id	sid	tid	token	lemma	pos
gi-4938	1	1	efficient	efficient	ADJ
gi-4938	1	2	plotting	plot	VERB
gi-4938	1	3	the	the	DET
gi-4938	1	4	functions	function	NOUN
gi-4938	1	5	with	with	ADP
gi-4938	1	6	discontinuities	discontinuity	NOUN
gi-4938	1	7	based	base	VERB
gi-4938	1	8	on	on	ADP
gi-4938	1	9	combined	combined	ADJ
gi-4938	1	10	sampling	sample	VERB
gi-4938	1	11	efficient	efficient	ADJ
gi-4938	1	12	plotting	plot	VERB
gi-4938	1	13	the	the	DET
gi-4938	1	14	functions	function	NOUN
gi-4938	1	15	with	with	ADP
gi-4938	1	16	discontinuities	discontinuity	NOUN
gi-4938	1	17	based	base	VERB
gi-4938	1	18	on	on	ADP
gi-4938	1	19	combined	combine	VERB
gi-4938	1	20	sampling	sampling	NOUN
gi-4938	1	21	tomáš	tomáš	ADP
gi-4938	1	22	bayer	bayer	PROPN
gi-4938	1	23	department	department	PROPN
gi-4938	1	24	of	of	ADP
gi-4938	1	25	applied	apply	VERB
gi-4938	1	26	geoinformatics	geoinformatic	NOUN
gi-4938	1	27	and	and	CCONJ
gi-4938	1	28	cartography	cartography	NOUN
gi-4938	1	29	,	,	PUNCT
gi-4938	1	30	faculty	faculty	NOUN
gi-4938	1	31	of	of	ADP
gi-4938	1	32	science	science	NOUN
gi-4938	1	33	,	,	PUNCT
gi-4938	1	34	charles	charles	PROPN
gi-4938	1	35	university	university	PROPN
gi-4938	1	36	,	,	PUNCT
gi-4938	1	37	czech	czech	PROPN
gi-4938	1	38	republic	republic	PROPN
gi-4938	1	39	bayertom@natur.cuni.cz	bayertom@natur.cuni.cz	PROPN
gi-4938	1	40	abstract	abstract	ADJ
gi-4938	1	41	.	.	PUNCT
gi-4938	2	1	this	this	DET
gi-4938	2	2	article	article	NOUN
gi-4938	2	3	presents	present	VERB
gi-4938	2	4	a	a	DET
gi-4938	2	5	new	new	ADJ
gi-4938	2	6	algorithm	algorithm	NOUN
gi-4938	2	7	for	for	ADP
gi-4938	2	8	interval	interval	NOUN
gi-4938	2	9	plotting	plotting	NOUN
gi-4938	2	10	of	of	ADP
gi-4938	2	11	the	the	DET
gi-4938	2	12	function	function	NOUN
gi-4938	2	13	y	y	PROPN
gi-4938	2	14	=	=	SYM
gi-4938	2	15	f(x	f(x	PROPN
gi-4938	2	16	)	)	PUNCT
gi-4938	2	17	based	base	VERB
gi-4938	2	18	on	on	ADP
gi-4938	2	19	combined	combined	ADJ
gi-4938	2	20	sampling	sampling	NOUN
gi-4938	2	21	.	.	PUNCT
gi-4938	3	1	the	the	DET
gi-4938	3	2	proposed	propose	VERB
gi-4938	3	3	method	method	NOUN
gi-4938	3	4	synthesizes	synthesize	VERB
gi-4938	3	5	the	the	DET
gi-4938	3	6	uniform	uniform	NOUN
gi-4938	3	7	and	and	CCONJ
gi-4938	3	8	adaptive	adaptive	ADJ
gi-4938	3	9	sampling	sampling	NOUN
gi-4938	3	10	approaches	approach	NOUN
gi-4938	3	11	and	and	CCONJ
gi-4938	3	12	provides	provide	VERB
gi-4938	3	13	a	a	DET
gi-4938	3	14	more	more	ADV
gi-4938	3	15	compact	compact	ADJ
gi-4938	3	16	and	and	CCONJ
gi-4938	3	17	efficient	efficient	ADJ
gi-4938	3	18	function	function	NOUN
gi-4938	3	19	representation	representation	NOUN
gi-4938	3	20	.	.	PUNCT
gi-4938	4	1	during	during	ADP
gi-4938	4	2	the	the	DET
gi-4938	4	3	combined	combined	ADJ
gi-4938	4	4	sampling	sampling	NOUN
gi-4938	4	5	,	,	PUNCT
gi-4938	4	6	the	the	DET
gi-4938	4	7	polygonal	polygonal	ADJ
gi-4938	4	8	approximation	approximation	NOUN
gi-4938	4	9	with	with	ADP
gi-4938	4	10	a	a	DET
gi-4938	4	11	given	give	VERB
gi-4938	4	12	threshold	threshold	NOUN
gi-4938	4	13	α	α	NOUN
gi-4938	4	14	between	between	ADP
gi-4938	4	15	the	the	DET
gi-4938	4	16	adjacent	adjacent	ADJ
gi-4938	4	17	segments	segment	NOUN
gi-4938	4	18	is	be	AUX
gi-4938	4	19	constructed	construct	VERB
gi-4938	4	20	.	.	PUNCT
gi-4938	5	1	the	the	DET
gi-4938	5	2	automated	automate	VERB
gi-4938	5	3	detection	detection	NOUN
gi-4938	5	4	and	and	CCONJ
gi-4938	5	5	treatment	treatment	NOUN
gi-4938	5	6	of	of	ADP
gi-4938	5	7	the	the	DET
gi-4938	5	8	discontinuities	discontinuity	NOUN
gi-4938	5	9	based	base	VERB
gi-4938	5	10	on	on	ADP
gi-4938	5	11	the	the	DET
gi-4938	5	12	lr	lr	NOUN
gi-4938	5	13	criterion	criterion	NOUN
gi-4938	5	14	are	be	AUX
gi-4938	5	15	involved	involve	VERB
gi-4938	5	16	.	.	PUNCT
gi-4938	6	1	two	two	NUM
gi-4938	6	2	implementations	implementation	NOUN
gi-4938	6	3	,	,	PUNCT
gi-4938	6	4	the	the	DET
gi-4938	6	5	recursive	recursive	ADV
gi-4938	6	6	-	-	PUNCT
gi-4938	6	7	based	base	VERB
gi-4938	6	8	and	and	CCONJ
gi-4938	6	9	stack	stack	NOUN
gi-4938	6	10	-	-	PUNCT
gi-4938	6	11	based	base	VERB
gi-4938	6	12	,	,	PUNCT
gi-4938	6	13	are	be	AUX
gi-4938	6	14	introduced	introduce	VERB
gi-4938	6	15	.	.	PUNCT
gi-4938	7	1	finally	finally	ADV
gi-4938	7	2	,	,	PUNCT
gi-4938	7	3	several	several	ADJ
gi-4938	7	4	tests	test	NOUN
gi-4938	7	5	of	of	ADP
gi-4938	7	6	the	the	DET
gi-4938	7	7	proposed	propose	VERB
gi-4938	7	8	algorithms	algorithm	NOUN
gi-4938	7	9	for	for	ADP
gi-4938	7	10	the	the	DET
gi-4938	7	11	different	different	ADJ
gi-4938	7	12	functions	function	NOUN
gi-4938	7	13	involving	involve	VERB
gi-4938	7	14	the	the	DET
gi-4938	7	15	discontinuities	discontinuity	NOUN
gi-4938	7	16	and	and	CCONJ
gi-4938	7	17	several	several	ADJ
gi-4938	7	18	map	map	NOUN
gi-4938	7	19	projection	projection	NOUN
gi-4938	7	20	graticules	graticule	NOUN
gi-4938	7	21	are	be	AUX
gi-4938	7	22	presented	present	VERB
gi-4938	7	23	.	.	PUNCT
gi-4938	8	1	the	the	DET
gi-4938	8	2	proposed	propose	VERB
gi-4938	8	3	method	method	NOUN
gi-4938	8	4	may	may	AUX
gi-4938	8	5	be	be	AUX
gi-4938	8	6	used	use	VERB
gi-4938	8	7	for	for	ADP
gi-4938	8	8	more	more	ADV
gi-4938	8	9	efficient	efficient	ADJ
gi-4938	8	10	sampling	sample	VERB
gi-4938	8	11	the	the	DET
gi-4938	8	12	curves	curve	NOUN
gi-4938	8	13	(	(	PUNCT
gi-4938	8	14	map	map	VERB
gi-4938	8	15	projection	projection	NOUN
gi-4938	8	16	graticules	graticule	NOUN
gi-4938	8	17	,	,	PUNCT
gi-4938	8	18	contour	contour	NOUN
gi-4938	8	19	lines	line	NOUN
gi-4938	8	20	,	,	PUNCT
gi-4938	8	21	or	or	CCONJ
gi-4938	8	22	buffers	buffer	NOUN
gi-4938	8	23	)	)	PUNCT
gi-4938	8	24	in	in	ADP
gi-4938	8	25	geoinformatics	geoinformatic	NOUN
gi-4938	8	26	.	.	PUNCT
gi-4938	9	1	keywords	keyword	NOUN
gi-4938	9	2	:	:	PUNCT
gi-4938	9	3	function	function	NOUN
gi-4938	9	4	;	;	PUNCT
gi-4938	9	5	adaptive	adaptive	ADJ
gi-4938	9	6	sampling	sampling	NOUN
gi-4938	9	7	;	;	PUNCT
gi-4938	9	8	combined	combined	ADJ
gi-4938	9	9	sampling	sampling	NOUN
gi-4938	9	10	;	;	PUNCT
gi-4938	9	11	recursive	recursive	ADJ
gi-4938	9	12	approach	approach	NOUN
gi-4938	9	13	;	;	PUNCT
gi-4938	9	14	stack	stack	NOUN
gi-4938	9	15	;	;	PUNCT
gi-4938	9	16	discontinuity	discontinuity	NOUN
gi-4938	9	17	;	;	PUNCT
gi-4938	9	18	polygonal	polygonal	ADJ
gi-4938	9	19	approximation	approximation	NOUN
gi-4938	9	20	;	;	PUNCT
gi-4938	9	21	visualization	visualization	NOUN
gi-4938	9	22	;	;	PUNCT
gi-4938	9	23	map	map	NOUN
gi-4938	9	24	projection	projection	NOUN
gi-4938	9	25	;	;	PUNCT
gi-4938	9	26	plotting	plotting	NOUN
gi-4938	9	27	;	;	PUNCT
gi-4938	9	28	gis	gis	NOUN
gi-4938	9	29	;	;	PUNCT
gi-4938	9	30	octave	octave	PROPN
gi-4938	9	31	;	;	PUNCT
gi-4938	9	32	mathematica	mathematica	PROPN
gi-4938	9	33	.	.	PROPN
gi-4938	10	1	1	1	X
gi-4938	10	2	.	.	X
gi-4938	10	3	introduction	introduction	NOUN
gi-4938	10	4	a	a	DET
gi-4938	10	5	function	function	NOUN
gi-4938	10	6	y	y	PROPN
gi-4938	10	7	=	=	SYM
gi-4938	10	8	f(x	f(x	PROPN
gi-4938	10	9	)	)	PUNCT
gi-4938	10	10	on	on	ADP
gi-4938	10	11	interval	interval	NOUN
gi-4938	10	12	ω	ω	PROPN
gi-4938	10	13	=	=	PUNCT
gi-4938	11	1	[	[	X
gi-4938	11	2	a	a	X
gi-4938	11	3	,	,	PUNCT
gi-4938	11	4	b	b	NOUN
gi-4938	11	5	]	]	X
gi-4938	11	6	may	may	AUX
gi-4938	11	7	have	have	VERB
gi-4938	11	8	different	different	ADJ
gi-4938	11	9	form	form	NOUN
gi-4938	11	10	.	.	PUNCT
gi-4938	12	1	for	for	ADP
gi-4938	12	2	efficient	efficient	ADJ
gi-4938	12	3	plotting	plotting	NOUN
gi-4938	12	4	,	,	PUNCT
gi-4938	12	5	its	its	PRON
gi-4938	12	6	polygonal	polygonal	ADJ
gi-4938	12	7	approximation	approximation	NOUN
gi-4938	12	8	needs	need	VERB
gi-4938	12	9	to	to	PART
gi-4938	12	10	be	be	AUX
gi-4938	12	11	constructed	construct	VERB
gi-4938	12	12	.	.	PUNCT
gi-4938	13	1	a	a	DET
gi-4938	13	2	current	current	ADJ
gi-4938	13	3	approach	approach	NOUN
gi-4938	13	4	concentrated	concentrate	VERB
gi-4938	13	5	on	on	ADP
gi-4938	13	6	uniform	uniform	ADJ
gi-4938	13	7	sampling	sample	VERB
gi-4938	13	8	with	with	ADP
gi-4938	13	9	the	the	DET
gi-4938	13	10	step	step	NOUN
gi-4938	13	11	δx	δx	NOUN
gi-4938	13	12	may	may	AUX
gi-4938	13	13	not	not	PART
gi-4938	13	14	be	be	AUX
gi-4938	13	15	sufficient	sufficient	ADJ
gi-4938	13	16	.	.	PUNCT
gi-4938	14	1	despite	despite	SCONJ
gi-4938	14	2	its	its	PRON
gi-4938	14	3	popularity	popularity	NOUN
gi-4938	14	4	,	,	PUNCT
gi-4938	14	5	the	the	DET
gi-4938	14	6	equally	equally	ADV
gi-4938	14	7	spaced	spaced	ADJ
gi-4938	14	8	points	point	NOUN
gi-4938	14	9	can	can	AUX
gi-4938	14	10	not	not	PART
gi-4938	14	11	describe	describe	VERB
gi-4938	14	12	its	its	PRON
gi-4938	14	13	course	course	NOUN
gi-4938	14	14	without	without	ADP
gi-4938	14	15	errors	error	NOUN
gi-4938	14	16	;	;	PUNCT
gi-4938	14	17	the	the	DET
gi-4938	14	18	problems	problem	NOUN
gi-4938	14	19	of	of	ADP
gi-4938	14	20	undersampling	undersample	VERB
gi-4938	14	21	or	or	CCONJ
gi-4938	14	22	oversampling	oversampling	ADJ
gi-4938	14	23	are	be	AUX
gi-4938	14	24	common	common	ADJ
gi-4938	14	25	.	.	PUNCT
gi-4938	15	1	adaptive	adaptive	ADJ
gi-4938	15	2	sampling	sampling	NOUN
gi-4938	15	3	brings	bring	VERB
gi-4938	15	4	several	several	ADJ
gi-4938	15	5	benefits	benefit	NOUN
gi-4938	15	6	,	,	PUNCT
gi-4938	15	7	it	it	PRON
gi-4938	15	8	adapts	adapt	VERB
gi-4938	15	9	to	to	ADP
gi-4938	15	10	a	a	DET
gi-4938	15	11	different	different	ADJ
gi-4938	15	12	curvature	curvature	NOUN
gi-4938	15	13	of	of	ADP
gi-4938	15	14	the	the	DET
gi-4938	15	15	function	function	NOUN
gi-4938	15	16	,	,	PUNCT
gi-4938	15	17	reduces	reduce	VERB
gi-4938	15	18	the	the	DET
gi-4938	15	19	amount	amount	NOUN
gi-4938	15	20	of	of	ADP
gi-4938	15	21	redundant	redundant	ADJ
gi-4938	15	22	data	datum	NOUN
gi-4938	15	23	and	and	CCONJ
gi-4938	15	24	provides	provide	VERB
gi-4938	15	25	a	a	DET
gi-4938	15	26	natural	natural	ADJ
gi-4938	15	27	and	and	CCONJ
gi-4938	15	28	smooth	smooth	ADJ
gi-4938	15	29	plot	plot	NOUN
gi-4938	15	30	of	of	ADP
gi-4938	15	31	the	the	DET
gi-4938	15	32	function	function	NOUN
gi-4938	15	33	without	without	ADP
gi-4938	15	34	the	the	DET
gi-4938	15	35	jumps	jump	NOUN
gi-4938	15	36	and	and	CCONJ
gi-4938	15	37	breaks	break	NOUN
gi-4938	15	38	.	.	PUNCT
gi-4938	16	1	this	this	DET
gi-4938	16	2	technique	technique	NOUN
gi-4938	16	3	is	be	AUX
gi-4938	16	4	popular	popular	ADJ
gi-4938	16	5	in	in	ADP
gi-4938	16	6	computer	computer	NOUN
gi-4938	16	7	graphics	graphic	NOUN
gi-4938	16	8	;	;	PUNCT
gi-4938	16	9	recall	recall	VERB
gi-4938	16	10	the	the	DET
gi-4938	16	11	well	well	ADV
gi-4938	16	12	-	-	PUNCT
gi-4938	16	13	known	know	VERB
gi-4938	16	14	decasteljau	decasteljau	NOUN
gi-4938	16	15	or	or	CCONJ
gi-4938	16	16	chaikin	chaikin	NOUN
gi-4938	16	17	’s	’s	PART
gi-4938	16	18	algorithms	algorithm	NOUN
gi-4938	16	19	for	for	ADP
gi-4938	16	20	the	the	DET
gi-4938	16	21	curve	curve	NOUN
gi-4938	16	22	approximation	approximation	NOUN
gi-4938	16	23	.	.	PUNCT
gi-4938	17	1	combining	combine	VERB
gi-4938	17	2	the	the	DET
gi-4938	17	3	uniform	uniform	NOUN
gi-4938	17	4	and	and	CCONJ
gi-4938	17	5	adaptive	adaptive	ADJ
gi-4938	17	6	sampling	sampling	NOUN
gi-4938	17	7	approaches	approach	NOUN
gi-4938	17	8	their	their	PRON
gi-4938	17	9	advantages	advantage	NOUN
gi-4938	17	10	can	can	AUX
gi-4938	17	11	be	be	AUX
gi-4938	17	12	synthesized	synthesize	VERB
gi-4938	17	13	.	.	PUNCT
gi-4938	18	1	the	the	DET
gi-4938	18	2	resulted	resulted	ADJ
gi-4938	18	3	representation	representation	NOUN
gi-4938	18	4	is	be	AUX
gi-4938	18	5	more	more	ADV
gi-4938	18	6	compact	compact	ADJ
gi-4938	18	7	,	,	PUNCT
gi-4938	18	8	efficient	efficient	ADJ
gi-4938	18	9	and	and	CCONJ
gi-4938	18	10	smooth	smooth	ADJ
gi-4938	18	11	.	.	PUNCT
gi-4938	19	1	a	a	DET
gi-4938	19	2	function	function	NOUN
gi-4938	19	3	may	may	AUX
gi-4938	19	4	contain	contain	VERB
gi-4938	19	5	points	point	NOUN
gi-4938	19	6	of	of	ADP
gi-4938	19	7	discontinuities	discontinuity	NOUN
gi-4938	19	8	that	that	PRON
gi-4938	19	9	need	need	VERB
gi-4938	19	10	to	to	PART
gi-4938	19	11	be	be	AUX
gi-4938	19	12	detected	detect	VERB
gi-4938	19	13	.	.	PUNCT
gi-4938	20	1	a	a	DET
gi-4938	20	2	subdivision	subdivision	NOUN
gi-4938	20	3	of	of	ADP
gi-4938	20	4	the	the	DET
gi-4938	20	5	given	give	VERB
gi-4938	20	6	interval	interval	NOUN
gi-4938	20	7	ω	ω	NOUN
gi-4938	20	8	,	,	PUNCT
gi-4938	20	9	to	to	ADP
gi-4938	20	10	the	the	DET
gi-4938	20	11	set	set	NOUN
gi-4938	20	12	of	of	ADP
gi-4938	20	13	disjoint	disjoint	NOUN
gi-4938	20	14	subintervals	subinterval	NOUN
gi-4938	20	15	ωg	ωg	ADP
gi-4938	20	16	k	k	PROPN
gi-4938	20	17	without	without	ADP
gi-4938	20	18	the	the	DET
gi-4938	20	19	internal	internal	ADJ
gi-4938	20	20	singularities	singularity	NOUN
gi-4938	20	21	,	,	PUNCT
gi-4938	20	22	containing	contain	VERB
gi-4938	20	23	only	only	ADV
gi-4938	20	24	“	"	PUNCT
gi-4938	20	25	good	good	ADJ
gi-4938	20	26	”	"	PUNCT
gi-4938	20	27	data	datum	NOUN
gi-4938	20	28	needs	need	VERB
gi-4938	20	29	to	to	PART
gi-4938	20	30	be	be	AUX
gi-4938	20	31	undertaken	undertake	VERB
gi-4938	20	32	.	.	PUNCT
gi-4938	21	1	in	in	ADP
gi-4938	21	2	other	other	ADJ
gi-4938	21	3	words	word	NOUN
gi-4938	21	4	,	,	PUNCT
gi-4938	21	5	the	the	DET
gi-4938	21	6	polygonal	polygonal	ADJ
gi-4938	21	7	approximation	approximation	NOUN
gi-4938	21	8	of	of	ADP
gi-4938	21	9	the	the	DET
gi-4938	21	10	function	function	NOUN
gi-4938	21	11	needs	need	VERB
gi-4938	21	12	to	to	PART
gi-4938	21	13	be	be	AUX
gi-4938	21	14	split	split	VERB
gi-4938	21	15	into	into	ADP
gi-4938	21	16	the	the	DET
gi-4938	21	17	several	several	ADJ
gi-4938	21	18	disjoint	disjoint	NOUN
gi-4938	21	19	parts	part	NOUN
gi-4938	21	20	.	.	PUNCT
gi-4938	22	1	the	the	DET
gi-4938	22	2	proposed	propose	VERB
gi-4938	22	3	method	method	NOUN
gi-4938	22	4	works	work	VERB
gi-4938	22	5	by	by	ADP
gi-4938	22	6	the	the	DET
gi-4938	22	7	requirements	requirement	NOUN
gi-4938	22	8	mentioned	mention	VERB
gi-4938	22	9	above	above	ADV
gi-4938	22	10	.	.	PUNCT
gi-4938	23	1	a	a	DET
gi-4938	23	2	broad	broad	ADJ
gi-4938	23	3	set	set	NOUN
gi-4938	23	4	of	of	ADP
gi-4938	23	5	the	the	DET
gi-4938	23	6	singularities	singularity	NOUN
gi-4938	23	7	can	can	AUX
gi-4938	23	8	be	be	AUX
gi-4938	23	9	detected	detect	VERB
gi-4938	23	10	and	and	CCONJ
gi-4938	23	11	treated	treat	VERB
gi-4938	23	12	using	use	VERB
gi-4938	23	13	the	the	DET
gi-4938	23	14	multiple	multiple	ADJ
gi-4938	23	15	criteria	criterion	NOUN
gi-4938	23	16	.	.	PUNCT
gi-4938	24	1	subsequently	subsequently	ADV
gi-4938	24	2	,	,	PUNCT
gi-4938	24	3	for	for	ADP
gi-4938	24	4	each	each	DET
gi-4938	24	5	interval	interval	NOUN
gi-4938	24	6	ωg	ωg	PROPN
gi-4938	24	7	k	k	PROPN
gi-4938	24	8	,	,	PUNCT
gi-4938	24	9	a	a	DET
gi-4938	24	10	polygonal	polygonal	ADJ
gi-4938	24	11	approximation	approximation	NOUN
gi-4938	24	12	of	of	ADP
gi-4938	24	13	f(x	f(x	PROPN
gi-4938	24	14	)	)	PUNCT
gi-4938	24	15	is	be	AUX
gi-4938	24	16	constructed	construct	VERB
gi-4938	24	17	using	use	VERB
gi-4938	24	18	combined	combined	ADJ
gi-4938	24	19	sampling	sampling	NOUN
gi-4938	24	20	.	.	PUNCT
gi-4938	25	1	since	since	SCONJ
gi-4938	25	2	there	there	PRON
gi-4938	25	3	are	be	VERB
gi-4938	25	4	many	many	ADJ
gi-4938	25	5	sophisticated	sophisticated	ADJ
gi-4938	25	6	solutions	solution	NOUN
gi-4938	25	7	built	build	VERB
gi-4938	25	8	-	-	PUNCT
gi-4938	25	9	in	in	ADP
gi-4938	25	10	the	the	DET
gi-4938	25	11	high	high	ADJ
gi-4938	25	12	-	-	PUNCT
gi-4938	25	13	end	end	NOUN
gi-4938	25	14	systems	system	NOUN
gi-4938	25	15	(	(	PUNCT
gi-4938	25	16	mathematica	mathematica	PROPN
gi-4938	25	17	,	,	PUNCT
gi-4938	25	18	maple	maple	NOUN
gi-4938	25	19	)	)	PUNCT
gi-4938	25	20	,	,	PUNCT
gi-4938	25	21	our	our	PRON
gi-4938	25	22	simple	simple	ADJ
gi-4938	25	23	algorithm	algorithm	NOUN
gi-4938	25	24	based	base	VERB
gi-4938	25	25	on	on	ADP
gi-4938	25	26	the	the	DET
gi-4938	25	27	recursive	recursive	ADJ
gi-4938	25	28	approach	approach	NOUN
gi-4938	25	29	is	be	AUX
gi-4938	25	30	efficient	efficient	ADJ
gi-4938	25	31	and	and	CCONJ
gi-4938	25	32	easy	easy	ADJ
gi-4938	25	33	-	-	PUNCT
gi-4938	25	34	to	to	PART
gi-4938	25	35	-	-	PUNCT
gi-4938	25	36	implement	implement	VERB
gi-4938	25	37	.	.	PUNCT
gi-4938	26	1	this	this	DET
gi-4938	26	2	paper	paper	NOUN
gi-4938	26	3	is	be	AUX
gi-4938	26	4	organized	organize	VERB
gi-4938	26	5	as	as	SCONJ
gi-4938	26	6	follows	follow	VERB
gi-4938	26	7	.	.	PUNCT
gi-4938	27	1	in	in	ADP
gi-4938	27	2	section	section	NOUN
gi-4938	27	3	3	3	NUM
gi-4938	27	4	,	,	PUNCT
gi-4938	27	5	the	the	DET
gi-4938	27	6	combined	combined	ADJ
gi-4938	27	7	sampling	sampling	NOUN
gi-4938	27	8	technique	technique	NOUN
gi-4938	27	9	for	for	ADP
gi-4938	27	10	1d	1d	NUM
gi-4938	27	11	functions	function	NOUN
gi-4938	27	12	is	be	AUX
gi-4938	27	13	presented	present	VERB
gi-4938	27	14	.	.	PUNCT
gi-4938	28	1	section	section	NOUN
gi-4938	28	2	4	4	NUM
gi-4938	28	3	deals	deal	NOUN
gi-4938	28	4	with	with	ADP
gi-4938	28	5	the	the	DET
gi-4938	28	6	detection	detection	NOUN
gi-4938	28	7	of	of	ADP
gi-4938	28	8	singularities	singularity	NOUN
gi-4938	28	9	,	,	PUNCT
gi-4938	28	10	section	section	NOUN
gi-4938	28	11	5	5	NUM
gi-4938	28	12	describes	describe	VERB
gi-4938	28	13	the	the	DET
gi-4938	28	14	combined	combined	ADJ
gi-4938	28	15	sampling	sampling	NOUN
gi-4938	28	16	of	of	ADP
gi-4938	28	17	the	the	DET
gi-4938	28	18	discontinuous	discontinuous	ADJ
gi-4938	28	19	functions	function	NOUN
gi-4938	28	20	.	.	PUNCT
gi-4938	29	1	in	in	ADP
gi-4938	29	2	section	section	NOUN
gi-4938	29	3	6	6	NUM
gi-4938	29	4	,	,	PUNCT
gi-4938	29	5	the	the	DET
gi-4938	29	6	combined	combine	VERB
gi-4938	29	7	sampling	sampling	NOUN
gi-4938	29	8	geoinformatics	geoinformatic	NOUN
gi-4938	29	9	fce	fce	VERB
gi-4938	29	10	ctu	ctu	NOUN
gi-4938	29	11	17(2	17(2	NUM
gi-4938	29	12	)	)	PUNCT
gi-4938	29	13	,	,	PUNCT
gi-4938	29	14	2018	2018	NUM
gi-4938	30	1	,	,	PUNCT
gi-4938	30	2	doi:10.14311	doi:10.14311	NOUN
gi-4938	30	3	/	/	SYM
gi-4938	30	4	gi.17.2.2	gi.17.2.2	PROPN
gi-4938	30	5	9	9	NUM
gi-4938	30	6	http://orcid.org/0000-0001-6279-1926	http://orcid.org/0000-0001-6279-1926	NOUN
gi-4938	30	7	http://dx.doi.org/10.14311/gi.17.2.2	http://dx.doi.org/10.14311/gi.17.2.2	PROPN
gi-4938	30	8	http://creativecommons.org/licenses/by/4.0/	http://creativecommons.org/licenses/by/4.0/	PROPN
gi-4938	30	9	t.	t.	PROPN
gi-4938	30	10	bayer	bayer	PROPN
gi-4938	30	11	:	:	PUNCT
gi-4938	30	12	efficient	efficient	ADJ
gi-4938	30	13	plotting	plot	VERB
gi-4938	30	14	the	the	DET
gi-4938	30	15	functions	function	NOUN
gi-4938	30	16	with	with	ADP
gi-4938	30	17	discontinuities	discontinuity	NOUN
gi-4938	30	18	technique	technique	NOUN
gi-4938	30	19	is	be	AUX
gi-4938	30	20	tested	test	VERB
gi-4938	30	21	on	on	ADP
gi-4938	30	22	the	the	DET
gi-4938	30	23	set	set	NOUN
gi-4938	30	24	of	of	ADP
gi-4938	30	25	several	several	ADJ
gi-4938	30	26	functions	function	NOUN
gi-4938	30	27	.	.	PUNCT
gi-4938	31	1	subsequently	subsequently	ADV
gi-4938	31	2	,	,	PUNCT
gi-4938	31	3	its	its	PRON
gi-4938	31	4	behavior	behavior	NOUN
gi-4938	31	5	on	on	ADP
gi-4938	31	6	four	four	NUM
gi-4938	31	7	map	map	NOUN
gi-4938	31	8	projections	projection	NOUN
gi-4938	31	9	is	be	AUX
gi-4938	31	10	analyzed	analyze	VERB
gi-4938	31	11	.	.	PUNCT
gi-4938	32	1	2	2	X
gi-4938	32	2	.	.	X
gi-4938	32	3	related	relate	VERB
gi-4938	32	4	work	work	NOUN
gi-4938	32	5	there	there	PRON
gi-4938	32	6	are	be	VERB
gi-4938	32	7	several	several	ADJ
gi-4938	32	8	strategies	strategy	NOUN
gi-4938	32	9	for	for	ADP
gi-4938	32	10	plotting	plot	VERB
gi-4938	32	11	the	the	DET
gi-4938	32	12	function	function	NOUN
gi-4938	32	13	y	y	PROPN
gi-4938	32	14	=	=	SYM
gi-4938	32	15	f(x	f(x	PROPN
gi-4938	32	16	)	)	PUNCT
gi-4938	32	17	on	on	ADP
gi-4938	32	18	interval	interval	NOUN
gi-4938	32	19	ω	ω	PROPN
gi-4938	32	20	=	=	PUNCT
gi-4938	33	1	[	[	X
gi-4938	33	2	a	a	X
gi-4938	33	3	,	,	PUNCT
gi-4938	33	4	b	b	NOUN
gi-4938	33	5	]	]	X
gi-4938	33	6	.	.	PUNCT
gi-4938	34	1	the	the	DET
gi-4938	34	2	naive	naive	ADJ
gi-4938	34	3	approach	approach	NOUN
gi-4938	34	4	based	base	VERB
gi-4938	34	5	on	on	ADP
gi-4938	34	6	sampling	sample	VERB
gi-4938	34	7	of	of	ADP
gi-4938	34	8	f	f	PROPN
gi-4938	34	9	in	in	ADP
gi-4938	34	10	a	a	DET
gi-4938	34	11	fixed	fix	VERB
gi-4938	34	12	amount	amount	NOUN
gi-4938	34	13	of	of	ADP
gi-4938	34	14	the	the	DET
gi-4938	34	15	equally	equally	ADV
gi-4938	34	16	spaced	spaced	ADJ
gi-4938	34	17	points	point	NOUN
gi-4938	34	18	is	be	AUX
gi-4938	34	19	described	describe	VERB
gi-4938	34	20	in	in	ADP
gi-4938	34	21	[	[	X
gi-4938	34	22	20	20	NUM
gi-4938	34	23	]	]	PUNCT
gi-4938	34	24	.	.	PUNCT
gi-4938	35	1	the	the	DET
gi-4938	35	2	simple	simple	ADJ
gi-4938	35	3	functions	function	NOUN
gi-4938	35	4	suffer	suffer	VERB
gi-4938	35	5	from	from	ADP
gi-4938	35	6	oversampling	oversample	VERB
gi-4938	35	7	,	,	PUNCT
gi-4938	35	8	while	while	SCONJ
gi-4938	35	9	the	the	DET
gi-4938	35	10	oscillating	oscillating	NOUN
gi-4938	35	11	curves	curve	NOUN
gi-4938	35	12	are	be	AUX
gi-4938	35	13	under	under	ADV
gi-4938	35	14	-	-	PUNCT
gi-4938	35	15	sampled	sample	VERB
gi-4938	35	16	;	;	PUNCT
gi-4938	35	17	these	these	DET
gi-4938	35	18	issues	issue	NOUN
gi-4938	35	19	are	be	AUX
gi-4938	35	20	mentioned	mention	VERB
gi-4938	35	21	in	in	ADP
gi-4938	35	22	[	[	X
gi-4938	35	23	14	14	NUM
gi-4938	35	24	]	]	PUNCT
gi-4938	35	25	.	.	PUNCT
gi-4938	36	1	another	another	DET
gi-4938	36	2	approach	approach	NOUN
gi-4938	36	3	based	base	VERB
gi-4938	36	4	on	on	ADP
gi-4938	36	5	the	the	DET
gi-4938	36	6	interval	interval	NOUN
gi-4938	36	7	constraint	constraint	NOUN
gi-4938	36	8	plot	plot	NOUN
gi-4938	36	9	constructing	construct	VERB
gi-4938	36	10	a	a	DET
gi-4938	36	11	hull	hull	NOUN
gi-4938	36	12	of	of	ADP
gi-4938	36	13	the	the	DET
gi-4938	36	14	curve	curve	NOUN
gi-4938	36	15	was	be	AUX
gi-4938	36	16	described	describe	VERB
gi-4938	36	17	in	in	ADP
gi-4938	36	18	[	[	X
gi-4938	36	19	6	6	NUM
gi-4938	36	20	]	]	PUNCT
gi-4938	36	21	,	,	PUNCT
gi-4938	36	22	[	[	X
gi-4938	36	23	13	13	NUM
gi-4938	36	24	]	]	PUNCT
gi-4938	36	25	,	,	PUNCT
gi-4938	36	26	[	[	X
gi-4938	36	27	20	20	NUM
gi-4938	36	28	]	]	PUNCT
gi-4938	36	29	.	.	PUNCT
gi-4938	37	1	the	the	DET
gi-4938	37	2	automated	automate	VERB
gi-4938	37	3	detection	detection	NOUN
gi-4938	37	4	of	of	ADP
gi-4938	37	5	a	a	DET
gi-4938	37	6	useful	useful	ADJ
gi-4938	37	7	domain	domain	NOUN
gi-4938	37	8	and	and	CCONJ
gi-4938	37	9	a	a	DET
gi-4938	37	10	range	range	NOUN
gi-4938	37	11	of	of	ADP
gi-4938	37	12	the	the	DET
gi-4938	37	13	function	function	NOUN
gi-4938	37	14	is	be	AUX
gi-4938	37	15	mentioned	mention	VERB
gi-4938	37	16	in	in	ADP
gi-4938	37	17	[	[	X
gi-4938	37	18	41	41	NUM
gi-4938	37	19	]	]	PUNCT
gi-4938	37	20	;	;	PUNCT
gi-4938	37	21	the	the	DET
gi-4938	37	22	generalized	generalized	ADJ
gi-4938	37	23	interval	interval	NOUN
gi-4938	37	24	arithmetic	arithmetic	ADJ
gi-4938	37	25	approach	approach	NOUN
gi-4938	37	26	is	be	AUX
gi-4938	37	27	described	describe	VERB
gi-4938	37	28	in	in	ADP
gi-4938	37	29	[	[	X
gi-4938	37	30	40	40	NUM
gi-4938	37	31	]	]	PUNCT
gi-4938	37	32	.	.	PUNCT
gi-4938	38	1	a	a	DET
gi-4938	38	2	significant	significant	ADJ
gi-4938	38	3	refinement	refinement	NOUN
gi-4938	38	4	is	be	AUX
gi-4938	38	5	represented	represent	VERB
gi-4938	38	6	by	by	ADP
gi-4938	38	7	adaptive	adaptive	ADJ
gi-4938	38	8	sampling	sampling	NOUN
gi-4938	38	9	providing	provide	VERB
gi-4938	38	10	a	a	DET
gi-4938	38	11	higher	high	ADJ
gi-4938	38	12	sampling	sample	VERB
gi-4938	38	13	density	density	NOUN
gi-4938	38	14	in	in	ADP
gi-4938	38	15	the	the	DET
gi-4938	38	16	higher	high	ADJ
gi-4938	38	17	-	-	PUNCT
gi-4938	38	18	curvature	curvature	NOUN
gi-4938	38	19	regions	region	NOUN
gi-4938	38	20	.	.	PUNCT
gi-4938	39	1	the	the	PRON
gi-4938	39	2	are	be	AUX
gi-4938	39	3	several	several	ADJ
gi-4938	39	4	algorithms	algorithm	NOUN
gi-4938	39	5	for	for	ADP
gi-4938	39	6	the	the	DET
gi-4938	39	7	curve	curve	NOUN
gi-4938	39	8	interpolation	interpolation	NOUN
gi-4938	39	9	preserving	preserve	VERB
gi-4938	39	10	the	the	DET
gi-4938	39	11	speed	speed	NOUN
gi-4938	39	12	,	,	PUNCT
gi-4938	39	13	for	for	ADP
gi-4938	39	14	example	example	NOUN
gi-4938	39	15	:	:	PUNCT
gi-4938	40	1	[	[	X
gi-4938	40	2	37	37	NUM
gi-4938	40	3	]	]	PUNCT
gi-4938	40	4	,	,	PUNCT
gi-4938	40	5	[	[	X
gi-4938	40	6	42	42	NUM
gi-4938	40	7	]	]	PUNCT
gi-4938	40	8	,	,	PUNCT
gi-4938	40	9	[	[	X
gi-4938	40	10	43	43	NUM
gi-4938	40	11	]	]	PUNCT
gi-4938	40	12	.	.	PUNCT
gi-4938	41	1	the	the	DET
gi-4938	41	2	adaptive	adaptive	ADJ
gi-4938	41	3	feed	feed	NOUN
gi-4938	41	4	rate	rate	NOUN
gi-4938	41	5	technique	technique	NOUN
gi-4938	41	6	is	be	AUX
gi-4938	41	7	described	describe	VERB
gi-4938	41	8	in	in	ADP
gi-4938	41	9	[	[	X
gi-4938	41	10	44	44	NUM
gi-4938	41	11	]	]	PUNCT
gi-4938	41	12	.	.	PUNCT
gi-4938	42	1	an	an	DET
gi-4938	42	2	early	early	ADJ
gi-4938	42	3	implementation	implementation	NOUN
gi-4938	42	4	in	in	ADP
gi-4938	42	5	the	the	DET
gi-4938	42	6	mathematica	mathematica	PROPN
gi-4938	42	7	software	software	PROPN
gi-4938	42	8	is	be	AUX
gi-4938	42	9	presented	present	VERB
gi-4938	42	10	in	in	ADP
gi-4938	42	11	[	[	X
gi-4938	42	12	39	39	NUM
gi-4938	42	13	]	]	PUNCT
gi-4938	42	14	.	.	PUNCT
gi-4938	43	1	by	by	ADP
gi-4938	43	2	reducing	reduce	VERB
gi-4938	43	3	data	datum	NOUN
gi-4938	43	4	,	,	PUNCT
gi-4938	43	5	these	these	DET
gi-4938	43	6	methods	method	NOUN
gi-4938	43	7	are	be	AUX
gi-4938	43	8	very	very	ADV
gi-4938	43	9	efficient	efficient	ADJ
gi-4938	43	10	for	for	ADP
gi-4938	43	11	the	the	DET
gi-4938	43	12	curve	curve	NOUN
gi-4938	43	13	plotting	plotting	NOUN
gi-4938	43	14	.	.	PUNCT
gi-4938	44	1	the	the	DET
gi-4938	44	2	polygonal	polygonal	ADJ
gi-4938	44	3	approximation	approximation	NOUN
gi-4938	44	4	of	of	ADP
gi-4938	44	5	the	the	DET
gi-4938	44	6	parametric	parametric	ADJ
gi-4938	44	7	curve	curve	NOUN
gi-4938	44	8	based	base	VERB
gi-4938	44	9	on	on	ADP
gi-4938	44	10	adaptive	adaptive	ADJ
gi-4938	44	11	sampling	sampling	NOUN
gi-4938	44	12	is	be	AUX
gi-4938	44	13	mentioned	mention	VERB
gi-4938	44	14	in	in	ADP
gi-4938	44	15	the	the	DET
gi-4938	44	16	several	several	ADJ
gi-4938	44	17	papers	paper	NOUN
gi-4938	44	18	.	.	PUNCT
gi-4938	45	1	the	the	DET
gi-4938	45	2	refinement	refinement	NOUN
gi-4938	45	3	criteria	criterion	NOUN
gi-4938	45	4	,	,	PUNCT
gi-4938	45	5	as	as	ADV
gi-4938	45	6	well	well	ADV
gi-4938	45	7	as	as	ADP
gi-4938	45	8	the	the	DET
gi-4938	45	9	recursive	recursive	ADJ
gi-4938	45	10	approach	approach	NOUN
gi-4938	45	11	,	,	PUNCT
gi-4938	45	12	are	be	AUX
gi-4938	45	13	discussed	discuss	VERB
gi-4938	45	14	in	in	ADP
gi-4938	45	15	[	[	X
gi-4938	45	16	15	15	NUM
gi-4938	45	17	]	]	PUNCT
gi-4938	45	18	.	.	PUNCT
gi-4938	46	1	an	an	DET
gi-4938	46	2	approximation	approximation	NOUN
gi-4938	46	3	by	by	ADP
gi-4938	46	4	the	the	DET
gi-4938	46	5	polygonal	polygonal	ADJ
gi-4938	46	6	curves	curve	NOUN
gi-4938	46	7	is	be	AUX
gi-4938	46	8	described	describe	VERB
gi-4938	46	9	in	in	ADP
gi-4938	46	10	[	[	X
gi-4938	46	11	7	7	NUM
gi-4938	46	12	]	]	PUNCT
gi-4938	46	13	,	,	PUNCT
gi-4938	46	14	the	the	DET
gi-4938	46	15	robust	robust	ADJ
gi-4938	46	16	method	method	NOUN
gi-4938	46	17	for	for	ADP
gi-4938	46	18	the	the	DET
gi-4938	46	19	geometric	geometric	ADJ
gi-4938	46	20	and	and	CCONJ
gi-4938	46	21	spatial	spatial	ADJ
gi-4938	46	22	approximation	approximation	NOUN
gi-4938	46	23	of	of	ADP
gi-4938	46	24	the	the	DET
gi-4938	46	25	implicit	implicit	ADJ
gi-4938	46	26	curves	curve	NOUN
gi-4938	46	27	can	can	AUX
gi-4938	46	28	be	be	AUX
gi-4938	46	29	found	find	VERB
gi-4938	46	30	in	in	ADP
gi-4938	46	31	[	[	X
gi-4938	46	32	27	27	NUM
gi-4938	46	33	]	]	PUNCT
gi-4938	46	34	,	,	PUNCT
gi-4938	47	1	[	[	X
gi-4938	47	2	10	10	NUM
gi-4938	47	3	]	]	PUNCT
gi-4938	47	4	,	,	PUNCT
gi-4938	47	5	the	the	DET
gi-4938	47	6	affine	affine	NOUN
gi-4938	47	7	arithmetic	arithmetic	NOUN
gi-4938	47	8	working	work	VERB
gi-4938	47	9	in	in	ADP
gi-4938	47	10	the	the	DET
gi-4938	47	11	triangulated	triangulate	VERB
gi-4938	47	12	models	model	NOUN
gi-4938	47	13	in	in	ADP
gi-4938	47	14	[	[	X
gi-4938	47	15	32	32	NUM
gi-4938	47	16	]	]	PUNCT
gi-4938	47	17	.	.	PUNCT
gi-4938	48	1	however	however	ADV
gi-4938	48	2	,	,	PUNCT
gi-4938	48	3	the	the	DET
gi-4938	48	4	map	map	NOUN
gi-4938	48	5	projections	projection	NOUN
gi-4938	48	6	are	be	AUX
gi-4938	48	7	never	never	ADV
gi-4938	48	8	defined	define	VERB
gi-4938	48	9	by	by	ADP
gi-4938	48	10	the	the	DET
gi-4938	48	11	implicit	implicit	ADJ
gi-4938	48	12	equations	equation	NOUN
gi-4938	48	13	.	.	PUNCT
gi-4938	49	1	similar	similar	ADJ
gi-4938	49	2	approaches	approach	NOUN
gi-4938	49	3	can	can	AUX
gi-4938	49	4	be	be	AUX
gi-4938	49	5	used	use	VERB
gi-4938	49	6	for	for	ADP
gi-4938	49	7	graph	graph	NOUN
gi-4938	49	8	drawing	draw	VERB
gi-4938	49	9	[	[	X
gi-4938	49	10	21	21	NUM
gi-4938	49	11	]	]	PUNCT
gi-4938	49	12	.	.	PUNCT
gi-4938	50	1	other	other	ADJ
gi-4938	50	2	techniques	technique	NOUN
gi-4938	50	3	based	base	VERB
gi-4938	50	4	on	on	ADP
gi-4938	50	5	the	the	DET
gi-4938	50	6	approximation	approximation	NOUN
gi-4938	50	7	by	by	ADP
gi-4938	50	8	the	the	DET
gi-4938	50	9	breakpoints	breakpoint	NOUN
gi-4938	50	10	can	can	AUX
gi-4938	50	11	be	be	AUX
gi-4938	50	12	found	find	VERB
gi-4938	50	13	in	in	ADP
gi-4938	50	14	many	many	ADJ
gi-4938	50	15	papers	paper	NOUN
gi-4938	50	16	:	:	PUNCT
gi-4938	51	1	[	[	X
gi-4938	51	2	33	33	NUM
gi-4938	51	3	]	]	PUNCT
gi-4938	51	4	,	,	PUNCT
gi-4938	51	5	[	[	X
gi-4938	51	6	9	9	NUM
gi-4938	51	7	]	]	PUNCT
gi-4938	51	8	,	,	PUNCT
gi-4938	51	9	[	[	X
gi-4938	51	10	3	3	NUM
gi-4938	51	11	]	]	PUNCT
gi-4938	51	12	;	;	PUNCT
gi-4938	51	13	these	these	DET
gi-4938	51	14	approaches	approach	NOUN
gi-4938	51	15	are	be	AUX
gi-4938	51	16	used	use	VERB
gi-4938	51	17	for	for	ADP
gi-4938	51	18	the	the	DET
gi-4938	51	19	polygonal	polygonal	ADJ
gi-4938	51	20	approximation	approximation	NOUN
gi-4938	51	21	of	of	ADP
gi-4938	51	22	the	the	DET
gi-4938	51	23	closed	closed	ADJ
gi-4938	51	24	curves	curve	NOUN
gi-4938	51	25	and	and	CCONJ
gi-4938	51	26	applied	apply	VERB
gi-4938	51	27	in	in	ADP
gi-4938	51	28	computer	computer	NOUN
gi-4938	51	29	vision	vision	NOUN
gi-4938	51	30	.	.	PUNCT
gi-4938	52	1	3	3	X
gi-4938	52	2	.	.	X
gi-4938	52	3	combined	combined	ADJ
gi-4938	52	4	sampling	sampling	NOUN
gi-4938	52	5	in	in	ADP
gi-4938	52	6	this	this	DET
gi-4938	52	7	section	section	NOUN
gi-4938	52	8	,	,	PUNCT
gi-4938	52	9	the	the	DET
gi-4938	52	10	proposed	propose	VERB
gi-4938	52	11	combined	combined	ADJ
gi-4938	52	12	sampling	sampling	NOUN
gi-4938	52	13	technique	technique	NOUN
gi-4938	52	14	providing	provide	VERB
gi-4938	52	15	the	the	DET
gi-4938	52	16	polygonal	polygonal	ADJ
gi-4938	52	17	approximation	approximation	NOUN
gi-4938	52	18	of	of	ADP
gi-4938	52	19	the	the	DET
gi-4938	52	20	parametric	parametric	ADJ
gi-4938	52	21	curve	curve	NOUN
gi-4938	52	22	involving	involve	VERB
gi-4938	52	23	the	the	DET
gi-4938	52	24	discontinuities	discontinuity	NOUN
gi-4938	52	25	will	will	AUX
gi-4938	52	26	be	be	AUX
gi-4938	52	27	presented	present	VERB
gi-4938	52	28	.	.	PUNCT
gi-4938	53	1	the	the	DET
gi-4938	53	2	modified	modify	VERB
gi-4938	53	3	method	method	NOUN
gi-4938	53	4	will	will	AUX
gi-4938	53	5	be	be	AUX
gi-4938	53	6	used	use	VERB
gi-4938	53	7	for	for	ADP
gi-4938	53	8	the	the	DET
gi-4938	53	9	function	function	NOUN
gi-4938	53	10	f(x	f(x	PROPN
gi-4938	53	11	)	)	PUNCT
gi-4938	53	12	reconstruction	reconstruction	NOUN
gi-4938	53	13	and	and	CCONJ
gi-4938	53	14	plot	plot	NOUN
gi-4938	53	15	.	.	PUNCT
gi-4938	54	1	based	base	VERB
gi-4938	54	2	on	on	ADP
gi-4938	54	3	the	the	DET
gi-4938	54	4	ideas	idea	NOUN
gi-4938	54	5	of	of	ADP
gi-4938	54	6	splitting	split	VERB
gi-4938	54	7	the	the	DET
gi-4938	54	8	domain	domain	NOUN
gi-4938	54	9	into	into	ADP
gi-4938	54	10	the	the	DET
gi-4938	54	11	subintervals	subinterval	NOUN
gi-4938	54	12	without	without	ADP
gi-4938	54	13	the	the	DET
gi-4938	54	14	discontinuities	discontinuity	NOUN
gi-4938	54	15	,	,	PUNCT
gi-4938	54	16	it	it	PRON
gi-4938	54	17	represents	represent	VERB
gi-4938	54	18	a	a	DET
gi-4938	54	19	typical	typical	ADJ
gi-4938	54	20	problem	problem	NOUN
gi-4938	54	21	solvable	solvable	ADJ
gi-4938	54	22	by	by	ADP
gi-4938	54	23	the	the	DET
gi-4938	54	24	recursive	recursive	ADJ
gi-4938	54	25	approach	approach	NOUN
gi-4938	54	26	.	.	PUNCT
gi-4938	55	1	3.1	3.1	NUM
gi-4938	55	2	.	.	PUNCT
gi-4938	55	3	polygonal	polygonal	ADJ
gi-4938	55	4	approximation	approximation	NOUN
gi-4938	55	5	of	of	ADP
gi-4938	55	6	the	the	DET
gi-4938	55	7	curve	curve	NOUN
gi-4938	55	8	let	let	VERB
gi-4938	55	9	y	y	PROPN
gi-4938	55	10	=	=	SYM
gi-4938	55	11	f(x	f(x	PROPN
gi-4938	55	12	)	)	PUNCT
gi-4938	55	13	,	,	PUNCT
gi-4938	55	14	m	m	VERB
gi-4938	55	15	⊂	⊂	PROPN
gi-4938	55	16	r	r	NOUN
gi-4938	55	17	,	,	PUNCT
gi-4938	55	18	f	f	X
gi-4938	55	19	:	:	PUNCT
gi-4938	55	20	m	m	VERB
gi-4938	55	21	→	→	SYM
gi-4938	55	22	r	r	NOUN
gi-4938	55	23	be	be	AUX
gi-4938	55	24	a	a	DET
gi-4938	55	25	function	function	NOUN
gi-4938	55	26	of	of	ADP
gi-4938	55	27	a	a	DET
gi-4938	55	28	real	real	ADJ
gi-4938	55	29	variable	variable	NOUN
gi-4938	55	30	x	x	NOUN
gi-4938	55	31	,	,	PUNCT
gi-4938	55	32	and	and	CCONJ
gi-4938	55	33	the	the	DET
gi-4938	55	34	set	set	NOUN
gi-4938	55	35	m	m	VERB
gi-4938	55	36	represents	represent	VERB
gi-4938	55	37	the	the	DET
gi-4938	55	38	domain	domain	NOUN
gi-4938	55	39	of	of	ADP
gi-4938	55	40	the	the	DET
gi-4938	55	41	function	function	NOUN
gi-4938	55	42	f	f	PROPN
gi-4938	55	43	.	.	PUNCT
gi-4938	56	1	let	let	VERB
gi-4938	56	2	ω	ω	NOUN
gi-4938	56	3	=	=	PUNCT
gi-4938	57	1	[	[	X
gi-4938	57	2	a	a	X
gi-4938	57	3	,	,	PUNCT
gi-4938	57	4	b	b	NOUN
gi-4938	57	5	]	]	X
gi-4938	57	6	,	,	PUNCT
gi-4938	57	7	a	a	DET
gi-4938	57	8	∈	∈	NOUN
gi-4938	57	9	m	m	NOUN
gi-4938	57	10	,	,	PUNCT
gi-4938	57	11	b	b	X
gi-4938	57	12	∈	∈	PROPN
gi-4938	57	13	m	m	AUX
gi-4938	57	14	be	be	VERB
gi-4938	57	15	the	the	DET
gi-4938	57	16	subdomain	subdomain	NOUN
gi-4938	57	17	inside	inside	ADP
gi-4938	57	18	which	which	PRON
gi-4938	57	19	the	the	DET
gi-4938	57	20	polynomial	polynomial	ADJ
gi-4938	57	21	approximation	approximation	NOUN
gi-4938	57	22	pi	pi	NOUN
gi-4938	57	23	=	=	SYM
gi-4938	57	24	(	(	PUNCT
gi-4938	57	25	xi	xi	PROPN
gi-4938	57	26	,	,	PUNCT
gi-4938	57	27	f(xi	f(xi	PROPN
gi-4938	57	28	)	)	PUNCT
gi-4938	57	29	)	)	PUNCT
gi-4938	57	30	,	,	PUNCT
gi-4938	57	31	1	1	NUM
gi-4938	57	32	≤	≤	NUM
gi-4938	57	33	i	i	PRON
gi-4938	57	34	≤	≤	ADJ
gi-4938	57	35	n	n	PRON
gi-4938	57	36	of	of	ADP
gi-4938	57	37	the	the	DET
gi-4938	57	38	curve	curve	NOUN
gi-4938	57	39	f	f	PROPN
gi-4938	57	40	is	be	AUX
gi-4938	57	41	constructed	construct	VERB
gi-4938	57	42	,	,	PUNCT
gi-4938	58	1	where	where	SCONJ
gi-4938	58	2	x1	x1	PROPN
gi-4938	58	3	=	=	PUNCT
gi-4938	58	4	a	a	PRON
gi-4938	58	5	<	<	X
gi-4938	58	6	x1	x1	X
gi-4938	58	7	<	<	X
gi-4938	58	8	...	...	PUNCT
gi-4938	58	9	<	<	X
gi-4938	58	10	xn	xn	PUNCT
gi-4938	58	11	=	=	SYM
gi-4938	58	12	b.	b.	PROPN
gi-4938	58	13	this	this	DET
gi-4938	58	14	approach	approach	NOUN
gi-4938	58	15	leads	lead	VERB
gi-4938	58	16	to	to	ADP
gi-4938	58	17	a	a	DET
gi-4938	58	18	discrete	discrete	ADJ
gi-4938	58	19	reconstruction	reconstruction	NOUN
gi-4938	58	20	of	of	ADP
gi-4938	58	21	f	f	PROPN
gi-4938	58	22	from	from	ADP
gi-4938	58	23	the	the	DET
gi-4938	58	24	set	set	NOUN
gi-4938	58	25	of	of	ADP
gi-4938	58	26	sampled	sample	VERB
gi-4938	58	27	points	point	NOUN
gi-4938	58	28	.	.	PUNCT
gi-4938	59	1	the	the	DET
gi-4938	59	2	behavior	behavior	NOUN
gi-4938	59	3	of	of	ADP
gi-4938	59	4	f	f	PROPN
gi-4938	59	5	should	should	AUX
gi-4938	59	6	be	be	AUX
gi-4938	59	7	reconstructed	reconstruct	VERB
gi-4938	59	8	concerning	concern	VERB
gi-4938	59	9	its	its	PRON
gi-4938	59	10	curvature	curvature	NOUN
gi-4938	59	11	.	.	PUNCT
gi-4938	60	1	the	the	DET
gi-4938	60	2	classical	classical	ADJ
gi-4938	60	3	approach	approach	NOUN
gi-4938	60	4	based	base	VERB
gi-4938	60	5	on	on	ADP
gi-4938	60	6	uniform	uniform	ADJ
gi-4938	60	7	sampling	sample	VERB
gi-4938	60	8	from	from	ADP
gi-4938	60	9	the	the	DET
gi-4938	60	10	equidistant	equidistant	ADJ
gi-4938	60	11	points	point	NOUN
gi-4938	60	12	xi	xi	NOUN
gi-4938	60	13	with	with	ADP
gi-4938	60	14	the	the	DET
gi-4938	60	15	step	step	NOUN
gi-4938	60	16	δ	δ	PROPN
gi-4938	60	17	,	,	PUNCT
gi-4938	60	18	where	where	SCONJ
gi-4938	60	19	δ	δ	PROPN
gi-4938	60	20	=	=	SYM
gi-4938	60	21	xi+1−xi	xi+1−xi	PROPN
gi-4938	60	22	,	,	PUNCT
gi-4938	60	23	provides	provide	VERB
gi-4938	60	24	a	a	DET
gi-4938	60	25	good	good	ADJ
gi-4938	60	26	approximation	approximation	NOUN
gi-4938	60	27	only	only	ADV
gi-4938	60	28	if	if	SCONJ
gi-4938	60	29	δ	δ	PROPN
gi-4938	60	30	→	→	X
gi-4938	60	31	0	0	X
gi-4938	60	32	.	.	PUNCT
gi-4938	61	1	for	for	ADP
gi-4938	61	2	the	the	DET
gi-4938	61	3	straight	straight	ADJ
gi-4938	61	4	parts	part	NOUN
gi-4938	61	5	of	of	ADP
gi-4938	61	6	the	the	DET
gi-4938	61	7	curve	curve	NOUN
gi-4938	61	8	,	,	PUNCT
gi-4938	61	9	many	many	ADJ
gi-4938	61	10	geoinformatics	geoinformatic	NOUN
gi-4938	61	11	fce	fce	VERB
gi-4938	61	12	ctu	ctu	NOUN
gi-4938	61	13	17(2	17(2	NUM
gi-4938	61	14	)	)	PUNCT
gi-4938	61	15	,	,	PUNCT
gi-4938	61	16	2018	2018	NUM
gi-4938	61	17	10	10	NUM
gi-4938	61	18	t.	t.	NOUN
gi-4938	61	19	bayer	bayer	PROPN
gi-4938	61	20	:	:	PUNCT
gi-4938	61	21	efficient	efficient	ADJ
gi-4938	61	22	plotting	plot	VERB
gi-4938	61	23	the	the	DET
gi-4938	61	24	functions	function	NOUN
gi-4938	61	25	with	with	ADP
gi-4938	61	26	discontinuities	discontinuity	NOUN
gi-4938	61	27	-4	-4	PUNCT
gi-4938	62	1	-3	-3	INTJ
gi-4938	62	2	-2	-2	INTJ
gi-4938	63	1	-1	-1	NOUN
gi-4938	63	2	0	0	PUNCT
gi-4938	64	1	x	x	X
gi-4938	64	2	-2	-2	INTJ
gi-4938	65	1	-1	-1	SYM
gi-4938	65	2	0	0	NUM
gi-4938	65	3	1	1	NUM
gi-4938	65	4	2	2	NUM
gi-4938	65	5	f	f	X
gi-4938	65	6	(	(	PUNCT
gi-4938	65	7	x	x	SYM
gi-4938	65	8	)	)	PUNCT
gi-4938	65	9	as	as	ADP
gi-4938	65	10	:	:	PUNCT
gi-4938	65	11	α=1	α=1	PROPN
gi-4938	65	12	°	°	PROPN
gi-4938	65	13	,	,	PUNCT
gi-4938	65	14	83	83	NUM
gi-4938	65	15	sampled	sample	VERB
gi-4938	65	16	points	point	NOUN
gi-4938	65	17	-4	-4	INTJ
gi-4938	65	18	-3	-3	INTJ
gi-4938	65	19	-2	-2	INTJ
gi-4938	65	20	-1	-1	NOUN
gi-4938	65	21	0	0	PUNCT
gi-4938	65	22	x	x	X
gi-4938	65	23	-2	-2	INTJ
gi-4938	65	24	-1	-1	SYM
gi-4938	65	25	0	0	NUM
gi-4938	65	26	1	1	NUM
gi-4938	65	27	2	2	NUM
gi-4938	65	28	f	f	X
gi-4938	65	29	(	(	PUNCT
gi-4938	65	30	x	x	SYM
gi-4938	65	31	)	)	PUNCT
gi-4938	65	32	as	as	ADP
gi-4938	65	33	:	:	PUNCT
gi-4938	65	34	α=5	α=5	PROPN
gi-4938	65	35	°	°	PROPN
gi-4938	65	36	,	,	PUNCT
gi-4938	65	37	23	23	NUM
gi-4938	65	38	sampled	sample	VERB
gi-4938	65	39	points	point	NOUN
gi-4938	65	40	-4	-4	INTJ
gi-4938	65	41	-3	-3	INTJ
gi-4938	65	42	-2	-2	INTJ
gi-4938	66	1	-1	-1	NOUN
gi-4938	66	2	0	0	PUNCT
gi-4938	67	1	x	x	X
gi-4938	67	2	-2	-2	INTJ
gi-4938	68	1	-1	-1	SYM
gi-4938	68	2	0	0	NUM
gi-4938	68	3	1	1	NUM
gi-4938	68	4	2	2	NUM
gi-4938	68	5	f	f	X
gi-4938	68	6	(	(	PUNCT
gi-4938	68	7	x	x	SYM
gi-4938	68	8	)	)	PUNCT
gi-4938	68	9	as	as	ADP
gi-4938	68	10	:	:	PUNCT
gi-4938	68	11	α=10	α=10	NOUN
gi-4938	68	12	°	°	NOUN
gi-4938	68	13	,	,	PUNCT
gi-4938	68	14	11	11	NUM
gi-4938	68	15	sampled	sample	VERB
gi-4938	68	16	points	point	NOUN
gi-4938	68	17	-4	-4	INTJ
gi-4938	68	18	-3	-3	INTJ
gi-4938	68	19	-2	-2	INTJ
gi-4938	69	1	-1	-1	NOUN
gi-4938	69	2	0	0	PUNCT
gi-4938	70	1	x	x	X
gi-4938	70	2	-2	-2	INTJ
gi-4938	71	1	-1	-1	SYM
gi-4938	71	2	0	0	NUM
gi-4938	71	3	1	1	NUM
gi-4938	71	4	2	2	NUM
gi-4938	71	5	f	f	X
gi-4938	71	6	(	(	PUNCT
gi-4938	71	7	x	x	X
gi-4938	71	8	)	)	PUNCT
gi-4938	71	9	us	we	PRON
gi-4938	71	10	:	:	PUNCT
gi-4938	71	11	α=1	α=1	PROPN
gi-4938	71	12	°	°	PROPN
gi-4938	71	13	,	,	PUNCT
gi-4938	71	14	629	629	NUM
gi-4938	71	15	sampled	sample	VERB
gi-4938	71	16	points	point	NOUN
gi-4938	71	17	-4	-4	INTJ
gi-4938	71	18	-3	-3	INTJ
gi-4938	71	19	-2	-2	INTJ
gi-4938	71	20	-1	-1	NOUN
gi-4938	71	21	0	0	PUNCT
gi-4938	72	1	x	x	X
gi-4938	72	2	-2	-2	INTJ
gi-4938	73	1	-1	-1	SYM
gi-4938	73	2	0	0	NUM
gi-4938	73	3	1	1	NUM
gi-4938	73	4	2	2	NUM
gi-4938	73	5	f	f	X
gi-4938	73	6	(	(	PUNCT
gi-4938	73	7	x	x	X
gi-4938	73	8	)	)	PUNCT
gi-4938	73	9	us	we	PRON
gi-4938	73	10	:	:	PUNCT
gi-4938	73	11	α=5	α=5	PROPN
gi-4938	73	12	°	°	PROPN
gi-4938	73	13	,	,	PUNCT
gi-4938	73	14	117	117	NUM
gi-4938	73	15	sampled	sample	VERB
gi-4938	73	16	points	point	NOUN
gi-4938	73	17	-4	-4	INTJ
gi-4938	73	18	-3	-3	INTJ
gi-4938	73	19	-2	-2	INTJ
gi-4938	73	20	-1	-1	NOUN
gi-4938	73	21	0	0	PUNCT
gi-4938	74	1	x	x	X
gi-4938	74	2	-2	-2	INTJ
gi-4938	75	1	-1	-1	SYM
gi-4938	75	2	0	0	NUM
gi-4938	75	3	1	1	NUM
gi-4938	75	4	2	2	NUM
gi-4938	75	5	f	f	X
gi-4938	75	6	(	(	PUNCT
gi-4938	75	7	x	x	X
gi-4938	75	8	)	)	PUNCT
gi-4938	75	9	us	we	PRON
gi-4938	75	10	:	:	PUNCT
gi-4938	75	11	α=10	α=10	X
gi-4938	75	12	°	°	NOUN
gi-4938	75	13	,	,	PUNCT
gi-4938	75	14	63	63	NUM
gi-4938	75	15	sampled	sample	VERB
gi-4938	75	16	points	point	NOUN
gi-4938	75	17	figure	figure	NOUN
gi-4938	75	18	3.1	3.1	NUM
gi-4938	75	19	:	:	PUNCT
gi-4938	75	20	adaptive	adaptive	ADJ
gi-4938	75	21	(	(	PUNCT
gi-4938	75	22	as	as	ADP
gi-4938	75	23	)	)	PUNCT
gi-4938	75	24	and	and	CCONJ
gi-4938	75	25	uniform	uniform	NOUN
gi-4938	75	26	(	(	PUNCT
gi-4938	75	27	us	we	PRON
gi-4938	75	28	)	)	PUNCT
gi-4938	75	29	sampling	sampling	NOUN
gi-4938	75	30	of	of	ADP
gi-4938	75	31	the	the	DET
gi-4938	75	32	meridian	meridian	NOUN
gi-4938	75	33	of	of	ADP
gi-4938	75	34	the	the	DET
gi-4938	75	35	longitude	longitude	ADJ
gi-4938	75	36	λ	λ	NOUN
gi-4938	75	37	=	=	SYM
gi-4938	75	38	−180	−180	PROPN
gi-4938	75	39	◦	◦	NOUN
gi-4938	75	40	in	in	ADP
gi-4938	75	41	the	the	DET
gi-4938	75	42	sanson	sanson	PROPN
gi-4938	75	43	projection	projection	NOUN
gi-4938	75	44	for	for	ADP
gi-4938	75	45	angles	angle	NOUN
gi-4938	75	46	αi	αi	NOUN
gi-4938	75	47	=	=	SYM
gi-4938	75	48	1	1	NUM
gi-4938	75	49	◦	◦	NOUN
gi-4938	75	50	,	,	PUNCT
gi-4938	75	51	5	5	NUM
gi-4938	75	52	◦	◦	NOUN
gi-4938	75	53	,	,	PUNCT
gi-4938	75	54	10	10	NUM
gi-4938	75	55	◦	◦	NOUN
gi-4938	75	56	.	.	PUNCT
gi-4938	76	1	almost	almost	ADV
gi-4938	76	2	colinear	colinear	ADJ
gi-4938	76	3	segments	segment	NOUN
gi-4938	76	4	are	be	AUX
gi-4938	76	5	constructed	construct	VERB
gi-4938	76	6	;	;	PUNCT
gi-4938	76	7	too	too	ADV
gi-4938	76	8	much	much	ADJ
gi-4938	76	9	redundant	redundant	ADJ
gi-4938	76	10	data	datum	NOUN
gi-4938	76	11	is	be	AUX
gi-4938	76	12	generated	generate	VERB
gi-4938	76	13	.	.	PUNCT
gi-4938	77	1	conversely	conversely	ADV
gi-4938	77	2	,	,	PUNCT
gi-4938	77	3	for	for	ADP
gi-4938	77	4	larger	large	ADJ
gi-4938	77	5	δ	δ	PROPN
gi-4938	77	6	,	,	PUNCT
gi-4938	77	7	the	the	DET
gi-4938	77	8	shape	shape	NOUN
gi-4938	77	9	of	of	ADP
gi-4938	77	10	the	the	DET
gi-4938	77	11	function	function	NOUN
gi-4938	77	12	in	in	ADP
gi-4938	77	13	the	the	DET
gi-4938	77	14	high	high	ADJ
gi-4938	77	15	-	-	PUNCT
gi-4938	77	16	curvature	curvature	NOUN
gi-4938	77	17	areas	area	NOUN
gi-4938	77	18	may	may	AUX
gi-4938	77	19	not	not	PART
gi-4938	77	20	be	be	AUX
gi-4938	77	21	captured	capture	VERB
