
gi-4940	607	6	be	be	AUX
gi-4940	607	7	sampled	sample	VERB
gi-4940	607	8	,	,	PUNCT
gi-4940	607	9	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	607	10	,	,	PUNCT
gi-4940	607	11	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	607	12	,	,	PUNCT
gi-4940	607	13	ωϕ,j,3	ωϕ,j,3	PROPN
gi-4940	607	14	are	be	AUX
gi-4940	607	15	partitioned	partition	VERB
gi-4940	607	16	into	into	ADP
gi-4940	607	17	four	four	NUM
gi-4940	607	18	geoinformatics	geoinformatic	NOUN
gi-4940	607	19	fce	fce	VERB
gi-4940	607	20	ctu	ctu	NOUN
gi-4940	607	21	17(2	17(2	NUM
gi-4940	607	22	)	)	PUNCT
gi-4940	607	23	,	,	PUNCT
gi-4940	607	24	2018	2018	NUM
gi-4940	607	25	51	51	NUM
gi-4940	607	26	t.	t.	NOUN
gi-4940	607	27	bayer	bayer	NOUN
gi-4940	607	28	:	:	PUNCT
gi-4940	607	29	plotting	plot	VERB
gi-4940	607	30	the	the	DET
gi-4940	607	31	map	map	NOUN
gi-4940	607	32	projection	projection	NOUN
gi-4940	607	33	graticule	graticule	NOUN
gi-4940	607	34	with	with	ADP
gi-4940	607	35	discontinuities	discontinuity	NOUN
gi-4940	607	36	disjoint	disjoint	NOUN
gi-4940	607	37	subintervals	subinterval	NOUN
gi-4940	607	38	.	.	PUNCT
gi-4940	608	1	while	while	SCONJ
gi-4940	608	2	for	for	ADP
gi-4940	608	3	adaptive	adaptive	ADJ
gi-4940	608	4	meridian	meridian	PROPN
gi-4940	608	5	m(λ	m(λ	PROPN
gi-4940	608	6	)	)	PUNCT
gi-4940	608	7	sampling	sampling	NOUN
gi-4940	608	8	are	be	AUX
gi-4940	608	9	:	:	PUNCT
gi-4940	608	10	λ	λ	X
gi-4940	608	11	=	=	SYM
gi-4940	608	12	const	const	PROPN
gi-4940	608	13	,	,	PUNCT
gi-4940	608	14	ϕ	ϕ	PROPN
gi-4940	608	15	∈	∈	PROPN
gi-4940	608	16	ωϕ,j	ωϕ,j	PUNCT
gi-4940	608	17	,	,	PUNCT
gi-4940	608	18	for	for	ADP
gi-4940	608	19	parallel	parallel	ADJ
gi-4940	608	20	p(ϕ	p(ϕ	NOUN
gi-4940	608	21	)	)	PUNCT
gi-4940	608	22	sampling	sampling	NOUN
gi-4940	608	23	are	be	AUX
gi-4940	608	24	:	:	PUNCT
gi-4940	609	1	ϕ	ϕ	X
gi-4940	609	2	=	=	PUNCT
gi-4940	609	3	const	const	PROPN
gi-4940	609	4	,	,	PUNCT
gi-4940	609	5	λ	λ	PROPN
gi-4940	609	6	∈	∈	NOUN
gi-4940	609	7	ωλ	ωλ	VERB
gi-4940	609	8	,	,	PUNCT
gi-4940	609	9	j	j	PROPN
gi-4940	609	10	.	.	PUNCT
gi-4940	610	1	therefore	therefore	ADV
gi-4940	610	2	,	,	PUNCT
gi-4940	610	3	the	the	DET
gi-4940	610	4	randomly	randomly	ADV
gi-4940	610	5	generated	generate	VERB
gi-4940	610	6	parallel	parallel	ADJ
gi-4940	610	7	points	point	NOUN
gi-4940	610	8	λ1	λ1	ADJ
gi-4940	610	9	=	=	SYM
gi-4940	610	10	a+	a+	PUNCT
gi-4940	610	11	1	1	NUM
gi-4940	610	12	2r1(b−	2r1(b−	NUM
gi-4940	610	13	a	a	NOUN
gi-4940	610	14	)	)	PUNCT
gi-4940	610	15	,	,	PUNCT
gi-4940	610	16	λ2	λ2	NOUN
gi-4940	610	17	=	=	SYM
gi-4940	610	18	a+	a+	PUNCT
gi-4940	610	19	r2(b−	r2(b−	NOUN
gi-4940	610	20	a	a	PRON
gi-4940	610	21	)	)	PUNCT
gi-4940	610	22	,	,	PUNCT
gi-4940	610	23	λ3	λ3	PROPN
gi-4940	610	24	=	=	SYM
gi-4940	610	25	a+	a+	PUNCT
gi-4940	610	26	3	3	NUM
gi-4940	610	27	2r3(b−	2r3(b−	NUM
gi-4940	610	28	a	a	NOUN
gi-4940	610	29	)	)	PUNCT
gi-4940	610	30	,	,	PUNCT
gi-4940	610	31	split	split	VERB
gi-4940	610	32	the	the	DET
gi-4940	610	33	interval	interval	NOUN
gi-4940	610	34	ωλ	ωλ	VERB
gi-4940	610	35	,	,	PUNCT
gi-4940	610	36	j	j	PROPN
gi-4940	610	37	,	,	PUNCT
gi-4940	610	38	k	k	PROPN
gi-4940	610	39	to	to	ADP
gi-4940	610	40	the	the	DET
gi-4940	610	41	approximate	approximate	ADJ
gi-4940	610	42	quarters	quarter	NOUN
gi-4940	610	43	ωλ	ωλ	VERB
gi-4940	610	44	,	,	PUNCT
gi-4940	610	45	j	j	PROPN
gi-4940	610	46	,	,	PUNCT
gi-4940	610	47	k,1	k,1	PROPN
gi-4940	610	48	=	=	PUNCT
gi-4940	611	1	[	[	X
gi-4940	611	2	a	a	DET
gi-4940	611	3	,	,	PUNCT
gi-4940	611	4	λ1	λ1	PROPN
gi-4940	611	5	]	]	PUNCT
gi-4940	611	6	,	,	PUNCT
gi-4940	611	7	ωλ	ωλ	PROPN
gi-4940	611	8	,	,	PUNCT
gi-4940	611	9	j	j	PROPN
gi-4940	611	10	,	,	PUNCT
gi-4940	611	11	k,2	k,2	X
gi-4940	611	12	=	=	X
gi-4940	612	1	[	[	X
gi-4940	612	2	λ1	λ1	ADJ
gi-4940	612	3	,	,	PUNCT
gi-4940	612	4	λ2	λ2	PROPN
gi-4940	612	5	]	]	PUNCT
gi-4940	612	6	ωλ	ωλ	PROPN
gi-4940	612	7	,	,	PUNCT
gi-4940	612	8	j	j	PROPN
gi-4940	612	9	,	,	PUNCT
gi-4940	612	10	k,3	k,3	X
gi-4940	612	11	=	=	PUNCT
gi-4940	613	1	[	[	X
gi-4940	613	2	λ2	λ2	NUM
gi-4940	613	3	,	,	PUNCT
gi-4940	613	4	λ3	λ3	PROPN
gi-4940	613	5	]	]	NOUN
gi-4940	613	6	,	,	PUNCT
gi-4940	613	7	ωλ	ωλ	PROPN
gi-4940	613	8	,	,	PUNCT
gi-4940	613	9	j	j	PROPN
gi-4940	613	10	,	,	PUNCT
gi-4940	613	11	k,4	k,4	X
gi-4940	613	12	=	=	PUNCT
gi-4940	614	1	[	[	X
gi-4940	614	2	λ3	λ3	PROPN
gi-4940	614	3	,	,	PUNCT
gi-4940	614	4	b	b	NOUN
gi-4940	614	5	]	]	X
gi-4940	614	6	.	.	PUNCT
gi-4940	615	1	the	the	DET
gi-4940	615	2	remaining	remain	VERB
gi-4940	615	3	steps	step	NOUN
gi-4940	615	4	are	be	AUX
gi-4940	615	5	analogous	analogous	ADJ
gi-4940	615	6	.	.	PUNCT
gi-4940	616	1	this	this	DET
gi-4940	616	2	method	method	NOUN
gi-4940	616	3	can	can	AUX
gi-4940	616	4	treat	treat	VERB
gi-4940	616	5	all	all	DET
gi-4940	616	6	kinds	kind	NOUN
gi-4940	616	7	of	of	ADP
gi-4940	616	8	discontinuities	discontinuity	NOUN
gi-4940	616	9	,	,	PUNCT
gi-4940	616	10	without	without	ADP
gi-4940	616	11	specific	specific	ADJ
gi-4940	616	12	knowledge	knowledge	NOUN
gi-4940	616	13	of	of	ADP
gi-4940	616	14	ε	ε	PROPN
gi-4940	616	15	;	;	PUNCT
gi-4940	616	16	for	for	ADP
gi-4940	616	17	practical	practical	ADJ
gi-4940	616	18	computations	computation	NOUN
gi-4940	616	19	is	be	AUX
gi-4940	616	20	ε	ε	PROPN
gi-4940	616	21	=	=	SYM
gi-4940	616	22	0.001	0.001	NUM
gi-4940	616	23	◦	◦	NOUN
gi-4940	616	24	.	.	PUNCT
gi-4940	617	1	it	it	PRON
gi-4940	617	2	has	have	VERB
gi-4940	617	3	a	a	DET
gi-4940	617	4	disadvantage	disadvantage	NOUN
gi-4940	617	5	the	the	DET
gi-4940	617	6	duplication	duplication	NOUN
gi-4940	617	7	of	of	ADP
gi-4940	617	8	lines	line	NOUN
gi-4940	617	9	along	along	ADP
gi-4940	617	10	singularities	singularity	NOUN
gi-4940	617	11	if	if	SCONJ
gi-4940	617	12	the	the	DET
gi-4940	617	13	discontinuities	discontinuity	NOUN
gi-4940	617	14	are	be	AUX
gi-4940	617	15	not	not	PART
gi-4940	617	16	classified	classified	ADJ
gi-4940	617	17	.	.	PUNCT
gi-4940	618	1	for	for	ADP
gi-4940	618	2	the	the	DET
gi-4940	618	3	discontinuity	discontinuity	NOUN
gi-4940	618	4	c	c	NOUN
gi-4940	618	5	=	=	SYM
gi-4940	618	6	ϕ	ϕ	X
gi-4940	618	7	=	=	SYM
gi-4940	618	8	0	0	NUM
gi-4940	618	9	◦	◦	NOUN
gi-4940	618	10	in	in	ADP
gi-4940	618	11	the	the	DET
gi-4940	618	12	polyconic	polyconic	ADJ
gi-4940	618	13	projection	projection	NOUN
gi-4940	618	14	,	,	PUNCT
gi-4940	618	15	this	this	DET
gi-4940	618	16	issue	issue	NOUN
gi-4940	618	17	is	be	AUX
gi-4940	618	18	illustrated	illustrate	VERB
gi-4940	618	19	in	in	ADP
gi-4940	618	20	fig	fig	NOUN
gi-4940	618	21	.	.	PUNCT
gi-4940	619	1	4.3	4.3	NUM
gi-4940	619	2	.	.	PUNCT
gi-4940	620	1	a	a	DET
gi-4940	620	2	hemisphere	hemisphere	NOUN
gi-4940	620	3	constructed	construct	VERB
gi-4940	620	4	in	in	ADP
gi-4940	620	5	the	the	DET
gi-4940	620	6	normal	normal	ADJ
gi-4940	620	7	aspect	aspect	NOUN
gi-4940	620	8	is	be	AUX
gi-4940	620	9	composed	compose	VERB
gi-4940	620	10	of	of	ADP
gi-4940	620	11	two	two	NUM
gi-4940	620	12	sub	sub	NOUN
gi-4940	620	13	-	-	NOUN
gi-4940	620	14	intervals	interval	NOUN
gi-4940	620	15	[	[	X
gi-4940	620	16	−π/2	−π/2	PROPN
gi-4940	620	17	,	,	PUNCT
gi-4940	620	18	0	0	NUM
gi-4940	620	19	)	)	PUNCT
gi-4940	620	20	,	,	PUNCT
gi-4940	620	21	(	(	PUNCT
gi-4940	620	22	0	0	NUM
gi-4940	620	23	,	,	PUNCT
gi-4940	620	24	π/2	π/2	NUM
gi-4940	620	25	]	]	PUNCT
gi-4940	620	26	.	.	PUNCT
gi-4940	621	1	hence	hence	ADV
gi-4940	621	2	,	,	PUNCT
gi-4940	621	3	the	the	DET
gi-4940	621	4	equator	equator	NOUN
gi-4940	621	5	is	be	AUX
gi-4940	621	6	doubled	double	VERB
gi-4940	621	7	,	,	PUNCT
gi-4940	621	8	which	which	PRON
gi-4940	621	9	does	do	AUX
gi-4940	621	10	not	not	PART
gi-4940	621	11	look	look	VERB
gi-4940	621	12	aesthetically	aesthetically	ADV
gi-4940	621	13	pleasing	pleasing	ADJ
gi-4940	621	14	,	,	PUNCT
gi-4940	621	15	but	but	CCONJ
gi-4940	621	16	it	it	PRON
gi-4940	621	17	is	be	AUX
gi-4940	621	18	visible	visible	ADJ
gi-4940	621	19	only	only	ADV
gi-4940	621	20	under	under	ADP
gi-4940	621	21	magnification	magnification	NOUN
gi-4940	621	22	.	.	PUNCT
gi-4940	622	1	5	5	NUM
gi-4940	622	2	.	.	X
gi-4940	622	3	experiments	experiment	NOUN
gi-4940	622	4	and	and	CCONJ
gi-4940	622	5	results	result	VERB
gi-4940	622	6	the	the	DET
gi-4940	622	7	principles	principle	NOUN
gi-4940	622	8	mentioned	mention	VERB
gi-4940	622	9	above	above	ADV
gi-4940	622	10	will	will	AUX
gi-4940	622	11	be	be	AUX
gi-4940	622	12	illustrated	illustrate	VERB
gi-4940	622	13	on	on	ADP
gi-4940	622	14	the	the	DET
gi-4940	622	15	several	several	ADJ
gi-4940	622	16	tests	test	NOUN
gi-4940	622	17	.	.	PUNCT
gi-4940	623	1	while	while	SCONJ
gi-4940	623	2	the	the	DET
gi-4940	623	3	first	first	ADJ
gi-4940	623	4	analysis	analysis	NOUN
gi-4940	623	5	compares	compare	VERB
gi-4940	623	6	the	the	DET
gi-4940	623	7	behavior	behavior	NOUN
gi-4940	623	8	and	and	CCONJ
gi-4940	623	9	properties	property	NOUN
gi-4940	623	10	of	of	ADP
gi-4940	623	11	combined	combined	ADJ
gi-4940	623	12	sampling	sampling	NOUN
gi-4940	623	13	,	,	PUNCT
gi-4940	623	14	the	the	DET
gi-4940	623	15	second	second	ADJ
gi-4940	623	16	test	test	NOUN
gi-4940	623	17	reconstructs	reconstruct	VERB
gi-4940	623	18	the	the	DET
gi-4940	623	19	fournier	fournier	PROPN
gi-4940	623	20	i.	i.	PROPN
gi-4940	623	21	projection	projection	PROPN
gi-4940	623	22	graticule	graticule	NOUN
gi-4940	623	23	in	in	ADP
gi-4940	623	24	the	the	DET
gi-4940	623	25	oblique	oblique	ADJ
gi-4940	623	26	aspect	aspect	NOUN
gi-4940	623	27	(	(	PUNCT
gi-4940	623	28	several	several	ADJ
gi-4940	623	29	discontinuities	discontinuity	NOUN
gi-4940	623	30	in	in	ADP
gi-4940	623	31	the	the	DET
gi-4940	623	32	coordinate	coordinate	NOUN
gi-4940	623	33	functions	function	NOUN
gi-4940	623	34	are	be	AUX
gi-4940	623	35	involved	involve	VERB
gi-4940	623	36	)	)	PUNCT
gi-4940	623	37	.	.	PUNCT
gi-4940	624	1	finally	finally	ADV
gi-4940	624	2	,	,	PUNCT
gi-4940	624	3	the	the	DET
gi-4940	624	4	last	last	ADJ
gi-4940	624	5	experiment	experiment	NOUN
gi-4940	624	6	illustrates	illustrate	VERB
gi-4940	624	7	the	the	DET
gi-4940	624	8	splitting	splitting	NOUN
gi-4940	624	9	procedure	procedure	NOUN
gi-4940	624	10	efficiency	efficiency	NOUN
gi-4940	624	11	depending	depend	VERB
gi-4940	624	12	on	on	ADP
gi-4940	624	13	the	the	DET
gi-4940	624	14	threshold	threshold	NOUN
gi-4940	624	15	ε	ε	PROPN
gi-4940	624	16	.	.	PUNCT
gi-4940	625	1	the	the	DET
gi-4940	625	2	results	result	NOUN
gi-4940	625	3	are	be	AUX
gi-4940	625	4	summarized	summarize	VERB
gi-4940	625	5	in	in	ADP
gi-4940	625	6	tabs	tab	NOUN
gi-4940	625	7	.	.	PUNCT
gi-4940	626	1	1	1	NUM
gi-4940	626	2	-	-	SYM
gi-4940	626	3	5	5	NUM
gi-4940	626	4	.	.	NOUN
gi-4940	627	1	5.1	5.1	NUM
gi-4940	627	2	.	.	PUNCT
gi-4940	628	1	comparison	comparison	NOUN
gi-4940	628	2	of	of	ADP
gi-4940	628	3	uniform	uniform	NOUN
gi-4940	628	4	and	and	CCONJ
gi-4940	628	5	combined	combined	ADJ
gi-4940	628	6	sampling	sampling	NOUN
gi-4940	628	7	during	during	ADP
gi-4940	628	8	this	this	DET
gi-4940	628	9	test	test	NOUN
gi-4940	628	10	,	,	PUNCT
gi-4940	628	11	the	the	DET
gi-4940	628	12	uniform	uniform	NOUN
gi-4940	628	13	and	and	CCONJ
gi-4940	628	14	combined	combined	ADJ
gi-4940	628	15	sampling	sampling	NOUN
gi-4940	628	16	techniques	technique	NOUN
gi-4940	628	17	will	will	AUX
gi-4940	628	18	be	be	AUX
gi-4940	628	19	compared	compare	VERB
gi-4940	628	20	regarding	regard	VERB
gi-4940	628	21	the	the	DET
gi-4940	628	22	data	data	NOUN
gi-4940	628	23	representation	representation	NOUN
gi-4940	628	24	compactness	compactness	NOUN
gi-4940	628	25	measured	measure	VERB
gi-4940	628	26	by	by	ADP
gi-4940	628	27	the	the	DET
gi-4940	628	28	amount	amount	NOUN
gi-4940	628	29	of	of	ADP
gi-4940	628	30	the	the	DET
gi-4940	628	31	sampled	sample	VERB
gi-4940	628	32	meridian	meridian	PROPN
gi-4940	628	33	points	point	NOUN
gi-4940	628	34	nmer	nmer	ADJ
gi-4940	628	35	and	and	CCONJ
gi-4940	628	36	parallel	parallel	ADJ
gi-4940	628	37	points	point	NOUN
gi-4940	628	38	npar	npar	NOUN
gi-4940	628	39	.	.	PUNCT
gi-4940	629	1	additionally	additionally	ADV
gi-4940	629	2	,	,	PUNCT
gi-4940	629	3	the	the	DET
gi-4940	629	4	maximum	maximum	ADJ
gi-4940	629	5	angles	angle	VERB
gi-4940	629	6	αm	αm	ADV
gi-4940	629	7	,	,	PUNCT
gi-4940	629	8	αp	αp	NOUN
gi-4940	629	9	between	between	ADP
gi-4940	629	10	the	the	DET
gi-4940	629	11	sampled	sample	VERB
gi-4940	629	12	meridian	meridian	NOUN
gi-4940	629	13	and	and	CCONJ
gi-4940	629	14	parallel	parallel	ADJ
gi-4940	629	15	segments	segment	NOUN
gi-4940	629	16	together	together	ADV
gi-4940	629	17	with	with	ADP
gi-4940	629	18	their	their	PRON
gi-4940	629	19	mean	mean	ADJ
gi-4940	629	20	values	value	NOUN
gi-4940	629	21	α̃m	α̃m	VERB
gi-4940	629	22	,	,	PUNCT
gi-4940	629	23	α̃p	α̃p	PRON
gi-4940	629	24	are	be	AUX
gi-4940	629	25	measured	measure	VERB
gi-4940	629	26	;	;	PUNCT
gi-4940	629	27	these	these	DET
gi-4940	629	28	indicators	indicator	NOUN
gi-4940	629	29	depend	depend	VERB
gi-4940	629	30	on	on	ADP
gi-4940	629	31	the	the	DET
gi-4940	629	32	sampling	sample	VERB
gi-4940	629	33	density	density	NOUN
gi-4940	629	34	.	.	PUNCT
gi-4940	630	1	for	for	ADP
gi-4940	630	2	the	the	DET
gi-4940	630	3	uniform	uniform	NOUN
gi-4940	630	4	sampling	sampling	NOUN
gi-4940	630	5	,	,	PUNCT
gi-4940	630	6	the	the	DET
gi-4940	630	7	sampling	sampling	NOUN
gi-4940	630	8	steps	step	NOUN
gi-4940	630	9	δϕ	δϕ	NOUN
gi-4940	630	10	,	,	PUNCT
gi-4940	630	11	δλ	δλ	NOUN
gi-4940	630	12	are	be	AUX
gi-4940	630	13	fixed	fix	VERB
gi-4940	630	14	,	,	PUNCT
gi-4940	630	15	while	while	SCONJ
gi-4940	630	16	the	the	DET
gi-4940	630	17	adaptive	adaptive	ADJ
gi-4940	630	18	sampling	sampling	NOUN
gi-4940	630	19	is	be	AUX
gi-4940	630	20	driven	drive	VERB
gi-4940	630	21	by	by	ADP
gi-4940	630	22	the	the	DET
gi-4940	630	23	sampling	sample	VERB
gi-4940	630	24	angle	angle	NOUN
gi-4940	630	25	α	α	NOUN
gi-4940	630	26	.	.	PUNCT
gi-4940	631	1	our	our	PRON
gi-4940	631	2	experiments	experiment	NOUN
gi-4940	631	3	will	will	AUX
gi-4940	631	4	be	be	AUX
gi-4940	631	5	carried	carry	VERB
gi-4940	631	6	out	out	ADP
gi-4940	631	7	for	for	ADP
gi-4940	631	8	combined	combined	ADJ
gi-4940	631	9	sampling	sampling	NOUN
gi-4940	631	10	with	with	ADP
gi-4940	631	11	α	α	NOUN
gi-4940	631	12	=	=	SYM
gi-4940	631	13	1	1	NUM
gi-4940	631	14	◦	◦	NOUN
gi-4940	631	15	,	,	PUNCT
gi-4940	631	16	2	2	NUM
gi-4940	631	17	◦	◦	NOUN
gi-4940	631	18	,	,	PUNCT
gi-4940	631	19	5	5	NUM
gi-4940	631	20	◦	◦	NOUN
gi-4940	631	21	,	,	PUNCT
gi-4940	631	22	the	the	DET
gi-4940	631	23	recursive	recursive	ADJ
gi-4940	631	24	depth	depth	NOUN
gi-4940	631	25	is	be	AUX
gi-4940	631	26	d	d	NOUN
gi-4940	631	27	=	=	SYM
gi-4940	631	28	1	1	NUM
gi-4940	631	29	,	,	PUNCT
gi-4940	631	30	and	and	CCONJ
gi-4940	631	31	for	for	ADP
gi-4940	631	32	the	the	DET
gi-4940	631	33	uniform	uniform	NOUN
gi-4940	631	34	sampling	sample	VERB
gi-4940	631	35	where	where	SCONJ
gi-4940	631	36	δϕ	δϕ	X
gi-4940	631	37	,	,	PUNCT
gi-4940	631	38	δλ	δλ	PROPN
gi-4940	631	39	will	will	AUX
gi-4940	631	40	be	be	AUX
gi-4940	631	41	set	set	VERB
gi-4940	631	42	providing	provide	VERB
gi-4940	631	43	the	the	DET
gi-4940	631	44	analogous	analogous	ADJ
gi-4940	631	45	amount	amount	NOUN
gi-4940	631	46	of	of	ADP
gi-4940	631	47	the	the	DET
gi-4940	631	48	sampled	sample	VERB
gi-4940	631	49	points	point	NOUN
gi-4940	631	50	.	.	PUNCT
gi-4940	632	1	8	8	NUM
gi-4940	632	2	projections	projection	NOUN
gi-4940	632	3	are	be	AUX
gi-4940	632	4	involved	involve	VERB
gi-4940	632	5	in	in	ADP
gi-4940	632	6	testing	testing	NOUN
gi-4940	632	7	:	:	PUNCT
gi-4940	632	8	equidistant	equidistant	VERB
gi-4940	632	9	cylindrical	cylindrical	ADJ
gi-4940	632	10	,	,	PUNCT
gi-4940	632	11	conic	conic	ADJ
gi-4940	632	12	,	,	PUNCT
gi-4940	632	13	azimuthal	azimuthal	NOUN
gi-4940	632	14	,	,	PUNCT
gi-4940	632	15	bonne	bonne	NOUN
gi-4940	632	16	and	and	CCONJ
gi-4940	632	17	hassler	hassler	PROPN
gi-4940	632	18	(	(	PUNCT
gi-4940	632	19	ϕ1	ϕ1	NOUN
gi-4940	632	20	=	=	NOUN
gi-4940	632	21	50	50	NUM
gi-4940	632	22	◦	◦	NOUN
gi-4940	632	23	)	)	PUNCT
gi-4940	632	24	,	,	PUNCT
gi-4940	632	25	nicolosi	nicolosi	NOUN
gi-4940	632	26	,	,	PUNCT
gi-4940	632	27	littrow	littrow	NOUN
gi-4940	632	28	,	,	PUNCT
gi-4940	632	29	and	and	CCONJ
gi-4940	632	30	adams	adams	PROPN
gi-4940	632	31	i	i	PROPN
gi-4940	632	32	world	world	PROPN
gi-4940	632	33	conformal	conformal	PROPN
gi-4940	632	34	.	.	PUNCT
gi-4940	633	1	the	the	DET
gi-4940	633	2	results	result	NOUN
gi-4940	633	3	are	be	AUX
gi-4940	633	4	summarized	summarize	VERB
gi-4940	633	5	in	in	ADP
gi-4940	633	6	tab	tab	NOUN
gi-4940	633	7	.	.	PUNCT
gi-4940	634	1	1	1	NUM
gi-4940	634	2	.	.	PUNCT
gi-4940	635	1	while	while	SCONJ
gi-4940	635	2	s1	s1	NOUN
gi-4940	635	3	,	,	PUNCT
gi-4940	635	4	s2	s2	NOUN
gi-4940	635	5	exceed	exceed	VERB
gi-4940	635	6	the	the	DET
gi-4940	635	7	αm	αm	NOUN
gi-4940	635	8	,	,	PUNCT
gi-4940	635	9	αp	αp	NOUN
gi-4940	635	10	values	value	NOUN
gi-4940	635	11	(	(	PUNCT
gi-4940	635	12	+20	+20	NUM
gi-4940	635	13	%	%	NOUN
gi-4940	635	14	for	for	ADP
gi-4940	635	15	s1	s1	NOUN
gi-4940	635	16	,	,	PUNCT
gi-4940	635	17	+15	+15	NUM
gi-4940	635	18	%	%	NOUN
gi-4940	635	19	for	for	ADP
gi-4940	635	20	s2	s2	PROPN
gi-4940	635	21	)	)	PUNCT
gi-4940	635	22	,	,	PUNCT
gi-4940	635	23	s3	s3	PROPN
gi-4940	635	24	provides	provide	VERB
gi-4940	635	25	values	value	NOUN
gi-4940	635	26	satisfying	satisfy	VERB
gi-4940	635	27	the	the	DET
gi-4940	635	28	given	give	VERB
gi-4940	635	29	criteria	criterion	NOUN
gi-4940	635	30	(	(	PUNCT
gi-4940	635	31	-7	-7	NOUN
gi-4940	635	32	%	%	NOUN
gi-4940	635	33	)	)	PUNCT
gi-4940	635	34	without	without	ADP
gi-4940	635	35	a	a	DET
gi-4940	635	36	significant	significant	ADJ
gi-4940	635	37	increment	increment	NOUN
gi-4940	635	38	of	of	ADP
gi-4940	635	39	sampled	sample	VERB
gi-4940	635	40	points	point	NOUN
gi-4940	635	41	.	.	PUNCT
gi-4940	636	1	cylindrical	cylindrical	ADJ
gi-4940	636	2	,	,	PUNCT
gi-4940	636	3	conic	conic	ADJ
gi-4940	636	4	and	and	CCONJ
gi-4940	636	5	azimuthal	azimuthal	ADJ
gi-4940	636	6	projections	projection	NOUN
gi-4940	636	7	illustrate	illustrate	VERB
gi-4940	636	8	the	the	DET
gi-4940	636	9	adaptive	adaptive	ADJ
gi-4940	636	10	sampling	sampling	NOUN
gi-4940	636	11	efficiency	efficiency	NOUN
gi-4940	636	12	;	;	PUNCT
gi-4940	636	13	for	for	ADP
gi-4940	636	14	the	the	DET
gi-4940	636	15	straight	straight	ADJ
gi-4940	636	16	meridians	meridian	NOUN
gi-4940	636	17	/	/	SYM
gi-4940	636	18	parallels	parallel	NOUN
gi-4940	636	19	,	,	PUNCT
gi-4940	636	20	only	only	ADV
gi-4940	636	21	2	2	NUM
gi-4940	636	22	%	%	NOUN
gi-4940	636	23	of	of	ADP
gi-4940	636	24	points	point	NOUN
gi-4940	636	25	are	be	AUX
gi-4940	636	26	sufficient	sufficient	ADJ
gi-4940	636	27	for	for	ADP
gi-4940	636	28	the	the	DET
gi-4940	636	29	shape	shape	NOUN
gi-4940	636	30	estimation	estimation	NOUN
gi-4940	636	31	(	(	PUNCT
gi-4940	636	32	uniform	uniform	ADJ
gi-4940	636	33	sampling	sample	VERB
gi-4940	636	34	can	can	AUX
gi-4940	636	35	not	not	PART
gi-4940	636	36	achieve	achieve	VERB
gi-4940	636	37	this	this	DET
gi-4940	636	38	efficiency	efficiency	NOUN
gi-4940	636	39	)	)	PUNCT
gi-4940	636	40	.	.	PUNCT
gi-4940	637	1	concerning	concern	VERB
gi-4940	637	2	the	the	DET
gi-4940	637	3	criteria	criterion	NOUN
gi-4940	637	4	mentioned	mention	VERB
gi-4940	637	5	above	above	ADP
gi-4940	637	6	the	the	DET
gi-4940	637	7	results	result	NOUN
gi-4940	637	8	are	be	AUX
gi-4940	637	9	compared	compare	VERB
gi-4940	637	10	in	in	ADP
gi-4940	637	11	tab	tab	NOUN
gi-4940	637	12	.	.	PUNCT
gi-4940	638	1	2	2	X
gi-4940	638	2	.	.	X
gi-4940	638	3	the	the	DET
gi-4940	638	4	sampling	sampling	NOUN
gi-4940	638	5	steps	step	NOUN
gi-4940	638	6	δϕ	δϕ	NOUN
gi-4940	638	7	,	,	PUNCT
gi-4940	638	8	δλ	δλ	NOUN
gi-4940	638	9	have	have	AUX
gi-4940	638	10	been	be	AUX
gi-4940	638	11	set	set	VERB
gi-4940	638	12	so	so	SCONJ
gi-4940	638	13	that	that	SCONJ
gi-4940	638	14	the	the	DET
gi-4940	638	15	amount	amount	NOUN
gi-4940	638	16	of	of	ADP
gi-4940	638	17	sampled	sample	VERB
gi-4940	638	18	points	point	NOUN
gi-4940	638	19	nmer	nmer	ADJ
gi-4940	638	20	,	,	PUNCT
gi-4940	638	21	npar	npar	NOUN
gi-4940	638	22	is	be	AUX
gi-4940	638	23	analogous	analogous	ADJ
gi-4940	638	24	.	.	PUNCT
gi-4940	639	1	in	in	ADP
gi-4940	639	2	geoinformatics	geoinformatic	NOUN
gi-4940	639	3	fce	fce	VERB
gi-4940	639	4	ctu	ctu	NOUN
gi-4940	639	5	17(2	17(2	NUM
gi-4940	639	6	)	)	PUNCT
gi-4940	639	7	,	,	PUNCT
gi-4940	639	8	2018	2018	NUM
gi-4940	639	9	52	52	NUM
gi-4940	639	10	t.	t.	NOUN
gi-4940	639	11	bayer	bayer	NOUN
gi-4940	639	12	:	:	PUNCT
gi-4940	639	13	plotting	plot	VERB
gi-4940	639	14	the	the	DET
gi-4940	639	15	map	map	NOUN
gi-4940	639	16	projection	projection	NOUN
gi-4940	639	17	graticule	graticule	NOUN
gi-4940	639	18	with	with	ADP
gi-4940	639	19	discontinuities	discontinuity	NOUN
gi-4940	639	20	table	table	NOUN
gi-4940	639	21	1	1	NUM
gi-4940	639	22	:	:	PUNCT
gi-4940	639	23	combined	combined	ADJ
gi-4940	639	24	sampling	sampling	NOUN
gi-4940	639	25	of	of	ADP
gi-4940	639	26	the	the	DET
gi-4940	639	27	graticule	graticule	NOUN
gi-4940	639	28	for	for	ADP
gi-4940	639	29	α	α	NOUN
gi-4940	639	30	=	=	SYM
gi-4940	639	31	1	1	NUM
gi-4940	639	32	◦	◦	NOUN
gi-4940	639	33	,	,	PUNCT
gi-4940	639	34	2	2	NUM
gi-4940	639	35	◦	◦	NOUN
gi-4940	639	36	,	,	PUNCT
gi-4940	639	37	5	5	NUM
gi-4940	639	38	◦	◦	NOUN
gi-4940	639	39	,	,	PUNCT
gi-4940	639	40	methods	method	NOUN
gi-4940	639	41	s1	s1	NOUN
gi-4940	639	42	,	,	PUNCT
gi-4940	639	43	s2	s2	PROPN
gi-4940	639	44	,	,	PUNCT
gi-4940	639	45	s3	s3	PROPN
gi-4940	639	46	are	be	AUX
gi-4940	639	47	compared	compare	VERB
gi-4940	639	48	.	.	PUNCT
gi-4940	640	1	projection	projection	NOUN
gi-4940	640	2	#	#	NOUN
gi-4940	640	3	nmer	nmer	ADJ
gi-4940	640	4	npar	npar	NOUN
gi-4940	640	5	αm	αm	PROPN
gi-4940	640	6	αp	αp	PROPN
gi-4940	640	7	α̃m	α̃m	VERB
gi-4940	640	8	α̃p	α̃p	AUX