gi-4938	77	22	adequately	adequately	ADV
gi-4938	77	23	,	,	PUNCT
gi-4938	77	24	which	which	PRON
gi-4938	77	25	is	be	AUX
gi-4938	77	26	discussed	discuss	VERB
gi-4938	77	27	in	in	ADP
gi-4938	77	28	[	[	X
gi-4938	77	29	15	15	NUM
gi-4938	77	30	]	]	PUNCT
gi-4938	77	31	.	.	PUNCT
gi-4938	78	1	in	in	ADP
gi-4938	78	2	general	general	ADJ
gi-4938	78	3	,	,	PUNCT
gi-4938	78	4	the	the	DET
gi-4938	78	5	main	main	ADJ
gi-4938	78	6	disadvantages	disadvantage	NOUN
gi-4938	78	7	of	of	ADP
gi-4938	78	8	uniform	uniform	ADJ
gi-4938	78	9	sampling	sampling	NOUN
gi-4938	78	10	,	,	PUNCT
gi-4938	78	11	the	the	DET
gi-4938	78	12	problems	problem	NOUN
gi-4938	78	13	of	of	ADP
gi-4938	78	14	undersampling	undersample	VERB
gi-4938	78	15	or	or	CCONJ
gi-4938	78	16	oversampling	oversampling	ADJ
gi-4938	78	17	,	,	PUNCT
gi-4938	78	18	are	be	AUX
gi-4938	78	19	referred	refer	VERB
gi-4938	78	20	.	.	PUNCT
gi-4938	79	1	for	for	ADP
gi-4938	79	2	a	a	DET
gi-4938	79	3	current	current	ADJ
gi-4938	79	4	density	density	NOUN
gi-4938	79	5	of	of	ADP
gi-4938	79	6	the	the	DET
gi-4938	79	7	sample	sample	NOUN
gi-4938	79	8	,	,	PUNCT
gi-4938	79	9	the	the	DET
gi-4938	79	10	equally	equally	ADV
gi-4938	79	11	spaced	spaced	ADJ
gi-4938	79	12	points	point	NOUN
gi-4938	79	13	can	can	AUX
gi-4938	79	14	not	not	PART
gi-4938	79	15	describe	describe	VERB
gi-4938	79	16	the	the	DET
gi-4938	79	17	function	function	NOUN
gi-4938	79	18	course	course	NOUN
gi-4938	79	19	without	without	ADP
gi-4938	79	20	errors	error	NOUN
gi-4938	79	21	.	.	PUNCT
gi-4938	80	1	3.2	3.2	NUM
gi-4938	80	2	.	.	PUNCT
gi-4938	80	3	combined	combine	VERB
gi-4938	80	4	sampling	sampling	NOUN
gi-4938	80	5	technique	technique	NOUN
gi-4938	80	6	by	by	ADP
gi-4938	80	7	avoiding	avoid	VERB
gi-4938	80	8	colinear	colinear	ADJ
gi-4938	80	9	segments	segment	NOUN
gi-4938	80	10	as	as	ADV
gi-4938	80	11	well	well	ADV
gi-4938	80	12	as	as	ADP
gi-4938	80	13	a	a	DET
gi-4938	80	14	better	well	ADJ
gi-4938	80	15	adaptation	adaptation	NOUN
gi-4938	80	16	to	to	ADP
gi-4938	80	17	the	the	DET
gi-4938	80	18	different	different	ADJ
gi-4938	80	19	curvature	curvature	NOUN
gi-4938	80	20	,	,	PUNCT
gi-4938	80	21	adaptive	adaptive	ADJ
gi-4938	80	22	sampling	sampling	NOUN
gi-4938	80	23	respects	respect	NOUN
gi-4938	80	24	the	the	DET
gi-4938	80	25	behavior	behavior	NOUN
gi-4938	80	26	of	of	ADP
gi-4938	80	27	the	the	DET
gi-4938	80	28	function	function	NOUN
gi-4938	80	29	more	more	ADV
gi-4938	80	30	naturally	naturally	ADV
gi-4938	80	31	.	.	PUNCT
gi-4938	81	1	it	it	PRON
gi-4938	81	2	leads	lead	VERB
gi-4938	81	3	to	to	ADP
gi-4938	81	4	the	the	DET
gi-4938	81	5	more	more	ADV
gi-4938	81	6	compact	compact	ADJ
gi-4938	81	7	data	datum	NOUN
gi-4938	81	8	representation	representation	NOUN
gi-4938	81	9	of	of	ADP
gi-4938	81	10	the	the	DET
gi-4938	81	11	curve	curve	NOUN
gi-4938	81	12	while	while	SCONJ
gi-4938	81	13	its	its	PRON
gi-4938	81	14	shape	shape	NOUN
gi-4938	81	15	,	,	PUNCT
gi-4938	81	16	as	as	ADV
gi-4938	81	17	well	well	ADV
gi-4938	81	18	as	as	ADP
gi-4938	81	19	its	its	PRON
gi-4938	81	20	aesthetic	aesthetic	ADJ
gi-4938	81	21	look	look	NOUN
gi-4938	81	22	,	,	PUNCT
gi-4938	81	23	are	be	AUX
gi-4938	81	24	preserved	preserve	VERB
gi-4938	81	25	.	.	PUNCT
gi-4938	82	1	a	a	DET
gi-4938	82	2	comparison	comparison	NOUN
gi-4938	82	3	of	of	ADP
gi-4938	82	4	adaptive	adaptive	ADJ
gi-4938	82	5	and	and	CCONJ
gi-4938	82	6	uniform	uniform	ADJ
gi-4938	82	7	sampling	sample	VERB
gi-4938	82	8	for	for	ADP
gi-4938	82	9	the	the	DET
gi-4938	82	10	meridian	meridian	PROPN
gi-4938	82	11	curve	curve	NOUN
gi-4938	82	12	is	be	AUX
gi-4938	82	13	illustrated	illustrate	VERB
gi-4938	82	14	in	in	ADP
gi-4938	82	15	fig	fig	NOUN
gi-4938	82	16	.	.	PUNCT
gi-4938	83	1	3.1	3.1	NUM
gi-4938	83	2	.	.	PUNCT
gi-4938	83	3	uniform	uniform	ADJ
gi-4938	83	4	sampling	sampling	NOUN
gi-4938	83	5	requires	require	VERB
gi-4938	83	6	more	more	ADJ
gi-4938	83	7	data	datum	NOUN
gi-4938	83	8	to	to	PART
gi-4938	83	9	maintain	maintain	VERB
gi-4938	83	10	the	the	DET
gi-4938	83	11	same	same	ADJ
gi-4938	83	12	curvature	curvature	NOUN
gi-4938	83	13	represented	represent	VERB
gi-4938	83	14	by	by	ADP
gi-4938	83	15	the	the	DET
gi-4938	83	16	angle	angle	NOUN
gi-4938	83	17	αi	αi	VERB
gi-4938	83	18	between	between	ADP
gi-4938	83	19	the	the	DET
gi-4938	83	20	adjacent	adjacent	ADJ
gi-4938	83	21	segments	segment	NOUN
gi-4938	83	22	(	(	PUNCT
gi-4938	83	23	pi−1	pi−1	NOUN
gi-4938	83	24	,	,	PUNCT
gi-4938	83	25	pi	pi	NOUN
gi-4938	83	26	)	)	PUNCT
gi-4938	83	27	and	and	CCONJ
gi-4938	83	28	(	(	PUNCT
gi-4938	83	29	pi	pi	NOUN
gi-4938	83	30	,	,	PUNCT
gi-4938	83	31	pi+1	pi+1	NOUN
gi-4938	83	32	)	)	PUNCT
gi-4938	83	33	.	.	PUNCT
gi-4938	84	1	the	the	DET
gi-4938	84	2	difference	difference	NOUN
gi-4938	84	3	increases	increase	VERB
gi-4938	84	4	depending	depend	VERB
gi-4938	84	5	on	on	ADP
gi-4938	84	6	the	the	DET
gi-4938	84	7	curvature	curvature	NOUN
gi-4938	84	8	.	.	PUNCT
gi-4938	85	1	in	in	ADP
gi-4938	85	2	general	general	ADJ
gi-4938	85	3	,	,	PUNCT
gi-4938	85	4	for	for	ADP
gi-4938	85	5	adaptive	adaptive	ADJ
gi-4938	85	6	sampling	sampling	NOUN
gi-4938	85	7	,	,	PUNCT
gi-4938	85	8	the	the	DET
gi-4938	85	9	required	require	VERB
gi-4938	85	10	amount	amount	NOUN
gi-4938	85	11	of	of	ADP
gi-4938	85	12	points	point	NOUN
gi-4938	85	13	is	be	AUX
gi-4938	85	14	about	about	ADV
gi-4938	85	15	one	one	NUM
gi-4938	85	16	order	order	NOUN
gi-4938	85	17	less	less	ADJ
gi-4938	85	18	.	.	PUNCT
gi-4938	86	1	unfortunately	unfortunately	ADV
gi-4938	86	2	,	,	PUNCT
gi-4938	86	3	two	two	NUM
gi-4938	86	4	issues	issue	NOUN
gi-4938	86	5	are	be	AUX
gi-4938	86	6	referred	refer	VERB
gi-4938	86	7	in	in	ADP
gi-4938	86	8	[	[	X
gi-4938	86	9	15	15	NUM
gi-4938	86	10	]	]	SYM
gi-4938	86	11	:	:	PUNCT
gi-4938	86	12	1	1	X
gi-4938	86	13	.	.	X
gi-4938	86	14	for	for	ADP
gi-4938	86	15	specific	specific	ADJ
gi-4938	86	16	functions	function	NOUN
gi-4938	86	17	,	,	PUNCT
gi-4938	86	18	some	some	DET
gi-4938	86	19	narrow	narrow	ADJ
gi-4938	86	20	subintervals	subinterval	NOUN
gi-4938	86	21	in	in	ADP
gi-4938	86	22	the	the	DET
gi-4938	86	23	early	early	ADJ
gi-4938	86	24	iterations	iteration	NOUN
gi-4938	86	25	may	may	AUX
gi-4938	86	26	be	be	AUX
gi-4938	86	27	skipped	skip	VERB
gi-4938	86	28	and	and	CCONJ
gi-4938	86	29	stay	stay	VERB
gi-4938	86	30	unprocessed	unprocessed	ADJ
gi-4938	86	31	.	.	PUNCT
gi-4938	87	1	2	2	X
gi-4938	87	2	.	.	X
gi-4938	87	3	for	for	ADP
gi-4938	87	4	some	some	DET
gi-4938	87	5	periodic	periodic	ADJ
gi-4938	87	6	functions	function	NOUN
gi-4938	87	7	,	,	PUNCT
gi-4938	87	8	a	a	DET
gi-4938	87	9	refinement	refinement	NOUN
gi-4938	87	10	based	base	VERB
gi-4938	87	11	on	on	ADP
gi-4938	87	12	the	the	DET
gi-4938	87	13	iterative	iterative	NOUN
gi-4938	87	14	subdivision	subdivision	NOUN
gi-4938	87	15	into	into	ADP
gi-4938	87	16	the	the	DET
gi-4938	87	17	segments	segment	NOUN
gi-4938	87	18	of	of	ADP
gi-4938	87	19	the	the	DET
gi-4938	87	20	same	same	ADJ
gi-4938	87	21	length	length	NOUN
gi-4938	87	22	may	may	AUX
gi-4938	87	23	not	not	PART
gi-4938	87	24	be	be	AUX
gi-4938	87	25	successful	successful	ADJ
gi-4938	87	26	,	,	PUNCT
gi-4938	87	27	if	if	SCONJ
gi-4938	87	28	the	the	DET
gi-4938	87	29	function	function	NOUN
gi-4938	87	30	values	value	NOUN
gi-4938	87	31	at	at	ADP
gi-4938	87	32	these	these	DET
gi-4938	87	33	points	point	NOUN
gi-4938	87	34	are	be	AUX
gi-4938	87	35	equal	equal	ADJ
gi-4938	87	36	.	.	PUNCT
gi-4938	88	1	to	to	PART
gi-4938	88	2	avoid	avoid	VERB
gi-4938	88	3	the	the	DET
gi-4938	88	4	problems	problem	NOUN
gi-4938	88	5	in	in	ADP
gi-4938	88	6	the	the	DET
gi-4938	88	7	first	first	ADJ
gi-4938	88	8	case	case	NOUN
gi-4938	88	9	,	,	PUNCT
gi-4938	88	10	it	it	PRON
gi-4938	88	11	is	be	AUX
gi-4938	88	12	natural	natural	ADJ
gi-4938	88	13	to	to	PART
gi-4938	88	14	take	take	VERB
gi-4938	88	15	advantage	advantage	NOUN
gi-4938	88	16	of	of	ADP
gi-4938	88	17	both	both	DET
gi-4938	88	18	methods	method	NOUN
gi-4938	88	19	geoinformatics	geoinformatic	NOUN
gi-4938	88	20	fce	fce	VERB
gi-4938	88	21	ctu	ctu	NOUN
gi-4938	88	22	17(2	17(2	NUM
gi-4938	88	23	)	)	PUNCT
gi-4938	88	24	,	,	PUNCT
gi-4938	88	25	2018	2018	NUM
gi-4938	88	26	11	11	NUM
gi-4938	88	27	t.	t.	NOUN
gi-4938	88	28	bayer	bayer	NOUN
gi-4938	88	29	:	:	PUNCT
gi-4938	88	30	efficient	efficient	ADJ
gi-4938	88	31	plotting	plot	VERB
gi-4938	88	32	the	the	DET
gi-4938	88	33	functions	function	NOUN
gi-4938	88	34	with	with	ADP
gi-4938	88	35	discontinuities	discontinuity	NOUN
gi-4938	88	36	-2	-2	INTJ
gi-4938	89	1	-1	-1	NOUN
gi-4938	89	2	0	0	NUM
gi-4938	90	1	1	1	NUM
gi-4938	90	2	2	2	NUM
gi-4938	90	3	x	x	SYM
gi-4938	90	4	0	0	NUM
gi-4938	90	5	0.5	0.5	NUM
gi-4938	90	6	1	1	NUM
gi-4938	90	7	1.5	1.5	NUM
gi-4938	90	8	2	2	NUM
gi-4938	90	9	2.5	2.5	NUM
gi-4938	90	10	3	3	NUM
gi-4938	90	11	3.5	3.5	NUM
gi-4938	90	12	4	4	NUM
gi-4938	90	13	f	f	NOUN
gi-4938	90	14	(	(	PUNCT
gi-4938	90	15	x	x	SYM
gi-4938	90	16	)	)	PUNCT
gi-4938	90	17	as	as	ADP
gi-4938	90	18	:	:	PUNCT
gi-4938	90	19	d=1	d=1	NOUN
gi-4938	90	20	-2	-2	INTJ
gi-4938	90	21	-1	-1	NOUN
gi-4938	90	22	0	0	NUM
gi-4938	91	1	1	1	NUM
gi-4938	91	2	2	2	NUM
gi-4938	91	3	x	x	SYM
gi-4938	91	4	0	0	NUM
gi-4938	91	5	0.5	0.5	NUM
gi-4938	91	6	1	1	NUM
gi-4938	91	7	1.5	1.5	NUM
gi-4938	91	8	2	2	NUM
gi-4938	91	9	2.5	2.5	NUM
gi-4938	91	10	3	3	NUM
gi-4938	91	11	3.5	3.5	NUM
gi-4938	91	12	4	4	NUM
gi-4938	91	13	f	f	NOUN
gi-4938	91	14	(	(	PUNCT
gi-4938	91	15	x	x	SYM
gi-4938	91	16	)	)	PUNCT
gi-4938	91	17	as	as	ADP
gi-4938	91	18	:	:	PUNCT
gi-4938	91	19	d=2	d=2	X
gi-4938	91	20	-2	-2	INTJ
gi-4938	91	21	-1	-1	SYM
gi-4938	91	22	0	0	NUM
gi-4938	92	1	1	1	NUM
gi-4938	92	2	2	2	NUM
gi-4938	92	3	x	x	SYM
gi-4938	92	4	0	0	NUM
gi-4938	92	5	0.5	0.5	NUM
gi-4938	92	6	1	1	NUM
gi-4938	92	7	1.5	1.5	NUM
gi-4938	92	8	2	2	NUM
gi-4938	92	9	2.5	2.5	NUM
gi-4938	92	10	3	3	NUM
gi-4938	92	11	3.5	3.5	NUM
gi-4938	92	12	4	4	NUM
gi-4938	92	13	f	f	NOUN
gi-4938	92	14	(	(	PUNCT
gi-4938	92	15	x	x	SYM
gi-4938	92	16	)	)	PUNCT
gi-4938	92	17	as	as	SCONJ
gi-4938	92	18	:	:	PUNCT
gi-4938	92	19	d=3	d=3	PRON
gi-4938	92	20	figure	figure	VERB
gi-4938	92	21	3.2	3.2	NUM
gi-4938	92	22	:	:	PUNCT
gi-4938	92	23	illustration	illustration	NOUN
gi-4938	92	24	of	of	ADP
gi-4938	92	25	the	the	DET
gi-4938	92	26	proposed	propose	VERB
gi-4938	92	27	algorithm	algorithm	NOUN
gi-4938	92	28	:	:	PUNCT
gi-4938	92	29	an	an	DET
gi-4938	92	30	adaptive	adaptive	ADJ
gi-4938	92	31	sampling	sampling	NOUN
gi-4938	92	32	of	of	ADP
gi-4938	92	33	the	the	DET
gi-4938	92	34	function	function	NOUN
gi-4938	92	35	y	y	PROPN
gi-4938	92	36	=	=	SYM
gi-4938	92	37	x2	x2	PROPN
gi-4938	92	38	,	,	PUNCT
gi-4938	92	39	x	x	SYM
gi-4938	92	40	∈	∈	PROPN
gi-4938	93	1	[	[	X
gi-4938	93	2	−2	−2	X
gi-4938	93	3	,	,	PUNCT
gi-4938	93	4	2	2	NUM
gi-4938	93	5	]	]	PUNCT
gi-4938	93	6	for	for	ADP
gi-4938	93	7	the	the	DET
gi-4938	93	8	depths	depth	NOUN
gi-4938	93	9	of	of	ADP
gi-4938	93	10	recursion	recursion	NOUN
gi-4938	93	11	d	d	NOUN
gi-4938	93	12	=	=	SYM
gi-4938	93	13	1	1	NUM
gi-4938	93	14	,	,	PUNCT
gi-4938	93	15	2	2	NUM
gi-4938	93	16	,	,	PUNCT
gi-4938	93	17	3	3	NUM
gi-4938	93	18	.	.	PUNCT
gi-4938	94	1	and	and	CCONJ
gi-4938	94	2	propose	propose	VERB
gi-4938	94	3	the	the	DET
gi-4938	94	4	combined	combine	VERB
gi-4938	94	5	sampling	sampling	NOUN
gi-4938	94	6	method	method	NOUN
gi-4938	94	7	.	.	PUNCT
gi-4938	95	1	uniform	uniform	ADJ
gi-4938	95	2	sampling	sampling	NOUN
gi-4938	95	3	represents	represent	VERB
gi-4938	95	4	the	the	DET
gi-4938	95	5	initial	initial	ADJ
gi-4938	95	6	step	step	NOUN
gi-4938	95	7	,	,	PUNCT
gi-4938	95	8	later	later	ADV
gi-4938	95	9	steps	step	NOUN
gi-4938	95	10	refining	refine	VERB
gi-4938	95	11	the	the	DET
gi-4938	95	12	curve	curve	NOUN
gi-4938	95	13	approximation	approximation	NOUN
gi-4938	95	14	are	be	AUX
gi-4938	95	15	provided	provide	VERB
gi-4938	95	16	by	by	ADP
gi-4938	95	17	adaptive	adaptive	ADJ
gi-4938	95	18	sampling	sampling	NOUN
gi-4938	95	19	.	.	PUNCT
gi-4938	96	1	the	the	DET
gi-4938	96	2	second	second	ADJ
gi-4938	96	3	problem	problem	NOUN
gi-4938	96	4	may	may	AUX
gi-4938	96	5	overcome	overcome	VERB
gi-4938	96	6	adding	add	VERB
gi-4938	96	7	the	the	DET
gi-4938	96	8	partial	partial	ADJ
gi-4938	96	9	randomness	randomness	NOUN
gi-4938	96	10	to	to	ADP
gi-4938	96	11	the	the	DET
gi-4938	96	12	generated	generate	VERB
gi-4938	96	13	segments	segment	NOUN
gi-4938	96	14	.	.	PUNCT
gi-4938	97	1	refinement	refinement	NOUN
gi-4938	97	2	criteria	criterion	NOUN
gi-4938	97	3	.	.	PUNCT
gi-4938	98	1	an	an	DET
gi-4938	98	2	important	important	ADJ
gi-4938	98	3	role	role	NOUN
gi-4938	98	4	is	be	AUX
gi-4938	98	5	played	play	VERB
gi-4938	98	6	by	by	ADP
gi-4938	98	7	the	the	DET
gi-4938	98	8	refinement	refinement	NOUN
gi-4938	98	9	criteria	criterion	NOUN
gi-4938	98	10	smoothing	smooth	VERB
gi-4938	98	11	the	the	DET
gi-4938	98	12	polyline	polyline	NOUN
gi-4938	98	13	[	[	X
gi-4938	98	14	15	15	NUM
gi-4938	98	15	]	]	PUNCT
gi-4938	98	16	.	.	PUNCT
gi-4938	99	1	suppose	suppose	VERB
gi-4938	99	2	(	(	PUNCT
gi-4938	99	3	pi−1	pi−1	PROPN
gi-4938	99	4	,	,	PUNCT
gi-4938	99	5	pi	pi	NOUN
gi-4938	99	6	,	,	PUNCT
gi-4938	99	7	pi+1	pi+1	NOUN
gi-4938	99	8	)	)	PUNCT
gi-4938	99	9	to	to	PART
gi-4938	99	10	be	be	AUX
gi-4938	99	11	three	three	NUM
gi-4938	99	12	consecutive	consecutive	ADJ
gi-4938	99	13	sampled	sample	VERB
gi-4938	99	14	points	point	NOUN
gi-4938	99	15	of	of	ADP
gi-4938	99	16	the	the	DET
gi-4938	99	17	curve	curve	NOUN
gi-4938	99	18	.	.	PUNCT
gi-4938	100	1	the	the	DET
gi-4938	100	2	primary	primary	ADJ
gi-4938	100	3	criterion	criterion	NOUN
gi-4938	100	4	is	be	AUX
gi-4938	100	5	represented	represent	VERB
gi-4938	100	6	by	by	ADP
gi-4938	100	7	the	the	DET
gi-4938	100	8	angular	angular	ADJ
gi-4938	100	9	difference	difference	NOUN
gi-4938	100	10	of	of	ADP
gi-4938	100	11	both	both	DET
gi-4938	100	12	segments	segment	NOUN
gi-4938	100	13	αi	αi	ADV
gi-4938	100	14	=	=	SYM
gi-4938	100	15	α(pi−1	α(pi−1	PROPN
gi-4938	100	16	,	,	PUNCT
gi-4938	100	17	pi	pi	NOUN
gi-4938	100	18	,	,	PUNCT
gi-4938	100	19	pi+2	pi+2	NUM
gi-4938	100	20	)	)	PUNCT
gi-4938	100	21	=	=	PRON
gi-4938	100	22	arccos	arcco	VERB
gi-4938	100	23	|u	|u	ADJ
gi-4938	100	24	·	·	PUNCT
gi-4938	100	25	v|	v|	NOUN
gi-4938	100	26	‖u‖	‖u‖	PROPN
gi-4938	100	27	‖v‖	‖v‖	PROPN
gi-4938	100	28	±	±	NUM
gi-4938	100	29	π	π	PROPN
gi-4938	100	30	,	,	PUNCT
gi-4938	100	31	u	u	NOUN
gi-4938	100	32	=	=	NOUN
gi-4938	100	33	pi+1	pi+1	NUM
gi-4938	100	34	−	−	PROPN
gi-4938	100	35	pi	pi	NOUN
gi-4938	100	36	,	,	PUNCT
gi-4938	100	37	v	v	NOUN
gi-4938	100	38	=	=	NOUN
gi-4938	100	39	pi−1	pi−1	NOUN
gi-4938	100	40	−	−	PROPN
gi-4938	100	41	pi	pi	NOUN
gi-4938	100	42	.	.	PUNCT
gi-4938	101	1	different	different	ADJ
gi-4938	101	2	criteria	criterion	NOUN
gi-4938	101	3	can	can	AUX
gi-4938	101	4	provide	provide	VERB
gi-4938	101	5	the	the	DET
gi-4938	101	6	analogous	analogous	ADJ
gi-4938	101	7	results	result	NOUN
gi-4938	101	8	:	:	PUNCT
gi-4938	101	9	recall	recall	VERB
gi-4938	101	10	the	the	DET
gi-4938	101	11	distance	distance	NOUN
gi-4938	101	12	of	of	ADP
gi-4938	101	13	pi	pi	NOUN
gi-4938	101	14	from	from	ADP
gi-4938	101	15	pi−1	pi−1	PROPN
gi-4938	101	16	,	,	PUNCT
gi-4938	101	17	pi+1	pi+1	NOUN
gi-4938	101	18	,	,	PUNCT
gi-4938	101	19	or	or	CCONJ
gi-4938	101	20	,	,	PUNCT
gi-4938	101	21	the	the	DET
gi-4938	101	22	local	local	ADJ
gi-4938	101	23	length	length	NOUN
gi-4938	101	24	ratio	ratio	NOUN
gi-4938	101	25	[	[	X
gi-4938	101	26	29	29	NUM
gi-4938	101	27	]	]	PUNCT
gi-4938	101	28	.	.	PUNCT
gi-4938	102	1	combined	combine	VERB
gi-4938	102	2	sampling	sample	VERB
gi-4938	102	3	algorithm	algorithm	NOUN
gi-4938	102	4	without	without	ADP
gi-4938	102	5	the	the	DET
gi-4938	102	6	singularities	singularity	NOUN
gi-4938	102	7	the	the	DET
gi-4938	102	8	combined	combined	ADJ
gi-4938	102	9	sampling	sampling	NOUN
gi-4938	102	10	algorithm	algorithm	NOUN
gi-4938	102	11	is	be	AUX
gi-4938	102	12	based	base	VERB
gi-4938	102	13	on	on	ADP
gi-4938	102	14	the	the	DET
gi-4938	102	15	idea	idea	NOUN
gi-4938	102	16	of	of	ADP
gi-4938	102	17	the	the	DET
gi-4938	102	18	hierarchical	hierarchical	ADJ
gi-4938	102	19	reconstruction	reconstruction	NOUN
gi-4938	102	20	of	of	ADP
gi-4938	102	21	the	the	DET
gi-4938	102	22	curve	curve	NOUN
gi-4938	102	23	shape	shape	NOUN
gi-4938	102	24	,	,	PUNCT
gi-4938	102	25	which	which	PRON
gi-4938	102	26	follows	follow	VERB
gi-4938	102	27	the	the	DET
gi-4938	102	28	recursive	recursive	ADJ
gi-4938	102	29	approach	approach	NOUN
gi-4938	102	30	with	with	ADP
gi-4938	102	31	the	the	DET
gi-4938	102	32	multiple	multiple	ADJ
gi-4938	102	33	calls	call	NOUN
gi-4938	102	34	mixing	mix	VERB
gi-4938	102	35	the	the	DET
gi-4938	102	36	uniform	uniform	NOUN
gi-4938	102	37	and	and	CCONJ
gi-4938	102	38	adaptive	adaptive	ADJ
gi-4938	102	39	techniques	technique	NOUN
gi-4938	102	40	.	.	PUNCT
gi-4938	103	1	unlike	unlike	ADP
gi-4938	103	2	a	a	DET
gi-4938	103	3	simple	simple	ADJ
gi-4938	103	4	algorithm	algorithm	NOUN
gi-4938	103	5	discussed	discuss	VERB
gi-4938	103	6	in	in	ADP
gi-4938	103	7	[	[	X
gi-4938	103	8	15	15	NUM
gi-4938	103	9	]	]	PUNCT
gi-4938	103	10	,	,	PUNCT
gi-4938	103	11	the	the	DET
gi-4938	103	12	proposed	propose	VERB
gi-4938	103	13	method	method	NOUN
gi-4938	103	14	can	can	AUX
gi-4938	103	15	handle	handle	VERB
gi-4938	103	16	the	the	DET
gi-4938	103	17	singularities	singularity	NOUN
gi-4938	103	18	and	and	CCONJ
gi-4938	103	19	discontinuities	discontinuity	NOUN
gi-4938	103	20	of	of	ADP
gi-4938	103	21	f	f	PROPN
gi-4938	103	22	and	and	CCONJ
gi-4938	103	23	requires	require	VERB
gi-4938	103	24	a	a	DET
gi-4938	103	25	lower	low	ADJ
gi-4938	103	26	recursion	recursion	NOUN
gi-4938	103	27	depth	depth	NOUN
gi-4938	103	28	.	.	PUNCT
gi-4938	104	1	initially	initially	ADV
gi-4938	104	2	,	,	PUNCT
gi-4938	104	3	sampling	sample	VERB
gi-4938	104	4	without	without	ADP
gi-4938	104	5	the	the	DET
gi-4938	104	6	treatment	treatment	NOUN
gi-4938	104	7	of	of	ADP
gi-4938	104	8	singularities	singularity	NOUN
gi-4938	104	9	will	will	AUX
gi-4938	104	10	be	be	AUX
gi-4938	104	11	presented	present	VERB
gi-4938	104	12	.	.	PUNCT
gi-4938	105	1	suppose	suppose	VERB
gi-4938	105	2	d	d	AUX
gi-4938	105	3	to	to	PART
gi-4938	105	4	be	be	AUX
gi-4938	105	5	the	the	DET
gi-4938	105	6	current	current	ADJ
gi-4938	105	7	depth	depth	NOUN
gi-4938	105	8	of	of	ADP
gi-4938	105	9	the	the	DET
gi-4938	105	10	recursion	recursion	NOUN
gi-4938	105	11	,	,	PUNCT
gi-4938	105	12	d	d	X
gi-4938	105	13	to	to	PART
gi-4938	105	14	be	be	AUX
gi-4938	105	15	the	the	DET
gi-4938	105	16	minimum	minimum	NOUN
gi-4938	105	17	and	and	CCONJ
gi-4938	105	18	d	d	NOUN
gi-4938	105	19	to	to	PART
gi-4938	105	20	be	be	AUX
gi-4938	105	21	the	the	DET
gi-4938	105	22	maximum	maximum	ADJ
gi-4938	105	23	recursion	recursion	NOUN
gi-4938	105	24	depth	depth	NOUN
gi-4938	105	25	.	.	PUNCT
gi-4938	106	1	combined	combine	VERB
gi-4938	106	2	sampling	sampling	NOUN
gi-4938	106	3	returns	return	NOUN
gi-4938	106	4	a	a	DET
gi-4938	106	5	polynomial	polynomial	ADJ
gi-4938	106	6	approximation	approximation	NOUN
gi-4938	106	7	of	of	ADP
gi-4938	106	8	the	the	DET
gi-4938	106	9	curve	curve	NOUN
gi-4938	106	10	by	by	ADP
gi-4938	106	11	the	the	DET
gi-4938	106	12	refinement	refinement	NOUN
gi-4938	106	13	criteria	criterion	NOUN
gi-4938	106	14	α	α	PROPN
gi-4938	106	15	and	and	CCONJ
gi-4938	106	16	the	the	DET
gi-4938	106	17	recursion	recursion	NOUN
gi-4938	106	18	depth	depth	NOUN
gi-4938	106	19	d.	d.	NOUN
gi-4938	106	20	our	our	PRON
gi-4938	106	21	algorithm	algorithm	NOUN
gi-4938	106	22	combines	combine	VERB
gi-4938	106	23	the	the	DET
gi-4938	106	24	uniform	uniform	NOUN
gi-4938	106	25	and	and	CCONJ
gi-4938	106	26	adaptive	adaptive	ADJ
gi-4938	106	27	sampling	sampling	NOUN
gi-4938	106	28	techniques	technique	NOUN
gi-4938	106	29	and	and	CCONJ
gi-4938	106	30	subdivides	subdivide	VERB
gi-4938	106	31	ω	ω	NUM
gi-4938	106	32	into	into	ADP
gi-4938	106	33	a	a	DET
gi-4938	106	34	specified	specified	ADJ
gi-4938	106	35	number	number	NOUN
gi-4938	106	36	of	of	ADP
gi-4938	106	37	the	the	DET
gi-4938	106	38	disjoint	disjoint	NOUN
gi-4938	106	39	subintervals	subinterval	NOUN
gi-4938	106	40	ωk	ωk	ADP
gi-4938	106	41	of	of	ADP
gi-4938	106	42	the	the	DET
gi-4938	106	43	similar	similar	ADJ
gi-4938	106	44	size	size	NOUN
gi-4938	106	45	during	during	ADP
gi-4938	106	46	each	each	DET
gi-4938	106	47	recursive	recursive	ADJ
gi-4938	106	48	step	step	NOUN
gi-4938	106	49	,	,	PUNCT
gi-4938	106	50	where	where	SCONJ
gi-4938	106	51	k	k	PROPN
gi-4938	106	52	=	=	NOUN
gi-4938	106	53	4	4	X
gi-4938	106	54	.	.	PUNCT
gi-4938	106	55	hence	hence	ADV
gi-4938	106	56	,	,	PUNCT
gi-4938	106	57	ω	ω	PROPN
gi-4938	106	58	is	be	AUX
gi-4938	106	59	split	split	VERB
gi-4938	106	60	into	into	ADP
gi-4938	106	61	the	the	DET
gi-4938	106	62	approximate	approximate	ADJ
gi-4938	106	63	quarters	quarter	NOUN
gi-4938	106	64	with	with	ADP
gi-4938	106	65	the	the	DET
gi-4938	106	66	randomly	randomly	ADV
gi-4938	106	67	shifting	shift	VERB
gi-4938	106	68	borders	border	NOUN
gi-4938	106	69	,	,	PUNCT
gi-4938	106	70	which	which	PRON
gi-4938	106	71	are	be	AUX
gi-4938	106	72	not	not	PART
gi-4938	106	73	a	a	DET
gi-4938	106	74	direct	direct	ADJ
gi-4938	106	75	multiple	multiple	NOUN
gi-4938	106	76	of	of	ADP
gi-4938	106	77	0.25	0.25	NUM
gi-4938	106	78	.	.	PUNCT
gi-4938	107	1	initially	initially	ADV
gi-4938	107	2	,	,	PUNCT
gi-4938	107	3	if	if	SCONJ
gi-4938	107	4	d	d	AUX
gi-4938	107	5	≤	≤	PROPN
gi-4938	107	6	d	d	NOUN
gi-4938	107	7	the	the	DET
gi-4938	107	8	interval	interval	NOUN
gi-4938	107	9	is	be	AUX
gi-4938	107	10	subdivided	subdivide	VERB
gi-4938	107	11	into	into	ADP
gi-4938	107	12	four	four	NUM
gi-4938	107	13	subintervals	subinterval	NOUN
gi-4938	107	14	regardless	regardless	ADV
gi-4938	107	15	of	of	ADP
gi-4938	107	16	α	α	NOUN
gi-4938	107	17	;	;	PUNCT
gi-4938	107	18	four	four	NUM
gi-4938	107	19	new	new	ADJ
gi-4938	107	20	segments	segment	NOUN
gi-4938	107	21	of	of	ADP
gi-4938	107	22	the	the	DET
gi-4938	107	23	polygonal	polygonal	ADJ
gi-4938	107	24	approximation	approximation	NOUN
gi-4938	107	25	are	be	AUX
gi-4938	107	26	created	create	VERB
gi-4938	107	27	.	.	PUNCT
gi-4938	108	1	subsequently	subsequently	ADV
gi-4938	108	2	,	,	PUNCT
gi-4938	108	3	when	when	SCONJ
gi-4938	108	4	d	d	PROPN
gi-4938	108	5	>	>	X
gi-4938	108	6	d	d	PROPN
gi-4938	108	7	,	,	PUNCT
gi-4938	108	8	between	between	ADP
gi-4938	108	9	geoinformatics	geoinformatic	NOUN
gi-4938	108	10	fce	fce	VERB
gi-4938	108	11	ctu	ctu	NOUN
gi-4938	108	12	17(2	17(2	NUM
gi-4938	108	13	)	)	PUNCT
gi-4938	108	14	,	,	PUNCT
gi-4938	108	15	2018	2018	NUM
gi-4938	108	16	12	12	NUM
gi-4938	108	17	t.	t.	NOUN
gi-4938	108	18	bayer	bayer	NOUN
gi-4938	108	19	:	:	PUNCT
gi-4938	108	20	efficient	efficient	ADJ
gi-4938	108	21	plotting	plot	VERB
gi-4938	108	22	the	the	DET
gi-4938	108	23	functions	function	NOUN
gi-4938	108	24	with	with	ADP
gi-4938	108	25	discontinuities	discontinuity	NOUN
gi-4938	108	26	algorithm	algorithm	NOUN
gi-4938	108	27	1	1	NUM
gi-4938	108	28	combined	combine	VERB
gi-4938	108	29	sampling	sampling	NOUN
gi-4938	108	30	,	,	PUNCT
gi-4938	108	31	the	the	DET
gi-4938	108	32	initial	initial	ADJ
gi-4938	108	33	phase	phase	NOUN
gi-4938	108	34	.	.	PUNCT
gi-4938	109	1	1	1	NUM
gi-4938	109	2	:	:	PUNCT
gi-4938	109	3	function	function	NOUN
gi-4938	109	4	csinit(f	csinit(f	PROPN
gi-4938	109	5	,	,	PUNCT
gi-4938	109	6	l	l	PROPN
gi-4938	109	7	,	,	PUNCT
gi-4938	109	8	a	a	PRON
gi-4938	109	9	,	,	PUNCT
gi-4938	109	10	b	b	NOUN
gi-4938	109	11	,	,	PUNCT
gi-4938	109	12	d	d	PROPN
gi-4938	109	13	,	,	PUNCT
gi-4938	109	14	d	d	NOUN
gi-4938	109	15	,	,	PUNCT
gi-4938	109	16	d	d	PROPN
gi-4938	109	17	,	,	PUNCT
gi-4938	109	18	ε	ε	PROPN
gi-4938	109	19	,	,	PUNCT
gi-4938	109	20	α	α	NOUN
gi-4938	109	21	)	)	PUNCT
gi-4938	109	22	2	2	NUM
gi-4938	109	23	:	:	PUNCT
gi-4938	109	24	l	l	NOUN
gi-4938	109	25	=	=	NOUN
gi-4938	109	26	∅	∅	NOUN
gi-4938	109	27	3	3	NUM
gi-4938	109	28	:	:	PUNCT
gi-4938	109	29	ya	ya	PROPN
gi-4938	109	30	=	=	SYM
gi-4938	109	31	f(a	f(a	PROPN
gi-4938	109	32	)	)	PUNCT
gi-4938	109	33	,	,	PUNCT
gi-4938	109	34	yb	yb	PROPN
gi-4938	109	35	=	=	SYM
gi-4938	109	36	f(b	f(b	PROPN
gi-4938	109	37	)	)	PUNCT
gi-4938	109	38	4	4	NUM
gi-4938	109	39	:	:	PUNCT
gi-4938	109	40	if	if	SCONJ
gi-4938	109	41	discontinuity	discontinuity	NOUN
gi-4938	109	42	in	in	ADP
gi-4938	109	43	a	a	DET
gi-4938	109	44	then	then	ADV
gi-4938	109	45	5	5	NUM
gi-4938	109	46	:	:	PUNCT
gi-4938	109	47	throw	throw	VERB
gi-4938	109	48	singularityexception	singularityexception	NOUN
gi-4938	109	49	(	(	PUNCT
gi-4938	109	50	a	a	NOUN
gi-4938	109	51	)	)	PUNCT
gi-4938	109	52	6	6	NUM
gi-4938	109	53	:	:	PUNCT
gi-4938	109	54	if	if	SCONJ
gi-4938	109	55	discontinuity	discontinuity	NOUN
gi-4938	109	56	in	in	ADP
gi-4938	109	57	b	b	NOUN
gi-4938	109	58	then	then	ADV
gi-4938	109	59	7	7	NUM
gi-4938	109	60	:	:	PUNCT
gi-4938	109	61	throw	throw	VERB
gi-4938	109	62	singularityexception	singularityexception	NOUN
gi-4938	109	63	(	(	PUNCT
gi-4938	109	64	b	b	NOUN
gi-4938	109	65	)	)	PUNCT
gi-4938	109	66	8	8	NUM
gi-4938	109	67	:	:	PUNCT
gi-4938	110	1	l←	l←	NUM
gi-4938	110	2	point(a	point(a	NOUN
gi-4938	110	3	,	,	PUNCT
gi-4938	110	4	ya	ya	NOUN
gi-4938	110	5	)	)	PUNCT
gi-4938	110	6	9	9	NUM
gi-4938	110	7	:	:	PUNCT
gi-4938	110	8	as(f	as(f	NUM
gi-4938	110	9	,	,	PUNCT
gi-4938	110	10	l	l	NOUN
gi-4938	110	11	,	,	PUNCT
gi-4938	110	12	a	a	DET
gi-4938	110	13	,	,	PUNCT
gi-4938	110	14	b	b	PROPN
gi-4938	110	15	,	,	PUNCT
gi-4938	110	16	ya	ya	PROPN
gi-4938	110	17	,	,	PUNCT
gi-4938	110	18	yb	yb	PROPN
gi-4938	110	19	,	,	PUNCT
gi-4938	110	20	d	d	PROPN
gi-4938	110	21	,	,	PUNCT
gi-4938	110	22	d	d	NOUN
gi-4938	110	23	,	,	PUNCT
gi-4938	110	24	d	d	PROPN
gi-4938	110	25	,	,	PUNCT
gi-4938	110	26	ε	ε	PROPN
gi-4938	110	27	,	,	PUNCT
gi-4938	110	28	α	α	NOUN
gi-4938	110	29	)	)	PUNCT
gi-4938	110	30	10	10	NUM
gi-4938	110	31	:	:	PUNCT
gi-4938	110	32	l←	l←	NUM
gi-4938	111	1	point(b	point(b	PROPN
gi-4938	111	2	,	,	PUNCT
gi-4938	111	3	yb	yb	PROPN
gi-4938	111	4	)	)	PUNCT
gi-4938	111	5	each	each	DET
gi-4938	111	6	pair	pair	NOUN
gi-4938	111	7	of	of	ADP
gi-4938	111	8	four	four	NUM
gi-4938	111	9	new	new	ADJ
gi-4938	111	10	consecutive	consecutive	ADJ
gi-4938	111	11	segments	segment	NOUN
gi-4938	111	12	,	,	PUNCT
gi-4938	111	13	the	the	DET
gi-4938	111	14	refinement	refinement	NOUN
gi-4938	111	15	criterion	criterion	NOUN
gi-4938	111	16	αk	αk	NOUN
gi-4938	111	17	,	,	PUNCT
gi-4938	111	18	k	k	PROPN
gi-4938	111	19	=	=	SYM
gi-4938	111	20	1	1	NUM
gi-4938	111	21	,	,	PUNCT
gi-4938	111	22	...	...	PUNCT
gi-4938	111	23	,	,	PUNCT
gi-4938	111	24	3	3	NUM
gi-4938	111	25	,	,	PUNCT
gi-4938	111	26	is	be	AUX
gi-4938	111	27	evaluated	evaluate	VERB
gi-4938	111	28	and	and	CCONJ
gi-4938	111	29	compared	compare	VERB
gi-4938	111	30	to	to	ADP
gi-4938	111	31	α	α	PRON
gi-4938	111	32	.	.	PUNCT
gi-4938	112	1	if	if	SCONJ
gi-4938	112	2	αk	αk	NOUN
gi-4938	112	3	>	>	X
gi-4938	112	4	a	a	PRON
gi-4938	112	5	and	and	CCONJ
gi-4938	112	6	b−	b−	PROPN
gi-4938	112	7	a	a	PRON
gi-4938	112	8	>	>	X
gi-4938	112	9	ε	ε	PROPN
gi-4938	112	10	,	,	PUNCT
gi-4938	112	11	two	two	NUM
gi-4938	112	12	adjacent	adjacent	ADJ
gi-4938	112	13	segments	segment	NOUN
gi-4938	112	14	are	be	AUX
gi-4938	112	15	created	create	VERB
gi-4938	112	16	.	.	PUNCT
gi-4938	113	1	the	the	DET
gi-4938	113	2	interval	interval	NOUN
gi-4938	113	3	is	be	AUX
gi-4938	113	4	subdivided	subdivide	VERB
gi-4938	113	5	into	into	ADP
gi-4938	113	6	2	2	NUM
gi-4938	113	7	-	-	SYM
gi-4938	113	8	4	4	NUM
gi-4938	113	9	new	new	ADJ
gi-4938	113	10	until	until	SCONJ
gi-4938	113	11	the	the	DET
gi-4938	113	12	visually	visually	ADV
gi-4938	113	13	“	"	PUNCT
gi-4938	113	14	smooth	smooth	ADJ
gi-4938	113	15	”	"	PUNCT
gi-4938	113	16	polynomial	polynomial	ADJ
gi-4938	113	17	approximation	approximation	NOUN
gi-4938	113	18	of	of	ADP
gi-4938	113	19	the	the	DET
gi-4938	113	20	curve	curve	NOUN
gi-4938	113	21	is	be	AUX
gi-4938	113	22	obtained	obtain	VERB
gi-4938	113	23	.	.	PUNCT
gi-4938	114	1	in	in	ADP
gi-4938	114	2	other	other	ADJ
gi-4938	114	3	words	word	NOUN
gi-4938	114	4	,	,	PUNCT
gi-4938	114	5	uniform	uniform	ADJ
gi-4938	114	6	sampling	sampling	NOUN
gi-4938	114	7	is	be	AUX
gi-4938	114	8	followed	follow	VERB
gi-4938	114	9	by	by	ADP
gi-4938	114	10	adaptive	adaptive	ADJ
gi-4938	114	11	sampling	sampling	NOUN
gi-4938	114	12	refining	refine	VERB
gi-4938	114	13	the	the	DET
gi-4938	114	14	properties	property	NOUN
gi-4938	114	15	of	of	ADP
gi-4938	114	16	the	the	DET
gi-4938	114	17	insufficiently	insufficiently	ADV
gi-4938	114	18	estimated	estimate	VERB
gi-4938	114	19	segments	segment	NOUN
gi-4938	114	20	.	.	PUNCT
gi-4938	115	1	let	let	VERB
gi-4938	115	2	l	l	NOUN
gi-4938	115	3	=	=	PUNCT
gi-4938	115	4	{	{	PUNCT
gi-4938	115	5	pi}ni=1	pi}ni=1	ADV
gi-4938	115	6	be	be	AUX
gi-4938	115	7	the	the	DET
gi-4938	115	8	polynomial	polynomial	ADJ
gi-4938	115	9	approximation	approximation	NOUN
gi-4938	115	10	of	of	ADP
gi-4938	115	11	f(x	f(x	PROPN
gi-4938	115	12	)	)	PUNCT
gi-4938	115	13	and	and	CCONJ
gi-4938	116	1	ω	ω	X
gi-4938	116	2	=	=	PUNCT
gi-4938	117	1	[	[	X
gi-4938	117	2	a	a	X
gi-4938	117	3	,	,	PUNCT
gi-4938	117	4	b	b	NOUN
gi-4938	117	5	]	]	X
gi-4938	117	6	a	a	DET
gi-4938	117	7	subdomain	subdomain	NOUN
gi-4938	117	8	.	.	PUNCT
gi-4938	118	1	the	the	DET
gi-4938	118	2	algorithm	algorithm	NOUN
gi-4938	118	3	may	may	AUX
gi-4938	118	4	be	be	AUX
gi-4938	118	5	summarized	summarize	VERB
gi-4938	118	6	as	as	SCONJ
gi-4938	118	7	follows	follow	VERB
gi-4938	118	8	:	:	PUNCT
gi-4938	119	1	1	1	X
gi-4938	119	2	.	.	X
gi-4938	119	3	the	the	DET
gi-4938	119	4	initial	initial	ADJ
gi-4938	119	5	phase	phase	NOUN
gi-4938	119	6	let	let	VERB
gi-4938	119	7	l	l	NOUN
gi-4938	119	8	=	=	NOUN
gi-4938	119	9	∅	∅	NOUN
gi-4938	119	10	be	be	AUX
gi-4938	119	11	the	the	DET
gi-4938	119	12	empty	empty	ADJ
gi-4938	119	13	set	set	NOUN
gi-4938	119	14	.	.	PUNCT
gi-4938	120	1	compute	compute	NOUN
gi-4938	120	2	ya	ya	PROPN
gi-4938	120	3	=	=	SYM
gi-4938	120	4	f(a	f(a	PROPN
gi-4938	120	5	)	)	PUNCT
gi-4938	120	6	and	and	CCONJ
gi-4938	120	7	yb	yb	PROPN
gi-4938	120	8	=	=	SYM
gi-4938	120	9	f(b	f(b	PROPN
gi-4938	120	10	)	)	PUNCT
gi-4938	120	11	.	.	PUNCT
gi-4938	121	1	if	if	SCONJ
gi-4938	121	2	a	a	DET
gi-4938	121	3	singularity	singularity	NOUN
gi-4938	121	4	in	in	ADP
gi-4938	121	5	a	a	DET
gi-4938	121	6	or	or	CCONJ
gi-4938	121	7	b	b	NOUN
gi-4938	121	8	is	be	AUX
gi-4938	121	9	detected	detect	VERB
gi-4938	121	10	,	,	PUNCT
gi-4938	121	11	throw	throw	VERB
gi-4938	121	12	the	the	DET
gi-4938	121	13	exception	exception	NOUN
gi-4938	121	14	.	.	PUNCT
gi-4938	122	1	add	add	VERB
gi-4938	122	2	the	the	DET
gi-4938	122	3	initial	initial	ADJ
gi-4938	122	4	vertex	vertex	NOUN
gi-4938	122	5	to	to	ADP
gi-4938	122	6	l	l	NOUN
gi-4938	122	7	:	:	PUNCT
gi-4938	122	8	l	l	PROPN
gi-4938	122	9	←	←	PROPN
gi-4938	122	10	pa	pa	PROPN
gi-4938	122	11	,	,	PUNCT
gi-4938	122	12	where	where	SCONJ
gi-4938	122	13	pa	pa	PROPN
gi-4938	122	14	=	=	SYM
gi-4938	122	15	(	(	PUNCT
gi-4938	122	16	xa	xa	PROPN
gi-4938	122	17	,	,	PUNCT
gi-4938	122	18	ya	ya	PROPN
gi-4938	122	19	)	)	PUNCT
gi-4938	122	20	.	.	PUNCT
gi-4938	123	1	set	set	VERB
gi-4938	123	2	the	the	DET
gi-4938	123	3	recursion	recursion	NOUN
gi-4938	123	4	depth	depth	NOUN
gi-4938	123	5	d	d	X
gi-4938	123	6	=	=	SYM
gi-4938	123	7	1	1	NUM
gi-4938	123	8	.	.	NOUN
gi-4938	123	9	2	2	NUM
gi-4938	123	10	.	.	PUNCT
gi-4938	124	1	the	the	DET
gi-4938	124	2	recursive	recursive	ADJ
gi-4938	124	3	step	step	NOUN
gi-4938	124	4	enter	enter	VERB
gi-4938	124	5	the	the	DET
gi-4938	124	6	recursive	recursive	ADJ
gi-4938	124	7	procedure	procedure	NOUN
gi-4938	124	8	and	and	CCONJ
gi-4938	124	9	do	do	VERB
gi-4938	124	10	the	the	DET
gi-4938	124	11	following	follow	VERB
gi-4938	124	12	substeps	substep	NOUN
gi-4938	124	13	:	:	PUNCT
gi-4938	124	14	(	(	PUNCT
gi-4938	124	15	a	a	X
gi-4938	124	16	)	)	PUNCT
gi-4938	124	17	if	if	SCONJ
gi-4938	124	18	d	d	PROPN
gi-4938	124	19	>	>	X
gi-4938	124	20	d	d	PROPN
gi-4938	124	21	or	or	CCONJ
gi-4938	124	22	b−	b−	PRON
gi-4938	124	23	a	a	DET
gi-4938	124	24	<	<	X
gi-4938	124	25	ε	ε	PROPN
gi-4938	124	26	stop	stop	VERB
gi-4938	124	27	the	the	DET
gi-4938	124	28	recursive	recursive	ADJ
gi-4938	124	29	procedure	procedure	NOUN
gi-4938	124	30	and	and	CCONJ
gi-4938	124	31	go	go	VERB
gi-4938	124	32	to	to	PART
gi-4938	124	33	step	step	VERB
gi-4938	124	34	3	3	NUM
gi-4938	124	35	.	.	PUNCT
gi-4938	125	1	(	(	PUNCT
gi-4938	125	2	b	b	X
gi-4938	125	3	)	)	PUNCT
gi-4938	125	4	for	for	ADP
gi-4938	125	5	a	a	DET
gi-4938	125	6	given	give	VERB
gi-4938	125	7	ω	ω	NOUN
gi-4938	125	8	=	=	PUNCT
gi-4938	126	1	[	[	X
gi-4938	126	2	a	a	X
gi-4938	126	3	,	,	PUNCT
gi-4938	126	4	b	b	NOUN
gi-4938	126	5	]	]	X
gi-4938	126	6	,	,	PUNCT
gi-4938	126	7	the	the	DET
gi-4938	126	8	interval	interval	NOUN
gi-4938	126	9	is	be	AUX
gi-4938	126	10	split	split	VERB
gi-4938	126	11	by	by	ADP
gi-4938	126	12	the	the	DET
gi-4938	126	13	three	three	NUM
gi-4938	126	14	points	point	NOUN
gi-4938	126	15	x1	x1	PROPN
gi-4938	127	1	=	=	SYM
gi-4938	127	2	a+	a+	PUNCT
gi-4938	127	3	1	1	NUM
gi-4938	127	4	2r1(b−	2r1(b−	NUM
gi-4938	127	5	a	a	NOUN
gi-4938	127	6	)	)	PUNCT
gi-4938	127	7	,	,	PUNCT
gi-4938	127	8	x2	x2	NOUN
gi-4938	127	9	=	=	PRON
gi-4938	127	10	a+	a+	PUNCT
gi-4938	127	11	r2(b−	r2(b−	NOUN
gi-4938	127	12	a	a	PRON
gi-4938	127	13	)	)	PUNCT
gi-4938	128	1	,	,	PUNCT
gi-4938	128	2	x3	x3	NOUN
gi-4938	128	3	=	=	SYM
gi-4938	128	4	a+	a+	PUNCT
gi-4938	128	5	3	3	NUM
gi-4938	128	6	2r3(b−	2r3(b−	NUM
gi-4938	128	7	a	a	NOUN
gi-4938	128	8	)	)	PUNCT
gi-4938	128	9	,	,	PUNCT
gi-4938	128	10	into	into	ADP
gi-4938	128	11	the	the	DET
gi-4938	128	12	approximate	approximate	ADJ
gi-4938	128	13	quarters	quarter	NOUN
gi-4938	128	14	ω1	ω1	PROPN
gi-4938	128	15	=	=	PUNCT
gi-4938	129	1	[	[	X
gi-4938	129	2	a	a	X
gi-4938	129	3	,	,	PUNCT
gi-4938	129	4	x1	x1	PROPN
gi-4938	129	5	]	]	X
gi-4938	129	6	,	,	PUNCT
gi-4938	129	7	ω2	ω2	NOUN
gi-4938	129	8	=	=	PUNCT
gi-4938	130	1	[	[	X
gi-4938	130	2	x1	x1	PROPN
gi-4938	130	3	,	,	PUNCT
gi-4938	130	4	x2	x2	PROPN
gi-4938	130	5	]	]	PUNCT
gi-4938	130	6	ω3	ω3	NOUN
gi-4938	130	7	=	=	PUNCT
gi-4938	131	1	[	[	X
gi-4938	131	2	x2	x2	X
gi-4938	131	3	,	,	PUNCT
gi-4938	131	4	x3	x3	ADJ
gi-4938	131	5	]	]	PUNCT
gi-4938	131	6	,	,	PUNCT
gi-4938	131	7	ω4	ω4	NOUN
gi-4938	131	8	=	=	PUNCT
gi-4938	132	1	[	[	X
gi-4938	132	2	x3	x3	ADJ
gi-4938	132	3	,	,	PUNCT
gi-4938	132	4	b	b	NOUN
gi-4938	132	5	]	]	X
gi-4938	132	6	,	,	PUNCT
gi-4938	132	7	where	where	SCONJ
gi-4938	132	8	r1	r1	PROPN
gi-4938	132	9	,	,	PUNCT
gi-4938	132	10	r2	r2	PROPN
gi-4938	132	11	,	,	PUNCT
gi-4938	132	12	r3	r3	PROPN
gi-4938	132	13	are	be	AUX
gi-4938	132	14	the	the	DET
gi-4938	132	15	random	random	ADJ
gi-4938	132	16	numbers	number	NOUN
gi-4938	132	17	inside	inside	ADP
gi-4938	132	18	the	the	DET
gi-4938	132	19	interval	interval	NOUN
gi-4938	132	20	[	[	X
gi-4938	132	21	0.45	0.45	NUM
gi-4938	132	22	,	,	PUNCT
gi-4938	132	23	0.55	0.55	NUM
gi-4938	132	24	]	]	PUNCT
gi-4938	132	25	.	.	PUNCT
gi-4938	133	1	this	this	DET
gi-4938	133	2	step	step	NOUN
gi-4938	133	3	prevents	prevent	VERB
gi-4938	133	4	a	a	DET
gi-4938	133	5	situation	situation	NOUN
gi-4938	133	6	,	,	PUNCT
gi-4938	133	7	when	when	SCONJ
gi-4938	133	8	f(a	f(a	NOUN
gi-4938	133	9	)	)	PUNCT
gi-4938	133	10	=	=	SYM
gi-4938	133	11	f(b	f(b	X
gi-4938	133	12	)	)	PUNCT
gi-4938	133	13	=	=	SYM
gi-4938	133	14	f(x1	f(x1	X
gi-4938	133	15	)	)	PUNCT
gi-4938	133	16	=	=	SYM
gi-4938	133	17	f(x2	f(x2	NOUN
gi-4938	133	18	)	)	PUNCT
gi-4938	133	19	=	=	PUNCT
gi-4938	134	1	f(x3	f(x3	X
gi-4938	134	2	)	)	PUNCT
gi-4938	134	3	,	,	PUNCT
gi-4938	134	4	but	but	CCONJ
gi-4938	134	5	their	their	PRON
gi-4938	134	6	intermediate	intermediate	ADJ
gi-4938	134	7	points	point	NOUN
gi-4938	134	8	do	do	AUX
gi-4938	134	9	not	not	PART
gi-4938	134	10	held	hold	VERB
gi-4938	134	11	this	this	DET
gi-4938	134	12	condition	condition	NOUN
gi-4938	134	13	;	;	PUNCT
gi-4938	134	14	it	it	PRON
gi-4938	134	15	is	be	AUX
gi-4938	134	16	typical	typical	ADJ
gi-4938	134	17	for	for	ADP
gi-4938	134	18	some	some	DET
gi-4938	134	19	periodic	periodic	ADJ
gi-4938	134	20	functions	function	NOUN
gi-4938	134	21	(	(	PUNCT
gi-4938	134	22	for	for	ADP
gi-4938	134	23	example	example	NOUN
gi-4938	134	24	,	,	PUNCT
gi-4938	134	25	if	if	SCONJ
gi-4938	134	26	y	y	PROPN
gi-4938	134	27	=	=	PUNCT
gi-4938	134	28	sin	sin	NOUN
gi-4938	134	29	2x	2x	NUM
gi-4938	134	30	,	,	PUNCT
gi-4938	134	31	and	and	CCONJ
gi-4938	135	1	ω	ω	X
gi-4938	135	2	=	=	PUNCT
gi-4938	136	1	[	[	X
gi-4938	136	2	0	0	NUM
gi-4938	136	3	,	,	PUNCT
gi-4938	136	4	2π	2π	NOUN
gi-4938	136	5	]	]	PUNCT
gi-4938	136	6	)	)	PUNCT
gi-4938	136	7	.	.	PUNCT
gi-4938	137	1	(	(	PUNCT
gi-4938	137	2	c	c	X
gi-4938	137	3	)	)	PUNCT
gi-4938	137	4	if	if	SCONJ
gi-4938	137	5	a	a	DET
gi-4938	137	6	singularity	singularity	NOUN
gi-4938	137	7	in	in	ADP
gi-4938	137	8	x1	x1	PROPN
gi-4938	137	9	,	,	PUNCT
gi-4938	137	10	x2	x2	PROPN
gi-4938	137	11	,	,	PUNCT
gi-4938	137	12	or	or	CCONJ
gi-4938	137	13	x3	x3	PROPN
gi-4938	137	14	occurs	occur	VERB
gi-4938	137	15	,	,	PUNCT
gi-4938	137	16	throw	throw	VERB
gi-4938	137	17	the	the	DET
gi-4938	137	18	new	new	ADJ
gi-4938	137	19	exception	exception	NOUN
gi-4938	137	20	with	with	ADP
gi-4938	137	21	the	the	DET
gi-4938	137	22	argument	argument	NOUN
gi-4938	137	23	indicating	indicate	VERB
gi-4938	137	24	the	the	DET
gi-4938	137	25	singularity	singularity	NOUN
gi-4938	137	26	.	.	PUNCT
gi-4938	138	1	(	(	PUNCT
gi-4938	138	2	d	d	X
gi-4938	138	3	)	)	PUNCT
gi-4938	138	4	evaluate	evaluate	VERB
gi-4938	138	5	the	the	DET
gi-4938	138	6	function	function	NOUN
gi-4938	138	7	values	value	NOUN
gi-4938	138	8	y1	y1	INTJ
gi-4938	138	9	=	=	PUNCT
gi-4938	138	10	f(x1	f(x1	NOUN
gi-4938	138	11	)	)	PUNCT
gi-4938	138	12	,	,	PUNCT
gi-4938	138	13	y2	y2	NOUN
gi-4938	138	14	=	=	SYM
gi-4938	138	15	f(x2	f(x2	NOUN
gi-4938	138	16	)	)	PUNCT
gi-4938	138	17	,	,	PUNCT
gi-4938	138	18	and	and	CCONJ
gi-4938	138	19	y3	y3	NOUN
gi-4938	138	20	=	=	SYM
gi-4938	138	21	f(x3	f(x3	NUM
gi-4938	138	22	)	)	PUNCT
gi-4938	138	23	at	at	ADP
gi-4938	138	24	new	new	ADJ
gi-4938	138	25	vertices	vertex	NOUN
gi-4938	138	26	p1	p1	NOUN
gi-4938	138	27	,	,	PUNCT
gi-4938	138	28	p2	p2	NOUN
gi-4938	138	29	,	,	PUNCT
gi-4938	138	30	p3	p3	PROPN
gi-4938	138	31	.	.	PUNCT
gi-4938	139	1	geoinformatics	geoinformatic	NOUN
gi-4938	139	2	fce	fce	VERB
gi-4938	139	3	ctu	ctu	NOUN
gi-4938	139	4	17(2	17(2	NUM
gi-4938	139	5	)	)	PUNCT
gi-4938	139	6	,	,	PUNCT
gi-4938	139	7	2018	2018	NUM
gi-4938	139	8	13	13	NUM
gi-4938	139	9	t.	t.	NOUN
gi-4938	139	10	bayer	bayer	NOUN
gi-4938	139	11	:	:	PUNCT
gi-4938	139	12	efficient	efficient	ADJ
gi-4938	139	13	plotting	plot	VERB
gi-4938	139	14	the	the	DET
gi-4938	139	15	functions	function	NOUN
gi-4938	139	16	with	with	ADP
gi-4938	139	17	discontinuities	discontinuity	NOUN
gi-4938	139	18	algorithm	algorithm	NOUN
gi-4938	139	19	2	2	NUM
gi-4938	139	20	combined	combine	VERB
gi-4938	139	21	sampling	sampling	NOUN
gi-4938	139	22	,	,	PUNCT
gi-4938	139	23	the	the	DET
gi-4938	139	24	recursive	recursive	ADJ
gi-4938	139	25	phase	phase	NOUN
gi-4938	139	26	.	.	PUNCT
gi-4938	140	1	1	1	NUM
gi-4938	140	2	:	:	PUNCT
gi-4938	140	3	function	function	NOUN
gi-4938	140	4	cs(f	cs(f	PART
gi-4938	140	5	,	,	PUNCT
gi-4938	140	6	l	l	NOUN
gi-4938	140	7	,	,	PUNCT
gi-4938	140	8	a	a	DET
gi-4938	140	9	,	,	PUNCT
gi-4938	140	10	b	b	PROPN
gi-4938	140	11	,	,	PUNCT
gi-4938	140	12	ya	ya	PROPN
gi-4938	140	13	,	,	PUNCT
gi-4938	140	14	yb	yb	PROPN
gi-4938	140	15	,	,	PUNCT
gi-4938	140	16	d	d	PROPN
gi-4938	140	17	,	,	PUNCT
gi-4938	140	18	d	d	NOUN
gi-4938	140	19	,	,	PUNCT
gi-4938	140	20	d	d	PROPN
gi-4938	140	21	,	,	PUNCT
gi-4938	140	22	α	α	NOUN
gi-4938	140	23	)	)	PUNCT
gi-4938	140	24	2	2	NUM
gi-4938	140	25	:	:	PUNCT
gi-4938	140	26	if	if	SCONJ
gi-4938	140	27	d	d	PROPN
gi-4938	140	28	>	>	X
gi-4938	140	29	d	d	X
gi-4938	140	30	∨	∨	X
gi-4938	140	31	(	(	PUNCT
gi-4938	140	32	b−	b−	PROPN
gi-4938	140	33	a	a	DET
gi-4938	140	34	<	<	X
gi-4938	140	35	ε	ε	PROPN
gi-4938	140	36	)	)	PUNCT
gi-4938	140	37	then	then	ADV
gi-4938	140	38	3	3	NUM
gi-4938	140	39	:	:	PUNCT
gi-4938	140	40	return	return	VERB
gi-4938	140	41	4	4	NUM
gi-4938	140	42	:	:	PUNCT
gi-4938	140	43	r1	r1	PROPN
gi-4938	140	44	=	=	PUNCT
gi-4938	140	45	rand(0.45	rand(0.45	NOUN
gi-4938	140	46	,	,	PUNCT
gi-4938	140	47	0.55	0.55	NUM
gi-4938	140	48	)	)	PUNCT
gi-4938	140	49	,	,	PUNCT
gi-4938	140	50	r2	r2	PROPN
gi-4938	140	51	=	=	SYM
gi-4938	140	52	rand(0.45	rand(0.45	NOUN
gi-4938	140	53	,	,	PUNCT
gi-4938	140	54	0.55	0.55	NUM
gi-4938	140	55	)	)	PUNCT
gi-4938	140	56	,	,	PUNCT
gi-4938	140	57	r3	r3	PROPN
gi-4938	140	58	=	=	SYM
gi-4938	140	59	rand(0.45	rand(0.45	PROPN
gi-4938	140	60	,	,	PUNCT
gi-4938	140	61	0.55	0.55	NUM
gi-4938	140	62	)	)	PUNCT
gi-4938	140	63	5	5	NUM
gi-4938	140	64	:	:	PUNCT
gi-4938	140	65	x1	x1	PROPN
gi-4938	140	66	=	=	SYM
gi-4938	140	67	a+	a+	PUNCT
gi-4938	140	68	1	1	NUM
gi-4938	140	69	2r1(b−	2r1(b−	NUM
gi-4938	140	70	a	a	NOUN
gi-4938	140	71	)	)	PUNCT
gi-4938	140	72	,	,	PUNCT
gi-4938	140	73	x2	x2	NOUN
gi-4938	140	74	=	=	PRON
gi-4938	140	75	a+	a+	PUNCT
gi-4938	140	76	r2(b−	r2(b−	NOUN
gi-4938	140	77	a	a	PRON
gi-4938	140	78	)	)	PUNCT
gi-4938	140	79	,	,	PUNCT
gi-4938	140	80	x3	x3	NOUN
gi-4938	140	81	=	=	SYM
gi-4938	140	82	a+	a+	PUNCT
gi-4938	140	83	3	3	NUM
gi-4938	140	84	2r3(b−	2r3(b−	NUM
gi-4938	140	85	a	a	NOUN
gi-4938	140	86	)	)	PUNCT
gi-4938	140	87	6	6	NUM
gi-4938	140	88	:	:	PUNCT
gi-4938	140	89	if	if	SCONJ
gi-4938	140	90	discontinuity	discontinuity	NOUN
gi-4938	140	91	in	in	ADP
gi-4938	140	92	xi	xi	ADP
gi-4938	140	93	then	then	ADV
gi-4938	140	94	7	7	NUM
gi-4938	140	95	:	:	PUNCT
gi-4938	140	96	throw	throw	VERB
gi-4938	140	97	singularityexception	singularityexception	NOUN
gi-4938	140	98	(	(	PUNCT
gi-4938	140	99	xi	xi	PROPN
gi-4938	140	100	)	)	PUNCT
gi-4938	140	101	,	,	PUNCT
gi-4938	140	102	i	i	PRON
gi-4938	140	103	=	=	NOUN
gi-4938	140	104	1	1	NUM
gi-4938	140	105	,	,	PUNCT
gi-4938	140	106	2	2	NUM
gi-4938	140	107	,	,	PUNCT
gi-4938	140	108	3	3	NUM
gi-4938	140	109	8	8	NUM
gi-4938	140	110	:	:	PUNCT
gi-4938	140	111	y1	y1	NOUN
gi-4938	140	112	=	=	SYM
gi-4938	140	113	f(x1	f(x1	NOUN
gi-4938	140	114	)	)	PUNCT
gi-4938	140	115	,	,	PUNCT
gi-4938	140	116	y2	y2	NOUN
gi-4938	140	117	=	=	SYM
gi-4938	140	118	f(x2	f(x2	NOUN
gi-4938	140	119	)	)	PUNCT
gi-4938	140	120	,	,	PUNCT
gi-4938	140	121	y3	y3	NOUN
gi-4938	140	122	=	=	SYM
gi-4938	140	123	f(x3	f(x3	NUM
gi-4938	140	124	)	)	PUNCT
gi-4938	140	125	9	9	NUM
gi-4938	140	126	:	:	PUNCT
gi-4938	140	127	pa	pa	PROPN
gi-4938	140	128	=	=	SYM
gi-4938	140	129	point(a	point(a	PROPN
gi-4938	140	130	,	,	PUNCT
gi-4938	140	131	ya	ya	PROPN
gi-4938	140	132	)	)	PUNCT
gi-4938	140	133	,	,	PUNCT
gi-4938	140	134	pb	pb	ADP
gi-4938	140	135	=	=	PROPN
gi-4938	140	136	point(b	point(b	PROPN
gi-4938	140	137	,	,	PUNCT
gi-4938	140	138	yb	yb	PROPN
gi-4938	140	139	)	)	PUNCT
gi-4938	140	140	,	,	PUNCT
gi-4938	140	141	pi	pi	NOUN