gi-4940	640	9	equidistant	equidistant	VERB
gi-4940	640	10	cylindrical	cylindrical	ADJ
gi-4940	640	11	s1	s1	NOUN
gi-4940	641	1	195/195/195	195/195/195	NUM
gi-4940	641	2	190/190/190	190/190/190	NUM
gi-4940	641	3	0/0/0	0/0/0	NUM
gi-4940	641	4	0/0/0	0/0/0	NUM
gi-4940	641	5	0/0/0	0/0/0	NUM
gi-4940	641	6	0/0/0	0/0/0	PROPN
gi-4940	641	7	s2	s2	NOUN
gi-4940	641	8	195/195/195	195/195/195	NUM
gi-4940	642	1	190/190/190	190/190/190	NUM
gi-4940	642	2	0/0/0	0/0/0	NUM
gi-4940	642	3	0/0/0	0/0/0	NUM
gi-4940	642	4	0/0/0	0/0/0	NUM
gi-4940	642	5	0/0/0	0/0/0	NUM
gi-4940	642	6	s3	s3	NOUN
gi-4940	642	7	195/195/195	195/195/195	NUM
gi-4940	642	8	190/190/190	190/190/190	NUM
gi-4940	642	9	0/0/0	0/0/0	NUM
gi-4940	642	10	0/0/0	0/0/0	NUM
gi-4940	642	11	0/0/0	0/0/0	PROPN
gi-4940	642	12	0/0/0	0/0/0	NUM
gi-4940	642	13	equidistant	equidistant	ADJ
gi-4940	642	14	conic	conic	ADJ
gi-4940	642	15	s1	s1	NOUN
gi-4940	642	16	195/195/195	195/195/195	NUM
gi-4940	642	17	9961/6973/2464	9961/6973/2464	NOUN
gi-4940	642	18	0/0/0	0/0/0	PROPN
gi-4940	642	19	1.02/2.27/4.98	1.02/2.27/4.98	NUM
gi-4940	642	20	0/0/0	0/0/0	NUM
gi-4940	643	1	0.53/0.75/2.16	0.53/0.75/2.16	NOUN
gi-4940	643	2	s2	s2	VERB
gi-4940	643	3	195/195/195	195/195/195	NUM
gi-4940	643	4	10066/7678/2470	10066/7678/2470	NUM
gi-4940	643	5	0/0/0	0/0/0	NUM
gi-4940	643	6	1.00/2.13/4.06	1.00/2.13/4.06	NUM
gi-4940	643	7	0/0/0	0/0/0	PROPN
gi-4940	644	1	0.52/0.69/2.16	0.52/0.69/2.16	PROPN
gi-4940	644	2	s3	s3	PROPN
gi-4940	645	1	195/195/195	195/195/195	NUM
gi-4940	645	2	10090/8734/2470	10090/8734/2470	NUM
gi-4940	645	3	0/0/0	0/0/0	NUM
gi-4940	646	1	0.99/1.99/4.41	0.99/1.99/4.41	PROPN
gi-4940	647	1	0/0/0	0/0/0	NUM
gi-4940	648	1	0.52/0.60/2.16	0.52/0.60/2.16	NOUN
gi-4940	648	2	equidistant	equidistant	ADJ
gi-4940	648	3	azimuthal	azimuthal	NOUN
gi-4940	648	4	s1	s1	NOUN
gi-4940	648	5	195/195/195	195/195/195	NUM
gi-4940	648	6	12352/9091/2494	12352/9091/2494	NUM
gi-4940	648	7	0/0/0	0/0/0	NUM
gi-4940	648	8	1.08/2.04/4.87	1.08/2.04/4.87	NUM
gi-4940	648	9	0/0/0	0/0/0	NUM
gi-4940	649	1	0.56/0.76/2.78	0.56/0.76/2.78	NOUN
gi-4940	649	2	s2	s2	NOUN
gi-4940	649	3	195/195/195	195/195/195	NUM
gi-4940	649	4	13186/9238/2494	13186/9238/2494	NUM
gi-4940	649	5	0/0/0	0/0/0	NUM
gi-4940	649	6	1.09/2.06/4.89	1.09/2.06/4.89	NUM
gi-4940	649	7	0/0/0	0/0/0	NUM
gi-4940	650	1	0.52/0.74/2.78	0.52/0.74/2.78	NUM
gi-4940	651	1	s3	s3	NOUN
gi-4940	652	1	195/195/195	195/195/195	NUM
gi-4940	652	2	13786/9706/2506	13786/9706/2506	NOUN
gi-4940	652	3	0/0/0	0/0/0	PROPN
gi-4940	652	4	1.00/1.90/4.78	1.00/1.90/4.78	NUM
gi-4940	652	5	0/0/0	0/0/0	NUM
gi-4940	652	6	0.50/0.71/2.77	0.50/0.71/2.77	NUM
gi-4940	652	7	bonne	bonne	PROPN
gi-4940	652	8	s1	s1	PROPN
gi-4940	652	9	14250/7206/2901	14250/7206/2901	NUM
gi-4940	652	10	6610/3613/1576	6610/3613/1576	NUM
gi-4940	653	1	1.21/2.27/5.68	1.21/2.27/5.68	NUM
gi-4940	653	2	1.05/2.06/4.98	1.05/2.06/4.98	NUM
gi-4940	653	3	0.45/0.88/2.20	0.45/0.88/2.20	NUM
gi-4940	653	4	0.46/0.84/1.98	0.46/0.84/1.98	NUM
gi-4940	653	5	s2	s2	PROPN
gi-4940	653	6	15171/7599/3099	15171/7599/3099	NUM
gi-4940	653	7	6766/3778/1630	6766/3778/1630	NUM
gi-4940	653	8	1.05/2.52/5.00	1.05/2.52/5.00	NUM
gi-4940	653	9	1.00/2.00/4.82	1.00/2.00/4.82	NUM
gi-4940	653	10	0.42/0.84/2.07	0.42/0.84/2.07	NUM
gi-4940	654	1	0.45/0.81/1.91	0.45/0.81/1.91	PROPN
gi-4940	654	2	s3	s3	PROPN
gi-4940	654	3	16839/8367/3483	16839/8367/3483	PROPN
gi-4940	654	4	6958/4330/1654	6958/4330/1654	NUM
gi-4940	654	5	1.00/1.99/4.98	1.00/1.99/4.98	NUM
gi-4940	654	6	1.00/1.99/4.96	1.00/1.99/4.96	NUM
gi-4940	654	7	0.38/0.76/1.84	0.38/0.76/1.84	PROPN
gi-4940	655	1	0.44/0.71/1.82	0.44/0.71/1.82	NUM
gi-4940	655	2	hassler	hassler	PROPN
gi-4940	655	3	s1	s1	PROPN
gi-4940	655	4	16452/7170/3342	16452/7170/3342	NUM
gi-4940	655	5	8839/5779/1912	8839/5779/1912	NUM
gi-4940	655	6	1.14/2.13/5.77	1.14/2.13/5.77	NUM
gi-4940	655	7	1.22/2.25/4.91	1.22/2.25/4.91	NUM
gi-4940	655	8	0.41/0.96/2.09	0.41/0.96/2.09	NUM
gi-4940	655	9	0.51/0.78/2.39	0.51/0.78/2.39	NUM
gi-4940	656	1	s2	s2	VERB
gi-4940	656	2	17391/7479/3519	17391/7479/3519	NUM
gi-4940	656	3	9370/5974/1966	9370/5974/1966	NUM
gi-4940	657	1	1.07/2.17/5.20	1.07/2.17/5.20	NUM
gi-4940	657	2	1.03/2.11/4.99	1.03/2.11/4.99	NUM
gi-4940	657	3	0.40/0.92/1.99	0.40/0.92/1.99	PROPN
gi-4940	657	4	0.48/0.75/2.32	0.48/0.75/2.32	NUM
gi-4940	657	5	s3	s3	PROPN
gi-4940	657	6	19899/8379/4191	19899/8379/4191	X
gi-4940	657	7	9826/6670/2002	9826/6670/2002	NUM
gi-4940	657	8	1.00/2.00/4.96	1.00/2.00/4.96	NUM
gi-4940	658	1	1.00/1.99/4.76	1.00/1.99/4.76	NUM
gi-4940	658	2	0.35/0.82/1.66	0.35/0.82/1.66	NUM
gi-4940	658	3	0.46/0.67/2.28	0.46/0.67/2.28	PROPN
gi-4940	658	4	nicolosi	nicolosi	NOUN
gi-4940	658	5	s1	s1	NOUN
gi-4940	658	6	14018/6503/3227	14018/6503/3227	NUM
gi-4940	658	7	5519/2495/1124	5519/2495/1124	NUM
gi-4940	658	8	1.14/2.29/5.64	1.14/2.29/5.64	NUM
gi-4940	658	9	1.15/2.16/5.50	1.15/2.16/5.50	NUM
gi-4940	658	10	0.43/0.94/1.92	0.43/0.94/1.92	NUM
gi-4940	658	11	0.42/0.95/2.12	0.42/0.95/2.12	NUM
gi-4940	658	12	s2	s2	VERB
gi-4940	658	13	14468/6944/3320	14468/6944/3320	NUM
gi-4940	658	14	5804/2564/1208	5804/2564/1208	NUM
gi-4940	658	15	1.00/2.00/4.96	1.00/2.00/4.96	NUM
gi-4940	658	16	1.01/2.00/4.94	1.01/2.00/4.94	NUM
gi-4940	658	17	0.42/0.88/1.86	0.42/0.88/1.86	PROPN
gi-4940	658	18	0.40/0.92/1.96	0.40/0.92/1.96	PROPN
gi-4940	658	19	s3	s3	PROPN
gi-4940	658	20	15176/8156/3488	15176/8156/3488	NUM
gi-4940	658	21	6224/2912/1352	6224/2912/1352	NUM
gi-4940	658	22	1.00/2.00/4.93	1.00/2.00/4.93	NUM
gi-4940	658	23	1.00/1.99/4.89	1.00/1.99/4.89	NUM
gi-4940	658	24	0.40/0.74/1.77	0.40/0.74/1.77	NUM
gi-4940	659	1	0.37/0.81/1.76	0.37/0.81/1.76	NUM
gi-4940	659	2	littrow	littrow	NOUN
gi-4940	659	3	s1	s1	NOUN
gi-4940	659	4	6513/3279/1470	6513/3279/1470	NUM
gi-4940	659	5	12011/7052/2507	12011/7052/2507	NUM
gi-4940	659	6	1.10/2.15/5.43	1.10/2.15/5.43	NUM
gi-4940	659	7	1.14/2.27/5.17	1.14/2.27/5.17	NUM
gi-4940	659	8	0.50/1.00/2.30	0.50/1.00/2.30	NUM
gi-4940	659	9	0.51/0.87/2.48	0.51/0.87/2.48	PROPN
gi-4940	660	1	s2	s2	VERB
gi-4940	660	2	6963/3615/1587	6963/3615/1587	NUM
gi-4940	660	3	12242/7334/2606	12242/7334/2606	NUM
gi-4940	660	4	1.06/2.22/4.90	1.06/2.22/4.90	NUM
gi-4940	660	5	1.05/1.99/5.27	1.05/1.99/5.27	NUM
gi-4940	660	6	0.47/0.91/2.12	0.47/0.91/2.12	NUM
gi-4940	660	7	0.50/0.84/2.38	0.50/0.84/2.38	NUM
gi-4940	661	1	s3	s3	NOUN
gi-4940	661	2	8121/4374/2151	8121/4374/2151	NUM
gi-4940	661	3	13796/7931/2903	13796/7931/2903	PROPN
gi-4940	661	4	1.00/2.00/4.86	1.00/2.00/4.86	NUM
gi-4940	661	5	1.00/1.98/4.98	1.00/1.98/4.98	NUM
gi-4940	661	6	0.40/0.75/1.55	0.40/0.75/1.55	NOUN
gi-4940	661	7	0.45/0.77/2.13	0.45/0.77/2.13	PROPN
gi-4940	661	8	adams	adams	PROPN
gi-4940	661	9	i.	i.	PROPN
gi-4940	661	10	s1	s1	PROPN
gi-4940	661	11	7083/3669/1788	7083/3669/1788	NUM
gi-4940	661	12	4430/2285/887	4430/2285/887	NUM
gi-4940	661	13	1.07/2.00/4.93	1.07/2.00/4.93	NUM
gi-4940	662	1	1.06/2.10/6.16	1.06/2.10/6.16	NUM
gi-4940	662	2	0.44/0.86/1.82	0.44/0.86/1.82	NUM
gi-4940	662	3	0.44/0.83/2.04	0.44/0.83/2.04	PROPN
gi-4940	662	4	s2	s2	PROPN
gi-4940	662	5	7449/4017/2097	7449/4017/2097	PUNCT
gi-4940	662	6	4778/2534/1046	4778/2534/1046	NUM
gi-4940	662	7	1.07/2.08/4.96	1.07/2.08/4.96	PROPN
gi-4940	662	8	1.02/2.01/4.86	1.02/2.01/4.86	NUM
gi-4940	662	9	0.42/0.78/1.53	0.42/0.78/1.53	PROPN
gi-4940	662	10	0.41/0.74/1.74	0.41/0.74/1.74	VERB
gi-4940	662	11	s3	s3	PROPN
gi-4940	662	12	8085/4689/2148	8085/4689/2148	NUM
gi-4940	662	13	4562/2618/1058	4562/2618/1058	NUM
gi-4940	662	14	1.00/2.00/4.89	1.00/2.00/4.89	NUM
gi-4940	662	15	0.98/1.99/4.44	0.98/1.99/4.44	NUM
gi-4940	662	16	0.38/0.67/1.49	0.38/0.67/1.49	PUNCT
gi-4940	663	1	0.40/0.72/1.72	0.40/0.72/1.72	NOUN
gi-4940	663	2	table	table	NOUN
gi-4940	663	3	2	2	NUM
gi-4940	663	4	:	:	PUNCT
gi-4940	663	5	uniform	uniform	ADJ
gi-4940	663	6	sampling	sampling	NOUN
gi-4940	663	7	of	of	ADP
gi-4940	663	8	the	the	DET
gi-4940	663	9	graticule	graticule	NOUN
gi-4940	663	10	with	with	ADP
gi-4940	663	11	the	the	DET
gi-4940	663	12	determined	determined	ADJ
gi-4940	663	13	steps	step	NOUN
gi-4940	663	14	δϕ	δϕ	NOUN
gi-4940	663	15	,	,	PUNCT
gi-4940	663	16	δλ	δλ	NOUN
gi-4940	663	17	compared	compare	VERB
gi-4940	663	18	to	to	ADP
gi-4940	663	19	s3	s3	PROPN
gi-4940	663	20	;	;	PUNCT
gi-4940	663	21	the	the	DET
gi-4940	663	22	amounts	amount	NOUN
gi-4940	663	23	of	of	ADP
gi-4940	663	24	sampled	sample	VERB
gi-4940	663	25	points	point	NOUN
gi-4940	663	26	nmer	nmer	ADJ
gi-4940	663	27	,	,	PUNCT
gi-4940	663	28	npar	npar	NOUN
gi-4940	663	29	are	be	AUX
gi-4940	663	30	preserved	preserve	VERB
gi-4940	663	31	.	.	PUNCT
gi-4940	664	1	projection	projection	NOUN
gi-4940	664	2	α	α	PROPN
gi-4940	664	3	δϕ	δϕ	PROPN
gi-4940	664	4	δλ	δλ	PROPN
gi-4940	664	5	nmer	nmer	ADJ
gi-4940	664	6	∆nmer	∆nmer	NUM
gi-4940	664	7	npar	npar	NOUN
gi-4940	664	8	∆npar	∆npar	NOUN
gi-4940	664	9	αm	αm	PROPN
gi-4940	664	10	∆αm	∆αm	PROPN
gi-4940	664	11	αp	αp	NOUN
gi-4940	664	12	∆αp	∆αp	PROPN
gi-4940	664	13	α̃m	α̃m	ADV
gi-4940	664	14	∆α̃m	∆α̃m	ADV
gi-4940	664	15	α̃p	α̃p	PRON
gi-4940	664	16	∆α̃p	∆α̃p	ADV
gi-4940	664	17	equidistant	equidistant	ADJ
gi-4940	664	18	cylindrical	cylindrical	ADJ
gi-4940	664	19	1	1	NUM
gi-4940	664	20	40.00	40.00	NUM
gi-4940	664	21	45.00	45.00	NUM
gi-4940	664	22	195	195	NUM
gi-4940	664	23	+0.0	+0.0	NUM
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gi-4940	671	44	%	%	NOUN
gi-4940	671	45	2	2	NUM
gi-4940	671	46	1.52	1.52	NUM
gi-4940	671	47	2.73	2.73	NUM
gi-4940	671	48	4719	4719	NUM
gi-4940	671	49	+0.6	+0.6	NUM
gi-4940	671	50	%	%	NOUN
gi-4940	671	51	2622	2622	NUM
gi-4940	671	52	+0.1	+0.1	NOUN
gi-4940	671	53	%	%	NOUN
gi-4940	672	1	9.26	9.26	NUM
gi-4940	672	2	+363.0	+363.0	NUM
gi-4940	672	3	%	%	NOUN
gi-4940	672	4	8.29	8.29	NUM
gi-4940	672	5	+316.6	+316.6	NUM
gi-4940	672	6	%	%	NOUN
gi-4940	672	7	0.74	0.74	NUM
gi-4940	672	8	+10.5	+10.5	NUM
gi-4940	672	9	%	%	NOUN
gi-4940	672	10	0.54	0.54	NUM
gi-4940	672	11	-25.0	-25.0	NUM
gi-4940	672	12	%	%	NOUN
gi-4940	672	13	5	5	NUM
gi-4940	672	14	3.35	3.35	NUM
gi-4940	672	15	6.49	6.49	NUM
gi-4940	672	16	2145	2145	NUM
gi-4940	672	17	-0.1	-0.1	NUM
gi-4940	672	18	%	%	NOUN
gi-4940	672	19	1064	1064	NUM
gi-4940	672	20	+0.6	+0.6	NUM
gi-4940	672	21	%	%	NOUN
gi-4940	672	22	9.96	9.96	NUM
gi-4940	672	23	+103.7	+103.7	NOUN
gi-4940	672	24	%	%	NOUN
gi-4940	672	25	9.00	9.00	NUM
gi-4940	672	26	+102.7	+102.7	NUM
gi-4940	672	27	%	%	NOUN
gi-4940	672	28	1.62	1.62	NUM
gi-4940	672	29	+8.7	+8.7	NOUN
gi-4940	672	30	%	%	NOUN
gi-4940	672	31	1.26	1.26	NUM
gi-4940	672	32	-26.7	-26.7	PROPN
gi-4940	672	33	%	%	NOUN
gi-4940	672	34	geoinformatics	geoinformatic	NOUN
gi-4940	672	35	fce	fce	VERB
gi-4940	672	36	ctu	ctu	NOUN
gi-4940	672	37	17(2	17(2	NUM
gi-4940	672	38	)	)	PUNCT
gi-4940	672	39	,	,	PUNCT
gi-4940	672	40	2018	2018	NUM
gi-4940	672	41	53	53	NUM
gi-4940	672	42	t.	t.	NOUN
gi-4940	672	43	bayer	bayer	PROPN
gi-4940	672	44	:	:	PUNCT
gi-4940	672	45	plotting	plot	VERB
gi-4940	672	46	the	the	DET
gi-4940	672	47	map	map	NOUN
gi-4940	672	48	projection	projection	NOUN
gi-4940	672	49	graticule	graticule	NOUN
gi-4940	672	50	with	with	ADP
gi-4940	672	51	discontinuities	discontinuity	NOUN
gi-4940	672	52	a	a	PRON
gi-4940	672	53	)	)	PUNCT
gi-4940	672	54	b	b	NOUN
gi-4940	672	55	)	)	PUNCT
gi-4940	672	56	figure	figure	NOUN
gi-4940	672	57	5.1	5.1	NUM
gi-4940	672	58	:	:	PUNCT
gi-4940	672	59	comparison	comparison	NOUN
gi-4940	672	60	of	of	ADP
gi-4940	672	61	the	the	DET
gi-4940	672	62	uniform	uniform	NOUN
gi-4940	672	63	a	a	NOUN
gi-4940	672	64	)	)	PUNCT
gi-4940	672	65	and	and	CCONJ
gi-4940	672	66	combined	combine	VERB
gi-4940	672	67	b	b	NOUN
gi-4940	672	68	)	)	PUNCT
gi-4940	672	69	sampling	sample	VERB
gi-4940	672	70	(	(	PUNCT
gi-4940	672	71	s3	s3	PROPN
gi-4940	672	72	)	)	PUNCT
gi-4940	672	73	for	for	ADP
gi-4940	672	74	the	the	DET
gi-4940	672	75	bonne	bonne	PROPN
gi-4940	672	76	projection	projection	PROPN
gi-4940	672	77	,	,	PUNCT
gi-4940	672	78	α	α	NOUN
gi-4940	672	79	=	=	SYM
gi-4940	672	80	5	5	NUM
gi-4940	672	81	◦	◦	NOUN
gi-4940	672	82	;	;	PUNCT
gi-4940	672	83	the	the	DET
gi-4940	672	84	adaptive	adaptive	ADJ
gi-4940	672	85	polygonal	polygonal	ADJ
gi-4940	672	86	approximation	approximation	NOUN
gi-4940	672	87	is	be	AUX
gi-4940	672	88	smoother	smooth	ADJ
gi-4940	672	89	.	.	PUNCT
gi-4940	673	1	the	the	DET
gi-4940	673	2	higher	high	ADJ
gi-4940	673	3	-	-	PUNCT
gi-4940	673	4	curvature	curvature	NOUN
gi-4940	673	5	regions	region	NOUN
gi-4940	673	6	,	,	PUNCT
gi-4940	673	7	the	the	DET
gi-4940	673	8	combined	combine	VERB
gi-4940	673	9	sampling	sampling	NOUN
gi-4940	673	10	technique	technique	NOUN
gi-4940	673	11	provides	provide	VERB
gi-4940	673	12	a	a	DET
gi-4940	673	13	smoother	smooth	ADJ
gi-4940	673	14	approximation	approximation	NOUN
gi-4940	673	15	of	of	ADP
gi-4940	673	16	the	the	DET
gi-4940	673	17	meridians	meridian	NOUN
gi-4940	673	18	/	/	SYM
gi-4940	673	19	parallels	parallel	NOUN
gi-4940	673	20	.	.	PUNCT
gi-4940	674	1	a	a	DET
gi-4940	674	2	typical	typical	ADJ
gi-4940	674	3	example	example	NOUN
gi-4940	674	4	is	be	AUX
gi-4940	674	5	represented	represent	VERB
gi-4940	674	6	by	by	ADP
gi-4940	674	7	the	the	DET
gi-4940	674	8	bonne	bonne	PROPN
gi-4940	674	9	,	,	PUNCT
gi-4940	674	10	littrow	littrow	PROPN
gi-4940	674	11	or	or	CCONJ
gi-4940	674	12	adams	adams	PROPN
gi-4940	674	13	i.	i.	PROPN
gi-4940	674	14	projections	projection	NOUN
gi-4940	674	15	,	,	PUNCT
gi-4940	674	16	where	where	SCONJ
gi-4940	674	17	uniform	uniform	ADJ
gi-4940	674	18	sampling	sampling	NOUN
gi-4940	674	19	does	do	AUX
gi-4940	674	20	not	not	PART
gi-4940	674	21	provide	provide	VERB
gi-4940	674	22	good	good	ADJ
gi-4940	674	23	results	result	NOUN
gi-4940	674	24	.	.	PUNCT
gi-4940	675	1	the	the	DET
gi-4940	675	2	maximum	maximum	ADJ
gi-4940	675	3	angles	angle	NOUN
gi-4940	675	4	between	between	ADP
gi-4940	675	5	the	the	DET
gi-4940	675	6	sampled	sample	VERB
gi-4940	675	7	elements	element	NOUN
gi-4940	675	8	are	be	AUX
gi-4940	675	9	more	more	ADJ
gi-4940	675	10	than	than	ADP
gi-4940	675	11	five	five	NUM
gi-4940	675	12	times	time	NOUN
gi-4940	675	13	higher	high	ADJ
gi-4940	675	14	.	.	PUNCT
gi-4940	676	1	if	if	SCONJ
gi-4940	676	2	meridians	meridian	NOUN
gi-4940	676	3	or	or	CCONJ
gi-4940	676	4	parallels	parallel	NOUN
gi-4940	676	5	are	be	AUX
gi-4940	676	6	represented	represent	VERB
gi-4940	676	7	by	by	ADP
gi-4940	676	8	the	the	DET
gi-4940	676	9	circular	circular	ADJ
gi-4940	676	10	arcs	arc	NOUN
gi-4940	676	11	,	,	PUNCT
gi-4940	676	12	the	the	DET
gi-4940	676	13	combined	combine	VERB
gi-4940	676	14	sampling	sampling	NOUN
gi-4940	676	15	does	do	AUX
gi-4940	676	16	not	not	PART
gi-4940	676	17	bring	bring	VERB
gi-4940	676	18	any	any	DET
gi-4940	676	19	advantage	advantage	NOUN
gi-4940	676	20	and	and	CCONJ
gi-4940	676	21	may	may	AUX
gi-4940	676	22	cause	cause	VERB
gi-4940	676	23	a	a	DET
gi-4940	676	24	minor	minor	ADJ
gi-4940	676	25	deterioration	deterioration	NOUN
gi-4940	676	26	of	of	ADP
gi-4940	676	27	the	the	DET
gi-4940	676	28	average	average	ADJ
gi-4940	676	29	values	value	NOUN
gi-4940	676	30	αm	αm	VERB
gi-4940	676	31	,	,	PUNCT
gi-4940	676	32	αp	αp	INTJ
gi-4940	676	33	(	(	PUNCT
gi-4940	676	34	nicolosi	nicolosi	NOUN
gi-4940	676	35	projection	projection	NOUN
gi-4940	676	36	)	)	PUNCT
gi-4940	676	37	.	.	PUNCT
gi-4940	677	1	raise	raise	VERB
gi-4940	677	2	the	the	DET
gi-4940	677	3	steps	step	NOUN
gi-4940	677	4	δϕ	δϕ	NOUN
gi-4940	677	5	,	,	PUNCT
gi-4940	677	6	δλ	δλ	PRON
gi-4940	677	7	reduces	reduce	VERB
gi-4940	677	8	the	the	DET
gi-4940	677	9	advantage	advantage	NOUN
gi-4940	677	10	of	of	ADP
gi-4940	677	11	adaptive	adaptive	ADJ
gi-4940	677	12	sampling	sampling	NOUN
gi-4940	677	13	(	(	PUNCT
gi-4940	677	14	and	and	CCONJ
gi-4940	677	15	thus	thus	ADV
gi-4940	677	16	α	α	X
gi-4940	677	17	)	)	PUNCT
gi-4940	677	18	even	even	ADV
gi-4940	677	19	for	for	ADP
gi-4940	677	20	the	the	DET
gi-4940	677	21	highcurvature	highcurvature	NOUN
gi-4940	677	22	regions	region	NOUN
gi-4940	677	23	(	(	PUNCT
gi-4940	677	24	see	see	VERB
gi-4940	677	25	bonne	bonne	PROPN
gi-4940	677	26	projection	projection	PROPN
gi-4940	677	27	in	in	ADP
gi-4940	677	28	fig	fig	NOUN
gi-4940	677	29	.	.	PUNCT
gi-4940	678	1	5.1	5.1	NUM
gi-4940	678	2	)	)	PUNCT
gi-4940	678	3	.	.	PUNCT
gi-4940	679	1	in	in	ADP
gi-4940	679	2	general	general	ADJ
gi-4940	679	3	,	,	PUNCT
gi-4940	679	4	uniform	uniform	ADJ
gi-4940	679	5	sampling	sample	VERB
gi-4940	679	6	preserves	preserve	VERB
gi-4940	679	7	the	the	DET
gi-4940	679	8	curvature	curvature	NOUN
gi-4940	679	9	worse	bad	ADJ
gi-4940	679	10	and	and	CCONJ
gi-4940	679	11	provides	provide	VERB
gi-4940	679	12	more	more	ADJ
gi-4940	679	13	redundant	redundant	ADJ
gi-4940	679	14	data	datum	NOUN
gi-4940	679	15	.	.	PUNCT
gi-4940	680	1	5.2	5.2	NUM
gi-4940	680	2	.	.	PUNCT
gi-4940	680	3	detection	detection	NOUN
gi-4940	680	4	of	of	ADP
gi-4940	680	5	discontinuities	discontinuity	NOUN
gi-4940	680	6	:	:	PUNCT
gi-4940	680	7	fournier	fournier	PROPN
gi-4940	680	8	i.	i.	PROPN
gi-4940	680	9	projection	projection	PROPN
gi-4940	680	10	the	the	DET
gi-4940	680	11	fournier	fournier	PROPN
gi-4940	680	12	i.	i.	PROPN
gi-4940	680	13	projection	projection	PROPN
gi-4940	680	14	equations	equation	NOUN
gi-4940	680	15	have	have	VERB
gi-4940	680	16	a	a	DET
gi-4940	680	17	complex	complex	ADJ
gi-4940	680	18	form	form	NOUN
gi-4940	680	19	and	and	CCONJ
gi-4940	680	20	contain	contain	VERB
gi-4940	680	21	several	several	ADJ
gi-4940	680	22	discontinuities	discontinuity	NOUN
gi-4940	680	23	both	both	CCONJ
gi-4940	680	24	in	in	ADP
gi-4940	680	25	the	the	DET
gi-4940	680	26	latitudinal	latitudinal	ADJ
gi-4940	680	27	and	and	CCONJ
gi-4940	680	28	longitudinal	longitudinal	ADJ
gi-4940	680	29	directions	direction	NOUN
gi-4940	680	30	.	.	PUNCT
gi-4940	681	1	in	in	ADP
gi-4940	681	2	accordance	accordance	NOUN
gi-4940	681	3	with	with	ADP
gi-4940	681	4	[	[	X
gi-4940	681	5	24	24	NUM
gi-4940	681	6	]	]	PUNCT
gi-4940	681	7	,	,	PUNCT
gi-4940	681	8	the	the	DET
gi-4940	681	9	projection	projection	NOUN
gi-4940	681	10	equations	equation	NOUN
gi-4940	681	11	are	be	AUX
gi-4940	681	12	written	write	VERB
gi-4940	681	13	as	as	SCONJ
gi-4940	681	14	follows	follow	VERB
gi-4940	681	15	.	.	PUNCT
gi-4940	682	1	if	if	SCONJ
gi-4940	682	2	(	(	PUNCT
gi-4940	682	3	λ−	λ−	PROPN
gi-4940	682	4	λ0	λ0	NOUN
gi-4940	682	5	)	)	PUNCT
gi-4940	682	6	=	=	SYM
gi-4940	682	7	0	0	NUM
gi-4940	682	8	or	or	CCONJ
gi-4940	682	9	|ϕ|	|ϕ|	NOUN
gi-4940	682	10	=	=	SYM
gi-4940	682	11	π/2	π/2	NUM
gi-4940	682	12	,	,	PUNCT
gi-4940	682	13	x	x	PUNCT
gi-4940	682	14	=	=	SYM
gi-4940	682	15	0	0	NUM
gi-4940	682	16	,	,	PUNCT
gi-4940	682	17	y	y	NOUN
gi-4940	682	18	=	=	PUNCT
gi-4940	682	19	rϕ.	rϕ.	AUX
gi-4940	682	20	if	if	SCONJ
gi-4940	682	21	ϕ	ϕ	NOUN
gi-4940	682	22	=	=	SYM
gi-4940	682	23	0	0	PROPN
gi-4940	682	24	,	,	PUNCT
gi-4940	682	25	x	x	X
gi-4940	682	26	=	=	SYM
gi-4940	682	27	r	r	X
gi-4940	682	28	(	(	PUNCT
gi-4940	682	29	λ−	λ−	PROPN
gi-4940	682	30	λ0	λ0	NOUN
gi-4940	682	31	)	)	PUNCT
gi-4940	682	32	,	,	PUNCT
gi-4940	682	33	y	y	PROPN
gi-4940	682	34	=	=	PUNCT
gi-4940	682	35	0	0	PROPN
gi-4940	682	36	.	.	PUNCT
gi-4940	683	1	if	if	SCONJ
gi-4940	683	2	|λ−	|λ−	NOUN
gi-4940	683	3	λ0|	λ0|	PRON
gi-4940	683	4	=	=	SYM
gi-4940	683	5	π/2	π/2	NUM
gi-4940	683	6	,	,	PUNCT
gi-4940	683	7	x	x	X
gi-4940	683	8	=	=	SYM
gi-4940	683	9	r	r	X
gi-4940	683	10	(	(	PUNCT
gi-4940	683	11	λ−	λ−	PROPN
gi-4940	683	12	λ0	λ0	NOUN
gi-4940	683	13	)	)	PUNCT
gi-4940	683	14	cosϕ	cosϕ	NOUN
gi-4940	683	15	,	,	PUNCT
gi-4940	683	16	y	y	NOUN
gi-4940	683	17	=	=	SYM
gi-4940	683	18	r	r	NOUN
gi-4940	683	19	π	π	SYM
gi-4940	683	20	2	2	NUM
gi-4940	683	21	sinϕ.	sinϕ.	VERB
gi-4940	683	22	otherwise	otherwise	ADV
gi-4940	683	23	,	,	PUNCT
gi-4940	683	24	c	c	NOUN
gi-4940	683	25	=	=	SYM
gi-4940	684	1	π2	π2	ADP
gi-4940	684	2	4	4	NUM
gi-4940	684	3	,	,	PUNCT
gi-4940	684	4	p	p	NOUN
gi-4940	684	5	=	=	PUNCT
gi-4940	684	6	π	π	PROPN
gi-4940	684	7	|sinϕ|	|sinϕ|	NUM
gi-4940	684	8	,	,	PUNCT
gi-4940	684	9	s	s	PART
gi-4940	685	1	=	=	SYM
gi-4940	685	2	c	c	NOUN
gi-4940	685	3	−	−	NOUN
gi-4940	686	1	ϕ2	ϕ2	ADV
gi-4940	686	2	p	p	NOUN
gi-4940	686	3	−	−	PROPN
gi-4940	686	4	2	2	NUM
gi-4940	686	5	|ϕ|	|ϕ|	NOUN
gi-4940	686	6	,	,	PUNCT
gi-4940	686	7	a	a	PRON
gi-4940	686	8	=	=	X
gi-4940	686	9	(	(	PUNCT
gi-4940	686	10	λ−	λ−	PROPN
gi-4940	687	1	λ0)2	λ0)2	X
gi-4940	687	2	c	c	PROPN
gi-4940	687	3	−	−	PROPN
gi-4940	687	4	1	1	NUM
gi-4940	687	5	,	,	PUNCT
gi-4940	687	6	b	b	X
gi-4940	687	7	=	=	SYM
gi-4940	687	8	s2	s2	PROPN
gi-4940	687	9	−a[c	−a[c	NOUN
gi-4940	687	10	−	−	PROPN
gi-4940	687	11	ps	ps	NOUN
gi-4940	687	12	−	−	PROPN
gi-4940	688	1	(	(	PUNCT
gi-4940	688	2	λ−	λ−	PROPN
gi-4940	688	3	λ0)2	λ0)2	X
gi-4940	688	4	]	]	X
gi-4940	688	5	,	,	PUNCT
gi-4940	688	6	and	and	CCONJ
gi-4940	688	7	y	y	PROPN
gi-4940	688	8	=	=	SYM
gi-4940	688	9	r	r	NOUN
gi-4940	688	10	signϕ	signϕ	NOUN
gi-4940	688	11	√	√	NUM
gi-4940	688	12	b	b	NOUN
gi-4940	689	1	−	−	NOUN
gi-4940	689	2	s	s	VERB
gi-4940	689	3	a	a	DET
gi-4940	689	4	,	,	PUNCT
gi-4940	689	5	x	x	PUNCT
gi-4940	689	6	=	=	SYM
gi-4940	689	7	r(λ−	r(λ−	NUM
gi-4940	689	8	λ0	λ0	NOUN
gi-4940	689	9	)	)	PUNCT
gi-4940	689	10	√	√	NOUN
gi-4940	689	11	1−	1−	NUM
gi-4940	689	12	y	y	PROPN
gi-4940	689	13	2	2	NUM
gi-4940	689	14	r2c	r2c	NOUN
gi-4940	689	15	,	,	PUNCT
gi-4940	689	16	where	where	SCONJ
gi-4940	689	17	y	y	PROPN
gi-4940	689	18	takes	take	VERB
gi-4940	689	19	the	the	DET
gi-4940	689	20	sign	sign	NOUN
gi-4940	689	21	of	of	ADP
gi-4940	689	22	ϕ.	ϕ.	PROPN
gi-4940	689	23	the	the	DET
gi-4940	689	24	singularities	singularity	NOUN
gi-4940	689	25	are	be	AUX
gi-4940	689	26	shown	show	VERB
gi-4940	689	27	in	in	ADP
gi-4940	689	28	fig	fig	NOUN