gi-4938	140	142	=	=	SYM
gi-4938	140	143	point(xi	point(xi	PROPN
gi-4938	140	144	,	,	PUNCT
gi-4938	140	145	yi	yi	PROPN
gi-4938	140	146	)	)	PUNCT
gi-4938	140	147	,	,	PUNCT
gi-4938	140	148	i	i	PRON
gi-4938	140	149	=	=	NOUN
gi-4938	140	150	1	1	NUM
gi-4938	140	151	,	,	PUNCT
gi-4938	140	152	2	2	NUM
gi-4938	140	153	,	,	PUNCT
gi-4938	140	154	3	3	NUM
gi-4938	140	155	10	10	NUM
gi-4938	140	156	:	:	PUNCT
gi-4938	140	157	α1	α1	PROPN
gi-4938	140	158	=	=	SYM
gi-4938	140	159	α(pa	α(pa	NOUN
gi-4938	140	160	,	,	PUNCT
gi-4938	140	161	p1	p1	NOUN
gi-4938	140	162	,	,	PUNCT
gi-4938	140	163	p2	p2	NOUN
gi-4938	140	164	)	)	PUNCT
gi-4938	140	165	,	,	PUNCT
gi-4938	140	166	α2	α2	PROPN
gi-4938	140	167	=	=	SYM
gi-4938	140	168	α(p1	α(p1	NOUN
gi-4938	140	169	,	,	PUNCT
gi-4938	140	170	p2	p2	NOUN
gi-4938	140	171	,	,	PUNCT
gi-4938	140	172	p3	p3	PROPN
gi-4938	140	173	)	)	PUNCT
gi-4938	140	174	,	,	PUNCT
gi-4938	140	175	α3	α3	NOUN
gi-4938	140	176	=	=	SYM
gi-4938	140	177	α(p2	α(p2	ADJ
gi-4938	140	178	,	,	PUNCT
gi-4938	140	179	p3	p3	PROPN
gi-4938	140	180	,	,	PUNCT
gi-4938	140	181	pb	pb	ADP
gi-4938	140	182	)	)	PUNCT
gi-4938	140	183	11	11	NUM
gi-4938	140	184	:	:	PUNCT
gi-4938	140	185	if	if	SCONJ
gi-4938	140	186	(	(	PUNCT
gi-4938	140	187	α1	α1	PROPN
gi-4938	140	188	>	>	X
gi-4938	140	189	α	α	PROPN
gi-4938	140	190	)	)	PUNCT
gi-4938	140	191	∨	∨	PROPN
gi-4938	140	192	(	(	PUNCT
gi-4938	140	193	d	d	X
gi-4938	140	194	<	<	X
gi-4938	140	195	=	=	SYM
gi-4938	140	196	d	d	NOUN
gi-4938	140	197	)	)	PUNCT
gi-4938	140	198	then	then	ADV
gi-4938	140	199	12	12	NUM
gi-4938	140	200	:	:	PUNCT
gi-4938	140	201	cs(f	cs(f	NUM
gi-4938	140	202	,	,	PUNCT
gi-4938	140	203	l	l	NOUN
gi-4938	140	204	,	,	PUNCT
gi-4938	140	205	a	a	DET
gi-4938	140	206	,	,	PUNCT
gi-4938	140	207	x1	x1	PROPN
gi-4938	140	208	,	,	PUNCT
gi-4938	140	209	ya	ya	PROPN
gi-4938	140	210	,	,	PUNCT
gi-4938	140	211	y1	y1	PROPN
gi-4938	140	212	,	,	PUNCT
gi-4938	140	213	d+	d+	X
gi-4938	140	214	1	1	NUM
gi-4938	140	215	,	,	PUNCT
gi-4938	140	216	d	d	NOUN
gi-4938	140	217	,	,	PUNCT
gi-4938	140	218	d	d	PROPN
gi-4938	140	219	,	,	PUNCT
gi-4938	140	220	α	α	NOUN
gi-4938	140	221	)	)	PUNCT
gi-4938	140	222	;	;	PUNCT
gi-4938	140	223	13	13	NUM
gi-4938	140	224	:	:	PUNCT
gi-4938	140	225	l←	l←	NUM
gi-4938	140	226	point(x1	point(x1	NOUN
gi-4938	140	227	,	,	PUNCT
gi-4938	140	228	y1	y1	NOUN
gi-4938	140	229	)	)	PUNCT
gi-4938	140	230	14	14	NUM
gi-4938	140	231	:	:	PUNCT
gi-4938	140	232	if	if	SCONJ
gi-4938	140	233	(	(	PUNCT
gi-4938	140	234	α1	α1	PROPN
gi-4938	140	235	>	>	X
gi-4938	140	236	α	α	PROPN
gi-4938	140	237	)	)	PUNCT
gi-4938	140	238	∨	∨	PROPN
gi-4938	140	239	(	(	PUNCT
gi-4938	140	240	α2	α2	NOUN
gi-4938	140	241	>	>	X
gi-4938	140	242	α	α	PROPN
gi-4938	140	243	)	)	PUNCT
gi-4938	140	244	∨	∨	PROPN
gi-4938	140	245	(	(	PUNCT
gi-4938	140	246	d	d	X
gi-4938	140	247	<	<	X
gi-4938	140	248	=	=	SYM
gi-4938	140	249	d	d	NOUN
gi-4938	140	250	)	)	PUNCT
gi-4938	140	251	then	then	ADV
gi-4938	140	252	15	15	NUM
gi-4938	140	253	:	:	PUNCT
gi-4938	140	254	cs(f	cs(f	NUM
gi-4938	140	255	,	,	PUNCT
gi-4938	140	256	l	l	NOUN
gi-4938	140	257	,	,	PUNCT
gi-4938	140	258	x1	x1	PROPN
gi-4938	140	259	,	,	PUNCT
gi-4938	140	260	x2	x2	PROPN
gi-4938	140	261	,	,	PUNCT
gi-4938	140	262	y1	y1	NOUN
gi-4938	140	263	,	,	PUNCT
gi-4938	140	264	y2	y2	PROPN
gi-4938	140	265	,	,	PUNCT
gi-4938	140	266	d+	d+	X
gi-4938	140	267	1	1	NUM
gi-4938	140	268	,	,	PUNCT
gi-4938	140	269	d	d	NOUN
gi-4938	140	270	,	,	PUNCT
gi-4938	140	271	d	d	PROPN
gi-4938	140	272	,	,	PUNCT
gi-4938	140	273	α	α	NOUN
gi-4938	140	274	)	)	PUNCT
gi-4938	140	275	;	;	PUNCT
gi-4938	140	276	16	16	NUM
gi-4938	140	277	:	:	PUNCT
gi-4938	140	278	l←	l←	NUM
gi-4938	140	279	point(x2	point(x2	NOUN
gi-4938	140	280	,	,	PUNCT
gi-4938	140	281	y2	y2	PROPN
gi-4938	140	282	)	)	PUNCT
gi-4938	140	283	17	17	NUM
gi-4938	140	284	:	:	PUNCT
gi-4938	140	285	if	if	SCONJ
gi-4938	140	286	(	(	PUNCT
gi-4938	140	287	α2	α2	ADJ
gi-4938	140	288	>	>	X
gi-4938	140	289	α	α	X
gi-4938	140	290	)	)	PUNCT
gi-4938	140	291	∨	∨	PROPN
gi-4938	140	292	(	(	PUNCT
gi-4938	140	293	α3	α3	NOUN
gi-4938	140	294	>	>	NOUN
gi-4938	140	295	α	α	PROPN
gi-4938	140	296	)	)	PUNCT
gi-4938	140	297	∨	∨	PROPN
gi-4938	140	298	(	(	PUNCT
gi-4938	140	299	d	d	X
gi-4938	140	300	<	<	X
gi-4938	140	301	=	=	SYM
gi-4938	140	302	d	d	NOUN
gi-4938	140	303	)	)	PUNCT
gi-4938	140	304	then	then	ADV
gi-4938	140	305	18	18	NUM
gi-4938	140	306	:	:	PUNCT
gi-4938	140	307	cs(f	cs(f	NUM
gi-4938	140	308	,	,	PUNCT
gi-4938	140	309	l	l	NOUN
gi-4938	140	310	,	,	PUNCT
gi-4938	140	311	x2	x2	PROPN
gi-4938	140	312	,	,	PUNCT
gi-4938	140	313	x3	x3	ADJ
gi-4938	140	314	,	,	PUNCT
gi-4938	140	315	y3	y3	PROPN
gi-4938	140	316	,	,	PUNCT
gi-4938	140	317	y3	y3	NOUN
gi-4938	140	318	,	,	PUNCT
gi-4938	140	319	d+	d+	PUNCT
gi-4938	140	320	1	1	NUM
gi-4938	140	321	,	,	PUNCT
gi-4938	140	322	d	d	NOUN
gi-4938	140	323	,	,	PUNCT
gi-4938	140	324	d	d	PROPN
gi-4938	140	325	,	,	PUNCT
gi-4938	140	326	α	α	NOUN
gi-4938	140	327	)	)	PUNCT
gi-4938	140	328	;	;	PUNCT
gi-4938	140	329	19	19	NUM
gi-4938	140	330	:	:	PUNCT
gi-4938	140	331	l←	l←	NUM
gi-4938	140	332	point(x3	point(x3	NOUN
gi-4938	140	333	,	,	PUNCT
gi-4938	140	334	y3	y3	NOUN
gi-4938	140	335	)	)	PUNCT
gi-4938	140	336	20	20	NUM
gi-4938	140	337	:	:	PUNCT
gi-4938	140	338	if	if	SCONJ
gi-4938	140	339	(	(	PUNCT
gi-4938	140	340	α3	α3	INTJ
gi-4938	140	341	>	>	X
gi-4938	140	342	α	α	PROPN
gi-4938	140	343	)	)	PUNCT
gi-4938	140	344	∨	∨	PROPN
gi-4938	140	345	(	(	PUNCT
gi-4938	140	346	d	d	X
gi-4938	140	347	<	<	X
gi-4938	140	348	=	=	SYM
gi-4938	140	349	d	d	NOUN
gi-4938	140	350	)	)	PUNCT
gi-4938	140	351	then	then	ADV
gi-4938	140	352	21	21	NUM
gi-4938	140	353	:	:	PUNCT
gi-4938	140	354	cs(f	cs(f	NUM
gi-4938	140	355	,	,	PUNCT
gi-4938	140	356	l	l	NOUN
gi-4938	140	357	,	,	PUNCT
gi-4938	140	358	x3	x3	ADJ
gi-4938	140	359	,	,	PUNCT
gi-4938	140	360	xb	xb	PROPN
gi-4938	140	361	,	,	PUNCT
gi-4938	140	362	y3	y3	PROPN
gi-4938	140	363	,	,	PUNCT
gi-4938	140	364	yb	yb	PROPN
gi-4938	140	365	,	,	PUNCT
gi-4938	140	366	d+	d+	PUNCT
gi-4938	140	367	1	1	NUM
gi-4938	140	368	,	,	PUNCT
gi-4938	140	369	d	d	NOUN
gi-4938	140	370	,	,	PUNCT
gi-4938	140	371	d	d	PROPN
gi-4938	140	372	,	,	PUNCT
gi-4938	140	373	α	α	NOUN
gi-4938	140	374	)	)	PUNCT
gi-4938	140	375	;	;	PUNCT
gi-4938	140	376	(	(	PUNCT
gi-4938	140	377	e	e	NOUN
gi-4938	140	378	)	)	PUNCT
gi-4938	140	379	check	check	VERB
gi-4938	140	380	the	the	DET
gi-4938	140	381	refinement	refinement	NOUN
gi-4938	140	382	criteria	criterion	NOUN
gi-4938	140	383	α1	α1	PROPN
gi-4938	140	384	=	=	SYM
gi-4938	140	385	α(pa	α(pa	NUM
gi-4938	140	386	,	,	PUNCT
gi-4938	140	387	p1	p1	NOUN
gi-4938	140	388	,	,	PUNCT
gi-4938	140	389	p2	p2	NOUN
gi-4938	140	390	)	)	PUNCT
gi-4938	140	391	,	,	PUNCT
gi-4938	140	392	α2	α2	PROPN
gi-4938	140	393	=	=	SYM
gi-4938	140	394	α(p1	α(p1	NOUN
gi-4938	140	395	,	,	PUNCT
gi-4938	140	396	p2	p2	NOUN
gi-4938	140	397	,	,	PUNCT
gi-4938	140	398	p3	p3	PROPN
gi-4938	140	399	)	)	PUNCT
gi-4938	140	400	,	,	PUNCT
gi-4938	140	401	α3	α3	NOUN
gi-4938	140	402	=	=	SYM
gi-4938	140	403	α(p2	α(p2	ADJ
gi-4938	140	404	,	,	PUNCT
gi-4938	140	405	p3	p3	PROPN
gi-4938	140	406	,	,	PUNCT
gi-4938	140	407	pb	pb	PROPN
gi-4938	140	408	)	)	PUNCT
gi-4938	140	409	,	,	PUNCT
gi-4938	140	410	and	and	CCONJ
gi-4938	140	411	the	the	DET
gi-4938	140	412	recursive	recursive	ADJ
gi-4938	140	413	depth	depth	NOUN
gi-4938	140	414	d.	d.	NOUN
gi-4938	140	415	when	when	SCONJ
gi-4938	140	416	the	the	DET
gi-4938	140	417	curve	curve	NOUN
gi-4938	140	418	is	be	AUX
gi-4938	140	419	not	not	PART
gi-4938	140	420	sufficiently	sufficiently	ADV
gi-4938	140	421	smooth	smooth	ADJ
gi-4938	140	422	,	,	PUNCT
gi-4938	140	423	or	or	CCONJ
gi-4938	140	424	d	d	X
gi-4938	140	425	≤	≤	NUM
gi-4938	140	426	d	d	X
gi-4938	140	427	,	,	PUNCT
gi-4938	140	428	it	it	PRON
gi-4938	140	429	needs	need	VERB
gi-4938	140	430	to	to	PART
gi-4938	140	431	be	be	AUX
gi-4938	140	432	refined	refine	VERB
gi-4938	140	433	.	.	PUNCT
gi-4938	141	1	for	for	ADP
gi-4938	141	2	d	d	PROPN
gi-4938	141	3	≤	≤	PROPN
gi-4938	141	4	d	d	X
gi-4938	141	5	,	,	PUNCT
gi-4938	141	6	this	this	DET
gi-4938	141	7	step	step	NOUN
gi-4938	141	8	begins	begin	VERB
gi-4938	141	9	with	with	ADP
gi-4938	141	10	uniform	uniform	ADJ
gi-4938	141	11	sampling	sampling	NOUN
gi-4938	141	12	;	;	PUNCT
gi-4938	141	13	for	for	ADP
gi-4938	141	14	d	d	PROPN
gi-4938	141	15	>	>	X
gi-4938	141	16	d	d	X
gi-4938	141	17	it	it	PRON
gi-4938	141	18	transforms	transform	VERB
gi-4938	141	19	to	to	ADP
gi-4938	141	20	adaptive	adaptive	ADJ
gi-4938	141	21	sampling	sampling	NOUN
gi-4938	141	22	.	.	PUNCT
gi-4938	142	1	(	(	PUNCT
gi-4938	142	2	f	f	X
gi-4938	142	3	)	)	PUNCT
gi-4938	142	4	if	if	SCONJ
gi-4938	142	5	α1	α1	PROPN
gi-4938	142	6	>	>	X
gi-4938	142	7	α	α	PROPN
gi-4938	142	8	,	,	PUNCT
gi-4938	142	9	call	call	VERB
gi-4938	142	10	the	the	DET
gi-4938	142	11	recursive	recursive	ADJ
gi-4938	142	12	procedure	procedure	NOUN
gi-4938	142	13	with	with	ADP
gi-4938	142	14	the	the	DET
gi-4938	142	15	increased	increase	VERB
gi-4938	142	16	depth	depth	NOUN
gi-4938	142	17	d	d	X
gi-4938	142	18	=	=	SYM
gi-4938	142	19	d+	d+	PUNCT
gi-4938	142	20	1	1	NUM
gi-4938	142	21	for	for	ADP
gi-4938	142	22	the	the	DET
gi-4938	142	23	interval	interval	NOUN
gi-4938	142	24	[	[	X
gi-4938	142	25	a	a	X
gi-4938	142	26	,	,	PUNCT
gi-4938	142	27	x1	x1	PROPN
gi-4938	142	28	)	)	PUNCT
gi-4938	142	29	.	.	PUNCT
gi-4938	143	1	(	(	PUNCT
gi-4938	143	2	g	g	NOUN
gi-4938	143	3	)	)	PUNCT
gi-4938	143	4	add	add	VERB
gi-4938	143	5	new	new	ADJ
gi-4938	143	6	point	point	NOUN
gi-4938	143	7	p1	p1	NOUN
gi-4938	143	8	to	to	ADP
gi-4938	143	9	the	the	DET
gi-4938	143	10	polynomial	polynomial	ADJ
gi-4938	143	11	approximation	approximation	NOUN
gi-4938	143	12	of	of	ADP
gi-4938	143	13	f(x	f(x	PROPN
gi-4938	143	14	):	):	PUNCT
gi-4938	143	15	l←	l←	X
gi-4938	143	16	p1	p1	NOUN
gi-4938	143	17	.	.	PUNCT
gi-4938	144	1	(	(	PUNCT
gi-4938	144	2	h	h	NOUN
gi-4938	144	3	)	)	PUNCT
gi-4938	144	4	if	if	SCONJ
gi-4938	144	5	α1	α1	PROPN
gi-4938	144	6	>	>	X
gi-4938	144	7	α∨α2	α∨α2	PROPN
gi-4938	144	8	>	>	X
gi-4938	144	9	α	α	X
gi-4938	144	10	,	,	PUNCT
gi-4938	144	11	call	call	VERB
gi-4938	144	12	the	the	DET
gi-4938	144	13	recursive	recursive	ADJ
gi-4938	144	14	procedure	procedure	NOUN
gi-4938	144	15	with	with	ADP
gi-4938	144	16	the	the	DET
gi-4938	144	17	increased	increase	VERB
gi-4938	144	18	depth	depth	NOUN
gi-4938	144	19	d	d	NOUN
gi-4938	144	20	=	=	SYM
gi-4938	144	21	d+1	d+1	PROPN
gi-4938	144	22	for	for	ADP
gi-4938	144	23	the	the	DET
gi-4938	144	24	interval	interval	NOUN
gi-4938	144	25	(	(	PUNCT
gi-4938	144	26	x1	x1	PROPN
gi-4938	144	27	,	,	PUNCT
gi-4938	144	28	x2	x2	PROPN
gi-4938	144	29	)	)	PUNCT
gi-4938	144	30	.	.	PUNCT
gi-4938	145	1	(	(	PUNCT
gi-4938	145	2	i	i	NOUN
gi-4938	145	3	)	)	PUNCT
gi-4938	145	4	add	add	VERB
gi-4938	145	5	new	new	ADJ
gi-4938	145	6	point	point	NOUN
gi-4938	145	7	p2	p2	NOUN
gi-4938	145	8	to	to	ADP
gi-4938	145	9	the	the	DET
gi-4938	145	10	polynomial	polynomial	ADJ
gi-4938	145	11	approximation	approximation	NOUN
gi-4938	145	12	of	of	ADP
gi-4938	145	13	f(x	f(x	PROPN
gi-4938	145	14	):	):	PUNCT
gi-4938	145	15	l←	l←	X
gi-4938	145	16	p2	p2	NOUN
gi-4938	145	17	.	.	PUNCT
gi-4938	146	1	(	(	PUNCT
gi-4938	146	2	j	j	NOUN
gi-4938	146	3	)	)	PUNCT
gi-4938	146	4	if	if	SCONJ
gi-4938	146	5	α2	α2	PROPN
gi-4938	146	6	>	>	X
gi-4938	146	7	α∨α3	α∨α3	PUNCT
gi-4938	146	8	>	>	PUNCT
gi-4938	146	9	α	α	X
gi-4938	146	10	,	,	PUNCT
gi-4938	146	11	call	call	VERB
gi-4938	146	12	the	the	DET
gi-4938	146	13	recursive	recursive	ADJ
gi-4938	146	14	procedure	procedure	NOUN
gi-4938	146	15	with	with	ADP
gi-4938	146	16	the	the	DET
gi-4938	146	17	increased	increase	VERB
gi-4938	146	18	depth	depth	NOUN
gi-4938	146	19	d	d	NOUN
gi-4938	146	20	=	=	SYM
gi-4938	146	21	d+1	d+1	PROPN
gi-4938	146	22	for	for	ADP
gi-4938	146	23	the	the	DET
gi-4938	146	24	interval	interval	NOUN
gi-4938	146	25	(	(	PUNCT
gi-4938	146	26	x2	x2	PROPN
gi-4938	146	27	,	,	PUNCT
gi-4938	146	28	x3	x3	ADJ
gi-4938	146	29	)	)	PUNCT
gi-4938	146	30	.	.	PUNCT
gi-4938	147	1	(	(	PUNCT
gi-4938	147	2	k	k	X
gi-4938	147	3	)	)	PUNCT
gi-4938	147	4	add	add	VERB
gi-4938	147	5	new	new	ADJ
gi-4938	147	6	point	point	NOUN
gi-4938	147	7	p3	p3	NOUN
gi-4938	147	8	to	to	ADP
gi-4938	147	9	the	the	DET
gi-4938	147	10	polynomial	polynomial	ADJ
gi-4938	147	11	approximation	approximation	NOUN
gi-4938	147	12	of	of	ADP
gi-4938	147	13	f(x	f(x	PROPN
gi-4938	147	14	):	):	PUNCT
gi-4938	147	15	l←	l←	X
gi-4938	147	16	p3	p3	NOUN
gi-4938	147	17	.	.	PUNCT
gi-4938	148	1	(	(	PUNCT
gi-4938	148	2	l	l	NOUN
gi-4938	148	3	)	)	PUNCT
gi-4938	148	4	if	if	SCONJ
gi-4938	148	5	α3	α3	PROPN
gi-4938	148	6	>	>	X
gi-4938	148	7	α	α	PROPN
gi-4938	148	8	,	,	PUNCT
gi-4938	148	9	call	call	VERB
gi-4938	148	10	the	the	DET
gi-4938	148	11	recursive	recursive	ADJ
gi-4938	148	12	procedure	procedure	NOUN
gi-4938	148	13	for	for	ADP
gi-4938	148	14	the	the	DET
gi-4938	148	15	interval	interval	NOUN
gi-4938	148	16	(	(	PUNCT
gi-4938	148	17	x3	x3	PROPN
gi-4938	148	18	,	,	PUNCT
gi-4938	148	19	xb	xb	PROPN
gi-4938	148	20	]	]	PUNCT
gi-4938	148	21	.	.	PUNCT
gi-4938	149	1	3	3	X
gi-4938	149	2	.	.	X
gi-4938	149	3	final	final	ADJ
gi-4938	149	4	step	step	NOUN
gi-4938	149	5	add	add	VERB
gi-4938	149	6	the	the	DET
gi-4938	149	7	last	last	ADJ
gi-4938	149	8	point	point	NOUN
gi-4938	149	9	pb	pb	ADP
gi-4938	149	10	to	to	ADP
gi-4938	149	11	the	the	DET
gi-4938	149	12	polynomial	polynomial	ADJ
gi-4938	149	13	approximation	approximation	NOUN
gi-4938	149	14	of	of	ADP
gi-4938	149	15	f(x	f(x	PROPN
gi-4938	149	16	)	)	PUNCT
gi-4938	149	17	:	:	PUNCT
gi-4938	149	18	l←	l←	NUM
gi-4938	149	19	pb	pb	X
gi-4938	149	20	and	and	CCONJ
gi-4938	149	21	finish	finish	VERB
gi-4938	149	22	the	the	DET
gi-4938	149	23	combined	combine	VERB
gi-4938	149	24	sampling	sampling	NOUN
gi-4938	149	25	procedure	procedure	NOUN
gi-4938	149	26	.	.	PUNCT
gi-4938	150	1	geoinformatics	geoinformatic	NOUN
gi-4938	150	2	fce	fce	VERB
gi-4938	150	3	ctu	ctu	NOUN
gi-4938	150	4	17(2	17(2	NUM
gi-4938	150	5	)	)	PUNCT
gi-4938	150	6	,	,	PUNCT
gi-4938	150	7	2018	2018	NUM
gi-4938	150	8	14	14	NUM
gi-4938	150	9	t.	t.	NOUN
gi-4938	150	10	bayer	bayer	PROPN
gi-4938	150	11	:	:	PUNCT
gi-4938	150	12	efficient	efficient	ADJ
gi-4938	150	13	plotting	plot	VERB
gi-4938	150	14	the	the	DET
gi-4938	150	15	functions	function	NOUN
gi-4938	150	16	with	with	ADP
gi-4938	150	17	discontinuities	discontinuity	NOUN
gi-4938	150	18	method	method	NOUN
gi-4938	150	19	m3	m3	PROPN
gi-4938	150	20	.	.	PUNCT
gi-4938	151	1	by	by	ADP
gi-4938	151	2	summarizing	summarize	VERB
gi-4938	151	3	the	the	DET
gi-4938	151	4	facts	fact	NOUN
gi-4938	151	5	mentioned	mention	VERB
gi-4938	151	6	above	above	ADP
gi-4938	151	7	the	the	DET
gi-4938	151	8	proposed	propose	VERB
gi-4938	151	9	algorithm	algorithm	NOUN
gi-4938	151	10	uses	use	VERB
gi-4938	151	11	a	a	DET
gi-4938	151	12	triple	triple	ADJ
gi-4938	151	13	recursion	recursion	NOUN
gi-4938	151	14	.	.	PUNCT
gi-4938	152	1	in	in	ADP
gi-4938	152	2	each	each	DET
gi-4938	152	3	step	step	NOUN
gi-4938	152	4	,	,	PUNCT
gi-4938	152	5	the	the	DET
gi-4938	152	6	refined	refined	ADJ
gi-4938	152	7	f(x	f(x	PROPN
gi-4938	152	8	)	)	PUNCT
gi-4938	152	9	is	be	AUX
gi-4938	152	10	approximated	approximate	VERB
gi-4938	152	11	by	by	ADP
gi-4938	152	12	at	at	ADV
gi-4938	152	13	least	least	ADV
gi-4938	152	14	three	three	NUM
gi-4938	152	15	new	new	ADJ
gi-4938	152	16	points	point	NOUN
gi-4938	152	17	.	.	PUNCT
gi-4938	153	1	for	for	ADP
gi-4938	153	2	the	the	DET
gi-4938	153	3	pseudocode	pseudocode	NOUN
gi-4938	153	4	,	,	PUNCT
gi-4938	153	5	see	see	VERB
gi-4938	153	6	algs	algs	NOUN
gi-4938	153	7	.	.	PUNCT
gi-4938	154	1	1	1	NUM
gi-4938	154	2	,	,	PUNCT
gi-4938	154	3	2	2	NUM
gi-4938	154	4	.	.	PUNCT
gi-4938	154	5	compared	compare	VERB
gi-4938	154	6	to	to	ADP
gi-4938	154	7	[	[	X
gi-4938	154	8	15	15	NUM
gi-4938	154	9	]	]	PUNCT
gi-4938	154	10	,	,	PUNCT
gi-4938	154	11	this	this	DET
gi-4938	154	12	solution	solution	NOUN
gi-4938	154	13	has	have	VERB
gi-4938	154	14	a	a	DET
gi-4938	154	15	dramatically	dramatically	ADV
gi-4938	154	16	improved	improve	VERB
gi-4938	154	17	performance	performance	NOUN
gi-4938	154	18	and	and	CCONJ
gi-4938	154	19	requires	require	VERB
gi-4938	154	20	fewer	few	ADJ
gi-4938	154	21	subdivisions	subdivision	NOUN
gi-4938	154	22	.	.	PUNCT
gi-4938	155	1	due	due	ADP
gi-4938	155	2	to	to	ADP
gi-4938	155	3	the	the	DET
gi-4938	155	4	significantly	significantly	ADV
gi-4938	155	5	higher	high	ADJ
gi-4938	155	6	recursion	recursion	NOUN
gi-4938	155	7	depth	depth	NOUN
gi-4938	155	8	d	d	NOUN
gi-4938	155	9	,	,	PUNCT
gi-4938	155	10	for	for	ADP
gi-4938	155	11	fast	fast	ADJ
gi-4938	155	12	and	and	CCONJ
gi-4938	155	13	efficient	efficient	ADJ
gi-4938	155	14	estimation	estimation	NOUN
gi-4938	155	15	of	of	ADP
gi-4938	155	16	the	the	DET
gi-4938	155	17	f(x	f(x	PROPN
gi-4938	155	18	)	)	PUNCT
gi-4938	155	19	curvature	curvature	NOUN
gi-4938	155	20	,	,	PUNCT
gi-4938	155	21	a	a	DET
gi-4938	155	22	single	single	ADJ
gi-4938	155	23	recursive	recursive	ADJ
gi-4938	155	24	step	step	NOUN
gi-4938	155	25	is	be	AUX
gi-4938	155	26	not	not	PART
gi-4938	155	27	sufficient	sufficient	ADJ
gi-4938	155	28	.	.	PUNCT
gi-4938	156	1	this	this	DET
gi-4938	156	2	issue	issue	NOUN
gi-4938	156	3	is	be	AUX
gi-4938	156	4	illustrated	illustrate	VERB
gi-4938	156	5	in	in	ADP
gi-4938	156	6	tab	tab	NOUN
gi-4938	156	7	.	.	PUNCT
gi-4938	157	1	1	1	NUM
gi-4938	157	2	;	;	PUNCT
gi-4938	157	3	our	our	PRON
gi-4938	157	4	method	method	NOUN
gi-4938	157	5	is	be	AUX
gi-4938	157	6	labeled	label	VERB
gi-4938	157	7	as	as	ADP
gi-4938	157	8	m3	m3	PROPN
gi-4938	157	9	,	,	PUNCT
gi-4938	157	10	a	a	DET
gi-4938	157	11	single	single	ADJ
gi-4938	157	12	recursion	recursion	NOUN
gi-4938	157	13	step	step	NOUN
gi-4938	157	14	method	method	NOUN
gi-4938	157	15	as	as	ADP
gi-4938	157	16	m1	m1	PROPN
gi-4938	157	17	.	.	PUNCT
gi-4938	158	1	4	4	X
gi-4938	158	2	.	.	X
gi-4938	158	3	singularity	singularity	NOUN
gi-4938	158	4	detection	detection	NOUN
gi-4938	158	5	this	this	DET
gi-4938	158	6	section	section	NOUN
gi-4938	158	7	describes	describe	VERB
gi-4938	158	8	several	several	ADJ
gi-4938	158	9	simple	simple	ADJ
gi-4938	158	10	strategies	strategy	NOUN
gi-4938	158	11	for	for	ADP
gi-4938	158	12	handling	handle	VERB
gi-4938	158	13	and	and	CCONJ
gi-4938	158	14	detecting	detect	VERB
gi-4938	158	15	the	the	DET
gi-4938	158	16	discontinuities	discontinuity	NOUN
gi-4938	158	17	;	;	PUNCT
gi-4938	158	18	their	their	PRON
gi-4938	158	19	overview	overview	NOUN
gi-4938	158	20	can	can	AUX
gi-4938	158	21	be	be	AUX
gi-4938	158	22	found	find	VERB
gi-4938	158	23	in	in	ADP
gi-4938	158	24	[	[	X
gi-4938	158	25	24	24	NUM
gi-4938	158	26	]	]	PUNCT
gi-4938	158	27	,	,	PUNCT
gi-4938	158	28	[	[	X
gi-4938	158	29	2	2	NUM
gi-4938	158	30	]	]	PUNCT
gi-4938	158	31	,	,	PUNCT
gi-4938	158	32	[	[	X
gi-4938	158	33	26	26	NUM
gi-4938	158	34	]	]	PUNCT
gi-4938	158	35	.	.	PUNCT
gi-4938	159	1	early	early	ADJ
gi-4938	159	2	methods	method	NOUN
gi-4938	159	3	are	be	AUX
gi-4938	159	4	based	base	VERB
gi-4938	159	5	on	on	ADP
gi-4938	159	6	the	the	DET
gi-4938	159	7	markov	markov	NOUN
gi-4938	159	8	models	model	NOUN
gi-4938	159	9	[	[	X
gi-4938	159	10	18	18	NUM
gi-4938	159	11	]	]	PUNCT
gi-4938	159	12	,	,	PUNCT
gi-4938	159	13	[	[	X
gi-4938	159	14	28	28	NUM
gi-4938	159	15	]	]	PUNCT
gi-4938	159	16	,	,	PUNCT
gi-4938	159	17	[	[	X
gi-4938	159	18	25	25	NUM
gi-4938	159	19	]	]	PUNCT
gi-4938	159	20	.	.	PUNCT
gi-4938	160	1	currently	currently	ADV
gi-4938	160	2	,	,	PUNCT
gi-4938	160	3	there	there	PRON
gi-4938	160	4	are	be	VERB
gi-4938	160	5	several	several	ADJ
gi-4938	160	6	approaches	approach	NOUN
gi-4938	160	7	:	:	PUNCT
gi-4938	160	8	applications	application	NOUN
gi-4938	160	9	of	of	ADP
gi-4938	160	10	the	the	DET
gi-4938	160	11	fourier	fourier	ADJ
gi-4938	160	12	transformation	transformation	NOUN
gi-4938	161	1	[	[	X
gi-4938	161	2	5	5	NUM
gi-4938	161	3	]	]	PUNCT
gi-4938	161	4	,	,	PUNCT
gi-4938	161	5	[	[	X
gi-4938	161	6	12	12	NUM
gi-4938	161	7	]	]	PUNCT
gi-4938	161	8	,	,	PUNCT
gi-4938	162	1	[	[	X
gi-4938	162	2	4	4	NUM
gi-4938	162	3	]	]	PUNCT
gi-4938	162	4	,	,	PUNCT
gi-4938	162	5	[	[	X
gi-4938	162	6	23	23	NUM
gi-4938	162	7	]	]	PUNCT
gi-4938	162	8	,	,	PUNCT
gi-4938	163	1	[	[	X
gi-4938	163	2	17	17	NUM
gi-4938	163	3	]	]	PUNCT
gi-4938	163	4	,	,	PUNCT
gi-4938	163	5	[	[	X
gi-4938	163	6	16	16	NUM
gi-4938	163	7	]	]	PUNCT
gi-4938	163	8	,	,	PUNCT
gi-4938	163	9	[	[	X
gi-4938	163	10	11	11	NUM
gi-4938	163	11	]	]	PUNCT
gi-4938	163	12	,	,	PUNCT
gi-4938	163	13	wavelets	wavelet	VERB
gi-4938	163	14	[	[	X
gi-4938	163	15	35	35	NUM
gi-4938	163	16	]	]	PUNCT
gi-4938	163	17	,	,	PUNCT
gi-4938	163	18	[	[	X
gi-4938	163	19	45	45	NUM
gi-4938	163	20	]	]	PUNCT
gi-4938	163	21	,	,	PUNCT
gi-4938	163	22	chebyshev	chebyshev	PROPN
gi-4938	163	23	series	series	PROPN
gi-4938	163	24	[	[	X
gi-4938	163	25	31	31	NUM
gi-4938	163	26	]	]	PUNCT
gi-4938	163	27	,	,	PUNCT
gi-4938	163	28	triangulations	triangulation	VERB
gi-4938	163	29	[	[	X
gi-4938	163	30	19	19	NUM
gi-4938	163	31	]	]	PUNCT
gi-4938	163	32	.	.	PUNCT
gi-4938	164	1	geometric	geometric	ADJ
gi-4938	164	2	measures	measure	NOUN
gi-4938	164	3	of	of	ADP
gi-4938	164	4	the	the	DET
gi-4938	164	5	curvature	curvature	NOUN
gi-4938	164	6	are	be	AUX
gi-4938	164	7	described	describe	VERB
gi-4938	164	8	in	in	ADP
gi-4938	164	9	[	[	X
gi-4938	164	10	38	38	NUM
gi-4938	164	11	]	]	PUNCT
gi-4938	164	12	,	,	PUNCT
gi-4938	165	1	[	[	X
gi-4938	165	2	22	22	NUM
gi-4938	165	3	]	]	PUNCT
gi-4938	165	4	,	,	PUNCT
gi-4938	166	1	[	[	X
gi-4938	166	2	34	34	NUM
gi-4938	166	3	]	]	PUNCT
gi-4938	166	4	,	,	PUNCT
gi-4938	167	1	[	[	X
gi-4938	167	2	1	1	NUM
gi-4938	167	3	]	]	PUNCT
gi-4938	167	4	,	,	PUNCT
gi-4938	167	5	[	[	X
gi-4938	167	6	30	30	NUM
gi-4938	167	7	]	]	PUNCT
gi-4938	167	8	,	,	PUNCT
gi-4938	167	9	[	[	X
gi-4938	167	10	36	36	NUM
gi-4938	167	11	]	]	PUNCT
gi-4938	167	12	,	,	PUNCT
gi-4938	167	13	the	the	DET
gi-4938	167	14	statistical	statistical	ADJ
gi-4938	167	15	-	-	PUNCT
gi-4938	167	16	based	base	VERB
gi-4938	167	17	methods	method	NOUN
gi-4938	167	18	in	in	ADP
gi-4938	167	19	[	[	X
gi-4938	167	20	8	8	NUM
gi-4938	167	21	]	]	PUNCT
gi-4938	167	22	,	,	PUNCT
gi-4938	167	23	[	[	X
gi-4938	167	24	26	26	NUM
gi-4938	167	25	]	]	PUNCT
gi-4938	167	26	.	.	PUNCT
gi-4938	168	1	unlike	unlike	ADP
gi-4938	168	2	the	the	DET
gi-4938	168	3	solutions	solution	NOUN
gi-4938	168	4	searching	search	VERB
gi-4938	168	5	for	for	ADP
gi-4938	168	6	all	all	DET
gi-4938	168	7	discontinuities	discontinuity	NOUN
gi-4938	168	8	of	of	ADP
gi-4938	168	9	f	f	PROPN
gi-4938	168	10	at	at	ADP
gi-4938	168	11	entire	entire	ADJ
gi-4938	168	12	ω	ω	NOUN
gi-4938	168	13	,	,	PUNCT
gi-4938	168	14	each	each	DET
gi-4938	168	15	sampled	sample	VERB
gi-4938	168	16	point	point	NOUN
gi-4938	168	17	xi	xi	INTJ
gi-4938	168	18	is	be	AUX
gi-4938	168	19	checked	check	VERB
gi-4938	168	20	for	for	ADP
gi-4938	168	21	a	a	DET
gi-4938	168	22	discontinuity	discontinuity	NOUN
gi-4938	168	23	;	;	PUNCT
gi-4938	168	24	the	the	DET
gi-4938	168	25	removable	removable	ADJ
gi-4938	168	26	,	,	PUNCT
gi-4938	168	27	jump	jump	NOUN
gi-4938	168	28	and	and	CCONJ
gi-4938	168	29	infinite	infinite	ADJ
gi-4938	168	30	discontinuities	discontinuity	NOUN
gi-4938	168	31	are	be	AUX
gi-4938	168	32	involved	involve	VERB
gi-4938	168	33	.	.	PUNCT
gi-4938	169	1	these	these	DET
gi-4938	169	2	testing	testing	NOUN
gi-4938	169	3	criteria	criterion	NOUN
gi-4938	169	4	are	be	AUX
gi-4938	169	5	local	local	ADJ
gi-4938	169	6	,	,	PUNCT
gi-4938	169	7	they	they	PRON
gi-4938	169	8	analyze	analyze	VERB
gi-4938	169	9	behavior	behavior	NOUN
gi-4938	169	10	of	of	ADP
gi-4938	169	11	the	the	DET
gi-4938	169	12	function	function	NOUN
gi-4938	169	13	in	in	ADP
gi-4938	169	14	a	a	DET
gi-4938	169	15	boundary	boundary	ADJ
gi-4938	169	16	b(xi	b(xi	PROPN
gi-4938	169	17	,	,	PUNCT
gi-4938	169	18	ε	ε	PROPN
gi-4938	169	19	)	)	PUNCT
gi-4938	169	20	of	of	ADP
gi-4938	169	21	xi	xi	PROPN
gi-4938	169	22	,	,	PUNCT
gi-4938	169	23	covered	cover	VERB
gi-4938	169	24	by	by	ADP
gi-4938	169	25	the	the	DET
gi-4938	169	26	equally	equally	ADV
gi-4938	169	27	spaced	spaced	ADJ
gi-4938	169	28	points	point	NOUN
gi-4938	169	29	xi−2	xi−2	NOUN
gi-4938	169	30	=	=	SYM
gi-4938	169	31	xi−	xi−	PUNCT
gi-4938	169	32	2h	2h	NUM
gi-4938	169	33	,	,	PUNCT
gi-4938	169	34	xi−1	xi−1	PROPN
gi-4938	169	35	=	=	SYM
gi-4938	170	1	xi−	xi−	PUNCT
gi-4938	170	2	h	h	NOUN
gi-4938	170	3	,	,	PUNCT
gi-4938	170	4	and	and	CCONJ
gi-4938	170	5	,	,	PUNCT
gi-4938	170	6	xi+1	xi+1	PROPN
gi-4938	170	7	=	=	PUNCT
gi-4938	170	8	xi	xi	PROPN
gi-4938	171	1	+	+	CCONJ
gi-4938	171	2	h	h	NOUN
gi-4938	171	3	,	,	PUNCT
gi-4938	171	4	xi+2	xi+2	PUNCT
gi-4938	172	1	=	=	SYM
gi-4938	172	2	xi+2h	xi+2h	PROPN
gi-4938	172	3	,	,	PUNCT
gi-4938	172	4	where	where	SCONJ
gi-4938	172	5	h	h	NOUN
gi-4938	172	6	=	=	SYM
gi-4938	172	7	ε/2	ε/2	PROPN
gi-4938	172	8	.	.	PUNCT
gi-4938	173	1	for	for	ADP
gi-4938	173	2	practical	practical	ADJ
gi-4938	173	3	computation	computation	NOUN
gi-4938	173	4	ε	ε	NOUN
gi-4938	173	5	=	=	SYM
gi-4938	173	6	0.001	0.001	NUM
gi-4938	173	7	.	.	PUNCT
gi-4938	174	1	an	an	DET
gi-4938	174	2	infinite	infinite	ADJ
gi-4938	174	3	discontinuity	discontinuity	NOUN
gi-4938	174	4	is	be	AUX
gi-4938	174	5	detected	detect	VERB
gi-4938	174	6	if	if	SCONJ
gi-4938	174	7	(	(	PUNCT
gi-4938	174	8	|fi−k|	|fi−k|	PROPN
gi-4938	174	9	>	>	SYM
gi-4938	174	10	y	y	PROPN
gi-4938	174	11	)	)	PUNCT
gi-4938	174	12	∨	∨	PROPN
gi-4938	174	13	(	(	PUNCT
gi-4938	174	14	fi−k	fi−k	PROPN
gi-4938	174	15	≡	≡	PROPN
gi-4938	174	16	±inf	±inf	PRON
gi-4938	174	17	)	)	PUNCT
gi-4938	174	18	∨	∨	NOUN
gi-4938	174	19	(	(	PUNCT
gi-4938	174	20	fi−k	fi−k	PROPN
gi-4938	174	21	≡	≡	PROPN
gi-4938	174	22	nan	nan	PROPN
gi-4938	174	23	)	)	PUNCT
gi-4938	174	24	,	,	PUNCT
gi-4938	175	1	k	k	NOUN
gi-4938	175	2	=	=	SYM
gi-4938	175	3	−2	−2	PROPN
gi-4938	175	4	,	,	PUNCT
gi-4938	175	5	..	..	PUNCT
gi-4938	175	6	,	,	PUNCT
gi-4938	175	7	2	2	X
gi-4938	175	8	.	.	X
gi-4938	175	9	where	where	SCONJ
gi-4938	175	10	y	y	PROPN
gi-4938	175	11	is	be	AUX
gi-4938	175	12	the	the	DET
gi-4938	175	13	given	give	VERB
gi-4938	175	14	threshold	threshold	NOUN
gi-4938	175	15	,	,	PUNCT
gi-4938	175	16	nan	nan	PROPN
gi-4938	175	17	and	and	CCONJ
gi-4938	175	18	inf	inf	PROPN
gi-4938	175	19	are	be	AUX
gi-4938	175	20	the	the	DET
gi-4938	175	21	symbols	symbol	NOUN
gi-4938	175	22	for	for	ADP
gi-4938	175	23	the	the	DET
gi-4938	175	24	positive	positive	ADJ
gi-4938	175	25	infinity	infinity	NOUN
gi-4938	175	26	and	and	CCONJ
gi-4938	175	27	the	the	DET
gi-4938	175	28	result	result	NOUN
gi-4938	175	29	of	of	ADP
gi-4938	175	30	the	the	DET
gi-4938	175	31	undefined	undefined	ADJ
gi-4938	175	32	operation	operation	NOUN
gi-4938	175	33	.	.	PUNCT
gi-4938	176	1	the	the	DET
gi-4938	176	2	remaining	remain	VERB
gi-4938	176	3	discontinuities	discontinuity	NOUN
gi-4938	176	4	may	may	AUX
gi-4938	176	5	be	be	AUX
gi-4938	176	6	found	find	VERB
gi-4938	176	7	using	use	VERB
gi-4938	176	8	the	the	DET
gi-4938	176	9	criteria	criterion	NOUN
gi-4938	176	10	measuring	measure	VERB
gi-4938	176	11	the	the	DET
gi-4938	176	12	smoothness	smoothness	NOUN
gi-4938	176	13	by	by	ADP
gi-4938	176	14	changes	change	NOUN
gi-4938	176	15	in	in	ADP
gi-4938	176	16	the	the	DET
gi-4938	176	17	variation	variation	NOUN
gi-4938	176	18	.	.	PUNCT
gi-4938	177	1	two	two	NUM
gi-4938	177	2	criteria	criterion	NOUN
gi-4938	177	3	,	,	PUNCT
gi-4938	177	4	weno	weno	PROPN
gi-4938	177	5	and	and	CCONJ
gi-4938	177	6	lr	lr	PROPN
gi-4938	177	7	,	,	PUNCT
gi-4938	177	8	described	describe	VERB
gi-4938	177	9	in	in	ADP
gi-4938	177	10	[	[	X
gi-4938	177	11	30	30	NUM
gi-4938	177	12	]	]	PUNCT
gi-4938	177	13	,	,	PUNCT
gi-4938	177	14	are	be	AUX
gi-4938	177	15	presented	present	VERB
gi-4938	177	16	.	.	PUNCT
gi-4938	178	1	the	the	DET
gi-4938	178	2	weno	weno	PROPN
gi-4938	178	3	criterion	criterion	NOUN
gi-4938	178	4	wj(x	wj(x	PUNCT
gi-4938	178	5	)	)	PUNCT
gi-4938	178	6	,	,	PUNCT
gi-4938	178	7	j	j	PROPN
gi-4938	178	8	=	=	SYM
gi-4938	178	9	0	0	NUM
gi-4938	178	10	,	,	PUNCT
gi-4938	178	11	1	1	NUM
gi-4938	178	12	,	,	PUNCT
gi-4938	178	13	2	2	NUM
gi-4938	178	14	,	,	PUNCT
gi-4938	178	15	is	be	AUX
gi-4938	178	16	written	write	VERB
gi-4938	178	17	as	as	ADP
gi-4938	178	18	wj(x	wj(x	PUNCT
gi-4938	178	19	)	)	PUNCT
gi-4938	179	1	=	=	SYM
gi-4938	179	2	αi∑2	αi∑2	NOUN
gi-4938	179	3	j=0	j=0	PROPN
gi-4938	179	4	αi	αi	ADV
gi-4938	179	5	,	,	PUNCT
gi-4938	179	6	αj	αj	NOUN
gi-4938	179	7	=	=	SYM
gi-4938	179	8	1	1	NUM
gi-4938	179	9	(	(	PUNCT
gi-4938	179	10	isj	isj	NOUN
gi-4938	179	11	+	+	CCONJ
gi-4938	179	12	ε)2	ε)2	NOUN
gi-4938	179	13	,	,	PUNCT
gi-4938	179	14	where	where	SCONJ
gi-4938	179	15	is0	is0	PROPN
gi-4938	179	16	=	=	SYM
gi-4938	179	17	13	13	NUM
gi-4938	179	18	12(fi−2	12(fi−2	NUM
gi-4938	179	19	−	−	PROPN
gi-4938	179	20	2fi−1	2fi−1	NUM
gi-4938	179	21	+	+	CCONJ
gi-4938	179	22	fi)2	fi)2	NOUN
gi-4938	179	23	+	+	CCONJ
gi-4938	179	24	1	1	NUM
gi-4938	179	25	4(fi−2	4(fi−2	NUM
gi-4938	179	26	−	−	PROPN
gi-4938	179	27	4fi−1	4fi−1	PROPN
gi-4938	179	28	+	+	CCONJ
gi-4938	179	29	fi)2	fi)2	PROPN
gi-4938	179	30	,	,	PUNCT
gi-4938	179	31	is1	is1	PROPN
gi-4938	179	32	=	=	SYM
gi-4938	179	33	13	13	NUM
gi-4938	179	34	12(fi−1	12(fi−1	NUM
gi-4938	179	35	−	−	PROPN
gi-4938	179	36	2fi	2fi	ADJ
gi-4938	179	37	+	+	CCONJ
gi-4938	179	38	fi+1)2	fi+1)2	ADJ
gi-4938	179	39	+	+	CCONJ
gi-4938	179	40	1	1	NUM
gi-4938	179	41	4(fi−1	4(fi−1	NUM
gi-4938	179	42	−	−	PROPN
gi-4938	179	43	fi+1)2	fi+1)2	ADJ
gi-4938	179	44	,	,	PUNCT
gi-4938	179	45	is2	is2	NOUN
gi-4938	179	46	=	=	PUNCT
gi-4938	179	47	13	13	NUM
gi-4938	179	48	12(fi+2	12(fi+2	NUM
gi-4938	179	49	−	−	NUM
gi-4938	179	50	2fi+1	2fi+1	NOUN
gi-4938	179	51	+	+	CCONJ
gi-4938	179	52	fi)2	fi)2	NOUN
gi-4938	179	53	+	+	CCONJ
gi-4938	179	54	1	1	NUM
gi-4938	179	55	4(fi+2	4(fi+2	NUM
gi-4938	180	1	−	−	NUM
gi-4938	180	2	4fi+1	4fi+1	NOUN
gi-4938	181	1	+	+	CCONJ
gi-4938	181	2	fi)2	fi)2	NOUN
gi-4938	181	3	.	.	PUNCT
gi-4938	182	1	if	if	SCONJ
gi-4938	182	2	w0(x	w0(x	PROPN
gi-4938	182	3	)	)	PUNCT
gi-4938	182	4	>	>	X
gi-4938	183	1	1/3∨w1(x	1/3∨w1(x	NUM
gi-4938	183	2	)	)	PUNCT
gi-4938	183	3	>	>	X
gi-4938	183	4	1/3∨w2(x	1/3∨w2(x	NUM
gi-4938	183	5	)	)	PUNCT
gi-4938	183	6	>	>	X
gi-4938	184	1	1/3	1/3	NUM
gi-4938	184	2	,	,	PUNCT
gi-4938	184	3	f	f	PROPN
gi-4938	184	4	is	be	AUX
gi-4938	184	5	probably	probably	ADV
gi-4938	184	6	not	not	PART
gi-4938	184	7	smooth	smooth	ADJ
gi-4938	184	8	at	at	ADP
gi-4938	184	9	xi	xi	PROPN
gi-4938	184	10	.	.	PUNCT
gi-4938	185	1	the	the	DET
gi-4938	185	2	lr	lr	NOUN
gi-4938	185	3	criterion	criterion	NOUN
gi-4938	185	4	has	have	VERB
gi-4938	185	5	the	the	DET
gi-4938	185	6	following	follow	VERB
gi-4938	185	7	form	form	NOUN
gi-4938	185	8	lr(x	lr(x	PROPN
gi-4938	185	9	)	)	PUNCT
gi-4938	185	10	=	=	PUNCT
gi-4938	185	11	∣∣f2	∣∣f2	VERB
gi-4938	185	12	r	r	NOUN
gi-4938	185	13	−	−	NOUN
gi-4938	185	14	f2	f2	PROPN
gi-4938	185	15	l	l	NOUN
gi-4938	185	16	∣∣	∣∣	X
gi-4938	185	17	f2	f2	PROPN
gi-4938	185	18	r	r	NOUN
gi-4938	185	19	+	+	CCONJ
gi-4938	185	20	f2	f2	PROPN
gi-4938	185	21	l	l	NOUN
gi-4938	185	22	,	,	PUNCT
gi-4938	185	23	(	(	PUNCT
gi-4938	185	24	4.1	4.1	NUM
gi-4938	185	25	)	)	PUNCT
gi-4938	186	1	where	where	SCONJ
gi-4938	186	2	fr	fr	AUX
gi-4938	186	3	=	=	PUNCT
gi-4938	186	4	3fi−	3fi−	NUM
gi-4938	186	5	4fi+1	4fi+1	NUM
gi-4938	187	1	+	+	CCONJ
gi-4938	187	2	fi+2	fi+2	NUM
gi-4938	187	3	,	,	PUNCT
gi-4938	187	4	fl	fl	NOUN
gi-4938	187	5	=	=	SYM
gi-4938	187	6	3fi−	3fi−	NUM
gi-4938	187	7	4fi−1	4fi−1	PROPN
gi-4938	187	8	+	+	CCONJ
gi-4938	187	9	fi−2	fi−2	NOUN
gi-4938	187	10	.	.	PUNCT
gi-4938	188	1	if	if	SCONJ
gi-4938	188	2	lr	lr	X
gi-4938	188	3	>	>	X
gi-4938	188	4	0.8	0.8	NUM
gi-4938	188	5	,	,	PUNCT
gi-4938	188	6	f	f	PROPN
gi-4938	188	7	is	be	AUX
gi-4938	188	8	probably	probably	ADV
gi-4938	188	9	not	not	PART
gi-4938	188	10	smooth	smooth	ADJ
gi-4938	188	11	at	at	ADP
gi-4938	188	12	xi	xi	PROPN
gi-4938	188	13	.	.	PUNCT
gi-4938	189	1	for	for	ADP
gi-4938	189	2	practical	practical	ADJ
gi-4938	189	3	computations	computation	NOUN
gi-4938	189	4	,	,	PUNCT
gi-4938	189	5	the	the	DET
gi-4938	189	6	criteria	criterion	NOUN
gi-4938	189	7	provide	provide	VERB
gi-4938	189	8	similar	similar	ADJ
gi-4938	189	9	results	result	NOUN
gi-4938	189	10	.	.	PUNCT
gi-4938	190	1	however	however	ADV
gi-4938	190	2	,	,	PUNCT
gi-4938	190	3	the	the	DET
gi-4938	190	4	weno	weno	NOUN
gi-4938	190	5	criterion	criterion	NOUN
gi-4938	190	6	seems	seem	VERB
gi-4938	190	7	to	to	PART
gi-4938	190	8	be	be	AUX
gi-4938	190	9	more	more	ADV
gi-4938	190	10	sensitive	sensitive	ADJ
gi-4938	190	11	,	,	PUNCT
gi-4938	190	12	and	and	CCONJ
gi-4938	190	13	a	a	DET
gi-4938	190	14	steep	steep	ADJ
gi-4938	190	15	slope	slope	NOUN
gi-4938	190	16	classifies	classify	VERB
gi-4938	190	17	as	as	ADP
gi-4938	190	18	the	the	DET
gi-4938	190	19	jump	jump	NOUN
gi-4938	190	20	discontinuity	discontinuity	NOUN
gi-4938	190	21	.	.	PUNCT
gi-4938	191	1	this	this	DET
gi-4938	191	2	issue	issue	NOUN
gi-4938	191	3	is	be	AUX
gi-4938	191	4	widely	widely	ADV
gi-4938	191	5	discussed	discuss	VERB
gi-4938	191	6	in	in	ADP
gi-4938	191	7	[	[	X
gi-4938	191	8	30	30	NUM
gi-4938	191	9	]	]	PUNCT
gi-4938	191	10	.	.	PUNCT
gi-4938	192	1	geoinformatics	geoinformatic	NOUN
gi-4938	192	2	fce	fce	VERB
gi-4938	192	3	ctu	ctu	NOUN
gi-4938	192	4	17(2	17(2	NUM
gi-4938	192	5	)	)	PUNCT
gi-4938	192	6	,	,	PUNCT
gi-4938	192	7	2018	2018	NUM
gi-4938	192	8	15	15	NUM
gi-4938	192	9	t.	t.	NOUN
gi-4938	192	10	bayer	bayer	NOUN
gi-4938	192	11	:	:	PUNCT
gi-4938	192	12	efficient	efficient	ADJ
gi-4938	192	13	plotting	plot	VERB
gi-4938	192	14	the	the	DET
gi-4938	192	15	functions	function	NOUN
gi-4938	192	16	with	with	ADP
gi-4938	192	17	discontinuities	discontinuity	NOUN
gi-4938	192	18	table	table	NOUN
gi-4938	192	19	1	1	NUM
gi-4938	192	20	:	:	PUNCT
gi-4938	192	21	the	the	DET
gi-4938	192	22	depth	depth	NOUN
gi-4938	192	23	of	of	ADP
gi-4938	192	24	recursion	recursion	NOUN
gi-4938	192	25	for	for	ADP
gi-4938	192	26	different	different	ADJ
gi-4938	192	27	values	value	NOUN
gi-4938	192	28	of	of	ADP
gi-4938	192	29	the	the	DET
gi-4938	192	30	refinement	refinement	NOUN
gi-4938	192	31	criteria	criterion	NOUN
gi-4938	192	32	α	α	PROPN
gi-4938	192	33	in	in	ADP
gi-4938	192	34	the	the	DET
gi-4938	192	35	methods	method	NOUN
gi-4938	192	36	m1	m1	PROPN
gi-4938	192	37	and	and	CCONJ
gi-4938	192	38	m3	m3	PROPN
gi-4938	192	39	(	(	PUNCT
gi-4938	192	40	proposed	propose	VERB
gi-4938	192	41	)	)	PUNCT
gi-4938	192	42	.	.	PUNCT
gi-4938	193	1	method	method	NOUN
gi-4938	193	2	refinement	refinement	NOUN
gi-4938	193	3	criterion	criterion	NOUN
gi-4938	193	4	α	α	PRON
gi-4938	193	5	[	[	X
gi-4938	193	6	◦	◦	NOUN
gi-4938	193	7	]	]	X
gi-4938	193	8	20	20	NUM
gi-4938	193	9	15	15	NUM
gi-4938	193	10	10	10	NUM
gi-4938	193	11	5	5	NUM
gi-4938	193	12	2	2	NUM
gi-4938	193	13	1	1	NUM
gi-4938	193	14	0.5	0.5	NUM
gi-4938	193	15	0.2	0.2	NUM
gi-4938	193	16	0.1	0.1	NUM
gi-4938	193	17	m1	m1	NOUN
gi-4938	193	18	7	7	NUM
gi-4938	193	19	9	9	NUM
gi-4938	193	20	9	9	NUM
gi-4938	193	21	19	19	NUM
gi-4938	193	22	55	55	NUM
gi-4938	193	23	105	105	NUM
gi-4938	193	24	217	217	NUM
gi-4938	193	25	535	535	NUM
gi-4938	193	26	1071	1071	NUM
gi-4938	193	27	m3	m3	PROPN
gi-4938	193	28	3	3	NUM
gi-4938	193	29	3	3	NUM
gi-4938	193	30	3	3	NUM
gi-4938	193	31	7	7	NUM
gi-4938	193	32	15	15	NUM
gi-4938	193	33	27	27	NUM
gi-4938	193	34	57	57	NUM
gi-4938	193	35	121	121	NUM
gi-4938	193	36	297	297	NUM
gi-4938	193	37	5	5	NUM
gi-4938	193	38	.	.	PUNCT
gi-4938	193	39	combined	combine	VERB
gi-4938	193	40	sampling	sample	VERB
gi-4938	193	41	with	with	ADP
gi-4938	193	42	the	the	DET
gi-4938	193	43	singularities	singularity	NOUN
gi-4938	193	44	the	the	DET
gi-4938	193	45	proposed	propose	VERB
gi-4938	193	46	method	method	NOUN
gi-4938	193	47	checks	check	NOUN
gi-4938	193	48	for	for	ADP
gi-4938	193	49	a	a	DET
gi-4938	193	50	discontinuity	discontinuity	NOUN
gi-4938	193	51	at	at	ADP
gi-4938	193	52	each	each	DET
gi-4938	193	53	sampled	sample	VERB
gi-4938	193	54	point	point	NOUN
gi-4938	193	55	xi	xi	ADP
gi-4938	193	56	∈	∈	PROPN
gi-4938	193	57	ω	ω	NOUN
gi-4938	193	58	using	use	VERB
gi-4938	193	59	the	the	DET
gi-4938	193	60	rules	rule	NOUN
gi-4938	193	61	mentioned	mention	VERB
gi-4938	193	62	above	above	ADP
gi-4938	193	63	,	,	PUNCT
gi-4938	193	64	where	where	SCONJ
gi-4938	193	65	the	the	DET
gi-4938	193	66	amount	amount	NOUN
gi-4938	193	67	of	of	ADP
gi-4938	193	68	discontinuities	discontinuity	NOUN
gi-4938	193	69	denoted	denote	VERB
gi-4938	193	70	as	as	SCONJ
gi-4938	193	71	k	k	PROPN
gi-4938	193	72	is	be	AUX
gi-4938	193	73	not	not	PART
gi-4938	193	74	a	a	DET
gi-4938	193	75	priori	priori	ADV
gi-4938	193	76	known	know	VERB
gi-4938	193	77	.	.	PUNCT
gi-4938	194	1	it	it	PRON
gi-4938	194	2	does	do	AUX
gi-4938	194	3	not	not	PART
gi-4938	194	4	represent	represent	VERB
gi-4938	194	5	a	a	DET
gi-4938	194	6	rigid	rigid	ADJ
gi-4938	194	7	mathematical	mathematical	ADJ
gi-4938	194	8	solution	solution	NOUN
gi-4938	194	9	describing	describe	VERB
gi-4938	194	10	the	the	DET
gi-4938	194	11	behavior	behavior	NOUN
gi-4938	194	12	of	of	ADP
gi-4938	194	13	the	the	DET
gi-4938	194	14	analyzed	analyze	VERB
gi-4938	194	15	function	function	NOUN
gi-4938	194	16	,	,	PUNCT
gi-4938	194	17	but	but	CCONJ
gi-4938	194	18	only	only	ADV
gi-4938	194	19	a	a	DET
gi-4938	194	20	simple	simple	ADJ
gi-4938	194	21	method	method	NOUN
gi-4938	194	22	applicable	applicable	ADJ
gi-4938	194	23	to	to	ADP
gi-4938	194	24	the	the	DET
gi-4938	194	25	technical	technical	ADJ
gi-4938	194	26	computing	computing	NOUN
gi-4938	194	27	.	.	PUNCT
gi-4938	195	1	our	our	PRON
gi-4938	195	2	approach	approach	NOUN
gi-4938	195	3	follows	follow	VERB
gi-4938	195	4	a	a	DET
gi-4938	195	5	heuristic	heuristic	ADJ
gi-4938	195	6	sufficient	sufficient	ADJ
gi-4938	195	7	for	for	ADP
gi-4938	195	8	most	most	ADJ
gi-4938	195	9	functions	function	NOUN
gi-4938	195	10	,	,	PUNCT
gi-4938	195	11	especially	especially	ADV
gi-4938	195	12	for	for	ADP
gi-4938	195	13	the	the	DET
gi-4938	195	14	meridian	meridian	ADJ
gi-4938	195	15	or	or	CCONJ
gi-4938	195	16	parallel	parallel	ADJ
gi-4938	195	17	coordinate	coordinate	NOUN
gi-4938	195	18	functions	function	NOUN
gi-4938	195	19	.	.	PUNCT
gi-4938	196	1	as	as	ADP
gi-4938	196	2	a	a	DET
gi-4938	196	3	result	result	NOUN
gi-4938	196	4	,	,	PUNCT
gi-4938	196	5	the	the	DET
gi-4938	196	6	set	set	NOUN
gi-4938	196	7	of	of	ADP
gi-4938	196	8	disjoint	disjoint	NOUN
gi-4938	196	9	subsets	subset	NOUN
gi-4938	196	10	ωg	ωg	NOUN
gi-4938	196	11	,	,	PUNCT
gi-4938	196	12	ωg	ωg	ADP
gi-4938	196	13	⊆	⊆	NUM
gi-4938	196	14	ω	ω	NUM
gi-4938	196	15	,	,	PUNCT
gi-4938	196	16	containing	contain	VERB
gi-4938	196	17	“	"	PUNCT
gi-4938	196	18	good	good	ADJ
gi-4938	196	19	”	"	PUNCT
gi-4938	196	20	data	datum	NOUN
gi-4938	196	21	that	that	PRON
gi-4938	196	22	allows	allow	VERB
gi-4938	196	23	for	for	ADP
gi-4938	196	24	adaptive	adaptive	ADJ
gi-4938	196	25	sampling	sampling	NOUN
gi-4938	196	26	is	be	AUX
gi-4938	196	27	constructed	construct	VERB
gi-4938	196	28	;	;	PUNCT
gi-4938	196	29	this	this	DET
gi-4938	196	30	technique	technique	NOUN
gi-4938	196	31	was	be	AUX
gi-4938	196	32	used	use	VERB
gi-4938	196	33	in	in	ADP
gi-4938	196	34	[	[	X
gi-4938	196	35	26	26	NUM
gi-4938	196	36	]	]	PUNCT
gi-4938	196	37	.	.	PUNCT
gi-4938	197	1	the	the	DET
gi-4938	197	2	point	point	NOUN
gi-4938	197	3	xi	xi	INTJ
gi-4938	197	4	is	be	AUX
gi-4938	197	5	classified	classify	VERB
gi-4938	197	6	as	as	ADP
gi-4938	197	7	“	"	PUNCT
gi-4938	197	8	good	good	ADJ
gi-4938	197	9	”	"	PUNCT
gi-4938	197	10	if	if	SCONJ
gi-4938	197	11	no	no	DET
gi-4938	197	12	singularity	singularity	NOUN
gi-4938	197	13	at	at	ADP
gi-4938	197	14	f(xi	f(xi	NOUN
gi-4938	197	15	)	)	PUNCT
gi-4938	197	16	occurs	occur	VERB
gi-4938	197	17	.	.	PUNCT
gi-4938	198	1	an	an	DET
gi-4938	198	2	interval	interval	NOUN
gi-4938	198	3	ω	ω	NOUN
gi-4938	198	4	containing	contain	VERB
gi-4938	198	5	only	only	ADV
gi-4938	198	6	“	"	PUNCT
gi-4938	198	7	good	good	ADJ
gi-4938	198	8	”	"	PUNCT
gi-4938	198	9	points	point	NOUN
gi-4938	198	10	is	be	AUX
gi-4938	198	11	classified	classify	VERB
gi-4938	198	12	as	as	ADP
gi-4938	198	13	“	"	PUNCT
gi-4938	198	14	good	good	ADJ
gi-4938	198	15	”	"	PUNCT
gi-4938	198	16	and	and	CCONJ
gi-4938	198	17	labeled	label	VERB
gi-4938	198	18	as	as	ADP
gi-4938	198	19	ωg	ωg	NOUN
gi-4938	198	20	.	.	PUNCT
gi-4938	199	1	unfortunately	unfortunately	ADV
gi-4938	199	2	,	,	PUNCT
gi-4938	199	3	the	the	DET
gi-4938	199	4	procedure	procedure	NOUN
gi-4938	199	5	can	can	AUX
gi-4938	199	6	not	not	PART
gi-4938	199	7	be	be	AUX
gi-4938	199	8	generalized	generalize	VERB
gi-4938	199	9	for	for	ADP
gi-4938	199	10	higher	high	ADJ
gi-4938	199	11	-	-	PUNCT
gi-4938	199	12	dimensional	dimensional	ADJ
gi-4938	199	13	problems	problem	NOUN
gi-4938	199	14	.	.	PUNCT
gi-4938	200	1	suppose	suppose	VERB
gi-4938	200	2	the	the	DET
gi-4938	200	3	j	j	PROPN
gi-4938	200	4	−	−	X
gi-4938	200	5	th	th	X
gi-4938	200	6	interval	interval	NOUN
gi-4938	200	7	ωj	ωj	ADP
gi-4938	200	8	=	=	SYM
gi-4938	201	1	[	[	X
gi-4938	201	2	aj	aj	PROPN
gi-4938	201	3	,	,	PUNCT
gi-4938	201	4	bj	bj	VERB
gi-4938	201	5	]	]	PUNCT
gi-4938	201	6	containing	contain	VERB
gi-4938	201	7	a	a	DET
gi-4938	201	8	singularity	singularity	NOUN
gi-4938	201	9	c	c	NOUN
gi-4938	201	10	,	,	PUNCT
gi-4938	201	11	c	c	PROPN
gi-4938	201	12	∈	∈	PROPN
gi-4938	201	13	ωj	ωj	ADP
gi-4938	201	14	,	,	PUNCT
gi-4938	201	15	and	and	CCONJ
gi-4938	201	16	ε	ε	PROPN
gi-4938	201	17	,	,	PUNCT
gi-4938	201	18	ε	ε	PROPN
gi-4938	201	19	>	>	X
gi-4938	201	20	0	0	PROPN
gi-4938	201	21	,	,	PUNCT
gi-4938	201	22	representing	represent	VERB
gi-4938	201	23	the	the	DET
gi-4938	201	24	numerical	numerical	ADJ
gi-4938	201	25	threshold	threshold	NOUN
gi-4938	201	26	.	.	PUNCT
gi-4938	202	1	in	in	ADP
gi-4938	202	2	general	general	ADJ
gi-4938	202	3	,	,	PUNCT
gi-4938	202	4	several	several	ADJ
gi-4938	202	5	cases	case	NOUN
gi-4938	202	6	need	need	VERB
gi-4938	202	7	to	to	PART
gi-4938	202	8	be	be	AUX
gi-4938	202	9	distinguished	distinguish	VERB
gi-4938	202	10	:	:	PUNCT
gi-4938	202	11	•	•	NUM
gi-4938	202	12	case	case	NOUN
gi-4938	202	13	1	1	NUM
gi-4938	202	14	:	:	PUNCT
gi-4938	202	15	the	the	DET
gi-4938	202	16	coincidence	coincidence	NOUN
gi-4938	202	17	with	with	ADP
gi-4938	202	18	the	the	DET
gi-4938	202	19	lower	lower	ADV
gi-4938	202	20	bound	bind	VERB
gi-4938	202	21	if	if	SCONJ
gi-4938	202	22	aj	aj	PROPN
gi-4938	202	23	≡	≡	PROPN
gi-4938	202	24	c	c	PROPN
gi-4938	202	25	,	,	PUNCT
gi-4938	202	26	the	the	DET
gi-4938	202	27	discontinuity	discontinuity	NOUN
gi-4938	202	28	c	c	NOUN
gi-4938	202	29	coincides	coincide	VERB
gi-4938	202	30	with	with	ADP
gi-4938	202	31	the	the	DET
gi-4938	202	32	lower	low	ADJ
gi-4938	202	33	bound	bind	VERB
gi-4938	202	34	of	of	ADP
gi-4938	202	35	the	the	DET
gi-4938	202	36	interval	interval	NOUN