gi-4940	689	29	.	.	PUNCT
gi-4940	690	1	5.2	5.2	NUM
gi-4940	690	2	.	.	PUNCT
gi-4940	690	3	geoinformatics	geoinformatic	NOUN
gi-4940	690	4	fce	fce	VERB
gi-4940	690	5	ctu	ctu	NOUN
gi-4940	690	6	17(2	17(2	NUM
gi-4940	690	7	)	)	PUNCT
gi-4940	690	8	,	,	PUNCT
gi-4940	690	9	2018	2018	NUM
gi-4940	690	10	54	54	NUM
gi-4940	690	11	t.	t.	NOUN
gi-4940	690	12	bayer	bayer	PROPN
gi-4940	690	13	:	:	PUNCT
gi-4940	690	14	plotting	plot	VERB
gi-4940	690	15	the	the	DET
gi-4940	690	16	map	map	NOUN
gi-4940	690	17	projection	projection	NOUN
gi-4940	690	18	graticule	graticule	NOUN
gi-4940	690	19	with	with	ADP
gi-4940	690	20	discontinuities	discontinuity	NOUN
gi-4940	690	21	-1	-1	PUNCT
gi-4940	690	22	80	80	NUM
gi-4940	690	23	.0	.0	NUM
gi-4940	690	24	-1	-1	ADP
gi-4940	690	25	70	70	NUM
gi-4940	690	26	.0	.0	NUM
gi-4940	690	27	-1	-1	NOUN
gi-4940	690	28	60	60	NUM
gi-4940	690	29	.0	.0	NUM
gi-4940	690	30	-1	-1	ADP
gi-4940	690	31	50	50	NUM
gi-4940	690	32	.0	.0	NUM
gi-4940	690	33	-1	-1	ADP
gi-4940	690	34	40	40	NUM
gi-4940	690	35	.0	.0	NUM
gi-4940	690	36	-1	-1	ADP
gi-4940	690	37	30	30	NUM
gi-4940	690	38	.0	.0	NUM
gi-4940	690	39	-1	-1	ADP
gi-4940	690	40	20	20	NUM
gi-4940	690	41	.0	.0	NUM
gi-4940	690	42	-1	-1	ADP
gi-4940	690	43	10	10	NUM
gi-4940	690	44	.0	.0	NUM
gi-4940	690	45	-1	-1	NOUN
gi-4940	690	46	00	00	NUM
gi-4940	691	1	.0	.0	NUM
gi-4940	691	2	-9	-9	PROPN
gi-4940	691	3	0	0	NUM
gi-4940	691	4	.	.	NOUN
gi-4940	691	5	0	0	NUM
gi-4940	692	1	-8	-8	NUM
gi-4940	692	2	0	0	NUM
gi-4940	692	3	.	.	NUM
gi-4940	692	4	0	0	NUM
gi-4940	693	1	-7	-7	NOUN
gi-4940	693	2	0	0	NUM
gi-4940	693	3	.	.	NOUN
gi-4940	693	4	0	0	NUM
gi-4940	694	1	-6	-6	NOUN
gi-4940	694	2	0	0	NUM
gi-4940	694	3	.	.	NOUN
gi-4940	694	4	0	0	NUM
gi-4940	695	1	-5	-5	NUM
gi-4940	695	2	0	0	NUM
gi-4940	695	3	.	.	NUM
gi-4940	695	4	0	0	NUM
gi-4940	696	1	-4	-4	SYM
gi-4940	696	2	0	0	NUM
gi-4940	696	3	.	.	NOUN
gi-4940	696	4	0	0	NUM
gi-4940	697	1	-3	-3	PUNCT
gi-4940	697	2	0	0	NUM
gi-4940	697	3	.	.	NUM
gi-4940	697	4	0	0	NUM
gi-4940	698	1	-2	-2	NOUN
gi-4940	698	2	0	0	NUM
gi-4940	698	3	.	.	NOUN
gi-4940	698	4	0	0	NUM
gi-4940	699	1	-1	-1	NOUN
gi-4940	699	2	0	0	NUM
gi-4940	700	1	.	.	NOUN
gi-4940	700	2	0	0	NUM
gi-4940	700	3	0	0	NUM
gi-4940	700	4	.	.	NOUN
gi-4940	700	5	0	0	NUM
gi-4940	701	1	10	10	NUM
gi-4940	701	2	.0	.0	NUM
gi-4940	701	3	2	2	NUM
gi-4940	701	4	0	0	NUM
gi-4940	701	5	.0	.0	NUM
gi-4940	701	6	30	30	NUM
gi-4940	701	7	.0	.0	NUM
gi-4940	701	8	40	40	NUM
gi-4940	701	9	.0	.0	NUM
gi-4940	701	10	5	5	NUM
gi-4940	701	11	0	0	NUM
gi-4940	701	12	.0	.0	NUM
gi-4940	701	13	60	60	NUM
gi-4940	701	14	.0	.0	NUM
gi-4940	701	15	70	70	NUM
gi-4940	701	16	.0	.0	NUM
gi-4940	701	17	80	80	NUM
gi-4940	701	18	.0	.0	NUM
gi-4940	701	19	90	90	NUM
gi-4940	701	20	.0	.0	NUM
gi-4940	701	21	1	1	NUM
gi-4940	701	22	0	0	NUM
gi-4940	701	23	0	0	NUM
gi-4940	701	24	.	.	NOUN
gi-4940	701	25	0	0	NUM
gi-4940	702	1	1	1	NUM
gi-4940	702	2	1	1	NUM
gi-4940	702	3	0	0	NUM
gi-4940	702	4	.	.	NOUN
gi-4940	702	5	0	0	NUM
gi-4940	703	1	12	12	NUM
gi-4940	703	2	0	0	NUM
gi-4940	703	3	.	.	PUNCT
gi-4940	703	4	0	0	NUM
gi-4940	704	1	13	13	NUM
gi-4940	704	2	0	0	NUM
gi-4940	704	3	.	.	PUNCT
gi-4940	704	4	0	0	NUM
gi-4940	705	1	14	14	NUM
gi-4940	705	2	0	0	NUM
gi-4940	705	3	.	.	NOUN
gi-4940	705	4	0	0	NUM
gi-4940	706	1	15	15	NUM
gi-4940	706	2	0	0	NUM
gi-4940	706	3	.	.	NOUN
gi-4940	706	4	0	0	NUM
gi-4940	707	1	16	16	NUM
gi-4940	707	2	0	0	NUM
gi-4940	707	3	.	.	PUNCT
gi-4940	707	4	0	0	NUM
gi-4940	708	1	17	17	NUM
gi-4940	708	2	0	0	NUM
gi-4940	708	3	.	.	PUNCT
gi-4940	708	4	0	0	NUM
gi-4940	709	1	18	18	NUM
gi-4940	709	2	0	0	NUM
gi-4940	709	3	.	.	NOUN
gi-4940	709	4	0	0	NUM
gi-4940	710	1	-0	-0	PUNCT
gi-4940	710	2	.0	.0	NUM
gi-4940	710	3	0	0	NUM
gi-4940	710	4	.	.	NOUN
gi-4940	710	5	0	0	NUM
gi-4940	711	1	-90.0	-90.0	NUM
gi-4940	711	2	-	-	SYM
gi-4940	711	3	90.0	90.0	NUM
gi-4940	711	4	-8	-8	NUM
gi-4940	711	5	0.0	0.0	NUM
gi-4940	711	6	-80.0	-80.0	PRON
gi-4940	711	7	-7	-7	NOUN
gi-4940	712	1	0.0	0.0	NUM
gi-4940	712	2	-70.0	-70.0	NOUN
gi-4940	712	3	-60	-60	SYM
gi-4940	712	4	.0	.0	NUM
gi-4940	713	1	-60.0	-60.0	NOUN
gi-4940	713	2	-50	-50	NUM
gi-4940	714	1	.0	.0	NUM
gi-4940	715	1	-50.0	-50.0	NUM
gi-4940	715	2	-40	-40	NUM
gi-4940	715	3	.0	.0	NUM
gi-4940	716	1	-40.0	-40.0	NOUN
gi-4940	716	2	-30.0	-30.0	NOUN
gi-4940	716	3	-30.0	-30.0	NOUN
gi-4940	716	4	-20.0	-20.0	NOUN
gi-4940	716	5	-20.0	-20.0	NOUN
gi-4940	717	1	-10.0	-10.0	PROPN
gi-4940	718	1	-10.0	-10.0	PROPN
gi-4940	718	2	0.0	0.0	NUM
gi-4940	718	3	0.0	0.0	NUM
gi-4940	718	4	10.0	10.0	NUM
gi-4940	718	5	10.0	10.0	NUM
gi-4940	718	6	20.0	20.0	NUM
gi-4940	718	7	20.0	20.0	NUM
gi-4940	718	8	30.0	30.0	NUM
gi-4940	718	9	30.0	30.0	NUM
gi-4940	718	10	40.0	40.0	NUM
gi-4940	718	11	40.0	40.0	NUM
gi-4940	718	12	50.0	50.0	NUM
gi-4940	718	13	50	50	NUM
gi-4940	718	14	.	.	PUNCT
gi-4940	718	15	0	0	NUM
gi-4940	719	1	60.0	60.0	NUM
gi-4940	719	2	60	60	NUM
gi-4940	719	3	.0	.0	NUM
gi-4940	719	4	70.0	70.0	NUM
gi-4940	719	5	70	70	NUM
gi-4940	719	6	.0	.0	NUM
gi-4940	719	7	80.0	80.0	NUM
gi-4940	719	8	80	80	NUM
gi-4940	719	9	.0	.0	NUM
gi-4940	719	10	90.090.0	90.090.0	NUM
gi-4940	719	11	figure	figure	NOUN
gi-4940	719	12	5.2	5.2	NUM
gi-4940	719	13	:	:	PUNCT
gi-4940	719	14	fournier	fournier	PROPN
gi-4940	719	15	i.	i.	PROPN
gi-4940	719	16	projection	projection	PROPN
gi-4940	719	17	with	with	ADP
gi-4940	719	18	the	the	DET
gi-4940	719	19	highlighted	highlight	VERB
gi-4940	719	20	singularities	singularity	NOUN
gi-4940	719	21	leading	lead	VERB
gi-4940	719	22	to	to	ADP
gi-4940	719	23	the	the	DET
gi-4940	719	24	subdivision	subdivision	NOUN
gi-4940	719	25	into	into	ADP
gi-4940	719	26	the	the	DET
gi-4940	719	27	tiles	tile	NOUN
gi-4940	719	28	;	;	PUNCT
gi-4940	719	29	normal	normal	ADJ
gi-4940	719	30	aspect	aspect	NOUN
gi-4940	719	31	of	of	ADP
gi-4940	719	32	the	the	DET
gi-4940	719	33	projection	projection	NOUN
gi-4940	719	34	.	.	PUNCT
gi-4940	720	1	testing	test	VERB
gi-4940	720	2	a	a	DET
gi-4940	720	3	normal	normal	ADJ
gi-4940	720	4	aspect	aspect	NOUN
gi-4940	720	5	of	of	ADP
gi-4940	720	6	the	the	DET
gi-4940	720	7	projection	projection	NOUN
gi-4940	720	8	.	.	PUNCT
gi-4940	721	1	suppose	suppose	VERB
gi-4940	721	2	that	that	SCONJ
gi-4940	721	3	the	the	DET
gi-4940	721	4	graticule	graticule	NOUN
gi-4940	721	5	will	will	AUX
gi-4940	721	6	be	be	AUX
gi-4940	721	7	generated	generate	VERB
gi-4940	721	8	over	over	ADP
gi-4940	721	9	the	the	DET
gi-4940	721	10	entire	entire	ADJ
gi-4940	721	11	planisphere	planisphere	NOUN
gi-4940	721	12	,	,	PUNCT
gi-4940	721	13	so	so	ADV
gi-4940	721	14	ω	ω	X
gi-4940	721	15	=	=	NOUN
gi-4940	721	16	ωϕ	ωϕ	PRON
gi-4940	721	17	×ωλ	×ωλ	PROPN
gi-4940	721	18	,	,	PUNCT
gi-4940	721	19	ωϕ	ωϕ	PRON
gi-4940	721	20	=	=	NOUN
gi-4940	722	1	[	[	X
gi-4940	722	2	−π/2	−π/2	PROPN
gi-4940	722	3	,	,	PUNCT
gi-4940	722	4	π/2	π/2	NUM
gi-4940	722	5	]	]	PUNCT
gi-4940	722	6	,	,	PUNCT
gi-4940	722	7	ωλ	ωλ	ADP
gi-4940	723	1	=	=	SYM
gi-4940	724	1	[	[	X
gi-4940	724	2	−π	−π	X
gi-4940	724	3	,	,	PUNCT
gi-4940	724	4	π	π	X
gi-4940	724	5	]	]	X
gi-4940	724	6	with	with	ADP
gi-4940	724	7	the	the	DET
gi-4940	724	8	offset	offset	NOUN
gi-4940	724	9	of	of	ADP
gi-4940	724	10	meridians	meridian	NOUN
gi-4940	724	11	and	and	CCONJ
gi-4940	724	12	parallels	parallel	VERB
gi-4940	724	13	∆ϕ	∆ϕ	NOUN
gi-4940	724	14	=	=	SYM
gi-4940	724	15	∆λ	∆λ	NOUN
gi-4940	724	16	=	=	NOUN
gi-4940	724	17	15	15	NUM
gi-4940	724	18	◦	◦	NOUN
gi-4940	724	19	,	,	PUNCT
gi-4940	724	20	the	the	DET
gi-4940	724	21	sampling	sample	VERB
gi-4940	724	22	step	step	NOUN
gi-4940	724	23	is	be	AUX
gi-4940	724	24	α	α	NOUN
gi-4940	724	25	=	=	SYM
gi-4940	724	26	1	1	NUM
gi-4940	724	27	◦	◦	NOUN
gi-4940	724	28	.	.	PUNCT
gi-4940	725	1	let	let	VERB
gi-4940	725	2	us	we	PRON
gi-4940	725	3	describe	describe	VERB
gi-4940	725	4	the	the	DET
gi-4940	725	5	selected	select	VERB
gi-4940	725	6	steps	step	NOUN
gi-4940	725	7	of	of	ADP
gi-4940	725	8	the	the	DET
gi-4940	725	9	algorithm	algorithm	NOUN
gi-4940	725	10	;	;	PUNCT
gi-4940	725	11	see	see	VERB
gi-4940	725	12	fig	fig	NOUN
gi-4940	725	13	.	.	PUNCT
gi-4940	726	1	5.3	5.3	NUM
gi-4940	726	2	:	:	SYM
gi-4940	726	3	•	•	NOUN
gi-4940	726	4	initialize	initialize	VERB
gi-4940	726	5	“	"	PUNCT
gi-4940	726	6	good	good	ADJ
gi-4940	726	7	data	datum	NOUN
gi-4940	726	8	”	"	PUNCT
gi-4940	726	9	as	as	ADP
gi-4940	726	10	ωg	ωg	PROPN
gi-4940	726	11	=	=	PROPN
gi-4940	726	12	ω	ω	PROPN
gi-4940	726	13	and	and	CCONJ
gi-4940	726	14	push	push	NOUN
gi-4940	726	15	s	s	PART
gi-4940	726	16	←	←	PROPN
gi-4940	726	17	ωg	ωg	PROPN
gi-4940	726	18	.	.	PROPN
gi-4940	726	19	pop	pop	VERB
gi-4940	726	20	the	the	DET
gi-4940	726	21	current	current	ADJ
gi-4940	726	22	interval	interval	NOUN
gi-4940	726	23	ωj	ωj	ADP
gi-4940	726	24	=	=	SYM
gi-4940	726	25	ωϕ,j	ωϕ,j	SYM
gi-4940	726	26	×	×	PROPN
gi-4940	726	27	ωλ	ωλ	PROPN
gi-4940	726	28	,	,	PUNCT
gi-4940	726	29	j	j	PROPN
gi-4940	726	30	from	from	ADP
gi-4940	726	31	s	s	PROPN
gi-4940	726	32	,	,	PUNCT
gi-4940	726	33	detect	detect	VERB
gi-4940	726	34	the	the	DET
gi-4940	726	35	removable	removable	ADJ
gi-4940	726	36	discontinuity	discontinuity	NOUN
gi-4940	726	37	at	at	ADP
gi-4940	726	38	ϕ	ϕ	NOUN
gi-4940	726	39	=	=	SYM
gi-4940	726	40	0	0	NUM
gi-4940	726	41	,	,	PUNCT
gi-4940	726	42	split	split	VERB
gi-4940	726	43	ωj	ωj	ADP
gi-4940	726	44	to	to	ADP
gi-4940	726	45	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	726	46	=	=	PUNCT
gi-4940	727	1	[	[	X
gi-4940	727	2	−π/2	−π/2	PROPN
gi-4940	727	3	,	,	PUNCT
gi-4940	727	4	0	0	NUM
gi-4940	727	5	)	)	PUNCT
gi-4940	727	6	,	,	PUNCT
gi-4940	727	7	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	727	8	=	=	SYM
gi-4940	727	9	(	(	PUNCT
gi-4940	727	10	0	0	NUM
gi-4940	727	11	,	,	PUNCT
gi-4940	727	12	π/2	π/2	NUM
gi-4940	727	13	]	]	PUNCT
gi-4940	727	14	;	;	PUNCT
gi-4940	727	15	see	see	VERB
gi-4940	727	16	step	step	NOUN
gi-4940	727	17	b	b	NOUN
gi-4940	727	18	)	)	PUNCT
gi-4940	727	19	.	.	PUNCT
gi-4940	728	1	create	create	VERB
gi-4940	728	2	the	the	DET
gi-4940	728	3	new	new	ADJ
gi-4940	728	4	subintervalsωj,1	subintervalsωj,1	NOUN
gi-4940	728	5	=	=	SYM
gi-4940	728	6	ωϕ,j,1×ωλ	ωϕ,j,1×ωλ	NOUN
gi-4940	728	7	,	,	PUNCT
gi-4940	728	8	j	j	PROPN
gi-4940	728	9	,	,	PUNCT
gi-4940	728	10	ω	ω	PROPN
gi-4940	728	11	,	,	PUNCT
gi-4940	728	12	j,2	j,2	NOUN
gi-4940	728	13	=	=	SYM
gi-4940	728	14	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	728	15	×ωλ	×ωλ	PROPN
gi-4940	728	16	,	,	PUNCT
gi-4940	728	17	j	j	NOUN
gi-4940	728	18	,	,	PUNCT
gi-4940	728	19	and	and	CCONJ
gi-4940	728	20	push	push	VERB
gi-4940	728	21	s	s	PART
gi-4940	728	22	←	←	PROPN
gi-4940	728	23	ωj,1	ωj,1	NOUN
gi-4940	728	24	,	,	PUNCT
gi-4940	728	25	s	s	PART
gi-4940	728	26	←	←	PROPN
gi-4940	728	27	ωj,2	ωj,2	NOUN
gi-4940	728	28	.	.	PUNCT
gi-4940	729	1	•	•	NUM
gi-4940	729	2	due	due	ADP
gi-4940	729	3	to	to	ADP
gi-4940	729	4	the	the	DET
gi-4940	729	5	discontinuity	discontinuity	NOUN
gi-4940	729	6	at	at	ADP
gi-4940	729	7	λ	λ	X
gi-4940	729	8	=	=	SYM
gi-4940	729	9	−π/2	−π/2	PROPN
gi-4940	729	10	,	,	PUNCT
gi-4940	729	11	the	the	DET
gi-4940	729	12	current	current	ADJ
gi-4940	729	13	interval	interval	NOUN
gi-4940	729	14	ωj	ωj	ADP
gi-4940	729	15	popped	pop	VERB
gi-4940	729	16	from	from	ADP
gi-4940	729	17	the	the	DET
gi-4940	729	18	stack	stack	NOUN
gi-4940	729	19	is	be	AUX
gi-4940	729	20	split	split	VERB
gi-4940	729	21	to	to	PART
gi-4940	729	22	ωλ	ωλ	VERB
gi-4940	729	23	,	,	PUNCT
gi-4940	729	24	j,1	j,1	X
gi-4940	729	25	=	=	PUNCT
gi-4940	730	1	[	[	X
gi-4940	730	2	−π,−π/2	−π,−π/2	NUM
gi-4940	730	3	)	)	PUNCT
gi-4940	730	4	,	,	PUNCT
gi-4940	730	5	ωϕ,λ,2	ωϕ,λ,2	PROPN
gi-4940	730	6	=	=	SYM
gi-4940	730	7	(	(	PUNCT
gi-4940	730	8	−π/2	−π/2	PROPN
gi-4940	730	9	,	,	PUNCT
gi-4940	730	10	π	π	PROPN
gi-4940	730	11	]	]	X
gi-4940	730	12	;	;	PUNCT
gi-4940	730	13	see	see	VERB
gi-4940	730	14	step	step	NOUN
gi-4940	730	15	c	c	NOUN
gi-4940	730	16	)	)	PUNCT
gi-4940	730	17	.	.	PUNCT
gi-4940	731	1	the	the	DET
gi-4940	731	2	created	create	VERB
gi-4940	731	3	subintervals	subinterval	NOUN
gi-4940	731	4	ωj,1	ωj,1	NOUN
gi-4940	731	5	=	=	SYM
gi-4940	731	6	ωϕ,j	ωϕ,j	PUNCT
gi-4940	731	7	×ωλ	×ωλ	PROPN
gi-4940	731	8	,	,	PUNCT
gi-4940	731	9	j,1	j,1	NOUN
gi-4940	731	10	,	,	PUNCT
gi-4940	731	11	ωj,2	ωj,2	NOUN
gi-4940	731	12	=	=	SYM
gi-4940	731	13	ωϕ,j	ωϕ,j	PUNCT
gi-4940	731	14	×ωλ	×ωλ	PROPN
gi-4940	731	15	,	,	PUNCT
gi-4940	731	16	j,2	j,2	NOUN
gi-4940	731	17	are	be	AUX
gi-4940	731	18	pushed	push	VERB
gi-4940	731	19	to	to	ADP
gi-4940	731	20	the	the	DET
gi-4940	731	21	stack	stack	NOUN
gi-4940	731	22	s	s	PART
gi-4940	731	23	←	←	PROPN
gi-4940	731	24	ωj,1	ωj,1	NOUN
gi-4940	731	25	,	,	PUNCT
gi-4940	731	26	s	s	PART
gi-4940	731	27	←	←	PROPN
gi-4940	731	28	ωj,2	ωj,2	NOUN
gi-4940	731	29	.	.	PUNCT
gi-4940	732	1	•	•	NOUN
gi-4940	732	2	subsequently	subsequently	ADV
gi-4940	732	3	,	,	PUNCT
gi-4940	732	4	the	the	DET
gi-4940	732	5	current	current	ADJ
gi-4940	732	6	interval	interval	NOUN
gi-4940	732	7	ωj	ωj	ADP
gi-4940	732	8	=	=	SYM
gi-4940	732	9	(	(	PUNCT
gi-4940	732	10	0,−π/2	0,−π/2	NUM
gi-4940	732	11	]	]	X
gi-4940	732	12	×	×	NOUN
gi-4940	733	1	[	[	X
gi-4940	733	2	−π,−π/2	−π,−π/2	NUM
gi-4940	733	3	)	)	PUNCT
gi-4940	733	4	popped	pop	VERB
gi-4940	733	5	out	out	ADP
gi-4940	733	6	from	from	ADP
gi-4940	733	7	the	the	DET
gi-4940	733	8	stack	stack	NOUN
gi-4940	733	9	is	be	AUX
gi-4940	733	10	free	free	ADJ
gi-4940	733	11	from	from	ADP
gi-4940	733	12	singularities	singularity	NOUN
gi-4940	733	13	,	,	PUNCT
gi-4940	733	14	the	the	DET
gi-4940	733	15	graticule	graticule	NOUN
gi-4940	733	16	fragment	fragment	VERB
gi-4940	733	17	over	over	ADP
gi-4940	733	18	ωj	ωj	ADV
gi-4940	733	19	is	be	AUX
gi-4940	733	20	constructed	construct	VERB
gi-4940	733	21	;	;	PUNCT
gi-4940	733	22	see	see	VERB
gi-4940	733	23	step	step	NOUN
gi-4940	733	24	d	d	NOUN
gi-4940	733	25	)	)	PUNCT
gi-4940	733	26	.	.	PUNCT
gi-4940	734	1	•	•	PUNCT
gi-4940	734	2	unfortunately	unfortunately	ADV
gi-4940	734	3	,	,	PUNCT
gi-4940	734	4	the	the	DET
gi-4940	734	5	next	next	ADJ
gi-4940	734	6	current	current	ADJ
gi-4940	734	7	interval	interval	NOUN
gi-4940	734	8	ωj	ωj	ADP
gi-4940	734	9	=	=	PUNCT
gi-4940	734	10	(	(	PUNCT
gi-4940	734	11	0,−π/2]×(−π/2	0,−π/2]×(−π/2	PROPN
gi-4940	734	12	,	,	PUNCT
gi-4940	734	13	π	π	PROPN
gi-4940	734	14	]	]	X
gi-4940	734	15	contains	contain	VERB
gi-4940	734	16	a	a	DET
gi-4940	734	17	removable	removable	ADJ
gi-4940	734	18	singularity	singularity	NOUN
gi-4940	734	19	at	at	ADP
gi-4940	734	20	λ	λ	PROPN
gi-4940	734	21	=	=	PUNCT
gi-4940	734	22	π/2	π/2	NUM
gi-4940	734	23	.	.	PUNCT
gi-4940	735	1	it	it	PRON
gi-4940	735	2	is	be	AUX
gi-4940	735	3	split	split	VERB
gi-4940	735	4	to	to	PART
gi-4940	735	5	ωλ	ωλ	VERB
gi-4940	735	6	,	,	PUNCT
gi-4940	735	7	j,1	j,1	X
gi-4940	735	8	=	=	PUNCT
gi-4940	736	1	[	[	X
gi-4940	736	2	−π/2	−π/2	PROPN
gi-4940	736	3	,	,	PUNCT
gi-4940	736	4	π/2	π/2	NUM
gi-4940	736	5	)	)	PUNCT
gi-4940	736	6	,	,	PUNCT
gi-4940	736	7	ωϕ,λ,2	ωϕ,λ,2	PROPN
gi-4940	736	8	=	=	SYM
gi-4940	736	9	(	(	PUNCT
gi-4940	736	10	π/2	π/2	NUM
gi-4940	736	11	,	,	PUNCT
gi-4940	736	12	π	π	PROPN
gi-4940	736	13	]	]	X
gi-4940	736	14	,	,	PUNCT
gi-4940	736	15	the	the	DET
gi-4940	736	16	created	create	VERB
gi-4940	736	17	subintervals	subinterval	NOUN
gi-4940	736	18	ωj,1	ωj,1	NOUN
gi-4940	736	19	=	=	SYM
gi-4940	736	20	ωϕ,j×ωλ	ωϕ,j×ωλ	PROPN
gi-4940	736	21	,	,	PUNCT
gi-4940	736	22	j,1	j,1	PROPN
gi-4940	736	23	,	,	PUNCT
gi-4940	736	24	ω	ω	PROPN
gi-4940	736	25	,	,	PUNCT
gi-4940	736	26	j,2	j,2	NOUN
gi-4940	736	27	=	=	SYM
gi-4940	736	28	ωϕ,j×ωλ	ωϕ,j×ωλ	PROPN
gi-4940	736	29	,	,	PUNCT
gi-4940	736	30	j,2	j,2	NOUN
gi-4940	736	31	are	be	AUX
gi-4940	736	32	pushed	push	VERB
gi-4940	736	33	to	to	ADP
gi-4940	736	34	the	the	DET
gi-4940	736	35	stack	stack	NOUN
gi-4940	736	36	s	s	PART
gi-4940	736	37	←	←	PROPN
gi-4940	736	38	ωj,1	ωj,1	NOUN
gi-4940	736	39	,	,	PUNCT
gi-4940	736	40	s	s	PART
gi-4940	736	41	←	←	PROPN
gi-4940	736	42	ωj,2	ωj,2	NOUN
gi-4940	736	43	;	;	PUNCT
gi-4940	736	44	see	see	VERB
gi-4940	736	45	step	step	NOUN
gi-4940	736	46	e	e	NOUN
gi-4940	736	47	)	)	PUNCT
gi-4940	736	48	.	.	PUNCT
gi-4940	737	1	•	•	NUM
gi-4940	737	2	subsequently	subsequently	ADV
gi-4940	737	3	,	,	PUNCT
gi-4940	737	4	the	the	DET
gi-4940	737	5	current	current	ADJ
gi-4940	737	6	interval	interval	NOUN
gi-4940	737	7	ωj	ωj	ADP
gi-4940	737	8	=	=	PUNCT
gi-4940	737	9	(	(	PUNCT
gi-4940	737	10	0,−π/2]×	0,−π/2]×	NOUN
gi-4940	738	1	[	[	X
gi-4940	738	2	−π/2	−π/2	PROPN
gi-4940	738	3	,	,	PUNCT
gi-4940	738	4	π/2	π/2	NUM
gi-4940	738	5	)	)	PUNCT
gi-4940	738	6	popped	pop	VERB
gi-4940	738	7	from	from	ADP
gi-4940	738	8	the	the	DET
gi-4940	738	9	stack	stack	NOUN
gi-4940	738	10	is	be	AUX
gi-4940	738	11	free	free	ADJ
gi-4940	738	12	from	from	ADP
gi-4940	738	13	singularities	singularity	NOUN
gi-4940	738	14	,	,	PUNCT
gi-4940	738	15	the	the	DET
gi-4940	738	16	graticule	graticule	NOUN
gi-4940	738	17	fragment	fragment	VERB
gi-4940	738	18	over	over	ADP
gi-4940	738	19	ωj	ωj	ADV
gi-4940	738	20	is	be	AUX
gi-4940	738	21	constructed	construct	VERB
gi-4940	738	22	;	;	PUNCT
gi-4940	738	23	see	see	VERB
gi-4940	738	24	step	step	NOUN
gi-4940	738	25	f	f	NOUN
gi-4940	738	26	)	)	PUNCT
gi-4940	738	27	.	.	PUNCT
gi-4940	739	1	the	the	DET
gi-4940	739	2	lack	lack	NOUN
gi-4940	739	3	of	of	ADP
gi-4940	739	4	discontinuities	discontinuity	NOUN
gi-4940	739	5	refers	refer	VERB
gi-4940	739	6	to	to	ADP
gi-4940	739	7	the	the	DET
gi-4940	739	8	next	next	ADJ
gi-4940	739	9	popped	pop	VERB
gi-4940	739	10	interval	interval	NOUN
gi-4940	739	11	ωj	ωj	ADP
gi-4940	739	12	=	=	PUNCT
gi-4940	739	13	(	(	PUNCT
gi-4940	739	14	0,−π/2]×	0,−π/2]×	NOUN
gi-4940	739	15	[	[	X
gi-4940	739	16	π/2	π/2	NUM
gi-4940	739	17	,	,	PUNCT
gi-4940	739	18	π	π	NOUN
gi-4940	739	19	)	)	PUNCT
gi-4940	739	20	,	,	PUNCT
gi-4940	739	21	over	over	ADP
gi-4940	739	22	which	which	PRON
gi-4940	739	23	the	the	DET
gi-4940	739	24	graticule	graticule	NOUN
gi-4940	739	25	is	be	AUX
gi-4940	739	26	constructed	construct	VERB
gi-4940	739	27	;	;	PUNCT
gi-4940	739	28	see	see	VERB
gi-4940	739	29	step	step	NOUN
gi-4940	739	30	g	g	NOUN
gi-4940	739	31	)	)	PUNCT
gi-4940	739	32	.	.	PUNCT
gi-4940	740	1	geoinformatics	geoinformatic	NOUN
gi-4940	740	2	fce	fce	VERB
gi-4940	740	3	ctu	ctu	NOUN
gi-4940	740	4	17(2	17(2	NUM
gi-4940	740	5	)	)	PUNCT
gi-4940	740	6	,	,	PUNCT
gi-4940	740	7	2018	2018	NUM
gi-4940	740	8	55	55	NUM
gi-4940	740	9	t.	t.	NOUN
gi-4940	740	10	bayer	bayer	NOUN
gi-4940	740	11	:	:	PUNCT
gi-4940	740	12	plotting	plot	VERB
gi-4940	740	13	the	the	DET
gi-4940	740	14	map	map	NOUN
gi-4940	740	15	projection	projection	NOUN
gi-4940	740	16	graticule	graticule	NOUN
gi-4940	740	17	with	with	ADP
gi-4940	740	18	discontinuities	discontinuity	NOUN
gi-4940	740	19	a	a	DET
gi-4940	740	20	)	)	PUNCT
gi-4940	740	21	b	b	NOUN
gi-4940	740	22	)	)	PUNCT
gi-4940	740	23	c	c	NOUN
gi-4940	740	24	)	)	PUNCT
gi-4940	740	25	d	d	NOUN
gi-4940	740	26	)	)	PUNCT
gi-4940	740	27	e	e	NOUN
gi-4940	740	28	)	)	PUNCT
gi-4940	740	29	f	f	NOUN
gi-4940	740	30	)	)	PUNCT
gi-4940	740	31	g	g	NOUN
gi-4940	740	32	)	)	PUNCT
gi-4940	740	33	h	h	NOUN
gi-4940	740	34	)	)	PUNCT
gi-4940	740	35	i	i	NOUN
gi-4940	740	36	)	)	PUNCT
gi-4940	740	37	j	j	PROPN
gi-4940	740	38	)	)	PUNCT
gi-4940	740	39	k	k	NOUN
gi-4940	740	40	)	)	PUNCT
gi-4940	740	41	l	l	NOUN
gi-4940	740	42	)	)	PUNCT
gi-4940	740	43	figure	figure	NOUN
gi-4940	740	44	5.3	5.3	NUM
gi-4940	740	45	:	:	PUNCT
gi-4940	740	46	reconstruction	reconstruction	NOUN
gi-4940	740	47	of	of	ADP
gi-4940	740	48	the	the	DET
gi-4940	740	49	graticule	graticule	NOUN
gi-4940	740	50	from	from	ADP
gi-4940	740	51	the	the	DET
gi-4940	740	52	tiles	tile	NOUN
gi-4940	740	53	generated	generate	VERB
gi-4940	740	54	along	along	ADP
gi-4940	740	55	the	the	DET
gi-4940	740	56	set	set	NOUN
gi-4940	740	57	of	of	ADP
gi-4940	740	58	ωg	ωg	PROPN
gi-4940	740	59	,	,	PUNCT
gi-4940	740	60	fournier	fournier	PROPN
gi-4940	740	61	i	i	PROPN
gi-4940	740	62	projection	projection	NOUN
gi-4940	740	63	.	.	PUNCT
gi-4940	741	1	geoinformatics	geoinformatic	NOUN
gi-4940	741	2	fce	fce	VERB
gi-4940	741	3	ctu	ctu	NOUN
gi-4940	741	4	17(2	17(2	NUM
gi-4940	741	5	)	)	PUNCT
gi-4940	741	6	,	,	PUNCT
gi-4940	742	1	2018	2018	NUM
gi-4940	742	2	56	56	NUM
gi-4940	742	3	t.	t.	NOUN
gi-4940	742	4	bayer	bayer	NOUN
gi-4940	742	5	:	:	PUNCT
gi-4940	742	6	plotting	plot	VERB
gi-4940	742	7	the	the	DET
gi-4940	742	8	map	map	NOUN
gi-4940	742	9	projection	projection	NOUN
gi-4940	742	10	graticule	graticule	NOUN
gi-4940	742	11	with	with	ADP
gi-4940	742	12	discontinuities	discontinuity	NOUN
gi-4940	742	13	1	1	NUM
gi-4940	742	14	1	1	NUM
gi-4940	742	15	0	0	NUM
gi-4940	742	16	.0	.0	NUM
gi-4940	742	17	1	1	NUM
gi-4940	742	18	2	2	NUM
gi-4940	742	19	0	0	NUM
gi-4940	742	20	.0	.0	NUM
gi-4940	742	21	1	1	NUM
gi-4940	742	22	3	3	NUM
gi-4940	742	23	5	5	NUM
gi-4940	742	24	.0	.0	NUM
gi-4940	742	25	1	1	NUM
gi-4940	742	26	5	5	NUM
gi-4940	742	27	0	0	NUM
gi-4940	742	28	.0	.0	NUM
gi-4940	742	29	1	1	NUM
gi-4940	742	30	6	6	NUM
gi-4940	742	31	5	5	NUM
gi-4940	742	32	.0	.0	NUM
gi-4940	742	33	1	1	NUM
gi-4940	742	34	8	8	NUM
gi-4940	742	35	0	0	NUM
gi-4940	742	36	.0	.0	NUM
gi-4940	743	1	-7	-7	NOUN
gi-4940	743	2	0	0	NUM
gi-4940	744	1	.0	.0	NUM
gi-4940	745	1	-6	-6	NOUN
gi-4940	745	2	0	0	NUM
gi-4940	746	1	.0	.0	NUM
gi-4940	746	2	-4	-4	NOUN
gi-4940	747	1	5	5	NUM
gi-4940	747	2	.	.	NUM
gi-4940	747	3	0	0	NUM
gi-4940	747	4	-3	-3	PUNCT
gi-4940	747	5	0	0	NUM
gi-4940	747	6	.	.	NOUN
gi-4940	747	7	0	0	NUM
gi-4940	748	1	-15	-15	SYM
gi-4940	748	2	.0	.0	NUM
gi-4940	748	3	0.0	0.0	NUM
gi-4940	748	4	15.0	15.0	NUM
gi-4940	748	5	30.0	30.0	NUM
gi-4940	748	6	45	45	NUM
gi-4940	748	7	.0	.0	NUM
gi-4940	748	8	60	60	NUM
gi-4940	748	9	.0	.0	NUM
gi-4940	748	10	75	75	NUM
gi-4940	748	11	.0	.0	NUM
gi-4940	748	12	90	90	NUM