gi-4938	202	37	ωj	ωj	ADP
gi-4938	202	38	.	.	PUNCT
gi-4938	203	1	•	•	NUM
gi-4938	203	2	case	case	NOUN
gi-4938	203	3	2	2	NUM
gi-4938	203	4	:	:	PUNCT
gi-4938	203	5	the	the	DET
gi-4938	203	6	proximity	proximity	NOUN
gi-4938	203	7	to	to	ADP
gi-4938	203	8	the	the	DET
gi-4938	203	9	lower	lower	ADV
gi-4938	203	10	bound	bind	VERB
gi-4938	203	11	if	if	SCONJ
gi-4938	203	12	aj	aj	PROPN
gi-4938	203	13	<	<	X
gi-4938	203	14	c	c	PROPN
gi-4938	203	15	∧	∧	PROPN
gi-4938	203	16	|c−	|c−	NOUN
gi-4938	203	17	aj	aj	PROPN
gi-4938	203	18	|	|	ADV
gi-4938	203	19	<	<	X
gi-4938	203	20	ε	ε	PROPN
gi-4938	203	21	,	,	PUNCT
gi-4938	203	22	the	the	DET
gi-4938	203	23	discontinuity	discontinuity	NOUN
gi-4938	203	24	c	c	NOUN
gi-4938	203	25	is	be	AUX
gi-4938	203	26	close	close	ADJ
gi-4938	203	27	the	the	DET
gi-4938	203	28	lower	low	ADJ
gi-4938	203	29	bound	bind	VERB
gi-4938	203	30	of	of	ADP
gi-4938	203	31	the	the	DET
gi-4938	203	32	interval	interval	NOUN
gi-4938	203	33	ωj	ωj	ADP
gi-4938	203	34	.	.	PUNCT
gi-4938	204	1	•	•	NUM
gi-4938	204	2	case	case	NOUN
gi-4938	204	3	3	3	NUM
gi-4938	204	4	:	:	PUNCT
gi-4938	204	5	the	the	DET
gi-4938	204	6	coincidence	coincidence	NOUN
gi-4938	204	7	with	with	ADP
gi-4938	204	8	the	the	DET
gi-4938	204	9	upper	upper	ADJ
gi-4938	204	10	bound	bind	VERB
gi-4938	204	11	if	if	SCONJ
gi-4938	204	12	bj	bj	VERB
gi-4938	204	13	≡	≡	PROPN
gi-4938	204	14	c	c	PROPN
gi-4938	204	15	,	,	PUNCT
gi-4938	204	16	the	the	DET
gi-4938	204	17	discontinuity	discontinuity	NOUN
gi-4938	204	18	c	c	NOUN
gi-4938	204	19	coincides	coincide	VERB
gi-4938	204	20	with	with	ADP
gi-4938	204	21	the	the	DET
gi-4938	204	22	upper	upper	ADJ
gi-4938	204	23	bound	bound	NOUN
gi-4938	204	24	of	of	ADP
gi-4938	204	25	the	the	DET
gi-4938	204	26	interval	interval	NOUN
gi-4938	204	27	ωj	ωj	ADP
gi-4938	204	28	.	.	PUNCT
gi-4938	205	1	•	•	NUM
gi-4938	205	2	case	case	NOUN
gi-4938	205	3	4	4	NUM
gi-4938	205	4	:	:	PUNCT
gi-4938	205	5	the	the	DET
gi-4938	205	6	proximity	proximity	NOUN
gi-4938	205	7	to	to	ADP
gi-4938	205	8	the	the	DET
gi-4938	205	9	upper	upper	ADJ
gi-4938	205	10	bound	bind	VERB
gi-4938	205	11	if	if	SCONJ
gi-4938	205	12	bj	bj	VERB
gi-4938	205	13	>	>	X
gi-4938	205	14	c	c	X
gi-4938	206	1	∧	∧	NOUN
gi-4938	206	2	|c−	|c−	NOUN
gi-4938	206	3	bj	bj	VERB
gi-4938	206	4	|	|	ADV
gi-4938	206	5	<	<	X
gi-4938	206	6	ε	ε	PROPN
gi-4938	206	7	,	,	PUNCT
gi-4938	206	8	the	the	DET
gi-4938	206	9	discontinuity	discontinuity	NOUN
gi-4938	206	10	c	c	NOUN
gi-4938	206	11	is	be	AUX
gi-4938	206	12	close	close	VERB
gi-4938	206	13	the	the	DET
gi-4938	206	14	upper	upper	ADJ
gi-4938	206	15	bound	bind	VERB
gi-4938	206	16	of	of	ADP
gi-4938	206	17	the	the	DET
gi-4938	206	18	interval	interval	NOUN
gi-4938	206	19	ωj	ωj	ADP
gi-4938	206	20	.	.	PUNCT
gi-4938	207	1	•	•	NUM
gi-4938	207	2	case	case	NOUN
gi-4938	207	3	5	5	NUM
gi-4938	207	4	:	:	PUNCT
gi-4938	207	5	the	the	DET
gi-4938	207	6	interior	interior	ADJ
gi-4938	207	7	singularity	singularity	NOUN
gi-4938	207	8	if	if	SCONJ
gi-4938	207	9	aj	aj	PROPN
gi-4938	207	10	<	<	X
gi-4938	207	11	c	c	X
gi-4938	207	12	<	<	X
gi-4938	207	13	bj	bj	NOUN
gi-4938	207	14	,	,	PUNCT
gi-4938	207	15	where	where	SCONJ
gi-4938	207	16	|c−	|c−	NOUN
gi-4938	207	17	aj	aj	PROPN
gi-4938	207	18	|	|	ADV
gi-4938	207	19	>	>	X
gi-4938	207	20	ε∧|c−	ε∧|c−	NOUN
gi-4938	207	21	bj	bj	ADP
gi-4938	207	22	|	|	ADV
gi-4938	207	23	>	>	X
gi-4938	207	24	ε	ε	PROPN
gi-4938	207	25	,	,	PUNCT
gi-4938	207	26	the	the	DET
gi-4938	207	27	discontinuity	discontinuity	NOUN
gi-4938	207	28	c	c	NOUN
gi-4938	207	29	lies	lie	VERB
gi-4938	207	30	inside	inside	ADP
gi-4938	207	31	the	the	DET
gi-4938	207	32	interval	interval	NOUN
gi-4938	207	33	ωj	ωj	ADP
gi-4938	207	34	.	.	PUNCT
gi-4938	208	1	for	for	ADP
gi-4938	208	2	practical	practical	ADJ
gi-4938	208	3	computation	computation	NOUN
gi-4938	208	4	in	in	ADP
gi-4938	208	5	the	the	DET
gi-4938	208	6	floating	float	VERB
gi-4938	208	7	-	-	PUNCT
gi-4938	208	8	point	point	NOUN
gi-4938	208	9	arithmetic	arithmetic	ADJ
gi-4938	208	10	,	,	PUNCT
gi-4938	208	11	cases	case	NOUN
gi-4938	208	12	1	1	NUM
gi-4938	208	13	,	,	PUNCT
gi-4938	208	14	2	2	NUM
gi-4938	208	15	and	and	CCONJ
gi-4938	208	16	cases	case	NOUN
gi-4938	208	17	3	3	NUM
gi-4938	208	18	,	,	PUNCT
gi-4938	208	19	4	4	NUM
gi-4938	208	20	may	may	AUX
gi-4938	208	21	be	be	AUX
gi-4938	208	22	joined	join	VERB
gi-4938	208	23	,	,	PUNCT
gi-4938	208	24	and	and	CCONJ
gi-4938	208	25	we	we	PRON
gi-4938	208	26	search	search	VERB
gi-4938	208	27	for	for	ADP
gi-4938	208	28	the	the	DET
gi-4938	208	29	discontinuity	discontinuity	NOUN
gi-4938	208	30	close	close	ADV
gi-4938	208	31	to	to	ADP
gi-4938	208	32	the	the	DET
gi-4938	208	33	lower	low	ADJ
gi-4938	208	34	or	or	CCONJ
gi-4938	208	35	upper	upper	ADJ
gi-4938	208	36	bounds	bound	NOUN
gi-4938	208	37	.	.	PUNCT
gi-4938	209	1	the	the	DET
gi-4938	209	2	modified	modify	VERB
gi-4938	209	3	conditions	condition	NOUN
gi-4938	209	4	are	be	AUX
gi-4938	209	5	:	:	PUNCT
gi-4938	209	6	•	•	NUM
gi-4938	209	7	cases	case	NOUN
gi-4938	209	8	1	1	NUM
gi-4938	209	9	+	+	NOUN
gi-4938	209	10	2	2	NUM
gi-4938	209	11	:	:	PUNCT
gi-4938	209	12	the	the	DET
gi-4938	209	13	proximity	proximity	NOUN
gi-4938	209	14	/	/	SYM
gi-4938	209	15	coincidence	coincidence	NOUN
gi-4938	209	16	to	to	ADP
gi-4938	209	17	the	the	DET
gi-4938	209	18	lower	lower	ADV
gi-4938	209	19	bound	bind	VERB
gi-4938	209	20	if	if	SCONJ
gi-4938	209	21	aj	aj	PROPN
gi-4938	209	22	≤	≤	PROPN
gi-4938	209	23	c	c	VERB
gi-4938	210	1	∧	∧	PROPN
gi-4938	210	2	|c−	|c−	NOUN
gi-4938	210	3	aj	aj	PROPN
gi-4938	210	4	|	|	ADV
gi-4938	210	5	<	<	X
gi-4938	210	6	ε	ε	PROPN
gi-4938	210	7	,	,	PUNCT
gi-4938	210	8	the	the	DET
gi-4938	210	9	discontinuity	discontinuity	NOUN
gi-4938	210	10	c	c	NOUN
gi-4938	210	11	coincides	coincide	VERB
gi-4938	211	1	or	or	CCONJ
gi-4938	211	2	it	it	PRON
gi-4938	211	3	is	be	AUX
gi-4938	211	4	close	close	ADJ
gi-4938	211	5	to	to	ADP
gi-4938	211	6	the	the	DET
gi-4938	211	7	lower	low	ADJ
gi-4938	211	8	bound	bind	VERB
gi-4938	211	9	of	of	ADP
gi-4938	211	10	the	the	DET
gi-4938	211	11	interval	interval	NOUN
gi-4938	211	12	ωj	ωj	ADP
gi-4938	211	13	.	.	PUNCT
gi-4938	212	1	geoinformatics	geoinformatic	NOUN
gi-4938	212	2	fce	fce	VERB
gi-4938	212	3	ctu	ctu	NOUN
gi-4938	212	4	17(2	17(2	NUM
gi-4938	212	5	)	)	PUNCT
gi-4938	212	6	,	,	PUNCT
gi-4938	212	7	2018	2018	NUM
gi-4938	212	8	16	16	NUM
gi-4938	212	9	t.	t.	NOUN
gi-4938	212	10	bayer	bayer	PROPN
gi-4938	212	11	:	:	PUNCT
gi-4938	213	1	efficient	efficient	ADJ
gi-4938	213	2	plotting	plot	VERB
gi-4938	213	3	the	the	DET
gi-4938	213	4	functions	function	NOUN
gi-4938	213	5	with	with	ADP
gi-4938	213	6	discontinuities	discontinuity	NOUN
gi-4938	213	7	•	•	NOUN
gi-4938	213	8	cases	case	NOUN
gi-4938	213	9	3	3	NUM
gi-4938	213	10	+	+	NOUN
gi-4938	213	11	4	4	NUM
gi-4938	213	12	:	:	PUNCT
gi-4938	213	13	the	the	DET
gi-4938	213	14	proximity	proximity	NOUN
gi-4938	213	15	/	/	SYM
gi-4938	213	16	coincidence	coincidence	NOUN
gi-4938	213	17	to	to	ADP
gi-4938	213	18	the	the	DET
gi-4938	213	19	upper	upper	ADJ
gi-4938	213	20	bound	bind	VERB
gi-4938	213	21	if	if	SCONJ
gi-4938	213	22	bj	bj	ADP
gi-4938	213	23	≥	≥	NOUN
gi-4938	213	24	c∧	c∧	VERB
gi-4938	213	25	|c−	|c−	NOUN
gi-4938	213	26	bj	bj	ADP
gi-4938	213	27	|	|	ADV
gi-4938	213	28	<	<	X
gi-4938	213	29	ε	ε	PROPN
gi-4938	213	30	,	,	PUNCT
gi-4938	213	31	the	the	DET
gi-4938	213	32	discontinuity	discontinuity	NOUN
gi-4938	213	33	c	c	NOUN
gi-4938	213	34	coincides	coincide	VERB
gi-4938	214	1	or	or	CCONJ
gi-4938	214	2	it	it	PRON
gi-4938	214	3	is	be	AUX
gi-4938	214	4	close	close	ADJ
gi-4938	214	5	to	to	ADP
gi-4938	214	6	the	the	DET
gi-4938	214	7	upper	upper	ADJ
gi-4938	214	8	bound	bound	NOUN
gi-4938	214	9	of	of	ADP
gi-4938	214	10	the	the	DET
gi-4938	214	11	interval	interval	NOUN
gi-4938	214	12	ωj	ωj	ADP
gi-4938	214	13	.	.	PUNCT
gi-4938	215	1	another	another	DET
gi-4938	215	2	two	two	NUM
gi-4938	215	3	essential	essential	ADJ
gi-4938	215	4	cases	case	NOUN
gi-4938	215	5	need	need	VERB
gi-4938	215	6	to	to	PART
gi-4938	215	7	be	be	AUX
gi-4938	215	8	resolved	resolve	VERB
gi-4938	215	9	:	:	PUNCT
gi-4938	215	10	•	•	NUM
gi-4938	215	11	case	case	NOUN
gi-4938	215	12	6	6	NUM
gi-4938	215	13	:	:	PUNCT
gi-4938	215	14	too	too	ADV
gi-4938	215	15	narrow	narrow	ADJ
gi-4938	215	16	interval	interval	NOUN
gi-4938	215	17	if	if	SCONJ
gi-4938	215	18	bj	bj	VERB
gi-4938	215	19	−	−	PROPN
gi-4938	215	20	aj	aj	PROPN
gi-4938	215	21	<	<	X
gi-4938	215	22	ε	ε	PROPN
gi-4938	215	23	,	,	PUNCT
gi-4938	215	24	an	an	DET
gi-4938	215	25	“	"	PUNCT
gi-4938	215	26	empty	empty	ADJ
gi-4938	215	27	”	"	PUNCT
gi-4938	215	28	interval	interval	NOUN
gi-4938	215	29	ωj	ωj	ADP
gi-4938	215	30	arises	arise	VERB
gi-4938	215	31	.	.	PUNCT
gi-4938	216	1	•	•	NUM
gi-4938	216	2	case	case	NOUN
gi-4938	216	3	7	7	NUM
gi-4938	216	4	:	:	PUNCT
gi-4938	216	5	the	the	DET
gi-4938	216	6	incorrect	incorrect	ADJ
gi-4938	216	7	interval	interval	NOUN
gi-4938	216	8	if	if	SCONJ
gi-4938	216	9	aj	aj	PROPN
gi-4938	216	10	>	>	X
gi-4938	216	11	bj	bj	NOUN
gi-4938	216	12	,	,	PUNCT
gi-4938	216	13	the	the	DET
gi-4938	216	14	incorrect	incorrect	ADJ
gi-4938	216	15	interval	interval	NOUN
gi-4938	216	16	ωj	ωj	ADP
gi-4938	216	17	appears	appear	VERB
gi-4938	216	18	.	.	PUNCT
gi-4938	217	1	in	in	ADP
gi-4938	217	2	general	general	ADJ
gi-4938	217	3	,	,	PUNCT
gi-4938	217	4	they	they	PRON
gi-4938	217	5	occur	occur	VERB
gi-4938	217	6	due	due	ADP
gi-4938	217	7	to	to	ADP
gi-4938	217	8	the	the	DET
gi-4938	217	9	behavior	behavior	NOUN
gi-4938	217	10	of	of	ADP
gi-4938	217	11	the	the	DET
gi-4938	217	12	sampled	sample	VERB
gi-4938	217	13	function	function	NOUN
gi-4938	217	14	as	as	ADV
gi-4938	217	15	well	well	ADV
gi-4938	217	16	as	as	ADP
gi-4938	217	17	a	a	DET
gi-4938	217	18	result	result	NOUN
gi-4938	217	19	of	of	ADP
gi-4938	217	20	the	the	DET
gi-4938	217	21	floating	float	VERB
gi-4938	217	22	-	-	PUNCT
gi-4938	217	23	point	point	NOUN
gi-4938	217	24	arithmetic	arithmetic	NOUN
gi-4938	217	25	.	.	PUNCT
gi-4938	218	1	for	for	ADP
gi-4938	218	2	our	our	PRON
gi-4938	218	3	problem	problem	NOUN
gi-4938	218	4	,	,	PUNCT
gi-4938	218	5	the	the	DET
gi-4938	218	6	empty	empty	ADJ
gi-4938	218	7	interval	interval	NOUN
gi-4938	218	8	is	be	AUX
gi-4938	218	9	“	"	PUNCT
gi-4938	218	10	unpromising	unpromising	ADJ
gi-4938	218	11	”	"	PUNCT
gi-4938	218	12	and	and	CCONJ
gi-4938	218	13	(	(	PUNCT
gi-4938	218	14	probably	probably	ADV
gi-4938	218	15	)	)	PUNCT
gi-4938	218	16	does	do	AUX
gi-4938	218	17	not	not	PART
gi-4938	218	18	contain	contain	VERB
gi-4938	218	19	any	any	DET
gi-4938	218	20	important	important	ADJ
gi-4938	218	21	data1	data1	NOUN
gi-4938	218	22	.	.	PUNCT
gi-4938	219	1	moreover	moreover	ADV
gi-4938	219	2	,	,	PUNCT
gi-4938	219	3	there	there	PRON
gi-4938	219	4	is	be	VERB
gi-4938	219	5	no	no	DET
gi-4938	219	6	chance	chance	NOUN
gi-4938	219	7	of	of	ADP
gi-4938	219	8	the	the	DET
gi-4938	219	9	possible	possible	ADJ
gi-4938	219	10	improvement	improvement	NOUN
gi-4938	219	11	;	;	PUNCT
gi-4938	219	12	the	the	DET
gi-4938	219	13	interval	interval	NOUN
gi-4938	219	14	can	can	AUX
gi-4938	219	15	not	not	PART
gi-4938	219	16	be	be	AUX
gi-4938	219	17	expanded	expand	VERB
gi-4938	219	18	.	.	PUNCT
gi-4938	220	1	in	in	ADP
gi-4938	220	2	most	most	ADJ
gi-4938	220	3	cases	case	NOUN
gi-4938	220	4	,	,	PUNCT
gi-4938	220	5	the	the	DET
gi-4938	220	6	“	"	PUNCT
gi-4938	220	7	incorrect	incorrect	ADJ
gi-4938	220	8	”	"	PUNCT
gi-4938	220	9	intervals	interval	NOUN
gi-4938	220	10	are	be	AUX
gi-4938	220	11	also	also	ADV
gi-4938	220	12	empty	empty	ADJ
gi-4938	220	13	,	,	PUNCT
gi-4938	220	14	or	or	CCONJ
gi-4938	220	15	they	they	PRON
gi-4938	220	16	become	become	VERB
gi-4938	220	17	empty	empty	ADJ
gi-4938	220	18	during	during	ADP
gi-4938	220	19	the	the	DET
gi-4938	220	20	next	next	ADJ
gi-4938	220	21	processing	processing	NOUN
gi-4938	220	22	.	.	PUNCT
gi-4938	221	1	in	in	ADP
gi-4938	221	2	general	general	ADJ
gi-4938	221	3	,	,	PUNCT
gi-4938	221	4	these	these	DET
gi-4938	221	5	intervals	interval	NOUN
gi-4938	221	6	may	may	AUX
gi-4938	221	7	be	be	AUX
gi-4938	221	8	rejected	reject	VERB
gi-4938	221	9	from	from	ADP
gi-4938	221	10	further	further	ADJ
gi-4938	221	11	processing	processing	NOUN
gi-4938	221	12	;	;	PUNCT
gi-4938	221	13	cases	case	NOUN
gi-4938	221	14	6	6	NUM
gi-4938	221	15	,	,	PUNCT
gi-4938	221	16	7	7	NUM
gi-4938	221	17	can	can	AUX
gi-4938	221	18	be	be	AUX
gi-4938	221	19	solved	solve	VERB
gi-4938	221	20	simultaneously	simultaneously	ADV
gi-4938	221	21	.	.	PUNCT
gi-4938	222	1	depending	depend	VERB
gi-4938	222	2	on	on	ADP
gi-4938	222	3	the	the	DET
gi-4938	222	4	position	position	NOUN
gi-4938	222	5	of	of	ADP
gi-4938	222	6	the	the	DET
gi-4938	222	7	singularity	singularity	NOUN
gi-4938	222	8	c	c	NOUN
gi-4938	222	9	,	,	PUNCT
gi-4938	222	10	three	three	NUM
gi-4938	222	11	types	type	NOUN
gi-4938	222	12	of	of	ADP
gi-4938	222	13	operations	operation	NOUN
gi-4938	222	14	are	be	AUX
gi-4938	222	15	performed	perform	VERB
gi-4938	222	16	:	:	PUNCT
gi-4938	222	17	•	•	NUM
gi-4938	222	18	delete	delete	ADJ
gi-4938	222	19	empty	empty	ADJ
gi-4938	222	20	/	/	SYM
gi-4938	222	21	incorrect	incorrect	ADJ
gi-4938	222	22	ωj	ωj	ADP
gi-4938	222	23	the	the	DET
gi-4938	222	24	empty	empty	ADJ
gi-4938	222	25	or	or	CCONJ
gi-4938	222	26	incorrect	incorrect	ADJ
gi-4938	222	27	interval	interval	NOUN
gi-4938	222	28	ωj	ωj	ADP
gi-4938	222	29	is	be	AUX
gi-4938	222	30	deleted	delete	VERB
gi-4938	222	31	.	.	PUNCT
gi-4938	223	1	•	•	NOUN
gi-4938	223	2	shrinking	shrink	VERB
gi-4938	223	3	ωj	ωj	ADP
gi-4938	223	4	the	the	DET
gi-4938	223	5	interval	interval	NOUN
gi-4938	223	6	ωj	ωj	ADP
gi-4938	223	7	with	with	ADP
gi-4938	223	8	the	the	DET
gi-4938	223	9	discontinuity	discontinuity	NOUN
gi-4938	223	10	c	c	X
gi-4938	223	11	close	close	ADJ
gi-4938	223	12	to	to	ADP
gi-4938	223	13	the	the	DET
gi-4938	223	14	bounds	bound	NOUN
gi-4938	223	15	is	be	AUX
gi-4938	223	16	shrunk	shrink	VERB
gi-4938	223	17	from	from	ADP
gi-4938	223	18	the	the	DET
gi-4938	223	19	left	left	ADJ
gi-4938	223	20	/	/	SYM
gi-4938	223	21	right	right	NOUN
gi-4938	223	22	.	.	PUNCT
gi-4938	224	1	for	for	ADP
gi-4938	224	2	cases	case	NOUN
gi-4938	224	3	1	1	NUM
gi-4938	224	4	+	+	SYM
gi-4938	224	5	2	2	NUM
gi-4938	224	6	,	,	PUNCT
gi-4938	224	7	aj	aj	PROPN
gi-4938	224	8	=	=	PROPN
gi-4938	224	9	aj	aj	PROPN
gi-4938	224	10	+	+	SYM
gi-4938	224	11	ε	ε	PROPN
gi-4938	224	12	,	,	PUNCT
gi-4938	224	13	for	for	ADP
gi-4938	224	14	cases	case	NOUN
gi-4938	224	15	3	3	NUM
gi-4938	224	16	+	+	SYM
gi-4938	224	17	4	4	NUM
gi-4938	224	18	,	,	PUNCT
gi-4938	224	19	bj	bj	ADP
gi-4938	224	20	=	=	NOUN
gi-4938	224	21	bj	bj	NOUN
gi-4938	224	22	−	−	PROPN
gi-4938	224	23	ε	ε	PROPN
gi-4938	224	24	.	.	NOUN
gi-4938	224	25	•	•	NOUN
gi-4938	224	26	splitting	splitting	NOUN
gi-4938	224	27	ωj	ωj	ADP
gi-4938	224	28	the	the	DET
gi-4938	224	29	interval	interval	NOUN
gi-4938	224	30	ωj	ωj	ADP
gi-4938	224	31	with	with	ADP
gi-4938	224	32	the	the	DET
gi-4938	224	33	internal	internal	ADJ
gi-4938	224	34	discontinuity	discontinuity	NOUN
gi-4938	224	35	c	c	NOUN
gi-4938	224	36	is	be	AUX
gi-4938	224	37	split	split	VERB
gi-4938	224	38	so	so	SCONJ
gi-4938	224	39	that	that	SCONJ
gi-4938	224	40	the	the	DET
gi-4938	224	41	new	new	ADJ
gi-4938	224	42	disjoint	disjoint	NOUN
gi-4938	224	43	intervals	interval	NOUN
gi-4938	224	44	ωj,1	ωj,1	NOUN
gi-4938	224	45	=	=	PUNCT
gi-4938	225	1	[	[	X
gi-4938	225	2	aj	aj	PROPN
gi-4938	225	3	,	,	PUNCT
gi-4938	225	4	c−	c−	PROPN
gi-4938	225	5	ε	ε	PROPN
gi-4938	225	6	]	]	X
gi-4938	225	7	,	,	PUNCT
gi-4938	225	8	and	and	CCONJ
gi-4938	225	9	ωj,2	ωj,2	NOUN
gi-4938	225	10	=	=	SYM
gi-4938	226	1	[	[	X
gi-4938	226	2	c+	c+	NOUN
gi-4938	226	3	ε	ε	NOUN
gi-4938	226	4	,	,	PUNCT
gi-4938	226	5	bj	bj	NOUN
gi-4938	226	6	)	)	PUNCT
gi-4938	226	7	are	be	AUX
gi-4938	226	8	created	create	VERB
gi-4938	226	9	.	.	PUNCT
gi-4938	227	1	it	it	PRON
gi-4938	227	2	is	be	AUX
gi-4938	227	3	obvious	obvious	ADJ
gi-4938	227	4	that	that	SCONJ
gi-4938	227	5	the	the	DET
gi-4938	227	6	case	case	NOUN
gi-4938	227	7	6	6	NUM
gi-4938	227	8	appears	appear	VERB
gi-4938	227	9	as	as	ADP
gi-4938	227	10	the	the	DET
gi-4938	227	11	result	result	NOUN
gi-4938	227	12	of	of	ADP
gi-4938	227	13	the	the	DET
gi-4938	227	14	incorrect	incorrect	ADJ
gi-4938	227	15	split	split	NOUN
gi-4938	227	16	or	or	CCONJ
gi-4938	227	17	shrink	shrink	ADJ
gi-4938	227	18	operations	operation	NOUN
gi-4938	227	19	,	,	PUNCT
gi-4938	227	20	while	while	SCONJ
gi-4938	227	21	the	the	DET
gi-4938	227	22	case	case	NOUN
gi-4938	227	23	7	7	NUM
gi-4938	227	24	is	be	AUX
gi-4938	227	25	the	the	DET
gi-4938	227	26	result	result	NOUN
gi-4938	227	27	of	of	ADP
gi-4938	227	28	the	the	DET
gi-4938	227	29	incorrect	incorrect	ADJ
gi-4938	227	30	shrink	shrink	NOUN
gi-4938	227	31	operation	operation	NOUN
gi-4938	227	32	.	.	PUNCT
gi-4938	228	1	5.1	5.1	NUM
gi-4938	228	2	.	.	PUNCT
gi-4938	229	1	combined	combine	VERB
gi-4938	229	2	sampling	sample	VERB
gi-4938	229	3	algorithm	algorithm	NOUN
gi-4938	229	4	involving	involve	VERB
gi-4938	229	5	the	the	DET
gi-4938	229	6	singularities	singularity	NOUN
gi-4938	229	7	let	let	VERB
gi-4938	229	8	us	we	PRON
gi-4938	229	9	summarize	summarize	VERB
gi-4938	229	10	the	the	DET
gi-4938	229	11	facts	fact	NOUN
gi-4938	229	12	mentioned	mention	VERB
gi-4938	229	13	above	above	ADV
gi-4938	229	14	into	into	ADP
gi-4938	229	15	the	the	DET
gi-4938	229	16	algorithm	algorithm	NOUN
gi-4938	229	17	.	.	PUNCT
gi-4938	230	1	our	our	PRON
gi-4938	230	2	implementation	implementation	NOUN
gi-4938	230	3	is	be	AUX
gi-4938	230	4	based	base	VERB
gi-4938	230	5	on	on	ADP
gi-4938	230	6	the	the	DET
gi-4938	230	7	stack	stack	NOUN
gi-4938	230	8	s	s	PART
gi-4938	230	9	,	,	PUNCT
gi-4938	230	10	see	see	VERB
gi-4938	230	11	alg	alg	PROPN
gi-4938	230	12	.	.	PROPN
gi-4938	231	1	3	3	NUM
gi-4938	231	2	,	,	PUNCT
gi-4938	231	3	the	the	DET
gi-4938	231	4	amount	amount	NOUN
gi-4938	231	5	of	of	ADP
gi-4938	231	6	ωj	ωj	ADP
gi-4938	231	7	splits	split	NOUN
gi-4938	231	8	denoted	denote	VERB
gi-4938	231	9	s	s	PART
gi-4938	231	10	represents	represent	VERB
gi-4938	231	11	the	the	DET
gi-4938	231	12	recursion	recursion	NOUN
gi-4938	231	13	depth	depth	NOUN
gi-4938	231	14	.	.	PUNCT
gi-4938	232	1	the	the	DET
gi-4938	232	2	basic	basic	ADJ
gi-4938	232	3	idea	idea	NOUN
gi-4938	232	4	is	be	AUX
gi-4938	232	5	to	to	PART
gi-4938	232	6	set	set	VERB
gi-4938	232	7	ωg	ωg	PROPN
gi-4938	232	8	≡	≡	PROPN
gi-4938	232	9	ω	ω	PROPN
gi-4938	232	10	,	,	PUNCT
gi-4938	232	11	to	to	PART
gi-4938	232	12	loop	loop	VERB
gi-4938	232	13	over	over	ADP
gi-4938	232	14	all	all	DET
gi-4938	232	15	the	the	DET
gi-4938	232	16	adaptively	adaptively	ADV
gi-4938	232	17	sampled	sample	VERB
gi-4938	232	18	points	point	NOUN
gi-4938	232	19	pi	pi	NOUN
gi-4938	232	20	,	,	PUNCT
gi-4938	232	21	to	to	PART
gi-4938	232	22	check	check	VERB
gi-4938	232	23	for	for	ADP
gi-4938	232	24	a	a	DET
gi-4938	232	25	singularity	singularity	NOUN
gi-4938	232	26	c	c	NOUN
gi-4938	232	27	in	in	ADP
gi-4938	232	28	the	the	DET
gi-4938	232	29	boundary	boundary	ADJ
gi-4938	232	30	b(xi	b(xi	PROPN
gi-4938	232	31	,	,	PUNCT
gi-4938	232	32	ε	ε	PROPN
gi-4938	232	33	)	)	PUNCT
gi-4938	232	34	of	of	ADP
gi-4938	232	35	pi	pi	NOUN
gi-4938	232	36	and	and	CCONJ
gi-4938	232	37	to	to	PART
gi-4938	232	38	make	make	VERB
gi-4938	232	39	a	a	DET
gi-4938	232	40	decision	decision	NOUN
gi-4938	232	41	about	about	ADP
gi-4938	232	42	the	the	DET
gi-4938	232	43	ωj	ωj	ADP
gi-4938	232	44	boundaries	boundary	NOUN
gi-4938	232	45	.	.	PUNCT
gi-4938	233	1	if	if	SCONJ
gi-4938	233	2	no	no	DET
gi-4938	233	3	singularity	singularity	NOUN
gi-4938	233	4	occurs	occur	VERB
gi-4938	233	5	,	,	PUNCT
gi-4938	233	6	all	all	DET
gi-4938	233	7	points	point	NOUN
gi-4938	233	8	are	be	AUX
gi-4938	233	9	classified	classify	VERB
gi-4938	233	10	as	as	ADP
gi-4938	233	11	good	good	ADJ
gi-4938	233	12	,	,	PUNCT
gi-4938	233	13	and	and	CCONJ
gi-4938	233	14	the	the	DET
gi-4938	233	15	polygonal	polygonal	ADJ
gi-4938	233	16	approximation	approximation	NOUN
gi-4938	233	17	lj	lj	INTJ
gi-4938	233	18	of	of	ADP
gi-4938	233	19	the	the	DET
gi-4938	233	20	curve	curve	NOUN
gi-4938	233	21	is	be	AUX
gi-4938	233	22	constructed	construct	VERB
gi-4938	233	23	.	.	PUNCT
gi-4938	234	1	all	all	DET
gi-4938	234	2	disjoint	disjoint	ADJ
gi-4938	234	3	polygonal	polygonal	ADJ
gi-4938	234	4	approximations	approximation	NOUN
gi-4938	234	5	lj	lj	PRON
gi-4938	234	6	are	be	AUX
gi-4938	234	7	stored	store	VERB
gi-4938	234	8	in	in	ADP
gi-4938	234	9	the	the	DET
gi-4938	234	10	list	list	NOUN
gi-4938	234	11	l.	l.	NOUN
gi-4938	235	1	the	the	DET
gi-4938	235	2	discontinuities	discontinuity	NOUN
gi-4938	235	3	are	be	AUX
gi-4938	235	4	localized	localize	VERB
gi-4938	235	5	successively	successively	ADV
gi-4938	235	6	,	,	PUNCT
gi-4938	235	7	one	one	NUM
gi-4938	235	8	by	by	ADP
gi-4938	235	9	one	one	NUM
gi-4938	235	10	.	.	PUNCT
gi-4938	236	1	the	the	DET
gi-4938	236	2	stack	stack	NOUN
gi-4938	236	3	-	-	PUNCT
gi-4938	236	4	based	base	VERB
gi-4938	236	5	approach	approach	NOUN
gi-4938	236	6	consists	consist	VERB
gi-4938	236	7	of	of	ADP
gi-4938	236	8	two	two	NUM
gi-4938	236	9	phases	phase	NOUN
gi-4938	236	10	(	(	PUNCT
gi-4938	236	11	initial	initial	ADJ
gi-4938	236	12	and	and	CCONJ
gi-4938	236	13	recursive	recursive	ADJ
gi-4938	236	14	):	):	PUNCT
gi-4938	236	15	1however	1however	NUM
gi-4938	236	16	,	,	PUNCT
gi-4938	236	17	for	for	ADP
gi-4938	236	18	some	some	DET
gi-4938	236	19	specific	specific	ADJ
gi-4938	236	20	types	type	NOUN
gi-4938	236	21	of	of	ADP
gi-4938	236	22	non	non	ADJ
gi-4938	236	23	-	-	ADJ
gi-4938	236	24	continuous	continuous	ADJ
gi-4938	236	25	functions	function	NOUN
gi-4938	236	26	this	this	DET
gi-4938	236	27	data	datum	NOUN
gi-4938	236	28	may	may	AUX
gi-4938	236	29	be	be	AUX
gi-4938	236	30	important	important	ADJ
gi-4938	236	31	(	(	PUNCT
gi-4938	236	32	functions	function	NOUN
gi-4938	236	33	with	with	ADP
gi-4938	236	34	isolated	isolated	ADJ
gi-4938	236	35	points	point	NOUN
gi-4938	236	36	)	)	PUNCT
gi-4938	236	37	and	and	CCONJ
gi-4938	236	38	can	can	AUX
gi-4938	236	39	not	not	PART
gi-4938	236	40	be	be	AUX
gi-4938	236	41	skipped	skip	VERB
gi-4938	236	42	.	.	PUNCT
gi-4938	237	1	geoinformatics	geoinformatic	NOUN
gi-4938	237	2	fce	fce	VERB
gi-4938	237	3	ctu	ctu	NOUN
gi-4938	237	4	17(2	17(2	NUM
gi-4938	237	5	)	)	PUNCT
gi-4938	237	6	,	,	PUNCT
gi-4938	237	7	2018	2018	NUM
gi-4938	237	8	17	17	NUM
gi-4938	237	9	t.	t.	NOUN
gi-4938	237	10	bayer	bayer	PROPN
gi-4938	237	11	:	:	PUNCT
gi-4938	237	12	efficient	efficient	ADJ
gi-4938	237	13	plotting	plot	VERB
gi-4938	237	14	the	the	DET
gi-4938	237	15	functions	function	NOUN
gi-4938	237	16	with	with	ADP
gi-4938	237	17	discontinuities	discontinuity	NOUN
gi-4938	237	18	algorithm	algorithm	NOUN
gi-4938	237	19	3	3	NUM
gi-4938	237	20	combined	combine	VERB
gi-4938	237	21	sampling	sample	VERB
gi-4938	237	22	with	with	ADP
gi-4938	237	23	the	the	DET
gi-4938	237	24	singularities	singularity	NOUN
gi-4938	237	25	,	,	PUNCT
gi-4938	237	26	the	the	DET
gi-4938	237	27	stack	stack	NOUN
gi-4938	237	28	implementation	implementation	NOUN
gi-4938	237	29	.	.	PUNCT
gi-4938	238	1	1	1	NUM
gi-4938	238	2	:	:	PUNCT
gi-4938	238	3	function	function	NOUN
gi-4938	238	4	cssingstack(f	cssingstack(f	NOUN
gi-4938	238	5	,	,	PUNCT
gi-4938	238	6	l	l	PROPN
gi-4938	238	7	,	,	PUNCT
gi-4938	238	8	aj	aj	PROPN
gi-4938	238	9	,	,	PUNCT
gi-4938	238	10	bj	bj	VERB
gi-4938	238	11	,	,	PUNCT
gi-4938	238	12	s	s	X
gi-4938	238	13	,	,	PUNCT
gi-4938	238	14	d	d	NOUN
gi-4938	238	15	,	,	PUNCT
gi-4938	238	16	d	d	PROPN
gi-4938	238	17	,	,	PUNCT
gi-4938	238	18	ε	ε	PROPN
gi-4938	238	19	,	,	PUNCT
gi-4938	238	20	α	α	NOUN
gi-4938	238	21	)	)	PUNCT
gi-4938	238	22	2	2	NUM
gi-4938	238	23	:	:	PUNCT
gi-4938	238	24	s	s	NOUN
gi-4938	238	25	=	=	NOUN
gi-4938	238	26	∅	∅	NOUN
gi-4938	238	27	,	,	PUNCT
gi-4938	238	28	s	s	NOUN
gi-4938	238	29	=	=	NOUN
gi-4938	238	30	0	0	NUM
gi-4938	238	31	3	3	NUM
gi-4938	238	32	:	:	PUNCT
gi-4938	238	33	s	s	X
gi-4938	238	34	←	←	PROPN
gi-4938	238	35	ωj	ωj	ADP
gi-4938	238	36	=	=	SYM
gi-4938	239	1	[	[	X
gi-4938	239	2	aj	aj	PROPN
gi-4938	239	3	,	,	PUNCT
gi-4938	239	4	bj	bj	VERB
gi-4938	239	5	]	]	PUNCT
gi-4938	239	6	4	4	NUM
gi-4938	239	7	:	:	PUNCT
gi-4938	239	8	while	while	SCONJ
gi-4938	239	9	s	s	PROPN
gi-4938	239	10	6=	6=	PROPN
gi-4938	239	11	∅	∅	NOUN
gi-4938	239	12	do	do	VERB
gi-4938	239	13	5	5	NUM
gi-4938	239	14	:	:	PUNCT
gi-4938	239	15	ωj	ωj	ADP
gi-4938	239	16	=	=	SYM
gi-4938	239	17	s.pop	s.pop	PROPN
gi-4938	239	18	(	(	PUNCT
gi-4938	239	19	)	)	PUNCT
gi-4938	239	20	6	6	NUM
gi-4938	239	21	:	:	PUNCT
gi-4938	239	22	try	try	VERB
gi-4938	239	23	7	7	NUM
gi-4938	239	24	:	:	PUNCT
gi-4938	239	25	lj	lj	ADJ
gi-4938	239	26	=	=	NOUN
gi-4938	239	27	∅	∅	NOUN
gi-4938	239	28	8	8	NUM
gi-4938	239	29	:	:	PUNCT
gi-4938	239	30	csinit(f	csinit(f	NOUN
gi-4938	239	31	,	,	PUNCT
gi-4938	239	32	lj	lj	PROPN
gi-4938	239	33	,	,	PUNCT
gi-4938	239	34	aj	aj	PROPN
gi-4938	239	35	,	,	PUNCT
gi-4938	239	36	bj	bj	VERB
gi-4938	239	37	,	,	PUNCT
gi-4938	239	38	1	1	NUM
gi-4938	239	39	,	,	PUNCT
gi-4938	239	40	1	1	NUM
gi-4938	239	41	,	,	PUNCT
gi-4938	239	42	d	d	NOUN
gi-4938	239	43	,	,	PUNCT
gi-4938	239	44	d	d	PROPN
gi-4938	239	45	,	,	PUNCT
gi-4938	239	46	ε	ε	PROPN
gi-4938	239	47	,	,	PUNCT
gi-4938	239	48	α	α	NOUN
gi-4938	239	49	)	)	PUNCT
gi-4938	239	50	9	9	NUM
gi-4938	239	51	:	:	PUNCT
gi-4938	239	52	l←	l←	NUM
gi-4938	239	53	lj	lj	ADJ
gi-4938	239	54	10	10	NUM
gi-4938	239	55	:	:	PUNCT
gi-4938	239	56	catch	catch	NOUN
gi-4938	239	57	(	(	PUNCT
gi-4938	239	58	singularityexception	singularityexception	NOUN
gi-4938	239	59	e	e	NOUN
gi-4938	239	60	)	)	PUNCT
gi-4938	239	61	11	11	NUM
gi-4938	239	62	:	:	PUNCT
gi-4938	239	63	c	c	NOUN
gi-4938	239	64	=	=	SYM
gi-4938	239	65	e.x	e.x	PROPN
gi-4938	239	66	12	12	NUM
gi-4938	239	67	:	:	PUNCT
gi-4938	239	68	if	if	SCONJ
gi-4938	239	69	(	(	PUNCT
gi-4938	239	70	s	s	X
gi-4938	239	71	>	>	X
gi-4938	239	72	s	s	PROPN
gi-4938	239	73	)	)	PUNCT
gi-4938	239	74	then	then	ADV
gi-4938	239	75	13	13	NUM
gi-4938	239	76	:	:	PUNCT
gi-4938	239	77	l	l	NOUN
gi-4938	239	78	=	=	PUNCT
gi-4938	239	79	∅	∅	NOUN
gi-4938	239	80	14	14	NUM
gi-4938	239	81	:	:	PUNCT
gi-4938	239	82	return	return	VERB
gi-4938	239	83	15	15	NUM
gi-4938	239	84	:	:	PUNCT
gi-4938	239	85	else	else	ADV
gi-4938	239	86	16	16	NUM
gi-4938	239	87	:	:	PUNCT
gi-4938	240	1	k	k	X
gi-4938	240	2	=	=	SYM
gi-4938	240	3	0	0	NUM
gi-4938	240	4	,	,	PUNCT
gi-4938	240	5	ωj,1	ωj,1	NOUN
gi-4938	240	6	=	=	SYM
gi-4938	240	7	ωj	ωj	ADP
gi-4938	240	8	,	,	PUNCT
gi-4938	240	9	ωj,2	ωj,2	NOUN
gi-4938	240	10	=	=	SYM
gi-4938	240	11	ωj	ωj	ADP
gi-4938	240	12	17	17	NUM
gi-4938	240	13	:	:	PUNCT
gi-4938	240	14	processint(ωj	processint(ωj	ADJ
gi-4938	240	15	,	,	PUNCT
gi-4938	240	16	c	c	NOUN
gi-4938	240	17	,	,	PUNCT
gi-4938	240	18	ωj,1	ωj,1	NOUN
gi-4938	240	19	,	,	PUNCT
gi-4938	240	20	ωj,2	ωj,2	NOUN
gi-4938	240	21	,	,	PUNCT
gi-4938	240	22	k	k	PROPN
gi-4938	240	23	,	,	PUNCT
gi-4938	240	24	s	s	PROPN
gi-4938	240	25	,	,	PUNCT
gi-4938	240	26	ε	ε	PROPN
gi-4938	240	27	)	)	PUNCT
gi-4938	240	28	18	18	NUM
gi-4938	240	29	:	:	PUNCT
gi-4938	240	30	if	if	SCONJ
gi-4938	240	31	(	(	PUNCT
gi-4938	240	32	k	k	X
gi-4938	240	33	>	>	X
gi-4938	240	34	0	0	NUM
gi-4938	240	35	)	)	PUNCT
gi-4938	240	36	then	then	ADV
gi-4938	240	37	19	19	NUM
gi-4938	240	38	:	:	PUNCT
gi-4938	240	39	s	s	X
gi-4938	240	40	←	←	PROPN
gi-4938	240	41	ωj,1	ωj,1	NOUN
gi-4938	240	42	20	20	NUM
gi-4938	240	43	:	:	PUNCT
gi-4938	240	44	else	else	ADV
gi-4938	240	45	if	if	SCONJ
gi-4938	240	46	(	(	PUNCT
gi-4938	240	47	k	k	X
gi-4938	240	48	>	>	X
gi-4938	240	49	1	1	NUM
gi-4938	240	50	)	)	PUNCT
gi-4938	240	51	then	then	ADV
gi-4938	240	52	21	21	NUM
gi-4938	240	53	:	:	PUNCT
gi-4938	240	54	s	s	X
gi-4938	240	55	←	←	PROPN
gi-4938	240	56	ω2,1	ω2,1	PROPN
gi-4938	240	57	1	1	NUM
gi-4938	240	58	.	.	PUNCT
gi-4938	241	1	the	the	DET
gi-4938	241	2	initial	initial	ADJ
gi-4938	241	3	phase	phase	NOUN
gi-4938	241	4	initialize	initialize	VERB
gi-4938	241	5	the	the	DET
gi-4938	241	6	empty	empty	ADJ
gi-4938	241	7	stack	stack	NOUN
gi-4938	241	8	s	s	PART
gi-4938	241	9	=	=	PUNCT
gi-4938	241	10	∅.	∅.	VERB
gi-4938	241	11	create	create	VERB
gi-4938	241	12	ωg	ωg	X
gi-4938	241	13	=	=	PUNCT
gi-4938	242	1	[	[	X
gi-4938	242	2	a	a	X
gi-4938	242	3	,	,	PUNCT
gi-4938	242	4	b	b	NOUN
gi-4938	242	5	]	]	PUNCT
gi-4938	242	6	and	and	CCONJ
gi-4938	242	7	push	push	VERB
gi-4938	242	8	s	s	PART
gi-4938	242	9	←	←	PROPN
gi-4938	242	10	ωg	ωg	PROPN
gi-4938	242	11	.	.	PROPN
gi-4938	242	12	2	2	NUM
gi-4938	242	13	.	.	PUNCT
gi-4938	243	1	the	the	DET
gi-4938	243	2	recursive	recursive	ADJ
gi-4938	243	3	steps	step	NOUN
gi-4938	243	4	repeat	repeat	VERB
gi-4938	243	5	the	the	DET
gi-4938	243	6	following	follow	VERB
gi-4938	243	7	steps	step	NOUN
gi-4938	243	8	until	until	SCONJ
gi-4938	243	9	s	s	NOUN
gi-4938	243	10	is	be	AUX
gi-4938	243	11	empty	empty	ADJ
gi-4938	243	12	:	:	PUNCT
gi-4938	243	13	(	(	PUNCT
gi-4938	243	14	a	a	X
gi-4938	243	15	)	)	PUNCT
gi-4938	243	16	pop	pop	NOUN
gi-4938	243	17	the	the	DET
gi-4938	243	18	actual	actual	ADJ
gi-4938	243	19	good	good	ADJ
gi-4938	243	20	interval	interval	NOUN
gi-4938	243	21	ωg	ωg	PROPN
gi-4938	243	22	j	j	PROPN
gi-4938	243	23	←	←	PROPN
gi-4938	243	24	s	s	PROPN
gi-4938	243	25	from	from	ADP
gi-4938	243	26	s	s	PRON
gi-4938	243	27	and	and	CCONJ
gi-4938	243	28	get	get	VERB
gi-4938	243	29	aj	aj	PROPN
gi-4938	243	30	,	,	PUNCT
gi-4938	243	31	bj	bj	VERB
gi-4938	243	32	.	.	PUNCT
gi-4938	244	1	(	(	PUNCT
gi-4938	244	2	b	b	X
gi-4938	244	3	)	)	PUNCT
gi-4938	244	4	create	create	VERB
gi-4938	244	5	the	the	DET
gi-4938	244	6	empty	empty	ADJ
gi-4938	244	7	list	list	NOUN
gi-4938	244	8	lj	lj	PUNCT
gi-4938	245	1	=	=	PUNCT
gi-4938	245	2	∅.	∅.	X
gi-4938	245	3	(	(	PUNCT
gi-4938	245	4	c	c	NOUN
gi-4938	245	5	)	)	PUNCT
gi-4938	245	6	create	create	VERB
gi-4938	245	7	the	the	DET
gi-4938	245	8	temporary	temporary	ADJ
gi-4938	245	9	polygonal	polygonal	ADJ
gi-4938	245	10	approximation	approximation	NOUN
gi-4938	245	11	of	of	ADP
gi-4938	245	12	f	f	PROPN
gi-4938	245	13	on	on	ADP
gi-4938	245	14	ωj	ωj	ADP
gi-4938	245	15	=	=	SYM
gi-4938	246	1	[	[	X
gi-4938	246	2	aj	aj	PROPN
gi-4938	246	3	,	,	PUNCT
gi-4938	246	4	bj	bj	VERB
gi-4938	246	5	]	]	PUNCT
gi-4938	246	6	using	use	VERB
gi-4938	246	7	combined	combined	ADJ
gi-4938	246	8	sampling	sampling	NOUN
gi-4938	246	9	stored	store	VERB
gi-4938	246	10	in	in	ADP
gi-4938	246	11	lj	lj	PROPN
gi-4938	246	12	.	.	PUNCT
gi-4938	247	1	(	(	PUNCT
gi-4938	247	2	d	d	X
gi-4938	247	3	)	)	PUNCT
gi-4938	247	4	if	if	SCONJ
gi-4938	247	5	no	no	DET
gi-4938	247	6	discontinuity	discontinuity	NOUN
gi-4938	247	7	appears	appear	VERB
gi-4938	247	8	,	,	PUNCT
gi-4938	247	9	add	add	VERB
gi-4938	247	10	lj	lj	ADV
gi-4938	247	11	to	to	ADP
gi-4938	247	12	l	l	NOUN
gi-4938	247	13	:	:	PUNCT
gi-4938	247	14	l	l	NOUN
gi-4938	247	15	←	←	PROPN
gi-4938	247	16	lj	lj	PROPN
gi-4938	247	17	and	and	CCONJ
gi-4938	247	18	go	go	VERB
gi-4938	247	19	to	to	PART
gi-4938	247	20	step	step	VERB
gi-4938	247	21	(	(	PUNCT
gi-4938	247	22	a	a	NOUN
gi-4938	247	23	)	)	PUNCT
gi-4938	247	24	.	.	PUNCT
gi-4938	248	1	otherwise	otherwise	ADV
gi-4938	248	2	,	,	PUNCT
gi-4938	248	3	c	c	PROPN
gi-4938	248	4	represents	represent	VERB
gi-4938	248	5	the	the	DET
gi-4938	248	6	discontinuity	discontinuity	NOUN
gi-4938	248	7	that	that	PRON
gi-4938	248	8	must	must	AUX
gi-4938	248	9	be	be	AUX
gi-4938	248	10	treated	treat	VERB
gi-4938	248	11	in	in	ADP
gi-4938	248	12	steps	step	NOUN
gi-4938	248	13	e	e	NOUN
gi-4938	248	14	-	-	NOUN
gi-4938	248	15	h	h	NOUN
gi-4938	248	16	)	)	PUNCT
gi-4938	248	17	.	.	PUNCT
gi-4938	249	1	(	(	PUNCT
gi-4938	249	2	e	e	X
gi-4938	249	3	)	)	PUNCT
gi-4938	249	4	if	if	SCONJ
gi-4938	249	5	s	s	VERB
gi-4938	249	6	>	>	X
gi-4938	249	7	s	s	PROPN
gi-4938	249	8	,	,	PUNCT
gi-4938	249	9	the	the	DET
gi-4938	249	10	maximum	maximum	ADJ
gi-4938	249	11	allowed	allow	VERB
gi-4938	249	12	recursion	recursion	NOUN
gi-4938	249	13	depth	depth	NOUN
gi-4938	249	14	is	be	AUX
gi-4938	249	15	exceeded	exceed	VERB
gi-4938	249	16	without	without	ADP
gi-4938	249	17	a	a	DET
gi-4938	249	18	reasonable	reasonable	ADJ
gi-4938	249	19	solution	solution	NOUN
gi-4938	249	20	.	.	PUNCT
gi-4938	250	1	clear	clear	ADJ
gi-4938	250	2	the	the	DET
gi-4938	250	3	polygonal	polygonal	ADJ
gi-4938	250	4	approximation	approximation	NOUN
gi-4938	250	5	l.	l.	NOUN
gi-4938	250	6	(	(	PUNCT
gi-4938	250	7	f	f	X
gi-4938	250	8	)	)	PUNCT
gi-4938	250	9	otherwise	otherwise	ADV
gi-4938	250	10	,	,	PUNCT
gi-4938	250	11	initialize	initialize	VERB
gi-4938	250	12	the	the	DET
gi-4938	250	13	newly	newly	ADV
gi-4938	250	14	created	create	VERB
gi-4938	250	15	intervals	interval	NOUN
gi-4938	250	16	ωj,1	ωj,1	NOUN
gi-4938	250	17	=	=	PUNCT
gi-4938	251	1	[	[	X
gi-4938	251	2	aj,1	aj,1	NOUN
gi-4938	251	3	,	,	PUNCT
gi-4938	251	4	bj,1	bj,1	NOUN
gi-4938	251	5	]	]	PUNCT
gi-4938	251	6	,	,	PUNCT
gi-4938	251	7	ωj,2	ωj,2	NOUN
gi-4938	251	8	=	=	PUNCT
gi-4938	252	1	[	[	X
gi-4938	252	2	aj,2	aj,2	NOUN
gi-4938	252	3	,	,	PUNCT
gi-4938	252	4	bj,2	bj,2	PROPN
gi-4938	252	5	]	]	PUNCT
gi-4938	252	6	,	,	PUNCT
gi-4938	252	7	as	as	ADP
gi-4938	252	8	ωj,1	ωj,1	NOUN
gi-4938	252	9	=	=	SYM
gi-4938	252	10	ωj	ωj	ADP
gi-4938	252	11	,	,	PUNCT
gi-4938	252	12	ωj,2	ωj,2	NOUN
gi-4938	252	13	=	=	SYM
gi-4938	252	14	ωj	ωj	NOUN
gi-4938	252	15	,	,	PUNCT
gi-4938	252	16	and	and	CCONJ
gi-4938	252	17	the	the	DET
gi-4938	252	18	amount	amount	NOUN
gi-4938	252	19	of	of	ADP
gi-4938	252	20	created	create	VERB
gi-4938	252	21	intervals	interval	NOUN
gi-4938	252	22	as	as	ADP
gi-4938	252	23	k	k	PROPN
gi-4938	252	24	=	=	PROPN
gi-4938	252	25	0	0	PROPN
gi-4938	252	26	.	.	PUNCT
gi-4938	253	1	(	(	PUNCT
gi-4938	253	2	g	g	NOUN
gi-4938	253	3	)	)	PUNCT
gi-4938	253	4	call	call	VERB
gi-4938	253	5	the	the	DET
gi-4938	253	6	function	function	NOUN
gi-4938	253	7	processint	processint	NOUN
gi-4938	253	8	with	with	ADP
gi-4938	253	9	parameters	parameter	NOUN
gi-4938	253	10	ωj	ωj	ADP
gi-4938	253	11	,	,	PUNCT
gi-4938	253	12	c	c	NOUN
gi-4938	253	13	,	,	PUNCT
gi-4938	253	14	ωj,1	ωj,1	NOUN
gi-4938	253	15	,	,	PUNCT
gi-4938	253	16	ωj,2	ωj,2	NOUN
gi-4938	253	17	,	,	PUNCT
gi-4938	253	18	k	k	PROPN
gi-4938	253	19	,	,	PUNCT
gi-4938	253	20	s	s	PROPN
gi-4938	253	21	,	,	PUNCT
gi-4938	253	22	ε	ε	PROPN
gi-4938	253	23	refining	refine	VERB
gi-4938	253	24	the	the	DET
gi-4938	253	25	interval	interval	NOUN
gi-4938	253	26	ωj	ωj	ADP
gi-4938	253	27	;	;	PUNCT
gi-4938	253	28	see	see	VERB
gi-4938	253	29	alg	alg	PROPN
gi-4938	253	30	.	.	PUNCT
gi-4938	254	1	4	4	NUM
gi-4938	254	2	.	.	X
gi-4938	255	1	the	the	DET
gi-4938	255	2	subintervals	subinterval	NOUN
gi-4938	255	3	ωj,1	ωj,1	NOUN
gi-4938	255	4	,	,	PUNCT
gi-4938	255	5	ωj,2	ωj,2	NOUN
gi-4938	255	6	are	be	AUX
gi-4938	255	7	passing	pass	VERB
gi-4938	255	8	by	by	ADP
gi-4938	255	9	reference	reference	NOUN
gi-4938	255	10	.	.	PUNCT
gi-4938	256	1	geoinformatics	geoinformatic	NOUN
gi-4938	256	2	fce	fce	VERB
gi-4938	256	3	ctu	ctu	NOUN
gi-4938	256	4	17(2	17(2	NUM
gi-4938	256	5	)	)	PUNCT
gi-4938	256	6	,	,	PUNCT
gi-4938	256	7	2018	2018	NUM
gi-4938	256	8	18	18	NUM
gi-4938	256	9	t.	t.	NOUN
gi-4938	256	10	bayer	bayer	NOUN
gi-4938	256	11	:	:	PUNCT
gi-4938	256	12	efficient	efficient	ADJ
gi-4938	256	13	plotting	plot	VERB
gi-4938	256	14	the	the	DET
gi-4938	256	15	functions	function	NOUN
gi-4938	256	16	with	with	ADP
gi-4938	256	17	discontinuities	discontinuity	NOUN
gi-4938	256	18	(	(	PUNCT
gi-4938	256	19	h	h	NOUN
gi-4938	256	20	)	)	PUNCT
gi-4938	256	21	if	if	SCONJ
gi-4938	256	22	at	at	ADV
gi-4938	256	23	least	least	ADV
gi-4938	256	24	one	one	NUM
gi-4938	256	25	new	new	ADJ
gi-4938	256	26	interval	interval	NOUN
gi-4938	256	27	needs	need	VERB
gi-4938	256	28	to	to	PART
gi-4938	256	29	be	be	AUX
gi-4938	256	30	created	create	VERB
gi-4938	256	31	,	,	PUNCT
gi-4938	256	32	then	then	ADV
gi-4938	256	33	k	k	X
gi-4938	256	34	>	>	X
gi-4938	257	1	0	0	X
gi-4938	257	2	.	.	PUNCT
gi-4938	258	1	push	push	VERB
gi-4938	258	2	ωj,1	ωj,1	NOUN
gi-4938	258	3	to	to	ADP
gi-4938	258	4	the	the	DET
gi-4938	258	5	stack	stack	NOUN
gi-4938	258	6	:	:	PUNCT
gi-4938	258	7	s	s	PART
gi-4938	258	8	←	←	PROPN
gi-4938	258	9	ωj,1	ωj,1	NOUN
gi-4938	258	10	.	.	PUNCT
gi-4938	259	1	if	if	SCONJ
gi-4938	259	2	k	k	PROPN
gi-4938	259	3	>	>	X
gi-4938	259	4	1	1	NUM
gi-4938	259	5	,	,	PUNCT
gi-4938	259	6	push	push	VERB
gi-4938	259	7	the	the	DET
gi-4938	259	8	second	second	ADJ
gi-4938	259	9	interval	interval	NOUN
gi-4938	259	10	ωj,2	ωj,2	NOUN
gi-4938	259	11	to	to	ADP
gi-4938	259	12	the	the	DET
gi-4938	259	13	stack	stack	NOUN
gi-4938	259	14	:	:	PUNCT
gi-4938	259	15	s	s	PART
gi-4938	259	16	←	←	PROPN
gi-4938	259	17	ωj,2	ωj,2	NOUN
gi-4938	259	18	.	.	PUNCT
gi-4938	260	1	processing	process	VERB
gi-4938	260	2	the	the	DET
gi-4938	260	3	interval	interval	NOUN
gi-4938	260	4	.	.	PUNCT
gi-4938	261	1	the	the	DET
gi-4938	261	2	procedure	procedure	NOUN
gi-4938	261	3	processint(ωj	processint(ωj	NOUN
gi-4938	261	4	,	,	PUNCT
gi-4938	261	5	c	c	NOUN
gi-4938	261	6	,	,	PUNCT
gi-4938	261	7	ωj,1	ωj,1	NOUN
gi-4938	261	8	,	,	PUNCT
gi-4938	261	9	ωj,2	ωj,2	NOUN
gi-4938	261	10	,	,	PUNCT
gi-4938	261	11	k	k	PROPN
gi-4938	261	12	,	,	PUNCT
gi-4938	261	13	s	s	PROPN
gi-4938	261	14	,	,	PUNCT
gi-4938	261	15	ε	ε	PROPN
gi-4938	261	16	)	)	PUNCT
gi-4938	261	17	refines	refine	VERB
gi-4938	261	18	the	the	DET
gi-4938	261	19	interval	interval	NOUN
gi-4938	261	20	ωj	ωj	ADP
gi-4938	261	21	.	.	PUNCT
gi-4938	262	1	depending	depend	VERB
gi-4938	262	2	on	on	ADP
gi-4938	262	3	the	the	DET
gi-4938	262	4	c	c	NOUN
gi-4938	262	5	value	value	NOUN
gi-4938	262	6	,	,	PUNCT
gi-4938	262	7	the	the	DET
gi-4938	262	8	ωj	ωj	ADP
gi-4938	262	9	bounds	bound	NOUN
gi-4938	262	10	are	be	AUX
gi-4938	262	11	shifted	shift	VERB
gi-4938	262	12	,	,	PUNCT
gi-4938	262	13	or	or	CCONJ
gi-4938	262	14	ωj	ωj	PROPN
gi-4938	262	15	is	be	AUX
gi-4938	262	16	split	split	VERB
gi-4938	262	17	to	to	ADP
gi-4938	262	18	ωj,1	ωj,1	NOUN
gi-4938	262	19	,	,	PUNCT
gi-4938	262	20	ωj,2	ωj,2	NOUN
gi-4938	262	21	.	.	PUNCT
gi-4938	263	1	it	it	PRON
gi-4938	263	2	can	can	AUX
gi-4938	263	3	be	be	AUX
gi-4938	263	4	summarized	summarize	VERB
gi-4938	263	5	as	as	SCONJ
gi-4938	263	6	follows	follow	VERB
gi-4938	263	7	:	:	PUNCT
gi-4938	264	1	1	1	X
gi-4938	264	2	.	.	X
gi-4938	264	3	if	if	SCONJ
gi-4938	264	4	aj	aj	PROPN
gi-4938	264	5	>	>	X
gi-4938	264	6	bj	bj	NOUN
gi-4938	264	7	,	,	PUNCT
gi-4938	264	8	ωj	ωj	CCONJ
gi-4938	264	9	represents	represent	VERB
gi-4938	264	10	an	an	DET
gi-4938	264	11	incorrect	incorrect	ADJ
gi-4938	264	12	interval	interval	NOUN
gi-4938	264	13	,	,	PUNCT
gi-4938	264	14	return	return	NOUN
gi-4938	264	15	.	.	PUNCT
gi-4938	265	1	2	2	X
gi-4938	265	2	.	.	X
gi-4938	266	1	if	if	SCONJ
gi-4938	266	2	|bj	|bj	PROPN
gi-4938	266	3	−	−	PROPN
gi-4938	266	4	aj	aj	VERB
gi-4938	266	5	|	|	ADV
gi-4938	266	6	<	<	X
gi-4938	266	7	ε	ε	PROPN
gi-4938	266	8	,	,	PUNCT
gi-4938	266	9	ωj	ωj	ADP
gi-4938	266	10	represents	represent	VERB
gi-4938	266	11	an	an	DET
gi-4938	266	12	“	"	PUNCT
gi-4938	266	13	empty	empty	ADJ
gi-4938	266	14	”	"	PUNCT
gi-4938	266	15	interval	interval	NOUN
gi-4938	266	16	,	,	PUNCT
gi-4938	266	17	return	return	NOUN
gi-4938	266	18	.	.	PUNCT
gi-4938	267	1	as	as	SCONJ
gi-4938	267	2	mentioned	mention	VERB
gi-4938	267	3	above	above	ADV
gi-4938	267	4	,	,	PUNCT
gi-4938	267	5	for	for	ADP
gi-4938	267	6	some	some	DET
gi-4938	267	7	functions	function	NOUN
gi-4938	267	8	with	with	ADP
gi-4938	267	9	the	the	DET
gi-4938	267	10	multiple	multiple	ADJ
gi-4938	267	11	jump	jump	NOUN
gi-4938	267	12	discontinuities	discontinuity	NOUN
gi-4938	267	13	the	the	DET
gi-4938	267	14	empty	empty	ADJ
gi-4938	267	15	interval	interval	NOUN
gi-4938	267	16	can	can	AUX
gi-4938	267	17	not	not	PART
gi-4938	267	18	be	be	AUX
gi-4938	267	19	skipped	skip	VERB
gi-4938	267	20	.	.	PUNCT
gi-4938	268	1	3	3	X
gi-4938	268	2	.	.	X
gi-4938	268	3	if	if	SCONJ
gi-4938	268	4	aj	aj	PROPN
gi-4938	268	5	≤	≤	PROPN
gi-4938	268	6	c∧|c−	c∧|c−	PROPN
gi-4938	268	7	aj	aj	PROPN
gi-4938	268	8	|	|	ADV
gi-4938	268	9	<	<	X
gi-4938	268	10	ε	ε	PROPN
gi-4938	268	11	,	,	PUNCT
gi-4938	268	12	the	the	DET
gi-4938	268	13	discontinuity	discontinuity	NOUN
gi-4938	268	14	c	c	NOUN
gi-4938	268	15	is	be	AUX
gi-4938	268	16	close	close	ADJ
gi-4938	268	17	to	to	ADP
gi-4938	268	18	the	the	DET
gi-4938	268	19	lower	low	ADJ
gi-4938	268	20	bound	bind	VERB
gi-4938	268	21	of	of	ADP
gi-4938	268	22	the	the	DET
gi-4938	268	23	interval	interval	NOUN
gi-4938	268	24	ωj	ωj	ADP
gi-4938	268	25	.	.	PUNCT
gi-4938	269	1	shift	shift	VERB
gi-4938	269	2	the	the	DET
gi-4938	269	3	lower	lower	ADV
gi-4938	269	4	bound	bind	VERB
gi-4938	269	5	aj,1	aj,1	NOUN
gi-4938	269	6	=	=	SYM
gi-4938	269	7	aj	aj	PROPN
gi-4938	269	8	+	+	PROPN
gi-4938	269	9	ε	ε	PROPN
gi-4938	269	10	of	of	ADP
gi-4938	269	11	ωj,1	ωj,1	NOUN
gi-4938	269	12	and	and	CCONJ
gi-4938	269	13	increase	increase	VERB
gi-4938	269	14	the	the	DET
gi-4938	269	15	amount	amount	NOUN
gi-4938	269	16	of	of	ADP
gi-4938	269	17	created	create	VERB
gi-4938	269	18	intervals	interval	NOUN
gi-4938	269	19	k	k	NOUN
gi-4938	270	1	=	=	PUNCT
gi-4938	270	2	k	k	PROPN
gi-4938	271	1	+	+	PROPN
gi-4938	271	2	1	1	NUM
gi-4938	271	3	.	.	NOUN
gi-4938	271	4	4	4	NUM
gi-4938	271	5	.	.	X
gi-4938	272	1	if	if	SCONJ
gi-4938	272	2	bj	bj	VERB
gi-4938	272	3	≥	≥	PRON
gi-4938	272	4	c∧|c−	c∧|c−	NOUN
gi-4938	272	5	bj	bj	NOUN
gi-4938	272	6	|	|	ADV
gi-4938	272	7	<	<	X
gi-4938	272	8	ε	ε	PROPN
gi-4938	272	9	,	,	PUNCT
gi-4938	272	10	the	the	DET
gi-4938	272	11	discontinuity	discontinuity	NOUN
gi-4938	272	12	c	c	NOUN
gi-4938	272	13	is	be	AUX
gi-4938	272	14	close	close	ADJ
gi-4938	272	15	to	to	ADP
gi-4938	272	16	the	the	DET
gi-4938	272	17	upper	upper	ADJ
gi-4938	272	18	bound	bound	NOUN
gi-4938	272	19	of	of	ADP
gi-4938	272	20	the	the	DET
gi-4938	272	21	interval	interval	NOUN
gi-4938	272	22	ωj	ωj	ADP
gi-4938	272	23	.	.	PUNCT
gi-4938	273	1	shift	shift	VERB
gi-4938	273	2	the	the	DET
gi-4938	273	3	upper	upper	ADJ
gi-4938	273	4	bound	bind	VERB
gi-4938	273	5	bj,1	bj,1	NOUN
gi-4938	273	6	=	=	PRON
gi-4938	273	7	bj	bj	VERB
gi-4938	273	8	−	−	PROPN
gi-4938	273	9	ε	ε	PROPN
gi-4938	273	10	of	of	ADP
gi-4938	273	11	ωj,1	ωj,1	NOUN
gi-4938	273	12	and	and	CCONJ
gi-4938	273	13	increase	increase	VERB
gi-4938	273	14	the	the	DET
gi-4938	273	15	amount	amount	NOUN
gi-4938	273	16	of	of	ADP
gi-4938	273	17	created	create	VERB
gi-4938	273	18	intervals	interval	NOUN
gi-4938	274	1	k	k	NOUN
gi-4938	274	2	=	=	PUNCT
gi-4938	274	3	k	k	PROPN
gi-4938	275	1	+	+	PROPN
gi-4938	275	2	1	1	NUM
gi-4938	275	3	.	.	NOUN
gi-4938	275	4	5	5	NUM
gi-4938	275	5	.	.	PUNCT
gi-4938	276	1	if	if	SCONJ
gi-4938	276	2	aj	aj	PROPN
gi-4938	276	3	<	<	X
gi-4938	276	4	c	c	X
gi-4938	276	5	<	<	X
gi-4938	276	6	bj	bj	X
gi-4938	276	7	,	,	PUNCT
gi-4938	276	8	then	then	ADV
gi-4938	276	9	|c−	|c−	VERB
gi-4938	276	10	aj	aj	PROPN
gi-4938	276	11	|	|	ADV