gi-4940	748	13	.0	.0	NUM
gi-4940	748	14	1	1	NUM
gi-4940	748	15	0	0	NUM
gi-4940	748	16	5	5	NUM
gi-4940	748	17	.0	.0	NUM
gi-4940	748	18	1	1	NUM
gi-4940	748	19	1	1	NUM
gi-4940	748	20	0	0	NUM
gi-4940	748	21	.0	.0	NUM
gi-4940	749	1	20.020.0	20.020.0	NUM
gi-4940	749	2	-1	-1	SYM
gi-4940	750	1	8	8	NUM
gi-4940	750	2	0	0	NUM
gi-4940	751	1	.0	.0	NUM
gi-4940	752	1	-1	-1	NOUN
gi-4940	752	2	6	6	NUM
gi-4940	752	3	5	5	NUM
gi-4940	752	4	.0	.0	NUM
gi-4940	752	5	-1	-1	NOUN
gi-4940	753	1	5	5	NUM
gi-4940	753	2	0	0	NUM
gi-4940	753	3	.0	.0	NUM
gi-4940	753	4	-1	-1	NOUN
gi-4940	753	5	3	3	NUM
gi-4940	753	6	5	5	NUM
gi-4940	753	7	.0	.0	NUM
gi-4940	753	8	-1	-1	NOUN
gi-4940	753	9	2	2	NUM
gi-4940	753	10	0	0	NUM
gi-4940	753	11	.0	.0	NUM
gi-4940	754	1	-1	-1	NOUN
gi-4940	754	2	0	0	NUM
gi-4940	754	3	5	5	NUM
gi-4940	754	4	.0	.0	NUM
gi-4940	754	5	-9	-9	NOUN
gi-4940	754	6	0	0	NUM
gi-4940	754	7	.0	.0	NUM
gi-4940	755	1	-7	-7	NOUN
gi-4940	755	2	5	5	NUM
gi-4940	755	3	.0	.0	NUM
gi-4940	756	1	-7	-7	NOUN
gi-4940	756	2	0	0	NUM
gi-4940	757	1	.0	.0	NUM
gi-4940	757	2	-1	-1	NOUN
gi-4940	758	1	6	6	NUM
gi-4940	758	2	0	0	NUM
gi-4940	758	3	.0	.0	NUM
gi-4940	758	4	-1	-1	NOUN
gi-4940	759	1	6	6	NUM
gi-4940	759	2	0	0	NUM
gi-4940	759	3	.0	.0	NUM
gi-4940	760	1	-90.0	-90.0	NOUN
gi-4940	760	2	-75.0	-75.0	NOUN
gi-4940	761	1	-60.0	-60.0	NOUN
gi-4940	761	2	-45.0	-45.0	NUM
gi-4940	762	1	-30.0	-30.0	NOUN
gi-4940	762	2	-15.0	-15.0	PUNCT
gi-4940	762	3	0.0	0.0	NUM
gi-4940	762	4	15.0	15.0	NUM
gi-4940	762	5	30.0	30.0	NUM
gi-4940	762	6	45.0	45.0	NUM
gi-4940	762	7	60.0	60.0	NUM
gi-4940	762	8	75.0	75.0	NUM
gi-4940	762	9	90.0	90.0	NUM
gi-4940	762	10	-90.0	-90.0	NUM
gi-4940	762	11	-	-	PUNCT
gi-4940	762	12	90.0	90.0	NUM
gi-4940	762	13	-75.0	-75.0	NOUN
gi-4940	763	1	-75.0	-75.0	NOUN
gi-4940	763	2	-60	-60	PUNCT
gi-4940	764	1	.0	.0	NUM
gi-4940	765	1	-60.0	-60.0	NOUN
gi-4940	765	2	-4	-4	NUM
gi-4940	765	3	5.0	5.0	NUM
gi-4940	765	4	-45.0	-45.0	NUM
gi-4940	765	5	-3	-3	NOUN
gi-4940	765	6	0	0	NUM
gi-4940	765	7	.	.	NOUN
gi-4940	765	8	0	0	NUM
gi-4940	766	1	-30.0	-30.0	NOUN
gi-4940	766	2	-1	-1	ADP
gi-4940	766	3	5	5	NUM
gi-4940	766	4	.0	.0	NUM
gi-4940	766	5	-1	-1	ADP
gi-4940	767	1	5	5	NUM
gi-4940	767	2	.0	.0	NUM
gi-4940	767	3	0	0	NUM
gi-4940	768	1	.0	.0	NUM
gi-4940	768	2	0	0	NUM
gi-4940	769	1	.0	.0	NUM
gi-4940	769	2	1	1	NUM
gi-4940	769	3	5	5	NUM
gi-4940	769	4	.0	.0	NUM
gi-4940	769	5	1	1	NUM
gi-4940	769	6	5	5	NUM
gi-4940	769	7	.0	.0	NUM
gi-4940	769	8	30	30	NUM
gi-4940	769	9	.0	.0	NUM
gi-4940	769	10	30.0	30.0	NUM
gi-4940	769	11	45	45	NUM
gi-4940	769	12	.0	.0	NUM
gi-4940	769	13	45.0	45.0	NUM
gi-4940	769	14	60	60	NUM
gi-4940	769	15	.0	.0	NUM
gi-4940	769	16	60.0	60.0	NUM
gi-4940	769	17	75	75	NUM
gi-4940	769	18	.0	.0	NUM
gi-4940	769	19	75.0	75.0	NUM
gi-4940	769	20	90	90	NUM
gi-4940	769	21	.0	.0	NUM
gi-4940	769	22	90.0	90.0	NUM
gi-4940	769	23	-90.0	-90.0	NOUN
gi-4940	769	24	-90	-90	PUNCT
gi-4940	769	25	.	.	PUNCT
gi-4940	769	26	0	0	NUM
gi-4940	770	1	-75.0	-75.0	NUM
gi-4940	771	1	-75.0	-75.0	NOUN
gi-4940	772	1	-60.0	-60.0	NOUN
gi-4940	772	2	-60.0	-60.0	INTJ
gi-4940	773	1	-45.0	-45.0	INTJ
gi-4940	773	2	-45	-45	PUNCT
gi-4940	774	1	.0	.0	NUM
gi-4940	774	2	-30.0	-30.0	NOUN
gi-4940	774	3	-30	-30	SYM
gi-4940	774	4	.0	.0	NUM
gi-4940	774	5	-15.0	-15.0	PRON
gi-4940	774	6	-15	-15	NUM
gi-4940	774	7	.0	.0	NUM
gi-4940	774	8	0.0	0.0	NUM
gi-4940	774	9	0.0	0.0	NUM
gi-4940	774	10	15.0	15.0	NUM
gi-4940	774	11	15	15	NUM
gi-4940	774	12	.0	.0	NUM
gi-4940	774	13	30.0	30.0	NUM
gi-4940	774	14	30	30	NUM
gi-4940	774	15	.0	.0	NUM
gi-4940	774	16	45.0	45.0	NUM
gi-4940	774	17	45	45	NUM
gi-4940	774	18	.0	.0	NUM
gi-4940	775	1	60.0	60.0	NUM
gi-4940	775	2	60	60	NUM
gi-4940	775	3	.0	.0	NUM
gi-4940	775	4	75.0	75.0	NUM
gi-4940	775	5	75	75	NUM
gi-4940	775	6	.0	.0	NUM
gi-4940	776	1	90.090	90.090	NUM
gi-4940	776	2	.0	.0	NUM
gi-4940	776	3	figure	figure	NOUN
gi-4940	776	4	5.4	5.4	NUM
gi-4940	776	5	:	:	PUNCT
gi-4940	776	6	fournier	fournier	PROPN
gi-4940	776	7	i.	i.	PROPN
gi-4940	776	8	projection	projection	PROPN
gi-4940	776	9	with	with	ADP
gi-4940	776	10	the	the	DET
gi-4940	776	11	highlighted	highlight	VERB
gi-4940	776	12	singularities	singularity	NOUN
gi-4940	776	13	leading	lead	VERB
gi-4940	776	14	to	to	ADP
gi-4940	776	15	the	the	DET
gi-4940	776	16	subdivision	subdivision	NOUN
gi-4940	776	17	into	into	ADP
gi-4940	776	18	the	the	DET
gi-4940	776	19	tiles	tile	NOUN
gi-4940	776	20	;	;	PUNCT
gi-4940	776	21	an	an	DET
gi-4940	776	22	oblique	oblique	ADJ
gi-4940	776	23	aspect	aspect	NOUN
gi-4940	776	24	of	of	ADP
gi-4940	776	25	the	the	DET
gi-4940	776	26	projection	projection	NOUN
gi-4940	776	27	,	,	PUNCT
gi-4940	776	28	k	k	X
gi-4940	776	29	=	=	PUNCT
gi-4940	777	1	[	[	X
gi-4940	777	2	50	50	NUM
gi-4940	777	3	◦	◦	NOUN
gi-4940	777	4	,	,	PUNCT
gi-4940	777	5	20	20	NUM
gi-4940	777	6	◦	◦	NOUN
gi-4940	777	7	]	]	PUNCT
gi-4940	777	8	.	.	PUNCT
gi-4940	778	1	testing	test	VERB
gi-4940	778	2	an	an	DET
gi-4940	778	3	oblique	oblique	ADJ
gi-4940	778	4	aspect	aspect	NOUN
gi-4940	778	5	of	of	ADP
gi-4940	778	6	the	the	DET
gi-4940	778	7	projection	projection	NOUN
gi-4940	778	8	.	.	PUNCT
gi-4940	779	1	for	for	ADP
gi-4940	779	2	the	the	DET
gi-4940	779	3	oblique	oblique	ADJ
gi-4940	779	4	aspect	aspect	NOUN
gi-4940	779	5	of	of	ADP
gi-4940	779	6	the	the	DET
gi-4940	779	7	projection	projection	NOUN
gi-4940	779	8	,	,	PUNCT
gi-4940	779	9	several	several	ADJ
gi-4940	779	10	new	new	ADJ
gi-4940	779	11	discontinuities	discontinuity	NOUN
gi-4940	779	12	appear	appear	VERB
gi-4940	779	13	.	.	PUNCT
gi-4940	780	1	suppose	suppose	VERB
gi-4940	780	2	the	the	DET
gi-4940	780	3	arbitrary	arbitrary	ADJ
gi-4940	780	4	pole	pole	NOUN
gi-4940	780	5	k	k	X
gi-4940	781	1	=	=	PUNCT
gi-4940	782	1	[	[	X
gi-4940	782	2	50	50	NUM
gi-4940	782	3	◦	◦	NOUN
gi-4940	782	4	,	,	PUNCT
gi-4940	782	5	20	20	NUM
gi-4940	782	6	◦	◦	NOUN
gi-4940	782	7	]	]	PUNCT
gi-4940	782	8	,	,	PUNCT
gi-4940	782	9	the	the	DET
gi-4940	782	10	central	central	ADJ
gi-4940	782	11	meridian	meridian	PROPN
gi-4940	782	12	shift	shift	NOUN
gi-4940	782	13	is	be	AUX
gi-4940	782	14	λ′0	λ′0	NOUN
gi-4940	782	15	=	=	SYM
gi-4940	782	16	0	0	NUM
gi-4940	782	17	◦	◦	NOUN
gi-4940	782	18	.	.	NOUN
gi-4940	783	1	due	due	ADP
gi-4940	783	2	to	to	ADP
gi-4940	783	3	the	the	DET
gi-4940	783	4	latitude	latitude	NOUN
gi-4940	783	5	singularity	singularity	NOUN
gi-4940	783	6	at	at	ADP
gi-4940	783	7	ϕk	ϕk	NOUN
gi-4940	783	8	=	=	SYM
gi-4940	783	9	50	50	NUM
gi-4940	783	10	◦	◦	NOUN
gi-4940	783	11	,	,	PUNCT
gi-4940	783	12	the	the	DET
gi-4940	783	13	latitude	latitude	NOUN
gi-4940	783	14	interval	interval	NOUN
gi-4940	783	15	ωϕ,j	ωϕ,j	PUNCT
gi-4940	783	16	will	will	AUX
gi-4940	783	17	be	be	AUX
gi-4940	783	18	split	split	VERB
gi-4940	783	19	into	into	ADP
gi-4940	783	20	two	two	NUM
gi-4940	783	21	parts	part	NOUN
gi-4940	783	22	:	:	PUNCT
gi-4940	783	23	ωϕ,j,1	ωϕ,j,1	PROPN
gi-4940	783	24	=	=	PUNCT
gi-4940	784	1	[	[	X
gi-4940	784	2	−90	−90	NOUN
gi-4940	784	3	◦	◦	NOUN
gi-4940	784	4	,	,	PUNCT
gi-4940	784	5	50	50	NUM
gi-4940	784	6	◦	◦	NOUN
gi-4940	784	7	)	)	PUNCT
gi-4940	784	8	,	,	PUNCT
gi-4940	784	9	ωϕ,j,2	ωϕ,j,2	PROPN
gi-4940	784	10	=	=	SYM
gi-4940	784	11	(	(	PUNCT
gi-4940	784	12	50	50	NUM
gi-4940	784	13	◦	◦	NOUN
gi-4940	784	14	,	,	PUNCT
gi-4940	784	15	90	90	NUM
gi-4940	784	16	◦	◦	NOUN
gi-4940	784	17	]	]	PUNCT
gi-4940	784	18	.	.	PUNCT
gi-4940	785	1	analogously	analogously	ADV
gi-4940	785	2	,	,	PUNCT
gi-4940	785	3	the	the	DET
gi-4940	785	4	longitude	longitude	ADJ
gi-4940	785	5	singularity	singularity	NOUN
gi-4940	785	6	at	at	ADP
gi-4940	785	7	λk	λk	PROPN
gi-4940	785	8	−	−	PROPN
gi-4940	785	9	180	180	NUM
gi-4940	785	10	◦	◦	NOUN
gi-4940	785	11	=	=	SYM
gi-4940	785	12	−160	−160	NOUN
gi-4940	785	13	◦	◦	NOUN
gi-4940	785	14	splits	split	VERB
gi-4940	785	15	the	the	DET
gi-4940	785	16	interval	interval	NOUN
gi-4940	785	17	ωλ	ωλ	VERB
gi-4940	785	18	,	,	PUNCT
gi-4940	785	19	j	j	PROPN
gi-4940	785	20	into	into	ADP
gi-4940	785	21	the	the	DET
gi-4940	785	22	three	three	NUM
gi-4940	785	23	parts	part	NOUN
gi-4940	785	24	:	:	PUNCT
gi-4940	785	25	ωλ	ωλ	ADJ
gi-4940	785	26	,	,	PUNCT
gi-4940	785	27	j,1	j,1	X
gi-4940	786	1	=	=	PUNCT
gi-4940	787	1	[	[	X
gi-4940	787	2	−180	−180	X
gi-4940	787	3	◦	◦	NOUN
gi-4940	787	4	,−160	,−160	PUNCT
gi-4940	787	5	◦	◦	NOUN
gi-4940	787	6	)	)	PUNCT
gi-4940	787	7	,	,	PUNCT
gi-4940	787	8	ωλ	ωλ	ADJ
gi-4940	787	9	,	,	PUNCT
gi-4940	787	10	j,2	j,2	NOUN
gi-4940	787	11	=	=	SYM
gi-4940	787	12	(	(	PUNCT
gi-4940	787	13	−160	−160	PROPN
gi-4940	787	14	◦	◦	NOUN
gi-4940	787	15	,	,	PUNCT
gi-4940	787	16	15	15	NUM
gi-4940	787	17	◦	◦	NOUN
gi-4940	787	18	)	)	PUNCT
gi-4940	787	19	,	,	PUNCT
gi-4940	787	20	ωλ	ωλ	ADJ
gi-4940	787	21	,	,	PUNCT
gi-4940	787	22	j.3	j.3	X
gi-4940	788	1	=	=	PUNCT
gi-4940	789	1	(	(	PUNCT
gi-4940	789	2	15	15	NUM
gi-4940	789	3	◦	◦	NOUN
gi-4940	789	4	,	,	PUNCT
gi-4940	789	5	180	180	NUM
gi-4940	789	6	◦	◦	NOUN
gi-4940	789	7	]	]	PUNCT
gi-4940	789	8	.	.	PUNCT
gi-4940	790	1	the	the	DET
gi-4940	790	2	reconstructed	reconstruct	VERB
gi-4940	790	3	graticule	graticule	NOUN
gi-4940	790	4	with	with	ADP
gi-4940	790	5	the	the	DET
gi-4940	790	6	highlighted	highlight	VERB
gi-4940	790	7	singularities	singularity	NOUN
gi-4940	790	8	is	be	AUX
gi-4940	790	9	depicted	depict	VERB
gi-4940	790	10	in	in	ADP
gi-4940	790	11	fig	fig	NOUN
gi-4940	790	12	.	.	PUNCT
gi-4940	791	1	5.4	5.4	NUM
gi-4940	791	2	.	.	X
gi-4940	792	1	5.3	5.3	NUM
gi-4940	792	2	.	.	PUNCT
gi-4940	792	3	measuring	measure	VERB
gi-4940	792	4	the	the	DET
gi-4940	792	5	quantitative	quantitative	ADJ
gi-4940	792	6	parameters	parameter	NOUN
gi-4940	792	7	of	of	ADP
gi-4940	792	8	the	the	DET
gi-4940	792	9	algorithm	algorithm	NOUN
gi-4940	792	10	the	the	DET
gi-4940	792	11	algorithms	algorithm	NOUN
gi-4940	792	12	have	have	AUX
gi-4940	792	13	been	be	AUX
gi-4940	792	14	tested	test	VERB
gi-4940	792	15	on	on	ADP
gi-4940	792	16	the	the	DET
gi-4940	792	17	construction	construction	NOUN
gi-4940	792	18	of	of	ADP
gi-4940	792	19	the	the	DET
gi-4940	792	20	several	several	ADJ
gi-4940	792	21	graticules	graticule	NOUN
gi-4940	792	22	with	with	ADP
gi-4940	792	23	the	the	DET
gi-4940	792	24	shifted	shift	VERB
gi-4940	792	25	central	central	ADJ
gi-4940	792	26	meridian	meridian	NOUN
gi-4940	792	27	λ0	λ0	NOUN
gi-4940	792	28	.	.	PUNCT
gi-4940	793	1	in	in	ADP
gi-4940	793	2	all	all	DET
gi-4940	793	3	cases	case	NOUN
gi-4940	793	4	,	,	PUNCT
gi-4940	793	5	the	the	DET
gi-4940	793	6	entire	entire	ADJ
gi-4940	793	7	planisphere	planisphere	NOUN
gi-4940	793	8	is	be	AUX
gi-4940	793	9	covered	cover	VERB
gi-4940	793	10	by	by	ADP
gi-4940	793	11	the	the	DET
gi-4940	793	12	graticule	graticule	NOUN
gi-4940	793	13	with	with	ADP
gi-4940	793	14	the	the	DET
gi-4940	793	15	offset	offset	NOUN
gi-4940	793	16	of	of	ADP
gi-4940	793	17	∆ϕ	∆ϕ	NOUN
gi-4940	793	18	=	=	SYM
gi-4940	793	19	∆λ	∆λ	NOUN
gi-4940	793	20	=	=	NOUN
gi-4940	793	21	10	10	NUM
gi-4940	793	22	◦	◦	NOUN
gi-4940	793	23	.	.	PUNCT
gi-4940	794	1	only	only	ADV
gi-4940	794	2	the	the	DET
gi-4940	794	3	map	map	NOUN
gi-4940	794	4	projections	projection	NOUN
gi-4940	794	5	with	with	ADP
gi-4940	794	6	the	the	DET
gi-4940	794	7	singularities	singularity	NOUN
gi-4940	794	8	are	be	AUX
gi-4940	794	9	involved	involve	VERB
gi-4940	794	10	in	in	ADP
gi-4940	794	11	testing	testing	NOUN
gi-4940	794	12	:	:	PUNCT
gi-4940	794	13	fournier	fournier	PROPN
gi-4940	794	14	i.	i.	PROPN
gi-4940	794	15	,	,	PUNCT
gi-4940	794	16	van	van	PROPN
gi-4940	794	17	der	der	NOUN
gi-4940	794	18	grinten	grinten	PROPN
gi-4940	794	19	i.	i.	PROPN
gi-4940	794	20	,	,	PUNCT
gi-4940	794	21	ortelius	ortelius	ADJ
gi-4940	794	22	oval	oval	NOUN
gi-4940	794	23	,	,	PUNCT
gi-4940	794	24	nicolosi	nicolosi	NOUN
gi-4940	794	25	,	,	PUNCT
gi-4940	794	26	hassler	hassler	NOUN
gi-4940	794	27	.	.	PUNCT
gi-4940	795	1	while	while	SCONJ
gi-4940	795	2	the	the	DET
gi-4940	795	3	hassler	hassler	PROPN
gi-4940	795	4	projection	projection	PROPN
gi-4940	795	5	has	have	VERB
gi-4940	795	6	the	the	DET
gi-4940	795	7	only	only	ADJ
gi-4940	795	8	singularity	singularity	NOUN
gi-4940	795	9	at	at	ADP
gi-4940	795	10	ϕ	ϕ	NOUN
gi-4940	795	11	=	=	SYM
gi-4940	795	12	0	0	NUM
gi-4940	795	13	◦	◦	NOUN
gi-4940	795	14	,	,	PUNCT
gi-4940	795	15	the	the	DET
gi-4940	795	16	ortelius	ortelius	ADJ
gi-4940	795	17	projection	projection	NOUN
gi-4940	795	18	is	be	AUX
gi-4940	795	19	singular	singular	ADJ
gi-4940	795	20	at	at	ADP
gi-4940	795	21	λ−λ0	λ−λ0	ADV
gi-4940	795	22	=	=	SYM
gi-4940	795	23	0	0	NUM
gi-4940	795	24	,	,	PUNCT
gi-4940	795	25	and	and	CCONJ
gi-4940	795	26	the	the	DET
gi-4940	795	27	fournier	fournier	PROPN
gi-4940	795	28	i.	i.	PROPN
gi-4940	795	29	,	,	PUNCT
gi-4940	795	30	van	van	PROPN
gi-4940	795	31	der	der	NOUN
gi-4940	795	32	grinten	grinten	PROPN
gi-4940	795	33	i.	i.	PROPN
gi-4940	795	34	,	,	PUNCT
gi-4940	795	35	and	and	CCONJ
gi-4940	795	36	nicolosi	nicolosi	NOUN
gi-4940	795	37	projections	projection	NOUN
gi-4940	795	38	add	add	VERB
gi-4940	795	39	singularities	singularity	NOUN
gi-4940	795	40	at	at	ADP
gi-4940	795	41	λ−λ0	λ−λ0	ADV
gi-4940	795	42	=	=	SYM
gi-4940	795	43	±π	±π	X
gi-4940	795	44	2	2	NUM
gi-4940	795	45	.	.	PUNCT
gi-4940	796	1	the	the	DET
gi-4940	796	2	graphical	graphical	ADJ
gi-4940	796	3	issues	issue	NOUN
gi-4940	796	4	,	,	PUNCT
gi-4940	796	5	amount	amount	NOUN
gi-4940	796	6	of	of	ADP
gi-4940	796	7	splits	split	NOUN
gi-4940	796	8	ns	n	VERB
gi-4940	796	9	,	,	PUNCT
gi-4940	796	10	processed	process	VERB
gi-4940	796	11	tiles	tile	NOUN
gi-4940	796	12	nt	not	PART
gi-4940	796	13	,	,	PUNCT
gi-4940	796	14	interval	interval	NOUN
gi-4940	796	15	resizing	resize	VERB
gi-4940	796	16	nr	nr	PRON
gi-4940	796	17	,	,	PUNCT
gi-4940	796	18	deleted	delete	VERB
gi-4940	796	19	intervals	interval	NOUN
gi-4940	796	20	nd	nd	PRON
gi-4940	796	21	,	,	PUNCT
gi-4940	796	22	and	and	CCONJ
gi-4940	796	23	possible	possible	ADJ
gi-4940	796	24	failures	failure	NOUN
gi-4940	796	25	of	of	ADP
gi-4940	796	26	the	the	DET
gi-4940	796	27	algorithm	algorithm	NOUN
gi-4940	796	28	will	will	AUX
gi-4940	796	29	be	be	AUX
gi-4940	796	30	investigated	investigate	VERB
gi-4940	796	31	.	.	PUNCT
gi-4940	797	1	the	the	DET
gi-4940	797	2	impact	impact	NOUN
gi-4940	797	3	of	of	ADP
gi-4940	797	4	the	the	DET
gi-4940	797	5	central	central	ADJ
gi-4940	797	6	meridian	meridian	PROPN
gi-4940	797	7	shift	shift	NOUN
gi-4940	797	8	λ′0	λ′0	PROPN
gi-4940	797	9	.	.	PUNCT
gi-4940	798	1	to	to	PART
gi-4940	798	2	verify	verify	VERB
gi-4940	798	3	the	the	DET
gi-4940	798	4	properties	property	NOUN
gi-4940	798	5	,	,	PUNCT
gi-4940	798	6	behavior	behavior	NOUN
gi-4940	798	7	and	and	CCONJ
gi-4940	798	8	numerical	numerical	ADJ
gi-4940	798	9	stability	stability	NOUN
gi-4940	798	10	of	of	ADP
gi-4940	798	11	the	the	DET
gi-4940	798	12	procedures	procedure	NOUN
gi-4940	798	13	,	,	PUNCT
gi-4940	798	14	the	the	DET
gi-4940	798	15	following	follow	VERB
gi-4940	798	16	shifts	shift	NOUN
gi-4940	798	17	λ′0	λ′0	X
gi-4940	799	1	=	=	PRON
gi-4940	799	2	{	{	PUNCT
gi-4940	799	3	0	0	NUM
gi-4940	799	4	◦	◦	NOUN
gi-4940	799	5	,	,	PUNCT
gi-4940	799	6	30	30	NUM
gi-4940	799	7	◦	◦	NOUN
gi-4940	799	8	,	,	PUNCT
gi-4940	799	9	...	...	PUNCT
gi-4940	799	10	,	,	PUNCT
gi-4940	799	11	150	150	NUM
gi-4940	799	12	◦	◦	NOUN
gi-4940	799	13	,	,	PUNCT
gi-4940	799	14	180	180	NUM
gi-4940	799	15	◦	◦	NOUN
gi-4940	799	16	}	}	PUNCT
gi-4940	799	17	of	of	ADP
gi-4940	799	18	the	the	DET
gi-4940	799	19	geoinformatics	geoinformatic	NOUN
gi-4940	799	20	fce	fce	VERB
gi-4940	799	21	ctu	ctu	NOUN
gi-4940	799	22	17(2	17(2	NUM
gi-4940	799	23	)	)	PUNCT
gi-4940	799	24	,	,	PUNCT
gi-4940	799	25	2018	2018	NUM
gi-4940	799	26	57	57	NUM
gi-4940	799	27	t.	t.	NOUN
gi-4940	799	28	bayer	bayer	NOUN
gi-4940	799	29	:	:	PUNCT
gi-4940	799	30	plotting	plot	VERB
gi-4940	799	31	the	the	DET
gi-4940	799	32	map	map	NOUN
gi-4940	799	33	projection	projection	NOUN
gi-4940	799	34	graticule	graticule	NOUN
gi-4940	799	35	with	with	ADP
gi-4940	799	36	discontinuities	discontinuity	NOUN
gi-4940	799	37	table	table	NOUN
gi-4940	799	38	3	3	NUM
gi-4940	799	39	:	:	PUNCT
gi-4940	799	40	the	the	DET
gi-4940	799	41	amount	amount	NOUN
gi-4940	799	42	of	of	ADP
gi-4940	799	43	splits	split	NOUN
gi-4940	799	44	ns	n	VERB
gi-4940	799	45	,	,	PUNCT
gi-4940	799	46	processed	process	VERB
gi-4940	799	47	tiles	tile	NOUN
gi-4940	799	48	nt	not	PART
gi-4940	799	49	,	,	PUNCT
gi-4940	799	50	interval	interval	NOUN
gi-4940	799	51	resizing	resize	VERB
gi-4940	799	52	nr	nr	PRON
gi-4940	799	53	,	,	PUNCT
gi-4940	799	54	and	and	CCONJ
gi-4940	799	55	deleted	delete	VERB
gi-4940	799	56	intervals	interval	NOUN
gi-4940	799	57	nd	nd	INTJ
gi-4940	799	58	for	for	ADP
gi-4940	799	59	different	different	ADJ
gi-4940	799	60	values	value	NOUN
gi-4940	799	61	of	of	ADP
gi-4940	799	62	λ′0	λ′0	NOUN
gi-4940	799	63	representing	represent	VERB
gi-4940	799	64	multiples	multiple	NOUN
gi-4940	799	65	of	of	ADP
gi-4940	799	66	30	30	NUM
gi-4940	799	67	◦	◦	NOUN
gi-4940	799	68	.	.	PUNCT
gi-4940	800	1	projection	projection	NOUN
gi-4940	800	2	λ′0	λ′0	NOUN
gi-4940	800	3	0	0	NUM
gi-4940	800	4	◦	◦	NOUN
gi-4940	800	5	30	30	NUM
gi-4940	800	6	◦	◦	NOUN
gi-4940	800	7	60	60	NUM
gi-4940	800	8	◦	◦	NOUN
gi-4940	800	9	90	90	NUM
gi-4940	800	10	◦	◦	NOUN
gi-4940	800	11	120	120	NUM
gi-4940	800	12	◦	◦	NOUN
gi-4940	800	13	150	150	NUM
gi-4940	800	14	◦	◦	NOUN
gi-4940	800	15	180	180	NUM
gi-4940	800	16	◦	◦	NOUN
gi-4940	800	17	fournier	fournier	PROPN
gi-4940	800	18	i.	i.	PROPN
gi-4940	800	19	nt	not	PART
gi-4940	800	20	7	7	NUM
gi-4940	800	21	3	3	NUM
gi-4940	800	22	3	3	NUM
gi-4940	800	23	11	11	NUM
gi-4940	800	24	3	3	NUM
gi-4940	800	25	3	3	NUM
gi-4940	800	26	7	7	NUM
gi-4940	800	27	ns	ns	NUM
gi-4940	800	28	3	3	NUM
gi-4940	800	29	1	1	NUM
gi-4940	800	30	1	1	NUM
gi-4940	800	31	5	5	NUM
gi-4940	800	32	1	1	NUM
gi-4940	800	33	1	1	NUM
gi-4940	800	34	3	3	NUM
gi-4940	800	35	nr	nr	NOUN
gi-4940	800	36	0	0	NUM
gi-4940	800	37	0	0	NUM
gi-4940	800	38	0	0	NUM
gi-4940	800	39	0	0	NUM
gi-4940	800	40	0	0	NUM
gi-4940	800	41	0	0	NUM
gi-4940	800	42	0	0	NUM
gi-4940	800	43	nd	nd	NOUN
gi-4940	800	44	0	0	NUM
gi-4940	800	45	0	0	NUM
gi-4940	800	46	0	0	NUM
gi-4940	800	47	0	0	NUM
gi-4940	800	48	0	0	NUM
gi-4940	800	49	0	0	SYM
gi-4940	800	50	0	0	NUM
gi-4940	800	51	van	van	PROPN
gi-4940	800	52	der	der	NOUN
gi-4940	800	53	grinten	grinten	PROPN
gi-4940	800	54	i.	i.	PROPN
gi-4940	800	55	nt	not	PART
gi-4940	800	56	7	7	NUM
gi-4940	800	57	3	3	NUM
gi-4940	800	58	3	3	NUM
gi-4940	800	59	3	3	NUM
gi-4940	800	60	3	3	NUM
gi-4940	800	61	3	3	NUM
gi-4940	800	62	3	3	NUM
gi-4940	800	63	ns	ns	NUM
gi-4940	800	64	3	3	NUM
gi-4940	800	65	1	1	NUM
gi-4940	800	66	1	1	NUM
gi-4940	800	67	1	1	NUM
gi-4940	800	68	1	1	NUM
gi-4940	800	69	1	1	NUM
gi-4940	800	70	1	1	NUM
gi-4940	800	71	nr	nr	NOUN
gi-4940	800	72	0	0	NUM
gi-4940	800	73	0	0	NUM
gi-4940	800	74	0	0	NUM
gi-4940	800	75	0	0	NUM
gi-4940	800	76	0	0	NUM
gi-4940	800	77	0	0	NUM
gi-4940	800	78	0	0	NUM
gi-4940	800	79	nd	nd	NOUN
gi-4940	800	80	0	0	NUM
gi-4940	800	81	0	0	NUM
gi-4940	800	82	0	0	NUM
gi-4940	800	83	0	0	NUM
gi-4940	800	84	0	0	NUM
gi-4940	800	85	0	0	NUM
gi-4940	800	86	0	0	NUM
gi-4940	800	87	ortelius	ortelius	ADJ
gi-4940	800	88	oval	oval	NOUN
gi-4940	800	89	nt	not	PART
gi-4940	800	90	3	3	NUM
gi-4940	800	91	1	1	NUM
gi-4940	800	92	1	1	NUM
gi-4940	800	93	1	1	NUM
gi-4940	800	94	1	1	NUM
gi-4940	800	95	1	1	NUM
gi-4940	800	96	1	1	NUM
gi-4940	800	97	ns	ns	NUM
gi-4940	800	98	1	1	NUM
gi-4940	800	99	1	1	NUM
gi-4940	800	100	1	1	NUM
gi-4940	800	101	1	1	NUM
gi-4940	800	102	1	1	NUM
gi-4940	800	103	1	1	NUM
gi-4940	800	104	1	1	NUM
gi-4940	800	105	nr	nr	NOUN
gi-4940	800	106	0	0	NUM
gi-4940	800	107	0	0	NUM
gi-4940	800	108	0	0	NUM
gi-4940	800	109	0	0	NUM
gi-4940	800	110	0	0	NUM
gi-4940	800	111	0	0	NUM
gi-4940	800	112	0	0	NUM
gi-4940	800	113	nd	nd	NOUN
gi-4940	800	114	0	0	NUM
gi-4940	800	115	0	0	NUM
gi-4940	800	116	0	0	NUM
gi-4940	800	117	0	0	NUM
gi-4940	800	118	0	0	NUM
gi-4940	800	119	0	0	NUM
gi-4940	800	120	0	0	NUM
gi-4940	800	121	nicolosi	nicolosi	NOUN
gi-4940	800	122	nt	not	PART
gi-4940	800	123	7	7	NUM
gi-4940	800	124	3	3	NUM
gi-4940	800	125	3	3	NUM
gi-4940	800	126	7	7	NUM
gi-4940	800	127	3	3	NUM
gi-4940	800	128	3	3	NUM
gi-4940	800	129	3	3	NUM
gi-4940	800	130	ns	ns	NUM
gi-4940	800	131	3	3	NUM
gi-4940	800	132	1	1	NUM
gi-4940	800	133	1	1	NUM
gi-4940	800	134	3	3	NUM
gi-4940	800	135	1	1	NUM
gi-4940	800	136	1	1	NUM
gi-4940	800	137	1	1	NUM
gi-4940	800	138	nr	nr	NOUN
gi-4940	800	139	0	0	NUM
gi-4940	800	140	0	0	NUM
gi-4940	800	141	0	0	NUM
gi-4940	800	142	0	0	NUM
gi-4940	800	143	0	0	NUM
gi-4940	800	144	0	0	NUM
gi-4940	800	145	0	0	NUM
gi-4940	800	146	nd	nd	NOUN
gi-4940	800	147	0	0	NUM
gi-4940	800	148	0	0	NUM
gi-4940	800	149	0	0	NUM
gi-4940	800	150	0	0	NUM
gi-4940	800	151	0	0	NUM
gi-4940	800	152	0	0	NUM
gi-4940	800	153	0	0	NUM
gi-4940	800	154	hassler	hassler	PROPN
gi-4940	800	155	nt	not	PART
gi-4940	800	156	1	1	NUM
gi-4940	800	157	1	1	NUM
gi-4940	800	158	1	1	NUM
gi-4940	800	159	1	1	NUM
gi-4940	800	160	1	1	NUM
gi-4940	800	161	1	1	NUM
gi-4940	800	162	1	1	NUM
gi-4940	800	163	ns	ns	NUM
gi-4940	800	164	1	1	NUM
gi-4940	800	165	1	1	NUM
gi-4940	800	166	1	1	NUM
gi-4940	800	167	1	1	NUM
gi-4940	800	168	1	1	NUM
gi-4940	800	169	1	1	NUM
gi-4940	800	170	1	1	NUM
gi-4940	800	171	nr	nr	NOUN
gi-4940	800	172	0	0	NUM
gi-4940	800	173	0	0	NUM
gi-4940	800	174	0	0	NUM
gi-4940	800	175	0	0	NUM
gi-4940	800	176	0	0	NUM
gi-4940	800	177	0	0	NUM
gi-4940	800	178	0	0	NUM
gi-4940	800	179	nd	nd	NOUN
gi-4940	800	180	0	0	NUM
gi-4940	800	181	0	0	NUM
gi-4940	800	182	0	0	NUM
gi-4940	800	183	0	0	NUM
gi-4940	800	184	0	0	NUM
gi-4940	800	185	0	0	NUM
gi-4940	800	186	0	0	NUM
gi-4940	800	187	table	table	NOUN
gi-4940	800	188	4	4	NUM
gi-4940	800	189	:	:	PUNCT
gi-4940	800	190	the	the	DET