gi-4938	276	12	>	>	X
gi-4938	276	13	ε	ε	PROPN
gi-4938	276	14	∧	∧	PROPN
gi-4938	276	15	|c−	|c−	NOUN
gi-4938	276	16	bj	bj	ADP
gi-4938	276	17	|	|	ADV
gi-4938	276	18	>	>	X
gi-4938	276	19	ε	ε	PROPN
gi-4938	276	20	,	,	PUNCT
gi-4938	276	21	the	the	DET
gi-4938	276	22	discontinuity	discontinuity	NOUN
gi-4938	276	23	c	c	NOUN
gi-4938	276	24	is	be	AUX
gi-4938	276	25	inside	inside	ADP
gi-4938	276	26	the	the	DET
gi-4938	276	27	interval	interval	NOUN
gi-4938	276	28	ωj	ωj	ADP
gi-4938	276	29	which	which	PRON
gi-4938	276	30	needs	need	VERB
gi-4938	276	31	to	to	PART
gi-4938	276	32	be	be	AUX
gi-4938	276	33	split	split	VERB
gi-4938	276	34	to	to	ADP
gi-4938	276	35	ωj,1	ωj,1	NOUN
gi-4938	276	36	,	,	PUNCT
gi-4938	276	37	ωj,2	ωj,2	NOUN
gi-4938	276	38	.	.	PUNCT
gi-4938	277	1	shift	shift	VERB
gi-4938	277	2	the	the	DET
gi-4938	277	3	upper	upper	ADJ
gi-4938	277	4	bound	bind	VERB
gi-4938	277	5	bj,1	bj,1	NOUN
gi-4938	277	6	=	=	PUNCT
gi-4938	277	7	c	c	PROPN
gi-4938	277	8	−	−	PROPN
gi-4938	277	9	ε	ε	PROPN
gi-4938	277	10	of	of	ADP
gi-4938	277	11	ωj,1	ωj,1	NOUN
gi-4938	277	12	and	and	CCONJ
gi-4938	277	13	the	the	DET
gi-4938	277	14	lower	lower	ADV
gi-4938	277	15	bound	bind	VERB
gi-4938	277	16	aj,2	aj,2	NOUN
gi-4938	277	17	=	=	SYM
gi-4938	278	1	c	c	PROPN
gi-4938	278	2	+	+	NUM
gi-4938	278	3	ε	ε	PROPN
gi-4938	278	4	of	of	ADP
gi-4938	278	5	ωj,2	ωj,2	NOUN
gi-4938	278	6	.	.	PUNCT
gi-4938	279	1	increase	increase	VERB
gi-4938	279	2	the	the	DET
gi-4938	279	3	amount	amount	NOUN
gi-4938	279	4	of	of	ADP
gi-4938	279	5	the	the	DET
gi-4938	279	6	created	create	VERB
gi-4938	279	7	intervals	interval	NOUN
gi-4938	279	8	k	k	X
gi-4938	279	9	=	=	PUNCT
gi-4938	279	10	k	k	PROPN
gi-4938	280	1	+	+	CCONJ
gi-4938	280	2	2	2	NUM
gi-4938	280	3	and	and	CCONJ
gi-4938	280	4	splits	split	VERB
gi-4938	280	5	s	s	NOUN
gi-4938	280	6	=	=	PUNCT
gi-4938	280	7	s+	s+	PUNCT
gi-4938	280	8	1	1	NUM
gi-4938	280	9	.	.	NOUN
gi-4938	280	10	6	6	NUM
gi-4938	280	11	.	.	PUNCT
gi-4938	281	1	if	if	SCONJ
gi-4938	281	2	at	at	ADV
gi-4938	281	3	least	least	ADV
gi-4938	281	4	one	one	NUM
gi-4938	281	5	new	new	ADJ
gi-4938	281	6	interval	interval	NOUN
gi-4938	281	7	needs	need	VERB
gi-4938	281	8	to	to	PART
gi-4938	281	9	be	be	AUX
gi-4938	281	10	created	create	VERB
gi-4938	281	11	,	,	PUNCT
gi-4938	281	12	then	then	ADV
gi-4938	281	13	k	k	X
gi-4938	281	14	>	>	X
gi-4938	281	15	0	0	X
gi-4938	281	16	.	.	PUNCT
gi-4938	282	1	push	push	VERB
gi-4938	282	2	ωj,1	ωj,1	NOUN
gi-4938	282	3	to	to	ADP
gi-4938	282	4	the	the	DET
gi-4938	282	5	stack	stack	NOUN
gi-4938	282	6	:	:	PUNCT
gi-4938	282	7	s	s	PART
gi-4938	282	8	←	←	PROPN
gi-4938	282	9	ωj,1	ωj,1	NOUN
gi-4938	282	10	.	.	PUNCT
gi-4938	283	1	if	if	SCONJ
gi-4938	283	2	k	k	PROPN
gi-4938	283	3	>	>	X
gi-4938	283	4	1	1	NUM
gi-4938	283	5	,	,	PUNCT
gi-4938	283	6	push	push	VERB
gi-4938	283	7	the	the	DET
gi-4938	283	8	second	second	ADJ
gi-4938	283	9	interval	interval	NOUN
gi-4938	283	10	ωj,2	ωj,2	NOUN
gi-4938	283	11	to	to	ADP
gi-4938	283	12	the	the	DET
gi-4938	283	13	stack	stack	NOUN
gi-4938	283	14	:	:	PUNCT
gi-4938	283	15	s	s	PART
gi-4938	283	16	←	←	PROPN
gi-4938	283	17	ωj,2	ωj,2	NOUN
gi-4938	283	18	.	.	PUNCT
gi-4938	284	1	for	for	ADP
gi-4938	284	2	the	the	DET
gi-4938	284	3	implementation	implementation	NOUN
gi-4938	284	4	,	,	PUNCT
gi-4938	284	5	see	see	VERB
gi-4938	284	6	alg	alg	PROPN
gi-4938	284	7	.	.	PUNCT
gi-4938	285	1	4	4	NUM
gi-4938	285	2	.	.	X
gi-4938	285	3	analogously	analogously	ADV
gi-4938	285	4	,	,	PUNCT
gi-4938	285	5	the	the	DET
gi-4938	285	6	singularity	singularity	NOUN
gi-4938	285	7	value	value	NOUN
gi-4938	285	8	c	c	NOUN
gi-4938	285	9	is	be	AUX
gi-4938	285	10	stored	store	VERB
gi-4938	285	11	in	in	ADP
gi-4938	285	12	the	the	DET
gi-4938	285	13	thrown	throw	VERB
gi-4938	285	14	exception	exception	NOUN
gi-4938	285	15	,	,	PUNCT
gi-4938	285	16	and	and	CCONJ
gi-4938	285	17	processed	process	VERB
gi-4938	285	18	in	in	ADP
gi-4938	285	19	the	the	DET
gi-4938	285	20	try	try	NOUN
gi-4938	285	21	-	-	PUNCT
gi-4938	285	22	catch	catch	NOUN
gi-4938	285	23	block	block	NOUN
gi-4938	285	24	.	.	PUNCT
gi-4938	286	1	in	in	ADP
gi-4938	286	2	general	general	ADJ
gi-4938	286	3	,	,	PUNCT
gi-4938	286	4	the	the	DET
gi-4938	286	5	stack	stack	NOUN
gi-4938	286	6	-	-	PUNCT
gi-4938	286	7	based	base	VERB
gi-4938	286	8	implementation	implementation	NOUN
gi-4938	286	9	is	be	AUX
gi-4938	286	10	more	more	ADV
gi-4938	286	11	stable	stable	ADJ
gi-4938	286	12	than	than	ADP
gi-4938	286	13	a	a	DET
gi-4938	286	14	common	common	ADJ
gi-4938	286	15	recursion	recursion	NOUN
gi-4938	286	16	and	and	CCONJ
gi-4938	286	17	does	do	AUX
gi-4938	286	18	not	not	PART
gi-4938	286	19	suffer	suffer	VERB
gi-4938	286	20	from	from	ADP
gi-4938	286	21	too	too	ADV
gi-4938	286	22	high	high	ADJ
gi-4938	286	23	value	value	NOUN
gi-4938	286	24	of	of	ADP
gi-4938	286	25	the	the	DET
gi-4938	286	26	recursion	recursion	NOUN
gi-4938	286	27	depth	depth	NOUN
gi-4938	286	28	d	d	NOUN
gi-4938	286	29	;	;	PUNCT
gi-4938	286	30	especially	especially	ADV
gi-4938	286	31	for	for	ADP
gi-4938	286	32	the	the	DET
gi-4938	286	33	small	small	ADJ
gi-4938	286	34	values	value	NOUN
gi-4938	286	35	of	of	ADP
gi-4938	286	36	ε	ε	PROPN
gi-4938	286	37	.	.	PROPN
gi-4938	286	38	5.2	5.2	NUM
gi-4938	286	39	.	.	PUNCT
gi-4938	287	1	utilization	utilization	NOUN
gi-4938	287	2	in	in	ADP
gi-4938	287	3	geoinformatics	geoinformatic	NOUN
gi-4938	287	4	the	the	DET
gi-4938	287	5	proposed	propose	VERB
gi-4938	287	6	methods	method	NOUN
gi-4938	287	7	may	may	AUX
gi-4938	287	8	be	be	AUX
gi-4938	287	9	used	use	VERB
gi-4938	287	10	for	for	ADP
gi-4938	287	11	the	the	DET
gi-4938	287	12	polygonal	polygonal	ADJ
gi-4938	287	13	approximation	approximation	NOUN
gi-4938	287	14	of	of	ADP
gi-4938	287	15	curves	curve	NOUN
gi-4938	287	16	when	when	SCONJ
gi-4938	287	17	a	a	DET
gi-4938	287	18	more	more	ADV
gi-4938	287	19	compact	compact	ADJ
gi-4938	287	20	and	and	CCONJ
gi-4938	287	21	efficient	efficient	ADJ
gi-4938	287	22	representation	representation	NOUN
gi-4938	287	23	is	be	AUX
gi-4938	287	24	required	require	VERB
gi-4938	287	25	.	.	PUNCT
gi-4938	288	1	the	the	DET
gi-4938	288	2	circles	circle	NOUN
gi-4938	288	3	,	,	PUNCT
gi-4938	288	4	circular	circular	ADJ
gi-4938	288	5	arcs	arc	NOUN
gi-4938	288	6	,	,	PUNCT
gi-4938	288	7	ellipses	ellipsis	NOUN
gi-4938	288	8	or	or	CCONJ
gi-4938	288	9	offsets	offset	NOUN
gi-4938	288	10	of	of	ADP
gi-4938	288	11	curves	curve	NOUN
gi-4938	288	12	(	(	PUNCT
gi-4938	288	13	e.g.	e.g.	ADV
gi-4938	288	14	,	,	PUNCT
gi-4938	288	15	buffers	buffer	NOUN
gi-4938	288	16	)	)	PUNCT
gi-4938	288	17	can	can	AUX
gi-4938	288	18	not	not	PART
gi-4938	288	19	be	be	AUX
gi-4938	288	20	internally	internally	ADV
gi-4938	288	21	stored	store	VERB
gi-4938	288	22	in	in	ADP
gi-4938	288	23	the	the	DET
gi-4938	288	24	*	*	NOUN
gi-4938	288	25	.shp	.shp	NOUN
gi-4938	288	26	files	file	NOUN
gi-4938	288	27	.	.	PUNCT
gi-4938	289	1	it	it	PRON
gi-4938	289	2	can	can	AUX
gi-4938	289	3	also	also	ADV
gi-4938	289	4	be	be	AUX
gi-4938	289	5	used	use	VERB
gi-4938	289	6	for	for	ADP
gi-4938	289	7	the	the	DET
gi-4938	289	8	contour	contour	NOUN
gi-4938	289	9	lines	line	NOUN
gi-4938	289	10	simplification	simplification	NOUN
gi-4938	289	11	(	(	PUNCT
gi-4938	289	12	removing	remove	VERB
gi-4938	289	13	the	the	DET
gi-4938	289	14	adjacent	adjacent	ADJ
gi-4938	289	15	segments	segment	NOUN
gi-4938	289	16	,	,	PUNCT
gi-4938	289	17	where	where	SCONJ
gi-4938	289	18	αi	αi	ADV
gi-4938	289	19	<	<	X
gi-4938	289	20	α	α	X
gi-4938	289	21	)	)	PUNCT
gi-4938	289	22	.	.	PUNCT
gi-4938	290	1	another	another	DET
gi-4938	290	2	utilization	utilization	NOUN
gi-4938	290	3	for	for	ADP
gi-4938	290	4	which	which	PRON
gi-4938	290	5	the	the	DET
gi-4938	290	6	algorithm	algorithm	NOUN
gi-4938	290	7	was	be	AUX
gi-4938	290	8	originally	originally	ADV
gi-4938	290	9	developed	develop	VERB
gi-4938	290	10	,	,	PUNCT
gi-4938	290	11	is	be	AUX
gi-4938	290	12	a	a	DET
gi-4938	290	13	more	more	ADV
gi-4938	290	14	efficient	efficient	ADJ
gi-4938	290	15	reconstruction	reconstruction	NOUN
gi-4938	290	16	of	of	ADP
gi-4938	290	17	the	the	DET
gi-4938	290	18	map	map	NOUN
gi-4938	290	19	projection	projection	NOUN
gi-4938	290	20	graticule	graticule	NOUN
gi-4938	290	21	.	.	PUNCT
gi-4938	291	1	the	the	DET
gi-4938	291	2	coordinate	coordinate	NOUN
gi-4938	291	3	functions	function	NOUN
gi-4938	291	4	f	f	X
gi-4938	291	5	(	(	PUNCT
gi-4938	291	6	ϕ	ϕ	PROPN
gi-4938	291	7	,	,	PUNCT
gi-4938	291	8	λ	λ	NOUN
gi-4938	291	9	)	)	PUNCT
gi-4938	291	10	,	,	PUNCT
gi-4938	291	11	g(ϕ	g(ϕ	PROPN
gi-4938	291	12	,	,	PUNCT
gi-4938	291	13	λ	λ	NOUN
gi-4938	291	14	)	)	PUNCT
gi-4938	291	15	of	of	ADP
gi-4938	291	16	the	the	DET
gi-4938	291	17	map	map	NOUN
gi-4938	291	18	projection	projection	NOUN
gi-4938	291	19	depend	depend	VERB
gi-4938	291	20	on	on	ADP
gi-4938	291	21	ϕ	ϕ	NOUN
gi-4938	291	22	,	,	PUNCT
gi-4938	291	23	λ	λ	PROPN
gi-4938	291	24	and	and	CCONJ
gi-4938	291	25	may	may	AUX
gi-4938	291	26	contain	contain	VERB
gi-4938	291	27	several	several	ADJ
gi-4938	291	28	discontinuities	discontinuity	NOUN
gi-4938	291	29	.	.	PUNCT
gi-4938	292	1	therefore	therefore	ADV
gi-4938	292	2	,	,	PUNCT
gi-4938	292	3	the	the	DET
gi-4938	292	4	problem	problem	NOUN
gi-4938	292	5	needs	need	VERB
gi-4938	292	6	to	to	PART
gi-4938	292	7	be	be	AUX
gi-4938	292	8	generalized	generalize	VERB
gi-4938	292	9	,	,	PUNCT
gi-4938	292	10	and	and	CCONJ
gi-4938	292	11	its	its	PRON
gi-4938	292	12	solution	solution	NOUN
gi-4938	292	13	must	must	AUX
gi-4938	292	14	be	be	AUX
gi-4938	292	15	adapted	adapt	VERB
gi-4938	292	16	for	for	ADP
gi-4938	292	17	these	these	DET
gi-4938	292	18	facts	fact	NOUN
gi-4938	292	19	.	.	PUNCT
gi-4938	293	1	the	the	DET
gi-4938	293	2	algorithm	algorithm	NOUN
gi-4938	293	3	for	for	ADP
gi-4938	293	4	the	the	DET
gi-4938	293	5	map	map	NOUN
gi-4938	293	6	projection	projection	NOUN
gi-4938	293	7	graticule	graticule	NOUN
gi-4938	293	8	construction	construction	NOUN
gi-4938	293	9	will	will	AUX
gi-4938	293	10	be	be	AUX
gi-4938	293	11	presented	present	VERB
gi-4938	293	12	in	in	ADP
gi-4938	293	13	the	the	DET
gi-4938	293	14	next	next	ADJ
gi-4938	293	15	paper	paper	NOUN
gi-4938	293	16	.	.	PUNCT
gi-4938	294	1	6	6	NUM
gi-4938	294	2	.	.	X
gi-4938	294	3	experiments	experiment	NOUN
gi-4938	294	4	and	and	CCONJ
gi-4938	294	5	results	result	NOUN
gi-4938	294	6	.	.	PUNCT
gi-4938	295	1	the	the	DET
gi-4938	295	2	proposed	propose	VERB
gi-4938	295	3	methods	method	NOUN
gi-4938	295	4	for	for	ADP
gi-4938	295	5	combined	combined	ADJ
gi-4938	295	6	sampling	sampling	NOUN
gi-4938	295	7	have	have	AUX
gi-4938	295	8	been	be	AUX
gi-4938	295	9	tested	test	VERB
gi-4938	295	10	for	for	ADP
gi-4938	295	11	the	the	DET
gi-4938	295	12	set	set	NOUN
gi-4938	295	13	of	of	ADP
gi-4938	295	14	9	9	NUM
gi-4938	295	15	functions	function	NOUN
gi-4938	295	16	;	;	PUNCT
gi-4938	295	17	the	the	DET
gi-4938	295	18	ability	ability	NOUN
gi-4938	295	19	to	to	PART
gi-4938	295	20	detect	detect	VERB
gi-4938	295	21	and	and	CCONJ
gi-4938	295	22	treat	treat	VERB
gi-4938	295	23	the	the	DET
gi-4938	295	24	discontinuities	discontinuity	NOUN
gi-4938	295	25	represents	represent	VERB
gi-4938	295	26	an	an	DET
gi-4938	295	27	important	important	ADJ
gi-4938	295	28	factor	factor	NOUN
gi-4938	295	29	.	.	PUNCT
gi-4938	296	1	geoinformatics	geoinformatic	NOUN
gi-4938	296	2	fce	fce	VERB
gi-4938	296	3	ctu	ctu	NOUN
gi-4938	296	4	17(2	17(2	NUM
gi-4938	296	5	)	)	PUNCT
gi-4938	296	6	,	,	PUNCT
gi-4938	296	7	2018	2018	NUM
gi-4938	296	8	19	19	NUM
gi-4938	296	9	t.	t.	NOUN
gi-4938	296	10	bayer	bayer	NOUN
gi-4938	296	11	:	:	PUNCT
gi-4938	296	12	efficient	efficient	ADJ
gi-4938	296	13	plotting	plot	VERB
gi-4938	296	14	the	the	DET
gi-4938	296	15	functions	function	NOUN
gi-4938	296	16	with	with	ADP
gi-4938	296	17	discontinuities	discontinuity	NOUN
gi-4938	296	18	algorithm	algorithm	NOUN
gi-4938	296	19	4	4	NUM
gi-4938	296	20	processing	process	VERB
gi-4938	296	21	the	the	DET
gi-4938	296	22	interval	interval	NOUN
gi-4938	296	23	:	:	PUNCT
gi-4938	296	24	shift	shift	NOUN
gi-4938	296	25	bounds	bound	NOUN
gi-4938	296	26	or	or	CCONJ
gi-4938	296	27	split	split	NOUN
gi-4938	296	28	.	.	PUNCT
gi-4938	297	1	1	1	NUM
gi-4938	297	2	:	:	PUNCT
gi-4938	297	3	function	function	NOUN
gi-4938	297	4	processint(ωj	processint(ωj	NOUN
gi-4938	297	5	,	,	PUNCT
gi-4938	297	6	c	c	NOUN
gi-4938	297	7	,	,	PUNCT
gi-4938	297	8	ωj,1	ωj,1	NOUN
gi-4938	297	9	,	,	PUNCT
gi-4938	297	10	ωj,2	ωj,2	NOUN
gi-4938	297	11	,	,	PUNCT
gi-4938	297	12	k	k	PROPN
gi-4938	297	13	,	,	PUNCT
gi-4938	297	14	s	s	PROPN
gi-4938	297	15	,	,	PUNCT
gi-4938	297	16	ε	ε	PROPN
gi-4938	297	17	)	)	PUNCT
gi-4938	297	18	2	2	NUM
gi-4938	297	19	:	:	PUNCT
gi-4938	297	20	if	if	SCONJ
gi-4938	297	21	(	(	PUNCT
gi-4938	297	22	aj	aj	PROPN
gi-4938	297	23	>	>	X
gi-4938	297	24	bj	bj	PROPN
gi-4938	297	25	)	)	PUNCT
gi-4938	297	26	then	then	ADV
gi-4938	297	27	3	3	NUM
gi-4938	297	28	:	:	PUNCT
gi-4938	297	29	return	return	VERB
gi-4938	297	30	4	4	NUM
gi-4938	297	31	:	:	PUNCT
gi-4938	297	32	if	if	SCONJ
gi-4938	297	33	|bj	|bj	PROPN
gi-4938	297	34	−	−	PROPN
gi-4938	297	35	aj	aj	VERB
gi-4938	297	36	|	|	ADV
gi-4938	297	37	<	<	X
gi-4938	297	38	ε	ε	PROPN
gi-4938	297	39	then	then	ADV
gi-4938	297	40	5	5	NUM
gi-4938	297	41	:	:	PUNCT
gi-4938	297	42	return	return	VERB
gi-4938	297	43	6	6	NUM
gi-4938	297	44	:	:	PUNCT
gi-4938	297	45	if	if	SCONJ
gi-4938	297	46	(	(	PUNCT
gi-4938	297	47	aj	aj	PROPN
gi-4938	297	48	≤	≤	PROPN
gi-4938	297	49	c	c	NOUN
gi-4938	297	50	)	)	PUNCT
gi-4938	297	51	∧	∧	PROPN
gi-4938	297	52	(	(	PUNCT
gi-4938	297	53	|c−	|c−	NOUN
gi-4938	297	54	aj	aj	PROPN
gi-4938	297	55	|	|	ADV
gi-4938	297	56	≤	≤	NUM
gi-4938	297	57	ε	ε	PROPN
gi-4938	297	58	)	)	PUNCT
gi-4938	297	59	then	then	ADV
gi-4938	297	60	7	7	NUM
gi-4938	297	61	:	:	PUNCT
gi-4938	297	62	aj,1	aj,1	NOUN
gi-4938	297	63	=	=	SYM
gi-4938	297	64	aj	aj	PROPN
gi-4938	297	65	+	+	CCONJ
gi-4938	297	66	ε	ε	PROPN
gi-4938	297	67	8	8	NUM
gi-4938	297	68	:	:	PUNCT
gi-4938	297	69	k	k	X
gi-4938	298	1	=	=	PUNCT
gi-4938	298	2	k	k	PROPN
gi-4938	299	1	+	+	CCONJ
gi-4938	299	2	1	1	NUM
gi-4938	299	3	9	9	NUM
gi-4938	299	4	:	:	PUNCT
gi-4938	299	5	else	else	ADV
gi-4938	299	6	if	if	SCONJ
gi-4938	299	7	(	(	PUNCT
gi-4938	299	8	bj	bj	ADP
gi-4938	299	9	≥	≥	NOUN
gi-4938	299	10	c	c	NOUN
gi-4938	299	11	)	)	PUNCT
gi-4938	299	12	∧	∧	NOUN
gi-4938	299	13	(	(	PUNCT
gi-4938	299	14	|c−	|c−	NOUN
gi-4938	299	15	bj	bj	VERB
gi-4938	299	16	|	|	ADV
gi-4938	299	17	≤	≤	NUM
gi-4938	299	18	ε	ε	PROPN
gi-4938	299	19	)	)	PUNCT
gi-4938	299	20	then	then	ADV
gi-4938	299	21	10	10	NUM
gi-4938	299	22	:	:	PUNCT
gi-4938	299	23	bj,1	bj,1	NOUN
gi-4938	299	24	=	=	PRON
gi-4938	299	25	bj	bj	VERB
gi-4938	299	26	−	−	PROPN
gi-4938	299	27	ε	ε	PROPN
gi-4938	299	28	11	11	NUM
gi-4938	299	29	:	:	PUNCT
gi-4938	300	1	k	k	X
gi-4938	300	2	=	=	PUNCT
gi-4938	301	1	k	k	PROPN
gi-4938	302	1	+	+	CCONJ
gi-4938	302	2	1	1	NUM
gi-4938	302	3	12	12	NUM
gi-4938	302	4	:	:	PUNCT
gi-4938	302	5	else	else	ADV
gi-4938	302	6	if	if	SCONJ
gi-4938	302	7	(	(	PUNCT
gi-4938	302	8	aj	aj	X
gi-4938	302	9	<	<	X
gi-4938	302	10	c	c	X
gi-4938	302	11	<	<	X
gi-4938	302	12	bj	bj	NOUN
gi-4938	302	13	)	)	PUNCT
gi-4938	302	14	∧	∧	PROPN
gi-4938	302	15	(	(	PUNCT
gi-4938	302	16	|c−	|c−	NOUN
gi-4938	302	17	aj	aj	PROPN
gi-4938	302	18	|	|	ADV
gi-4938	302	19	>	>	X
gi-4938	302	20	ε	ε	PROPN
gi-4938	302	21	)	)	PUNCT
gi-4938	302	22	∧	∧	PROPN
gi-4938	302	23	(	(	PUNCT
gi-4938	302	24	|c−	|c−	NOUN
gi-4938	302	25	bj	bj	VERB
gi-4938	302	26	|	|	ADV
gi-4938	302	27	>	>	X
gi-4938	302	28	ε	ε	PROPN
gi-4938	302	29	)	)	PUNCT
gi-4938	302	30	then	then	ADV
gi-4938	302	31	13	13	NUM
gi-4938	302	32	:	:	PUNCT
gi-4938	302	33	bj,1	bj,1	NOUN
gi-4938	302	34	=	=	SYM
gi-4938	302	35	c−	c−	X
gi-4938	302	36	ε	ε	PROPN
gi-4938	302	37	,	,	PUNCT
gi-4938	302	38	aj,2	aj,2	PROPN
gi-4938	302	39	=	=	SYM
gi-4938	302	40	c+	c+	X
gi-4938	302	41	ε	ε	PROPN
gi-4938	302	42	14	14	NUM
gi-4938	302	43	:	:	PUNCT
gi-4938	303	1	k	k	X
gi-4938	303	2	=	=	PUNCT
gi-4938	303	3	k	k	PROPN
gi-4938	303	4	+	+	CCONJ
gi-4938	303	5	2	2	NUM
gi-4938	303	6	15	15	NUM
gi-4938	303	7	:	:	PUNCT
gi-4938	303	8	s	s	X
gi-4938	303	9	=	=	PUNCT
gi-4938	303	10	s+	s+	NUM
gi-4938	303	11	1	1	NUM
gi-4938	303	12	6.1	6.1	NUM
gi-4938	303	13	.	.	PUNCT
gi-4938	304	1	list	list	NOUN
gi-4938	304	2	of	of	ADP
gi-4938	304	3	functions	function	NOUN
gi-4938	304	4	in	in	ADP
gi-4938	304	5	all	all	DET
gi-4938	304	6	cases	case	NOUN
gi-4938	304	7	is	be	AUX
gi-4938	304	8	ω	ω	NOUN
gi-4938	304	9	=	=	PUNCT
gi-4938	305	1	[	[	X
gi-4938	305	2	−5π	−5π	PROPN
gi-4938	305	3	,	,	PUNCT
gi-4938	305	4	5π	5π	NUM
gi-4938	305	5	]	]	PUNCT
gi-4938	305	6	,	,	PUNCT
gi-4938	305	7	ε	ε	PROPN
gi-4938	305	8	=	=	SYM
gi-4938	305	9	0.001	0.001	NUM
gi-4938	305	10	,	,	PUNCT
gi-4938	305	11	α	α	NOUN
gi-4938	305	12	=	=	SYM
gi-4938	305	13	1	1	NUM
gi-4938	305	14	◦	◦	NOUN
gi-4938	305	15	,	,	PUNCT
gi-4938	305	16	the	the	DET
gi-4938	305	17	thresholds	threshold	NOUN
gi-4938	305	18	s	s	PART
gi-4938	305	19	,	,	PUNCT
gi-4938	305	20	d	d	PRON
gi-4938	305	21	have	have	AUX
gi-4938	305	22	not	not	PART
gi-4938	305	23	been	be	AUX
gi-4938	305	24	set	set	VERB
gi-4938	305	25	.	.	PUNCT
gi-4938	306	1	the	the	DET
gi-4938	306	2	first	first	ADJ
gi-4938	306	3	function	function	NOUN
gi-4938	306	4	f1(x	f1(x	NOUN
gi-4938	306	5	)	)	PUNCT
gi-4938	306	6	=	=	PRON
gi-4938	306	7	{	{	PUNCT
gi-4938	306	8	1	1	NUM
gi-4938	306	9	+	+	CCONJ
gi-4938	306	10	x	x	NOUN
gi-4938	306	11	,	,	PUNCT
gi-4938	306	12	x	x	X
gi-4938	306	13	≥	≥	NOUN
gi-4938	306	14	0	0	NUM
gi-4938	306	15	,	,	PUNCT
gi-4938	306	16	0	0	NUM
gi-4938	306	17	,	,	PUNCT
gi-4938	306	18	x	x	X
gi-4938	306	19	<	<	X
gi-4938	306	20	0	0	NUM
gi-4938	306	21	,	,	PUNCT
gi-4938	306	22	has	have	VERB
gi-4938	306	23	the	the	DET
gi-4938	306	24	jump	jump	NOUN
gi-4938	306	25	discontinuity	discontinuity	NOUN
gi-4938	306	26	at	at	ADP
gi-4938	306	27	x	x	X
gi-4938	307	1	=	=	SYM
gi-4938	307	2	0	0	NUM
gi-4938	307	3	.	.	PUNCT
gi-4938	308	1	the	the	DET
gi-4938	308	2	polyline	polyline	PROPN
gi-4938	308	3	representation	representation	NOUN
gi-4938	308	4	contains	contain	VERB
gi-4938	308	5	only	only	ADV
gi-4938	308	6	4	4	NUM
gi-4938	308	7	points	point	NOUN
gi-4938	308	8	divided	divide	VERB
gi-4938	308	9	into	into	ADP
gi-4938	308	10	two	two	NUM
gi-4938	308	11	intervals	interval	NOUN
gi-4938	308	12	ωg	ωg	PUNCT
gi-4938	308	13	1	1	NUM
gi-4938	308	14	=	=	SYM
gi-4938	309	1	[	[	X
gi-4938	309	2	−5π,−1.3	−5π,−1.3	PROPN
gi-4938	309	3	·	·	SYM
gi-4938	309	4	10−4	10−4	PROPN
gi-4938	309	5	]	]	X
gi-4938	309	6	,	,	PUNCT
gi-4938	309	7	ωg	ωg	X
gi-4938	309	8	2	2	NUM
gi-4938	309	9	=	=	PUNCT
gi-4938	310	1	[	[	X
gi-4938	310	2	1.6	1.6	NUM
gi-4938	310	3	·	·	SYM
gi-4938	310	4	10−4	10−4	NUM
gi-4938	310	5	,	,	PUNCT
gi-4938	310	6	5π	5π	NUM
gi-4938	310	7	]	]	PUNCT
gi-4938	310	8	,	,	PUNCT
gi-4938	310	9	the	the	DET
gi-4938	310	10	amount	amount	NOUN
gi-4938	310	11	of	of	ADP
gi-4938	310	12	splits	split	NOUN
gi-4938	310	13	is	be	AUX
gi-4938	310	14	s	s	NOUN
gi-4938	310	15	=	=	SYM
gi-4938	310	16	1	1	NUM
gi-4938	310	17	,	,	PUNCT
gi-4938	310	18	no	no	DET
gi-4938	310	19	recursion	recursion	NOUN
gi-4938	310	20	is	be	AUX
gi-4938	310	21	required	require	VERB
gi-4938	310	22	d	d	PROPN
gi-4938	310	23	=	=	SYM
gi-4938	310	24	0	0	PROPN
gi-4938	310	25	.	.	PUNCT
gi-4938	311	1	the	the	DET
gi-4938	311	2	second	second	ADJ
gi-4938	311	3	function	function	NOUN
gi-4938	311	4	f2(x	f2(x	PROPN
gi-4938	311	5	)	)	PUNCT
gi-4938	311	6	=	=	SYM
gi-4938	311	7	e−500x2	e−500x2	NOUN
gi-4938	311	8	,	,	PUNCT
gi-4938	311	9	is	be	AUX
gi-4938	311	10	quite	quite	ADV
gi-4938	311	11	steep	steep	ADJ
gi-4938	311	12	and	and	CCONJ
gi-4938	311	13	does	do	AUX
gi-4938	311	14	not	not	PART
gi-4938	311	15	contain	contain	VERB
gi-4938	311	16	any	any	DET
gi-4938	311	17	discontinuity	discontinuity	NOUN
gi-4938	311	18	.	.	PUNCT
gi-4938	312	1	these	these	DET
gi-4938	312	2	facts	fact	NOUN
gi-4938	312	3	led	lead	VERB
gi-4938	312	4	to	to	ADP
gi-4938	312	5	the	the	DET
gi-4938	312	6	polygonal	polygonal	ADJ
gi-4938	312	7	approximation	approximation	NOUN
gi-4938	312	8	formed	form	VERB
gi-4938	312	9	by	by	ADP
gi-4938	312	10	266	266	NUM
gi-4938	312	11	points	point	NOUN
gi-4938	312	12	,	,	PUNCT
gi-4938	312	13	ωg	ωg	NOUN
gi-4938	312	14	=	=	PROPN
gi-4938	312	15	ω	ω	PROPN
gi-4938	312	16	,	,	PUNCT
gi-4938	312	17	no	no	DET
gi-4938	312	18	splits	split	NOUN
gi-4938	312	19	,	,	PUNCT
gi-4938	312	20	s	s	PART
gi-4938	312	21	=	=	SYM
gi-4938	312	22	0	0	NUM
gi-4938	312	23	,	,	PUNCT
gi-4938	312	24	the	the	DET
gi-4938	312	25	maximum	maximum	ADJ
gi-4938	312	26	recursion	recursion	NOUN
gi-4938	312	27	depth	depth	NOUN
gi-4938	312	28	is	be	AUX
gi-4938	312	29	d	d	NOUN
gi-4938	312	30	=	=	SYM
gi-4938	312	31	3	3	X
gi-4938	312	32	.	.	PUNCT
gi-4938	313	1	the	the	DET
gi-4938	313	2	third	third	ADJ
gi-4938	313	3	function	function	NOUN
gi-4938	313	4	f3(x	f3(x	NUM
gi-4938	313	5	)	)	PUNCT
gi-4938	313	6	=	=	SYM
gi-4938	313	7	sin(x)/x	sin(x)/x	PROPN
gi-4938	313	8	,	,	PUNCT
gi-4938	313	9	has	have	VERB
gi-4938	313	10	a	a	DET
gi-4938	313	11	removable	removable	ADJ
gi-4938	313	12	discontinuity	discontinuity	NOUN
gi-4938	313	13	at	at	ADP
gi-4938	313	14	x	x	X
gi-4938	313	15	=	=	SYM
gi-4938	313	16	0	0	NUM
gi-4938	313	17	,	,	PUNCT
gi-4938	313	18	where	where	SCONJ
gi-4938	313	19	f(0	f(0	NOUN
gi-4938	313	20	)	)	PUNCT
gi-4938	313	21	=	=	SYM
gi-4938	314	1	1	1	X
gi-4938	314	2	.	.	X
gi-4938	314	3	ω	ω	PROPN
gi-4938	314	4	is	be	AUX
gi-4938	314	5	divided	divide	VERB
gi-4938	314	6	into	into	ADP
gi-4938	314	7	two	two	NUM
gi-4938	314	8	subintervals	subinterval	NOUN
gi-4938	314	9	ωg	ωg	ADP
gi-4938	314	10	1	1	NUM
gi-4938	314	11	=	=	SYM
gi-4938	315	1	[	[	X
gi-4938	315	2	−5π,−1.3	−5π,−1.3	PROPN
gi-4938	315	3	·	·	SYM
gi-4938	315	4	10−4	10−4	PROPN
gi-4938	315	5	]	]	X
gi-4938	315	6	,	,	PUNCT
gi-4938	315	7	ωg	ωg	X
gi-4938	315	8	2	2	NUM
gi-4938	315	9	=	=	PUNCT
gi-4938	316	1	[	[	X
gi-4938	316	2	1.6	1.6	NUM
gi-4938	316	3	·	·	SYM
gi-4938	316	4	10−4	10−4	NUM
gi-4938	316	5	,	,	PUNCT
gi-4938	316	6	5π	5π	NUM
gi-4938	316	7	]	]	PUNCT
gi-4938	316	8	,	,	PUNCT
gi-4938	316	9	the	the	DET
gi-4938	316	10	amount	amount	NOUN
gi-4938	316	11	of	of	ADP
gi-4938	316	12	splits	split	NOUN
gi-4938	316	13	is	be	AUX
gi-4938	316	14	s	s	NOUN
gi-4938	316	15	=	=	SYM
gi-4938	316	16	1	1	NUM
gi-4938	316	17	,	,	PUNCT
gi-4938	316	18	no	no	DET
gi-4938	316	19	recursion	recursion	NOUN
gi-4938	316	20	required	require	VERB
gi-4938	316	21	d	d	NOUN
gi-4938	316	22	=	=	SYM
gi-4938	316	23	0	0	NUM
gi-4938	316	24	,	,	PUNCT
gi-4938	316	25	the	the	DET
gi-4938	316	26	polygonal	polygonal	ADJ
gi-4938	316	27	approximation	approximation	NOUN
gi-4938	316	28	contains	contain	VERB
gi-4938	316	29	122	122	NUM
gi-4938	316	30	points	point	NOUN
gi-4938	316	31	.	.	PUNCT
gi-4938	317	1	the	the	DET
gi-4938	317	2	fourth	fourth	ADJ
gi-4938	317	3	function	function	NOUN
gi-4938	317	4	f4(x	f4(x	NUM
gi-4938	317	5	)	)	PUNCT
gi-4938	317	6	=	=	PUNCT
gi-4938	317	7	x/	x/	NOUN
gi-4938	317	8	sin(x	sin(x	PROPN
gi-4938	317	9	)	)	PUNCT
gi-4938	317	10	,	,	PUNCT
gi-4938	317	11	has	have	AUX
gi-4938	317	12	jump	jump	VERB
gi-4938	317	13	discontinuities	discontinuity	NOUN
gi-4938	317	14	at	at	ADP
gi-4938	317	15	x	x	X
gi-4938	317	16	=	=	SYM
gi-4938	317	17	±π	±π	X
gi-4938	317	18	±	±	NUM
gi-4938	317	19	kπ	kπ	PROPN
gi-4938	317	20	.	.	PUNCT
gi-4938	318	1	hence	hence	ADV
gi-4938	318	2	,	,	PUNCT
gi-4938	318	3	ω	ω	PROPN
gi-4938	318	4	is	be	AUX
gi-4938	318	5	split	split	VERB
gi-4938	318	6	into	into	ADP
gi-4938	318	7	9	9	NUM
gi-4938	318	8	sub	sub	NOUN
gi-4938	318	9	intervals	interval	NOUN
gi-4938	318	10	:	:	PUNCT
gi-4938	318	11	ωg	ωg	NOUN
gi-4938	318	12	1	1	NUM
gi-4938	318	13	=	=	SYM
gi-4938	319	1	[	[	X
gi-4938	319	2	−15.692,−12.579	−15.692,−12.579	NOUN
gi-4938	319	3	]	]	PUNCT
gi-4938	319	4	,	,	PUNCT
gi-4938	319	5	ωg	ωg	X
gi-4938	319	6	2	2	NUM
gi-4938	319	7	=	=	SYM
gi-4938	320	1	[	[	X
gi-4938	320	2	−12.554,−9.434	−12.554,−9.434	X
gi-4938	320	3	]	]	PUNCT
gi-4938	320	4	,	,	PUNCT
gi-4938	320	5	ωg	ωg	ADP
gi-4938	320	6	3	3	NUM
gi-4938	320	7	=	=	SYM
gi-4938	321	1	[	[	X
gi-4938	321	2	−9.415,−6.290	−9.415,−6.290	X
gi-4938	321	3	]	]	PUNCT
gi-4938	321	4	,	,	PUNCT
gi-4938	321	5	ωg	ωg	ADP
gi-4938	321	6	4	4	NUM
gi-4938	321	7	=	=	SYM
gi-4938	322	1	[	[	X
gi-4938	322	2	−6.277,−3.145	−6.277,−3.145	NUM
gi-4938	322	3	]	]	X
gi-4938	322	4	,	,	PUNCT
gi-4938	322	5	ωg	ωg	ADP
gi-4938	322	6	5	5	NUM
gi-4938	323	1	=	=	SYM
gi-4938	324	1	[	[	X
gi-4938	324	2	−3.138	−3.138	PROPN
gi-4938	324	3	,	,	PUNCT
gi-4938	324	4	3.138	3.138	NUM
gi-4938	324	5	]	]	PUNCT
gi-4938	324	6	,	,	PUNCT
gi-4938	324	7	ωg	ωg	X
gi-4938	324	8	6	6	NUM
gi-4938	324	9	=	=	SYM
gi-4938	325	1	[	[	X
gi-4938	325	2	3.145	3.145	NUM
gi-4938	325	3	,	,	PUNCT
gi-4938	325	4	6.277	6.277	NUM
gi-4938	325	5	]	]	PUNCT
gi-4938	325	6	,	,	PUNCT
gi-4938	325	7	ωg	ωg	X
gi-4938	325	8	7	7	NUM
gi-4938	325	9	=	=	SYM
gi-4938	326	1	[	[	X
gi-4938	326	2	6.290	6.290	NUM
gi-4938	326	3	,	,	PUNCT
gi-4938	326	4	9.415	9.415	NUM
gi-4938	326	5	]	]	PUNCT
gi-4938	326	6	,	,	PUNCT
gi-4938	326	7	ωg	ωg	X
gi-4938	326	8	8	8	NUM
gi-4938	326	9	=	=	PUNCT
gi-4938	327	1	[	[	X
gi-4938	327	2	9.434	9.434	NUM
gi-4938	327	3	,	,	PUNCT
gi-4938	327	4	12.554	12.554	NUM
gi-4938	327	5	]	]	PUNCT
gi-4938	327	6	,	,	PUNCT
gi-4938	327	7	ωg	ωg	ADP
gi-4938	327	8	9	9	NUM
gi-4938	327	9	=	=	SYM
gi-4938	328	1	[	[	X
gi-4938	328	2	12.579	12.579	NUM
gi-4938	328	3	,	,	PUNCT
gi-4938	328	4	15.692	15.692	NUM
gi-4938	328	5	]	]	PUNCT
gi-4938	328	6	.	.	PUNCT
gi-4938	329	1	the	the	DET
gi-4938	329	2	amount	amount	NOUN
gi-4938	329	3	of	of	ADP
gi-4938	329	4	splits	split	NOUN
gi-4938	329	5	s	s	NOUN
gi-4938	329	6	=	=	NOUN
gi-4938	329	7	8	8	NUM
gi-4938	329	8	as	as	ADV
gi-4938	329	9	well	well	ADV
gi-4938	329	10	as	as	ADP
gi-4938	329	11	the	the	DET
gi-4938	329	12	recursion	recursion	NOUN
gi-4938	329	13	depth	depth	NOUN
gi-4938	329	14	d	d	X
gi-4938	329	15	=	=	SYM
gi-4938	329	16	6	6	NUM
gi-4938	329	17	,	,	PUNCT
gi-4938	329	18	provide	provide	VERB
gi-4938	329	19	the	the	DET
gi-4938	329	20	polygonal	polygonal	ADJ
gi-4938	329	21	approximation	approximation	NOUN
gi-4938	329	22	containing	contain	VERB
gi-4938	329	23	984	984	NUM
gi-4938	329	24	points	point	NOUN
gi-4938	329	25	.	.	PUNCT
gi-4938	330	1	the	the	DET
gi-4938	330	2	next	next	ADJ
gi-4938	330	3	function	function	NOUN
gi-4938	330	4	f5(x	f5(x	NOUN
gi-4938	330	5	)	)	PUNCT
gi-4938	330	6	=	=	NOUN
gi-4938	330	7	x	x	SYM
gi-4938	330	8	sin(5	sin(5	NOUN
gi-4938	330	9	/	/	SYM
gi-4938	330	10	x	x	NOUN
gi-4938	330	11	)	)	PUNCT
gi-4938	330	12	,	,	PUNCT
gi-4938	330	13	geoinformatics	geoinformatic	NOUN
gi-4938	330	14	fce	fce	VERB
gi-4938	330	15	ctu	ctu	NOUN
gi-4938	330	16	17(2	17(2	NUM
gi-4938	330	17	)	)	PUNCT
gi-4938	330	18	,	,	PUNCT
gi-4938	330	19	2018	2018	NUM
gi-4938	330	20	20	20	NUM
gi-4938	330	21	t.	t.	NOUN
gi-4938	330	22	bayer	bayer	NOUN
gi-4938	330	23	:	:	PUNCT
gi-4938	330	24	efficient	efficient	ADJ
gi-4938	330	25	plotting	plot	VERB
gi-4938	330	26	the	the	DET
gi-4938	330	27	functions	function	NOUN
gi-4938	330	28	with	with	ADP
gi-4938	330	29	discontinuities	discontinuity	NOUN
gi-4938	330	30	-10	-10	PUNCT
gi-4938	330	31	0	0	NUM
gi-4938	331	1	10	10	NUM
gi-4938	331	2	x	x	SYM
gi-4938	331	3	0	0	NUM
gi-4938	331	4	5	5	NUM
gi-4938	331	5	10	10	NUM
gi-4938	331	6	15	15	NUM
gi-4938	331	7	20	20	NUM
gi-4938	331	8	f	f	NOUN
gi-4938	331	9	(	(	PUNCT
gi-4938	331	10	x	x	SYM
gi-4938	331	11	)	)	PUNCT
gi-4938	331	12	f1(x	f1(x	NUM
gi-4938	331	13	)	)	PUNCT
gi-4938	331	14	,	,	PUNCT
gi-4938	331	15	4	4	NUM
gi-4938	331	16	sampled	sample	VERB
gi-4938	331	17	points	point	NOUN
gi-4938	331	18	-10	-10	PUNCT
gi-4938	331	19	0	0	NUM
gi-4938	331	20	10	10	NUM
gi-4938	331	21	x	x	NOUN
gi-4938	331	22	-10	-10	PUNCT
gi-4938	331	23	-5	-5	PUNCT
gi-4938	331	24	0	0	NUM
gi-4938	331	25	5	5	NUM
gi-4938	331	26	10	10	NUM
gi-4938	331	27	f	f	NOUN
gi-4938	331	28	(	(	PUNCT
gi-4938	331	29	x	x	SYM
gi-4938	331	30	)	)	PUNCT
gi-4938	331	31	f2(x	f2(x	PROPN
gi-4938	331	32	)	)	PUNCT
gi-4938	331	33	,	,	PUNCT
gi-4938	331	34	266	266	NUM
gi-4938	331	35	sampled	sample	VERB
gi-4938	331	36	points	point	NOUN
gi-4938	331	37	-10	-10	PUNCT
gi-4938	331	38	0	0	NUM
gi-4938	331	39	10	10	NUM
gi-4938	331	40	x	x	NOUN
gi-4938	331	41	-10	-10	PUNCT
gi-4938	331	42	-5	-5	PUNCT
gi-4938	331	43	0	0	NUM
gi-4938	331	44	5	5	NUM
gi-4938	331	45	10	10	NUM
gi-4938	331	46	f	f	NOUN
gi-4938	331	47	(	(	PUNCT
gi-4938	331	48	x	x	SYM
gi-4938	331	49	)	)	PUNCT
gi-4938	331	50	f3(x	f3(x	PROPN
gi-4938	331	51	)	)	PUNCT
gi-4938	331	52	,	,	PUNCT
gi-4938	331	53	122	122	NUM
gi-4938	331	54	sampled	sample	VERB
gi-4938	331	55	points	point	NOUN
gi-4938	331	56	-10	-10	PUNCT
gi-4938	331	57	0	0	NUM
gi-4938	331	58	10	10	NUM
gi-4938	331	59	x	x	NOUN
gi-4938	331	60	-10	-10	PUNCT
gi-4938	332	1	-5	-5	PUNCT
gi-4938	332	2	0	0	NUM
gi-4938	332	3	5	5	NUM
gi-4938	332	4	10	10	NUM
gi-4938	332	5	f	f	NOUN
gi-4938	332	6	(	(	PUNCT
gi-4938	332	7	x	x	SYM
gi-4938	332	8	)	)	PUNCT
gi-4938	332	9	f4(x	f4(x	NUM
gi-4938	332	10	)	)	PUNCT
gi-4938	332	11	,	,	PUNCT
gi-4938	332	12	984	984	NUM
gi-4938	332	13	sampled	sample	VERB
gi-4938	332	14	points	point	NOUN
gi-4938	332	15	-10	-10	PUNCT
gi-4938	332	16	0	0	NUM
gi-4938	332	17	10	10	NUM
gi-4938	332	18	x	x	SYM
gi-4938	332	19	-5	-5	NUM
gi-4938	332	20	0	0	NUM
gi-4938	332	21	5	5	NUM
gi-4938	332	22	10	10	NUM
gi-4938	332	23	f	f	NOUN
gi-4938	332	24	(	(	PUNCT
gi-4938	332	25	x	x	X
gi-4938	332	26	)	)	PUNCT
gi-4938	332	27	f5(x	f5(x	NOUN
gi-4938	332	28	)	)	PUNCT
gi-4938	332	29	,	,	PUNCT
gi-4938	332	30	6032	6032	NUM
gi-4938	332	31	sampled	sample	VERB
gi-4938	332	32	points	point	NOUN
gi-4938	332	33	-10	-10	PUNCT
gi-4938	332	34	0	0	NUM
gi-4938	332	35	10	10	NUM
gi-4938	332	36	x	x	NOUN
gi-4938	332	37	-10	-10	PUNCT
gi-4938	333	1	-5	-5	PUNCT
gi-4938	333	2	0	0	NUM
gi-4938	333	3	5	5	NUM
gi-4938	333	4	10	10	NUM
gi-4938	333	5	f	f	NOUN
gi-4938	333	6	(	(	PUNCT
gi-4938	333	7	x	x	X
gi-4938	333	8	)	)	PUNCT
gi-4938	333	9	f6(x	f6(x	PROPN
gi-4938	333	10	)	)	PUNCT
gi-4938	333	11	,	,	PUNCT
gi-4938	333	12	755	755	NUM
gi-4938	333	13	sampled	sample	VERB
gi-4938	333	14	points	point	NOUN
gi-4938	333	15	-10	-10	PUNCT
gi-4938	333	16	0	0	NUM
gi-4938	333	17	10	10	NUM
gi-4938	333	18	x	x	NOUN
gi-4938	333	19	-10	-10	PUNCT
gi-4938	334	1	-5	-5	PUNCT
gi-4938	334	2	0	0	NUM
gi-4938	334	3	5	5	NUM
gi-4938	334	4	10	10	NUM
gi-4938	334	5	f	f	NOUN
gi-4938	334	6	(	(	PUNCT
gi-4938	334	7	x	x	SYM
gi-4938	334	8	)	)	PUNCT
gi-4938	334	9	f7(x	f7(x	ADJ
gi-4938	334	10	)	)	PUNCT
gi-4938	334	11	,	,	PUNCT
gi-4938	334	12	163	163	NUM
gi-4938	334	13	sampled	sample	VERB
gi-4938	334	14	points	point	NOUN
gi-4938	334	15	-10	-10	PUNCT
gi-4938	334	16	0	0	NUM
gi-4938	334	17	10	10	NUM
gi-4938	334	18	x	x	NOUN
gi-4938	334	19	-10	-10	PUNCT
gi-4938	335	1	-5	-5	PUNCT
gi-4938	335	2	0	0	NUM
gi-4938	335	3	5	5	NUM
gi-4938	335	4	10	10	NUM
gi-4938	335	5	f	f	NOUN
gi-4938	335	6	(	(	PUNCT
gi-4938	335	7	x	x	SYM
gi-4938	335	8	)	)	PUNCT
gi-4938	335	9	f8(x	f8(x	NUM
gi-4938	335	10	)	)	PUNCT
gi-4938	335	11	,	,	PUNCT
gi-4938	335	12	1948	1948	NUM
gi-4938	335	13	sampled	sample	VERB
gi-4938	335	14	points	point	NOUN
gi-4938	335	15	-10	-10	PUNCT
gi-4938	335	16	0	0	NUM
gi-4938	335	17	10	10	NUM
gi-4938	335	18	x	x	NOUN
gi-4938	335	19	-10	-10	PUNCT
gi-4938	336	1	-5	-5	PUNCT
gi-4938	336	2	0	0	NUM
gi-4938	336	3	5	5	NUM
gi-4938	336	4	10	10	NUM
gi-4938	336	5	f	f	NOUN
gi-4938	336	6	(	(	PUNCT
gi-4938	336	7	x	x	SYM
gi-4938	336	8	)	)	PUNCT
gi-4938	336	9	f9(x	f9(x	PROPN
gi-4938	336	10	)	)	PUNCT
gi-4938	336	11	,	,	PUNCT
gi-4938	336	12	1109	1109	NUM
gi-4938	336	13	sampled	sample	VERB
gi-4938	336	14	points	point	NOUN
gi-4938	336	15	figure	figure	VERB
gi-4938	336	16	5.1	5.1	NUM
gi-4938	336	17	:	:	PUNCT
gi-4938	336	18	the	the	DET
gi-4938	336	19	polygonal	polygonal	ADJ
gi-4938	336	20	approximation	approximation	NOUN
gi-4938	336	21	of	of	ADP
gi-4938	336	22	functions	function	NOUN
gi-4938	336	23	f1(x	f1(x	NUM
gi-4938	336	24	)	)	PUNCT
gi-4938	336	25	,	,	PUNCT
gi-4938	336	26	...	...	PUNCT
gi-4938	336	27	,	,	PUNCT
gi-4938	336	28	f9(x	f9(x	X
gi-4938	336	29	)	)	PUNCT
gi-4938	336	30	created	create	VERB
gi-4938	336	31	by	by	ADP
gi-4938	336	32	the	the	DET
gi-4938	336	33	combined	combined	ADJ
gi-4938	336	34	sampling	sampling	NOUN
gi-4938	336	35	technique	technique	NOUN
gi-4938	336	36	;	;	PUNCT
gi-4938	336	37	the	the	DET
gi-4938	336	38	discontinuities	discontinuity	NOUN
gi-4938	336	39	involved	involve	VERB
gi-4938	336	40	.	.	PUNCT
gi-4938	337	1	has	have	VERB
gi-4938	337	2	a	a	DET
gi-4938	337	3	discontinuity	discontinuity	NOUN
gi-4938	337	4	at	at	ADP
gi-4938	337	5	x	x	X
gi-4938	337	6	=	=	SYM
gi-4938	337	7	0	0	NUM
gi-4938	337	8	,	,	PUNCT
gi-4938	337	9	and	and	CCONJ
gi-4938	337	10	f(0	f(0	NOUN
gi-4938	337	11	)	)	PUNCT
gi-4938	337	12	=	=	SYM
gi-4938	338	1	0	0	X
gi-4938	338	2	.	.	X
gi-4938	339	1	ω	ω	PROPN
gi-4938	339	2	should	should	AUX
gi-4938	339	3	be	be	AUX
gi-4938	339	4	divided	divide	VERB
gi-4938	339	5	in	in	ADP
gi-4938	339	6	two	two	NUM
gi-4938	339	7	subintervals	subinterval	NOUN
gi-4938	339	8	,	,	PUNCT
gi-4938	339	9	but	but	CCONJ
gi-4938	339	10	the	the	DET
gi-4938	339	11	algorithm	algorithm	NOUN
gi-4938	339	12	creates	create	VERB
gi-4938	339	13	12	12	NUM
gi-4938	339	14	subintervals	subinterval	NOUN
gi-4938	339	15	in	in	ADP
gi-4938	339	16	42	42	NUM
gi-4938	339	17	splits	split	NOUN
gi-4938	339	18	:	:	PUNCT
gi-4938	339	19	ωg	ωg	NOUN
gi-4938	340	1	1	1	NUM
gi-4938	340	2	=	=	SYM
gi-4938	341	1	[	[	X
gi-4938	341	2	−15.708,−0.015	−15.708,−0.015	PROPN
gi-4938	341	3	]	]	PUNCT
gi-4938	341	4	,	,	PUNCT
gi-4938	341	5	ωg	ωg	X
gi-4938	341	6	2	2	NUM
gi-4938	341	7	=	=	SYM
gi-4938	342	1	[	[	X
gi-4938	342	2	−0.009,−0.008	−0.009,−0.008	NOUN
gi-4938	342	3	]	]	PUNCT
gi-4938	342	4	,	,	PUNCT
gi-4938	342	5	ωg	ωg	ADP
gi-4938	342	6	3	3	NUM
gi-4938	342	7	=	=	SYM
gi-4938	343	1	[	[	X
gi-4938	343	2	−0.007,−0.006	−0.007,−0.006	X
gi-4938	343	3	]	]	X
gi-4938	343	4	,	,	PUNCT
gi-4938	343	5	ωg	ωg	ADP
gi-4938	343	6	4	4	NUM
gi-4938	343	7	=	=	SYM
gi-4938	344	1	[	[	X
gi-4938	344	2	−0.005,−0.004	−0.005,−0.004	X
gi-4938	344	3	]	]	X
gi-4938	344	4	,	,	PUNCT
gi-4938	344	5	ωg	ωg	X
gi-4938	344	6	5	5	NUM
gi-4938	344	7	=	=	SYM
gi-4938	345	1	[	[	X
gi-4938	345	2	−0.004,−0.003	−0.004,−0.003	NOUN
gi-4938	345	3	]	]	PUNCT
gi-4938	345	4	,	,	PUNCT
gi-4938	345	5	ωg	ωg	X
gi-4938	345	6	6	6	NUM
gi-4938	345	7	=	=	SYM
gi-4938	346	1	[	[	X
gi-4938	346	2	−0.003	−0.003	PROPN
gi-4938	346	3	,	,	PUNCT
gi-4938	346	4	0.003	0.003	NUM
gi-4938	346	5	]	]	PUNCT
gi-4938	346	6	,	,	PUNCT
gi-4938	346	7	ωg	ωg	X
gi-4938	346	8	7	7	NUM
gi-4938	346	9	=	=	PUNCT
gi-4938	347	1	[	[	X
gi-4938	347	2	0.003	0.003	NUM
gi-4938	347	3	,	,	PUNCT
gi-4938	347	4	0.004	0.004	NUM
gi-4938	347	5	]	]	PUNCT
gi-4938	347	6	,	,	PUNCT
gi-4938	347	7	ωg	ωg	X
gi-4938	347	8	8	8	NUM
gi-4938	347	9	=	=	PUNCT
gi-4938	348	1	[	[	X
gi-4938	348	2	0.004	0.004	NUM
gi-4938	348	3	,	,	PUNCT
gi-4938	348	4	0.005	0.005	NUM
gi-4938	348	5	]	]	PUNCT
gi-4938	348	6	,	,	PUNCT
gi-4938	348	7	ωg	ωg	ADP
gi-4938	348	8	9	9	NUM
gi-4938	348	9	=	=	SYM
gi-4938	349	1	[	[	X
gi-4938	349	2	0.005	0.005	NUM
gi-4938	349	3	,	,	PUNCT
gi-4938	349	4	0.006	0.006	NUM
gi-4938	349	5	]	]	PUNCT
gi-4938	349	6	,	,	PUNCT
gi-4938	349	7	ωg	ωg	ADP
gi-4938	349	8	10	10	NUM
gi-4938	349	9	=	=	PUNCT
gi-4938	350	1	[	[	X
gi-4938	350	2	0.006	0.006	NUM
gi-4938	350	3	,	,	PUNCT
gi-4938	350	4	0.007	0.007	NUM
gi-4938	350	5	]	]	PUNCT
gi-4938	350	6	,	,	PUNCT
gi-4938	350	7	ωg	ωg	X
gi-4938	350	8	11	11	NUM
gi-4938	350	9	=	=	SYM
gi-4938	351	1	[	[	X
gi-4938	351	2	0.008	0.008	NUM
gi-4938	351	3	,	,	PUNCT
gi-4938	351	4	0.009	0.009	NUM
gi-4938	351	5	]	]	PUNCT
gi-4938	351	6	,	,	PUNCT
gi-4938	351	7	ωg	ωg	ADP
gi-4938	351	8	12	12	NUM
gi-4938	351	9	=	=	PUNCT
gi-4938	352	1	[	[	X
gi-4938	352	2	0.015	0.015	NUM
gi-4938	352	3	,	,	PUNCT
gi-4938	352	4	15.708	15.708	NUM
gi-4938	352	5	]	]	PUNCT
gi-4938	352	6	.	.	PUNCT
gi-4938	353	1	as	as	ADP
gi-4938	353	2	a	a	DET
gi-4938	353	3	result	result	NOUN
gi-4938	353	4	of	of	ADP
gi-4938	353	5	the	the	DET
gi-4938	353	6	recursion	recursion	NOUN
gi-4938	353	7	depth	depth	NOUN
gi-4938	353	8	d	d	NOUN
gi-4938	353	9	=	=	SYM
gi-4938	353	10	9	9	NUM
gi-4938	353	11	,	,	PUNCT
gi-4938	353	12	the	the	DET
gi-4938	353	13	total	total	ADJ
gi-4938	353	14	amount	amount	NOUN
gi-4938	353	15	of	of	ADP
gi-4938	353	16	points	point	NOUN
gi-4938	353	17	is	be	AUX
gi-4938	353	18	n	n	PRON
gi-4938	353	19	=	=	SYM
gi-4938	353	20	6032	6032	NUM
gi-4938	353	21	.	.	PUNCT
gi-4938	354	1	while	while	SCONJ
gi-4938	354	2	the	the	DET
gi-4938	354	3	graphical	graphical	ADJ
gi-4938	354	4	representation	representation	NOUN
gi-4938	354	5	is	be	AUX
gi-4938	354	6	aesthetically	aesthetically	ADV
gi-4938	354	7	pleasing	pleasing	ADJ
gi-4938	354	8	,	,	PUNCT
gi-4938	354	9	the	the	DET
gi-4938	354	10	polygonal	polygonal	ADJ
gi-4938	354	11	representation	representation	NOUN
gi-4938	354	12	contains	contain	VERB
gi-4938	354	13	redundant	redundant	ADJ
gi-4938	354	14	data	datum	NOUN
gi-4938	354	15	;	;	PUNCT
gi-4938	354	16	this	this	PRON
gi-4938	354	17	is	be	AUX
gi-4938	354	18	due	due	ADJ
gi-4938	354	19	to	to	ADP
gi-4938	354	20	the	the	DET
gi-4938	354	21	false	false	ADJ
gi-4938	354	22	detection	detection	NOUN
gi-4938	354	23	of	of	ADP
gi-4938	354	24	discontinuities	discontinuity	NOUN
gi-4938	354	25	provide	provide	VERB
gi-4938	354	26	by	by	ADP
gi-4938	354	27	lr	lr	NOUN
gi-4938	354	28	criterion	criterion	NOUN
gi-4938	354	29	.	.	PUNCT
gi-4938	355	1	the	the	DET
gi-4938	355	2	next	next	ADJ
gi-4938	355	3	function	function	NOUN
gi-4938	355	4	f6(x	f6(x	PROPN
gi-4938	355	5	)	)	PUNCT
gi-4938	355	6	=	=	PUNCT
gi-4938	355	7	1/(tan	1/(tan	NUM
gi-4938	355	8	2x	2x	NUM
gi-4938	355	9	tan	tan	PROPN
gi-4938	355	10	0.5x	0.5x	NUM
gi-4938	355	11	)	)	PUNCT
gi-4938	355	12	,	,	PUNCT
gi-4938	355	13	has	have	VERB
gi-4938	355	14	the	the	DET
gi-4938	355	15	infinite	infinite	ADJ
gi-4938	355	16	singularities	singularity	NOUN
gi-4938	355	17	at	at	ADP
gi-4938	355	18	x	x	X
gi-4938	355	19	=	=	PRON
gi-4938	355	20	±1/2π	±1/2π	NUM
gi-4938	355	21	±	±	NUM
gi-4938	355	22	kπ	kπ	PROPN
gi-4938	355	23	,	,	PUNCT
gi-4938	355	24	and	and	CCONJ
gi-4938	355	25	at	at	ADP
gi-4938	355	26	x	x	X
gi-4938	355	27	=	=	SYM
gi-4938	355	28	0	0	NUM
gi-4938	355	29	±	±	NUM
gi-4938	355	30	k2π	k2π	PROPN
gi-4938	355	31	(	(	PUNCT
gi-4938	355	32	total	total	NOUN
gi-4938	355	33	15	15	NUM
gi-4938	355	34	)	)	PUNCT
gi-4938	355	35	.	.	PUNCT
gi-4938	356	1	the	the	DET
gi-4938	356	2	adaptive	adaptive	ADJ
gi-4938	356	3	sampling	sample	VERB
gi-4938	356	4	procedure	procedure	NOUN
gi-4938	356	5	with	with	ADP
gi-4938	356	6	the	the	DET
gi-4938	356	7	recursion	recursion	NOUN
gi-4938	356	8	depth	depth	NOUN
gi-4938	356	9	d	d	NOUN
gi-4938	356	10	=	=	SYM
gi-4938	356	11	7	7	NUM
gi-4938	356	12	creates	create	VERB
gi-4938	356	13	755	755	NUM
gi-4938	356	14	points	point	NOUN
gi-4938	356	15	in	in	ADP
gi-4938	356	16	16	16	NUM
gi-4938	356	17	new	new	ADJ
gi-4938	356	18	intervals	interval	NOUN
gi-4938	356	19	ωg	ωg	PUNCT
gi-4938	356	20	1	1	NUM
gi-4938	356	21	=	=	SYM
gi-4938	357	1	[	[	X
gi-4938	357	2	−15.708,−14.138	−15.708,−14.138	PROPN
gi-4938	357	3	,	,	PUNCT
gi-4938	357	4	ωg	ωg	NOUN
gi-4938	357	5	2	2	NUM
gi-4938	357	6	=	=	SYM
gi-4938	358	1	[	[	X
gi-4938	358	2	−14.137,−12.598	−14.137,−12.598	PROPN
gi-4938	358	3	]	]	PUNCT
gi-4938	358	4	,	,	PUNCT
gi-4938	358	5	ωg	ωg	ADP
gi-4938	358	6	3	3	NUM
gi-4938	358	7	=	=	SYM
gi-4938	359	1	[	[	X
gi-4938	359	2	−12.535,−10.996	−12.535,−10.996	PROPN
gi-4938	359	3	]	]	PUNCT
gi-4938	359	4	,	,	PUNCT
gi-4938	359	5	ωg	ωg	ADP
gi-4938	359	6	4	4	NUM
gi-4938	359	7	=	=	SYM
gi-4938	360	1	[	[	X
gi-4938	360	2	−10.995	−10.995	ADJ
gi-4938	360	3	−	−	NOUN
gi-4938	360	4	7.855	7.855	NUM
gi-4938	360	5	]	]	PUNCT
gi-4938	360	6	,	,	PUNCT
gi-4938	360	7	ωg	ωg	X
gi-4938	360	8	5	5	NUM
gi-4938	360	9	=	=	SYM
gi-4938	361	1	[	[	X
gi-4938	361	2	−7.853,−6.315	−7.853,−6.315	X
gi-4938	361	3	]	]	PUNCT
gi-4938	361	4	,	,	PUNCT
gi-4938	361	5	ωg	ωg	X
gi-4938	361	6	6	6	NUM
gi-4938	361	7	=	=	SYM
gi-4938	362	1	[	[	X
gi-4938	362	2	−6.251,−4.713	−6.251,−4.713	X
gi-4938	362	3	]	]	PUNCT
gi-4938	362	4	,	,	PUNCT
gi-4938	362	5	ωg	ωg	X
gi-4938	362	6	7	7	NUM
gi-4938	362	7	=	=	SYM
gi-4938	363	1	[	[	X
gi-4938	363	2	−4.712,−1.571	−4.712,−1.571	X
gi-4938	363	3	]	]	X
gi-4938	363	4	,	,	PUNCT
gi-4938	363	5	ωg	ωg	X
gi-4938	363	6	8	8	NUM
gi-4938	363	7	=	=	PUNCT
gi-4938	364	1	[	[	X
gi-4938	364	2	−1.570,−0.032	−1.570,−0.032	X
gi-4938	364	3	]	]	PUNCT
gi-4938	364	4	,	,	PUNCT
gi-4938	364	5	ωg	ωg	ADP
gi-4938	364	6	9	9	NUM
gi-4938	364	7	=	=	SYM
gi-4938	365	1	[	[	X
gi-4938	365	2	0.032	0.032	NUM
gi-4938	365	3	,	,	PUNCT
gi-4938	365	4	1.570	1.570	NUM
gi-4938	365	5	]	]	PUNCT
gi-4938	365	6	,	,	PUNCT
gi-4938	365	7	ωg	ωg	ADP
gi-4938	365	8	10	10	NUM
gi-4938	365	9	=	=	PUNCT
gi-4938	366	1	[	[	X
gi-4938	366	2	1.571	1.571	NUM
gi-4938	366	3	,	,	PUNCT
gi-4938	366	4	4.712	4.712	NUM
gi-4938	366	5	]	]	PUNCT
gi-4938	366	6	,	,	PUNCT
gi-4938	366	7	ωg	ωg	X
gi-4938	366	8	11	11	NUM
gi-4938	366	9	=	=	PUNCT
gi-4938	367	1	[	[	X
gi-4938	367	2	4.713	4.713	NUM
gi-4938	367	3	,	,	PUNCT
gi-4938	367	4	6.251	6.251	NUM
gi-4938	367	5	]	]	PUNCT
gi-4938	367	6	,	,	PUNCT
gi-4938	367	7	ωg	ωg	ADP
gi-4938	367	8	12	12	NUM
gi-4938	367	9	=	=	PUNCT
gi-4938	368	1	[	[	X
gi-4938	368	2	6.315	6.315	NUM
gi-4938	368	3	,	,	PUNCT
gi-4938	368	4	7.853	7.853	NUM
gi-4938	368	5	]	]	PUNCT
gi-4938	368	6	,	,	PUNCT
gi-4938	368	7	ωg	ωg	ADP
gi-4938	368	8	13	13	NUM
gi-4938	368	9	=	=	PUNCT
gi-4938	369	1	[	[	X
gi-4938	369	2	7.855	7.855	NUM
gi-4938	369	3	,	,	PUNCT
gi-4938	369	4	10.995	10.995	NUM
gi-4938	369	5	]	]	PUNCT
gi-4938	369	6	,	,	PUNCT
gi-4938	369	7	ωg	ωg	PROPN
gi-4938	369	8	14	14	NUM
gi-4938	369	9	=	=	SYM
gi-4938	370	1	[	[	X
gi-4938	370	2	10.996	10.996	NUM
gi-4938	370	3	,	,	PUNCT
gi-4938	370	4	12.535	12.535	NUM
gi-4938	370	5	]	]	PUNCT
gi-4938	370	6	,	,	PUNCT
gi-4938	370	7	ωg	ωg	PROPN
gi-4938	370	8	15	15	NUM
gi-4938	370	9	=	=	SYM
gi-4938	371	1	[	[	X
gi-4938	371	2	12.598	12.598	NUM
gi-4938	371	3	,	,	PUNCT
gi-4938	371	4	14.137	14.137	NUM
gi-4938	371	5	]	]	PUNCT
gi-4938	371	6	,	,	PUNCT
gi-4938	371	7	ωg	ωg	ADP
gi-4938	371	8	16	16	NUM
gi-4938	371	9	=	=	SYM
gi-4938	372	1	[	[	X
gi-4938	372	2	14.138	14.138	NUM
gi-4938	372	3	,	,	PUNCT
gi-4938	372	4	15.708	15.708	NUM
gi-4938	372	5	]	]	PUNCT
gi-4938	372	6	with	with	ADP
gi-4938	372	7	s	s	NOUN
gi-4938	372	8	=	=	SYM
gi-4938	372	9	15	15	NUM
gi-4938	372	10	splits	split	NOUN
gi-4938	372	11	.	.	PUNCT
gi-4938	373	1	the	the	DET
gi-4938	373	2	next	next	ADJ
gi-4938	373	3	function	function	NOUN
gi-4938	373	4	f7(x	f7(x	NOUN
gi-4938	373	5	)	)	PUNCT
gi-4938	373	6	=	=	PUNCT
gi-4938	373	7	e−2x/(x−	e−2x/(x−	PROPN
gi-4938	373	8	1	1	NUM
gi-4938	373	9	)	)	PUNCT
gi-4938	373	10	,	,	PUNCT
gi-4938	373	11	geoinformatics	geoinformatic	NOUN
gi-4938	373	12	fce	fce	VERB
gi-4938	373	13	ctu	ctu	NOUN
gi-4938	373	14	17(2	17(2	NUM
gi-4938	373	15	)	)	PUNCT
gi-4938	373	16	,	,	PUNCT
gi-4938	373	17	2018	2018	NUM
gi-4938	373	18	21	21	NUM
gi-4938	373	19	t.	t.	NOUN
gi-4938	373	20	bayer	bayer	NOUN
gi-4938	373	21	:	:	PUNCT
gi-4938	373	22	efficient	efficient	ADJ
gi-4938	373	23	plotting	plot	VERB
gi-4938	373	24	the	the	DET
gi-4938	373	25	functions	function	NOUN
gi-4938	373	26	with	with	ADP
gi-4938	373	27	discontinuities	discontinuity	NOUN
gi-4938	373	28	algorithm	algorithm	NOUN
gi-4938	373	29	5	5	NUM
gi-4938	373	30	plotting	plot	VERB
gi-4938	373	31	the	the	DET
gi-4938	373	32	function	function	NOUN
gi-4938	373	33	f9(x	f9(x	NOUN
gi-4938	373	34	)	)	PUNCT
gi-4938	373	35	involving	involve	VERB
gi-4938	373	36	discontinuities	discontinuity	NOUN
gi-4938	373	37	in	in	ADP
gi-4938	373	38	the	the	DET
gi-4938	373	39	octave	octave	NOUN
gi-4938	373	40	v.	v.	ADP
gi-4938	373	41	4.4	4.4	NUM
gi-4938	373	42	scripting	scripting	NOUN
gi-4938	373	43	language	language	NOUN
gi-4938	373	44	.	.	PUNCT
gi-4938	374	1	xmin	xmin	NOUN
gi-4938	374	2	=	=	PROPN
gi-4938	374	3	-5*pi	-5*pi	PROPN
gi-4938	374	4	;	;	PUNCT
gi-4938	374	5	xmax	xmax	PROPN
gi-4938	374	6	=	=	SYM
gi-4938	374	7	-xmin	-xmin	PROPN
gi-4938	374	8	;	;	PUNCT
gi-4938	374	9	eps	eps	X
gi-4938	374	10	=	=	NOUN
gi-4938	374	11	0.001	0.001	NUM
gi-4938	374	12	;	;	PUNCT
gi-4938	374	13	lrmax	lrmax	NOUN
gi-4938	374	14	=	=	NUM
gi-4938	374	15	0.8	0.8	NUM
gi-4938	374	16	;	;	PUNCT
gi-4938	374	17	x	x	SYM
gi-4938	374	18	=	=	SYM
gi-4938	374	19	xmin:0.001	xmin:0.001	PROPN
gi-4938	374	20	:	:	PUNCT
gi-4938	374	21	xmax	xmax	PROPN
gi-4938	374	22	;	;	PUNCT
gi-4938	374	23	f	f	PROPN
gi-4938	374	24	=	=	SYM
gi-4938	374	25	@(x)exp(x)./tan(x	@(x)exp(x)./tan(x	PROPN
gi-4938	374	26	)	)	PUNCT
gi-4938	374	27	;	;	PUNCT
gi-4938	374	28	y	y	PROPN
gi-4938	374	29	=	=	SYM
gi-4938	374	30	f(x	f(x	PROPN
gi-4938	374	31	)	)	PUNCT
gi-4938	374	32	;	;	PUNCT
gi-4938	375	1	d	d	X
gi-4938	375	2	=	=	SYM
gi-4938	375	3	lr	lr	X
gi-4938	375	4	(	(	PUNCT
gi-4938	375	5	f	f	PROPN
gi-4938	375	6	,	,	PUNCT
gi-4938	375	7	x	x	PROPN
gi-4938	375	8	,	,	PUNCT
gi-4938	375	9	eps	eps	PROPN
gi-4938	375	10	)	)	PUNCT
gi-4938	375	11	>	>	X
gi-4938	375	12	lrmax	lrmax	PROPN
gi-4938	375	13	;	;	PUNCT
gi-4938	375	14	x(d==1	x(d==1	NUM
gi-4938	375	15	)	)	PUNCT
gi-4938	376	1	=	=	SYM
gi-4938	376	2	nan	nan	PROPN
gi-4938	376	3	;	;	PUNCT
gi-4938	376	4	y(d==1	y(d==1	NUM
gi-4938	376	5	)	)	PUNCT
gi-4938	377	1	=	=	SYM
gi-4938	377	2	nan	nan	PROPN
gi-4938	377	3	;	;	PUNCT
gi-4938	377	4	plot(x	plot(x	PROPN
gi-4938	377	5	,	,	PUNCT
gi-4938	377	6	y,’-r	y,’-r	NOUN
gi-4938	377	7	’	'	PUNCT
gi-4938	377	8	)	)	PUNCT
gi-4938	377	9	;	;	PUNCT
gi-4938	377	10	xlim([xmin	xlim([xmin	PROPN
gi-4938	377	11	,	,	PUNCT
gi-4938	377	12	xmax	xmax	PROPN
gi-4938	377	13	]	]	X
gi-4938	377	14	)	)	PUNCT
gi-4938	377	15	ylim([xmin	ylim([xmin	PROPN
gi-4938	377	16	,	,	PUNCT
gi-4938	377	17	xmax	xmax	PROPN
gi-4938	377	18	]	]	PUNCT
gi-4938	377	19	)	)	PUNCT
gi-4938	377	20	set(gca,’xlim’,[xmin	set(gca,’xlim’,[xmin	X
gi-4938	377	21	xmax	xmax	PROPN
gi-4938	377	22	]	]	X
gi-4938	377	23	)	)	PUNCT
gi-4938	377	24	set(gca,’ylim’,[xmin	set(gca,’ylim’,[xmin	PROPN
gi-4938	377	25	xmax	xmax	X
gi-4938	377	26	]	]	X
gi-4938	377	27	]	]	X
gi-4938	377	28	)	)	PUNCT
gi-4938	377	29	xlabel(’x	xlabel(’x	PROPN
gi-4938	377	30	’	'	PUNCT
gi-4938	377	31	)	)	PUNCT
gi-4938	377	32	;	;	PUNCT
gi-4938	377	33	ylabel(’f(x	ylabel(’f(x	PROPN
gi-4938	377	34	)	)	PUNCT
gi-4938	377	35	’	'	PUNCT
gi-4938	377	36	)	)	PUNCT
gi-4938	377	37	;	;	PUNCT
gi-4938	377	38	axis	axis	NOUN
gi-4938	377	39	equal	equal	ADJ
gi-4938	377	40	;	;	PUNCT
gi-4938	377	41	has	have	VERB
gi-4938	377	42	the	the	DET
gi-4938	377	43	infinite	infinite	ADJ
gi-4938	377	44	singularity	singularity	NOUN
gi-4938	377	45	at	at	ADP
gi-4938	377	46	x	x	X
gi-4938	377	47	=	=	SYM
gi-4938	377	48	1	1	NUM
gi-4938	377	49	,	,	PUNCT
gi-4938	377	50	ω	ω	PROPN
gi-4938	377	51	is	be	AUX
gi-4938	377	52	divided	divide	VERB
gi-4938	377	53	into	into	ADP
gi-4938	377	54	two	two	NUM
gi-4938	377	55	subintervals	subinterval	NOUN
gi-4938	377	56	ωg	ωg	ADP
gi-4938	377	57	1	1	NUM
gi-4938	377	58	=	=	SYM
gi-4938	378	1	[	[	X
gi-4938	378	2	−4.286	−4.286	X
gi-4938	378	3	,	,	PUNCT
gi-4938	378	4	1.000	1.000	NUM
gi-4938	378	5	]	]	PUNCT
gi-4938	378	6	,	,	PUNCT
gi-4938	378	7	ωg	ωg	PROPN
gi-4938	378	8	2	2	NUM
gi-4938	378	9	=	=	SYM
gi-4938	379	1	[	[	X
gi-4938	379	2	1.000	1.000	NUM
gi-4938	379	3	,	,	PUNCT
gi-4938	379	4	15.708	15.708	NUM
gi-4938	379	5	]	]	PUNCT
gi-4938	379	6	.	.	PUNCT
gi-4938	380	1	the	the	DET
gi-4938	380	2	amount	amount	NOUN
gi-4938	380	3	of	of	ADP
gi-4938	380	4	splits	split	NOUN
gi-4938	380	5	is	be	AUX
gi-4938	380	6	s	s	NOUN
gi-4938	380	7	=	=	SYM
gi-4938	380	8	1	1	NUM
gi-4938	380	9	as	as	ADV
gi-4938	380	10	well	well	ADV
gi-4938	380	11	as	as	ADP
gi-4938	380	12	the	the	DET
gi-4938	380	13	recursion	recursion	NOUN
gi-4938	380	14	depth	depth	NOUN
gi-4938	380	15	d	d	X
gi-4938	380	16	=	=	SYM
gi-4938	380	17	6	6	NUM
gi-4938	380	18	,	,	PUNCT
gi-4938	380	19	provide	provide	VERB
gi-4938	380	20	the	the	DET
gi-4938	380	21	polygonal	polygonal	ADJ
gi-4938	380	22	approximation	approximation	NOUN
gi-4938	380	23	by	by	ADP
gi-4938	380	24	163	163	NUM
gi-4938	380	25	points	point	NOUN
gi-4938	380	26	.	.	PUNCT
gi-4938	381	1	the	the	DET
gi-4938	381	2	next	next	ADJ
gi-4938	381	3	function	function	NOUN
gi-4938	381	4	f8(x	f8(x	NUM
gi-4938	381	5	)	)	PUNCT
gi-4938	381	6	=	=	SYM
gi-4938	381	7	x2	x2	PROPN
gi-4938	381	8	sin	sin	VERB
gi-4938	381	9	2x/(2x−	2x/(2x−	NUM
gi-4938	381	10	1	1	NUM
gi-4938	381	11	)	)	PUNCT
gi-4938	381	12	,	,	PUNCT
gi-4938	381	13	has	have	VERB
gi-4938	381	14	the	the	DET
gi-4938	381	15	infinity	infinity	NOUN
gi-4938	381	16	singularity	singularity	NOUN
gi-4938	381	17	at	at	ADP
gi-4938	381	18	x	x	X
gi-4938	381	19	=	=	SYM
gi-4938	381	20	0.5	0.5	NUM
gi-4938	381	21	,	,	PUNCT
gi-4938	381	22	ω	ω	PROPN
gi-4938	381	23	is	be	AUX
gi-4938	381	24	divided	divide	VERB
gi-4938	381	25	into	into	ADP
gi-4938	381	26	two	two	NUM
gi-4938	381	27	subintervalsωg	subintervalsωg	NOUN
gi-4938	381	28	1	1	NUM
gi-4938	381	29	=	=	SYM
gi-4938	382	1	[	[	X
gi-4938	382	2	−15.708	−15.708	ADJ
gi-4938	382	3	,	,	PUNCT
gi-4938	382	4	0.500	0.500	NUM
gi-4938	382	5	]	]	PUNCT
gi-4938	382	6	,	,	PUNCT
gi-4938	382	7	ωg	ωg	X
gi-4938	382	8	2	2	NUM
gi-4938	382	9	=	=	SYM
gi-4938	383	1	[	[	X
gi-4938	383	2	0.500	0.500	NUM
gi-4938	383	3	,	,	PUNCT
gi-4938	383	4	15.708	15.708	NUM
gi-4938	383	5	]	]	PUNCT
gi-4938	383	6	.	.	PUNCT
gi-4938	384	1	the	the	DET
gi-4938	384	2	amount	amount	NOUN
gi-4938	384	3	of	of	ADP
gi-4938	384	4	splits	split	NOUN
gi-4938	384	5	is	be	AUX
gi-4938	384	6	s	s	NOUN
gi-4938	384	7	=	=	SYM
gi-4938	384	8	1	1	NUM
gi-4938	384	9	and	and	CCONJ
gi-4938	384	10	the	the	DET
gi-4938	384	11	recursion	recursion	NOUN
gi-4938	384	12	depth	depth	NOUN
gi-4938	384	13	d	d	NOUN
gi-4938	384	14	=	=	SYM
gi-4938	384	15	7	7	NUM
gi-4938	384	16	bring	bring	VERB
gi-4938	384	17	the	the	DET
gi-4938	384	18	polygonal	polygonal	ADJ
gi-4938	384	19	approximation	approximation	NOUN
gi-4938	384	20	by	by	ADP
gi-4938	384	21	1948	1948	NUM
gi-4938	384	22	points	point	NOUN
gi-4938	384	23	.	.	PUNCT
gi-4938	385	1	the	the	DET
gi-4938	385	2	last	last	ADJ
gi-4938	385	3	function	function	NOUN
gi-4938	385	4	f9(x	f9(x	PART
gi-4938	385	5	)	)	PUNCT
gi-4938	385	6	=	=	SYM
gi-4938	385	7	ex/	ex/	NOUN
gi-4938	385	8	tan	tan	PROPN
gi-4938	385	9	x	x	X
gi-4938	385	10	,	,	PUNCT
gi-4938	385	11	has	have	VERB
gi-4938	385	12	infinite	infinite	ADJ
gi-4938	385	13	singularities	singularity	NOUN
gi-4938	385	14	at	at	ADP
gi-4938	385	15	x	x	X
gi-4938	385	16	=	=	X
gi-4938	385	17	±kπ	±kπ	NOUN
gi-4938	385	18	(	(	PUNCT
gi-4938	385	19	total	total	ADJ
gi-4938	385	20	11	11	NUM
gi-4938	385	21	)	)	PUNCT
gi-4938	385	22	.	.	PUNCT
gi-4938	386	1	the	the	DET
gi-4938	386	2	adaptive	adaptive	ADJ
gi-4938	386	3	sampling	sample	VERB
gi-4938	386	4	procedure	procedure	NOUN
gi-4938	386	5	with	with	ADP
gi-4938	386	6	the	the	DET
gi-4938	386	7	recursion	recursion	NOUN
gi-4938	386	8	depth	depth	NOUN
gi-4938	386	9	d	d	NOUN
gi-4938	386	10	=	=	SYM
gi-4938	386	11	6	6	NUM
gi-4938	386	12	creates	create	VERB
gi-4938	386	13	1109	1109	NUM
gi-4938	386	14	points	point	NOUN
gi-4938	386	15	in	in	ADP
gi-4938	386	16	10	10	NUM
gi-4938	386	17	new	new	ADJ
gi-4938	386	18	intervals	interval	NOUN
gi-4938	386	19	ωg	ωg	PUNCT
gi-4938	386	20	1	1	NUM
gi-4938	386	21	=	=	SYM
gi-4938	387	1	[	[	X
gi-4938	387	2	−15.708,−12.567	−15.708,−12.567	PROPN
gi-4938	387	3	]	]	PUNCT
gi-4938	387	4	,	,	PUNCT
gi-4938	387	5	ωg	ωg	X
gi-4938	387	6	2	2	NUM
gi-4938	387	7	=	=	SYM
gi-4938	388	1	[	[	X
gi-4938	388	2	−12.566,−9.425	−12.566,−9.425	X
gi-4938	388	3	]	]	X
gi-4938	388	4	,	,	PUNCT
gi-4938	388	5	ωg	ωg	ADP
gi-4938	388	6	3	3	NUM
gi-4938	388	7	=	=	SYM
gi-4938	389	1	[	[	X
gi-4938	389	2	−9.425,−6.283	−9.425,−6.283	X
gi-4938	389	3	]	]	PUNCT
gi-4938	389	4	,	,	PUNCT
gi-4938	389	5	ωg	ωg	ADP
gi-4938	389	6	4	4	NUM
gi-4938	389	7	=	=	SYM
gi-4938	390	1	[	[	X
gi-4938	390	2	−6.2837,−3.142	−6.2837,−3.142	X
gi-4938	390	3	]	]	X
gi-4938	390	4	,	,	PUNCT
gi-4938	390	5	ωg	ωg	X
gi-4938	390	6	5	5	NUM
gi-4938	390	7	=	=	SYM
gi-4938	391	1	[	[	X
gi-4938	391	2	−3.141,−0.001	−3.141,−0.001	X
gi-4938	391	3	]	]	PUNCT
gi-4938	391	4	,	,	PUNCT
gi-4938	391	5	ωg	ωg	ADP
gi-4938	391	6	6	6	NUM
gi-4938	391	7	=	=	SYM
gi-4938	392	1	[	[	X
gi-4938	392	2	0.001	0.001	NUM
gi-4938	392	3	,	,	PUNCT
gi-4938	392	4	3.119	3.119	NUM
gi-4938	392	5	]	]	PUNCT
gi-4938	392	6	,	,	PUNCT
gi-4938	392	7	ωg	ωg	X
gi-4938	392	8	7	7	NUM
gi-4938	392	9	=	=	PUNCT
gi-4938	393	1	[	[	X
gi-4938	393	2	3.165	3.165	NUM
gi-4938	393	3	,	,	PUNCT
gi-4938	393	4	5.925	5.925	NUM
gi-4938	393	5	]	]	PUNCT
gi-4938	393	6	,	,	PUNCT
gi-4938	393	7	ωg	ωg	X
gi-4938	393	8	8	8	NUM
gi-4938	393	9	=	=	PUNCT
gi-4938	394	1	[	[	X
gi-4938	394	2	7.224	7.224	NUM
gi-4938	394	3	,	,	PUNCT
gi-4938	394	4	8.138	8.138	NUM
gi-4938	394	5	]	]	PUNCT
gi-4938	394	6	,	,	PUNCT
gi-4938	394	7	ωg	ωg	ADP
gi-4938	394	8	9	9	NUM
gi-4938	394	9	=	=	SYM
gi-4938	395	1	[	[	X
gi-4938	395	2	10.979	10.979	NUM
gi-4938	395	3	,	,	PUNCT
gi-4938	395	4	11.012	11.012	NUM
gi-4938	395	5	]	]	PUNCT
gi-4938	395	6	,	,	PUNCT
gi-4938	395	7	ωg	ωg	ADP
gi-4938	395	8	10	10	NUM
gi-4938	395	9	=	=	PUNCT
gi-4938	396	1	[	[	X
gi-4938	396	2	14.137	14.137	NUM
gi-4938	396	3	,	,	PUNCT
gi-4938	396	4	14.138	14.138	NUM
gi-4938	396	5	]	]	PUNCT
gi-4938	396	6	,	,	PUNCT
gi-4938	396	7	with	with	ADP
gi-4938	396	8	s	s	NOUN
gi-4938	396	9	=	=	SYM
gi-4938	396	10	10	10	NUM
gi-4938	396	11	splits	split	VERB
gi-4938	396	12	.	.	PUNCT
gi-4938	397	1	the	the	DET
gi-4938	397	2	polygonal	polygonal	ADJ
gi-4938	397	3	approximations	approximation	NOUN
gi-4938	397	4	of	of	ADP
gi-4938	397	5	all	all	DET
gi-4938	397	6	analyzed	analyze	VERB
gi-4938	397	7	functions	function	NOUN
gi-4938	397	8	can	can	AUX
gi-4938	397	9	be	be	AUX
gi-4938	397	10	found	find	VERB
gi-4938	397	11	in	in	ADP
gi-4938	397	12	fig	fig	NOUN
gi-4938	397	13	.	.	PUNCT
gi-4938	398	1	5.1	5.1	NUM
gi-4938	398	2	.	.	PUNCT
gi-4938	399	1	it	it	PRON
gi-4938	399	2	is	be	AUX
gi-4938	399	3	evident	evident	ADJ
gi-4938	399	4	that	that	SCONJ
gi-4938	399	5	their	their	PRON
gi-4938	399	6	courses	course	NOUN
gi-4938	399	7	have	have	AUX
gi-4938	399	8	been	be	AUX
gi-4938	399	9	estimated	estimate	VERB
gi-4938	399	10	correctly	correctly	ADV
gi-4938	399	11	.	.	PUNCT
gi-4938	400	1	however	however	ADV
gi-4938	400	2	,	,	PUNCT
gi-4938	400	3	for	for	ADP
gi-4938	400	4	some	some	DET
gi-4938	400	5	functions	function	NOUN
gi-4938	400	6	,	,	PUNCT
gi-4938	400	7	the	the	DET
gi-4938	400	8	proposed	propose	VERB
gi-4938	400	9	combined	combined	ADJ
gi-4938	400	10	sampling	sampling	NOUN
gi-4938	400	11	algorithm	algorithm	NOUN
gi-4938	400	12	brings	bring	VERB
gi-4938	400	13	less	less	ADV
gi-4938	400	14	redundant	redundant	ADJ
gi-4938	400	15	representation	representation	NOUN
gi-4938	400	16	(	(	PUNCT
gi-4938	400	17	f5	f5	NOUN
gi-4938	400	18	)	)	PUNCT
gi-4938	400	19	.	.	PUNCT
gi-4938	401	1	in	in	ADP
gi-4938	401	2	general	general	ADJ
gi-4938	401	3	,	,	PUNCT
gi-4938	401	4	this	this	DET
gi-4938	401	5	method	method	NOUN
gi-4938	401	6	can	can	AUX
gi-4938	401	7	not	not	PART
gi-4938	401	8	compete	compete	VERB
gi-4938	401	9	with	with	ADP
gi-4938	401	10	the	the	DET
gi-4938	401	11	well	well	ADV
gi-4938	401	12	-	-	PUNCT
gi-4938	401	13	known	know	VERB
gi-4938	401	14	high	high	ADJ
gi-4938	401	15	-	-	PUNCT
gi-4938	401	16	end	end	NOUN
gi-4938	401	17	solutions	solution	NOUN
gi-4938	401	18	(	(	PUNCT
gi-4938	401	19	mathematica	mathematica	PROPN
gi-4938	401	20	)	)	PUNCT
gi-4938	401	21	involving	involve	VERB
gi-4938	401	22	the	the	DET
gi-4938	401	23	robust	robust	ADJ
gi-4938	401	24	numerical	numerical	ADJ
gi-4938	401	25	techniques	technique	NOUN
gi-4938	401	26	,	,	PUNCT
gi-4938	401	27	but	but	CCONJ
gi-4938	401	28	it	it	PRON
gi-4938	401	29	may	may	AUX
gi-4938	401	30	provide	provide	VERB
gi-4938	401	31	a	a	DET
gi-4938	401	32	reasonable	reasonable	ADJ
gi-4938	401	33	representation	representation	NOUN
gi-4938	401	34	of	of	ADP
gi-4938	401	35	functions	function	NOUN
gi-4938	401	36	in	in	ADP
gi-4938	401	37	technical	technical	ADJ
gi-4938	401	38	computing	computing	NOUN
gi-4938	401	39	.	.	PUNCT
gi-4938	402	1	6.2	6.2	NUM
gi-4938	402	2	.	.	PUNCT
gi-4938	402	3	comparison	comparison	NOUN
gi-4938	402	4	with	with	ADP
gi-4938	402	5	other	other	ADJ
gi-4938	402	6	systems	system	NOUN
gi-4938	402	7	for	for	ADP
gi-4938	402	8	comparison	comparison	NOUN
gi-4938	402	9	,	,	PUNCT
gi-4938	402	10	the	the	DET
gi-4938	402	11	functions	function	NOUN
gi-4938	402	12	will	will	AUX
gi-4938	402	13	be	be	AUX
gi-4938	402	14	plotted	plot	VERB
gi-4938	402	15	in	in	ADP
gi-4938	402	16	two	two	NUM
gi-4938	402	17	well	well	ADV
gi-4938	402	18	-	-	PUNCT
gi-4938	402	19	known	know	VERB
gi-4938	402	20	systems	system	NOUN
gi-4938	402	21	.	.	PUNCT
gi-4938	403	1	while	while	SCONJ
gi-4938	403	2	the	the	DET
gi-4938	403	3	opensource	opensource	NOUN
gi-4938	403	4	software	software	NOUN
gi-4938	403	5	is	be	AUX
gi-4938	403	6	represented	represent	VERB
gi-4938	403	7	by	by	ADP
gi-4938	403	8	octave	octave	NOUN
gi-4938	403	9	(	(	PUNCT
gi-4938	403	10	v.	v.	ADP
gi-4938	403	11	4.4	4.4	NUM
gi-4938	403	12	)	)	PUNCT
gi-4938	403	13	,	,	PUNCT
gi-4938	403	14	the	the	DET
gi-4938	403	15	commercial	commercial	ADJ
gi-4938	403	16	software	software	NOUN
gi-4938	403	17	by	by	ADP
gi-4938	403	18	wolfram	wolfram	PROPN
gi-4938	403	19	mathematica	mathematica	PROPN
gi-4938	403	20	(	(	PUNCT
gi-4938	403	21	v.	v.	ADP
gi-4938	403	22	11	11	NUM
gi-4938	403	23	)	)	PUNCT
gi-4938	403	24	.	.	PUNCT
gi-4938	404	1	geoinformatics	geoinformatic	NOUN
gi-4938	404	2	fce	fce	VERB
gi-4938	404	3	ctu	ctu	NOUN
gi-4938	404	4	17(2	17(2	NUM
gi-4938	404	5	)	)	PUNCT
gi-4938	404	6	,	,	PUNCT
gi-4938	404	7	2018	2018	NUM
gi-4938	404	8	22	22	NUM
gi-4938	404	9	t.	t.	NOUN
gi-4938	404	10	bayer	bayer	NOUN
gi-4938	404	11	:	:	PUNCT
gi-4938	404	12	efficient	efficient	ADJ
gi-4938	404	13	plotting	plot	VERB
gi-4938	404	14	the	the	DET
gi-4938	404	15	functions	function	NOUN
gi-4938	404	16	with	with	ADP
gi-4938	404	17	discontinuities	discontinuity	NOUN
gi-4938	404	18	x	x	X
gi-4938	405	1	f	f	NOUN
gi-4938	405	2	x	x	PUNCT
gi-4938	405	3	x	x	X
gi-4938	405	4	f	f	NOUN
gi-4938	405	5	x	x	PUNCT
gi-4938	405	6	x	x	X
gi-4938	405	7	f	f	NOUN
gi-4938	405	8	x	x	PUNCT
gi-4938	405	9	x	x	X
gi-4938	405	10	f	f	NOUN
gi-4938	405	11	x	x	PUNCT
gi-4938	405	12	x	x	X
gi-4938	405	13	f	f	NOUN
gi-4938	405	14	x	x	PUNCT
gi-4938	405	15	x	x	X
gi-4938	405	16	f	f	NOUN
gi-4938	405	17	x	x	PUNCT
gi-4938	405	18	x	x	X
gi-4938	405	19	f	f	NOUN
gi-4938	405	20	x	x	PUNCT
gi-4938	405	21	x	x	X
gi-4938	405	22	f	f	NOUN
gi-4938	405	23	x	x	PUNCT
gi-4938	405	24	x	x	SYM
gi-4938	405	25	f	f	X
gi-4938	405	26	x	x	SYM
gi-4938	405	27	f	f	PROPN
gi-4938	405	28	1	1	NUM
gi-4938	405	29	(	(	PUNCT
gi-4938	405	30	x	x	NOUN
gi-4938	405	31	)	)	PUNCT
gi-4938	405	32	f	f	PROPN
gi-4938	405	33	2	2	NUM
gi-4938	405	34	(	(	PUNCT
gi-4938	405	35	x	x	NOUN
gi-4938	405	36	)	)	PUNCT
gi-4938	405	37	f	f	PROPN
gi-4938	405	38	3	3	NUM
gi-4938	405	39	(	(	PUNCT
gi-4938	405	40	x	x	NOUN
gi-4938	405	41	)	)	PUNCT
gi-4938	405	42	f	f	PROPN
gi-4938	405	43	4	4	NUM
gi-4938	405	44	(	(	PUNCT
gi-4938	405	45	x	x	NOUN
gi-4938	405	46	)	)	PUNCT
gi-4938	405	47	f	f	NOUN
gi-4938	405	48	5	5	NUM
gi-4938	405	49	(	(	PUNCT
gi-4938	405	50	x	x	NOUN
gi-4938	405	51	)	)	PUNCT
gi-4938	405	52	f	f	PROPN
gi-4938	405	53	6	6	NUM
gi-4938	405	54	(	(	PUNCT
gi-4938	405	55	x	x	NOUN
gi-4938	405	56	)	)	PUNCT
gi-4938	405	57	f	f	PROPN
gi-4938	405	58	7	7	NUM
gi-4938	405	59	(	(	PUNCT
gi-4938	405	60	x	x	NOUN
gi-4938	405	61	)	)	PUNCT
gi-4938	405	62	f	f	PROPN
gi-4938	405	63	8	8	NUM
gi-4938	405	64	(	(	PUNCT
gi-4938	405	65	x	x	NOUN
gi-4938	405	66	)	)	PUNCT
gi-4938	405	67	f	f	NOUN
gi-4938	405	68	9	9	NUM
gi-4938	405	69	(	(	PUNCT
gi-4938	405	70	x	x	NOUN
gi-4938	405	71	)	)	PUNCT
gi-4938	405	72	figure	figure	VERB
gi-4938	405	73	6.1	6.1	NUM
gi-4938	405	74	:	:	PUNCT
gi-4938	405	75	functions	function	NOUN
gi-4938	405	76	f1(x	f1(x	NUM
gi-4938	405	77	)	)	PUNCT
gi-4938	405	78	,	,	PUNCT
gi-4938	405	79	...	...	PUNCT
gi-4938	405	80	,	,	PUNCT
gi-4938	405	81	f9(x	f9(x	X
gi-4938	405	82	)	)	PUNCT
gi-4938	405	83	plotted	plot	VERB
gi-4938	405	84	in	in	ADP
gi-4938	405	85	the	the	DET
gi-4938	405	86	wolfram	wolfram	PROPN
gi-4938	405	87	mathematica	mathematica	PROPN
gi-4938	405	88	software	software	PROPN
gi-4938	405	89	,	,	PUNCT
gi-4938	405	90	v.	v.	ADP
gi-4938	405	91	11	11	NUM
gi-4938	405	92	.	.	PUNCT
gi-4938	406	1	octave	octave	NOUN
gi-4938	406	2	.	.	PUNCT
gi-4938	407	1	unfortunately	unfortunately	ADV
gi-4938	407	2	,	,	PUNCT
gi-4938	407	3	the	the	DET
gi-4938	407	4	open	open	ADJ
gi-4938	407	5	-	-	PUNCT
gi-4938	407	6	source	source	NOUN
gi-4938	407	7	software	software	NOUN
gi-4938	407	8	octave	octave	NOUN
gi-4938	407	9	(	(	PUNCT
gi-4938	407	10	v.	v.	ADP
gi-4938	407	11	4.4	4.4	NUM
gi-4938	407	12	)	)	PUNCT
gi-4938	407	13	does	do	AUX
gi-4938	407	14	not	not	PART
gi-4938	407	15	support	support	VERB
gi-4938	407	16	a	a	DET
gi-4938	407	17	correct	correct	ADJ
gi-4938	407	18	plotting	plot	VERB
gi-4938	407	19	the	the	DET
gi-4938	407	20	functions	function	NOUN
gi-4938	407	21	involving	involve	VERB
gi-4938	407	22	discontinuities	discontinuity	NOUN
gi-4938	407	23	.	.	PUNCT
gi-4938	408	1	the	the	DET
gi-4938	408	2	main	main	ADJ
gi-4938	408	3	idea	idea	NOUN
gi-4938	408	4	of	of	ADP
gi-4938	408	5	our	our	PRON
gi-4938	408	6	solution	solution	NOUN
gi-4938	408	7	is	be	AUX
gi-4938	408	8	based	base	VERB
gi-4938	408	9	on	on	ADP
gi-4938	408	10	splitting	split	VERB
gi-4938	408	11	ω	ω	PROPN
gi-4938	408	12	to	to	ADP
gi-4938	408	13	the	the	DET
gi-4938	408	14	subintervals	subinterval	NOUN
gi-4938	408	15	ωg	ωg	VERB
gi-4938	408	16	by	by	ADP
gi-4938	408	17	putting	put	VERB
gi-4938	408	18	nan	nan	PROPN
gi-4938	408	19	numbers	number	NOUN
gi-4938	408	20	between	between	ADP
gi-4938	408	21	ωg	ωg	PROPN
gi-4938	408	22	,	,	PUNCT
gi-4938	408	23	where	where	SCONJ
gi-4938	408	24	the	the	DET
gi-4938	408	25	function	function	NOUN
gi-4938	408	26	is	be	AUX
gi-4938	408	27	undefined	undefined	ADJ
gi-4938	408	28	.	.	PUNCT
gi-4938	409	1	the	the	DET
gi-4938	409	2	discontinuities	discontinuity	NOUN
gi-4938	409	3	are	be	AUX
gi-4938	409	4	detected	detect	VERB
gi-4938	409	5	by	by	ADP
gi-4938	409	6	the	the	DET
gi-4938	409	7	lr	lr	NOUN
gi-4938	409	8	criterion	criterion	NOUN
gi-4938	409	9	given	give	VERB
gi-4938	409	10	by	by	ADP
gi-4938	409	11	eq	eq	PROPN
gi-4938	409	12	.	.	PROPN
gi-4938	409	13	4.1	4.1	NUM
gi-4938	409	14	.	.	PUNCT
gi-4938	410	1	from	from	ADP
gi-4938	410	2	a	a	DET
gi-4938	410	3	mathematic	mathematic	ADJ
gi-4938	410	4	point	point	NOUN
gi-4938	410	5	of	of	ADP
gi-4938	410	6	view	view	NOUN
gi-4938	410	7	,	,	PUNCT
gi-4938	410	8	more	more	ADJ
gi-4938	410	9	characteristics	characteristic	NOUN
gi-4938	410	10	of	of	ADP
gi-4938	410	11	the	the	DET
gi-4938	410	12	function	function	NOUN
gi-4938	410	13	behavior	behavior	NOUN
gi-4938	410	14	need	need	VERB
gi-4938	410	15	to	to	PART
gi-4938	410	16	be	be	AUX
gi-4938	410	17	studied	study	VERB
gi-4938	410	18	(	(	PUNCT
gi-4938	410	19	first	first	ADJ
gi-4938	410	20	and	and	CCONJ
gi-4938	410	21	second	second	ADJ
gi-4938	410	22	derivatives	derivative	NOUN
gi-4938	410	23	,	,	PUNCT
gi-4938	410	24	asymptotes	asymptote	NOUN
gi-4938	410	25	,	,	PUNCT
gi-4938	410	26	local	local	ADJ
gi-4938	410	27	/	/	SYM
gi-4938	410	28	global	global	ADJ
gi-4938	410	29	minima	minima	PROPN
gi-4938	410	30	,	,	PUNCT
gi-4938	410	31	...	...	PUNCT
gi-4938	410	32	)	)	PUNCT
gi-4938	410	33	,	,	PUNCT
gi-4938	410	34	but	but	CCONJ
gi-4938	410	35	this	this	PRON
gi-4938	410	36	is	be	AUX
gi-4938	410	37	outside	outside	ADP
gi-4938	410	38	the	the	DET
gi-4938	410	39	scope	scope	NOUN
gi-4938	410	40	of	of	ADP
gi-4938	410	41	the	the	DET
gi-4938	410	42	paper	paper	NOUN
gi-4938	410	43	.	.	PUNCT
gi-4938	411	1	the	the	DET
gi-4938	411	2	script	script	NOUN
gi-4938	411	3	can	can	AUX
gi-4938	411	4	be	be	AUX
gi-4938	411	5	found	find	VERB
gi-4938	411	6	in	in	ADP
gi-4938	411	7	alg	alg	PROPN
gi-4938	411	8	.	.	PUNCT
gi-4938	412	1	5	5	NUM
gi-4938	412	2	.	.	PUNCT
gi-4938	413	1	the	the	DET
gi-4938	413	2	previous	previous	ADJ
gi-4938	413	3	results	result	NOUN
gi-4938	413	4	set	set	VERB
gi-4938	413	5	the	the	DET
gi-4938	413	6	numerical	numerical	ADJ
gi-4938	413	7	characteristics	characteristic	NOUN
gi-4938	413	8	:	:	PUNCT
gi-4938	414	1	ω	ω	NOUN
gi-4938	414	2	=	=	PUNCT
gi-4938	415	1	[	[	X
gi-4938	415	2	−5π	−5π	PROPN
gi-4938	415	3	,	,	PUNCT
gi-4938	415	4	5π	5π	NUM
gi-4938	415	5	]	]	PUNCT
gi-4938	415	6	,	,	PUNCT
gi-4938	415	7	ε	ε	PROPN
gi-4938	415	8	=	=	SYM
gi-4938	415	9	0.001	0.001	NUM
gi-4938	415	10	,	,	PUNCT
gi-4938	415	11	lr	lr	X
gi-4938	415	12	=	=	PUNCT
gi-4938	415	13	0.8	0.8	NUM
gi-4938	415	14	,	,	PUNCT
gi-4938	415	15	sampling	sample	VERB
gi-4938	415	16	step	step	NOUN
gi-4938	415	17	h	h	NOUN
gi-4938	416	1	=	=	NOUN
gi-4938	416	2	0.001	0.001	NUM
gi-4938	416	3	.	.	PUNCT
gi-4938	417	1	a	a	DET
gi-4938	417	2	curve	curve	NOUN
gi-4938	417	3	is	be	AUX
gi-4938	417	4	sampled	sample	VERB
gi-4938	417	5	uniformly	uniformly	ADV
gi-4938	417	6	by	by	ADP
gi-4938	417	7	10000π	10000π	NOUN
gi-4938	417	8	(	(	PUNCT
gi-4938	417	9	approx	approx	PROPN
gi-4938	417	10	.	.	PUNCT
gi-4938	418	1	31	31	NUM
gi-4938	418	2	000	000	NUM
gi-4938	418	3	)	)	PUNCT
gi-4938	418	4	points	point	NOUN
gi-4938	418	5	;	;	PUNCT
gi-4938	418	6	this	this	DET
gi-4938	418	7	“	"	PUNCT
gi-4938	418	8	relatively	relatively	ADV
gi-4938	418	9	large	large	ADJ
gi-4938	418	10	”	"	PUNCT
gi-4938	418	11	value	value	NOUN
gi-4938	418	12	has	have	AUX
gi-4938	418	13	been	be	AUX
gi-4938	418	14	set	set	VERB
gi-4938	418	15	empirically	empirically	ADV
gi-4938	418	16	.	.	PUNCT
gi-4938	419	1	in	in	ADP
gi-4938	419	2	general	general	ADJ
gi-4938	419	3	,	,	PUNCT
gi-4938	419	4	the	the	DET
gi-4938	419	5	obtained	obtain	VERB
gi-4938	419	6	results	result	NOUN
gi-4938	419	7	are	be	AUX
gi-4938	419	8	analogous	analogous	ADJ
gi-4938	419	9	to	to	ADP
gi-4938	419	10	the	the	DET
gi-4938	419	11	proposed	propose	VERB
gi-4938	419	12	method	method	NOUN
gi-4938	419	13	.	.	PUNCT
gi-4938	420	1	unfortunately	unfortunately	ADV
gi-4938	420	2	,	,	PUNCT
gi-4938	420	3	the	the	DET
gi-4938	420	4	algorithm	algorithm	NOUN
gi-4938	420	5	is	be	AUX
gi-4938	420	6	sensitive	sensitive	ADJ
gi-4938	420	7	to	to	ADP
gi-4938	420	8	the	the	DET
gi-4938	420	9	values	value	NOUN
gi-4938	420	10	of	of	ADP
gi-4938	420	11	h	h	NOUN
gi-4938	420	12	,	,	PUNCT
gi-4938	420	13	and	and	CCONJ
gi-4938	420	14	lr	lr	NOUN
gi-4938	420	15	.	.	PROPN
gi-4938	420	16	for	for	ADP
gi-4938	420	17	the	the	DET
gi-4938	420	18	larger	large	ADJ
gi-4938	420	19	values	value	NOUN
gi-4938	420	20	of	of	ADP
gi-4938	420	21	h	h	NOUN
gi-4938	420	22	,	,	PUNCT
gi-4938	420	23	h	h	NOUN
gi-4938	421	1	=	=	NOUN
gi-4938	421	2	0.01	0.01	NUM
gi-4938	421	3	,	,	PUNCT
gi-4938	421	4	only	only	ADV
gi-4938	421	5	a	a	DET
gi-4938	421	6	subset	subset	NOUN
gi-4938	421	7	of	of	ADP
gi-4938	421	8	functions	function	NOUN
gi-4938	421	9	is	be	AUX
gi-4938	421	10	sampled	sample	VERB
gi-4938	421	11	geoinformatics	geoinformatic	NOUN
gi-4938	421	12	fce	fce	VERB
gi-4938	421	13	ctu	ctu	NOUN
gi-4938	421	14	17(2	17(2	NUM
gi-4938	421	15	)	)	PUNCT
gi-4938	421	16	,	,	PUNCT
gi-4938	421	17	2018	2018	NUM
gi-4938	421	18	23	23	NUM
gi-4938	421	19	t.	t.	NOUN
gi-4938	421	20	bayer	bayer	NOUN
gi-4938	421	21	:	:	PUNCT
gi-4938	421	22	efficient	efficient	ADJ
gi-4938	421	23	plotting	plot	VERB
gi-4938	421	24	the	the	DET
gi-4938	421	25	functions	function	NOUN
gi-4938	421	26	with	with	ADP
gi-4938	421	27	discontinuities	discontinuity	NOUN
gi-4938	421	28	table	table	NOUN
gi-4938	421	29	2	2	NUM
gi-4938	421	30	:	:	PUNCT
gi-4938	421	31	uniform	uniform	NOUN
gi-4938	421	32	and	and	CCONJ
gi-4938	421	33	combined	combined	ADJ
gi-4938	421	34	sampling	sampling	NOUN
gi-4938	421	35	of	of	ADP
gi-4938	421	36	the	the	DET
gi-4938	421	37	graticules	graticule	NOUN
gi-4938	421	38	of	of	ADP
gi-4938	421	39	the	the	DET
gi-4938	421	40	equal	equal	ADJ
gi-4938	421	41	area	area	NOUN
gi-4938	421	42	cylindrical	cylindrical	ADJ
gi-4938	421	43	,	,	PUNCT
gi-4938	421	44	conic	conic	ADJ
gi-4938	421	45	,	,	PUNCT
gi-4938	421	46	azimuthal	azimuthal	NOUN
gi-4938	421	47	and	and	CCONJ
gi-4938	421	48	werner	werner	NOUN
gi-4938	421	49	-	-	PUNCT
gi-4938	421	50	staab	staab	NOUN
gi-4938	421	51	projections	projection	NOUN
gi-4938	421	52	using	use	VERB
gi-4938	421	53	combined	combined	ADJ
gi-4938	421	54	sampling	sampling	NOUN
gi-4938	421	55	.	.	PUNCT
gi-4938	422	1	the	the	DET
gi-4938	422	2	quantitative	quantitative	ADJ
gi-4938	422	3	parameters	parameter	NOUN
gi-4938	422	4	are	be	AUX
gi-4938	422	5	presented	present	VERB
gi-4938	422	6	.	.	PUNCT
gi-4938	423	1	projection	projection	NOUN
gi-4938	423	2	sampling	sample	VERB
gi-4938	423	3	nmer	nmer	ADJ
gi-4938	423	4	npar	npar	NOUN
gi-4938	424	1	αm	αm	PROPN
gi-4938	424	2	αp	αp	NOUN
gi-4938	424	3	α̃m	α̃m	VERB
gi-4938	424	4	α̃p	α̃p	PRON
gi-4938	424	5	equal	equal	ADJ
gi-4938	424	6	area	area	NOUN
gi-4938	424	7	cylindrical	cylindrical	ADJ
gi-4938	424	8	uniform	uniform	NOUN
gi-4938	424	9	1443	1443	NUM
gi-4938	424	10	1406	1406	NUM
gi-4938	424	11	0.00	0.00	NUM
gi-4938	424	12	0.00	0.00	NUM
gi-4938	424	13	0.00	0.00	NUM
gi-4938	424	14	0.00	0.00	NUM
gi-4938	424	15	combined	combine	VERB
gi-4938	424	16	195	195	NUM
gi-4938	424	17	190	190	NUM
gi-4938	424	18	0.00	0.00	NUM
gi-4938	424	19	0.00	0.00	NUM
gi-4938	424	20	0.00	0.00	NUM
gi-4938	424	21	0.00	0.00	NUM
gi-4938	424	22	equal	equal	ADJ
gi-4938	424	23	area	area	NOUN
gi-4938	424	24	conic	conic	ADJ
gi-4938	424	25	uniform	uniform	NOUN
gi-4938	424	26	1443	1443	NUM
gi-4938	424	27	1406	1406	NUM
gi-4938	424	28	0.00	0.00	NUM
gi-4938	424	29	2.20	2.20	NUM
gi-4938	424	30	0.00	0.00	NUM
gi-4938	424	31	2.20	2.20	NUM
gi-4938	424	32	combined	combine	VERB
gi-4938	424	33	195	195	NUM
gi-4938	424	34	1612	1612	NUM
gi-4938	424	35	0.00	0.00	NUM
gi-4938	424	36	5.01	5.01	NUM
gi-4938	424	37	0.00	0.00	NUM
gi-4938	424	38	1.89	1.89	NUM
gi-4938	424	39	equal	equal	ADJ
gi-4938	424	40	area	area	NOUN
gi-4938	424	41	azimuthal	azimuthal	NOUN
gi-4938	424	42	uniform	uniform	NOUN
gi-4938	424	43	1443	1443	NUM
gi-4938	424	44	1406	1406	NUM
gi-4938	424	45	0.00	0.00	NUM
gi-4938	424	46	5.00	5.00	NUM
gi-4938	424	47	0.00	0.00	NUM
gi-4938	424	48	5.00	5.00	NUM
gi-4938	424	49	combined	combine	VERB
gi-4938	424	50	195	195	NUM
gi-4938	424	51	2476	2476	NUM
gi-4938	424	52	0.00	0.00	NUM
gi-4938	424	53	4.74	4.74	NUM
gi-4938	424	54	0.00	0.00	NUM
gi-4938	424	55	2.81	2.81	NUM
gi-4938	424	56	werner	werner	NOUN
gi-4938	424	57	-	-	PUNCT
gi-4938	424	58	staab	staab	NOUN
gi-4938	424	59	uniform	uniform	NOUN
gi-4938	424	60	1443	1443	NUM
gi-4938	424	61	1406	1406	NUM
gi-4938	424	62	9.27	9.27	NUM
gi-4938	424	63	5.00	5.00	NUM
gi-4938	424	64	3.86	3.86	NUM
gi-4938	424	65	2.93	2.93	NUM
gi-4938	424	66	combined	combine	VERB
gi-4938	424	67	2334	2334	NUM
gi-4938	424	68	1747	1747	NUM
gi-4938	424	69	4.99	4.99	NUM
gi-4938	424	70	5.00	5.00	NUM
gi-4938	424	71	2.36	2.36	NUM
gi-4938	424	72	2.34	2.34	NUM
gi-4938	424	73	correctly	correctly	ADV
gi-4938	424	74	.	.	PUNCT
gi-4938	425	1	mathematica	mathematica	PROPN
gi-4938	425	2	.	.	PUNCT
gi-4938	426	1	wolfram	wolfram	PROPN
gi-4938	426	2	mathematica	mathematica	PROPN
gi-4938	426	3	v.	v.	PROPN
gi-4938	426	4	11	11	NUM
gi-4938	426	5	,	,	PUNCT
gi-4938	426	6	the	the	DET
gi-4938	426	7	well	well	ADV
gi-4938	426	8	-	-	PUNCT
gi-4938	426	9	known	know	VERB
gi-4938	426	10	system	system	NOUN
gi-4938	426	11	for	for	ADP
gi-4938	426	12	technical	technical	ADJ
gi-4938	426	13	computing	computing	NOUN
gi-4938	426	14	,	,	PUNCT
gi-4938	426	15	developed	develop	VERB
gi-4938	426	16	for	for	ADP
gi-4938	426	17	three	three	NUM
gi-4938	426	18	decades	decade	NOUN
gi-4938	426	19	,	,	PUNCT
gi-4938	426	20	supports	support	VERB
gi-4938	426	21	automatic	automatic	ADJ
gi-4938	426	22	plotting	plot	VERB
gi-4938	426	23	the	the	DET
gi-4938	426	24	functions	function	NOUN
gi-4938	426	25	with	with	ADP
gi-4938	426	26	the	the	DET
gi-4938	426	27	discontinuities	discontinuity	NOUN
gi-4938	426	28	.	.	PUNCT
gi-4938	427	1	the	the	DET
gi-4938	427	2	script	script	NOUN
gi-4938	427	3	has	have	VERB
gi-4938	427	4	a	a	DET
gi-4938	427	5	straightforward	straightforward	ADJ
gi-4938	427	6	form	form	NOUN
gi-4938	427	7	;	;	PUNCT
gi-4938	427	8	see	see	VERB
gi-4938	427	9	alg	alg	PROPN
gi-4938	427	10	.	.	PROPN
gi-4938	428	1	6	6	NUM
gi-4938	428	2	.	.	X
gi-4938	428	3	for	for	ADP
gi-4938	428	4	the	the	DET
gi-4938	428	5	functions	function	NOUN
gi-4938	428	6	f1(x	f1(x	CCONJ
gi-4938	428	7	)	)	PUNCT
gi-4938	428	8	,	,	PUNCT
gi-4938	428	9	...	...	PUNCT
gi-4938	428	10	,	,	PUNCT
gi-4938	428	11	f8(x	f8(x	X
gi-4938	428	12	)	)	PUNCT
gi-4938	428	13	the	the	DET
gi-4938	428	14	analogous	analogous	ADJ
gi-4938	428	15	discontinuities	discontinuity	NOUN
gi-4938	428	16	have	have	AUX
gi-4938	428	17	been	be	AUX
gi-4938	428	18	detected	detect	VERB
gi-4938	428	19	.	.	PUNCT
gi-4938	429	1	unfortunately	unfortunately	ADV
gi-4938	429	2	,	,	PUNCT
gi-4938	429	3	for	for	ADP
gi-4938	429	4	f9	f9	PROPN
gi-4938	429	5	,	,	PUNCT
gi-4938	429	6	the	the	DET
gi-4938	429	7	asymptote	asymptote	ADJ
gi-4938	429	8	x	x	X
gi-4938	430	1	=	=	SYM
gi-4938	430	2	−3π	−3π	NOUN
gi-4938	430	3	has	have	AUX
gi-4938	430	4	not	not	PART
gi-4938	430	5	been	be	AUX
gi-4938	430	6	recognized	recognize	VERB
gi-4938	430	7	;	;	PUNCT
gi-4938	430	8	see	see	VERB
gi-4938	430	9	fig	fig	NOUN
gi-4938	430	10	.	.	PUNCT
gi-4938	431	1	6.1	6.1	NUM
gi-4938	431	2	.	.	PUNCT
gi-4938	432	1	moreover	moreover	ADV
gi-4938	432	2	,	,	PUNCT
gi-4938	432	3	the	the	DET
gi-4938	432	4	asymptote	asymptote	NOUN
gi-4938	432	5	x	x	X
gi-4938	432	6	=	=	PUNCT
gi-4938	432	7	−2π	−2π	NOUN
gi-4938	432	8	is	be	AUX
gi-4938	432	9	hard	hard	ADJ
gi-4938	432	10	to	to	PART
gi-4938	432	11	distinguish	distinguish	VERB
gi-4938	432	12	.	.	PUNCT
gi-4938	433	1	if	if	SCONJ
gi-4938	433	2	we	we	PRON
gi-4938	433	3	understand	understand	VERB
gi-4938	433	4	mathematica	mathematica	PROPN
gi-4938	433	5	as	as	ADP
gi-4938	433	6	the	the	DET
gi-4938	433	7	reference	reference	NOUN
gi-4938	433	8	software	software	NOUN
gi-4938	433	9	,	,	PUNCT
gi-4938	433	10	our	our	PRON
gi-4938	433	11	proposed	propose	VERB
gi-4938	433	12	algorithm	algorithm	NOUN
gi-4938	433	13	may	may	AUX
gi-4938	433	14	be	be	AUX
gi-4938	433	15	found	find	VERB
gi-4938	433	16	as	as	ADP
gi-4938	433	17	a	a	DET
gi-4938	433	18	simple	simple	ADJ
gi-4938	433	19	and	and	CCONJ
gi-4938	433	20	efficient	efficient	ADJ
gi-4938	433	21	tool	tool	NOUN
gi-4938	433	22	for	for	ADP
gi-4938	433	23	plotting	plot	VERB
gi-4938	433	24	a	a	DET
gi-4938	433	25	general	general	ADJ
gi-4938	433	26	function	function	NOUN
gi-4938	433	27	of	of	ADP
gi-4938	433	28	the	the	DET
gi-4938	433	29	one	one	NUM
gi-4938	433	30	variable	variable	NOUN
gi-4938	433	31	.	.	PUNCT
gi-4938	434	1	however	however	ADV
gi-4938	434	2	,	,	PUNCT
gi-4938	434	3	many	many	ADJ
gi-4938	434	4	situations	situation	NOUN
gi-4938	434	5	may	may	AUX
gi-4938	434	6	appear	appear	VERB
gi-4938	434	7	when	when	SCONJ
gi-4938	434	8	it	it	PRON
gi-4938	434	9	fails	fail	VERB
gi-4938	434	10	.	.	PUNCT
gi-4938	435	1	algorithm	algorithm	NOUN
gi-4938	435	2	6	6	NUM
gi-4938	435	3	plotting	plot	VERB
gi-4938	435	4	the	the	DET
gi-4938	435	5	function	function	NOUN
gi-4938	435	6	f9(x	f9(x	NOUN
gi-4938	435	7	)	)	PUNCT
gi-4938	435	8	involving	involve	VERB
gi-4938	435	9	the	the	DET
gi-4938	435	10	discontinuities	discontinuity	NOUN
gi-4938	435	11	in	in	ADP
gi-4938	435	12	the	the	DET
gi-4938	435	13	mathematica	mathematica	PROPN
gi-4938	435	14	v.	v.	ADP
gi-4938	435	15	11	11	NUM
gi-4938	435	16	scripting	scripting	NOUN
gi-4938	435	17	language	language	NOUN
gi-4938	435	18	.	.	PUNCT
gi-4938	436	1	xmin	xmin	NOUN
gi-4938	436	2	=	=	PROPN
gi-4938	436	3	-5*pi	-5*pi	PROPN
gi-4938	436	4	;	;	PUNCT
gi-4938	436	5	xmax	xmax	PROPN
gi-4938	436	6	=	=	SYM
gi-4938	436	7	-xmin	-xmin	PROPN
gi-4938	436	8	;	;	PUNCT
gi-4938	436	9	f[x	f[x	X
gi-4938	436	10	_	_	NOUN
gi-4938	436	11	]	]	X
gi-4938	436	12	:	:	PUNCT
gi-4938	436	13	=	=	SYM
gi-4938	436	14	exp[x]/tan[x	exp[x]/tan[x	PROPN
gi-4938	436	15	]	]	PUNCT
gi-4938	436	16	}	}	PUNCT
gi-4938	436	17	;	;	PUNCT
gi-4938	436	18	plot[f[x	plot[f[x	PROPN
gi-4938	436	19	]	]	X
gi-4938	436	20	,	,	PUNCT
gi-4938	436	21	x	x	PROPN
gi-4938	436	22	,	,	PUNCT
gi-4938	436	23	xmin	xmin	PROPN
gi-4938	436	24	,	,	PUNCT
gi-4938	436	25	xmax	xmax	PROPN
gi-4938	436	26	,	,	PUNCT
gi-4938	436	27	plotrange	plotrange	NOUN
gi-4938	436	28	-	-	PUNCT
gi-4938	436	29	>	>	X
gi-4938	436	30	xmin	xmin	PROPN
gi-4938	436	31	,	,	PUNCT
gi-4938	436	32	xmax	xmax	PROPN
gi-4938	436	33	,	,	PUNCT
gi-4938	436	34	xmin	xmin	PROPN
gi-4938	436	35	,	,	PUNCT
gi-4938	436	36	xmax	xmax	PROPN
gi-4938	436	37	,	,	PUNCT
gi-4938	436	38	axeslabel	axeslabel	PROPN
gi-4938	436	39	-	-	PUNCT
gi-4938	436	40	>	>	X
gi-4938	436	41	x	x	PROPN
gi-4938	436	42	,	,	PUNCT
gi-4938	436	43	f[x	f[x	PROPN
gi-4938	436	44	]	]	PUNCT
gi-4938	436	45	,	,	PUNCT
gi-4938	436	46	axesorigin	axesorigin	NOUN
gi-4938	436	47	-	-	PUNCT
gi-4938	436	48	>	>	X
gi-4938	436	49	0	0	NUM
gi-4938	436	50	,	,	PUNCT
gi-4938	436	51	0	0	NUM
gi-4938	436	52	,	,	PUNCT
gi-4938	436	53	aspectratio	aspectratio	ADP
gi-4938	436	54	-	-	PUNCT
gi-4938	436	55	>	>	X
gi-4938	436	56	automatic	automatic	ADJ
gi-4938	436	57	,	,	PUNCT
gi-4938	436	58	plotstyle	plotstyle	NOUN
gi-4938	436	59	-	-	PUNCT
gi-4938	436	60	>	>	X
gi-4938	436	61	red	red	PROPN
gi-4938	436	62	]	]	X
gi-4938	436	63	;	;	PUNCT
gi-4938	436	64	6.3	6.3	NUM
gi-4938	436	65	.	.	PUNCT
gi-4938	437	1	construction	construction	NOUN
gi-4938	437	2	of	of	ADP
gi-4938	437	3	the	the	DET
gi-4938	437	4	map	map	NOUN
gi-4938	437	5	projection	projection	NOUN
gi-4938	437	6	graticule	graticule	NOUN
gi-4938	437	7	in	in	ADP
gi-4938	437	8	the	the	DET
gi-4938	437	9	last	last	ADJ
gi-4938	437	10	test	test	NOUN
gi-4938	437	11	,	,	PUNCT
gi-4938	437	12	where	where	SCONJ
gi-4938	437	13	the	the	DET
gi-4938	437	14	graticules	graticule	NOUN
gi-4938	437	15	of	of	ADP
gi-4938	437	16	several	several	ADJ
gi-4938	437	17	map	map	NOUN
gi-4938	437	18	projections	projection	NOUN
gi-4938	437	19	are	be	AUX
gi-4938	437	20	reconstructed	reconstruct	VERB
gi-4938	437	21	,	,	PUNCT
gi-4938	437	22	the	the	DET
gi-4938	437	23	uniform	uniform	NOUN
gi-4938	437	24	and	and	CCONJ
gi-4938	437	25	adaptive	adaptive	ADJ
gi-4938	437	26	sampling	sampling	NOUN
gi-4938	437	27	techniques	technique	NOUN
gi-4938	437	28	are	be	AUX
gi-4938	437	29	compared	compare	VERB
gi-4938	437	30	regarding	regard	VERB
gi-4938	437	31	the	the	DET
gi-4938	437	32	data	data	NOUN
gi-4938	437	33	representation	representation	NOUN
gi-4938	437	34	compactness	compactness	NOUN
gi-4938	437	35	.	.	PUNCT
gi-4938	438	1	it	it	PRON
gi-4938	438	2	is	be	AUX
gi-4938	438	3	measured	measure	VERB
gi-4938	438	4	by	by	ADP
gi-4938	438	5	the	the	DET
gi-4938	438	6	amount	amount	NOUN
gi-4938	438	7	of	of	ADP
gi-4938	438	8	the	the	DET
gi-4938	438	9	sampled	sample	VERB
gi-4938	438	10	meridian	meridian	PROPN
gi-4938	438	11	points	point	NOUN
gi-4938	438	12	nmer	nmer	ADJ
gi-4938	438	13	,	,	PUNCT
gi-4938	438	14	and	and	CCONJ
gi-4938	438	15	parallel	parallel	ADJ
gi-4938	438	16	points	point	NOUN
gi-4938	438	17	npar	npar	NOUN
gi-4938	438	18	.	.	PUNCT
gi-4938	439	1	maximum	maximum	ADJ
gi-4938	439	2	angles	angle	NOUN
gi-4938	439	3	αm	αm	ADV
gi-4938	439	4	,	,	PUNCT
gi-4938	439	5	αp	αp	NOUN
gi-4938	439	6	between	between	ADP
gi-4938	439	7	the	the	DET
gi-4938	439	8	sampled	sample	VERB
gi-4938	439	9	meridian	meridian	NOUN
gi-4938	439	10	and	and	CCONJ
gi-4938	439	11	parallel	parallel	ADJ
gi-4938	439	12	segments	segment	NOUN
gi-4938	439	13	together	together	ADV
gi-4938	439	14	with	with	ADP
gi-4938	439	15	their	their	PRON
gi-4938	439	16	mean	mean	ADJ
gi-4938	439	17	values	value	NOUN
gi-4938	439	18	α̃m	α̃m	VERB
gi-4938	439	19	,	,	PUNCT
gi-4938	439	20	α̃p	α̃p	PRON
gi-4938	439	21	are	be	AUX
gi-4938	439	22	measured	measure	VERB
gi-4938	439	23	.	.	PUNCT
gi-4938	440	1	the	the	DET
gi-4938	440	2	graticule	graticule	NOUN
gi-4938	440	3	is	be	AUX
gi-4938	440	4	constructed	construct	VERB
gi-4938	440	5	over	over	ADP
gi-4938	440	6	the	the	DET
gi-4938	440	7	entire	entire	ADJ
gi-4938	440	8	planisphere	planisphere	NOUN
gi-4938	440	9	,	,	PUNCT
gi-4938	440	10	so	so	ADV
gi-4938	440	11	ω	ω	PROPN
gi-4938	440	12	=	=	SYM
gi-4938	440	13	ωϕ×ωλ	ωϕ×ωλ	PROPN
gi-4938	440	14	,	,	PUNCT
gi-4938	440	15	where	where	SCONJ
gi-4938	440	16	ϕ	ϕ	PROPN
gi-4938	440	17	∈	∈	PROPN
gi-4938	441	1	[	[	X
gi-4938	441	2	−π/2	−π/2	PROPN
gi-4938	441	3	,	,	PUNCT
gi-4938	441	4	π/2	π/2	NUM
gi-4938	441	5	]	]	PUNCT
gi-4938	441	6	,	,	PUNCT
gi-4938	441	7	and	and	CCONJ
gi-4938	441	8	λ	λ	X
gi-4938	441	9	∈	∈	PROPN
gi-4938	442	1	[	[	X
gi-4938	442	2	−π	−π	PROPN
gi-4938	442	3	,	,	PUNCT
gi-4938	442	4	π	π	PROPN
gi-4938	442	5	]	]	X
gi-4938	442	6	,	,	PUNCT
gi-4938	442	7	the	the	DET
gi-4938	442	8	offsets	offset	NOUN
gi-4938	442	9	between	between	ADP
gi-4938	442	10	the	the	DET
gi-4938	442	11	meridians	meridian	NOUN
gi-4938	442	12	and	and	CCONJ
gi-4938	442	13	parallels	parallel	NOUN
gi-4938	442	14	are	be	AUX
gi-4938	442	15	∆ϕ	∆ϕ	NOUN
gi-4938	442	16	=	=	SYM
gi-4938	442	17	∆λ	∆λ	NOUN
gi-4938	442	18	=	=	NOUN
gi-4938	442	19	10	10	NUM
gi-4938	442	20	◦	◦	NOUN
gi-4938	442	21	.	.	PUNCT
gi-4938	443	1	in	in	ADP
gi-4938	443	2	uniform	uniform	ADJ
gi-4938	443	3	sampling	sampling	NOUN
gi-4938	443	4	,	,	PUNCT
gi-4938	443	5	the	the	DET
gi-4938	443	6	sampling	sample	VERB
gi-4938	443	7	steps	step	NOUN
gi-4938	443	8	of	of	ADP
gi-4938	443	9	the	the	DET
gi-4938	443	10	meridians	meridian	NOUN
gi-4938	443	11	and	and	CCONJ
gi-4938	443	12	parallels	parallel	NOUN
gi-4938	443	13	are	be	AUX
gi-4938	443	14	δϕ	δϕ	ADJ
gi-4938	443	15	=	=	NOUN
gi-4938	443	16	δλ	δλ	NOUN
gi-4938	443	17	=	=	SYM
gi-4938	443	18	2	2	NUM
gi-4938	443	19	◦	◦	NOUN
gi-4938	443	20	;	;	PUNCT
gi-4938	443	21	combined	combine	VERB
gi-4938	443	22	sampling	sampling	NOUN
gi-4938	443	23	uses	use	VERB
gi-4938	443	24	α	α	NOUN
gi-4938	443	25	=	=	SYM
gi-4938	443	26	2	2	NUM
gi-4938	443	27	◦	◦	NOUN
gi-4938	443	28	.	.	NOUN
gi-4938	444	1	for	for	ADP
gi-4938	444	2	the	the	DET
gi-4938	444	3	circular	circular	ADJ
gi-4938	444	4	arcs	arc	NOUN
gi-4938	444	5	,	,	PUNCT
gi-4938	444	6	uniform	uniform	NOUN
gi-4938	444	7	and	and	CCONJ
gi-4938	444	8	combined	combined	ADJ
gi-4938	444	9	sampling	sampling	NOUN
gi-4938	444	10	provide	provide	VERB
gi-4938	444	11	the	the	DET
gi-4938	444	12	analogous	analogous	ADJ
gi-4938	444	13	density	density	NOUN
gi-4938	444	14	of	of	ADP
gi-4938	444	15	points	point	NOUN
gi-4938	444	16	representing	represent	VERB
gi-4938	444	17	the	the	DET
gi-4938	444	18	polygonal	polygonal	ADJ
gi-4938	444	19	approximation	approximation	NOUN
gi-4938	444	20	.	.	PUNCT
gi-4938	445	1	on	on	ADP
gi-4938	445	2	the	the	DET
gi-4938	445	3	contrary	contrary	NOUN
gi-4938	445	4	,	,	PUNCT
gi-4938	445	5	uniform	uniform	ADJ
gi-4938	445	6	sampling	sampling	NOUN
gi-4938	445	7	brings	bring	VERB
gi-4938	445	8	a	a	DET
gi-4938	445	9	higher	high	ADJ
gi-4938	445	10	density	density	NOUN
gi-4938	445	11	of	of	ADP
gi-4938	445	12	the	the	DET
gi-4938	445	13	sampled	sample	VERB
gi-4938	445	14	points	point	NOUN
gi-4938	445	15	for	for	ADP
gi-4938	445	16	the	the	DET
gi-4938	445	17	straight	straight	ADJ
gi-4938	445	18	lines	line	NOUN
gi-4938	445	19	and	and	CCONJ
gi-4938	445	20	vice	vice	ADV
gi-4938	445	21	versa	versa	ADV
gi-4938	445	22	for	for	ADP
gi-4938	445	23	most	most	ADJ
gi-4938	445	24	of	of	ADP
gi-4938	445	25	the	the	DET
gi-4938	445	26	curves	curve	NOUN
gi-4938	445	27	.	.	PUNCT
gi-4938	446	1	four	four	NUM
gi-4938	446	2	map	map	NOUN
gi-4938	446	3	geoinformatics	geoinformatic	NOUN
gi-4938	446	4	fce	fce	VERB
gi-4938	446	5	ctu	ctu	NOUN
gi-4938	446	6	17(2	17(2	NUM
gi-4938	446	7	)	)	PUNCT
gi-4938	446	8	,	,	PUNCT
gi-4938	446	9	2018	2018	NUM
gi-4938	446	10	24	24	NUM
gi-4938	446	11	t.	t.	NOUN
gi-4938	446	12	bayer	bayer	NOUN
gi-4938	446	13	:	:	PUNCT
gi-4938	446	14	efficient	efficient	ADJ
gi-4938	446	15	plotting	plot	VERB
gi-4938	446	16	the	the	DET
gi-4938	446	17	functions	function	NOUN
gi-4938	446	18	with	with	ADP
gi-4938	446	19	discontinuities	discontinuity	NOUN
gi-4938	446	20	-18	-18	PUNCT
gi-4938	446	21	0.0	0.0	NUM
gi-4938	446	22	-17	-17	SYM
gi-4938	446	23	0.0	0.0	NUM
gi-4938	446	24	-16	-16	PROPN
gi-4938	446	25	0.0	0.0	NUM
gi-4938	446	26	-15	-15	NUM
gi-4938	446	27	0.0	0.0	NUM
gi-4938	446	28	-14	-14	NUM
gi-4938	446	29	0.0	0.0	NUM
gi-4938	446	30	-13	-13	SYM
gi-4938	446	31	0.0	0.0	NUM
gi-4938	446	32	-12	-12	NOUN
gi-4938	446	33	0.0	0.0	NUM
gi-4938	446	34	-11	-11	SYM
gi-4938	446	35	0.0	0.0	NUM
gi-4938	446	36	-10	-10	SYM
gi-4938	446	37	0.0	0.0	NUM
gi-4938	446	38	-90	-90	PUNCT
gi-4938	446	39	.0	.0	NUM
gi-4938	446	40	-80	-80	PUNCT
gi-4938	446	41	.0	.0	NUM
gi-4938	447	1	-70	-70	PROPN
gi-4938	447	2	.0	.0	NUM
gi-4938	448	1	-60	-60	SYM
gi-4938	448	2	.0	.0	NUM
gi-4938	448	3	-50	-50	PUNCT
gi-4938	449	1	.0	.0	NUM
gi-4938	450	1	-40	-40	NUM
gi-4938	450	2	.0	.0	NUM
gi-4938	451	1	-30	-30	SYM
gi-4938	451	2	.0	.0	NUM
gi-4938	452	1	-20	-20	NUM
gi-4938	452	2	.0	.0	NUM
gi-4938	453	1	-10	-10	PUNCT
gi-4938	453	2	.0	.0	NUM
gi-4938	453	3	0.0	0.0	NUM
gi-4938	453	4	10	10	NUM
gi-4938	453	5	.	.	PUNCT
gi-4938	453	6	0	0	NUM
gi-4938	454	1	20	20	NUM
gi-4938	454	2	.	.	PUNCT
gi-4938	454	3	0	0	NUM
gi-4938	455	1	30	30	NUM
gi-4938	455	2	.	.	PUNCT
gi-4938	455	3	0	0	NUM
gi-4938	456	1	40	40	NUM
gi-4938	456	2	.	.	PUNCT
gi-4938	456	3	0	0	NUM
gi-4938	457	1	50	50	NUM
gi-4938	457	2	.	.	NOUN
gi-4938	457	3	0	0	NUM
gi-4938	458	1	60	60	NUM
gi-4938	458	2	.	.	PUNCT
gi-4938	458	3	0	0	NUM
gi-4938	459	1	70	70	NUM
gi-4938	459	2	.	.	PUNCT
gi-4938	459	3	0	0	NUM
gi-4938	460	1	80	80	NUM
gi-4938	460	2	.	.	PUNCT
gi-4938	460	3	0	0	NUM
gi-4938	461	1	90	90	NUM
gi-4938	461	2	.	.	PUNCT