gi-4940	800	191	amount	amount	NOUN
gi-4940	800	192	of	of	ADP
gi-4940	800	193	splits	split	NOUN
gi-4940	800	194	ns	n	VERB
gi-4940	800	195	,	,	PUNCT
gi-4940	800	196	processed	process	VERB
gi-4940	800	197	tiles	tile	NOUN
gi-4940	800	198	nt	not	PART
gi-4940	800	199	,	,	PUNCT
gi-4940	800	200	interval	interval	NOUN
gi-4940	800	201	resizing	resize	VERB
gi-4940	800	202	nr	nr	PRON
gi-4940	800	203	,	,	PUNCT
gi-4940	800	204	and	and	CCONJ
gi-4940	800	205	deleted	delete	VERB
gi-4940	800	206	intervals	interval	NOUN
gi-4940	800	207	nd	nd	INTJ
gi-4940	800	208	for	for	ADP
gi-4940	800	209	different	different	ADJ
gi-4940	800	210	values	value	NOUN
gi-4940	800	211	of	of	ADP
gi-4940	800	212	λ′0	λ′0	NOUN
gi-4940	800	213	which	which	PRON
gi-4940	800	214	are	be	AUX
gi-4940	800	215	not	not	PART
gi-4940	800	216	the	the	DET
gi-4940	800	217	exact	exact	ADJ
gi-4940	800	218	multiples	multiple	NOUN
gi-4940	800	219	of	of	ADP
gi-4940	800	220	30	30	NUM
gi-4940	800	221	◦	◦	NOUN
gi-4940	800	222	.	.	PUNCT
gi-4940	801	1	projection	projection	PROPN
gi-4940	801	2	λ′0	λ′0	PROPN
gi-4940	801	3	0.001	0.001	NUM
gi-4940	801	4	◦	◦	NOUN
gi-4940	801	5	30.001	30.001	NUM
gi-4940	801	6	◦	◦	NOUN
gi-4940	801	7	60.001	60.001	NUM
gi-4940	801	8	◦	◦	NOUN
gi-4940	801	9	90.001	90.001	NUM
gi-4940	801	10	◦	◦	NOUN
gi-4940	801	11	120.001	120.001	NUM
gi-4940	801	12	◦	◦	NOUN
gi-4940	801	13	150.001	150.001	NUM
gi-4940	801	14	◦	◦	NOUN
gi-4940	801	15	180.001	180.001	NUM
gi-4940	801	16	◦	◦	NOUN
gi-4940	801	17	fournier	fournier	PROPN
gi-4940	801	18	i.	i.	PROPN
gi-4940	801	19	nt	not	PART
gi-4940	801	20	5	5	NUM
gi-4940	801	21	3	3	NUM
gi-4940	801	22	3	3	NUM
gi-4940	801	23	8	8	NUM
gi-4940	801	24	3	3	NUM
gi-4940	801	25	3	3	NUM
gi-4940	801	26	5	5	NUM
gi-4940	801	27	ns	ns	NUM
gi-4940	801	28	1	1	NUM
gi-4940	801	29	1	1	NUM
gi-4940	801	30	1	1	NUM
gi-4940	801	31	3	3	NUM
gi-4940	801	32	1	1	NUM
gi-4940	801	33	1	1	NUM
gi-4940	801	34	1	1	NUM
gi-4940	801	35	nr	nr	NOUN
gi-4940	801	36	1	1	NUM
gi-4940	801	37	0	0	NUM
gi-4940	801	38	0	0	NUM
gi-4940	801	39	0	0	NUM
gi-4940	801	40	0	0	NUM
gi-4940	801	41	0	0	NUM
gi-4940	801	42	0	0	NUM
gi-4940	801	43	nd	nd	NOUN
gi-4940	801	44	0	0	NUM
gi-4940	801	45	0	0	NUM
gi-4940	801	46	0	0	NUM
gi-4940	801	47	0	0	NUM
gi-4940	801	48	0	0	NUM
gi-4940	801	49	0	0	SYM
gi-4940	801	50	0	0	NUM
gi-4940	801	51	van	van	PROPN
gi-4940	801	52	der	der	NOUN
gi-4940	801	53	grinten	grinten	PROPN
gi-4940	801	54	i.	i.	PROPN
gi-4940	801	55	nt	not	PART
gi-4940	801	56	4	4	NUM
gi-4940	801	57	3	3	NUM
gi-4940	801	58	3	3	NUM
gi-4940	801	59	4	4	NUM
gi-4940	801	60	3	3	NUM
gi-4940	801	61	3	3	NUM
gi-4940	801	62	4	4	NUM
gi-4940	801	63	ns	ns	NUM
gi-4940	801	64	1	1	NUM
gi-4940	801	65	1	1	NUM
gi-4940	801	66	1	1	NUM
gi-4940	801	67	1	1	NUM
gi-4940	801	68	1	1	NUM
gi-4940	801	69	1	1	NUM
gi-4940	801	70	1	1	NUM
gi-4940	801	71	nr	nr	NOUN
gi-4940	801	72	0	0	NUM
gi-4940	801	73	0	0	NUM
gi-4940	801	74	0	0	NUM
gi-4940	801	75	1	1	NUM
gi-4940	801	76	0	0	NUM
gi-4940	801	77	0	0	NUM
gi-4940	801	78	0	0	NUM
gi-4940	801	79	nd	nd	NOUN
gi-4940	801	80	0	0	NUM
gi-4940	801	81	0	0	NUM
gi-4940	801	82	0	0	NUM
gi-4940	801	83	0	0	NUM
gi-4940	801	84	0	0	NUM
gi-4940	801	85	0	0	NUM
gi-4940	801	86	0	0	NUM
gi-4940	801	87	ortelius	ortelius	ADJ
gi-4940	801	88	oval	oval	NOUN
gi-4940	801	89	nt	not	PART
gi-4940	801	90	2	2	NUM
gi-4940	801	91	1	1	NUM
gi-4940	801	92	1	1	NUM
gi-4940	801	93	2	2	NUM
gi-4940	801	94	1	1	NUM
gi-4940	801	95	1	1	NUM
gi-4940	801	96	1	1	NUM
gi-4940	801	97	ns	ns	NUM
gi-4940	801	98	0	0	NUM
gi-4940	801	99	0	0	NUM
gi-4940	801	100	0	0	NUM
gi-4940	801	101	0	0	NUM
gi-4940	801	102	0	0	NUM
gi-4940	801	103	0	0	NUM
gi-4940	801	104	0	0	NUM
gi-4940	801	105	nr	nr	NOUN
gi-4940	801	106	0	0	NUM
gi-4940	801	107	0	0	NUM
gi-4940	801	108	0	0	NUM
gi-4940	801	109	0	0	NUM
gi-4940	801	110	0	0	NUM
gi-4940	801	111	0	0	NUM
gi-4940	801	112	0	0	NUM
gi-4940	801	113	nd	nd	NOUN
gi-4940	801	114	0	0	NUM
gi-4940	801	115	0	0	NUM
gi-4940	801	116	0	0	NUM
gi-4940	801	117	0	0	NUM
gi-4940	801	118	0	0	NUM
gi-4940	801	119	0	0	NUM
gi-4940	801	120	0	0	NUM
gi-4940	801	121	nicolosi	nicolosi	NOUN
gi-4940	801	122	nt	not	PART
gi-4940	801	123	5	5	NUM
gi-4940	801	124	3	3	NUM
gi-4940	801	125	3	3	NUM
gi-4940	801	126	8	8	NUM
gi-4940	801	127	3	3	NUM
gi-4940	801	128	3	3	NUM
gi-4940	801	129	5	5	NUM
gi-4940	801	130	ns	ns	NUM
gi-4940	801	131	1	1	NUM
gi-4940	801	132	1	1	NUM
gi-4940	801	133	1	1	NUM
gi-4940	801	134	3	3	NUM
gi-4940	801	135	1	1	NUM
gi-4940	801	136	1	1	NUM
gi-4940	801	137	1	1	NUM
gi-4940	801	138	nr	nr	NOUN
gi-4940	801	139	1	1	NUM
gi-4940	801	140	0	0	NUM
gi-4940	801	141	0	0	NUM
gi-4940	801	142	0	0	NUM
gi-4940	801	143	0	0	NUM
gi-4940	801	144	0	0	NUM
gi-4940	801	145	1	1	NUM
gi-4940	801	146	nd	nd	NUM
gi-4940	801	147	0	0	NUM
gi-4940	801	148	0	0	NUM
gi-4940	801	149	0	0	NUM
gi-4940	801	150	0	0	NUM
gi-4940	801	151	0	0	NUM
gi-4940	801	152	0	0	NUM
gi-4940	801	153	0	0	NUM
gi-4940	801	154	hassler	hassler	PROPN
gi-4940	801	155	nt	nt	ADP
gi-4940	801	156	4	4	NUM
gi-4940	801	157	3	3	NUM
gi-4940	801	158	3	3	NUM
gi-4940	801	159	3	3	NUM
gi-4940	801	160	3	3	NUM
gi-4940	801	161	3	3	NUM
gi-4940	801	162	4	4	NUM
gi-4940	801	163	ns	ns	NUM
gi-4940	801	164	1	1	NUM
gi-4940	801	165	1	1	NUM
gi-4940	801	166	1	1	NUM
gi-4940	801	167	1	1	NUM
gi-4940	801	168	1	1	NUM
gi-4940	801	169	1	1	NUM
gi-4940	801	170	1	1	NUM
gi-4940	801	171	nr	nr	NOUN
gi-4940	801	172	0	0	NUM
gi-4940	801	173	0	0	NUM
gi-4940	801	174	0	0	NUM
gi-4940	801	175	0	0	NUM
gi-4940	801	176	0	0	NUM
gi-4940	801	177	0	0	NUM
gi-4940	801	178	0	0	NUM
gi-4940	801	179	nd	nd	NOUN
gi-4940	801	180	0	0	NUM
gi-4940	801	181	0	0	NUM
gi-4940	801	182	0	0	NUM
gi-4940	801	183	0	0	NUM
gi-4940	801	184	0	0	NUM
gi-4940	801	185	0	0	SYM
gi-4940	801	186	0	0	NUM
gi-4940	801	187	geoinformatics	geoinformatic	NOUN
gi-4940	801	188	fce	fce	VERB
gi-4940	801	189	ctu	ctu	NOUN
gi-4940	801	190	17(2	17(2	NUM
gi-4940	801	191	)	)	PUNCT
gi-4940	801	192	,	,	PUNCT
gi-4940	802	1	2018	2018	NUM
gi-4940	802	2	58	58	NUM
gi-4940	802	3	t.	t.	NOUN
gi-4940	802	4	bayer	bayer	PROPN
gi-4940	802	5	:	:	PUNCT
gi-4940	802	6	plotting	plot	VERB
gi-4940	802	7	the	the	DET
gi-4940	802	8	map	map	NOUN
gi-4940	802	9	projection	projection	NOUN
gi-4940	802	10	graticule	graticule	NOUN
gi-4940	802	11	with	with	ADP
gi-4940	802	12	discontinuities	discontinuity	NOUN
gi-4940	802	13	table	table	NOUN
gi-4940	802	14	5	5	NUM
gi-4940	802	15	:	:	PUNCT
gi-4940	802	16	the	the	DET
gi-4940	802	17	amount	amount	NOUN
gi-4940	802	18	of	of	ADP
gi-4940	802	19	splits	split	NOUN
gi-4940	802	20	ns	n	VERB
gi-4940	802	21	,	,	PUNCT
gi-4940	802	22	processed	process	VERB
gi-4940	802	23	tiles	tile	NOUN
gi-4940	802	24	nt	not	PART
gi-4940	802	25	,	,	PUNCT
gi-4940	802	26	interval	interval	NOUN
gi-4940	802	27	resizing	resize	VERB
gi-4940	802	28	nr	nr	PRON
gi-4940	802	29	,	,	PUNCT
gi-4940	802	30	deleted	delete	VERB
gi-4940	802	31	intervals	interval	NOUN
gi-4940	802	32	nd	nd	ADP
gi-4940	802	33	depending	depend	VERB
gi-4940	802	34	on	on	ADP
gi-4940	802	35	λ′0	λ′0	PROPN
gi-4940	802	36	and	and	CCONJ
gi-4940	802	37	the	the	DET
gi-4940	802	38	threshold	threshold	NOUN
gi-4940	802	39	ε	ε	PROPN
gi-4940	802	40	.	.	PROPN
gi-4940	802	41	projection	projection	PROPN
gi-4940	802	42	λ′0	λ′0	PROPN
gi-4940	802	43	0.001	0.001	NUM
gi-4940	802	44	◦	◦	NOUN
gi-4940	802	45	30.001	30.001	NUM
gi-4940	802	46	◦	◦	NOUN
gi-4940	802	47	60.001	60.001	NUM
gi-4940	802	48	◦	◦	NOUN
gi-4940	802	49	90.001	90.001	NUM
gi-4940	802	50	◦	◦	NOUN
gi-4940	802	51	120.001	120.001	NUM
gi-4940	802	52	◦	◦	NOUN
gi-4940	802	53	150.001	150.001	NUM
gi-4940	802	54	◦	◦	NOUN
gi-4940	802	55	179.999	179.999	NUM
gi-4940	802	56	◦	◦	NOUN
gi-4940	802	57	fournier	fourni	ADJ
gi-4940	802	58	i.	i.	PROPN
gi-4940	802	59	nt	nt	PROPN
gi-4940	802	60	4/17/145/	4/17/145/	PROPN
gi-4940	802	61	1435	1435	NUM
gi-4940	802	62	3/17/145/	3/17/145/	PROPN
gi-4940	802	63	1435	1435	NUM
gi-4940	802	64	3/17/145/	3/17/145/	PROPN
gi-4940	802	65	1435	1435	NUM
gi-4940	802	66	13/65/661/	13/65/661/	NUM
gi-4940	802	67	6591	6591	NUM
gi-4940	802	68	3/17/145/	3/17/145/	NUM
gi-4940	802	69	1435	1435	NUM
gi-4940	802	70	3/17/145/	3/17/145/	PROPN
gi-4940	802	71	1435	1435	NUM
gi-4940	802	72	4/17/145/	4/17/145/	PROPN
gi-4940	802	73	1435	1435	NUM
gi-4940	802	74	ns	ns	NUM
gi-4940	802	75	1/1/1/2	1/1/1/2	NUM
gi-4940	802	76	1/1/1/2	1/1/1/2	NUM
gi-4940	802	77	1/1/1/2	1/1/1/2	NUM
gi-4940	803	1	5/5/5/6	5/5/5/6	NUM
gi-4940	803	2	1/1/1/2	1/1/1/2	NUM
gi-4940	803	3	1/1/1/2	1/1/1/2	NUM
gi-4940	804	1	1/1/1/2	1/1/1/2	NUM
gi-4940	804	2	nr	nr	PRON
gi-4940	804	3	1/7/71/	1/7/71/	NUM
gi-4940	804	4	1212	1212	NUM
gi-4940	804	5	0/7/71/	0/7/71/	NUM
gi-4940	804	6	1212	1212	NUM
gi-4940	804	7	0/7/71/	0/7/71/	NUM
gi-4940	804	8	1212	1212	NUM
gi-4940	804	9	1/27/325/	1/27/325/	NUM
gi-4940	804	10	5786	5786	NUM
gi-4940	804	11	0/7/71/	0/7/71/	NUM
gi-4940	804	12	1212	1212	NUM
gi-4940	804	13	0/7/71/	0/7/71/	NUM
gi-4940	804	14	1212	1212	NUM
gi-4940	804	15	1/7/71/	1/7/71/	NUM
gi-4940	804	16	1212	1212	NUM
gi-4940	804	17	nd	nd	NOUN
gi-4940	804	18	0/0/0/1	0/0/0/1	NOUN
gi-4940	804	19	0/0/0/1	0/0/0/1	NOUN
gi-4940	804	20	0/0/0/1	0/0/0/1	NOUN
gi-4940	804	21	0/0/0/1	0/0/0/1	NOUN
gi-4940	804	22	0/0/0/1	0/0/0/1	NOUN
gi-4940	804	23	0/0/0/1	0/0/0/1	NOUN
gi-4940	804	24	0/0/0/1	0/0/0/1	X
gi-4940	805	1	van	van	PROPN
gi-4940	805	2	der	der	NOUN
gi-4940	805	3	grinten	grinten	PROPN
gi-4940	805	4	i.	i.	PROPN
gi-4940	805	5	nt	nt	PROPN
gi-4940	806	1	5/27/265/	5/27/265/	NUM
gi-4940	806	2	2633	2633	NUM
gi-4940	807	1	5/27/259/	5/27/259/	NUM
gi-4940	807	2	2577	2577	NUM
gi-4940	807	3	5/27/259/	5/27/259/	NUM
gi-4940	807	4	2577	2577	NUM
gi-4940	807	5	5/27/259/	5/27/259/	NUM
gi-4940	807	6	2577	2577	NUM
gi-4940	807	7	5/27/259/	5/27/259/	NUM
gi-4940	807	8	2577	2577	NUM
gi-4940	807	9	5/27/259/	5/27/259/	NUM
gi-4940	807	10	2577	2577	NUM
gi-4940	807	11	5/27/259/	5/27/259/	NUM
gi-4940	807	12	2633	2633	NUM
gi-4940	807	13	ns	ns	NUM
gi-4940	807	14	1/1/3/4	1/1/3/4	NUM
gi-4940	807	15	1/1/1/2	1/1/1/2	NUM
gi-4940	808	1	1/1/1/2	1/1/1/2	NUM
gi-4940	808	2	1/1/1/2	1/1/1/2	NUM
gi-4940	809	1	1/1/1/2	1/1/1/2	NUM
gi-4940	810	1	1/1/1/2	1/1/1/2	NUM
gi-4940	811	1	1/1/1/2	1/1/1/2	NUM
gi-4940	811	2	nr	nr	PROPN
gi-4940	811	3	1/12/130/	1/12/130/	PROPN
gi-4940	811	4	2311	2311	NUM
gi-4940	811	5	1/12/128/	1/12/128/	NUM
gi-4940	811	6	2283	2283	NUM
gi-4940	811	7	1/12/128/	1/12/128/	NUM
gi-4940	811	8	2283	2283	NUM
gi-4940	811	9	1/12/128/	1/12/128/	NUM
gi-4940	811	10	2283	2283	NUM
gi-4940	811	11	1/12/128/	1/12/128/	NUM
gi-4940	811	12	2283	2283	NUM
gi-4940	811	13	1/12/128/	1/12/128/	NUM
gi-4940	811	14	2283	2283	NUM
gi-4940	811	15	1/12/128/	1/12/128/	NUM
gi-4940	811	16	2311	2311	NUM
gi-4940	811	17	nd	nd	SYM
gi-4940	811	18	0/0/0/1	0/0/0/1	NOUN
gi-4940	811	19	0/0/0/1	0/0/0/1	NOUN
gi-4940	811	20	0/0/0/1	0/0/0/1	NOUN
gi-4940	811	21	0/0/0/1	0/0/0/1	NOUN
gi-4940	811	22	0/0/0/1	0/0/0/1	NOUN
gi-4940	811	23	0/0/0/1	0/0/0/1	X
gi-4940	811	24	0/0/0/1	0/0/0/1	X
gi-4940	811	25	ortelius	ortelius	ADJ
gi-4940	811	26	oval	oval	NOUN
gi-4940	811	27	nt	nt	ADP
gi-4940	811	28	2/2/5/58	2/2/5/58	PROPN
gi-4940	811	29	1/1/1/1	1/1/1/1	NUM
gi-4940	811	30	1/1/1/1	1/1/1/1	NUM
gi-4940	811	31	2/2/1/1	2/2/1/1	NUM
gi-4940	811	32	1/1/1/1	1/1/1/1	NUM
gi-4940	811	33	1/1/1/1	1/1/1/1	NUM
gi-4940	811	34	2/2/5/58	2/2/5/58	NUM
gi-4940	811	35	ns	ns	NUM
gi-4940	811	36	0/0/1/3	0/0/1/3	NOUN
gi-4940	811	37	0/0/0/0	0/0/0/0	NUM
gi-4940	811	38	0/0/0/0	0/0/0/0	NUM
gi-4940	812	1	0/0/0/0	0/0/0/0	NUM
gi-4940	812	2	0/0/0/0	0/0/0/0	NUM
gi-4940	813	1	0/0/0/0	0/0/0/0	NUM
gi-4940	813	2	0/0/1/3	0/0/1/3	NUM
gi-4940	814	1	nr	nr	NOUN
gi-4940	814	2	0/0/1/38	0/0/1/38	NOUN
gi-4940	814	3	0/0/0/0	0/0/0/0	NUM
gi-4940	815	1	0/0/0/0	0/0/0/0	NUM
gi-4940	815	2	1/1/0/0	1/1/0/0	NUM
gi-4940	815	3	0/0/0/0	0/0/0/0	NUM
gi-4940	816	1	0/0/0/0	0/0/0/0	NUM
gi-4940	816	2	1/1/2/39	1/1/2/39	NUM
gi-4940	817	1	nd	nd	NOUN
gi-4940	817	2	0/0/0/0	0/0/0/0	NUM
gi-4940	817	3	0/0/0/0	0/0/0/0	NUM
gi-4940	818	1	0/0/0/0	0/0/0/0	NUM
gi-4940	818	2	0/0/0/0	0/0/0/0	NUM
gi-4940	819	1	0/0/0/0	0/0/0/0	NUM
gi-4940	819	2	0/0/0/0	0/0/0/0	NUM
gi-4940	820	1	0/0/0/0	0/0/0/0	NUM
gi-4940	820	2	nicolosi	nicolosi	NOUN
gi-4940	820	3	nt	not	PART
gi-4940	821	1	5/47/453/	5/47/453/	NUM
gi-4940	821	2	4519	4519	NUM
gi-4940	821	3	3/47/453/	3/47/453/	ADJ
gi-4940	821	4	4519	4519	NUM
gi-4940	822	1	3/47/453/	3/47/453/	NUM
gi-4940	822	2	4519	4519	NUM
gi-4940	822	3	13/95/969/	13/95/969/	NUM
gi-4940	822	4	9576	9576	NUM
gi-4940	822	5	3/47/453/	3/47/453/	NUM
gi-4940	822	6	4519	4519	NUM
gi-4940	822	7	3/47/453/	3/47/453/	NUM
gi-4940	822	8	4519	4519	NUM
gi-4940	822	9	4/47/453/	4/47/453/	NUM
gi-4940	822	10	4519	4519	NUM
gi-4940	822	11	ns	ns	NUM
gi-4940	822	12	1/1/1/2	1/1/1/2	NUM
gi-4940	822	13	1/1/1/2	1/1/1/2	NUM
gi-4940	822	14	1/1/1/2	1/1/1/2	NUM
gi-4940	823	1	5/5/5/6	5/5/5/6	NUM
gi-4940	823	2	1/1/1/2	1/1/1/2	NUM
gi-4940	823	3	1/1/1/2	1/1/1/2	NUM
gi-4940	824	1	1/1/1/2	1/1/1/2	NUM
gi-4940	824	2	nr	nr	PROPN
gi-4940	824	3	1/22/225/	1/22/225/	PROPN
gi-4940	824	4	4254	4254	NUM
gi-4940	824	5	0/22/225/	0/22/225/	PROPN
gi-4940	824	6	4254	4254	NUM
gi-4940	824	7	0/22/225/	0/22/225/	PROPN
gi-4940	824	8	4254	4254	NUM
gi-4940	825	1	1/42/479/	1/42/479/	NUM
gi-4940	825	2	8828	8828	NUM
gi-4940	825	3	0/22/225/	0/22/225/	PROPN
gi-4940	825	4	4254	4254	NUM
gi-4940	825	5	0/22/225/	0/22/225/	NUM
gi-4940	825	6	4254	4254	NUM
gi-4940	826	1	1/22/225/	1/22/225/	NUM
gi-4940	826	2	4254	4254	NUM
gi-4940	826	3	nd	nd	NOUN
gi-4940	826	4	0/0/0/1	0/0/0/1	X
gi-4940	826	5	0/0/0/1	0/0/0/1	NUM
gi-4940	826	6	0/0/0/1	0/0/0/1	NOUN
gi-4940	826	7	0/0/0/1	0/0/0/1	NOUN
gi-4940	826	8	0/0/0/1	0/0/0/1	NUM
gi-4940	826	9	0/0/0/1	0/0/0/1	X
gi-4940	826	10	0/0/1/1	0/0/1/1	PROPN
gi-4940	826	11	hassler	hassler	PROPN
gi-4940	826	12	nt	nt	ADP
gi-4940	826	13	3/3/5/31	3/3/5/31	PROPN
gi-4940	827	1	3/3/5/31	3/3/5/31	NUM
gi-4940	827	2	3/3/5/31	3/3/5/31	NUM
gi-4940	828	1	3/3/5/31	3/3/5/31	NUM
gi-4940	829	1	3/3/5/31	3/3/5/31	NUM
gi-4940	830	1	3/3/5/31	3/3/5/31	NUM
gi-4940	830	2	3/3/5/31	3/3/5/31	NUM
gi-4940	830	3	ns	ns	NUM
gi-4940	830	4	1/1/1/1	1/1/1/1	NUM
gi-4940	830	5	1/1/1/1	1/1/1/1	NUM
gi-4940	830	6	1/1/1/1	1/1/1/1	NUM
gi-4940	830	7	1/1/1/1	1/1/1/1	NUM
gi-4940	830	8	1/1/1/1	1/1/1/1	NUM
gi-4940	830	9	1/1/1/1	1/1/1/1	NUM
gi-4940	830	10	1/1/1/1	1/1/1/1	NUM
gi-4940	830	11	nr	nr	NOUN
gi-4940	830	12	0/0/1/14	0/0/1/14	NUM
gi-4940	830	13	0/0/1/14	0/0/1/14	NUM
gi-4940	830	14	0/0/1/14	0/0/1/14	NUM
gi-4940	830	15	0/0/1/14	0/0/1/14	NUM
gi-4940	830	16	0/0/1/14	0/0/1/14	NUM
gi-4940	830	17	0/0/1/14	0/0/1/14	NUM
gi-4940	830	18	0/0/1/14	0/0/1/14	NUM
gi-4940	830	19	nd	nd	NOUN
gi-4940	830	20	0/0/0/0	0/0/0/0	NUM
gi-4940	830	21	0/0/0/0	0/0/0/0	NUM
gi-4940	831	1	0/0/0/0	0/0/0/0	NUM
gi-4940	831	2	0/0/0/0	0/0/0/0	NUM
gi-4940	832	1	0/0/0/0	0/0/0/0	NUM
gi-4940	833	1	0/0/0/0	0/0/0/0	NUM
gi-4940	834	1	0/0/0/0	0/0/0/0	NUM
gi-4940	834	2	central	central	ADJ
gi-4940	834	3	meridian	meridian	NOUN
gi-4940	834	4	representing	represent	VERB
gi-4940	834	5	multiples	multiple	NOUN
gi-4940	834	6	of	of	ADP
gi-4940	834	7	30	30	NUM
gi-4940	834	8	◦	◦	NOUN
gi-4940	834	9	,	,	PUNCT
gi-4940	834	10	are	be	AUX
gi-4940	834	11	involved	involve	VERB
gi-4940	834	12	.	.	PUNCT
gi-4940	835	1	all	all	DET
gi-4940	835	2	projections	projection	NOUN
gi-4940	835	3	are	be	AUX
gi-4940	835	4	proposed	propose	VERB
gi-4940	835	5	in	in	ADP
gi-4940	835	6	the	the	DET
gi-4940	835	7	oblique	oblique	ADJ
gi-4940	835	8	aspect	aspect	NOUN
gi-4940	835	9	,	,	PUNCT
gi-4940	835	10	where	where	SCONJ
gi-4940	835	11	k	k	NOUN
gi-4940	835	12	=	=	PUNCT
gi-4940	836	1	[	[	X
gi-4940	836	2	50	50	NUM
gi-4940	836	3	◦	◦	NOUN
gi-4940	836	4	,	,	PUNCT
gi-4940	836	5	20	20	NUM
gi-4940	836	6	◦	◦	NOUN
gi-4940	836	7	]	]	PUNCT
gi-4940	836	8	.	.	PUNCT
gi-4940	837	1	the	the	DET
gi-4940	837	2	results	result	NOUN
gi-4940	837	3	are	be	AUX
gi-4940	837	4	summarized	summarize	VERB
gi-4940	837	5	in	in	ADP
gi-4940	837	6	tab	tab	NOUN
gi-4940	837	7	.	.	PUNCT
gi-4940	838	1	3	3	X
gi-4940	838	2	.	.	X
gi-4940	839	1	it	it	PRON
gi-4940	839	2	is	be	AUX
gi-4940	839	3	evident	evident	ADJ
gi-4940	839	4	that	that	SCONJ
gi-4940	839	5	the	the	DET
gi-4940	839	6	quantitative	quantitative	ADJ
gi-4940	839	7	parameters	parameter	NOUN
gi-4940	839	8	of	of	ADP
gi-4940	839	9	the	the	DET
gi-4940	839	10	algorithm	algorithm	NOUN
gi-4940	839	11	depend	depend	VERB
gi-4940	839	12	on	on	ADP
gi-4940	839	13	λ′0	λ′0	PROPN
gi-4940	839	14	.	.	PUNCT
gi-4940	840	1	if	if	SCONJ
gi-4940	840	2	λ′0	λ′0	PROPN
gi-4940	840	3	coincides	coincide	VERB
gi-4940	840	4	with	with	ADP
gi-4940	840	5	the	the	DET
gi-4940	840	6	singularity	singularity	NOUN
gi-4940	840	7	,	,	PUNCT
gi-4940	840	8	the	the	DET
gi-4940	840	9	number	number	NOUN
gi-4940	840	10	of	of	ADP
gi-4940	840	11	interval	interval	NOUN
gi-4940	840	12	corrections	correction	NOUN
gi-4940	840	13	as	as	ADV
gi-4940	840	14	well	well	ADV
gi-4940	840	15	as	as	ADP
gi-4940	840	16	the	the	DET
gi-4940	840	17	amount	amount	NOUN
gi-4940	840	18	of	of	ADP
gi-4940	840	19	processed	process	VERB
gi-4940	840	20	tiles	tile	NOUN
gi-4940	840	21	increase	increase	NOUN
gi-4940	840	22	and	and	CCONJ
gi-4940	840	23	vice	vice	ADV
gi-4940	840	24	versa	versa	ADV
gi-4940	840	25	;	;	PUNCT
gi-4940	840	26	the	the	DET
gi-4940	840	27	maximum	maximum	ADJ
gi-4940	840	28	values	value	NOUN
gi-4940	840	29	can	can	AUX
gi-4940	840	30	be	be	AUX
gi-4940	840	31	found	find	VERB
gi-4940	840	32	for	for	ADP
gi-4940	840	33	λ′0	λ′0	NOUN
gi-4940	840	34	=	=	PUNCT
gi-4940	840	35	{	{	PUNCT
gi-4940	840	36	0	0	NUM
gi-4940	840	37	◦	◦	NOUN
gi-4940	840	38	,	,	PUNCT
gi-4940	840	39	90	90	NUM
gi-4940	840	40	◦	◦	NOUN
gi-4940	840	41	,	,	PUNCT
gi-4940	840	42	180	180	NUM
gi-4940	840	43	◦	◦	NOUN
gi-4940	840	44	}	}	PUNCT
gi-4940	840	45	,	,	PUNCT
gi-4940	840	46	which	which	PRON
gi-4940	840	47	is	be	AUX
gi-4940	840	48	in	in	ADP
gi-4940	840	49	accordance	accordance	NOUN
gi-4940	840	50	with	with	ADP
gi-4940	840	51	the	the	DET
gi-4940	840	52	detected	detect	VERB
gi-4940	840	53	singularities	singularity	NOUN
gi-4940	840	54	.	.	PUNCT
gi-4940	841	1	taking	take	VERB
gi-4940	841	2	into	into	ADP
gi-4940	841	3	account	account	NOUN
gi-4940	841	4	the	the	DET
gi-4940	841	5	complexity	complexity	NOUN
gi-4940	841	6	of	of	ADP
gi-4940	841	7	equations	equation	NOUN
gi-4940	841	8	,	,	PUNCT
gi-4940	841	9	the	the	DET
gi-4940	841	10	less	less	ADV
gi-4940	841	11	complicated	complicated	ADJ
gi-4940	841	12	formulas	formula	NOUN
gi-4940	841	13	with	with	ADP
gi-4940	841	14	few	few	ADJ
gi-4940	841	15	singularities	singularity	NOUN
gi-4940	841	16	are	be	AUX
gi-4940	841	17	constructed	construct	VERB
gi-4940	841	18	from	from	ADP
gi-4940	841	19	a	a	DET
gi-4940	841	20	smaller	small	ADJ
gi-4940	841	21	amount	amount	NOUN
gi-4940	841	22	of	of	ADP
gi-4940	841	23	tiles	tile	NOUN
gi-4940	841	24	.	.	PUNCT
gi-4940	842	1	due	due	ADP
gi-4940	842	2	to	to	ADP
gi-4940	842	3	the	the	DET
gi-4940	842	4	position	position	NOUN
gi-4940	842	5	of	of	ADP
gi-4940	842	6	k	k	PROPN
gi-4940	842	7	and	and	CCONJ
gi-4940	842	8	λ′0	λ′0	PROPN
gi-4940	842	9	,	,	PUNCT
gi-4940	842	10	there	there	PRON
gi-4940	842	11	are	be	VERB
gi-4940	842	12	neither	neither	CCONJ
gi-4940	842	13	resized	resized	ADJ
gi-4940	842	14	nor	nor	CCONJ
gi-4940	842	15	empty	empty	ADJ
gi-4940	842	16	intervals	interval	NOUN
gi-4940	842	17	.	.	PUNCT
gi-4940	843	1	in	in	ADP
gi-4940	843	2	general	general	ADJ
gi-4940	843	3	,	,	PUNCT
gi-4940	843	4	only	only	ADV
gi-4940	843	5	a	a	DET
gi-4940	843	6	few	few	ADJ
gi-4940	843	7	subdivisions	subdivision	NOUN
gi-4940	843	8	are	be	AUX
gi-4940	843	9	carried	carry	VERB
gi-4940	843	10	out	out	ADP
gi-4940	843	11	.	.	PUNCT
gi-4940	844	1	the	the	DET
gi-4940	844	2	impact	impact	NOUN
gi-4940	844	3	of	of	ADP
gi-4940	844	4	the	the	DET
gi-4940	844	5	numerical	numerical	ADJ
gi-4940	844	6	inaccuracy	inaccuracy	NOUN
gi-4940	844	7	.	.	PUNCT
gi-4940	845	1	the	the	DET
gi-4940	845	2	impact	impact	NOUN
gi-4940	845	3	of	of	ADP
gi-4940	845	4	numerical	numerical	ADJ
gi-4940	845	5	inaccuracies	inaccuracy	NOUN
gi-4940	845	6	will	will	AUX
gi-4940	845	7	also	also	ADV
gi-4940	845	8	be	be	AUX
gi-4940	845	9	illustrated	illustrate	VERB
gi-4940	845	10	.	.	PUNCT
gi-4940	846	1	all	all	DET
gi-4940	846	2	projections	projection	NOUN
gi-4940	846	3	are	be	AUX
gi-4940	846	4	proposed	propose	VERB
gi-4940	846	5	in	in	ADP
gi-4940	846	6	the	the	DET
gi-4940	846	7	transverse	transverse	NOUN
gi-4940	846	8	aspect	aspect	NOUN
gi-4940	846	9	,	,	PUNCT
gi-4940	846	10	where	where	SCONJ
gi-4940	846	11	k	k	NOUN
gi-4940	846	12	=	=	PUNCT
gi-4940	847	1	[	[	X
gi-4940	847	2	0	0	NUM
gi-4940	847	3	◦	◦	NOUN
gi-4940	847	4	,	,	PUNCT
gi-4940	847	5	90	90	NUM
gi-4940	847	6	◦	◦	NOUN
gi-4940	847	7	]	]	PUNCT
gi-4940	847	8	.	.	PUNCT
gi-4940	848	1	the	the	DET
gi-4940	848	2	central	central	ADJ
gi-4940	848	3	meridian	meridian	PROPN
gi-4940	848	4	shifts	shift	NOUN
gi-4940	848	5	are	be	AUX
gi-4940	848	6	not	not	PART
gi-4940	848	7	the	the	DET
gi-4940	848	8	exact	exact	ADJ
gi-4940	848	9	multiples	multiple	NOUN
gi-4940	848	10	of	of	ADP
gi-4940	848	11	30	30	NUM
gi-4940	848	12	◦	◦	NOUN
gi-4940	848	13	,	,	PUNCT
gi-4940	848	14	but	but	CCONJ
gi-4940	848	15	λ′0	λ′0	NOUN
gi-4940	848	16	=	=	PRON
gi-4940	848	17	{	{	PUNCT
gi-4940	848	18	0.001	0.001	NUM
gi-4940	848	19	◦	◦	NOUN
gi-4940	848	20	,	,	PUNCT
gi-4940	848	21	30.001	30.001	NUM
gi-4940	848	22	◦	◦	NOUN
gi-4940	848	23	,	,	PUNCT
gi-4940	848	24	...	...	PUNCT
gi-4940	848	25	,	,	PUNCT
gi-4940	848	26	150.001	150.001	NUM
gi-4940	848	27	◦	◦	NOUN
gi-4940	848	28	,	,	PUNCT
gi-4940	848	29	179.999	179.999	NUM
gi-4940	848	30	◦	◦	NOUN
gi-4940	848	31	}	}	PUNCT
gi-4940	848	32	.	.	PUNCT
gi-4940	849	1	therefore	therefore	ADV
gi-4940	849	2	,	,	PUNCT