gi-4938	461	3	0	0	NUM
gi-4938	462	1	100	100	NUM
gi-4938	462	2	.0	.0	NUM
gi-4938	462	3	110	110	NUM
gi-4938	462	4	.0	.0	NUM
gi-4938	462	5	120	120	NUM
gi-4938	462	6	.0	.0	NUM
gi-4938	462	7	130	130	NUM
gi-4938	462	8	.0	.0	NUM
gi-4938	462	9	140	140	NUM
gi-4938	462	10	.0	.0	NUM
gi-4938	462	11	150	150	NUM
gi-4938	462	12	.0	.0	NUM
gi-4938	462	13	160	160	NUM
gi-4938	462	14	.0	.0	NUM
gi-4938	462	15	170	170	NUM
gi-4938	462	16	.0	.0	NUM
gi-4938	462	17	180	180	NUM
gi-4938	462	18	.0	.0	NUM
gi-4938	462	19	-0.0	-0.0	NOUN
gi-4938	462	20	0.0	0.0	NUM
gi-4938	463	1	-90.0	-90.0	NOUN
gi-4938	464	1	-90.0	-90.0	NOUN
gi-4938	465	1	-80.0	-80.0	INTJ
gi-4938	466	1	-80.0	-80.0	INTJ
gi-4938	467	1	-70.0	-70.0	NOUN
gi-4938	467	2	-70.0	-70.0	NOUN
gi-4938	467	3	-60.0	-60.0	NOUN
gi-4938	468	1	-60.0	-60.0	NOUN
gi-4938	468	2	-50.0	-50.0	NOUN
gi-4938	469	1	-50.0	-50.0	NOUN
gi-4938	469	2	-40.0	-40.0	NOUN
gi-4938	469	3	-40.0	-40.0	NOUN
gi-4938	469	4	-30.0	-30.0	NOUN
gi-4938	469	5	-30.0	-30.0	NOUN
gi-4938	469	6	-20.0	-20.0	NOUN
gi-4938	469	7	-20.0	-20.0	NOUN
gi-4938	470	1	-10.0	-10.0	PROPN
gi-4938	471	1	-10.0	-10.0	PROPN
gi-4938	471	2	0.0	0.0	NUM
gi-4938	471	3	0.0	0.0	NUM
gi-4938	471	4	10.0	10.0	NUM
gi-4938	471	5	10.0	10.0	NUM
gi-4938	471	6	20.0	20.0	NUM
gi-4938	471	7	20.0	20.0	NUM
gi-4938	471	8	30.0	30.0	NUM
gi-4938	471	9	30.0	30.0	NUM
gi-4938	471	10	40.0	40.0	NUM
gi-4938	471	11	40.0	40.0	NUM
gi-4938	471	12	50.0	50.0	NUM
gi-4938	471	13	50.0	50.0	NUM
gi-4938	471	14	60.0	60.0	NUM
gi-4938	471	15	60.0	60.0	NUM
gi-4938	471	16	70.0	70.0	NUM
gi-4938	471	17	70.0	70.0	NUM
gi-4938	471	18	80.0	80.0	NUM
gi-4938	471	19	80.0	80.0	NUM
gi-4938	471	20	90.0	90.0	NUM
gi-4938	471	21	90.0	90.0	NUM
gi-4938	471	22	-180.0	-180.0	NOUN
gi-4938	472	1	-170.0	-170.0	PROPN
gi-4938	472	2	-160.0	-160.0	NOUN
gi-4938	472	3	-150.0	-150.0	NOUN
gi-4938	473	1	-140.0	-140.0	INTJ
gi-4938	473	2	-130.0	-130.0	INTJ
gi-4938	473	3	-120.0	-120.0	PROPN
gi-4938	473	4	-110.0	-110.0	PROPN
gi-4938	473	5	-100	-100	PROPN
gi-4938	473	6	.	.	PROPN
gi-4938	473	7	0	0	NUM
gi-4938	474	1	-90.0	-90.0	NOUN
gi-4938	474	2	-80.0	-80.0	INTJ
gi-4938	475	1	-70.0	-70.0	ADJ
gi-4938	475	2	-60	-60	PUNCT
gi-4938	475	3	.	.	PROPN
gi-4938	475	4	0	0	NUM
gi-4938	475	5	-50	-50	NUM
gi-4938	475	6	.	.	PUNCT
gi-4938	475	7	0	0	NUM
gi-4938	476	1	-40	-40	PROPN
gi-4938	476	2	.	.	PROPN
gi-4938	476	3	0	0	NUM
gi-4938	477	1	-30	-30	NUM
gi-4938	477	2	.	.	PUNCT
gi-4938	477	3	0	0	NUM
gi-4938	478	1	-20	-20	NUM
gi-4938	478	2	.	.	PUNCT
gi-4938	478	3	0	0	NUM
gi-4938	479	1	-10	-10	NUM
gi-4938	479	2	.	.	PUNCT
gi-4938	479	3	0	0	NUM
gi-4938	480	1	0.0	0.0	NUM
gi-4938	480	2	10.0	10.0	NUM
gi-4938	480	3	20.0	20.0	NUM
gi-4938	480	4	30.0	30.0	NUM
gi-4938	480	5	40.0	40.0	NUM
gi-4938	480	6	50.0	50.0	NUM
gi-4938	480	7	60.0	60.0	NUM
gi-4938	480	8	70.0	70.0	NUM
gi-4938	480	9	80.0	80.0	NUM
gi-4938	480	10	90.0	90.0	NUM
gi-4938	480	11	100.0	100.0	NUM
gi-4938	480	12	110.0	110.0	NUM
gi-4938	480	13	120.0	120.0	NUM
gi-4938	480	14	130.0	130.0	NUM
gi-4938	480	15	140.0	140.0	NUM
gi-4938	480	16	150.0	150.0	NUM
gi-4938	480	17	160.0	160.0	NUM
gi-4938	480	18	170.0	170.0	NUM
gi-4938	480	19	180.0	180.0	NUM
gi-4938	480	20	-0.0	-0.0	NOUN
gi-4938	480	21	0.0	0.0	NUM
gi-4938	480	22	-90.0	-90.0	NOUN
gi-4938	480	23	-90.0	-90.0	NOUN
gi-4938	480	24	-80.0	-80.0	INTJ
gi-4938	480	25	-80.0	-80.0	INTJ
gi-4938	481	1	-70.0	-70.0	NOUN
gi-4938	481	2	-70.0	-70.0	NOUN
gi-4938	481	3	-60.0	-60.0	NOUN
gi-4938	482	1	-60.0	-60.0	NOUN
gi-4938	482	2	-50.0	-50.0	NOUN
gi-4938	483	1	-50.0	-50.0	NOUN
gi-4938	483	2	-40.0	-40.0	NOUN
gi-4938	483	3	-40.0	-40.0	NOUN
gi-4938	483	4	-30.0	-30.0	NOUN
gi-4938	483	5	-30.0	-30.0	NOUN
gi-4938	483	6	-20.0	-20.0	NOUN
gi-4938	483	7	-20.0	-20.0	NOUN
gi-4938	484	1	-10.0	-10.0	PROPN
gi-4938	485	1	-10.0	-10.0	PROPN
gi-4938	485	2	0.0	0.0	NUM
gi-4938	485	3	0.0	0.0	NUM
gi-4938	485	4	10.0	10.0	NUM
gi-4938	485	5	10.0	10.0	NUM
gi-4938	485	6	20.0	20.0	NUM
gi-4938	485	7	20.0	20.0	NUM
gi-4938	485	8	30.0	30.0	NUM
gi-4938	485	9	30.0	30.0	NUM
gi-4938	485	10	40.0	40.0	NUM
gi-4938	485	11	40.0	40.0	NUM
gi-4938	485	12	50.0	50.0	NUM
gi-4938	485	13	50.0	50.0	NUM
gi-4938	485	14	60.0	60.0	NUM
gi-4938	485	15	60.0	60.0	NUM
gi-4938	485	16	70.0	70.0	NUM
gi-4938	485	17	70.0	70.0	NUM
gi-4938	485	18	80.0	80.0	NUM
gi-4938	485	19	80.0	80.0	NUM
gi-4938	485	20	90.0	90.0	NUM
gi-4938	485	21	90.0	90.0	NUM
gi-4938	485	22	-180.0	-180.0	NOUN
gi-4938	486	1	-170.0	-170.0	PROPN
gi-4938	486	2	-160.0	-160.0	NOUN
gi-4938	486	3	-150.0	-150.0	NOUN
gi-4938	487	1	-140.0	-140.0	INTJ
gi-4938	487	2	-130.0	-130.0	INTJ
gi-4938	488	1	-120.0	-120.0	PROPN
gi-4938	488	2	-110.0	-110.0	PROPN
gi-4938	488	3	-100.0	-100.0	NOUN
gi-4938	489	1	-90.0	-90.0	INTJ
gi-4938	489	2	-80.0	-80.0	NOUN
gi-4938	490	1	-70.0	-70.0	NOUN
gi-4938	490	2	-60.0	-60.0	NOUN
gi-4938	490	3	-50	-50	PUNCT
gi-4938	490	4	.	.	PUNCT
gi-4938	490	5	0	0	NUM
gi-4938	491	1	-40	-40	PUNCT
gi-4938	491	2	.0	.0	NUM
gi-4938	492	1	-30	-30	SYM
gi-4938	492	2	.0	.0	NUM
gi-4938	493	1	-20	-20	NUM
gi-4938	493	2	.0	.0	NUM
gi-4938	494	1	-10	-10	PUNCT
gi-4938	494	2	.0	.0	NUM
gi-4938	495	1	0.0	0.0	NUM
gi-4938	495	2	10	10	NUM
gi-4938	495	3	.0	.0	NUM
gi-4938	495	4	20	20	NUM
gi-4938	495	5	.0	.0	NUM
gi-4938	495	6	30	30	NUM
gi-4938	495	7	.	.	PUNCT
gi-4938	495	8	0	0	NUM
gi-4938	496	1	40.0	40.0	NUM
gi-4938	496	2	50.0	50.0	NUM
gi-4938	496	3	60.0	60.0	NUM
gi-4938	496	4	70.0	70.0	NUM
gi-4938	496	5	80.0	80.0	NUM
gi-4938	496	6	90.0	90.0	NUM
gi-4938	496	7	100.0	100.0	NUM
gi-4938	496	8	110.0	110.0	NUM
gi-4938	496	9	120.0	120.0	NUM
gi-4938	496	10	130.0	130.0	NUM
gi-4938	496	11	140.0	140.0	NUM
gi-4938	496	12	150.0	150.0	NUM
gi-4938	496	13	160.0	160.0	NUM
gi-4938	496	14	170.0	170.0	NUM
gi-4938	496	15	180.0	180.0	NUM
gi-4938	496	16	-0	-0	PUNCT
gi-4938	496	17	.	.	PROPN
gi-4938	496	18	0	0	NUM
gi-4938	496	19	0.0	0.0	NUM
gi-4938	496	20	-90.0	-90.0	NOUN
gi-4938	496	21	-90	-90	NUM
gi-4938	496	22	.0	.0	NUM
gi-4938	497	1	-80.0	-80.0	PRON
gi-4938	497	2	-80	-80	PUNCT
gi-4938	497	3	.0	.0	NUM
gi-4938	498	1	-70.0	-70.0	ADJ
gi-4938	498	2	-70	-70	PROPN
gi-4938	498	3	.0	.0	NUM
gi-4938	499	1	-60.0	-60.0	NOUN
gi-4938	500	1	60	60	NUM
gi-4938	500	2	.0	.0	NUM
gi-4938	501	1	-50.0	-50.0	NOUN
gi-4938	501	2	-50	-50	PUNCT
gi-4938	502	1	.0	.0	NUM
gi-4938	502	2	-40.0	-40.0	NOUN
gi-4938	502	3	-40	-40	PROPN
gi-4938	502	4	.0	.0	NUM
gi-4938	503	1	-30.0	-30.0	NOUN
gi-4938	503	2	-30	-30	SYM
gi-4938	503	3	.0	.0	NUM
gi-4938	504	1	-20.0	-20.0	NOUN
gi-4938	504	2	-20	-20	NUM
gi-4938	505	1	.0	.0	NUM
gi-4938	505	2	-10.0	-10.0	NOUN
gi-4938	505	3	-10	-10	PUNCT
gi-4938	506	1	.0	.0	NUM
gi-4938	506	2	0.0	0.0	NUM
gi-4938	506	3	0.0	0.0	NUM
gi-4938	506	4	10.0	10.0	NUM
gi-4938	506	5	10	10	NUM
gi-4938	506	6	.0	.0	NUM
gi-4938	506	7	20.0	20.0	NUM
gi-4938	506	8	20	20	NUM
gi-4938	506	9	.0	.0	NUM
gi-4938	506	10	30.0	30.0	NUM
gi-4938	506	11	30	30	NUM
gi-4938	506	12	.0	.0	NUM
gi-4938	506	13	40.0	40.0	NUM
gi-4938	506	14	40	40	NUM
gi-4938	506	15	.0	.0	NUM
gi-4938	506	16	50.0	50.0	NUM
gi-4938	506	17	50	50	NUM
gi-4938	506	18	.0	.0	NUM
gi-4938	507	1	60.0	60.0	NUM
gi-4938	507	2	60	60	NUM
gi-4938	507	3	.0	.0	NUM
gi-4938	507	4	70.0	70.0	NUM
gi-4938	507	5	70	70	NUM
gi-4938	507	6	.0	.0	NUM
gi-4938	507	7	80.0	80.0	NUM
gi-4938	507	8	80	80	NUM
gi-4938	507	9	.0	.0	NUM
gi-4938	507	10	90.0	90.0	NUM
gi-4938	507	11	90	90	NUM
gi-4938	507	12	.0	.0	NUM
gi-4938	508	1	-180.0	-180.0	INTJ
gi-4938	509	1	-170.0	-170.0	NOUN
gi-4938	510	1	-160	-160	X
gi-4938	510	2	.0	.0	NUM
gi-4938	511	1	-150	-150	NUM
gi-4938	511	2	.0	.0	NUM
gi-4938	512	1	-140	-140	NUM
gi-4938	512	2	.0	.0	NUM
gi-4938	512	3	-13	-13	PUNCT
gi-4938	512	4	0.0	0.0	NUM
gi-4938	512	5	-12	-12	NUM
gi-4938	512	6	0.0	0.0	NUM
gi-4938	512	7	-11	-11	SYM
gi-4938	512	8	0.0	0.0	NUM
gi-4938	512	9	-10	-10	SYM
gi-4938	512	10	0.0	0.0	NUM
gi-4938	512	11	-90	-90	PUNCT
gi-4938	512	12	.0	.0	NUM
gi-4938	512	13	-80	-80	PUNCT
gi-4938	512	14	.0	.0	NUM
gi-4938	513	1	-70	-70	PROPN
gi-4938	513	2	.0	.0	NUM
gi-4938	514	1	-60	-60	SYM
gi-4938	514	2	.0	.0	NUM
gi-4938	514	3	-50	-50	PUNCT
gi-4938	515	1	.0	.0	NUM
gi-4938	516	1	-40	-40	NUM
gi-4938	516	2	.0	.0	NUM
gi-4938	517	1	-30	-30	SYM
gi-4938	517	2	.0	.0	NUM
gi-4938	518	1	-20	-20	NUM
gi-4938	518	2	.0	.0	NUM
gi-4938	519	1	-10	-10	PUNCT
gi-4938	519	2	.0	.0	NUM
gi-4938	520	1	0.0	0.0	NUM
gi-4938	520	2	10	10	NUM
gi-4938	520	3	.0	.0	NUM
gi-4938	520	4	20	20	NUM
gi-4938	520	5	.0	.0	NUM
gi-4938	520	6	30	30	NUM
gi-4938	520	7	.0	.0	NUM
gi-4938	520	8	40	40	NUM
gi-4938	520	9	.0	.0	NUM
gi-4938	520	10	50	50	NUM
gi-4938	520	11	.0	.0	NUM
gi-4938	520	12	60	60	NUM
gi-4938	520	13	.0	.0	NUM
gi-4938	520	14	70	70	NUM
gi-4938	520	15	.0	.0	NUM
gi-4938	520	16	80	80	NUM
gi-4938	520	17	.0	.0	NUM
gi-4938	520	18	90	90	NUM
gi-4938	520	19	.0	.0	NUM
gi-4938	520	20	10	10	NUM
gi-4938	520	21	0.0	0.0	NUM
gi-4938	520	22	110	110	NUM
gi-4938	520	23	.0	.0	NUM
gi-4938	520	24	120	120	NUM
gi-4938	520	25	.0	.0	NUM
gi-4938	520	26	130	130	NUM
gi-4938	520	27	.0	.0	NUM
gi-4938	520	28	140	140	NUM
gi-4938	520	29	.0	.0	NUM
gi-4938	520	30	150.0	150.0	NUM
gi-4938	520	31	160	160	NUM
gi-4938	520	32	.	.	PUNCT
gi-4938	520	33	0	0	NUM
gi-4938	521	1	170.0	170.0	NUM
gi-4938	521	2	180.0	180.0	NUM
gi-4938	521	3	-0	-0	PUNCT
gi-4938	521	4	.	.	PROPN
gi-4938	521	5	0	0	NUM
gi-4938	522	1	0.0	0.0	NUM
gi-4938	522	2	-90.0	-90.0	NUM
gi-4938	522	3	-	-	SYM
gi-4938	522	4	90.0	90.0	NUM
gi-4938	522	5	-80.0	-80.0	NOUN
gi-4938	522	6	-80.0	-80.0	PRON
gi-4938	523	1	-70.0	-70.0	NOUN
gi-4938	523	2	-70.0	-70.0	NOUN
gi-4938	523	3	-60.0	-60.0	NOUN
gi-4938	524	1	-60.0	-60.0	NOUN
gi-4938	524	2	-50.0	-50.0	NOUN
gi-4938	525	1	-50.0	-50.0	NOUN
gi-4938	525	2	-40.0	-40.0	NOUN
gi-4938	525	3	-40.0	-40.0	NOUN
gi-4938	525	4	-30.0	-30.0	NOUN
gi-4938	525	5	-30.0	-30.0	NOUN
gi-4938	525	6	-20.0	-20.0	NOUN
gi-4938	525	7	-20	-20	NUM
gi-4938	525	8	.0	.0	NUM
gi-4938	526	1	-10.0	-10.0	NOUN
gi-4938	526	2	-10	-10	PUNCT
gi-4938	526	3	.	.	PUNCT
gi-4938	526	4	0	0	NUM
gi-4938	527	1	0.0	0.0	NUM
gi-4938	527	2	0.0	0.0	NUM
gi-4938	527	3	10.0	10.0	NUM
gi-4938	527	4	10	10	NUM
gi-4938	527	5	.	.	PUNCT
gi-4938	527	6	0	0	NUM
gi-4938	528	1	20.0	20.0	NUM
gi-4938	528	2	20	20	NUM
gi-4938	528	3	.0	.0	NUM
gi-4938	528	4	30.0	30.0	NUM
gi-4938	528	5	30	30	NUM
gi-4938	528	6	.0	.0	NUM
gi-4938	528	7	40.0	40.0	NUM
gi-4938	528	8	40	40	NUM
gi-4938	528	9	.0	.0	NUM
gi-4938	528	10	50.0	50.0	NUM
gi-4938	528	11	50	50	NUM
gi-4938	528	12	.0	.0	NUM
gi-4938	528	13	60.0	60.0	NUM
gi-4938	528	14	60	60	NUM
gi-4938	528	15	.0	.0	NUM
gi-4938	528	16	70.0	70.0	NUM
gi-4938	528	17	70	70	NUM
gi-4938	528	18	.0	.0	NUM
gi-4938	529	1	80.0	80.0	NUM
gi-4938	529	2	80	80	NUM
gi-4938	529	3	.0	.0	NUM
gi-4938	529	4	90.0	90.0	NUM
gi-4938	529	5	90	90	NUM
gi-4938	529	6	.0	.0	NUM
gi-4938	529	7	figure	figure	NOUN
gi-4938	529	8	6.2	6.2	NUM
gi-4938	529	9	:	:	PUNCT
gi-4938	529	10	the	the	DET
gi-4938	529	11	reconstructed	reconstructed	ADJ
gi-4938	529	12	graticules	graticule	NOUN
gi-4938	529	13	of	of	ADP
gi-4938	529	14	the	the	DET
gi-4938	529	15	equal	equal	ADJ
gi-4938	529	16	area	area	NOUN
gi-4938	529	17	cylindrical	cylindrical	ADJ
gi-4938	529	18	,	,	PUNCT
gi-4938	529	19	conic	conic	ADJ
gi-4938	529	20	,	,	PUNCT
gi-4938	529	21	azimuthal	azimuthal	NOUN
gi-4938	529	22	and	and	CCONJ
gi-4938	529	23	werner	werner	NOUN
gi-4938	529	24	-	-	PUNCT
gi-4938	529	25	staab	staab	NOUN
gi-4938	529	26	projections	projection	NOUN
gi-4938	529	27	using	use	VERB
gi-4938	529	28	the	the	DET
gi-4938	529	29	combined	combined	ADJ
gi-4938	529	30	sampling	sampling	NOUN
gi-4938	529	31	technique	technique	NOUN
gi-4938	529	32	.	.	PUNCT
gi-4938	530	1	projections	projection	NOUN
gi-4938	530	2	are	be	AUX
gi-4938	530	3	involved	involve	VERB
gi-4938	530	4	in	in	ADP
gi-4938	530	5	testing	testing	NOUN
gi-4938	530	6	:	:	PUNCT
gi-4938	530	7	equal	equal	ADJ
gi-4938	530	8	-	-	PUNCT
gi-4938	530	9	area	area	NOUN
gi-4938	530	10	cylindrical	cylindrical	ADJ
gi-4938	530	11	,	,	PUNCT
gi-4938	530	12	conic	conic	ADJ
gi-4938	530	13	(	(	PUNCT
gi-4938	530	14	ϕ1	ϕ1	NOUN
gi-4938	530	15	=	=	SYM
gi-4938	530	16	45	45	NUM
gi-4938	530	17	◦	◦	NOUN
gi-4938	530	18	)	)	PUNCT
gi-4938	530	19	,	,	PUNCT
gi-4938	530	20	azimuthal	azimuthal	NOUN
gi-4938	530	21	,	,	PUNCT
gi-4938	530	22	and	and	CCONJ
gi-4938	530	23	werner	werner	NOUN
gi-4938	530	24	-	-	PUNCT
gi-4938	530	25	staab	staab	NOUN
gi-4938	530	26	,	,	PUNCT
gi-4938	530	27	their	their	PRON
gi-4938	530	28	coordinate	coordinate	NOUN
gi-4938	530	29	functions	function	NOUN
gi-4938	530	30	are	be	AUX
gi-4938	530	31	continuous	continuous	ADJ
gi-4938	530	32	on	on	ADP
gi-4938	530	33	ω	ω	NUM
gi-4938	530	34	.	.	PUNCT
gi-4938	531	1	the	the	DET
gi-4938	531	2	results	result	NOUN
gi-4938	531	3	are	be	AUX
gi-4938	531	4	summarized	summarize	VERB
gi-4938	531	5	in	in	ADP
gi-4938	531	6	tab	tab	NOUN
gi-4938	531	7	.	.	PUNCT
gi-4938	532	1	2	2	NUM
gi-4938	532	2	.	.	X
gi-4938	532	3	for	for	ADP
gi-4938	532	4	the	the	DET
gi-4938	532	5	straight	straight	ADJ
gi-4938	532	6	segments	segment	NOUN
gi-4938	532	7	,	,	PUNCT
gi-4938	532	8	uniform	uniform	ADJ
gi-4938	532	9	sampling	sample	VERB
gi-4938	532	10	provides	provide	VERB
gi-4938	532	11	the	the	DET
gi-4938	532	12	redundant	redundant	ADJ
gi-4938	532	13	data	datum	NOUN
gi-4938	532	14	;	;	PUNCT
gi-4938	532	15	this	this	DET
gi-4938	532	16	issue	issue	NOUN
gi-4938	532	17	refers	refer	VERB
gi-4938	532	18	to	to	ADP
gi-4938	532	19	the	the	DET
gi-4938	532	20	cylindrical	cylindrical	ADJ
gi-4938	532	21	projection	projection	NOUN
gi-4938	532	22	as	as	ADV
gi-4938	532	23	well	well	ADV
gi-4938	532	24	as	as	ADP
gi-4938	532	25	to	to	ADP
gi-4938	532	26	the	the	DET
gi-4938	532	27	meridians	meridian	NOUN
gi-4938	532	28	of	of	ADP
gi-4938	532	29	the	the	DET
gi-4938	532	30	conic	conic	ADJ
gi-4938	532	31	and	and	CCONJ
gi-4938	532	32	azimuthal	azimuthal	ADJ
gi-4938	532	33	projections	projection	NOUN
gi-4938	532	34	.	.	PUNCT
gi-4938	533	1	while	while	SCONJ
gi-4938	533	2	the	the	DET
gi-4938	533	3	constant	constant	ADJ
gi-4938	533	4	curvature	curvature	NOUN
gi-4938	533	5	leads	lead	VERB
gi-4938	533	6	to	to	ADP
gi-4938	533	7	the	the	DET
gi-4938	533	8	similar	similar	ADJ
gi-4938	533	9	results	result	NOUN
gi-4938	533	10	(	(	PUNCT
gi-4938	533	11	parallels	parallel	NOUN
gi-4938	533	12	of	of	ADP
gi-4938	533	13	conic	conic	ADJ
gi-4938	533	14	,	,	PUNCT
gi-4938	533	15	azimuthal	azimuthal	NOUN
gi-4938	533	16	and	and	CCONJ
gi-4938	533	17	werner	werner	NOUN
gi-4938	533	18	-	-	PUNCT
gi-4938	533	19	staab	staab	NOUN
gi-4938	533	20	projections	projection	NOUN
gi-4938	533	21	)	)	PUNCT
gi-4938	533	22	,	,	PUNCT
gi-4938	533	23	in	in	ADP
gi-4938	533	24	the	the	DET
gi-4938	533	25	higher	high	ADJ
gi-4938	533	26	-	-	PUNCT
gi-4938	533	27	curvature	curvature	NOUN
gi-4938	533	28	regions	region	NOUN
gi-4938	533	29	,	,	PUNCT
gi-4938	533	30	the	the	DET
gi-4938	533	31	combined	combine	VERB
gi-4938	533	32	sampling	sampling	NOUN
gi-4938	533	33	provides	provide	VERB
gi-4938	533	34	a	a	DET
gi-4938	533	35	smoother	smooth	ADJ
gi-4938	533	36	approximation	approximation	NOUN
gi-4938	533	37	(	(	PUNCT
gi-4938	533	38	meridians	meridian	NOUN
gi-4938	533	39	of	of	ADP
gi-4938	533	40	werner	werner	NOUN
gi-4938	533	41	-	-	PUNCT
gi-4938	533	42	staab	staab	NOUN
gi-4938	533	43	projection	projection	NOUN
gi-4938	533	44	)	)	PUNCT
gi-4938	533	45	.	.	PUNCT
gi-4938	534	1	in	in	ADP
gi-4938	534	2	general	general	ADJ
gi-4938	534	3	,	,	PUNCT
gi-4938	534	4	combined	combined	ADJ
gi-4938	534	5	sampling	sample	VERB
gi-4938	534	6	preserves	preserve	VERB
gi-4938	534	7	the	the	DET
gi-4938	534	8	curvature	curvature	NOUN
gi-4938	534	9	better	well	ADV
gi-4938	534	10	(	(	PUNCT
gi-4938	534	11	see	see	VERB
gi-4938	534	12	αm	αm	NOUN
gi-4938	534	13	,	,	PUNCT
gi-4938	534	14	αp	αp	NOUN
gi-4938	534	15	,	,	PUNCT
gi-4938	534	16	α̃m	α̃m	NUM
gi-4938	534	17	,	,	PUNCT
gi-4938	534	18	α̃p	α̃p	NOUN
gi-4938	534	19	values	value	NOUN
gi-4938	534	20	)	)	PUNCT
gi-4938	534	21	and	and	CCONJ
gi-4938	534	22	brings	bring	VERB
gi-4938	534	23	less	less	ADV
gi-4938	534	24	redundant	redundant	ADJ
gi-4938	534	25	data	datum	NOUN
gi-4938	534	26	which	which	PRON
gi-4938	534	27	requires	require	VERB
gi-4938	534	28	more	more	ADV
gi-4938	534	29	sampled	sample	VERB
gi-4938	534	30	points	point	NOUN
gi-4938	534	31	.	.	PUNCT
gi-4938	535	1	the	the	DET
gi-4938	535	2	reconstructed	reconstructed	ADJ
gi-4938	535	3	graticules	graticule	NOUN
gi-4938	535	4	can	can	AUX
gi-4938	535	5	be	be	AUX
gi-4938	535	6	found	find	VERB
gi-4938	535	7	in	in	ADP
gi-4938	535	8	fig	fig	NOUN
gi-4938	535	9	.	.	PUNCT
gi-4938	536	1	6.2	6.2	NUM
gi-4938	536	2	.	.	PUNCT
gi-4938	537	1	the	the	DET
gi-4938	537	2	modified	modify	VERB
gi-4938	537	3	version	version	NOUN
gi-4938	537	4	of	of	ADP
gi-4938	537	5	the	the	DET
gi-4938	537	6	algorithm	algorithm	NOUN
gi-4938	537	7	treating	treat	VERB
gi-4938	537	8	the	the	DET
gi-4938	537	9	discontinuities	discontinuity	NOUN
gi-4938	537	10	in	in	ADP
gi-4938	537	11	the	the	DET
gi-4938	537	12	coordinate	coordinate	NOUN
gi-4938	537	13	functions	function	NOUN
gi-4938	537	14	f	f	X
gi-4938	537	15	,	,	PUNCT
gi-4938	537	16	g	g	PROPN
gi-4938	537	17	will	will	AUX
gi-4938	537	18	be	be	AUX
gi-4938	537	19	presented	present	VERB
gi-4938	537	20	in	in	ADP
gi-4938	537	21	the	the	DET
gi-4938	537	22	next	next	ADJ
gi-4938	537	23	paper	paper	NOUN
gi-4938	537	24	.	.	PUNCT
gi-4938	538	1	7	7	X
gi-4938	538	2	.	.	X
gi-4938	538	3	conclusion	conclusion	NOUN
gi-4938	538	4	this	this	DET
gi-4938	538	5	article	article	NOUN
gi-4938	538	6	presented	present	VERB
gi-4938	538	7	a	a	DET
gi-4938	538	8	new	new	ADJ
gi-4938	538	9	algorithm	algorithm	NOUN
gi-4938	538	10	combining	combine	VERB
gi-4938	538	11	the	the	DET
gi-4938	538	12	uniform	uniform	NOUN
gi-4938	538	13	and	and	CCONJ
gi-4938	538	14	adaptive	adaptive	ADJ
gi-4938	538	15	sampling	sample	VERB
gi-4938	538	16	techniques	technique	NOUN
gi-4938	538	17	applicable	applicable	ADJ
gi-4938	538	18	to	to	ADP
gi-4938	538	19	the	the	DET
gi-4938	538	20	functions	function	NOUN
gi-4938	538	21	involving	involve	VERB
gi-4938	538	22	the	the	DET
gi-4938	538	23	discontinuities	discontinuity	NOUN
gi-4938	538	24	,	,	PUNCT
gi-4938	538	25	which	which	PRON
gi-4938	538	26	are	be	AUX
gi-4938	538	27	detected	detect	VERB
gi-4938	538	28	by	by	ADP
gi-4938	538	29	the	the	DET
gi-4938	538	30	lr	lr	NOUN
gi-4938	538	31	criterion	criterion	NOUN
gi-4938	538	32	.	.	PUNCT
gi-4938	539	1	it	it	PRON
gi-4938	539	2	can	can	AUX
gi-4938	539	3	be	be	AUX
gi-4938	539	4	used	use	VERB
gi-4938	539	5	for	for	ADP
gi-4938	539	6	the	the	DET
gi-4938	539	7	polygonal	polygonal	ADJ
gi-4938	539	8	approximation	approximation	NOUN
gi-4938	539	9	of	of	ADP
gi-4938	539	10	the	the	DET
gi-4938	539	11	curves	curve	NOUN
gi-4938	539	12	when	when	SCONJ
gi-4938	539	13	a	a	DET
gi-4938	539	14	more	more	ADV
gi-4938	539	15	compact	compact	ADJ
gi-4938	539	16	,	,	PUNCT
gi-4938	539	17	efficient	efficient	ADJ
gi-4938	539	18	and	and	CCONJ
gi-4938	539	19	less	less	ADV
gi-4938	539	20	redundant	redundant	ADJ
gi-4938	539	21	representation	representation	NOUN
gi-4938	539	22	is	be	AUX
gi-4938	539	23	required	require	VERB
gi-4938	539	24	.	.	PUNCT
gi-4938	540	1	a	a	DET
gi-4938	540	2	typical	typical	ADJ
gi-4938	540	3	example	example	NOUN
gi-4938	540	4	is	be	AUX
gi-4938	540	5	represented	represent	VERB
gi-4938	540	6	by	by	ADP
gi-4938	540	7	the	the	DET
gi-4938	540	8	circles	circle	NOUN
gi-4938	540	9	,	,	PUNCT
gi-4938	540	10	circular	circular	ADJ
gi-4938	540	11	arcs	arc	NOUN
gi-4938	540	12	,	,	PUNCT
gi-4938	540	13	ellipses	ellipsis	NOUN
gi-4938	540	14	or	or	CCONJ
gi-4938	540	15	offsets	offset	NOUN
gi-4938	540	16	of	of	ADP
gi-4938	540	17	curves	curve	NOUN
gi-4938	540	18	,	,	PUNCT
gi-4938	540	19	but	but	CCONJ
gi-4938	540	20	it	it	PRON
gi-4938	540	21	can	can	AUX
gi-4938	540	22	be	be	AUX
gi-4938	540	23	easily	easily	ADV
gi-4938	540	24	applicable	applicable	ADJ
gi-4938	540	25	to	to	ADP
gi-4938	540	26	the	the	DET
gi-4938	540	27	map	map	NOUN
gi-4938	540	28	geoinformatics	geoinformatic	NOUN
gi-4938	540	29	fce	fce	VERB
gi-4938	540	30	ctu	ctu	NOUN
gi-4938	540	31	17(2	17(2	NUM
gi-4938	540	32	)	)	PUNCT
gi-4938	540	33	,	,	PUNCT
gi-4938	540	34	2018	2018	NUM
gi-4938	540	35	25	25	NUM
gi-4938	540	36	t.	t.	NOUN
gi-4938	540	37	bayer	bayer	NOUN
gi-4938	540	38	:	:	PUNCT
gi-4938	540	39	efficient	efficient	ADJ
gi-4938	540	40	plotting	plot	VERB
gi-4938	540	41	the	the	DET
gi-4938	540	42	functions	function	NOUN
gi-4938	540	43	with	with	ADP
gi-4938	540	44	discontinuities	discontinuity	NOUN
gi-4938	540	45	projection	projection	NOUN
gi-4938	540	46	graticule	graticule	NOUN
gi-4938	540	47	and	and	CCONJ
gi-4938	540	48	similar	similar	ADJ
gi-4938	540	49	problems	problem	NOUN
gi-4938	540	50	in	in	ADP
gi-4938	540	51	gis	gis	NOUN
gi-4938	540	52	and	and	CCONJ
gi-4938	540	53	cartography	cartography	NOUN
gi-4938	540	54	.	.	PUNCT
gi-4938	541	1	the	the	DET
gi-4938	541	2	illustrating	illustrate	VERB
gi-4938	541	3	examples	example	NOUN
gi-4938	541	4	indicate	indicate	VERB
gi-4938	541	5	that	that	SCONJ
gi-4938	541	6	the	the	DET
gi-4938	541	7	functions	function	NOUN
gi-4938	541	8	involving	involve	VERB
gi-4938	541	9	the	the	DET
gi-4938	541	10	discontinuities	discontinuity	NOUN
gi-4938	541	11	widely	widely	ADV
gi-4938	541	12	applied	apply	VERB
gi-4938	541	13	in	in	ADP
gi-4938	541	14	technical	technical	ADJ
gi-4938	541	15	practice	practice	NOUN
gi-4938	541	16	can	can	AUX
gi-4938	541	17	be	be	AUX
gi-4938	541	18	plotted	plot	VERB
gi-4938	541	19	efficiently	efficiently	ADV
gi-4938	541	20	.	.	PUNCT
gi-4938	542	1	however	however	ADV
gi-4938	542	2	,	,	PUNCT
gi-4938	542	3	there	there	PRON
gi-4938	542	4	are	be	VERB
gi-4938	542	5	many	many	ADJ
gi-4938	542	6	more	more	ADV
gi-4938	542	7	complex	complex	ADJ
gi-4938	542	8	functions	function	NOUN
gi-4938	542	9	,	,	PUNCT
gi-4938	542	10	where	where	SCONJ
gi-4938	542	11	the	the	DET
gi-4938	542	12	proposed	propose	VERB
gi-4938	542	13	solutions	solution	NOUN
gi-4938	542	14	are	be	AUX
gi-4938	542	15	not	not	PART
gi-4938	542	16	sufficient	sufficient	ADJ
gi-4938	542	17	and	and	CCONJ
gi-4938	542	18	need	need	VERB
gi-4938	542	19	to	to	PART
gi-4938	542	20	be	be	AUX
gi-4938	542	21	refined	refine	VERB
gi-4938	542	22	.	.	PUNCT
gi-4938	543	1	a	a	DET
gi-4938	543	2	typical	typical	ADJ
gi-4938	543	3	situation	situation	NOUN
gi-4938	543	4	is	be	AUX
gi-4938	543	5	represented	represent	VERB
gi-4938	543	6	by	by	ADP
gi-4938	543	7	the	the	DET
gi-4938	543	8	isolated	isolated	ADJ
gi-4938	543	9	point	point	NOUN
gi-4938	543	10	,	,	PUNCT
gi-4938	543	11	which	which	PRON
gi-4938	543	12	is	be	AUX
gi-4938	543	13	currently	currently	ADV
gi-4938	543	14	thrown	throw	VERB
gi-4938	543	15	.	.	PUNCT
gi-4938	544	1	another	another	DET
gi-4938	544	2	benefit	benefit	NOUN
gi-4938	544	3	is	be	AUX
gi-4938	544	4	the	the	DET
gi-4938	544	5	relatively	relatively	ADV
gi-4938	544	6	simple	simple	ADJ
gi-4938	544	7	stack	stack	NOUN
gi-4938	544	8	-	-	PUNCT
gi-4938	544	9	based	base	VERB
gi-4938	544	10	implementation	implementation	NOUN
gi-4938	544	11	.	.	PUNCT
gi-4938	545	1	the	the	DET
gi-4938	545	2	source	source	NOUN
gi-4938	545	3	code	code	NOUN
gi-4938	545	4	written	write	VERB
gi-4938	545	5	in	in	ADP
gi-4938	545	6	java	java	PROPN
gi-4938	545	7	can	can	AUX
gi-4938	545	8	be	be	AUX
gi-4938	545	9	found	find	VERB
gi-4938	545	10	in	in	ADP
gi-4938	545	11	the	the	DET
gi-4938	545	12	github	github	PROPN
gi-4938	545	13	repository	repository	NOUN
gi-4938	545	14	https://github.com/bayertom/sampling	https://github.com/bayertom/sampling	NOUN
gi-4938	545	15	.	.	PUNCT
gi-4938	546	1	the	the	DET
gi-4938	546	2	next	next	ADJ
gi-4938	546	3	paper	paper	NOUN
gi-4938	546	4	brings	bring	VERB
gi-4938	546	5	an	an	DET
gi-4938	546	6	extension	extension	NOUN
gi-4938	546	7	of	of	ADP
gi-4938	546	8	this	this	DET
gi-4938	546	9	algorithm	algorithm	NOUN
gi-4938	546	10	for	for	ADP
gi-4938	546	11	combined	combined	ADJ
gi-4938	546	12	sampling	sampling	NOUN
gi-4938	546	13	of	of	ADP
gi-4938	546	14	the	the	DET
gi-4938	546	15	map	map	NOUN
gi-4938	546	16	projection	projection	NOUN
gi-4938	546	17	graticules	graticule	NOUN
gi-4938	546	18	,	,	PUNCT
gi-4938	546	19	when	when	SCONJ
gi-4938	546	20	the	the	DET
gi-4938	546	21	coordinate	coordinate	NOUN
gi-4938	546	22	functions	function	NOUN
gi-4938	546	23	f	f	X
gi-4938	546	24	,	,	PUNCT
gi-4938	546	25	g	g	PROPN
gi-4938	546	26	involve	involve	VERB
gi-4938	546	27	the	the	DET
gi-4938	546	28	discontinuities	discontinuity	NOUN
gi-4938	546	29	.	.	PUNCT
gi-4938	547	1	references	reference	NOUN
gi-4938	547	2	[	[	X
gi-4938	547	3	1	1	NUM
gi-4938	547	4	]	]	PUNCT
gi-4938	547	5	francesc	francesc	NOUN
gi-4938	547	6	arandiga	arandiga	PROPN
gi-4938	547	7	et	et	PROPN
gi-4938	547	8	al	al	PROPN
gi-4938	547	9	.	.	PUNCT
gi-4938	548	1	“	"	PUNCT
gi-4938	548	2	interpolation	interpolation	NOUN
gi-4938	548	3	and	and	CCONJ
gi-4938	548	4	approximation	approximation	NOUN
gi-4938	548	5	of	of	ADP
gi-4938	548	6	piecewise	piecewise	NOUN
gi-4938	548	7	smooth	smooth	ADJ
gi-4938	548	8	functions	function	NOUN
gi-4938	548	9	”	"	PUNCT
gi-4938	548	10	.	.	PUNCT
gi-4938	549	1	in	in	ADP
gi-4938	549	2	:	:	PUNCT
gi-4938	549	3	siam	siam	ADJ
gi-4938	549	4	journal	journal	PROPN
gi-4938	549	5	on	on	ADP
gi-4938	549	6	numerical	numerical	ADJ
gi-4938	549	7	analysis	analysis	NOUN
gi-4938	549	8	43.1	43.1	NUM
gi-4938	549	9	(	(	PUNCT
gi-4938	549	10	2005	2005	NUM
gi-4938	549	11	)	)	PUNCT
gi-4938	549	12	,	,	PUNCT
gi-4938	549	13	pp	pp	ADP
gi-4938	549	14	.	.	PUNCT
gi-4938	550	1	41–57	41–57	NUM
gi-4938	550	2	.	.	PUNCT
gi-4938	551	1	doi	doi	NOUN
gi-4938	551	2	:	:	PUNCT
gi-4938	551	3	10.1137/	10.1137/	NUM
gi-4938	551	4	s0036142903426245	s0036142903426245	NOUN
gi-4938	551	5	.	.	PUNCT
gi-4938	552	1	[	[	X
gi-4938	552	2	2	2	NUM
gi-4938	552	3	]	]	PUNCT
gi-4938	552	4	rick	rick	PROPN
gi-4938	552	5	archibald	archibald	PROPN
gi-4938	552	6	,	,	PUNCT
gi-4938	552	7	anne	anne	PROPN
gi-4938	552	8	gelb	gelb	PROPN
gi-4938	552	9	,	,	PUNCT
gi-4938	552	10	and	and	CCONJ
gi-4938	552	11	jungho	jungho	PROPN
gi-4938	552	12	yoon	yoon	PROPN
gi-4938	552	13	.	.	PUNCT
gi-4938	553	1	“	"	PUNCT
gi-4938	553	2	determining	determine	VERB
gi-4938	553	3	the	the	DET
gi-4938	553	4	locations	location	NOUN
gi-4938	553	5	and	and	CCONJ
gi-4938	553	6	discontinuities	discontinuity	NOUN
gi-4938	553	7	in	in	ADP
gi-4938	553	8	the	the	DET
gi-4938	553	9	derivatives	derivative	NOUN
gi-4938	553	10	of	of	ADP
gi-4938	553	11	functions	function	NOUN
gi-4938	553	12	”	"	PUNCT
gi-4938	553	13	.	.	PUNCT
gi-4938	554	1	in	in	ADP
gi-4938	554	2	:	:	PUNCT
gi-4938	554	3	applied	apply	VERB
gi-4938	554	4	numerical	numerical	ADJ
gi-4938	554	5	mathematics	mathematic	NOUN
gi-4938	554	6	58.5	58.5	NUM
gi-4938	554	7	(	(	PUNCT
gi-4938	554	8	2008	2008	NUM
gi-4938	554	9	)	)	PUNCT
gi-4938	554	10	,	,	PUNCT
gi-4938	554	11	pp	pp	ADP
gi-4938	554	12	.	.	PUNCT
gi-4938	555	1	577–592	577–592	NUM
gi-4938	555	2	.	.	PUNCT
gi-4938	556	1	[	[	X
gi-4938	556	2	3	3	NUM
gi-4938	556	3	]	]	PUNCT
gi-4938	556	4	andré	andré	PROPN
gi-4938	556	5	ricardo	ricardo	PROPN
gi-4938	556	6	backes	backes	PROPN
gi-4938	556	7	and	and	CCONJ
gi-4938	556	8	odemir	odemir	PROPN
gi-4938	556	9	martinez	martinez	PROPN
gi-4938	556	10	bruno	bruno	PROPN
gi-4938	556	11	.	.	PUNCT
gi-4938	557	1	“	"	PUNCT
gi-4938	557	2	polygonal	polygonal	ADJ
gi-4938	557	3	approximation	approximation	NOUN
gi-4938	557	4	of	of	ADP
gi-4938	557	5	digital	digital	ADJ
gi-4938	557	6	planar	planar	ADJ
gi-4938	557	7	curves	curve	NOUN
gi-4938	557	8	through	through	ADP
gi-4938	557	9	vertex	vertex	NOUN
gi-4938	557	10	betweenness	betweenness	NOUN
gi-4938	557	11	”	"	PUNCT
gi-4938	557	12	.	.	PUNCT
gi-4938	558	1	in	in	ADP
gi-4938	558	2	:	:	PUNCT
gi-4938	558	3	information	information	NOUN
gi-4938	558	4	sciences	science	NOUN
gi-4938	558	5	222	222	NUM
gi-4938	558	6	(	(	PUNCT
gi-4938	558	7	2013	2013	NUM
gi-4938	558	8	)	)	PUNCT
gi-4938	558	9	,	,	PUNCT
gi-4938	558	10	pp	pp	ADP
gi-4938	558	11	.	.	PUNCT
gi-4938	559	1	795–804	795–804	NUM
gi-4938	559	2	.	.	PUNCT
gi-4938	560	1	[	[	X
gi-4938	560	2	4	4	X
gi-4938	560	3	]	]	PUNCT
gi-4938	560	4	nana	nana	PROPN
gi-4938	560	5	s.	s.	PROPN
gi-4938	560	6	banerjee	banerjee	PROPN
gi-4938	560	7	,	,	PUNCT
gi-4938	560	8	james	james	PROPN
gi-4938	560	9	f.	f.	PROPN
gi-4938	560	10	geer	geer	PROPN
gi-4938	560	11	,	,	PUNCT
gi-4938	560	12	and	and	CCONJ
gi-4938	560	13	langley	langley	PROPN
gi-4938	560	14	research	research	NOUN
gi-4938	560	15	center	center	NOUN
gi-4938	560	16	.	.	PUNCT
gi-4938	561	1	exponential	exponential	ADJ
gi-4938	561	2	approximations	approximation	NOUN
gi-4938	561	3	using	use	VERB
gi-4938	561	4	fourier	fourier	PROPN
gi-4938	561	5	series	series	NOUN
gi-4938	561	6	partial	partial	ADJ
gi-4938	561	7	sums	sum	NOUN
gi-4938	562	1	[	[	X
gi-4938	562	2	microform	microform	X
gi-4938	562	3	]	]	X
gi-4938	562	4	/	/	SYM
gi-4938	562	5	nana	nana	PROPN
gi-4938	562	6	s.	s.	PROPN
gi-4938	562	7	banerjee	banerjee	PROPN
gi-4938	562	8	and	and	CCONJ
gi-4938	562	9	james	james	PROPN
gi-4938	562	10	f.	f.	PROPN
gi-4938	562	11	geer	geer	PROPN
gi-4938	562	12	.	.	PUNCT
gi-4938	563	1	english	english	PROPN
gi-4938	563	2	.	.	PUNCT
gi-4938	564	1	national	national	ADJ
gi-4938	564	2	aeronautics	aeronautics	PROPN
gi-4938	564	3	and	and	CCONJ
gi-4938	564	4	space	space	NOUN
gi-4938	564	5	administration	administration	NOUN
gi-4938	564	6	,	,	PUNCT
gi-4938	564	7	langley	langley	PROPN
gi-4938	564	8	research	research	NOUN
gi-4938	564	9	center	center	NOUN
gi-4938	564	10	;	;	PUNCT
gi-4938	564	11	national	national	PROPN
gi-4938	564	12	technical	technical	PROPN
gi-4938	564	13	information	information	PROPN
gi-4938	564	14	service	service	NOUN
gi-4938	564	15	,	,	PUNCT
gi-4938	564	16	distributor	distributor	PROPN
gi-4938	564	17	hampton	hampton	PROPN
gi-4938	564	18	,	,	PUNCT
gi-4938	564	19	va	va	PROPN
gi-4938	564	20	.	.	PUNCT
gi-4938	564	21	:	:	PUNCT
gi-4938	565	1	[	[	X
gi-4938	565	2	springfield	springfield	PROPN
gi-4938	565	3	,	,	PUNCT
gi-4938	565	4	va	va	PROPN
gi-4938	565	5	,	,	PUNCT
gi-4938	565	6	1997	1997	NUM
gi-4938	565	7	,	,	PUNCT
gi-4938	565	8	p.	p.	NOUN
gi-4938	565	9	1	1	NUM
gi-4938	566	1	v.	v.	ADP
gi-4938	566	2	[	[	X
gi-4938	566	3	5	5	X
gi-4938	566	4	]	]	X
gi-4938	566	5	robert	robert	PROPN
gi-4938	566	6	bruce	bruce	PROPN
gi-4938	566	7	bauer	bauer	PROPN
gi-4938	566	8	.	.	PUNCT
gi-4938	567	1	“	"	PUNCT
gi-4938	567	2	band	band	NOUN
gi-4938	567	3	pass	pass	NOUN
gi-4938	567	4	filters	filter	NOUN
gi-4938	567	5	for	for	ADP
gi-4938	567	6	determining	determine	VERB
gi-4938	567	7	shock	shock	NOUN
gi-4938	567	8	locations	location	NOUN
gi-4938	567	9	”	"	PUNCT
gi-4938	567	10	.	.	PUNCT
gi-4938	568	1	in	in	ADP
gi-4938	568	2	:	:	PUNCT
gi-4938	568	3	(	(	PUNCT
gi-4938	568	4	)	)	PUNCT
gi-4938	568	5	.	.	PUNCT
gi-4938	569	1	[	[	X
gi-4938	569	2	6	6	NUM
gi-4938	569	3	]	]	PUNCT
gi-4938	569	4	frédéric	frédéric	PROPN
gi-4938	569	5	benhamou	benhamou	PROPN
gi-4938	569	6	and	and	CCONJ
gi-4938	569	7	william	william	PROPN
gi-4938	569	8	j.	j.	PROPN
gi-4938	569	9	older	older	PROPN
gi-4938	569	10	.	.	PUNCT
gi-4938	570	1	“	"	PUNCT
gi-4938	570	2	applying	apply	VERB
gi-4938	570	3	interval	interval	NOUN
gi-4938	570	4	arithmetic	arithmetic	ADJ
gi-4938	570	5	to	to	ADP
gi-4938	570	6	real	real	ADJ
gi-4938	570	7	,	,	PUNCT
gi-4938	570	8	integer	integer	NOUN
gi-4938	570	9	,	,	PUNCT
gi-4938	570	10	and	and	CCONJ
gi-4938	570	11	boolean	boolean	ADJ
gi-4938	570	12	constraints	constraint	NOUN
gi-4938	570	13	”	"	PUNCT
gi-4938	570	14	.	.	PUNCT
gi-4938	571	1	in	in	ADP
gi-4938	571	2	:	:	PUNCT
gi-4938	571	3	the	the	DET
gi-4938	571	4	journal	journal	NOUN
gi-4938	571	5	of	of	ADP
gi-4938	571	6	logic	logic	NOUN
gi-4938	571	7	programming	program	VERB
gi-4938	571	8	32.1	32.1	NUM
gi-4938	571	9	(	(	PUNCT
gi-4938	571	10	1997	1997	NUM
gi-4938	571	11	)	)	PUNCT
gi-4938	571	12	,	,	PUNCT
gi-4938	571	13	pp	pp	PROPN
gi-4938	571	14	.	.	PUNCT
gi-4938	571	15	1–24	1–24	PROPN
gi-4938	571	16	.	.	PUNCT
gi-4938	572	1	issn	issn	PROPN
gi-4938	572	2	:	:	PUNCT
gi-4938	572	3	0743	0743	NUM
gi-4938	572	4	-	-	SYM
gi-4938	572	5	1066	1066	NUM
gi-4938	572	6	.	.	PUNCT
gi-4938	573	1	doi	doi	NOUN
gi-4938	573	2	:	:	PUNCT
gi-4938	573	3	https://doi.org/10.1016/s0743-1066(96)00142-2	https://doi.org/10.1016/s0743-1066(96)00142-2	NOUN
gi-4938	573	4	.	.	PUNCT
gi-4938	574	1	[	[	X
gi-4938	574	2	7	7	X
gi-4938	574	3	]	]	PUNCT
gi-4938	574	4	p.	p.	NOUN
gi-4938	574	5	binev	binev	PROPN
gi-4938	574	6	et	et	PROPN
gi-4938	574	7	al	al	PROPN
gi-4938	574	8	.	.	PUNCT
gi-4938	575	1	“	"	PUNCT
gi-4938	575	2	adaptive	adaptive	ADJ
gi-4938	575	3	approximation	approximation	NOUN
gi-4938	575	4	of	of	ADP
gi-4938	575	5	curves	curve	NOUN
gi-4938	575	6	”	"	PUNCT
gi-4938	575	7	.	.	PUNCT
gi-4938	576	1	in	in	ADP
gi-4938	576	2	:	:	PUNCT
gi-4938	576	3	approximation	approximation	NOUN
gi-4938	576	4	theory	theory	NOUN
gi-4938	576	5	(	(	PUNCT
gi-4938	576	6	2004	2004	NUM
gi-4938	576	7	)	)	PUNCT
gi-4938	576	8	,	,	PUNCT
gi-4938	576	9	pp	pp	ADV
gi-4938	576	10	.	.	PUNCT
gi-4938	577	1	43–57	43–57	NUM
gi-4938	577	2	.	.	PUNCT
gi-4938	578	1	[	[	X
gi-4938	578	2	8	8	NUM
gi-4938	578	3	]	]	X
gi-4938	578	4	mira	mira	X
gi-4938	578	5	bozzini	bozzini	VERB
gi-4938	578	6	and	and	CCONJ
gi-4938	578	7	milvia	milvia	VERB
gi-4938	578	8	rossini	rossini	PROPN
gi-4938	578	9	.	.	PUNCT
gi-4938	579	1	“	"	PUNCT
gi-4938	579	2	the	the	DET
gi-4938	579	3	detection	detection	NOUN
gi-4938	579	4	and	and	CCONJ
gi-4938	579	5	recovery	recovery	NOUN
gi-4938	579	6	of	of	ADP
gi-4938	579	7	discontinuity	discontinuity	NOUN
gi-4938	579	8	curves	curve	NOUN
gi-4938	579	9	from	from	ADP
gi-4938	579	10	scattered	scatter	VERB
gi-4938	579	11	data	datum	NOUN
gi-4938	579	12	”	"	PUNCT
gi-4938	579	13	.	.	PUNCT
gi-4938	580	1	in	in	ADP
gi-4938	580	2	:	:	PUNCT
gi-4938	580	3	journal	journal	NOUN
gi-4938	580	4	of	of	ADP
gi-4938	580	5	computational	computational	ADJ
gi-4938	580	6	and	and	CCONJ
gi-4938	580	7	applied	apply	VERB
gi-4938	580	8	mathematics	mathematic	NOUN
gi-4938	580	9	240.supplement	240.supplement	NUM
gi-4938	580	10	c	c	NOUN
gi-4938	580	11	(	(	PUNCT
gi-4938	580	12	2013	2013	NUM
gi-4938	580	13	)	)	PUNCT
gi-4938	580	14	.	.	PUNCT
gi-4938	581	1	mata	mata	PROPN
gi-4938	581	2	2012	2012	NUM
gi-4938	581	3	,	,	PUNCT
gi-4938	581	4	pp	pp	ADP
gi-4938	581	5	.	.	PUNCT
gi-4938	582	1	148–162	148–162	NUM
gi-4938	582	2	.	.	PUNCT
gi-4938	583	1	issn	issn	PROPN
gi-4938	583	2	:	:	PUNCT
gi-4938	583	3	0377	0377	NUM
gi-4938	583	4	-	-	SYM
gi-4938	583	5	0427	0427	NUM
gi-4938	583	6	.	.	PUNCT
gi-4938	584	1	doi	doi	NOUN
gi-4938	584	2	:	:	PUNCT
gi-4938	584	3	https://doi.org/	https://doi.org/	VERB
gi-4938	584	4	10.1016	10.1016	NUM
gi-4938	584	5	/	/	SYM
gi-4938	584	6	j.cam.2012.06.014	j.cam.2012.06.014	PROPN
gi-4938	584	7	.	.	PUNCT
gi-4938	585	1	[	[	X
gi-4938	585	2	9	9	NUM
gi-4938	585	3	]	]	PUNCT
gi-4938	585	4	a	a	DET
gi-4938	585	5	carmona	carmona	NOUN
gi-4938	585	6	-	-	PUNCT
gi-4938	585	7	poyato	poyato	NOUN
gi-4938	585	8	et	et	PROPN
gi-4938	585	9	al	al	PROPN
gi-4938	585	10	.	.	PUNCT
gi-4938	586	1	“	"	PUNCT
gi-4938	586	2	polygonal	polygonal	ADJ
gi-4938	586	3	approximation	approximation	NOUN
gi-4938	586	4	of	of	ADP
gi-4938	586	5	digital	digital	ADJ
gi-4938	586	6	planar	planar	ADJ
gi-4938	586	7	curves	curve	NOUN
gi-4938	586	8	through	through	ADP
gi-4938	586	9	break	break	NOUN
gi-4938	586	10	point	point	NOUN
gi-4938	586	11	suppression	suppression	NOUN
gi-4938	586	12	”	"	PUNCT
gi-4938	586	13	.	.	PUNCT
gi-4938	587	1	in	in	ADP
gi-4938	587	2	:	:	PUNCT
gi-4938	587	3	pattern	pattern	NOUN
gi-4938	587	4	recognition	recognition	NOUN
gi-4938	587	5	43.1	43.1	NUM
gi-4938	587	6	(	(	PUNCT
gi-4938	587	7	2010	2010	NUM
gi-4938	587	8	)	)	PUNCT
gi-4938	587	9	,	,	PUNCT
gi-4938	587	10	pp	pp	ADP
gi-4938	587	11	.	.	PUNCT
gi-4938	588	1	14–25	14–25	X
gi-4938	588	2	.	.	PUNCT
gi-4938	589	1	[	[	X
gi-4938	589	2	10	10	NUM
gi-4938	589	3	]	]	X
gi-4938	589	4	filipe	filipe	PROPN
gi-4938	589	5	de	de	PROPN
gi-4938	589	6	carvalho	carvalho	PROPN
gi-4938	589	7	nascimento	nascimento	PROPN
gi-4938	589	8	et	et	PROPN
gi-4938	589	9	al	al	PROPN
gi-4938	589	10	.	.	PUNCT
gi-4938	590	1	“	"	PUNCT
gi-4938	590	2	approximating	approximate	VERB
gi-4938	590	3	implicit	implicit	ADJ
gi-4938	590	4	curves	curve	NOUN
gi-4938	590	5	on	on	ADP
gi-4938	590	6	plane	plane	NOUN
gi-4938	590	7	and	and	CCONJ
gi-4938	590	8	surface	surface	NOUN
gi-4938	590	9	triangulations	triangulation	NOUN
gi-4938	590	10	with	with	ADP
gi-4938	590	11	affine	affine	NOUN
gi-4938	590	12	arithmetic	arithmetic	NOUN
gi-4938	590	13	”	"	PUNCT
gi-4938	590	14	.	.	PUNCT
gi-4938	591	1	in	in	ADP
gi-4938	591	2	:	:	PUNCT
gi-4938	591	3	computers	computer	NOUN
gi-4938	591	4	&	&	CCONJ
gi-4938	591	5	graphics	graphic	NOUN
gi-4938	591	6	40	40	NUM
gi-4938	591	7	(	(	PUNCT
gi-4938	591	8	2014	2014	NUM
gi-4938	591	9	)	)	PUNCT
gi-4938	591	10	,	,	PUNCT
gi-4938	591	11	pp	pp	ADJ
gi-4938	591	12	.	.	PUNCT
gi-4938	592	1	36–48	36–48	NUM
gi-4938	592	2	.	.	PUNCT
gi-4938	593	1	geoinformatics	geoinformatic	NOUN
gi-4938	593	2	fce	fce	VERB
gi-4938	593	3	ctu	ctu	NOUN
gi-4938	593	4	17(2	17(2	NUM
gi-4938	593	5	)	)	PUNCT
gi-4938	593	6	,	,	PUNCT
gi-4938	593	7	2018	2018	NUM
gi-4938	593	8	26	26	NUM
gi-4938	593	9	https://github.com/bayertom/sampling	https://github.com/bayertom/sampling	NOUN
gi-4938	593	10	https://doi.org/10.1137/s0036142903426245	https://doi.org/10.1137/s0036142903426245	PROPN
gi-4938	593	11	https://doi.org/10.1137/s0036142903426245	https://doi.org/10.1137/s0036142903426245	PROPN
gi-4938	593	12	https://doi.org/https://doi.org/10.1016/s0743-1066(96)00142-2	https://doi.org/https://doi.org/10.1016/s0743-1066(96)00142-2	PART
gi-4938	593	13	https://doi.org/https://doi.org/10.1016/j.cam.2012.06.014	https://doi.org/https://doi.org/10.1016/j.cam.2012.06.014	PROPN
gi-4938	593	14	https://doi.org/https://doi.org/10.1016/j.cam.2012.06.014	https://doi.org/https://doi.org/10.1016/j.cam.2012.06.014	PROPN
gi-4938	593	15	t.	t.	PROPN
gi-4938	593	16	bayer	bayer	PROPN
gi-4938	593	17	:	:	PUNCT
gi-4938	593	18	efficient	efficient	ADJ
gi-4938	593	19	plotting	plot	VERB
gi-4938	593	20	the	the	DET
gi-4938	593	21	functions	function	NOUN
gi-4938	593	22	with	with	ADP
gi-4938	593	23	discontinuities	discontinuity	NOUN
gi-4938	593	24	[	[	X
gi-4938	593	25	11	11	NUM
gi-4938	593	26	]	]	X
gi-4938	593	27	dennis	dennis	PROPN
gi-4938	593	28	cates	cates	PROPN
gi-4938	593	29	and	and	CCONJ
gi-4938	593	30	anne	anne	PROPN
gi-4938	593	31	gelb	gelb	PROPN
gi-4938	593	32	.	.	PUNCT
gi-4938	594	1	“	"	PUNCT
gi-4938	594	2	detecting	detect	VERB
gi-4938	594	3	derivative	derivative	ADJ
gi-4938	594	4	discontinuity	discontinuity	NOUN
gi-4938	594	5	locations	location	NOUN
gi-4938	594	6	in	in	ADP
gi-4938	594	7	piecewise	piecewise	NOUN
gi-4938	594	8	continuous	continuous	ADJ
gi-4938	594	9	functions	function	NOUN
gi-4938	594	10	from	from	ADP
gi-4938	594	11	fourier	fourier	ADJ
gi-4938	594	12	spectral	spectral	ADJ
gi-4938	594	13	data	datum	NOUN
gi-4938	594	14	”	"	PUNCT
gi-4938	594	15	.	.	PUNCT
gi-4938	595	1	in	in	ADP
gi-4938	595	2	:	:	PUNCT
gi-4938	595	3	numerical	numerical	ADJ
gi-4938	595	4	algorithms	algorithm	NOUN
gi-4938	595	5	46.1	46.1	NUM
gi-4938	595	6	(	(	PUNCT
gi-4938	595	7	2007	2007	NUM
gi-4938	595	8	)	)	PUNCT
gi-4938	595	9	,	,	PUNCT
gi-4938	595	10	pp	pp	ADP
gi-4938	595	11	.	.	PUNCT
gi-4938	596	1	59–84	59–84	NOUN
gi-4938	596	2	.	.	PUNCT
gi-4938	597	1	[	[	X
gi-4938	597	2	12	12	NUM
gi-4938	597	3	]	]	X
gi-4938	597	4	knut	knut	PROPN
gi-4938	597	5	s	s	PART
gi-4938	597	6	eckhoff	eckhoff	NOUN
gi-4938	597	7	.	.	PUNCT
gi-4938	598	1	“	"	PUNCT
gi-4938	598	2	accurate	accurate	ADJ
gi-4938	598	3	reconstructions	reconstruction	NOUN
gi-4938	598	4	of	of	ADP
gi-4938	598	5	functions	function	NOUN
gi-4938	598	6	of	of	ADP
gi-4938	598	7	finite	finite	ADJ
gi-4938	598	8	regularity	regularity	NOUN
gi-4938	598	9	from	from	ADP
gi-4938	598	10	truncated	truncated	ADJ
gi-4938	598	11	fourier	fourier	NOUN
gi-4938	598	12	series	series	PROPN
gi-4938	598	13	expansions	expansion	NOUN
gi-4938	598	14	”	"	PUNCT
gi-4938	598	15	.	.	PUNCT
gi-4938	599	1	in	in	ADP
gi-4938	599	2	:	:	PUNCT
gi-4938	599	3	mathematics	mathematic	NOUN
gi-4938	599	4	of	of	ADP
gi-4938	599	5	computation	computation	NOUN
gi-4938	599	6	64.210	64.210	NUM
gi-4938	599	7	(	(	PUNCT
gi-4938	599	8	1995	1995	NUM
gi-4938	599	9	)	)	PUNCT
gi-4938	599	10	,	,	PUNCT
gi-4938	599	11	pp	pp	ADV
gi-4938	599	12	.	.	PUNCT
gi-4938	599	13	671	671	NUM
gi-4938	599	14	–	–	PUNCT
gi-4938	599	15	690	690	NUM
gi-4938	599	16	.	.	PUNCT
gi-4938	600	1	[	[	X
gi-4938	600	2	13	13	NUM
gi-4938	600	3	]	]	X
gi-4938	600	4	m.h	m.h	PROPN
gi-4938	600	5	.	.	PROPN
gi-4938	600	6	van	van	PROPN
gi-4938	600	7	emden	emden	NOUN
gi-4938	600	8	.	.	PUNCT
gi-4938	601	1	“	"	PUNCT
gi-4938	601	2	value	value	NOUN
gi-4938	601	3	constraints	constraint	NOUN
gi-4938	601	4	in	in	ADP
gi-4938	601	5	the	the	DET
gi-4938	601	6	clp	clp	NOUN
gi-4938	601	7	scheme	scheme	NOUN
gi-4938	601	8	”	"	PUNCT
gi-4938	601	9	.	.	PUNCT
gi-4938	602	1	in	in	ADP
gi-4938	602	2	:	:	PUNCT
gi-4938	602	3	constraints	constraint	NOUN
gi-4938	602	4	2.2	2.2	NUM
gi-4938	602	5	(	(	PUNCT
gi-4938	602	6	oct	oct	PROPN
gi-4938	602	7	.	.	PROPN
gi-4938	602	8	1997	1997	NUM
gi-4938	602	9	)	)	PUNCT
gi-4938	602	10	,	,	PUNCT
gi-4938	602	11	pp	pp	ADP
gi-4938	602	12	.	.	PUNCT
gi-4938	603	1	163–183	163–183	NUM
gi-4938	603	2	.	.	PUNCT
gi-4938	604	1	issn	issn	PROPN
gi-4938	604	2	:	:	PUNCT
gi-4938	604	3	1572	1572	NUM
gi-4938	604	4	-	-	SYM
gi-4938	604	5	9354	9354	NUM
gi-4938	604	6	.	.	PUNCT
gi-4938	605	1	doi	doi	NOUN
gi-4938	605	2	:	:	PUNCT
gi-4938	605	3	10.1023	10.1023	NUM
gi-4938	605	4	/	/	SYM
gi-4938	605	5	a:1009705709733	a:1009705709733	NOUN
gi-4938	605	6	.	.	PUNCT
gi-4938	606	1	[	[	X
gi-4938	606	2	14	14	NUM
gi-4938	606	3	]	]	X
gi-4938	606	4	richard	richard	PROPN
gi-4938	606	5	fateman	fateman	PROPN
gi-4938	606	6	.	.	PUNCT
gi-4938	607	1	“	"	PUNCT
gi-4938	607	2	honest	honest	ADJ
gi-4938	607	3	plotting	plotting	NOUN
gi-4938	607	4	,	,	PUNCT
gi-4938	607	5	global	global	ADJ
gi-4938	607	6	extrema	extrema	NOUN
gi-4938	607	7	,	,	PUNCT
gi-4938	607	8	and	and	CCONJ
gi-4938	607	9	interval	interval	NOUN
gi-4938	607	10	arithmetic	arithmetic	NOUN
gi-4938	607	11	”	"	PUNCT
gi-4938	607	12	.	.	PUNCT
gi-4938	608	1	in	in	ADP
gi-4938	608	2	:	:	PUNCT
gi-4938	608	3	papers	paper	NOUN
gi-4938	608	4	from	from	ADP
gi-4938	608	5	the	the	DET
gi-4938	608	6	international	international	ADJ
gi-4938	608	7	symposium	symposium	NOUN
gi-4938	608	8	on	on	ADP
gi-4938	608	9	symbolic	symbolic	ADJ
gi-4938	608	10	and	and	CCONJ
gi-4938	608	11	algebraic	algebraic	ADJ
gi-4938	608	12	computation	computation	NOUN
gi-4938	608	13	.	.	PUNCT
gi-4938	609	1	issac	issac	NOUN
gi-4938	609	2	’	’	NOUN
gi-4938	609	3	92	92	NUM
gi-4938	609	4	.	.	PUNCT
gi-4938	610	1	berkeley	berkeley	PROPN
gi-4938	610	2	,	,	PUNCT