gi-4940	849	3	some	some	DET
gi-4940	849	4	resizing	resizing	NOUN
gi-4940	849	5	steps	step	NOUN
gi-4940	849	6	are	be	AUX
gi-4940	849	7	expected	expect	VERB
gi-4940	849	8	.	.	PUNCT
gi-4940	850	1	the	the	DET
gi-4940	850	2	results	result	NOUN
gi-4940	850	3	are	be	AUX
gi-4940	850	4	summarized	summarize	VERB
gi-4940	850	5	in	in	ADP
gi-4940	850	6	tab	tab	NOUN
gi-4940	850	7	.	.	PUNCT
gi-4940	851	1	4	4	X
gi-4940	851	2	.	.	X
gi-4940	851	3	comparing	compare	VERB
gi-4940	851	4	the	the	DET
gi-4940	851	5	quantitative	quantitative	ADJ
gi-4940	851	6	parameters	parameter	NOUN
gi-4940	851	7	,	,	PUNCT
gi-4940	851	8	the	the	DET
gi-4940	851	9	number	number	NOUN
gi-4940	851	10	of	of	ADP
gi-4940	851	11	processed	process	VERB
gi-4940	851	12	tiles	tile	NOUN
gi-4940	851	13	nt	not	PART
gi-4940	851	14	decreased	decrease	VERB
gi-4940	851	15	,	,	PUNCT
gi-4940	851	16	but	but	CCONJ
gi-4940	851	17	some	some	DET
gi-4940	851	18	intervals	interval	NOUN
gi-4940	851	19	need	need	VERB
gi-4940	851	20	to	to	PART
gi-4940	851	21	be	be	AUX
gi-4940	851	22	resized	resize	VERB
gi-4940	851	23	.	.	PUNCT
gi-4940	852	1	after	after	ADP
gi-4940	852	2	this	this	DET
gi-4940	852	3	refinement	refinement	NOUN
gi-4940	852	4	they	they	PRON
gi-4940	852	5	become	become	VERB
gi-4940	852	6	correct	correct	ADJ
gi-4940	852	7	;	;	PUNCT
gi-4940	852	8	only	only	ADV
gi-4940	852	9	a	a	DET
gi-4940	852	10	single	single	ADJ
gi-4940	852	11	resizing	resizing	NOUN
gi-4940	852	12	step	step	NOUN
gi-4940	852	13	is	be	AUX
gi-4940	852	14	required	require	VERB
gi-4940	852	15	.	.	PUNCT
gi-4940	853	1	however	however	ADV
gi-4940	853	2	,	,	PUNCT
gi-4940	853	3	there	there	PRON
gi-4940	853	4	was	be	VERB
gi-4940	853	5	no	no	DET
gi-4940	853	6	need	need	NOUN
gi-4940	853	7	for	for	ADP
gi-4940	853	8	a	a	DET
gi-4940	853	9	deletion	deletion	NOUN
gi-4940	853	10	of	of	ADP
gi-4940	853	11	the	the	DET
gi-4940	853	12	empty	empty	ADJ
gi-4940	853	13	interval	interval	NOUN
gi-4940	853	14	.	.	PUNCT
gi-4940	854	1	it	it	PRON
gi-4940	854	2	is	be	AUX
gi-4940	854	3	evident	evident	ADJ
gi-4940	854	4	that	that	SCONJ
gi-4940	854	5	“	"	PUNCT
gi-4940	854	6	simple	simple	ADJ
gi-4940	854	7	”	"	PUNCT
gi-4940	854	8	equations	equation	NOUN
gi-4940	854	9	are	be	AUX
gi-4940	854	10	insensitive	insensitive	ADJ
gi-4940	854	11	to	to	ADP
gi-4940	854	12	the	the	DET
gi-4940	854	13	projection	projection	NOUN
gi-4940	854	14	aspect	aspect	NOUN
gi-4940	854	15	.	.	PUNCT
gi-4940	855	1	geoinformatics	geoinformatic	NOUN
gi-4940	855	2	fce	fce	VERB
gi-4940	855	3	ctu	ctu	NOUN
gi-4940	855	4	17(2	17(2	NUM
gi-4940	855	5	)	)	PUNCT
gi-4940	855	6	,	,	PUNCT
gi-4940	855	7	2018	2018	NUM
gi-4940	855	8	59	59	NUM
gi-4940	855	9	t.	t.	NOUN
gi-4940	855	10	bayer	bayer	NOUN
gi-4940	855	11	:	:	PUNCT
gi-4940	855	12	plotting	plot	VERB
gi-4940	855	13	the	the	DET
gi-4940	855	14	map	map	NOUN
gi-4940	855	15	projection	projection	NOUN
gi-4940	855	16	graticule	graticule	NOUN
gi-4940	855	17	with	with	ADP
gi-4940	855	18	discontinuities	discontinuity	NOUN
gi-4940	855	19	figure	figure	VERB
gi-4940	855	20	5.5	5.5	NUM
gi-4940	855	21	:	:	PUNCT
gi-4940	855	22	the	the	DET
gi-4940	855	23	list	list	NOUN
gi-4940	855	24	of	of	ADP
gi-4940	855	25	reconstructed	reconstructed	ADJ
gi-4940	855	26	graticules	graticule	NOUN
gi-4940	855	27	of	of	ADP
gi-4940	855	28	fournier	fournier	PROPN
gi-4940	855	29	i.	i.	PROPN
gi-4940	855	30	,	,	PUNCT
gi-4940	855	31	van	van	PROPN
gi-4940	855	32	der	der	NOUN
gi-4940	855	33	grinten	grinten	PROPN
gi-4940	855	34	i.	i.	PROPN
gi-4940	855	35	,	,	PUNCT
gi-4940	855	36	ortelius	ortelius	ADJ
gi-4940	855	37	oval	oval	NOUN
gi-4940	855	38	,	,	PUNCT
gi-4940	855	39	nicolosi	nicolosi	NOUN
gi-4940	855	40	,	,	PUNCT
gi-4940	855	41	and	and	CCONJ
gi-4940	855	42	hassler	hassler	PROPN
gi-4940	855	43	projections	projection	NOUN
gi-4940	855	44	using	use	VERB
gi-4940	855	45	combined	combined	ADJ
gi-4940	855	46	sampling	sampling	NOUN
gi-4940	855	47	,	,	PUNCT
gi-4940	855	48	α	α	NOUN
gi-4940	855	49	=	=	SYM
gi-4940	855	50	5	5	NUM
gi-4940	855	51	◦	◦	NOUN
gi-4940	855	52	;	;	PUNCT
gi-4940	855	53	the	the	DET
gi-4940	855	54	central	central	ADJ
gi-4940	855	55	meridian	meridian	PROPN
gi-4940	855	56	shifts	shift	NOUN
gi-4940	855	57	λ′0	λ′0	X
gi-4940	856	1	=	=	SYM
gi-4940	856	2	90.001	90.001	NUM
gi-4940	856	3	◦	◦	NOUN
gi-4940	856	4	,	,	PUNCT
gi-4940	856	5	λ′0	λ′0	X
gi-4940	856	6	=	=	SYM
gi-4940	856	7	179.999	179.999	NUM
gi-4940	856	8	◦	◦	NOUN
gi-4940	856	9	.	.	PUNCT
gi-4940	857	1	geoinformatics	geoinformatic	NOUN
gi-4940	857	2	fce	fce	VERB
gi-4940	857	3	ctu	ctu	NOUN
gi-4940	857	4	17(2	17(2	NUM
gi-4940	857	5	)	)	PUNCT
gi-4940	857	6	,	,	PUNCT
gi-4940	857	7	2018	2018	NUM
gi-4940	857	8	60	60	NUM
gi-4940	857	9	t.	t.	NOUN
gi-4940	857	10	bayer	bayer	NOUN
gi-4940	857	11	:	:	PUNCT
gi-4940	857	12	plotting	plot	VERB
gi-4940	857	13	the	the	DET
gi-4940	857	14	map	map	NOUN
gi-4940	857	15	projection	projection	NOUN
gi-4940	857	16	graticule	graticule	NOUN
gi-4940	857	17	with	with	ADP
gi-4940	857	18	discontinuities	discontinuity	NOUN
gi-4940	857	19	the	the	DET
gi-4940	857	20	impact	impact	NOUN
gi-4940	857	21	of	of	ADP
gi-4940	857	22	the	the	DET
gi-4940	857	23	central	central	ADJ
gi-4940	857	24	meridian	meridian	PROPN
gi-4940	857	25	shift	shift	NOUN
gi-4940	857	26	λ′0	λ′0	PROPN
gi-4940	857	27	and	and	CCONJ
gi-4940	857	28	the	the	DET
gi-4940	857	29	numerical	numerical	ADJ
gi-4940	857	30	threshold	threshold	PROPN
gi-4940	857	31	ε	ε	PROPN
gi-4940	857	32	.	.	PUNCT
gi-4940	858	1	the	the	DET
gi-4940	858	2	last	last	ADJ
gi-4940	858	3	test	test	NOUN
gi-4940	858	4	measures	measure	VERB
gi-4940	858	5	the	the	DET
gi-4940	858	6	quantitative	quantitative	ADJ
gi-4940	858	7	parameters	parameter	NOUN
gi-4940	858	8	of	of	ADP
gi-4940	858	9	the	the	DET
gi-4940	858	10	algorithms	algorithm	NOUN
gi-4940	858	11	depending	depend	VERB
gi-4940	858	12	on	on	ADP
gi-4940	858	13	the	the	DET
gi-4940	858	14	value	value	NOUN
gi-4940	858	15	of	of	ADP
gi-4940	858	16	the	the	DET
gi-4940	858	17	threshold	threshold	NOUN
gi-4940	858	18	ε	ε	PROPN
gi-4940	858	19	.	.	PUNCT
gi-4940	859	1	this	this	DET
gi-4940	859	2	value	value	NOUN
gi-4940	859	3	has	have	VERB
gi-4940	859	4	a	a	DET
gi-4940	859	5	strong	strong	ADJ
gi-4940	859	6	influence	influence	NOUN
gi-4940	859	7	on	on	ADP
gi-4940	859	8	whether	whether	SCONJ
gi-4940	859	9	the	the	DET
gi-4940	859	10	result	result	NOUN
gi-4940	859	11	will	will	AUX
gi-4940	859	12	be	be	AUX
gi-4940	859	13	classified	classify	VERB
gi-4940	859	14	as	as	ADP
gi-4940	859	15	a	a	DET
gi-4940	859	16	singularity	singularity	NOUN
gi-4940	859	17	.	.	PUNCT
gi-4940	860	1	for	for	ADP
gi-4940	860	2	testing	testing	NOUN
gi-4940	860	3	,	,	PUNCT
gi-4940	860	4	the	the	DET
gi-4940	860	5	following	follow	VERB
gi-4940	860	6	values	value	NOUN
gi-4940	860	7	are	be	AUX
gi-4940	860	8	involved	involve	VERB
gi-4940	860	9	:	:	PUNCT
gi-4940	860	10	ε	ε	PROPN
gi-4940	860	11	=	=	PUNCT
gi-4940	860	12	{	{	PUNCT
gi-4940	860	13	1.0e−6	1.0e−6	NUM
gi-4940	860	14	,	,	PUNCT
gi-4940	860	15	1.0e−7	1.0e−7	NUM
gi-4940	860	16	,	,	PUNCT
gi-4940	860	17	1.0e−8	1.0e−8	NUM
gi-4940	860	18	,	,	PUNCT
gi-4940	860	19	1.0e−9	1.0e−9	NUM
gi-4940	860	20	}	}	PUNCT
gi-4940	860	21	;	;	PUNCT
gi-4940	860	22	the	the	DET
gi-4940	860	23	cartographic	cartographic	ADJ
gi-4940	860	24	parameters	parameter	NOUN
gi-4940	860	25	remain	remain	VERB
gi-4940	860	26	unchained	unchained	ADJ
gi-4940	860	27	.	.	PUNCT
gi-4940	861	1	the	the	DET
gi-4940	861	2	results	result	NOUN
gi-4940	861	3	are	be	AUX
gi-4940	861	4	summarized	summarize	VERB
gi-4940	861	5	in	in	ADP
gi-4940	861	6	tab	tab	NOUN
gi-4940	861	7	.	.	PUNCT
gi-4940	862	1	5	5	X
gi-4940	862	2	.	.	X
gi-4940	863	1	it	it	PRON
gi-4940	863	2	is	be	AUX
gi-4940	863	3	evident	evident	ADJ
gi-4940	863	4	that	that	SCONJ
gi-4940	863	5	the	the	DET
gi-4940	863	6	amount	amount	NOUN
gi-4940	863	7	of	of	ADP
gi-4940	863	8	tiles	tile	NOUN
gi-4940	863	9	nt	not	PART
gi-4940	863	10	strongly	strongly	ADV
gi-4940	863	11	depends	depend	VERB
gi-4940	863	12	on	on	ADP
gi-4940	863	13	ε	ε	PROPN
gi-4940	863	14	,	,	PUNCT
gi-4940	863	15	especially	especially	ADV
gi-4940	863	16	if	if	SCONJ
gi-4940	863	17	a	a	DET
gi-4940	863	18	singularity	singularity	NOUN
gi-4940	863	19	at	at	ADP
gi-4940	863	20	λ′	λ′	PROPN
gi-4940	863	21	exists	exist	VERB
gi-4940	863	22	.	.	PUNCT
gi-4940	864	1	increasing	increase	VERB
gi-4940	864	2	ε	ε	PROPN
gi-4940	864	3	by	by	ADP
gi-4940	864	4	one	one	NUM
gi-4940	864	5	order	order	NOUN
gi-4940	864	6	of	of	ADP
gi-4940	864	7	magnitude	magnitude	NOUN
gi-4940	864	8	,	,	PUNCT
gi-4940	864	9	the	the	DET
gi-4940	864	10	amount	amount	NOUN
gi-4940	864	11	of	of	ADP
gi-4940	864	12	tiles	tile	NOUN
gi-4940	864	13	nt	not	PART
gi-4940	864	14	changes	change	VERB
gi-4940	864	15	in	in	ADP
gi-4940	864	16	the	the	DET
gi-4940	864	17	same	same	ADJ
gi-4940	864	18	manner	manner	NOUN
gi-4940	864	19	.	.	PUNCT
gi-4940	865	1	taking	take	VERB
gi-4940	865	2	into	into	ADP
gi-4940	865	3	account	account	NOUN
gi-4940	865	4	the	the	DET
gi-4940	865	5	results	result	NOUN
gi-4940	865	6	,	,	PUNCT
gi-4940	865	7	it	it	PRON
gi-4940	865	8	does	do	AUX
gi-4940	865	9	not	not	PART
gi-4940	865	10	make	make	VERB
gi-4940	865	11	a	a	DET
gi-4940	865	12	sense	sense	NOUN
gi-4940	865	13	to	to	PART
gi-4940	865	14	use	use	VERB
gi-4940	865	15	values	value	NOUN
gi-4940	865	16	ε	ε	PROPN
gi-4940	865	17	<	<	X
gi-4940	865	18	1.0e−7	1.0e−7	NUM
gi-4940	865	19	.	.	PUNCT
gi-4940	866	1	the	the	DET
gi-4940	866	2	algorithm	algorithm	NOUN
gi-4940	866	3	is	be	AUX
gi-4940	866	4	slowing	slow	VERB
gi-4940	866	5	down	down	ADV
gi-4940	866	6	;	;	PUNCT
gi-4940	866	7	its	its	PRON
gi-4940	866	8	computational	computational	ADJ
gi-4940	866	9	demands	demand	NOUN
gi-4940	866	10	significantly	significantly	ADV
gi-4940	866	11	grow	grow	VERB
gi-4940	866	12	up	up	ADP
gi-4940	866	13	.	.	PUNCT
gi-4940	867	1	it	it	PRON
gi-4940	867	2	also	also	ADV
gi-4940	867	3	becomes	become	VERB
gi-4940	867	4	unstable	unstable	ADJ
gi-4940	867	5	and	and	CCONJ
gi-4940	867	6	may	may	AUX
gi-4940	867	7	lead	lead	VERB
gi-4940	867	8	to	to	ADP
gi-4940	867	9	the	the	DET
gi-4940	867	10	stack	stack	NOUN
gi-4940	867	11	overflow	overflow	NOUN
gi-4940	867	12	.	.	PUNCT
gi-4940	868	1	comparing	compare	VERB
gi-4940	868	2	the	the	DET
gi-4940	868	3	analyzed	analyze	VERB
gi-4940	868	4	projections	projection	NOUN
gi-4940	868	5	,	,	PUNCT
gi-4940	868	6	the	the	DET
gi-4940	868	7	worst	bad	ADJ
gi-4940	868	8	results	result	NOUN
gi-4940	868	9	are	be	AUX
gi-4940	868	10	provided	provide	VERB
gi-4940	868	11	by	by	ADP
gi-4940	868	12	the	the	DET
gi-4940	868	13	nicolosi	nicolosi	NOUN
gi-4940	868	14	projection	projection	NOUN
gi-4940	868	15	,	,	PUNCT
gi-4940	868	16	where	where	SCONJ
gi-4940	868	17	nt	not	PART
gi-4940	868	18	almost	almost	ADV
gi-4940	868	19	does	do	AUX
gi-4940	868	20	n’t	not	PART
gi-4940	868	21	depend	depend	VERB
gi-4940	868	22	on	on	ADP
gi-4940	868	23	λ′0	λ′0	PROPN
gi-4940	868	24	.	.	PUNCT
gi-4940	869	1	in	in	ADP
gi-4940	869	2	the	the	DET
gi-4940	869	3	most	most	ADV
gi-4940	869	4	pessimistic	pessimistic	ADJ
gi-4940	869	5	case	case	NOUN
gi-4940	869	6	,	,	PUNCT
gi-4940	869	7	almost	almost	ADV
gi-4940	869	8	10	10	NUM
gi-4940	869	9	000	000	NUM
gi-4940	869	10	tiles	tile	NOUN
gi-4940	869	11	are	be	AUX
gi-4940	869	12	required	require	VERB
gi-4940	869	13	.	.	PUNCT
gi-4940	870	1	on	on	ADP
gi-4940	870	2	the	the	DET
gi-4940	870	3	contrary	contrary	NOUN
gi-4940	870	4	,	,	PUNCT
gi-4940	870	5	the	the	DET
gi-4940	870	6	hassler	hassler	PROPN
gi-4940	870	7	projection	projection	NOUN
gi-4940	870	8	with	with	ADP
gi-4940	870	9	nt	not	PART
gi-4940	870	10	<	<	X
gi-4940	870	11	35	35	NUM
gi-4940	870	12	needs	need	VERB
gi-4940	870	13	less	less	ADJ
gi-4940	870	14	effort	effort	NOUN
gi-4940	870	15	.	.	PUNCT
gi-4940	871	1	summarize	summarize	VERB
gi-4940	871	2	the	the	DET
gi-4940	871	3	facts	fact	NOUN
gi-4940	871	4	,	,	PUNCT
gi-4940	871	5	the	the	DET
gi-4940	871	6	reconstruction	reconstruction	NOUN
gi-4940	871	7	algorithm	algorithm	NOUN
gi-4940	871	8	depends	depend	VERB
gi-4940	871	9	on	on	ADP
gi-4940	871	10	the	the	DET
gi-4940	871	11	number	number	NOUN
gi-4940	871	12	of	of	ADP
gi-4940	871	13	singularities	singularity	NOUN
gi-4940	871	14	as	as	ADV
gi-4940	871	15	well	well	ADV
gi-4940	871	16	as	as	ADP
gi-4940	871	17	on	on	ADP
gi-4940	871	18	the	the	DET
gi-4940	871	19	threshold	threshold	NOUN
gi-4940	871	20	ε	ε	PROPN
gi-4940	871	21	.	.	PROPN
gi-4940	872	1	for	for	ADP
gi-4940	872	2	ε	ε	PROPN
gi-4940	872	3	≥	≥	NUM
gi-4940	872	4	1.0e−6	1.0e−6	NUM
gi-4940	872	5	,	,	PUNCT
gi-4940	872	6	only	only	ADV
gi-4940	872	7	a	a	DET
gi-4940	872	8	few	few	ADJ
gi-4940	872	9	splits	split	NOUN
gi-4940	872	10	are	be	AUX
gi-4940	872	11	required	require	VERB
gi-4940	872	12	.	.	PUNCT
gi-4940	873	1	all	all	DET
gi-4940	873	2	the	the	DET
gi-4940	873	3	reconstructed	reconstructed	ADJ
gi-4940	873	4	graticules	graticules	NOUN
gi-4940	873	5	of	of	ADP
gi-4940	873	6	the	the	DET
gi-4940	873	7	analyzed	analyze	VERB
gi-4940	873	8	projections	projection	NOUN
gi-4940	873	9	for	for	ADP
gi-4940	873	10	λ′0	λ′0	PROPN
gi-4940	873	11	=	=	SYM
gi-4940	873	12	90.001	90.001	NUM
gi-4940	873	13	◦	◦	NOUN
gi-4940	873	14	,	,	PUNCT
gi-4940	873	15	and	and	CCONJ
gi-4940	873	16	λ′0	λ′0	NOUN
gi-4940	873	17	=	=	SYM
gi-4940	873	18	179.999	179.999	NUM
gi-4940	873	19	◦	◦	NOUN
gi-4940	873	20	can	can	AUX
gi-4940	873	21	be	be	AUX
gi-4940	873	22	found	find	VERB
gi-4940	873	23	in	in	ADP
gi-4940	873	24	fig	fig	NOUN
gi-4940	873	25	.	.	PUNCT
gi-4940	874	1	5.5	5.5	NUM
gi-4940	874	2	.	.	NOUN
gi-4940	875	1	6	6	NUM
gi-4940	875	2	.	.	X
gi-4940	875	3	conclusion	conclusion	NOUN
gi-4940	875	4	this	this	DET
gi-4940	875	5	article	article	NOUN
gi-4940	875	6	presented	present	VERB
gi-4940	875	7	a	a	DET
gi-4940	875	8	new	new	ADJ
gi-4940	875	9	algorithm	algorithm	NOUN
gi-4940	875	10	for	for	ADP
gi-4940	875	11	the	the	DET
gi-4940	875	12	combined	combine	VERB
gi-4940	875	13	sampling	sampling	NOUN
gi-4940	875	14	of	of	ADP
gi-4940	875	15	the	the	DET
gi-4940	875	16	projection	projection	NOUN
gi-4940	875	17	graticule	graticule	NOUN
gi-4940	875	18	handling	handle	VERB
gi-4940	875	19	all	all	DET
gi-4940	875	20	constant	constant	ADJ
gi-4940	875	21	values	value	NOUN
gi-4940	875	22	of	of	ADP
gi-4940	875	23	the	the	DET
gi-4940	875	24	projection	projection	NOUN
gi-4940	875	25	.	.	PUNCT
gi-4940	876	1	the	the	DET
gi-4940	876	2	proposed	propose	VERB
gi-4940	876	3	method	method	NOUN
gi-4940	876	4	combines	combine	VERB
gi-4940	876	5	the	the	DET
gi-4940	876	6	uniform	uniform	NOUN
gi-4940	876	7	and	and	CCONJ
gi-4940	876	8	adaptive	adaptive	ADJ
gi-4940	876	9	sampling	sample	VERB
gi-4940	876	10	techniques	technique	NOUN
gi-4940	876	11	with	with	ADP
gi-4940	876	12	the	the	DET
gi-4940	876	13	triple	triple	ADJ
gi-4940	876	14	recursive	recursive	ADJ
gi-4940	876	15	subdivision	subdivision	NOUN
gi-4940	876	16	.	.	PUNCT
gi-4940	877	1	it	it	PRON
gi-4940	877	2	controls	control	VERB
gi-4940	877	3	handling	handle	VERB
gi-4940	877	4	the	the	DET
gi-4940	877	5	discontinuities	discontinuity	NOUN
gi-4940	877	6	and	and	CCONJ
gi-4940	877	7	their	their	PRON
gi-4940	877	8	directions	direction	NOUN
gi-4940	877	9	;	;	PUNCT
gi-4940	877	10	the	the	DET
gi-4940	877	11	detection	detection	NOUN
gi-4940	877	12	criterion	criterion	NOUN
gi-4940	877	13	is	be	AUX
gi-4940	877	14	presented	present	VERB
gi-4940	877	15	in	in	ADP
gi-4940	877	16	sec	sec	PROPN
gi-4940	877	17	.	.	PROPN
gi-4940	877	18	3.1	3.1	NUM
gi-4940	877	19	.	.	PUNCT
gi-4940	878	1	in	in	ADP
gi-4940	878	2	general	general	ADJ
gi-4940	878	3	,	,	PUNCT
gi-4940	878	4	the	the	DET
gi-4940	878	5	splitting	splitting	NOUN
gi-4940	878	6	procedure	procedure	NOUN
gi-4940	878	7	is	be	AUX
gi-4940	878	8	sensitive	sensitive	ADJ
gi-4940	878	9	to	to	ADP
gi-4940	878	10	ε(if	ε(if	PROPN
gi-4940	878	11	λ′0	λ′0	PROPN
gi-4940	878	12	→	→	SYM
gi-4940	878	13	ε	ε	PROPN
gi-4940	878	14	)	)	PUNCT
gi-4940	878	15	as	as	ADV
gi-4940	878	16	well	well	ADV
gi-4940	878	17	as	as	ADP
gi-4940	878	18	to	to	ADP
gi-4940	878	19	the	the	DET
gi-4940	878	20	numerical	numerical	ADJ
gi-4940	878	21	errors	error	NOUN
gi-4940	878	22	of	of	ADP
gi-4940	878	23	intersections	intersection	NOUN
gi-4940	878	24	m′(λ	m′(λ	NOUN
gi-4940	878	25	)	)	PUNCT
gi-4940	878	26	and	and	CCONJ
gi-4940	878	27	m(λ	m(λ	PROPN
gi-4940	878	28	)	)	PUNCT
gi-4940	878	29	,	,	PUNCT
gi-4940	878	30	m′(λ	m′(λ	X
gi-4940	878	31	)	)	PUNCT
gi-4940	878	32	and	and	CCONJ
gi-4940	878	33	p(ϕ	p(ϕ	NUM
gi-4940	878	34	)	)	PUNCT
gi-4940	878	35	.	.	PUNCT
gi-4940	879	1	from	from	ADP
gi-4940	879	2	the	the	DET
gi-4940	879	3	topological	topological	ADJ
gi-4940	879	4	point	point	NOUN
gi-4940	879	5	of	of	ADP
gi-4940	879	6	view	view	NOUN
gi-4940	879	7	,	,	PUNCT
gi-4940	879	8	the	the	DET
gi-4940	879	9	meridian	meridian	ADJ
gi-4940	879	10	and	and	CCONJ
gi-4940	879	11	parallel	parallel	ADJ
gi-4940	879	12	intersections	intersection	NOUN
gi-4940	879	13	lack	lack	VERB
gi-4940	879	14	the	the	DET
gi-4940	879	15	vertex	vertex	NOUN
gi-4940	879	16	,	,	PUNCT
gi-4940	879	17	which	which	PRON
gi-4940	879	18	can	can	AUX
gi-4940	879	19	cause	cause	VERB
gi-4940	879	20	some	some	DET
gi-4940	879	21	problems	problem	NOUN
gi-4940	879	22	in	in	ADP
gi-4940	879	23	gis	gis	NOUN
gi-4940	879	24	processing	processing	NOUN
gi-4940	879	25	;	;	PUNCT
gi-4940	879	26	the	the	DET
gi-4940	879	27	dissolve	dissolve	NOUN
gi-4940	879	28	operation	operation	NOUN
gi-4940	879	29	needs	need	VERB
gi-4940	879	30	to	to	PART
gi-4940	879	31	be	be	AUX
gi-4940	879	32	applied	apply	VERB
gi-4940	879	33	before	before	ADV
gi-4940	879	34	.	.	PUNCT
gi-4940	880	1	the	the	DET
gi-4940	880	2	discontinuity	discontinuity	NOUN
gi-4940	880	3	detection	detection	NOUN
gi-4940	880	4	without	without	ADP
gi-4940	880	5	its	its	PRON
gi-4940	880	6	classification	classification	NOUN
gi-4940	880	7	(	(	PUNCT
gi-4940	880	8	or	or	CCONJ
gi-4940	880	9	,	,	PUNCT
gi-4940	880	10	a	a	DET
gi-4940	880	11	wrong	wrong	ADJ
gi-4940	880	12	classification	classification	NOUN
gi-4940	880	13	)	)	PUNCT
gi-4940	880	14	leads	lead	VERB
gi-4940	880	15	to	to	ADP
gi-4940	880	16	the	the	DET
gi-4940	880	17	duplication	duplication	NOUN
gi-4940	880	18	of	of	ADP
gi-4940	880	19	lines	line	NOUN
gi-4940	880	20	along	along	ADP
gi-4940	880	21	the	the	DET
gi-4940	880	22	singularities	singularity	NOUN
gi-4940	880	23	.	.	PUNCT
gi-4940	881	1	the	the	DET
gi-4940	881	2	idea	idea	NOUN
gi-4940	881	3	of	of	ADP
gi-4940	881	4	splitting	split	VERB
gi-4940	881	5	the	the	DET
gi-4940	881	6	interval	interval	NOUN
gi-4940	881	7	to	to	ADP
gi-4940	881	8	the	the	DET
gi-4940	881	9	set	set	NOUN
gi-4940	881	10	of	of	ADP
gi-4940	881	11	disjoint	disjoint	NOUN
gi-4940	881	12	intervals	interval	NOUN
gi-4940	881	13	without	without	ADP
gi-4940	881	14	the	the	DET
gi-4940	881	15	singularities	singularity	NOUN
gi-4940	881	16	is	be	AUX
gi-4940	881	17	efficient	efficient	ADJ
gi-4940	881	18	and	and	CCONJ
gi-4940	881	19	works	work	VERB
gi-4940	881	20	for	for	ADP
gi-4940	881	21	any	any	DET
gi-4940	881	22	common	common	ADJ
gi-4940	881	23	projection	projection	NOUN
gi-4940	881	24	and	and	CCONJ
gi-4940	881	25	its	its	PRON
gi-4940	881	26	coordinate	coordinate	NOUN
gi-4940	881	27	functions	function	NOUN
gi-4940	881	28	.	.	PUNCT
gi-4940	882	1	compared	compare	VERB
gi-4940	882	2	to	to	ADP
gi-4940	882	3	the	the	DET
gi-4940	882	4	uniform	uniform	NOUN
gi-4940	882	5	sampling	sampling	NOUN
gi-4940	882	6	,	,	PUNCT
gi-4940	882	7	our	our	PRON
gi-4940	882	8	experiments	experiment	NOUN
gi-4940	882	9	confirmed	confirm	VERB
gi-4940	882	10	that	that	SCONJ
gi-4940	882	11	the	the	DET
gi-4940	882	12	combined	combine	VERB
gi-4940	882	13	sampling	sample	VERB
gi-4940	882	14	techniques	technique	NOUN
gi-4940	882	15	s1	s1	NOUN
gi-4940	882	16	-	-	PUNCT
gi-4940	882	17	s3	s3	NOUN
gi-4940	882	18	require	require	VERB
gi-4940	882	19	fewer	few	ADJ
gi-4940	882	20	data	datum	NOUN
gi-4940	882	21	in	in	ADP
gi-4940	882	22	regions	region	NOUN
gi-4940	882	23	with	with	ADP
gi-4940	882	24	the	the	DET
gi-4940	882	25	high	high	ADJ
gi-4940	882	26	curvature	curvature	NOUN
gi-4940	882	27	(	(	PUNCT
gi-4940	882	28	more	more	ADJ
gi-4940	882	29	than	than	ADP
gi-4940	882	30	five	five	NUM
gi-4940	882	31	times	time	NOUN
gi-4940	882	32	lower	low	ADJ
gi-4940	882	33	values	value	NOUN
gi-4940	882	34	of	of	ADP
gi-4940	882	35	α	α	NOUN
gi-4940	882	36	)	)	PUNCT
gi-4940	882	37	.	.	PUNCT
gi-4940	883	1	for	for	ADP
gi-4940	883	2	the	the	DET
gi-4940	883	3	circular	circular	ADJ
gi-4940	883	4	arcs	arc	NOUN
gi-4940	883	5	,	,	PUNCT
gi-4940	883	6	circles	circle	NOUN
gi-4940	883	7	or	or	CCONJ
gi-4940	883	8	ellipses	ellipsis	NOUN
gi-4940	883	9	the	the	DET
gi-4940	883	10	uniform	uniform	ADJ
gi-4940	883	11	sampling	sample	VERB
gi-4940	883	12	is	be	AUX
gi-4940	883	13	slightly	slightly	ADV
gi-4940	883	14	more	more	ADV
gi-4940	883	15	efficient	efficient	ADJ
gi-4940	883	16	.	.	PUNCT
gi-4940	884	1	the	the	DET
gi-4940	884	2	lowest	low	ADJ
gi-4940	884	3	data	data	NOUN
gi-4940	884	4	redundancy	redundancy	NOUN
gi-4940	884	5	refers	refer	VERB
gi-4940	884	6	to	to	ADP
gi-4940	884	7	the	the	DET
gi-4940	884	8	straight	straight	ADJ
gi-4940	884	9	lines	line	NOUN
gi-4940	884	10	,	,	PUNCT
gi-4940	884	11	only	only	ADV
gi-4940	884	12	1	1	NUM
gi-4940	884	13	%	%	NOUN
gi-4940	884	14	of	of	ADP
gi-4940	884	15	the	the	DET
gi-4940	884	16	uniform	uniform	NOUN
gi-4940	884	17	sampling	sample	VERB
gi-4940	884	18	data	datum	NOUN
gi-4940	884	19	is	be	AUX
gi-4940	884	20	sufficient	sufficient	ADJ
gi-4940	884	21	for	for	ADP
gi-4940	884	22	the	the	DET
gi-4940	884	23	polygonal	polygonal	ADJ
gi-4940	884	24	approximation	approximation	NOUN
gi-4940	884	25	.	.	PUNCT
gi-4940	885	1	this	this	PRON