gi-4938	610	3	california	california	PROPN
gi-4938	610	4	,	,	PUNCT
gi-4938	610	5	usa	usa	PROPN
gi-4938	610	6	:	:	PUNCT
gi-4938	610	7	acm	acm	PROPN
gi-4938	610	8	,	,	PUNCT
gi-4938	610	9	1992	1992	NUM
gi-4938	610	10	,	,	PUNCT
gi-4938	610	11	pp	pp	ADV
gi-4938	610	12	.	.	PUNCT
gi-4938	611	1	216–223	216–223	NUM
gi-4938	611	2	.	.	PUNCT
gi-4938	612	1	isbn	isbn	ADJ
gi-4938	612	2	:	:	PUNCT
gi-4938	612	3	0	0	NUM
gi-4938	612	4	-	-	SYM
gi-4938	612	5	89791	89791	NUM
gi-4938	612	6	-	-	PUNCT
gi-4938	612	7	489	489	NUM
gi-4938	612	8	-	-	PUNCT
gi-4938	612	9	9	9	NUM
gi-4938	612	10	.	.	PUNCT
gi-4938	612	11	doi	doi	NOUN
gi-4938	612	12	:	:	PUNCT
gi-4938	612	13	10.1145/143242.143314	10.1145/143242.143314	NUM
gi-4938	612	14	.	.	PUNCT
gi-4938	613	1	[	[	X
gi-4938	613	2	15	15	NUM
gi-4938	613	3	]	]	X
gi-4938	613	4	luiz	luiz	PROPN
gi-4938	613	5	henrique	henrique	PROPN
gi-4938	613	6	de	de	PROPN
gi-4938	613	7	figueiredo	figueiredo	PROPN
gi-4938	613	8	.	.	PUNCT
gi-4938	614	1	“	"	PUNCT
gi-4938	614	2	adaptive	adaptive	ADJ
gi-4938	614	3	sampling	sampling	NOUN
gi-4938	614	4	of	of	ADP
gi-4938	614	5	parametric	parametric	ADJ
gi-4938	614	6	curves	curve	NOUN
gi-4938	614	7	”	"	PUNCT
gi-4938	614	8	.	.	PUNCT
gi-4938	615	1	in	in	ADP
gi-4938	615	2	:	:	PUNCT
gi-4938	615	3	graphics	graphic	NOUN
gi-4938	615	4	gems	gem	NOUN
gi-4938	615	5	v	v	ADP
gi-4938	615	6	5	5	NUM
gi-4938	615	7	(	(	PUNCT
gi-4938	615	8	1995	1995	NUM
gi-4938	615	9	)	)	PUNCT
gi-4938	615	10	,	,	PUNCT
gi-4938	615	11	pp	pp	ADP
gi-4938	615	12	.	.	PUNCT
gi-4938	616	1	173–178	173–178	NUM
gi-4938	616	2	.	.	PUNCT
gi-4938	617	1	[	[	X
gi-4938	617	2	16	16	NUM
gi-4938	617	3	]	]	X
gi-4938	617	4	anne	anne	PROPN
gi-4938	617	5	gelb	gelb	PROPN
gi-4938	617	6	and	and	CCONJ
gi-4938	617	7	eitan	eitan	PROPN
gi-4938	617	8	tadmor	tadmor	PROPN
gi-4938	617	9	.	.	PUNCT
gi-4938	618	1	“	"	PUNCT
gi-4938	618	2	adaptive	adaptive	ADJ
gi-4938	618	3	edge	edge	NOUN
gi-4938	618	4	detectors	detector	NOUN
gi-4938	618	5	for	for	ADP
gi-4938	618	6	piecewise	piecewise	NOUN
gi-4938	618	7	smooth	smooth	ADJ
gi-4938	618	8	data	datum	NOUN
gi-4938	618	9	based	base	VERB
gi-4938	618	10	on	on	ADP
gi-4938	618	11	the	the	DET
gi-4938	618	12	minmod	minmod	NOUN
gi-4938	618	13	limiter	limiter	NOUN
gi-4938	618	14	”	"	PUNCT
gi-4938	618	15	.	.	PUNCT
gi-4938	619	1	in	in	ADP
gi-4938	619	2	:	:	PUNCT
gi-4938	619	3	journal	journal	NOUN
gi-4938	619	4	of	of	ADP
gi-4938	619	5	scientific	scientific	ADJ
gi-4938	619	6	computing	computing	NOUN
gi-4938	619	7	28.2	28.2	NUM
gi-4938	619	8	(	(	PUNCT
gi-4938	619	9	2006	2006	NUM
gi-4938	619	10	)	)	PUNCT
gi-4938	619	11	,	,	PUNCT
gi-4938	619	12	pp	pp	ADP
gi-4938	619	13	.	.	PUNCT
gi-4938	620	1	279–306	279–306	NUM
gi-4938	620	2	.	.	PUNCT
gi-4938	621	1	[	[	X
gi-4938	621	2	17	17	NUM
gi-4938	621	3	]	]	X
gi-4938	621	4	anne	anne	PROPN
gi-4938	621	5	gelb	gelb	PROPN
gi-4938	621	6	and	and	CCONJ
gi-4938	621	7	eitan	eitan	PROPN
gi-4938	621	8	tadmor	tadmor	PROPN
gi-4938	621	9	.	.	PUNCT
gi-4938	622	1	“	"	PUNCT
gi-4938	622	2	spectral	spectral	ADJ
gi-4938	622	3	reconstruction	reconstruction	NOUN
gi-4938	622	4	of	of	ADP
gi-4938	622	5	piecewise	piecewise	NOUN
gi-4938	622	6	smooth	smooth	ADJ
gi-4938	622	7	functions	function	NOUN
gi-4938	622	8	from	from	ADP
gi-4938	622	9	their	their	PRON
gi-4938	622	10	discrete	discrete	ADJ
gi-4938	622	11	data	datum	NOUN
gi-4938	622	12	”	"	PUNCT
gi-4938	622	13	.	.	PUNCT
gi-4938	623	1	in	in	ADP
gi-4938	623	2	:	:	PUNCT
gi-4938	623	3	esaim	esaim	NOUN
gi-4938	623	4	:	:	PUNCT
gi-4938	623	5	mathematical	mathematical	ADJ
gi-4938	623	6	modelling	modelling	NOUN
gi-4938	623	7	and	and	CCONJ
gi-4938	623	8	numerical	numerical	ADJ
gi-4938	623	9	analysis	analysis	NOUN
gi-4938	623	10	36.2	36.2	NUM
gi-4938	623	11	(	(	PUNCT
gi-4938	623	12	2002	2002	NUM
gi-4938	623	13	)	)	PUNCT
gi-4938	623	14	,	,	PUNCT
gi-4938	623	15	pp	pp	ADP
gi-4938	623	16	.	.	PUNCT
gi-4938	624	1	155–175	155–175	NUM
gi-4938	624	2	.	.	PUNCT
gi-4938	625	1	[	[	X
gi-4938	625	2	18	18	NUM
gi-4938	625	3	]	]	X
gi-4938	625	4	stuart	stuart	PROPN
gi-4938	625	5	geman	geman	PROPN
gi-4938	625	6	and	and	CCONJ
gi-4938	625	7	donald	donald	PROPN
gi-4938	625	8	geman	geman	PROPN
gi-4938	625	9	.	.	PUNCT
gi-4938	626	1	“	"	PUNCT
gi-4938	626	2	stochastic	stochastic	ADJ
gi-4938	626	3	relaxation	relaxation	NOUN
gi-4938	626	4	,	,	PUNCT
gi-4938	626	5	gibbs	gibbs	PROPN
gi-4938	626	6	distributions	distribution	NOUN
gi-4938	626	7	,	,	PUNCT
gi-4938	626	8	and	and	CCONJ
gi-4938	626	9	the	the	DET
gi-4938	626	10	bayesian	bayesian	NOUN
gi-4938	626	11	restoration	restoration	NOUN
gi-4938	626	12	of	of	ADP
gi-4938	626	13	images	image	NOUN
gi-4938	626	14	”	"	PUNCT
gi-4938	626	15	.	.	PUNCT
gi-4938	627	1	in	in	ADP
gi-4938	627	2	:	:	PUNCT
gi-4938	627	3	ieee	ieee	NOUN
gi-4938	627	4	transactions	transaction	NOUN
gi-4938	627	5	on	on	ADP
gi-4938	627	6	pattern	pattern	NOUN
gi-4938	627	7	analysis	analysis	NOUN
gi-4938	627	8	and	and	CCONJ
gi-4938	627	9	machine	machine	NOUN
gi-4938	627	10	intelligence	intelligence	NOUN
gi-4938	627	11	6	6	NUM
gi-4938	627	12	(	(	PUNCT
gi-4938	627	13	1984	1984	NUM
gi-4938	627	14	)	)	PUNCT
gi-4938	627	15	,	,	PUNCT
gi-4938	627	16	pp	pp	ADP
gi-4938	627	17	.	.	PUNCT
gi-4938	628	1	721–741	721–741	NUM
gi-4938	628	2	.	.	PUNCT
gi-4938	629	1	[	[	X
gi-4938	629	2	19	19	NUM
gi-4938	629	3	]	]	PUNCT
gi-4938	629	4	tim	tim	PROPN
gi-4938	629	5	gutzmer	gutzmer	PROPN
gi-4938	629	6	and	and	CCONJ
gi-4938	629	7	armin	armin	PROPN
gi-4938	629	8	iske	iske	PROPN
gi-4938	629	9	.	.	PUNCT
gi-4938	630	1	“	"	PUNCT
gi-4938	630	2	detection	detection	NOUN
gi-4938	630	3	of	of	ADP
gi-4938	630	4	discontinuities	discontinuity	NOUN
gi-4938	630	5	in	in	ADP
gi-4938	630	6	scattered	scatter	VERB
gi-4938	630	7	data	datum	NOUN
gi-4938	630	8	approximation	approximation	NOUN
gi-4938	630	9	”	"	PUNCT
gi-4938	630	10	.	.	PUNCT
gi-4938	631	1	in	in	ADP
gi-4938	631	2	:	:	PUNCT
gi-4938	631	3	numerical	numerical	ADJ
gi-4938	631	4	algorithms	algorithm	NOUN
gi-4938	631	5	16.2	16.2	NUM
gi-4938	631	6	(	(	PUNCT
gi-4938	631	7	1997	1997	NUM
gi-4938	631	8	)	)	PUNCT
gi-4938	631	9	,	,	PUNCT
gi-4938	631	10	pp	pp	ADP
gi-4938	631	11	.	.	PUNCT
gi-4938	632	1	155–170	155–170	NUM
gi-4938	632	2	.	.	PUNCT
gi-4938	633	1	[	[	X
gi-4938	633	2	20	20	NUM
gi-4938	633	3	]	]	X
gi-4938	633	4	timothy	timothy	PROPN
gi-4938	633	5	j.	j.	PROPN
gi-4938	633	6	hickey	hickey	PROPN
gi-4938	633	7	,	,	PUNCT
gi-4938	633	8	zhe	zhe	PROPN
gi-4938	633	9	qju	qju	PROPN
gi-4938	633	10	,	,	PUNCT
gi-4938	633	11	and	and	CCONJ
gi-4938	633	12	maarten	maarten	PROPN
gi-4938	633	13	h.	h.	PROPN
gi-4938	633	14	van	van	PROPN
gi-4938	633	15	emden	emden	PROPN
gi-4938	633	16	.	.	PUNCT
gi-4938	634	1	“	"	PUNCT
gi-4938	634	2	interval	interval	NOUN
gi-4938	634	3	constraint	constraint	NOUN
gi-4938	634	4	plotting	plot	VERB
gi-4938	634	5	for	for	ADP
gi-4938	634	6	interactive	interactive	ADJ
gi-4938	634	7	visual	visual	ADJ
gi-4938	634	8	exploration	exploration	NOUN
gi-4938	634	9	of	of	ADP
gi-4938	634	10	implicitly	implicitly	ADV
gi-4938	634	11	defined	define	VERB
gi-4938	634	12	relations	relation	NOUN
gi-4938	634	13	”	"	PUNCT
gi-4938	634	14	.	.	PUNCT
gi-4938	635	1	in	in	ADP
gi-4938	635	2	:	:	PUNCT
gi-4938	635	3	reliable	reliable	ADJ
gi-4938	635	4	computing	compute	VERB
gi-4938	635	5	6.1	6.1	NUM
gi-4938	635	6	(	(	PUNCT
gi-4938	635	7	feb	feb	PROPN
gi-4938	635	8	.	.	PROPN
gi-4938	635	9	2000	2000	NUM
gi-4938	635	10	)	)	PUNCT
gi-4938	635	11	,	,	PUNCT
gi-4938	635	12	pp	pp	PROPN
gi-4938	635	13	.	.	PUNCT
gi-4938	636	1	81–92	81–92	NUM
gi-4938	636	2	.	.	PUNCT
gi-4938	637	1	issn	issn	PROPN
gi-4938	637	2	:	:	PUNCT
gi-4938	637	3	1573	1573	NUM
gi-4938	637	4	-	-	SYM
gi-4938	637	5	1340	1340	NUM
gi-4938	637	6	.	.	PUNCT
gi-4938	638	1	doi	doi	NOUN
gi-4938	638	2	:	:	PUNCT
gi-4938	638	3	10.1023	10.1023	NUM
gi-4938	638	4	/	/	SYM
gi-4938	638	5	a:1009950630139	a:1009950630139	NOUN
gi-4938	638	6	.	.	PUNCT
gi-4938	639	1	[	[	X
gi-4938	639	2	21	21	NUM
gi-4938	639	3	]	]	X
gi-4938	639	4	yifan	yifan	PROPN
gi-4938	639	5	hu	hu	PROPN
gi-4938	639	6	.	.	PUNCT
gi-4938	640	1	“	"	PUNCT
gi-4938	640	2	efficient	efficient	ADJ
gi-4938	640	3	,	,	PUNCT
gi-4938	640	4	high	high	ADJ
gi-4938	640	5	-	-	PUNCT
gi-4938	640	6	quality	quality	NOUN
gi-4938	640	7	force	force	NOUN
gi-4938	640	8	-	-	PUNCT
gi-4938	640	9	directed	direct	VERB
gi-4938	640	10	graph	graph	NOUN
gi-4938	640	11	drawing	drawing	NOUN
gi-4938	640	12	”	"	PUNCT
gi-4938	640	13	.	.	PUNCT
gi-4938	641	1	in	in	ADP
gi-4938	641	2	:	:	PUNCT
gi-4938	641	3	mathematica	mathematica	PROPN
gi-4938	641	4	journal	journal	PROPN
gi-4938	641	5	10.1	10.1	NUM
gi-4938	641	6	(	(	PUNCT
gi-4938	641	7	2005	2005	NUM
gi-4938	641	8	)	)	PUNCT
gi-4938	641	9	,	,	PUNCT
gi-4938	641	10	pp	pp	PROPN
gi-4938	641	11	.	.	PUNCT
gi-4938	641	12	37–71	37–71	NOUN
gi-4938	641	13	.	.	PUNCT
gi-4938	642	1	[	[	X
gi-4938	642	2	22	22	NUM
gi-4938	642	3	]	]	X
gi-4938	642	4	guang	guang	PROPN
gi-4938	642	5	-	-	PUNCT
gi-4938	642	6	shan	shan	PROPN
gi-4938	642	7	jiang	jiang	PROPN
gi-4938	642	8	and	and	CCONJ
gi-4938	642	9	chi	chi	PROPN
gi-4938	642	10	-	-	PUNCT
gi-4938	642	11	wang	wang	PROPN
gi-4938	642	12	shu	shu	PROPN
gi-4938	642	13	.	.	PUNCT
gi-4938	643	1	“	"	PUNCT
gi-4938	643	2	efficient	efficient	ADJ
gi-4938	643	3	implementation	implementation	NOUN
gi-4938	643	4	of	of	ADP
gi-4938	643	5	weighted	weight	VERB
gi-4938	643	6	eno	eno	PROPN
gi-4938	643	7	schemes	scheme	NOUN
gi-4938	643	8	”	"	PUNCT
gi-4938	643	9	.	.	PUNCT
gi-4938	644	1	in	in	ADP
gi-4938	644	2	:	:	PUNCT
gi-4938	644	3	journal	journal	NOUN
gi-4938	644	4	of	of	ADP
gi-4938	644	5	computational	computational	ADJ
gi-4938	644	6	physics	physic	NOUN
gi-4938	644	7	126.1	126.1	NUM
gi-4938	644	8	(	(	PUNCT
gi-4938	644	9	1996	1996	NUM
gi-4938	644	10	)	)	PUNCT
gi-4938	644	11	,	,	PUNCT
gi-4938	644	12	pp	pp	ADP
gi-4938	644	13	.	.	PUNCT
gi-4938	645	1	202–228	202–228	NUM
gi-4938	645	2	.	.	PUNCT
gi-4938	646	1	[	[	X
gi-4938	646	2	23	23	NUM
gi-4938	646	3	]	]	X
gi-4938	646	4	george	george	PROPN
gi-4938	646	5	kvernadze	kvernadze	PROPN
gi-4938	646	6	.	.	PUNCT
gi-4938	647	1	“	"	PUNCT
gi-4938	647	2	determination	determination	NOUN
gi-4938	647	3	of	of	ADP
gi-4938	647	4	the	the	DET
gi-4938	647	5	jumps	jump	NOUN
gi-4938	647	6	of	of	ADP
gi-4938	647	7	a	a	DET
gi-4938	647	8	bounded	bounded	ADJ
gi-4938	647	9	function	function	NOUN
gi-4938	647	10	by	by	ADP
gi-4938	647	11	its	its	PRON
gi-4938	647	12	fourier	fourier	NOUN
gi-4938	647	13	series	series	NOUN
gi-4938	647	14	”	"	PUNCT
gi-4938	647	15	.	.	PUNCT
gi-4938	648	1	in	in	ADP
gi-4938	648	2	:	:	PUNCT
gi-4938	648	3	journal	journal	NOUN
gi-4938	648	4	of	of	ADP
gi-4938	648	5	approximation	approximation	NOUN
gi-4938	648	6	theory	theory	NOUN
gi-4938	648	7	92.2	92.2	NUM
gi-4938	648	8	(	(	PUNCT
gi-4938	648	9	1998	1998	NUM
gi-4938	648	10	)	)	PUNCT
gi-4938	648	11	,	,	PUNCT
gi-4938	648	12	pp	pp	ADP
gi-4938	648	13	.	.	PUNCT
gi-4938	649	1	167–190	167–190	NUM
gi-4938	649	2	.	.	PUNCT
gi-4938	650	1	[	[	X
gi-4938	650	2	24	24	NUM
gi-4938	650	3	]	]	X
gi-4938	650	4	david	david	PROPN
gi-4938	650	5	lee	lee	PROPN
gi-4938	650	6	.	.	PUNCT
gi-4938	651	1	“	"	PUNCT
gi-4938	651	2	detection	detection	NOUN
gi-4938	651	3	,	,	PUNCT
gi-4938	651	4	classification	classification	NOUN
gi-4938	651	5	,	,	PUNCT
gi-4938	651	6	and	and	CCONJ
gi-4938	651	7	measurement	measurement	NOUN
gi-4938	651	8	of	of	ADP
gi-4938	651	9	discontinuities	discontinuity	NOUN
gi-4938	651	10	”	"	PUNCT
gi-4938	651	11	.	.	PUNCT
gi-4938	652	1	in	in	ADP
gi-4938	652	2	:	:	PUNCT
gi-4938	652	3	siam	siam	ADJ
gi-4938	652	4	journal	journal	NOUN
gi-4938	652	5	on	on	ADP
gi-4938	652	6	scientific	scientific	ADJ
gi-4938	652	7	and	and	CCONJ
gi-4938	652	8	statistical	statistical	ADJ
gi-4938	652	9	computing	computing	NOUN
gi-4938	652	10	12.2	12.2	NUM
gi-4938	652	11	(	(	PUNCT
gi-4938	652	12	1991	1991	NUM
gi-4938	652	13	)	)	PUNCT
gi-4938	652	14	,	,	PUNCT
gi-4938	652	15	pp	pp	ADP
gi-4938	652	16	.	.	PUNCT
gi-4938	653	1	311–341	311–341	NUM
gi-4938	653	2	.	.	PUNCT
gi-4938	653	3	doi	doi	NOUN
gi-4938	653	4	:	:	PUNCT
gi-4938	653	5	10	10	NUM
gi-4938	653	6	.	.	PUNCT
gi-4938	654	1	1137/0912018	1137/0912018	NUM
gi-4938	654	2	.	.	PUNCT
gi-4938	655	1	[	[	X
gi-4938	655	2	25	25	NUM
gi-4938	655	3	]	]	X
gi-4938	655	4	david	david	PROPN
gi-4938	655	5	lee	lee	PROPN
gi-4938	655	6	and	and	CCONJ
gi-4938	655	7	grzegorz	grzegorz	PROPN
gi-4938	655	8	w	w	PROPN
gi-4938	655	9	wasilkowski	wasilkowski	ADJ
gi-4938	655	10	.	.	PUNCT
gi-4938	656	1	“	"	PUNCT
gi-4938	656	2	discontinuity	discontinuity	NOUN
gi-4938	656	3	detection	detection	NOUN
gi-4938	656	4	and	and	CCONJ
gi-4938	656	5	thresholding	thresholding	NOUN
gi-4938	656	6	-	-	PUNCT
gi-4938	656	7	a	a	DET
gi-4938	656	8	stochastic	stochastic	ADJ
gi-4938	656	9	approach	approach	NOUN
gi-4938	656	10	”	"	PUNCT
gi-4938	656	11	.	.	PUNCT
gi-4938	657	1	in	in	ADP
gi-4938	657	2	:	:	PUNCT
gi-4938	657	3	journal	journal	NOUN
gi-4938	657	4	of	of	ADP
gi-4938	657	5	complexity	complexity	NOUN
gi-4938	657	6	9.1	9.1	NUM
gi-4938	657	7	(	(	PUNCT
gi-4938	657	8	1993	1993	NUM
gi-4938	657	9	)	)	PUNCT
gi-4938	657	10	,	,	PUNCT
gi-4938	657	11	pp	pp	ADJ
gi-4938	657	12	.	.	PUNCT
gi-4938	658	1	76–96	76–96	NUM
gi-4938	658	2	.	.	PUNCT
gi-4938	659	1	[	[	X
gi-4938	659	2	26	26	NUM
gi-4938	659	3	]	]	X
gi-4938	659	4	licia	licia	NOUN
gi-4938	659	5	lenarduzzi	lenarduzzi	PROPN
gi-4938	659	6	and	and	CCONJ
gi-4938	659	7	robert	robert	PROPN
gi-4938	659	8	schaback	schaback	PROPN
gi-4938	659	9	.	.	PUNCT
gi-4938	660	1	“	"	PUNCT
gi-4938	660	2	kernel	kernel	NOUN
gi-4938	660	3	-	-	PUNCT
gi-4938	660	4	based	base	VERB
gi-4938	660	5	adaptive	adaptive	ADJ
gi-4938	660	6	approximation	approximation	NOUN
gi-4938	660	7	of	of	ADP
gi-4938	660	8	functions	function	NOUN
gi-4938	660	9	with	with	ADP
gi-4938	660	10	discontinuities	discontinuity	NOUN
gi-4938	660	11	”	"	PUNCT
gi-4938	660	12	.	.	PUNCT
gi-4938	661	1	in	in	ADP
gi-4938	661	2	:	:	PUNCT
gi-4938	661	3	applied	applied	ADJ
gi-4938	661	4	mathematics	mathematic	NOUN
gi-4938	661	5	and	and	CCONJ
gi-4938	661	6	computation	computation	NOUN
gi-4938	661	7	307.supplement	307.supplement	NUM
gi-4938	661	8	c	c	NOUN
gi-4938	661	9	(	(	PUNCT
gi-4938	661	10	2017	2017	NUM
gi-4938	661	11	)	)	PUNCT
gi-4938	661	12	,	,	PUNCT
gi-4938	661	13	pp	pp	ADP
gi-4938	661	14	.	.	PUNCT
gi-4938	662	1	113–123	113–123	NUM
gi-4938	662	2	.	.	PUNCT
gi-4938	663	1	issn	issn	PROPN
gi-4938	663	2	:	:	PUNCT
gi-4938	663	3	0096	0096	NUM
gi-4938	663	4	-	-	SYM
gi-4938	663	5	3003	3003	NUM
gi-4938	663	6	.	.	PUNCT
gi-4938	664	1	doi	doi	NOUN
gi-4938	664	2	:	:	PUNCT
gi-4938	664	3	https://doi.org/10.1016/j.amc.2017	https://doi.org/10.1016/j.amc.2017	NOUN
gi-4938	664	4	.	.	PUNCT
gi-4938	665	1	02.043	02.043	NUM
gi-4938	665	2	.	.	PUNCT
gi-4938	666	1	geoinformatics	geoinformatic	NOUN
gi-4938	666	2	fce	fce	VERB
gi-4938	666	3	ctu	ctu	NOUN
gi-4938	666	4	17(2	17(2	NUM
gi-4938	666	5	)	)	PUNCT
gi-4938	666	6	,	,	PUNCT
gi-4938	666	7	2018	2018	NUM
gi-4938	666	8	27	27	NUM
gi-4938	666	9	https://doi.org/10.1023/a:1009705709733	https://doi.org/10.1023/a:1009705709733	ADJ
gi-4938	666	10	https://doi.org/10.1145/143242.143314	https://doi.org/10.1145/143242.143314	ADJ
gi-4938	666	11	https://doi.org/10.1023/a:1009950630139	https://doi.org/10.1023/a:1009950630139	ADJ
gi-4938	666	12	https://doi.org/10.1137/0912018	https://doi.org/10.1137/0912018	NOUN
gi-4938	666	13	https://doi.org/10.1137/0912018	https://doi.org/10.1137/0912018	NOUN
gi-4938	667	1	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-4938	667	2	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-4938	667	3	t.	t.	NOUN
gi-4938	667	4	bayer	bayer	PROPN
gi-4938	667	5	:	:	PUNCT
gi-4938	667	6	efficient	efficient	ADJ
gi-4938	667	7	plotting	plot	VERB
gi-4938	667	8	the	the	DET
gi-4938	667	9	functions	function	NOUN
gi-4938	667	10	with	with	ADP
gi-4938	667	11	discontinuities	discontinuity	NOUN
gi-4938	667	12	[	[	X
gi-4938	667	13	27	27	NUM
gi-4938	667	14	]	]	X
gi-4938	667	15	hélio	hélio	PROPN
gi-4938	667	16	lopes	lopes	PROPN
gi-4938	667	17	,	,	PUNCT
gi-4938	667	18	joão	joão	PROPN
gi-4938	667	19	batista	batista	PROPN
gi-4938	667	20	oliveira	oliveira	PROPN
gi-4938	667	21	,	,	PUNCT
gi-4938	667	22	and	and	CCONJ
gi-4938	667	23	luiz	luiz	PROPN
gi-4938	667	24	henrique	henrique	PROPN
gi-4938	667	25	de	de	PROPN
gi-4938	667	26	figueiredo	figueiredo	PROPN
gi-4938	667	27	.	.	PUNCT
gi-4938	668	1	“	"	PUNCT
gi-4938	668	2	robust	robust	ADJ
gi-4938	668	3	adaptive	adaptive	ADJ
gi-4938	668	4	polygonal	polygonal	ADJ
gi-4938	668	5	approximation	approximation	NOUN
gi-4938	668	6	of	of	ADP
gi-4938	668	7	implicit	implicit	ADJ
gi-4938	668	8	curves	curve	NOUN
gi-4938	668	9	”	"	PUNCT
gi-4938	668	10	.	.	PUNCT
gi-4938	669	1	in	in	ADP
gi-4938	669	2	:	:	PUNCT
gi-4938	669	3	computers	computer	NOUN
gi-4938	669	4	&	&	CCONJ
gi-4938	669	5	graphics	graphic	NOUN
gi-4938	669	6	26.6	26.6	NUM
gi-4938	669	7	(	(	PUNCT
gi-4938	669	8	2002	2002	NUM
gi-4938	669	9	)	)	PUNCT
gi-4938	669	10	,	,	PUNCT
gi-4938	669	11	pp	pp	ADP
gi-4938	669	12	.	.	PUNCT
gi-4938	670	1	841–852	841–852	NUM
gi-4938	670	2	.	.	PUNCT
gi-4938	671	1	[	[	X
gi-4938	671	2	28	28	NUM
gi-4938	671	3	]	]	X
gi-4938	671	4	jose	jose	NOUN
gi-4938	671	5	marroquin	marroquin	NOUN
gi-4938	671	6	,	,	PUNCT
gi-4938	671	7	sanjoy	sanjoy	NOUN
gi-4938	671	8	mitter	mitter	NOUN
gi-4938	671	9	,	,	PUNCT
gi-4938	671	10	and	and	CCONJ
gi-4938	671	11	tomaso	tomaso	NOUN
gi-4938	671	12	poggio	poggio	PROPN
gi-4938	671	13	.	.	PUNCT
gi-4938	672	1	“	"	PUNCT
gi-4938	672	2	probabilistic	probabilistic	ADJ
gi-4938	672	3	solution	solution	NOUN
gi-4938	672	4	of	of	ADP
gi-4938	672	5	ill	ill	ADV
gi-4938	672	6	-	-	PUNCT
gi-4938	672	7	posed	pose	VERB
gi-4938	672	8	problems	problem	NOUN
gi-4938	672	9	in	in	ADP
gi-4938	672	10	computational	computational	ADJ
gi-4938	672	11	vision	vision	NOUN
gi-4938	672	12	”	"	PUNCT
gi-4938	672	13	.	.	PUNCT
gi-4938	673	1	in	in	ADP
gi-4938	673	2	:	:	PUNCT
gi-4938	673	3	journal	journal	NOUN
gi-4938	673	4	of	of	ADP
gi-4938	673	5	the	the	DET
gi-4938	673	6	american	american	ADJ
gi-4938	673	7	statistical	statistical	ADJ
gi-4938	673	8	association	association	NOUN
gi-4938	673	9	82.397	82.397	NUM
gi-4938	673	10	(	(	PUNCT
gi-4938	673	11	1987	1987	NUM
gi-4938	673	12	)	)	PUNCT
gi-4938	673	13	,	,	PUNCT
gi-4938	673	14	pp	pp	ADP
gi-4938	673	15	.	.	PUNCT
gi-4938	674	1	76–89	76–89	X
gi-4938	674	2	.	.	PUNCT
gi-4938	675	1	[	[	X
gi-4938	675	2	29	29	NUM
gi-4938	675	3	]	]	PUNCT
gi-4938	675	4	byron	byron	PROPN
gi-4938	675	5	nakos	nakos	PROPN
gi-4938	675	6	and	and	CCONJ
gi-4938	675	7	v	v	ADP
gi-4938	675	8	miropoulos	miropoulo	NOUN
gi-4938	675	9	.	.	PUNCT
gi-4938	676	1	“	"	PUNCT
gi-4938	676	2	local	local	ADJ
gi-4938	676	3	length	length	NOUN
gi-4938	676	4	ratio	ratio	NOUN
gi-4938	676	5	as	as	ADP
gi-4938	676	6	a	a	DET
gi-4938	676	7	measure	measure	NOUN
gi-4938	676	8	of	of	ADP
gi-4938	676	9	critical	critical	ADJ
gi-4938	676	10	points	point	NOUN
gi-4938	676	11	detection	detection	NOUN
gi-4938	676	12	for	for	ADP
gi-4938	676	13	line	line	NOUN
gi-4938	676	14	simplification	simplification	NOUN
gi-4938	676	15	”	"	PUNCT
gi-4938	676	16	.	.	PUNCT
gi-4938	677	1	in	in	ADP
gi-4938	677	2	:	:	PUNCT
gi-4938	677	3	fifth	fifth	ADJ
gi-4938	677	4	workshop	workshop	NOUN
gi-4938	677	5	on	on	ADP
gi-4938	677	6	progress	progress	NOUN
gi-4938	677	7	in	in	ADP
gi-4938	677	8	automated	automate	VERB
gi-4938	677	9	map	map	NOUN
gi-4938	677	10	generalization	generalization	NOUN
gi-4938	677	11	,	,	PUNCT
gi-4938	677	12	paris	paris	PROPN
gi-4938	677	13	,	,	PUNCT
gi-4938	677	14	france	france	PROPN
gi-4938	677	15	.	.	PUNCT
gi-4938	677	16	2003	2003	NUM
gi-4938	677	17	.	.	PUNCT
gi-4938	678	1	[	[	X
gi-4938	678	2	30	30	NUM
gi-4938	678	3	]	]	X
gi-4938	678	4	m	m	VERB
gi-4938	678	5	oliveria	oliveria	INTJ
gi-4938	678	6	et	et	PROPN
gi-4938	678	7	al	al	PROPN
gi-4938	678	8	.	.	PUNCT
gi-4938	679	1	“	"	PUNCT
gi-4938	679	2	universal	universal	ADJ
gi-4938	679	3	high	high	ADJ
gi-4938	679	4	order	order	NOUN
gi-4938	679	5	subroutine	subroutine	NOUN
gi-4938	679	6	with	with	ADP
gi-4938	679	7	new	new	ADJ
gi-4938	679	8	shock	shock	NOUN
gi-4938	679	9	detector	detector	NOUN
gi-4938	679	10	for	for	ADP
gi-4938	679	11	shock	shock	NOUN
gi-4938	679	12	boundary	boundary	ADJ
gi-4938	679	13	layer	layer	NOUN
gi-4938	679	14	interaction	interaction	NOUN
gi-4938	679	15	”	"	PUNCT
gi-4938	679	16	.	.	PUNCT
gi-4938	680	1	in	in	ADP
gi-4938	680	2	:	:	PUNCT
gi-4938	680	3	in	in	ADP
gi-4938	680	4	other	other	ADJ
gi-4938	680	5	words	word	NOUN
gi-4938	680	6	10	10	NUM
gi-4938	680	7	(	(	PUNCT
gi-4938	680	8	2009	2009	NUM
gi-4938	680	9	)	)	PUNCT
gi-4938	680	10	,	,	PUNCT
gi-4938	680	11	pp	pp	ADP
gi-4938	680	12	.	.	PUNCT
gi-4938	681	1	1–2	1–2	X
gi-4938	681	2	.	.	PUNCT
gi-4938	682	1	[	[	X
gi-4938	682	2	31	31	NUM
gi-4938	682	3	]	]	PUNCT
gi-4938	682	4	ricardo	ricardo	PROPN
gi-4938	682	5	pachón	pachón	PROPN
gi-4938	682	6	,	,	PUNCT
gi-4938	682	7	rodrigo	rodrigo	PROPN
gi-4938	682	8	b	b	PROPN
gi-4938	682	9	platte	platte	PROPN
gi-4938	682	10	,	,	PUNCT
gi-4938	682	11	and	and	CCONJ
gi-4938	682	12	lloyd	lloyd	PROPN
gi-4938	682	13	n	n	ADV
gi-4938	682	14	trefethen	trefethen	NOUN
gi-4938	682	15	.	.	PUNCT
gi-4938	683	1	“	"	PUNCT
gi-4938	683	2	piecewise	piecewise	NOUN
gi-4938	683	3	-	-	PUNCT
gi-4938	683	4	smooth	smooth	ADJ
gi-4938	683	5	chebfuns	chebfun	NOUN
gi-4938	683	6	”	"	PUNCT
gi-4938	683	7	.	.	PUNCT
gi-4938	684	1	in	in	ADP
gi-4938	684	2	:	:	PUNCT
gi-4938	684	3	i	i	PRON
gi-4938	684	4	m	m	VERB
gi-4938	684	5	a	a	PRON
gi-4938	684	6	journal	journal	NOUN
gi-4938	684	7	of	of	ADP
gi-4938	684	8	numerical	numerical	ADJ
gi-4938	684	9	analysis	analysis	NOUN
gi-4938	684	10	30.4	30.4	NUM
gi-4938	684	11	(	(	PUNCT
gi-4938	684	12	2009	2009	NUM
gi-4938	684	13	)	)	PUNCT
gi-4938	684	14	,	,	PUNCT
gi-4938	684	15	pp	pp	ADP
gi-4938	684	16	.	.	PUNCT
gi-4938	685	1	898–916	898–916	NUM
gi-4938	685	2	.	.	PUNCT
gi-4938	686	1	[	[	X
gi-4938	686	2	32	32	NUM
gi-4938	686	3	]	]	PUNCT
gi-4938	686	4	afonso	afonso	PROPN
gi-4938	686	5	paiva	paiva	PROPN
gi-4938	686	6	et	et	PROPN
gi-4938	686	7	al	al	PROPN
gi-4938	686	8	.	.	PUNCT
gi-4938	687	1	“	"	PUNCT
gi-4938	687	2	approximating	approximate	VERB
gi-4938	687	3	implicit	implicit	ADJ
gi-4938	687	4	curves	curve	NOUN
gi-4938	687	5	on	on	ADP
gi-4938	687	6	triangulations	triangulation	NOUN
gi-4938	687	7	with	with	ADP
gi-4938	687	8	affine	affine	NOUN
gi-4938	687	9	arithmetic	arithmetic	NOUN
gi-4938	687	10	”	"	PUNCT
gi-4938	687	11	.	.	PUNCT
gi-4938	688	1	in	in	ADP
gi-4938	688	2	:	:	PUNCT
gi-4938	688	3	graphics	graphic	NOUN
gi-4938	688	4	,	,	PUNCT
gi-4938	688	5	patterns	pattern	NOUN
gi-4938	688	6	and	and	CCONJ
gi-4938	688	7	images	image	NOUN
gi-4938	688	8	(	(	PUNCT
gi-4938	688	9	sibgrapi	sibgrapi	ADJ
gi-4938	688	10	)	)	PUNCT
gi-4938	688	11	,	,	PUNCT
gi-4938	688	12	2012	2012	NUM
gi-4938	688	13	25th	25th	NOUN
gi-4938	688	14	sibgrapi	sibgrapi	ADJ
gi-4938	688	15	conference	conference	NOUN
gi-4938	688	16	on	on	ADP
gi-4938	688	17	.	.	PUNCT
gi-4938	688	18	ieee	ieee	PROPN
gi-4938	688	19	.	.	PROPN
gi-4938	688	20	2012	2012	NUM
gi-4938	688	21	,	,	PUNCT
gi-4938	688	22	pp	pp	ADV
gi-4938	688	23	.	.	PUNCT
gi-4938	689	1	94–101	94–101	NOUN
gi-4938	689	2	.	.	PUNCT
gi-4938	690	1	[	[	X
gi-4938	690	2	33	33	NUM
gi-4938	690	3	]	]	X
gi-4938	690	4	mohammad	mohammad	PROPN
gi-4938	690	5	tanvir	tanvir	PROPN
gi-4938	690	6	parvez	parvez	PROPN
gi-4938	690	7	and	and	CCONJ
gi-4938	690	8	sabri	sabri	PROPN
gi-4938	690	9	a	a	DET
gi-4938	690	10	mahmoud	mahmoud	PROPN
gi-4938	690	11	.	.	PUNCT
gi-4938	691	1	“	"	PUNCT
gi-4938	691	2	polygonal	polygonal	ADJ
gi-4938	691	3	approximation	approximation	NOUN
gi-4938	691	4	of	of	ADP
gi-4938	691	5	digital	digital	ADJ
gi-4938	691	6	planar	planar	ADJ
gi-4938	691	7	curves	curve	NOUN
gi-4938	691	8	through	through	ADP
gi-4938	691	9	adaptive	adaptive	ADJ
gi-4938	691	10	optimizations	optimization	NOUN
gi-4938	691	11	”	"	PUNCT
gi-4938	691	12	.	.	PUNCT
gi-4938	692	1	in	in	ADP
gi-4938	692	2	:	:	PUNCT
gi-4938	692	3	pattern	pattern	NOUN
gi-4938	692	4	recognition	recognition	NOUN
gi-4938	692	5	letters	letter	VERB
gi-4938	692	6	31.13	31.13	NUM
gi-4938	692	7	(	(	PUNCT
gi-4938	692	8	2010	2010	NUM
gi-4938	692	9	)	)	PUNCT
gi-4938	692	10	,	,	PUNCT
gi-4938	692	11	pp	pp	ADP
gi-4938	692	12	.	.	PUNCT
gi-4938	693	1	1997–2005	1997–2005	NUM
gi-4938	693	2	.	.	PUNCT
gi-4938	694	1	[	[	X
gi-4938	694	2	34	34	NUM
gi-4938	694	3	]	]	X
gi-4938	694	4	leszek	leszek	PROPN
gi-4938	694	5	plaskota	plaskota	NOUN
gi-4938	694	6	and	and	CCONJ
gi-4938	694	7	grzegorz	grzegorz	PROPN
gi-4938	694	8	w	w	PROPN
gi-4938	694	9	wasilkowski	wasilkowski	ADJ
gi-4938	694	10	.	.	PUNCT
gi-4938	695	1	“	"	PUNCT
gi-4938	695	2	adaption	adaption	NOUN
gi-4938	695	3	allows	allow	VERB
gi-4938	695	4	efficient	efficient	ADJ
gi-4938	695	5	integration	integration	NOUN
gi-4938	695	6	of	of	ADP
gi-4938	695	7	functions	function	NOUN
gi-4938	695	8	with	with	ADP
gi-4938	695	9	unknown	unknown	ADJ
gi-4938	695	10	singularities	singularity	NOUN
gi-4938	695	11	”	"	PUNCT
gi-4938	695	12	.	.	PUNCT
gi-4938	696	1	in	in	ADP
gi-4938	696	2	:	:	PUNCT
gi-4938	696	3	numerische	numerische	PROPN
gi-4938	696	4	mathematik	mathematik	PROPN
gi-4938	696	5	102.1	102.1	NUM
gi-4938	696	6	(	(	PUNCT
gi-4938	696	7	2005	2005	NUM
gi-4938	696	8	)	)	PUNCT
gi-4938	696	9	,	,	PUNCT
gi-4938	696	10	pp	pp	ADP
gi-4938	696	11	.	.	PUNCT
gi-4938	697	1	123–144	123–144	NUM
gi-4938	697	2	.	.	PUNCT
gi-4938	698	1	[	[	X
gi-4938	698	2	35	35	NUM
gi-4938	698	3	]	]	X
gi-4938	698	4	m.	m.	NOUN
gi-4938	698	5	rossini	rossini	PROPN
gi-4938	698	6	.	.	PUNCT
gi-4938	699	1	“	"	PUNCT
gi-4938	699	2	2d	2d	NOUN
gi-4938	699	3	-	-	PUNCT
gi-4938	699	4	discontinuity	discontinuity	NOUN
gi-4938	699	5	detection	detection	NOUN
gi-4938	699	6	from	from	ADP
gi-4938	699	7	scattered	scatter	VERB
gi-4938	699	8	data	datum	NOUN
gi-4938	699	9	”	"	PUNCT
gi-4938	699	10	.	.	PUNCT
gi-4938	700	1	in	in	ADP
gi-4938	700	2	:	:	PUNCT
gi-4938	700	3	computing	compute	VERB
gi-4938	700	4	61.3	61.3	NUM
gi-4938	700	5	(	(	PUNCT
gi-4938	700	6	sept	sept	PROPN
gi-4938	700	7	.	.	PROPN
gi-4938	700	8	1998	1998	NUM
gi-4938	700	9	)	)	PUNCT
gi-4938	700	10	,	,	PUNCT
gi-4938	700	11	pp	pp	ADP
gi-4938	700	12	.	.	PUNCT
gi-4938	701	1	215–234	215–234	NUM
gi-4938	701	2	.	.	PUNCT
gi-4938	702	1	issn	issn	PROPN
gi-4938	702	2	:	:	PUNCT
gi-4938	702	3	1436	1436	NUM
gi-4938	702	4	-	-	SYM
gi-4938	702	5	5057	5057	NUM
gi-4938	702	6	.	.	PUNCT
gi-4938	703	1	doi	doi	NOUN
gi-4938	703	2	:	:	PUNCT
gi-4938	703	3	10.1007	10.1007	NUM
gi-4938	703	4	/	/	SYM
gi-4938	703	5	bf02684351	bf02684351	NOUN
gi-4938	703	6	.	.	PUNCT
gi-4938	704	1	[	[	X
gi-4938	704	2	36	36	NUM
gi-4938	704	3	]	]	PUNCT
gi-4938	704	4	yiqing	yiqing	ADJ
gi-4938	704	5	shen	shen	PROPN
gi-4938	704	6	and	and	CCONJ
gi-4938	704	7	gecheng	gecheng	PROPN
gi-4938	704	8	zha	zha	PROPN
gi-4938	704	9	.	.	PUNCT
gi-4938	705	1	“	"	PUNCT
gi-4938	705	2	improvement	improvement	NOUN
gi-4938	705	3	of	of	ADP
gi-4938	705	4	the	the	DET
gi-4938	705	5	weno	weno	PROPN
gi-4938	705	6	scheme	scheme	PROPN
gi-4938	705	7	smoothness	smoothness	ADJ
gi-4938	705	8	estimator	estimator	NOUN
gi-4938	705	9	”	"	PUNCT
gi-4938	705	10	.	.	PUNCT
gi-4938	706	1	in	in	ADP
gi-4938	706	2	:	:	PUNCT
gi-4938	706	3	international	international	ADJ
gi-4938	706	4	journal	journal	NOUN
gi-4938	706	5	for	for	ADP
gi-4938	706	6	numerical	numerical	ADJ
gi-4938	706	7	methods	method	NOUN
gi-4938	706	8	in	in	ADP
gi-4938	706	9	fluids	fluid	NOUN
gi-4938	706	10	64.6	64.6	NUM
gi-4938	706	11	(	(	PUNCT
gi-4938	706	12	2010	2010	NUM
gi-4938	706	13	)	)	PUNCT
gi-4938	706	14	,	,	PUNCT
gi-4938	706	15	pp	pp	PROPN
gi-4938	706	16	.	.	PUNCT
gi-4938	706	17	653	653	NUM
gi-4938	706	18	–	–	PUNCT
gi-4938	706	19	675	675	NUM
gi-4938	706	20	.	.	PUNCT
gi-4938	706	21	issn	issn	PROPN
gi-4938	706	22	:	:	PUNCT
gi-4938	706	23	1097	1097	NUM
gi-4938	706	24	-	-	SYM
gi-4938	706	25	0363	0363	NUM
gi-4938	706	26	.	.	PUNCT
gi-4938	707	1	doi	doi	NOUN
gi-4938	707	2	:	:	PUNCT
gi-4938	707	3	10.1002	10.1002	NUM
gi-4938	707	4	/	/	SYM
gi-4938	707	5	fld.2168	fld.2168	PROPN
gi-4938	707	6	.	.	PUNCT
gi-4938	708	1	[	[	X
gi-4938	708	2	37	37	NUM
gi-4938	708	3	]	]	X
gi-4938	708	4	moshe	moshe	PROPN
gi-4938	708	5	shpitalni	shpitalni	PROPN
gi-4938	708	6	,	,	PUNCT
gi-4938	708	7	yoram	yoram	PROPN
gi-4938	708	8	koren	koren	PROPN
gi-4938	708	9	,	,	PUNCT
gi-4938	708	10	and	and	CCONJ
gi-4938	708	11	cc	cc	PROPN
gi-4938	708	12	lo	lo	PROPN
gi-4938	708	13	.	.	PUNCT
gi-4938	709	1	“	"	PUNCT
gi-4938	709	2	realtime	realtime	ADJ
gi-4938	709	3	curve	curve	NOUN
gi-4938	709	4	interpolators	interpolator	NOUN
gi-4938	709	5	”	"	PUNCT
gi-4938	709	6	.	.	PUNCT
gi-4938	710	1	in	in	ADP
gi-4938	710	2	:	:	PUNCT
gi-4938	710	3	computeraided	computeraide	VERB
gi-4938	710	4	design	design	NOUN
gi-4938	710	5	26.11	26.11	NUM
gi-4938	710	6	(	(	PUNCT
gi-4938	710	7	1994	1994	NUM
gi-4938	710	8	)	)	PUNCT
gi-4938	710	9	,	,	PUNCT
gi-4938	710	10	pp	pp	ADP
gi-4938	710	11	.	.	PUNCT
gi-4938	711	1	832–838	832–838	NUM
gi-4938	711	2	.	.	PUNCT
gi-4938	712	1	[	[	X
gi-4938	712	2	38	38	NUM
gi-4938	712	3	]	]	PUNCT
gi-4938	712	4	kaleem	kaleem	PROPN
gi-4938	712	5	siddiqi	siddiqi	PROPN
gi-4938	712	6	,	,	PUNCT
gi-4938	712	7	benjamin	benjamin	PROPN
gi-4938	712	8	b	b	PROPN
gi-4938	712	9	kimia	kimia	NOUN
gi-4938	712	10	,	,	PUNCT
gi-4938	712	11	and	and	CCONJ
gi-4938	712	12	chi	chi	PROPN
gi-4938	712	13	-	-	PUNCT
gi-4938	712	14	wang	wang	PROPN
gi-4938	712	15	shu	shu	PROPN
gi-4938	712	16	.	.	PUNCT
gi-4938	713	1	“	"	PUNCT
gi-4938	713	2	geometric	geometric	ADJ
gi-4938	713	3	shock	shock	NOUN
gi-4938	713	4	-	-	PUNCT
gi-4938	713	5	capturing	capture	VERB
gi-4938	713	6	eno	eno	NOUN
gi-4938	713	7	schemes	scheme	NOUN
gi-4938	713	8	for	for	ADP
gi-4938	713	9	subpixel	subpixel	ADJ
gi-4938	713	10	interpolation	interpolation	NOUN
gi-4938	713	11	,	,	PUNCT
gi-4938	713	12	computation	computation	NOUN
gi-4938	713	13	,	,	PUNCT
gi-4938	713	14	and	and	CCONJ
gi-4938	713	15	curve	curve	NOUN
gi-4938	713	16	evolution	evolution	NOUN
gi-4938	713	17	”	"	PUNCT
gi-4938	713	18	.	.	PUNCT
gi-4938	714	1	in	in	ADP
gi-4938	714	2	:	:	PUNCT
gi-4938	714	3	computer	computer	NOUN
gi-4938	714	4	vision	vision	NOUN
gi-4938	714	5	,	,	PUNCT
gi-4938	714	6	1995	1995	NUM
gi-4938	714	7	.	.	PUNCT
gi-4938	715	1	proceedings	proceeding	NOUN
gi-4938	715	2	.	.	PUNCT
gi-4938	716	1	,	,	PUNCT
gi-4938	716	2	international	international	ADJ
gi-4938	716	3	symposium	symposium	NOUN
gi-4938	716	4	on	on	ADP
gi-4938	716	5	.	.	PUNCT
gi-4938	717	1	ieee	ieee	PROPN
gi-4938	717	2	.	.	PUNCT
gi-4938	717	3	1995	1995	NUM
gi-4938	717	4	,	,	PUNCT
gi-4938	717	5	pp	pp	ADJ
gi-4938	717	6	.	.	PUNCT
gi-4938	718	1	437	437	NUM
gi-4938	718	2	–	–	PUNCT
gi-4938	718	3	442	442	NUM
gi-4938	718	4	.	.	PUNCT
gi-4938	719	1	[	[	X
gi-4938	719	2	39	39	NUM
gi-4938	719	3	]	]	PUNCT
gi-4938	719	4	c.	c.	PROPN
gi-4938	719	5	smith	smith	PROPN
gi-4938	719	6	and	and	CCONJ
gi-4938	719	7	n.	n.	PROPN
gi-4938	719	8	blachman	blachman	PROPN
gi-4938	719	9	.	.	PUNCT
gi-4938	720	1	the	the	DET
gi-4938	720	2	mathematica	mathematica	PROPN
gi-4938	720	3	graphics	graphics	PROPN
gi-4938	720	4	guidebook	guidebook	PROPN
gi-4938	720	5	.	.	PUNCT
gi-4938	721	1	addison	addison	PROPN
gi-4938	721	2	-	-	PUNCT
gi-4938	721	3	wesley	wesley	PROPN
gi-4938	721	4	,	,	PUNCT
gi-4938	721	5	1995	1995	NUM
gi-4938	721	6	.	.	PUNCT
gi-4938	722	1	isbn	isbn	NOUN
gi-4938	722	2	:	:	PUNCT
gi-4938	722	3	9780201826555	9780201826555	NUM
gi-4938	722	4	.	.	PUNCT
gi-4938	723	1	url	url	PROPN
gi-4938	723	2	:	:	PUNCT
gi-4938	723	3	https	https	NOUN
gi-4938	723	4	:	:	PUNCT
gi-4938	723	5	/	/	SYM
gi-4938	723	6	/	/	SYM
gi-4938	723	7	books	book	NOUN
gi-4938	723	8	.	.	PUNCT
gi-4938	724	1	google	google	PROPN
gi-4938	724	2	.	.	PUNCT
gi-4938	725	1	cz	cz	NOUN
gi-4938	725	2	/	/	SYM
gi-4938	725	3	books	book	NOUN
gi-4938	725	4	?	?	PUNCT
gi-4938	726	1	i	i	PRON
gi-4938	726	2	d	d	NOUN
gi-4938	726	3	=	=	SYM
gi-4938	727	1	l	l	NOUN
gi-4938	727	2	%	%	NOUN
gi-4938	727	3	5c	5c	X
gi-4938	727	4	_	_	PUNCT
gi-4938	728	1	myaqaaiaaj	myaqaaiaaj	NOUN
gi-4938	728	2	.	.	PUNCT
gi-4938	729	1	[	[	X
gi-4938	729	2	40	40	NUM
gi-4938	729	3	]	]	PUNCT
gi-4938	729	4	jeffrey	jeffrey	PROPN
gi-4938	729	5	allen	allen	PROPN
gi-4938	729	6	tupper	tupper	PROPN
gi-4938	729	7	.	.	PUNCT
gi-4938	730	1	graphing	graph	VERB
gi-4938	730	2	equations	equation	NOUN
gi-4938	730	3	with	with	ADP
gi-4938	730	4	generalized	generalized	ADJ
gi-4938	730	5	interval	interval	NOUN
gi-4938	730	6	arithmetic	arithmetic	NOUN
gi-4938	730	7	.	.	PUNCT
gi-4938	731	1	university	university	PROPN
gi-4938	731	2	of	of	ADP
gi-4938	731	3	toronto	toronto	PROPN
gi-4938	731	4	,	,	PUNCT
gi-4938	731	5	1996	1996	NUM
gi-4938	731	6	.	.	PUNCT
gi-4938	732	1	[	[	X
gi-4938	732	2	41	41	NUM
gi-4938	732	3	]	]	X
gi-4938	732	4	leland	leland	PROPN
gi-4938	732	5	wilkinson	wilkinson	PROPN
gi-4938	732	6	.	.	PUNCT
gi-4938	733	1	“	"	PUNCT
gi-4938	733	2	algorithms	algorithm	NOUN
gi-4938	733	3	for	for	ADP
gi-4938	733	4	choosing	choose	VERB
gi-4938	733	5	the	the	DET
gi-4938	733	6	domain	domain	NOUN
gi-4938	733	7	and	and	CCONJ
gi-4938	733	8	range	range	NOUN
gi-4938	733	9	when	when	SCONJ
gi-4938	733	10	plotting	plot	VERB
gi-4938	733	11	a	a	DET
gi-4938	733	12	function	function	NOUN
gi-4938	733	13	”	"	PUNCT
gi-4938	733	14	.	.	PUNCT
gi-4938	734	1	in	in	ADP
gi-4938	734	2	:	:	PUNCT
gi-4938	734	3	(	(	PUNCT
gi-4938	734	4	1991	1991	NUM
gi-4938	734	5	)	)	PUNCT
gi-4938	734	6	,	,	PUNCT
gi-4938	734	7	pp	pp	ADP
gi-4938	734	8	.	.	PUNCT
gi-4938	735	1	1–8	1–8	X
gi-4938	735	2	.	.	PUNCT
gi-4938	735	3	geoinformatics	geoinformatic	NOUN
gi-4938	735	4	fce	fce	VERB
gi-4938	735	5	ctu	ctu	NOUN
gi-4938	735	6	17(2	17(2	NUM
gi-4938	735	7	)	)	PUNCT
gi-4938	735	8	,	,	PUNCT
gi-4938	735	9	2018	2018	NUM
gi-4938	735	10	28	28	NUM
gi-4938	735	11	https://doi.org/10.1007/bf02684351	https://doi.org/10.1007/bf02684351	VERB
gi-4938	735	12	https://doi.org/10.1002/fld.2168	https://doi.org/10.1002/fld.2168	NOUN
gi-4938	735	13	https://books.google.cz/books?id=l%5c_myaqaaiaaj	https://books.google.cz/books?id=l%5c_myaqaaiaaj	ADJ
gi-4938	735	14	https://books.google.cz/books?id=l%5c_myaqaaiaaj	https://books.google.cz/books?id=l%5c_myaqaaiaaj	PROPN
gi-4938	735	15	t.	t.	PROPN
gi-4938	735	16	bayer	bayer	PROPN
gi-4938	735	17	:	:	PUNCT
gi-4938	735	18	efficient	efficient	ADJ
gi-4938	735	19	plotting	plot	VERB
gi-4938	735	20	the	the	DET
gi-4938	735	21	functions	function	NOUN
gi-4938	735	22	with	with	ADP
gi-4938	735	23	discontinuities	discontinuity	NOUN
gi-4938	735	24	[	[	X
gi-4938	736	1	42	42	NUM
gi-4938	736	2	]	]	X
gi-4938	736	3	daniel	daniel	PROPN
gi-4938	736	4	c.h	c.h	PROPN
gi-4938	736	5	.	.	PROPN
gi-4938	736	6	yang	yang	PROPN
gi-4938	736	7	and	and	CCONJ
gi-4938	736	8	tom	tom	PROPN
gi-4938	736	9	kong	kong	PROPN
gi-4938	736	10	.	.	PUNCT
gi-4938	737	1	“	"	PUNCT
gi-4938	737	2	parametric	parametric	ADJ
gi-4938	737	3	interpolator	interpolator	NOUN
gi-4938	737	4	versus	versus	ADP
gi-4938	737	5	linear	linear	ADJ
gi-4938	737	6	interpolator	interpolator	NOUN
gi-4938	737	7	for	for	ADP
gi-4938	737	8	precision	precision	NOUN
gi-4938	737	9	cnc	cnc	PROPN
gi-4938	737	10	machining	machining	NOUN
gi-4938	737	11	”	"	PUNCT
gi-4938	737	12	.	.	PUNCT
gi-4938	738	1	in	in	ADP
gi-4938	738	2	:	:	PUNCT
gi-4938	738	3	computer	computer	NOUN
gi-4938	738	4	-	-	PUNCT
gi-4938	738	5	aided	aid	VERB
gi-4938	738	6	design	design	NOUN
gi-4938	738	7	26.3	26.3	NUM
gi-4938	738	8	(	(	PUNCT
gi-4938	738	9	1994	1994	NUM
gi-4938	738	10	)	)	PUNCT
gi-4938	738	11	.	.	PUNCT
gi-4938	739	1	special	special	ADJ
gi-4938	739	2	issue	issue	NOUN
gi-4938	739	3	:	:	PUNCT
gi-4938	739	4	nc	nc	PROPN
gi-4938	739	5	machining	machining	NOUN
gi-4938	739	6	and	and	CCONJ
gi-4938	739	7	cutter	cutter	NOUN
gi-4938	739	8	-	-	PUNCT
gi-4938	739	9	path	path	NOUN
gi-4938	739	10	generation	generation	NOUN
gi-4938	739	11	,	,	PUNCT
gi-4938	739	12	pp	pp	ADJ
gi-4938	739	13	.	.	PUNCT
gi-4938	740	1	225–234	225–234	NUM
gi-4938	740	2	.	.	PUNCT
gi-4938	741	1	issn	issn	PROPN
gi-4938	741	2	:	:	PUNCT
gi-4938	741	3	0010	0010	NUM
gi-4938	741	4	-	-	SYM
gi-4938	741	5	4485	4485	NUM
gi-4938	741	6	.	.	PUNCT
gi-4938	742	1	doi	doi	NOUN
gi-4938	742	2	:	:	PUNCT
gi-4938	742	3	https://	https://	PROPN
gi-4938	742	4	doi.org/10.1016/0010-4485(94)90045-0	doi.org/10.1016/0010-4485(94)90045-0	PROPN
gi-4938	742	5	.	.	PUNCT
gi-4938	743	1	[	[	X
gi-4938	743	2	43	43	NUM
gi-4938	743	3	]	]	X
gi-4938	743	4	s	s	X
gi-4938	743	5	-	-	PUNCT
gi-4938	743	6	s	s	X
gi-4938	743	7	yeh	yeh	NOUN
gi-4938	743	8	and	and	CCONJ
gi-4938	743	9	p	p	PROPN
gi-4938	743	10	-	-	PUNCT
gi-4938	743	11	l	l	NOUN
gi-4938	743	12	hsu	hsu	NOUN
gi-4938	743	13	.	.	PUNCT
gi-4938	744	1	“	"	PUNCT
gi-4938	744	2	the	the	DET
gi-4938	744	3	speed	speed	NOUN
gi-4938	744	4	-	-	PUNCT
gi-4938	744	5	controlled	control	VERB
gi-4938	744	6	interpolator	interpolator	NOUN
gi-4938	744	7	for	for	ADP
gi-4938	744	8	machining	machine	VERB
gi-4938	744	9	parametric	parametric	ADJ
gi-4938	744	10	curves	curve	NOUN
gi-4938	744	11	”	"	PUNCT
gi-4938	744	12	.	.	PUNCT
gi-4938	745	1	in	in	ADP
gi-4938	745	2	:	:	PUNCT
gi-4938	745	3	computer	computer	NOUN
gi-4938	745	4	-	-	PUNCT
gi-4938	745	5	aided	aid	VERB
gi-4938	745	6	design	design	NOUN
gi-4938	745	7	31.5	31.5	NUM
gi-4938	745	8	(	(	PUNCT
gi-4938	745	9	1999	1999	NUM
gi-4938	745	10	)	)	PUNCT
gi-4938	745	11	,	,	PUNCT
gi-4938	745	12	pp	pp	ADP
gi-4938	745	13	.	.	PUNCT
gi-4938	746	1	349–357	349–357	NUM
gi-4938	746	2	.	.	PUNCT
gi-4938	747	1	[	[	X
gi-4938	747	2	44	44	NUM
gi-4938	747	3	]	]	X
gi-4938	747	4	syh	syh	PROPN
gi-4938	747	5	-	-	PUNCT
gi-4938	747	6	shiuh	shiuh	NOUN
gi-4938	747	7	yeh	yeh	PROPN
gi-4938	747	8	and	and	CCONJ
gi-4938	747	9	pau	pau	PROPN
gi-4938	747	10	-	-	PUNCT
gi-4938	747	11	lo	lo	PROPN
gi-4938	747	12	hsu	hsu	PROPN
gi-4938	747	13	.	.	PUNCT
gi-4938	748	1	“	"	PUNCT
gi-4938	748	2	adaptive	adaptive	ADJ
gi-4938	748	3	-	-	PUNCT
gi-4938	748	4	feedrate	feedrate	NOUN
gi-4938	748	5	interpolation	interpolation	NOUN
gi-4938	748	6	for	for	ADP
gi-4938	748	7	parametric	parametric	ADJ
gi-4938	748	8	curves	curve	NOUN
gi-4938	748	9	with	with	ADP
gi-4938	748	10	a	a	DET
gi-4938	748	11	confined	confine	VERB
gi-4938	748	12	chord	chord	NOUN
gi-4938	748	13	error	error	NOUN
gi-4938	748	14	”	"	PUNCT
gi-4938	748	15	.	.	PUNCT
gi-4938	749	1	in	in	ADP
gi-4938	749	2	:	:	PUNCT
gi-4938	749	3	computer	computer	NOUN
gi-4938	749	4	-	-	PUNCT
gi-4938	749	5	aided	aid	VERB
gi-4938	749	6	design	design	NOUN
gi-4938	749	7	34.3	34.3	NUM
gi-4938	749	8	(	(	PUNCT
gi-4938	749	9	2002	2002	NUM
gi-4938	749	10	)	)	PUNCT
gi-4938	749	11	,	,	PUNCT
gi-4938	749	12	pp	pp	ADP
gi-4938	749	13	.	.	PUNCT
gi-4938	750	1	229–237	229–237	NUM
gi-4938	750	2	.	.	PUNCT
gi-4938	751	1	[	[	X
gi-4938	751	2	45	45	NUM
gi-4938	751	3	]	]	PUNCT
gi-4938	751	4	tony	tony	PROPN
gi-4938	751	5	chan	chan	PROPN
gi-4938	751	6	zhou	zhou	PROPN
gi-4938	751	7	and	and	CCONJ
gi-4938	751	8	hm	hm	INTJ
gi-4938	751	9	zhou	zhou	PROPN
gi-4938	751	10	.	.	PUNCT
gi-4938	752	1	“	"	PUNCT
gi-4938	752	2	adaptive	adaptive	ADJ
gi-4938	752	3	eno	eno	PROPN
gi-4938	752	4	-	-	PUNCT
gi-4938	752	5	wavelet	wavelet	NOUN
gi-4938	752	6	transforms	transform	VERB
gi-4938	752	7	for	for	ADP
gi-4938	752	8	discontinuous	discontinuous	ADJ
gi-4938	752	9	functions	function	NOUN
gi-4938	752	10	”	"	PUNCT
gi-4938	752	11	.	.	PUNCT
gi-4938	753	1	in	in	ADP
gi-4938	753	2	:	:	PUNCT
gi-4938	753	3	cam	cam	VERB
gi-4938	753	4	report	report	NOUN
gi-4938	753	5	,	,	PUNCT
gi-4938	753	6	no	no	INTJ
gi-4938	753	7	.	.	NOUN
gi-4938	753	8	99	99	NUM
gi-4938	753	9	-	-	SYM
gi-4938	753	10	21	21	NUM
gi-4938	753	11	,	,	PUNCT
gi-4938	753	12	dept	dept	NOUN
gi-4938	753	13	.	.	PROPN
gi-4938	753	14	of	of	ADP
gi-4938	753	15	math	math	NOUN
gi-4938	753	16	.	.	PUNCT
gi-4938	753	17	,	,	PUNCT
gi-4938	753	18	ucla	ucla	PROPN
gi-4938	753	19	,	,	PUNCT
gi-4938	753	20	submit	submit	VERB
gi-4938	753	21	to	to	ADP
gi-4938	753	22	siam	siam	PROPN
gi-4938	753	23	numer	numer	PROPN
gi-4938	753	24	.	.	PUNCT
gi-4938	754	1	anal	anal	PROPN
gi-4938	754	2	.	.	PUNCT
gi-4938	754	3	citeseer	citeseer	NOUN
gi-4938	754	4	.	.	PUNCT
gi-4938	755	1	1999	1999	NUM
gi-4938	755	2	.	.	PUNCT
gi-4938	756	1	geoinformatics	geoinformatic	NOUN
gi-4938	756	2	fce	fce	VERB
gi-4938	756	3	ctu	ctu	NOUN
gi-4938	756	4	17(2	17(2	NUM
gi-4938	756	5	)	)	PUNCT
gi-4938	756	6	,	,	PUNCT
gi-4938	756	7	2018	2018	NUM
gi-4938	756	8	29	29	NUM
gi-4938	756	9	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	NOUN
gi-4938	756	10	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-4938	756	11	geoinformatics	geoinformatic	NOUN
gi-4938	756	12	fce	fce	VERB
gi-4938	756	13	ctu	ctu	NOUN
gi-4938	756	14	17(2	17(2	NUM
gi-4938	756	15	)	)	PUNCT
gi-4938	756	16	,	,	PUNCT
gi-4938	756	17	2018	2018	NUM
gi-4938	756	18	30	30	NUM
gi-4938	756	19	t.	t.	NOUN
gi-4938	756	20	bayer	bayer	NOUN
gi-4938	756	21	:	:	PUNCT
gi-4938	756	22	efficient	efficient	ADJ
gi-4938	756	23	plotting	plot	VERB
gi-4938	756	24	the	the	DET
gi-4938	756	25	functions	function	NOUN
gi-4938	756	26	with	with	ADP
gi-4938	756	27	discontinuities	discontinuity	NOUN
gi-4938	756	28	introduction	introduction	NOUN
gi-4938	756	29	related	relate	VERB
gi-4938	756	30	work	work	NOUN
gi-4938	756	31	combined	combine	VERB
gi-4938	756	32	sampling	sample	VERB
gi-4938	756	33	polygonal	polygonal	ADJ
gi-4938	756	34	approximation	approximation	NOUN
gi-4938	756	35	of	of	ADP
gi-4938	756	36	the	the	DET
gi-4938	756	37	curve	curve	NOUN
gi-4938	756	38	combined	combined	ADJ
gi-4938	756	39	sampling	sampling	NOUN
gi-4938	756	40	technique	technique	NOUN
gi-4938	756	41	singularity	singularity	NOUN
gi-4938	756	42	detection	detection	NOUN
gi-4938	756	43	combined	combine	VERB
gi-4938	756	44	sampling	sample	VERB
gi-4938	756	45	with	with	ADP
gi-4938	756	46	the	the	DET
gi-4938	756	47	singularities	singularity	NOUN
gi-4938	756	48	combined	combine	VERB
gi-4938	756	49	sampling	sample	VERB
gi-4938	756	50	algorithm	algorithm	NOUN
gi-4938	756	51	involving	involve	VERB
gi-4938	756	52	the	the	DET
gi-4938	756	53	singularities	singularity	NOUN
gi-4938	756	54	utilization	utilization	NOUN
gi-4938	756	55	in	in	ADP
gi-4938	756	56	geoinformatics	geoinformatic	NOUN
gi-4938	756	57	experiments	experiment	NOUN
gi-4938	756	58	and	and	CCONJ
gi-4938	756	59	results	result	NOUN
gi-4938	756	60	.	.	PUNCT
gi-4938	757	1	list	list	NOUN
gi-4938	757	2	of	of	ADP
gi-4938	757	3	functions	function	NOUN
gi-4938	757	4	comparison	comparison	NOUN
gi-4938	757	5	with	with	ADP
gi-4938	757	6	other	other	ADJ
gi-4938	757	7	systems	system	NOUN
gi-4938	757	8	construction	construction	NOUN
gi-4938	757	9	of	of	ADP
gi-4938	757	10	the	the	DET
gi-4938	757	11	map	map	NOUN
gi-4938	757	12	projection	projection	NOUN
gi-4938	757	13	graticule	graticule	NOUN
gi-4938	757	14	conclusion	conclusion	NOUN