gi-4940	885	2	is	be	AUX
gi-4940	885	3	beneficial	beneficial	ADJ
gi-4940	885	4	for	for	ADP
gi-4940	885	5	the	the	DET
gi-4940	885	6	cylindrical	cylindrical	ADJ
gi-4940	885	7	,	,	PUNCT
gi-4940	885	8	conic	conic	ADJ
gi-4940	885	9	,	,	PUNCT
gi-4940	885	10	azimuthal	azimuthal	ADJ
gi-4940	885	11	and	and	CCONJ
gi-4940	885	12	pseudocylindrical	pseudocylindrical	ADJ
gi-4940	885	13	projections	projection	NOUN
gi-4940	885	14	.	.	PUNCT
gi-4940	886	1	a	a	DET
gi-4940	886	2	minor	minor	ADJ
gi-4940	886	3	disadvantage	disadvantage	NOUN
gi-4940	886	4	of	of	ADP
gi-4940	886	5	the	the	DET
gi-4940	886	6	proposed	propose	VERB
gi-4940	886	7	solution	solution	NOUN
gi-4940	886	8	is	be	AUX
gi-4940	886	9	a	a	DET
gi-4940	886	10	slightly	slightly	ADV
gi-4940	886	11	complicated	complicated	ADJ
gi-4940	886	12	implementation	implementation	NOUN
gi-4940	886	13	of	of	ADP
gi-4940	886	14	the	the	DET
gi-4940	886	15	algorithms	algorithm	NOUN
gi-4940	886	16	,	,	PUNCT
gi-4940	886	17	the	the	DET
gi-4940	886	18	source	source	NOUN
gi-4940	886	19	code	code	NOUN
gi-4940	886	20	in	in	ADP
gi-4940	886	21	c++/java	c++/java	NOUN
gi-4940	886	22	is	be	AUX
gi-4940	886	23	available	available	ADJ
gi-4940	886	24	in	in	ADP
gi-4940	886	25	the	the	DET
gi-4940	886	26	github	github	PROPN
gi-4940	886	27	repository	repository	NOUN
gi-4940	886	28	https://github.com/bayertom/graticule	https://github.com/bayertom/graticule	NOUN
gi-4940	886	29	.	.	PUNCT
gi-4940	887	1	geoinformatics	geoinformatic	NOUN
gi-4940	887	2	fce	fce	VERB
gi-4940	887	3	ctu	ctu	NOUN
gi-4940	887	4	17(2	17(2	NUM
gi-4940	887	5	)	)	PUNCT
gi-4940	887	6	,	,	PUNCT
gi-4940	887	7	2018	2018	NUM
gi-4940	887	8	61	61	NUM
gi-4940	887	9	https://github.com/bayertom/graticule	https://github.com/bayertom/graticule	NOUN
gi-4940	887	10	t.	t.	NOUN
gi-4940	887	11	bayer	bayer	PROPN
gi-4940	887	12	:	:	PUNCT
gi-4940	887	13	plotting	plot	VERB
gi-4940	887	14	the	the	DET
gi-4940	887	15	map	map	NOUN
gi-4940	887	16	projection	projection	NOUN
gi-4940	887	17	graticule	graticule	NOUN
gi-4940	887	18	with	with	ADP
gi-4940	887	19	discontinuities	discontinuity	NOUN
gi-4940	887	20	references	reference	NOUN
gi-4940	887	21	[	[	X
gi-4940	887	22	1	1	NUM
gi-4940	887	23	]	]	PUNCT
gi-4940	887	24	giampietro	giampietro	NOUN
gi-4940	887	25	allasia	allasia	PROPN
gi-4940	887	26	,	,	PUNCT
gi-4940	887	27	renata	renata	PROPN
gi-4940	887	28	besenghi	besenghi	PROPN
gi-4940	887	29	,	,	PUNCT
gi-4940	887	30	and	and	CCONJ
gi-4940	887	31	roberto	roberto	PROPN
gi-4940	887	32	cavoretto	cavoretto	NOUN
gi-4940	887	33	.	.	PUNCT
gi-4940	888	1	“	"	PUNCT
gi-4940	888	2	adaptive	adaptive	ADJ
gi-4940	888	3	detection	detection	NOUN
gi-4940	888	4	and	and	CCONJ
gi-4940	888	5	approximation	approximation	NOUN
gi-4940	888	6	of	of	ADP
gi-4940	888	7	unknown	unknown	ADJ
gi-4940	888	8	surface	surface	NOUN
gi-4940	888	9	discontinuities	discontinuity	NOUN
gi-4940	888	10	from	from	ADP
gi-4940	888	11	scattered	scatter	VERB
gi-4940	888	12	data	datum	NOUN
gi-4940	888	13	”	"	PUNCT
gi-4940	888	14	.	.	PUNCT
gi-4940	889	1	in	in	ADP
gi-4940	889	2	:	:	PUNCT
gi-4940	889	3	simulation	simulation	NOUN
gi-4940	889	4	modelling	model	VERB
gi-4940	889	5	practice	practice	NOUN
gi-4940	889	6	and	and	CCONJ
gi-4940	889	7	theory	theory	NOUN
gi-4940	889	8	17.6	17.6	NUM
gi-4940	889	9	(	(	PUNCT
gi-4940	889	10	2009	2009	NUM
gi-4940	889	11	)	)	PUNCT
gi-4940	889	12	,	,	PUNCT
gi-4940	889	13	pp	pp	PROPN
gi-4940	889	14	.	.	PUNCT
gi-4940	889	15	1059–1070	1059–1070	NUM
gi-4940	889	16	.	.	PUNCT
gi-4940	890	1	[	[	X
gi-4940	890	2	2	2	NUM
gi-4940	890	3	]	]	PUNCT
gi-4940	890	4	francesc	francesc	NOUN
gi-4940	890	5	arandiga	arandiga	PROPN
gi-4940	890	6	et	et	PROPN
gi-4940	890	7	al	al	PROPN
gi-4940	890	8	.	.	PUNCT
gi-4940	891	1	“	"	PUNCT
gi-4940	891	2	interpolation	interpolation	NOUN
gi-4940	891	3	and	and	CCONJ
gi-4940	891	4	approximation	approximation	NOUN
gi-4940	891	5	of	of	ADP
gi-4940	891	6	piecewise	piecewise	NOUN
gi-4940	891	7	smooth	smooth	ADJ
gi-4940	891	8	functions	function	NOUN
gi-4940	891	9	”	"	PUNCT
gi-4940	891	10	.	.	PUNCT
gi-4940	892	1	in	in	ADP
gi-4940	892	2	:	:	PUNCT
gi-4940	892	3	siam	siam	ADJ
gi-4940	892	4	journal	journal	PROPN
gi-4940	892	5	on	on	ADP
gi-4940	892	6	numerical	numerical	ADJ
gi-4940	892	7	analysis	analysis	NOUN
gi-4940	892	8	43.1	43.1	NUM
gi-4940	892	9	(	(	PUNCT
gi-4940	892	10	2005	2005	NUM
gi-4940	892	11	)	)	PUNCT
gi-4940	892	12	,	,	PUNCT
gi-4940	892	13	pp	pp	ADP
gi-4940	892	14	.	.	PUNCT
gi-4940	893	1	41–57	41–57	NUM
gi-4940	893	2	.	.	PUNCT
gi-4940	894	1	doi	doi	NOUN
gi-4940	894	2	:	:	PUNCT
gi-4940	894	3	10.1137/	10.1137/	NUM
gi-4940	894	4	s0036142903426245	s0036142903426245	NOUN
gi-4940	894	5	.	.	PUNCT
gi-4940	895	1	[	[	X
gi-4940	895	2	3	3	X
gi-4940	895	3	]	]	X
gi-4940	895	4	rick	rick	PROPN
gi-4940	895	5	archibald	archibald	PROPN
gi-4940	895	6	,	,	PUNCT
gi-4940	895	7	anne	anne	PROPN
gi-4940	895	8	gelb	gelb	PROPN
gi-4940	895	9	,	,	PUNCT
gi-4940	895	10	and	and	CCONJ
gi-4940	895	11	jungho	jungho	PROPN
gi-4940	895	12	yoon	yoon	PROPN
gi-4940	895	13	.	.	PUNCT
gi-4940	896	1	“	"	PUNCT
gi-4940	896	2	determining	determine	VERB
gi-4940	896	3	the	the	DET
gi-4940	896	4	locations	location	NOUN
gi-4940	896	5	and	and	CCONJ
gi-4940	896	6	discontinuities	discontinuity	NOUN
gi-4940	896	7	in	in	ADP
gi-4940	896	8	the	the	DET
gi-4940	896	9	derivatives	derivative	NOUN
gi-4940	896	10	of	of	ADP
gi-4940	896	11	functions	function	NOUN
gi-4940	896	12	”	"	PUNCT
gi-4940	896	13	.	.	PUNCT
gi-4940	897	1	in	in	ADP
gi-4940	897	2	:	:	PUNCT
gi-4940	897	3	applied	apply	VERB
gi-4940	897	4	numerical	numerical	ADJ
gi-4940	897	5	mathematics	mathematic	NOUN
gi-4940	897	6	58.5	58.5	NUM
gi-4940	897	7	(	(	PUNCT
gi-4940	897	8	2008	2008	NUM
gi-4940	897	9	)	)	PUNCT
gi-4940	897	10	,	,	PUNCT
gi-4940	897	11	pp	pp	ADP
gi-4940	897	12	.	.	PUNCT
gi-4940	898	1	577–592	577–592	NUM
gi-4940	898	2	.	.	PUNCT
gi-4940	899	1	[	[	X
gi-4940	899	2	4	4	X
gi-4940	899	3	]	]	PUNCT
gi-4940	899	4	tomas	tomas	PROPN
gi-4940	899	5	bayer	bayer	PROPN
gi-4940	899	6	.	.	PUNCT
gi-4940	900	1	“	"	PUNCT
gi-4940	900	2	advanced	advanced	ADJ
gi-4940	900	3	methods	method	NOUN
gi-4940	900	4	for	for	ADP
gi-4940	900	5	the	the	DET
gi-4940	900	6	estimation	estimation	NOUN
gi-4940	900	7	of	of	ADP
gi-4940	900	8	an	an	DET
gi-4940	900	9	unknown	unknown	ADJ
gi-4940	900	10	projection	projection	NOUN
gi-4940	900	11	from	from	ADP
gi-4940	900	12	a	a	DET
gi-4940	900	13	map	map	NOUN
gi-4940	900	14	”	"	PUNCT
gi-4940	900	15	.	.	PUNCT
gi-4940	901	1	in	in	ADP
gi-4940	901	2	:	:	PUNCT
gi-4940	901	3	geoinformatica	geoinformatica	NOUN
gi-4940	901	4	20.2	20.2	NUM
gi-4940	901	5	(	(	PUNCT
gi-4940	901	6	2016	2016	NUM
gi-4940	901	7	)	)	PUNCT
gi-4940	901	8	,	,	PUNCT
gi-4940	901	9	pp	pp	ADP
gi-4940	901	10	.	.	PUNCT
gi-4940	902	1	241–284	241–284	NUM
gi-4940	902	2	.	.	PUNCT
gi-4940	903	1	doi	doi	NOUN
gi-4940	903	2	:	:	PUNCT
gi-4940	903	3	10.1007	10.1007	NUM
gi-4940	903	4	/	/	SYM
gi-4940	903	5	s10707	s10707	PROPN
gi-4940	903	6	-	-	PUNCT
gi-4940	903	7	015	015	NUM
gi-4940	903	8	-	-	PUNCT
gi-4940	903	9	0234	0234	NUM
gi-4940	903	10	-	-	PUNCT
gi-4940	903	11	x.	x.	NOUN
gi-4940	904	1	[	[	X
gi-4940	904	2	5	5	X
gi-4940	904	3	]	]	PUNCT
gi-4940	904	4	tomas	tomas	PROPN
gi-4940	904	5	bayer	bayer	PROPN
gi-4940	904	6	.	.	PUNCT
gi-4940	905	1	“	"	PUNCT
gi-4940	905	2	efficient	efficient	ADJ
gi-4940	905	3	plotting	plotting	NOUN
gi-4940	905	4	of	of	ADP
gi-4940	905	5	functions	function	NOUN
gi-4940	905	6	with	with	ADP
gi-4940	905	7	discontinuities	discontinuity	NOUN
gi-4940	905	8	based	base	VERB
gi-4940	905	9	on	on	ADP
gi-4940	905	10	combined	combined	ADJ
gi-4940	905	11	sampling	sampling	NOUN
gi-4940	905	12	”	"	PUNCT
gi-4940	905	13	.	.	PUNCT
gi-4940	906	1	english	english	PROPN
gi-4940	906	2	.	.	PUNCT
gi-4940	907	1	in	in	ADP
gi-4940	907	2	:	:	PUNCT
gi-4940	907	3	fce	fce	VERB
gi-4940	907	4	geoinformatics	geoinformatic	NOUN
gi-4940	907	5	18.3	18.3	NUM
gi-4940	907	6	(	(	PUNCT
gi-4940	907	7	2018	2018	NUM
gi-4940	907	8	)	)	PUNCT
gi-4940	907	9	,	,	PUNCT
gi-4940	907	10	pp	pp	ADJ
gi-4940	907	11	.	.	PUNCT
gi-4940	908	1	621–669	621–669	NUM
gi-4940	908	2	.	.	PUNCT
gi-4940	909	1	issn	issn	PROPN
gi-4940	909	2	:	:	PUNCT
gi-4940	909	3	1384	1384	NUM
gi-4940	909	4	-	-	SYM
gi-4940	909	5	6175	6175	NUM
gi-4940	909	6	.	.	PUNCT
gi-4940	910	1	doi	doi	NOUN
gi-4940	910	2	:	:	PUNCT
gi-4940	910	3	10.1007	10.1007	NUM
gi-4940	910	4	/	/	SYM
gi-4940	910	5	s10707	s10707	NOUN
gi-4940	910	6	-	-	PUNCT
gi-4940	910	7	013	013	NUM
gi-4940	910	8	-	-	PUNCT
gi-4940	910	9	0200	0200	NUM
gi-4940	910	10	-	-	PUNCT
gi-4940	910	11	4	4	NUM
gi-4940	910	12	.	.	PUNCT
gi-4940	911	1	[	[	X
gi-4940	911	2	6	6	NUM
gi-4940	911	3	]	]	PUNCT
gi-4940	911	4	tomas	tomas	PROPN
gi-4940	911	5	bayer	bayer	PROPN
gi-4940	911	6	.	.	PUNCT
gi-4940	912	1	“	"	PUNCT
gi-4940	912	2	estimation	estimation	NOUN
gi-4940	912	3	of	of	ADP
gi-4940	912	4	an	an	DET
gi-4940	912	5	unknown	unknown	ADJ
gi-4940	912	6	cartographic	cartographic	ADJ
gi-4940	912	7	projection	projection	NOUN
gi-4940	912	8	and	and	CCONJ
gi-4940	912	9	its	its	PRON
gi-4940	912	10	parameters	parameter	NOUN
gi-4940	912	11	from	from	ADP
gi-4940	912	12	the	the	DET
gi-4940	912	13	map	map	NOUN
gi-4940	912	14	”	"	PUNCT
gi-4940	912	15	.	.	PUNCT
gi-4940	913	1	english	english	PROPN
gi-4940	913	2	.	.	PUNCT
gi-4940	914	1	in	in	ADP
gi-4940	914	2	:	:	PUNCT
gi-4940	914	3	geoinformatica	geoinformatica	NOUN
gi-4940	914	4	18.3	18.3	NUM
gi-4940	914	5	(	(	PUNCT
gi-4940	914	6	2014	2014	NUM
gi-4940	914	7	)	)	PUNCT
gi-4940	914	8	,	,	PUNCT
gi-4940	914	9	pp	pp	ADJ
gi-4940	914	10	.	.	PUNCT
gi-4940	915	1	621–669	621–669	NUM
gi-4940	915	2	.	.	PUNCT
gi-4940	916	1	issn	issn	PROPN
gi-4940	916	2	:	:	PUNCT
gi-4940	916	3	1384	1384	NUM
gi-4940	916	4	-	-	SYM
gi-4940	916	5	6175	6175	NUM
gi-4940	916	6	.	.	PUNCT
gi-4940	917	1	doi	doi	NOUN
gi-4940	917	2	:	:	PUNCT
gi-4940	917	3	10.1007	10.1007	NUM
gi-4940	917	4	/	/	SYM
gi-4940	917	5	s10707	s10707	NOUN
gi-4940	917	6	-	-	PUNCT
gi-4940	917	7	013	013	NUM
gi-4940	917	8	-	-	PUNCT
gi-4940	917	9	0200	0200	NUM
gi-4940	917	10	-	-	PUNCT
gi-4940	917	11	4	4	NUM
gi-4940	917	12	.	.	PUNCT
gi-4940	918	1	[	[	X
gi-4940	918	2	7	7	X
gi-4940	918	3	]	]	PUNCT
gi-4940	918	4	p.	p.	NOUN
gi-4940	918	5	binev	binev	PROPN
gi-4940	918	6	et	et	PROPN
gi-4940	918	7	al	al	PROPN
gi-4940	918	8	.	.	PUNCT
gi-4940	919	1	“	"	PUNCT
gi-4940	919	2	adaptive	adaptive	ADJ
gi-4940	919	3	approximation	approximation	NOUN
gi-4940	919	4	of	of	ADP
gi-4940	919	5	curves	curve	NOUN
gi-4940	919	6	”	"	PUNCT
gi-4940	919	7	.	.	PUNCT
gi-4940	920	1	in	in	ADP
gi-4940	920	2	:	:	PUNCT
gi-4940	920	3	approximation	approximation	NOUN
gi-4940	920	4	theory	theory	NOUN
gi-4940	920	5	(	(	PUNCT
gi-4940	920	6	2004	2004	NUM
gi-4940	920	7	)	)	PUNCT
gi-4940	920	8	,	,	PUNCT
gi-4940	920	9	pp	pp	ADV
gi-4940	920	10	.	.	PUNCT
gi-4940	921	1	43–57	43–57	NUM
gi-4940	921	2	.	.	PUNCT
gi-4940	922	1	[	[	X
gi-4940	922	2	8	8	NUM
gi-4940	922	3	]	]	X
gi-4940	922	4	mira	mira	X
gi-4940	922	5	bozzini	bozzini	PROPN
gi-4940	922	6	,	,	PUNCT
gi-4940	922	7	licia	licia	PROPN
gi-4940	922	8	lenarduzzi	lenarduzzi	VERB
gi-4940	922	9	,	,	PUNCT
gi-4940	922	10	and	and	CCONJ
gi-4940	922	11	milvia	milvia	PROPN
gi-4940	922	12	rossini	rossini	PROPN
gi-4940	922	13	.	.	PUNCT
gi-4940	923	1	“	"	PUNCT
gi-4940	923	2	non	non	ADJ
gi-4940	923	3	-	-	ADJ
gi-4940	923	4	regular	regular	ADJ
gi-4940	923	5	surface	surface	NOUN
gi-4940	923	6	approximation	approximation	NOUN
gi-4940	923	7	”	"	PUNCT
gi-4940	923	8	.	.	PUNCT
gi-4940	924	1	in	in	ADP
gi-4940	924	2	:	:	PUNCT
gi-4940	924	3	mathematical	mathematical	ADJ
gi-4940	924	4	methods	method	NOUN
gi-4940	924	5	for	for	ADP
gi-4940	924	6	curves	curve	NOUN
gi-4940	924	7	and	and	CCONJ
gi-4940	924	8	surfaces	surface	NOUN
gi-4940	924	9	:	:	PUNCT
gi-4940	924	10	8th	8th	ADJ
gi-4940	924	11	international	international	ADJ
gi-4940	924	12	conference	conference	NOUN
gi-4940	924	13	,	,	PUNCT
gi-4940	924	14	mmcs	mmcs	PROPN
gi-4940	924	15	2012	2012	NUM
gi-4940	924	16	,	,	PUNCT
gi-4940	924	17	oslo	oslo	PROPN
gi-4940	924	18	,	,	PUNCT
gi-4940	924	19	norway	norway	PROPN
gi-4940	924	20	,	,	PUNCT
gi-4940	924	21	june	june	PROPN
gi-4940	924	22	28	28	NUM
gi-4940	924	23	–	–	PUNCT
gi-4940	924	24	july	july	PROPN
gi-4940	924	25	3	3	NUM
gi-4940	924	26	,	,	PUNCT
gi-4940	924	27	2012	2012	NUM
gi-4940	924	28	,	,	PUNCT
gi-4940	924	29	revised	revise	VERB
gi-4940	924	30	selected	select	VERB
gi-4940	924	31	papers	paper	NOUN
gi-4940	924	32	.	.	PUNCT
gi-4940	925	1	ed	ed	X
gi-4940	925	2	.	.	PUNCT
gi-4940	926	1	by	by	ADP
gi-4940	926	2	michael	michael	PROPN
gi-4940	926	3	floater	floater	PROPN
gi-4940	926	4	et	et	PROPN
gi-4940	926	5	al	al	PROPN
gi-4940	926	6	.	.	PROPN
gi-4940	926	7	berlin	berlin	PROPN
gi-4940	926	8	,	,	PUNCT
gi-4940	926	9	heidelberg	heidelberg	PROPN
gi-4940	926	10	:	:	PUNCT
gi-4940	926	11	springer	springer	PROPN
gi-4940	926	12	berlin	berlin	PROPN
gi-4940	926	13	heidelberg	heidelberg	PROPN
gi-4940	926	14	,	,	PUNCT
gi-4940	926	15	2014	2014	NUM
gi-4940	926	16	,	,	PUNCT
gi-4940	926	17	pp	pp	ADJ
gi-4940	926	18	.	.	PUNCT
gi-4940	927	1	68–87	68–87	NUM
gi-4940	927	2	.	.	PUNCT
gi-4940	928	1	isbn	isbn	ADJ
gi-4940	928	2	:	:	PUNCT
gi-4940	928	3	978	978	NUM
gi-4940	928	4	-	-	SYM
gi-4940	928	5	3	3	NUM
gi-4940	928	6	-	-	PUNCT
gi-4940	928	7	642	642	NUM
gi-4940	928	8	-	-	PUNCT
gi-4940	928	9	54382	54382	NUM
gi-4940	928	10	-	-	SYM
gi-4940	928	11	1	1	NUM
gi-4940	928	12	.	.	PUNCT
gi-4940	928	13	doi	doi	NOUN
gi-4940	928	14	:	:	PUNCT
gi-4940	928	15	10.1007/978	10.1007/978	NUM
gi-4940	928	16	-	-	SYM
gi-4940	928	17	3	3	NUM
gi-4940	928	18	-	-	PUNCT
gi-4940	928	19	642	642	NUM
gi-4940	928	20	-	-	PUNCT
gi-4940	928	21	54382	54382	NUM
gi-4940	928	22	-	-	SYM
gi-4940	928	23	1_5	1_5	NUM
gi-4940	928	24	.	.	PUNCT
gi-4940	929	1	[	[	X
gi-4940	929	2	9	9	NUM
gi-4940	929	3	]	]	X
gi-4940	929	4	mira	mira	X
gi-4940	929	5	bozzini	bozzini	PROPN
gi-4940	929	6	,	,	PUNCT
gi-4940	929	7	licia	licia	PROPN
gi-4940	929	8	lenarduzzi	lenarduzzi	VERB
gi-4940	929	9	,	,	PUNCT
gi-4940	929	10	and	and	CCONJ
gi-4940	929	11	robert	robert	PROPN
gi-4940	929	12	schaback	schaback	NOUN
gi-4940	929	13	.	.	PUNCT
gi-4940	930	1	“	"	PUNCT
gi-4940	930	2	adaptive	adaptive	ADJ
gi-4940	930	3	interpolation	interpolation	NOUN
gi-4940	930	4	by	by	ADP
gi-4940	930	5	scaled	scale	VERB
gi-4940	930	6	multiquadrics	multiquadric	NOUN
gi-4940	930	7	”	"	PUNCT
gi-4940	930	8	.	.	PUNCT
gi-4940	931	1	in	in	ADP
gi-4940	931	2	:	:	PUNCT
gi-4940	931	3	advances	advance	NOUN
gi-4940	931	4	in	in	ADP
gi-4940	931	5	computational	computational	ADJ
gi-4940	931	6	mathematics	mathematic	NOUN
gi-4940	931	7	16.4	16.4	NUM
gi-4940	931	8	(	(	PUNCT
gi-4940	931	9	may	may	PROPN
gi-4940	931	10	2002	2002	NUM
gi-4940	931	11	)	)	PUNCT
gi-4940	931	12	,	,	PUNCT
gi-4940	931	13	pp	pp	PROPN
gi-4940	931	14	.	.	PUNCT
gi-4940	931	15	375	375	NUM
gi-4940	931	16	–	–	PUNCT
gi-4940	931	17	387	387	NUM
gi-4940	931	18	.	.	X
gi-4940	931	19	issn	issn	PROPN
gi-4940	931	20	:	:	PUNCT
gi-4940	931	21	1572	1572	NUM
gi-4940	931	22	-	-	SYM
gi-4940	931	23	9044	9044	NUM
gi-4940	931	24	.	.	PUNCT
gi-4940	932	1	doi	doi	NOUN
gi-4940	932	2	:	:	PUNCT
gi-4940	932	3	10.1023	10.1023	NUM
gi-4940	932	4	/	/	SYM
gi-4940	932	5	a:1014584220418	a:1014584220418	NOUN
gi-4940	932	6	.	.	PUNCT
gi-4940	933	1	[	[	X
gi-4940	933	2	10	10	NUM
gi-4940	933	3	]	]	X
gi-4940	933	4	filipe	filipe	PROPN
gi-4940	933	5	de	de	PROPN
gi-4940	933	6	carvalho	carvalho	PROPN
gi-4940	933	7	nascimento	nascimento	PROPN
gi-4940	933	8	et	et	PROPN
gi-4940	933	9	al	al	PROPN
gi-4940	933	10	.	.	PUNCT
gi-4940	934	1	“	"	PUNCT
gi-4940	934	2	approximating	approximate	VERB
gi-4940	934	3	implicit	implicit	ADJ
gi-4940	934	4	curves	curve	NOUN
gi-4940	934	5	on	on	ADP
gi-4940	934	6	plane	plane	NOUN
gi-4940	934	7	and	and	CCONJ
gi-4940	934	8	surface	surface	NOUN
gi-4940	934	9	triangulations	triangulation	NOUN
gi-4940	934	10	with	with	ADP
gi-4940	934	11	affine	affine	NOUN
gi-4940	934	12	arithmetic	arithmetic	NOUN
gi-4940	934	13	”	"	PUNCT
gi-4940	934	14	.	.	PUNCT
gi-4940	935	1	in	in	ADP
gi-4940	935	2	:	:	PUNCT
gi-4940	935	3	computers	computer	NOUN
gi-4940	935	4	&	&	CCONJ
gi-4940	935	5	graphics	graphic	NOUN
gi-4940	935	6	40	40	NUM
gi-4940	935	7	(	(	PUNCT
gi-4940	935	8	2014	2014	NUM
gi-4940	935	9	)	)	PUNCT
gi-4940	935	10	,	,	PUNCT
gi-4940	935	11	pp	pp	ADJ
gi-4940	935	12	.	.	PUNCT
gi-4940	936	1	36–48	36–48	NUM
gi-4940	936	2	.	.	PUNCT
gi-4940	937	1	[	[	X
gi-4940	937	2	11	11	NUM
gi-4940	937	3	]	]	X
gi-4940	937	4	andrew	andrew	PROPN
gi-4940	937	5	crampton	crampton	PROPN
gi-4940	937	6	and	and	CCONJ
gi-4940	937	7	john	john	PROPN
gi-4940	937	8	c	c	PROPN
gi-4940	937	9	mason	mason	PROPN
gi-4940	937	10	.	.	PUNCT
gi-4940	938	1	“	"	PUNCT
gi-4940	938	2	detecting	detect	VERB
gi-4940	938	3	and	and	CCONJ
gi-4940	938	4	approximating	approximate	VERB
gi-4940	938	5	fault	fault	NOUN
gi-4940	938	6	lines	line	NOUN
gi-4940	938	7	from	from	ADP
gi-4940	938	8	randomly	randomly	ADV
gi-4940	938	9	scattered	scatter	VERB
gi-4940	938	10	data	datum	NOUN
gi-4940	938	11	”	"	PUNCT
gi-4940	938	12	.	.	PUNCT
gi-4940	939	1	in	in	ADP
gi-4940	939	2	:	:	PUNCT
gi-4940	939	3	numerical	numerical	ADJ
gi-4940	939	4	algorithms	algorithms	NOUN
gi-4940	939	5	39.1	39.1	NUM
gi-4940	939	6	(	(	PUNCT
gi-4940	939	7	2005	2005	NUM
gi-4940	939	8	)	)	PUNCT
gi-4940	939	9	,	,	PUNCT
gi-4940	939	10	pp	pp	ADP
gi-4940	939	11	.	.	PUNCT
gi-4940	939	12	115–130	115–130	NUM
gi-4940	939	13	.	.	PUNCT
gi-4940	940	1	[	[	X
gi-4940	940	2	12	12	NUM
gi-4940	940	3	]	]	PUNCT
gi-4940	940	4	luiz	luiz	PROPN
gi-4940	940	5	henrique	henrique	PROPN
gi-4940	940	6	de	de	PROPN
gi-4940	940	7	figueiredo	figueiredo	PROPN
gi-4940	940	8	.	.	PUNCT
gi-4940	941	1	“	"	PUNCT
gi-4940	941	2	adaptive	adaptive	ADJ
gi-4940	941	3	sampling	sampling	NOUN
gi-4940	941	4	of	of	ADP
gi-4940	941	5	parametric	parametric	ADJ
gi-4940	941	6	curves	curve	NOUN
gi-4940	941	7	”	"	PUNCT
gi-4940	941	8	.	.	PUNCT
gi-4940	942	1	in	in	ADP
gi-4940	942	2	:	:	PUNCT
gi-4940	942	3	graphics	graphic	NOUN
gi-4940	942	4	gems	gem	NOUN
gi-4940	942	5	v	v	ADP
gi-4940	942	6	5	5	NUM
gi-4940	942	7	(	(	PUNCT
gi-4940	942	8	1995	1995	NUM
gi-4940	942	9	)	)	PUNCT
gi-4940	942	10	,	,	PUNCT
gi-4940	942	11	pp	pp	ADP
gi-4940	942	12	.	.	PUNCT
gi-4940	943	1	173–178	173–178	NUM
gi-4940	943	2	.	.	PUNCT
gi-4940	944	1	[	[	X
gi-4940	944	2	13	13	NUM
gi-4940	944	3	]	]	PUNCT
gi-4940	944	4	tim	tim	PROPN
gi-4940	944	5	gutzmer	gutzmer	PROPN
gi-4940	944	6	and	and	CCONJ
gi-4940	944	7	armin	armin	PROPN
gi-4940	944	8	iske	iske	PROPN
gi-4940	944	9	.	.	PUNCT
gi-4940	945	1	“	"	PUNCT
gi-4940	945	2	detection	detection	NOUN
gi-4940	945	3	of	of	ADP
gi-4940	945	4	discontinuities	discontinuity	NOUN
gi-4940	945	5	in	in	ADP
gi-4940	945	6	scattered	scatter	VERB
gi-4940	945	7	data	datum	NOUN
gi-4940	945	8	approximation	approximation	NOUN
gi-4940	945	9	”	"	PUNCT
gi-4940	945	10	.	.	PUNCT
gi-4940	946	1	in	in	ADP
gi-4940	946	2	:	:	PUNCT
gi-4940	946	3	numerical	numerical	ADJ
gi-4940	946	4	algorithms	algorithm	NOUN
gi-4940	946	5	16.2	16.2	NUM
gi-4940	946	6	(	(	PUNCT
gi-4940	946	7	1997	1997	NUM
gi-4940	946	8	)	)	PUNCT
gi-4940	946	9	,	,	PUNCT
gi-4940	946	10	pp	pp	ADP
gi-4940	946	11	.	.	PUNCT
gi-4940	947	1	155–170	155–170	NUM
gi-4940	947	2	.	.	PUNCT
gi-4940	948	1	[	[	X
gi-4940	948	2	14	14	NUM
gi-4940	948	3	]	]	X
gi-4940	948	4	john	john	PROPN
gi-4940	948	5	krumm	krumm	PROPN
gi-4940	948	6	.	.	PUNCT
gi-4940	949	1	intersection	intersection	NOUN
gi-4940	949	2	of	of	ADP
gi-4940	949	3	two	two	NUM
gi-4940	949	4	planes	plane	NOUN
gi-4940	949	5	.	.	PUNCT
gi-4940	950	1	2016	2016	NUM
gi-4940	950	2	.	.	PUNCT
gi-4940	951	1	[	[	X
gi-4940	951	2	15	15	NUM
gi-4940	951	3	]	]	X
gi-4940	951	4	david	david	PROPN
gi-4940	951	5	lee	lee	PROPN
gi-4940	951	6	.	.	PUNCT
gi-4940	952	1	“	"	PUNCT
gi-4940	952	2	detection	detection	NOUN
gi-4940	952	3	,	,	PUNCT
gi-4940	952	4	classification	classification	NOUN
gi-4940	952	5	,	,	PUNCT
gi-4940	952	6	and	and	CCONJ
gi-4940	952	7	measurement	measurement	NOUN
gi-4940	952	8	of	of	ADP
gi-4940	952	9	discontinuities	discontinuity	NOUN
gi-4940	952	10	”	"	PUNCT
gi-4940	952	11	.	.	PUNCT
gi-4940	953	1	in	in	ADP
gi-4940	953	2	:	:	PUNCT
gi-4940	953	3	siam	siam	ADJ
gi-4940	953	4	journal	journal	NOUN
gi-4940	953	5	on	on	ADP
gi-4940	953	6	scientific	scientific	ADJ
gi-4940	953	7	and	and	CCONJ
gi-4940	953	8	statistical	statistical	ADJ
gi-4940	953	9	computing	computing	NOUN
gi-4940	953	10	12.2	12.2	NUM
gi-4940	953	11	(	(	PUNCT
gi-4940	953	12	1991	1991	NUM
gi-4940	953	13	)	)	PUNCT
gi-4940	953	14	,	,	PUNCT
gi-4940	953	15	pp	pp	ADP
gi-4940	953	16	.	.	PUNCT
gi-4940	954	1	311–341	311–341	NUM
gi-4940	954	2	.	.	PUNCT
gi-4940	954	3	doi	doi	NOUN
gi-4940	954	4	:	:	PUNCT
gi-4940	954	5	10	10	NUM
gi-4940	954	6	.	.	PUNCT
gi-4940	955	1	1137/0912018	1137/0912018	NUM
gi-4940	955	2	.	.	PUNCT
gi-4940	956	1	geoinformatics	geoinformatic	NOUN
gi-4940	956	2	fce	fce	VERB
gi-4940	956	3	ctu	ctu	NOUN
gi-4940	956	4	17(2	17(2	NUM
gi-4940	956	5	)	)	PUNCT
gi-4940	956	6	,	,	PUNCT
gi-4940	956	7	2018	2018	NUM
gi-4940	956	8	62	62	NUM
gi-4940	956	9	https://doi.org/10.1137/s0036142903426245	https://doi.org/10.1137/s0036142903426245	PROPN
gi-4940	956	10	https://doi.org/10.1137/s0036142903426245	https://doi.org/10.1137/s0036142903426245	PROPN
gi-4940	956	11	https://doi.org/10.1007/s10707-015-0234-x	https://doi.org/10.1007/s10707-015-0234-x	PROPN
gi-4940	956	12	https://doi.org/10.1007/s10707-013-0200-4	https://doi.org/10.1007/s10707-013-0200-4	PROPN
gi-4940	956	13	https://doi.org/10.1007/s10707-013-0200-4	https://doi.org/10.1007/s10707-013-0200-4	PROPN
gi-4940	956	14	https://doi.org/10.1007/978-3-642-54382-1_5	https://doi.org/10.1007/978-3-642-54382-1_5	PRON
gi-4940	956	15	https://doi.org/10.1023/a:1014584220418	https://doi.org/10.1023/a:1014584220418	NOUN
gi-4940	956	16	https://doi.org/10.1137/0912018	https://doi.org/10.1137/0912018	NOUN
gi-4940	956	17	https://doi.org/10.1137/0912018	https://doi.org/10.1137/0912018	NOUN
gi-4940	957	1	t.	t.	PROPN
gi-4940	957	2	bayer	bayer	PROPN
gi-4940	957	3	:	:	PUNCT
gi-4940	957	4	plotting	plot	VERB
gi-4940	957	5	the	the	DET
gi-4940	957	6	map	map	NOUN
gi-4940	957	7	projection	projection	NOUN
gi-4940	957	8	graticule	graticule	NOUN
gi-4940	957	9	with	with	ADP
gi-4940	957	10	discontinuities	discontinuity	NOUN
gi-4940	957	11	[	[	X
gi-4940	957	12	16	16	NUM
gi-4940	957	13	]	]	X
gi-4940	957	14	licia	licia	NOUN
gi-4940	957	15	lenarduzzi	lenarduzzi	PROPN
gi-4940	957	16	and	and	CCONJ
gi-4940	957	17	robert	robert	PROPN
gi-4940	957	18	schaback	schaback	PROPN
gi-4940	957	19	.	.	PUNCT
gi-4940	958	1	“	"	PUNCT
gi-4940	958	2	kernel	kernel	NOUN
gi-4940	958	3	-	-	PUNCT
gi-4940	958	4	based	base	VERB
gi-4940	958	5	adaptive	adaptive	ADJ
gi-4940	958	6	approximation	approximation	NOUN
gi-4940	958	7	of	of	ADP
gi-4940	958	8	functions	function	NOUN
gi-4940	958	9	with	with	ADP
gi-4940	958	10	discontinuities	discontinuity	NOUN
gi-4940	958	11	”	"	PUNCT
gi-4940	958	12	.	.	PUNCT
gi-4940	959	1	in	in	ADP
gi-4940	959	2	:	:	PUNCT
gi-4940	959	3	applied	applied	ADJ
gi-4940	959	4	mathematics	mathematic	NOUN
gi-4940	959	5	and	and	CCONJ
gi-4940	959	6	computation	computation	NOUN
gi-4940	959	7	307.supplement	307.supplement	NUM
gi-4940	959	8	c	c	NOUN
gi-4940	959	9	(	(	PUNCT
gi-4940	959	10	2017	2017	NUM
gi-4940	959	11	)	)	PUNCT
gi-4940	959	12	,	,	PUNCT
gi-4940	959	13	pp	pp	ADP
gi-4940	959	14	.	.	PUNCT
gi-4940	960	1	113–123	113–123	NUM
gi-4940	960	2	.	.	PUNCT
gi-4940	961	1	issn	issn	PROPN
gi-4940	961	2	:	:	PUNCT
gi-4940	961	3	0096	0096	NUM
gi-4940	961	4	-	-	SYM
gi-4940	961	5	3003	3003	NUM
gi-4940	961	6	.	.	PUNCT
gi-4940	962	1	doi	doi	NOUN
gi-4940	962	2	:	:	PUNCT
gi-4940	962	3	https://doi.org/10.1016/j.amc.2017	https://doi.org/10.1016/j.amc.2017	NOUN
gi-4940	962	4	.	.	PUNCT
gi-4940	962	5	02.043	02.043	NUM
gi-4940	962	6	.	.	PUNCT
gi-4940	963	1	[	[	X
gi-4940	963	2	17	17	NUM
gi-4940	963	3	]	]	X
gi-4940	963	4	hélio	hélio	PROPN
gi-4940	963	5	lopes	lopes	PROPN
gi-4940	963	6	,	,	PUNCT
gi-4940	963	7	joão	joão	PROPN
gi-4940	963	8	batista	batista	PROPN
gi-4940	963	9	oliveira	oliveira	PROPN
gi-4940	963	10	,	,	PUNCT
gi-4940	963	11	and	and	CCONJ
gi-4940	963	12	luiz	luiz	PROPN
gi-4940	963	13	henrique	henrique	PROPN
gi-4940	963	14	de	de	PROPN
gi-4940	963	15	figueiredo	figueiredo	PROPN
gi-4940	963	16	.	.	PUNCT
gi-4940	964	1	“	"	PUNCT
gi-4940	964	2	robust	robust	ADJ
gi-4940	964	3	adaptive	adaptive	ADJ
gi-4940	964	4	polygonal	polygonal	ADJ
gi-4940	964	5	approximation	approximation	NOUN
gi-4940	964	6	of	of	ADP
gi-4940	964	7	implicit	implicit	ADJ
gi-4940	964	8	curves	curve	NOUN
gi-4940	964	9	”	"	PUNCT
gi-4940	964	10	.	.	PUNCT
gi-4940	965	1	in	in	ADP
gi-4940	965	2	:	:	PUNCT
gi-4940	965	3	computers	computer	NOUN
gi-4940	965	4	&	&	CCONJ
gi-4940	965	5	graphics	graphic	NOUN
gi-4940	965	6	26.6	26.6	NUM
gi-4940	965	7	(	(	PUNCT
gi-4940	965	8	2002	2002	NUM
gi-4940	965	9	)	)	PUNCT
gi-4940	965	10	,	,	PUNCT
gi-4940	965	11	pp	pp	ADP
gi-4940	965	12	.	.	PUNCT
gi-4940	966	1	841–852	841–852	NUM
gi-4940	966	2	.	.	PUNCT
gi-4940	967	1	[	[	X
gi-4940	967	2	18	18	NUM
gi-4940	967	3	]	]	X
gi-4940	967	4	maría	maría	PROPN
gi-4940	967	5	cruz	cruz	PROPN
gi-4940	967	6	lópez	lópez	PROPN
gi-4940	967	7	de	de	PROPN
gi-4940	967	8	silanes	silanes	PROPN
gi-4940	967	9	,	,	PUNCT
gi-4940	967	10	maría	maría	PROPN
gi-4940	967	11	cruz	cruz	PROPN
gi-4940	967	12	parra	parra	PROPN
gi-4940	967	13	,	,	PUNCT
gi-4940	967	14	and	and	CCONJ
gi-4940	967	15	juan	juan	PROPN
gi-4940	967	16	josé	josé	PROPN
gi-4940	967	17	torrens	torrens	PROPN
gi-4940	967	18	.	.	PUNCT
gi-4940	968	1	“	"	PUNCT
gi-4940	968	2	on	on	ADP
gi-4940	968	3	a	a	DET
gi-4940	968	4	new	new	ADJ
gi-4940	968	5	characterization	characterization	NOUN
gi-4940	968	6	of	of	ADP
gi-4940	968	7	finite	finite	ADJ
gi-4940	968	8	jump	jump	NOUN
gi-4940	968	9	discontinuities	discontinuity	NOUN
gi-4940	968	10	and	and	CCONJ
gi-4940	968	11	its	its	PRON
gi-4940	968	12	application	application	NOUN
gi-4940	968	13	to	to	ADP
gi-4940	968	14	vertical	vertical	ADJ
gi-4940	968	15	fault	fault	NOUN
gi-4940	968	16	detection	detection	NOUN
gi-4940	968	17	”	"	PUNCT
gi-4940	968	18	.	.	PUNCT
gi-4940	969	1	in	in	ADP
gi-4940	969	2	:	:	PUNCT
gi-4940	969	3	math	math	NOUN
gi-4940	969	4	.	.	PUNCT
gi-4940	970	1	comput	comput	NOUN
gi-4940	970	2	.	.	PUNCT
gi-4940	971	1	simul	simul	PROPN
gi-4940	971	2	.	.	PUNCT
gi-4940	972	1	77.2	77.2	NUM
gi-4940	972	2	-	-	SYM
gi-4940	972	3	3	3	NUM
gi-4940	972	4	(	(	PUNCT
gi-4940	972	5	mar	mar	PROPN
gi-4940	972	6	.	.	PROPN
gi-4940	972	7	2008	2008	NUM
gi-4940	972	8	)	)	PUNCT
gi-4940	972	9	,	,	PUNCT
gi-4940	972	10	pp	pp	ADP
gi-4940	972	11	.	.	PUNCT
gi-4940	973	1	247–256	247–256	NUM
gi-4940	973	2	.	.	PUNCT
gi-4940	974	1	issn	issn	PROPN
gi-4940	974	2	:	:	PUNCT
gi-4940	974	3	0378	0378	NUM
gi-4940	974	4	-	-	SYM
gi-4940	974	5	4754	4754	NUM
gi-4940	974	6	.	.	PUNCT
gi-4940	975	1	doi	doi	NOUN
gi-4940	975	2	:	:	PUNCT
gi-4940	975	3	10.1016	10.1016	NUM
gi-4940	975	4	/	/	SYM
gi-4940	975	5	j.matcom.2007.08.008	j.matcom.2007.08.008	NOUN
gi-4940	975	6	.	.	PUNCT
gi-4940	976	1	[	[	X
gi-4940	976	2	19	19	NUM
gi-4940	976	3	]	]	X
gi-4940	976	4	maría	maría	PROPN
gi-4940	976	5	cruz	cruz	PROPN
gi-4940	976	6	lópez	lópez	PROPN
gi-4940	976	7	de	de	PROPN
gi-4940	976	8	silanes	silanes	PROPN
gi-4940	976	9	,	,	PUNCT
gi-4940	976	10	maría	maría	PROPN
gi-4940	976	11	cruz	cruz	PROPN
gi-4940	976	12	parra	parra	PROPN
gi-4940	976	13	,	,	PUNCT
gi-4940	976	14	and	and	CCONJ
gi-4940	976	15	juan	juan	PROPN
gi-4940	976	16	josé	josé	PROPN
gi-4940	976	17	torrens	torrens	PROPN
gi-4940	976	18	.	.	PUNCT
gi-4940	977	1	“	"	PUNCT
gi-4940	977	2	vertical	vertical	ADJ
gi-4940	977	3	and	and	CCONJ
gi-4940	977	4	oblique	oblique	ADJ
gi-4940	977	5	fault	fault	NOUN
gi-4940	977	6	detection	detection	NOUN
gi-4940	977	7	in	in	ADP
gi-4940	977	8	explicit	explicit	ADJ
gi-4940	977	9	surfaces	surface	NOUN
gi-4940	977	10	”	"	PUNCT
gi-4940	977	11	.	.	PUNCT
gi-4940	978	1	in	in	ADP
gi-4940	978	2	:	:	PUNCT
gi-4940	978	3	journal	journal	NOUN
gi-4940	978	4	of	of	ADP
gi-4940	978	5	computational	computational	ADJ
gi-4940	978	6	and	and	CCONJ
gi-4940	978	7	applied	applied	ADJ
gi-4940	978	8	mathematics	mathematic	NOUN
gi-4940	978	9	140.1	140.1	NUM
gi-4940	978	10	(	(	PUNCT
gi-4940	978	11	2002	2002	NUM
gi-4940	978	12	)	)	PUNCT
gi-4940	978	13	.	.	PUNCT
gi-4940	979	1	int	int	NOUN
gi-4940	979	2	.	.	PUNCT
gi-4940	980	1	congress	congress	PROPN
gi-4940	980	2	on	on	ADP
gi-4940	980	3	computational	computational	ADJ
gi-4940	980	4	and	and	CCONJ
gi-4940	980	5	applied	applied	ADJ
gi-4940	980	6	mathematics	mathematic	NOUN
gi-4940	980	7	2000	2000	NUM
gi-4940	980	8	,	,	PUNCT
gi-4940	980	9	pp	pp	ADP
gi-4940	980	10	.	.	PUNCT
gi-4940	981	1	559–585	559–585	NUM
gi-4940	981	2	.	.	PUNCT
gi-4940	982	1	issn	issn	PROPN
gi-4940	982	2	:	:	PUNCT
gi-4940	982	3	0377	0377	NUM
gi-4940	982	4	-	-	SYM
gi-4940	982	5	0427	0427	NUM
gi-4940	982	6	.	.	PUNCT
gi-4940	983	1	doi	doi	NOUN
gi-4940	983	2	:	:	PUNCT
gi-4940	983	3	https://doi.org/10.1016/s0377-0427(01	https://doi.org/10.1016/s0377-0427(01	NUM
gi-4940	983	4	)	)	PUNCT
gi-4940	983	5	00601	00601	NUM
gi-4940	983	6	-	-	PUNCT
gi-4940	983	7	x.	x.	NOUN
gi-4940	984	1	[	[	X
gi-4940	984	2	20	20	NUM
gi-4940	984	3	]	]	SYM
gi-4940	984	4	m	m	VERB
gi-4940	984	5	oliveria	oliveria	INTJ
gi-4940	984	6	et	et	PROPN
gi-4940	984	7	al	al	PROPN
gi-4940	984	8	.	.	PUNCT
gi-4940	985	1	“	"	PUNCT
gi-4940	985	2	universal	universal	ADJ
gi-4940	985	3	high	high	ADJ
gi-4940	985	4	order	order	NOUN
gi-4940	985	5	subroutine	subroutine	NOUN
gi-4940	985	6	with	with	ADP
gi-4940	985	7	new	new	ADJ
gi-4940	985	8	shock	shock	NOUN
gi-4940	985	9	detector	detector	NOUN
gi-4940	985	10	for	for	ADP
gi-4940	985	11	shock	shock	NOUN
gi-4940	985	12	boundary	boundary	ADJ
gi-4940	985	13	layer	layer	NOUN
gi-4940	985	14	interaction	interaction	NOUN
gi-4940	985	15	”	"	PUNCT
gi-4940	985	16	.	.	PUNCT
gi-4940	986	1	in	in	ADP
gi-4940	986	2	:	:	PUNCT
gi-4940	986	3	in	in	ADP
gi-4940	986	4	other	other	ADJ
gi-4940	986	5	words	word	NOUN
gi-4940	986	6	10	10	NUM
gi-4940	986	7	(	(	PUNCT
gi-4940	986	8	2009	2009	NUM
gi-4940	986	9	)	)	PUNCT
gi-4940	986	10	,	,	PUNCT
gi-4940	986	11	pp	pp	ADP
gi-4940	986	12	.	.	PUNCT
gi-4940	987	1	1–2	1–2	X
gi-4940	987	2	.	.	PUNCT
gi-4940	988	1	[	[	X
gi-4940	988	2	21	21	NUM
gi-4940	988	3	]	]	X
gi-4940	988	4	afonso	afonso	PROPN
gi-4940	988	5	paiva	paiva	PROPN
gi-4940	988	6	et	et	PROPN
gi-4940	988	7	al	al	PROPN
gi-4940	988	8	.	.	PUNCT
gi-4940	989	1	“	"	PUNCT
gi-4940	989	2	approximating	approximate	VERB
gi-4940	989	3	implicit	implicit	ADJ
gi-4940	989	4	curves	curve	NOUN
gi-4940	989	5	on	on	ADP
gi-4940	989	6	triangulations	triangulation	NOUN
gi-4940	989	7	with	with	ADP
gi-4940	989	8	affine	affine	NOUN
gi-4940	989	9	arithmetic	arithmetic	NOUN
gi-4940	989	10	”	"	PUNCT
gi-4940	989	11	.	.	PUNCT
gi-4940	990	1	in	in	ADP
gi-4940	990	2	:	:	PUNCT
gi-4940	990	3	graphics	graphic	NOUN
gi-4940	990	4	,	,	PUNCT
gi-4940	990	5	patterns	pattern	NOUN
gi-4940	990	6	and	and	CCONJ
gi-4940	990	7	images	image	NOUN
gi-4940	990	8	(	(	PUNCT
gi-4940	990	9	sibgrapi	sibgrapi	ADJ
gi-4940	990	10	)	)	PUNCT
gi-4940	990	11	,	,	PUNCT
gi-4940	990	12	2012	2012	NUM
gi-4940	990	13	25th	25th	NOUN
gi-4940	990	14	sibgrapi	sibgrapi	ADJ
gi-4940	990	15	conference	conference	NOUN
gi-4940	990	16	on	on	ADP
gi-4940	990	17	.	.	PUNCT
gi-4940	990	18	ieee	ieee	PROPN
gi-4940	990	19	.	.	PROPN
gi-4940	990	20	2012	2012	NUM
gi-4940	990	21	,	,	PUNCT
gi-4940	990	22	pp	pp	ADV
gi-4940	990	23	.	.	PUNCT
gi-4940	991	1	94–101	94–101	NOUN
gi-4940	991	2	.	.	PUNCT
gi-4940	992	1	[	[	X
gi-4940	992	2	22	22	NUM
gi-4940	992	3	]	]	PUNCT
gi-4940	992	4	m.	m.	NOUN
gi-4940	992	5	rossini	rossini	PROPN
gi-4940	992	6	.	.	PUNCT
gi-4940	993	1	“	"	PUNCT
gi-4940	993	2	2d	2d	NOUN
gi-4940	993	3	-	-	PUNCT
gi-4940	993	4	discontinuity	discontinuity	NOUN
gi-4940	993	5	detection	detection	NOUN
gi-4940	993	6	from	from	ADP
gi-4940	993	7	scattered	scatter	VERB
gi-4940	993	8	data	datum	NOUN
gi-4940	993	9	”	"	PUNCT
gi-4940	993	10	.	.	PUNCT
gi-4940	994	1	in	in	ADP
gi-4940	994	2	:	:	PUNCT
gi-4940	994	3	computing	compute	VERB
gi-4940	994	4	61.3	61.3	NUM
gi-4940	994	5	(	(	PUNCT
gi-4940	994	6	sept	sept	PROPN
gi-4940	994	7	.	.	PROPN
gi-4940	994	8	1998	1998	NUM
gi-4940	994	9	)	)	PUNCT
gi-4940	994	10	,	,	PUNCT
gi-4940	994	11	pp	pp	ADP
gi-4940	994	12	.	.	PUNCT
gi-4940	995	1	215–234	215–234	NUM
gi-4940	995	2	.	.	PUNCT
gi-4940	996	1	issn	issn	PROPN
gi-4940	996	2	:	:	PUNCT
gi-4940	996	3	1436	1436	NUM
gi-4940	996	4	-	-	SYM
gi-4940	996	5	5057	5057	NUM
gi-4940	996	6	.	.	PUNCT
gi-4940	997	1	doi	doi	NOUN
gi-4940	997	2	:	:	PUNCT
gi-4940	997	3	10.1007	10.1007	NUM
gi-4940	997	4	/	/	SYM
gi-4940	997	5	bf02684351	bf02684351	NOUN
gi-4940	997	6	.	.	PUNCT
gi-4940	998	1	[	[	X
gi-4940	998	2	23	23	NUM
gi-4940	998	3	]	]	X
gi-4940	998	4	moshe	moshe	PROPN
gi-4940	998	5	shpitalni	shpitalni	PROPN
gi-4940	998	6	,	,	PUNCT
gi-4940	998	7	yoram	yoram	PROPN
gi-4940	998	8	koren	koren	PROPN
gi-4940	998	9	,	,	PUNCT
gi-4940	998	10	and	and	CCONJ
gi-4940	998	11	cc	cc	PROPN
gi-4940	998	12	lo	lo	PROPN
gi-4940	998	13	.	.	PUNCT
gi-4940	999	1	“	"	PUNCT
gi-4940	999	2	realtime	realtime	ADJ
gi-4940	999	3	curve	curve	NOUN
gi-4940	999	4	interpolators	interpolator	NOUN
gi-4940	999	5	”	"	PUNCT
gi-4940	999	6	.	.	PUNCT
gi-4940	1000	1	in	in	ADP
gi-4940	1000	2	:	:	PUNCT
gi-4940	1000	3	computeraided	computeraide	VERB
gi-4940	1000	4	design	design	NOUN
gi-4940	1000	5	26.11	26.11	NUM
gi-4940	1000	6	(	(	PUNCT
gi-4940	1000	7	1994	1994	NUM
gi-4940	1000	8	)	)	PUNCT
gi-4940	1000	9	,	,	PUNCT
gi-4940	1000	10	pp	pp	ADP
gi-4940	1000	11	.	.	PUNCT
gi-4940	1001	1	832–838	832–838	NUM
gi-4940	1001	2	.	.	PUNCT
gi-4940	1002	1	[	[	X
gi-4940	1002	2	24	24	NUM
gi-4940	1002	3	]	]	X
gi-4940	1002	4	john	john	PROPN
gi-4940	1002	5	p.	p.	PROPN
gi-4940	1002	6	snyder	snyder	PROPN
gi-4940	1002	7	.	.	PUNCT
gi-4940	1003	1	map	map	VERB
gi-4940	1003	2	projections	projection	NOUN
gi-4940	1003	3	–	–	PUNCT
gi-4940	1003	4	a	a	DET
gi-4940	1003	5	working	work	VERB
gi-4940	1003	6	manual	manual	NOUN
gi-4940	1003	7	.	.	PUNCT
gi-4940	1004	1	tech	tech	NOUN
gi-4940	1004	2	.	.	PUNCT
gi-4940	1005	1	rep	rep	PROPN
gi-4940	1005	2	.	.	PROPN
gi-4940	1005	3	1395	1395	NUM
gi-4940	1005	4	.	.	PUNCT
gi-4940	1006	1	u.	u.	PROPN
gi-4940	1006	2	s.	s.	PROPN
gi-4940	1006	3	geological	geological	ADJ
gi-4940	1006	4	survey	survey	NOUN
gi-4940	1006	5	,	,	PUNCT
gi-4940	1006	6	1987	1987	NUM
gi-4940	1006	7	.	.	PUNCT
gi-4940	1007	1	url	url	PROPN
gi-4940	1007	2	:	:	PUNCT
gi-4940	1007	3	http://pubs.er.usgs.gov/usgspubs/pp/pp1395	http://pubs.er.usgs.gov/usgspubs/pp/pp1395	PROPN
gi-4940	1007	4	.	.	PUNCT
gi-4940	1008	1	[	[	X
gi-4940	1008	2	25	25	NUM
gi-4940	1008	3	]	]	X
gi-4940	1008	4	daniel	daniel	PROPN
gi-4940	1008	5	c.h	c.h	PROPN
gi-4940	1008	6	.	.	PROPN
gi-4940	1008	7	yang	yang	PROPN
gi-4940	1008	8	and	and	CCONJ
gi-4940	1008	9	tom	tom	PROPN
gi-4940	1008	10	kong	kong	PROPN
gi-4940	1008	11	.	.	PUNCT
gi-4940	1009	1	“	"	PUNCT
gi-4940	1009	2	parametric	parametric	ADJ
gi-4940	1009	3	interpolator	interpolator	NOUN
gi-4940	1009	4	versus	versus	ADP
gi-4940	1009	5	linear	linear	ADJ
gi-4940	1009	6	interpolator	interpolator	NOUN
gi-4940	1009	7	for	for	ADP
gi-4940	1009	8	precision	precision	NOUN
gi-4940	1009	9	cnc	cnc	PROPN
gi-4940	1009	10	machining	machining	NOUN
gi-4940	1009	11	”	"	PUNCT
gi-4940	1009	12	.	.	PUNCT
gi-4940	1010	1	in	in	ADP
gi-4940	1010	2	:	:	PUNCT
gi-4940	1010	3	computer	computer	NOUN
gi-4940	1010	4	-	-	PUNCT
gi-4940	1010	5	aided	aid	VERB
gi-4940	1010	6	design	design	NOUN
gi-4940	1010	7	26.3	26.3	NUM
gi-4940	1010	8	(	(	PUNCT
gi-4940	1010	9	1994	1994	NUM
gi-4940	1010	10	)	)	PUNCT
gi-4940	1010	11	.	.	PUNCT
gi-4940	1011	1	special	special	ADJ
gi-4940	1011	2	issue	issue	NOUN
gi-4940	1011	3	:	:	PUNCT
gi-4940	1011	4	nc	nc	PROPN
gi-4940	1011	5	machining	machining	NOUN
gi-4940	1011	6	and	and	CCONJ
gi-4940	1011	7	cutter	cutter	NOUN
gi-4940	1011	8	-	-	PUNCT
gi-4940	1011	9	path	path	NOUN
gi-4940	1011	10	generation	generation	NOUN
gi-4940	1011	11	,	,	PUNCT
gi-4940	1011	12	pp	pp	ADJ
gi-4940	1011	13	.	.	PUNCT
gi-4940	1012	1	225–234	225–234	NUM
gi-4940	1012	2	.	.	PUNCT
gi-4940	1013	1	issn	issn	PROPN
gi-4940	1013	2	:	:	PUNCT
gi-4940	1013	3	0010	0010	NUM
gi-4940	1013	4	-	-	SYM
gi-4940	1013	5	4485	4485	NUM
gi-4940	1013	6	.	.	PUNCT
gi-4940	1014	1	doi	doi	NOUN
gi-4940	1014	2	:	:	PUNCT
gi-4940	1014	3	https://	https://	PROPN
gi-4940	1014	4	doi.org/10.1016/0010-4485(94)90045-0	doi.org/10.1016/0010-4485(94)90045-0	PROPN
gi-4940	1014	5	.	.	PUNCT
gi-4940	1015	1	[	[	X
gi-4940	1015	2	26	26	NUM
gi-4940	1015	3	]	]	X
gi-4940	1015	4	s	s	X
gi-4940	1015	5	-	-	PUNCT
gi-4940	1015	6	s	s	X
gi-4940	1015	7	yeh	yeh	NOUN
gi-4940	1015	8	and	and	CCONJ
gi-4940	1015	9	p	p	PROPN
gi-4940	1015	10	-	-	PUNCT
gi-4940	1015	11	l	l	NOUN
gi-4940	1015	12	hsu	hsu	NOUN
gi-4940	1015	13	.	.	PUNCT
gi-4940	1016	1	“	"	PUNCT
gi-4940	1016	2	the	the	DET
gi-4940	1016	3	speed	speed	NOUN
gi-4940	1016	4	-	-	PUNCT
gi-4940	1016	5	controlled	control	VERB
gi-4940	1016	6	interpolator	interpolator	NOUN
gi-4940	1016	7	for	for	ADP
gi-4940	1016	8	machining	machine	VERB
gi-4940	1016	9	parametric	parametric	ADJ
gi-4940	1016	10	curves	curve	NOUN
gi-4940	1016	11	”	"	PUNCT
gi-4940	1016	12	.	.	PUNCT
gi-4940	1017	1	in	in	ADP
gi-4940	1017	2	:	:	PUNCT
gi-4940	1017	3	computer	computer	NOUN
gi-4940	1017	4	-	-	PUNCT
gi-4940	1017	5	aided	aid	VERB
gi-4940	1017	6	design	design	NOUN
gi-4940	1017	7	31.5	31.5	NUM
gi-4940	1017	8	(	(	PUNCT
gi-4940	1017	9	1999	1999	NUM
gi-4940	1017	10	)	)	PUNCT
gi-4940	1017	11	,	,	PUNCT
gi-4940	1017	12	pp	pp	ADP
gi-4940	1017	13	.	.	PUNCT
gi-4940	1018	1	349–357	349–357	NUM
gi-4940	1018	2	.	.	PUNCT
gi-4940	1019	1	[	[	X
gi-4940	1019	2	27	27	NUM
gi-4940	1019	3	]	]	X
gi-4940	1019	4	syh	syh	PROPN
gi-4940	1019	5	-	-	PUNCT
gi-4940	1019	6	shiuh	shiuh	NOUN
gi-4940	1019	7	yeh	yeh	PROPN
gi-4940	1019	8	and	and	CCONJ
gi-4940	1019	9	pau	pau	PROPN
gi-4940	1019	10	-	-	PUNCT
gi-4940	1019	11	lo	lo	PROPN
gi-4940	1019	12	hsu	hsu	PROPN
gi-4940	1019	13	.	.	PUNCT
gi-4940	1020	1	“	"	PUNCT
gi-4940	1020	2	adaptive	adaptive	ADJ
gi-4940	1020	3	-	-	PUNCT
gi-4940	1020	4	feedrate	feedrate	NOUN
gi-4940	1020	5	interpolation	interpolation	NOUN
gi-4940	1020	6	for	for	ADP
gi-4940	1020	7	parametric	parametric	ADJ
gi-4940	1020	8	curves	curve	NOUN
gi-4940	1020	9	with	with	ADP
gi-4940	1020	10	a	a	DET
gi-4940	1020	11	confined	confine	VERB
gi-4940	1020	12	chord	chord	NOUN
gi-4940	1020	13	error	error	NOUN
gi-4940	1020	14	”	"	PUNCT
gi-4940	1020	15	.	.	PUNCT
gi-4940	1021	1	in	in	ADP
gi-4940	1021	2	:	:	PUNCT
gi-4940	1021	3	computer	computer	NOUN
gi-4940	1021	4	-	-	PUNCT
gi-4940	1021	5	aided	aid	VERB
gi-4940	1021	6	design	design	NOUN
gi-4940	1021	7	34.3	34.3	NUM
gi-4940	1021	8	(	(	PUNCT
gi-4940	1021	9	2002	2002	NUM
gi-4940	1021	10	)	)	PUNCT
gi-4940	1021	11	,	,	PUNCT
gi-4940	1021	12	pp	pp	ADP
gi-4940	1021	13	.	.	PUNCT
gi-4940	1022	1	229–237	229–237	NUM
gi-4940	1022	2	.	.	PUNCT
gi-4940	1023	1	geoinformatics	geoinformatic	NOUN
gi-4940	1023	2	fce	fce	VERB
gi-4940	1023	3	ctu	ctu	NOUN
gi-4940	1023	4	17(2	17(2	NUM
gi-4940	1023	5	)	)	PUNCT
gi-4940	1023	6	,	,	PUNCT
gi-4940	1023	7	2018	2018	NUM
gi-4940	1023	8	63	63	NUM
gi-4940	1023	9	https://doi.org/https://doi.org/10.1016/j.amc.2017.02.043	https://doi.org/https://doi.org/10.1016/j.amc.2017.02.043	PROPN
gi-4940	1023	10	https://doi.org/https://doi.org/10.1016/j.amc.2017.02.043	https://doi.org/https://doi.org/10.1016/j.amc.2017.02.043	PROPN
gi-4940	1023	11	https://doi.org/10.1016/j.matcom.2007.08.008	https://doi.org/10.1016/j.matcom.2007.08.008	PROPN
gi-4940	1023	12	https://doi.org/https://doi.org/10.1016/s0377-0427(01)00601-x	https://doi.org/https://doi.org/10.1016/s0377-0427(01)00601-x	PROPN
gi-4940	1023	13	https://doi.org/https://doi.org/10.1016/s0377-0427(01)00601-x	https://doi.org/https://doi.org/10.1016/s0377-0427(01)00601-x	NOUN
gi-4940	1023	14	https://doi.org/10.1007/bf02684351	https://doi.org/10.1007/bf02684351	VERB
gi-4940	1023	15	http://pubs.er.usgs.gov/usgspubs/pp/pp1395	http://pubs.er.usgs.gov/usgspubs/pp/pp1395	NOUN
gi-4940	1023	16	https://doi.org/https://doi.org/10.1016/0010-4485(94)90045-0	https://doi.org/https://doi.org/10.1016/0010-4485(94)90045-0	PROPN
gi-4940	1023	17	https://doi.org/https://doi.org/10.1016/0010-4485(94)90045-0	https://doi.org/https://doi.org/10.1016/0010-4485(94)90045-0	PROPN
gi-4940	1023	18	geoinformatics	geoinformatic	NOUN
gi-4940	1023	19	fce	fce	VERB
gi-4940	1023	20	ctu	ctu	NOUN
gi-4940	1023	21	17(2	17(2	NUM
gi-4940	1023	22	)	)	PUNCT
gi-4940	1023	23	,	,	PUNCT
gi-4940	1023	24	2018	2018	NUM
gi-4940	1023	25	64	64	NUM
gi-4940	1023	26	t.	t.	NOUN
gi-4940	1023	27	bayer	bayer	NOUN
gi-4940	1023	28	:	:	PUNCT
gi-4940	1023	29	plotting	plot	VERB
gi-4940	1023	30	the	the	DET
gi-4940	1023	31	map	map	NOUN
gi-4940	1023	32	projection	projection	NOUN
gi-4940	1023	33	graticule	graticule	NOUN
gi-4940	1023	34	with	with	ADP
gi-4940	1023	35	discontinuities	discontinuity	NOUN
gi-4940	1023	36	introduction	introduction	NOUN
gi-4940	1023	37	related	relate	VERB
gi-4940	1023	38	work	work	NOUN
gi-4940	1023	39	map	map	NOUN
gi-4940	1023	40	projection	projection	NOUN
gi-4940	1023	41	and	and	CCONJ
gi-4940	1023	42	its	its	PRON
gi-4940	1023	43	properties	property	NOUN
gi-4940	1023	44	map	map	VERB
gi-4940	1023	45	projection	projection	NOUN
gi-4940	1023	46	singularities	singularity	NOUN
gi-4940	1023	47	intersection	intersection	NOUN
gi-4940	1023	48	of	of	ADP
gi-4940	1023	49	the	the	DET
gi-4940	1023	50	great	great	ADJ
gi-4940	1023	51	circle	circle	NOUN
gi-4940	1023	52	and	and	CCONJ
gi-4940	1023	53	meridian	meridian	PROPN
gi-4940	1023	54	/	/	SYM
gi-4940	1023	55	parallel	parallel	ADJ
gi-4940	1023	56	arcs	arcs	NOUN
gi-4940	1023	57	graticule	graticule	NOUN
gi-4940	1023	58	reconstruction	reconstruction	NOUN
gi-4940	1023	59	using	use	VERB
gi-4940	1023	60	the	the	DET
gi-4940	1023	61	combined	combine	VERB
gi-4940	1023	62	sampling	sample	VERB
gi-4940	1023	63	graticule	graticule	NOUN
gi-4940	1023	64	construction	construction	NOUN
gi-4940	1023	65	with	with	ADP
gi-4940	1023	66	singularities	singularity	NOUN
gi-4940	1023	67	combined	combine	VERB
gi-4940	1023	68	sampling	sampling	NOUN
gi-4940	1023	69	of	of	ADP
gi-4940	1023	70	meridian	meridian	NOUN
gi-4940	1023	71	and	and	CCONJ
gi-4940	1023	72	parallel	parallel	ADJ
gi-4940	1023	73	fragments	fragment	NOUN
gi-4940	1023	74	experiments	experiment	NOUN
gi-4940	1023	75	and	and	CCONJ
gi-4940	1023	76	results	result	VERB
gi-4940	1023	77	comparison	comparison	NOUN
gi-4940	1023	78	of	of	ADP
gi-4940	1023	79	uniform	uniform	NOUN
gi-4940	1023	80	and	and	CCONJ
gi-4940	1023	81	combined	combined	ADJ
gi-4940	1023	82	sampling	sample	VERB
gi-4940	1023	83	detection	detection	NOUN
gi-4940	1023	84	of	of	ADP
gi-4940	1023	85	discontinuities	discontinuity	NOUN
gi-4940	1023	86	:	:	PUNCT
gi-4940	1024	1	fournier	fournier	PROPN
gi-4940	1024	2	i.	i.	PROPN
gi-4940	1024	3	projection	projection	PROPN
gi-4940	1024	4	measuring	measure	VERB
gi-4940	1024	5	the	the	DET
gi-4940	1024	6	quantitative	quantitative	ADJ
gi-4940	1024	7	parameters	parameter	NOUN
gi-4940	1024	8	of	of	ADP
gi-4940	1024	9	the	the	DET
gi-4940	1024	10	algorithm	algorithm	NOUN
gi-4940	1024	11	conclusion	conclusion	NOUN