id	sid	tid	token	lemma	pos
gi-2729	1	1	the	the	DET
gi-2729	1	2	importance	importance	NOUN
gi-2729	1	3	of	of	ADP
gi-2729	1	4	computational	computational	ADJ
gi-2729	1	5	geometry	geometry	NOUN
gi-2729	1	6	for	for	ADP
gi-2729	1	7	digital	digital	ADJ
gi-2729	1	8	cartography	cartography	NOUN
gi-2729	1	9	tomáš	tomáš	PROPN
gi-2729	1	10	bayer	bayer	PROPN
gi-2729	1	11	faculty	faculty	NOUN
gi-2729	1	12	of	of	ADP
gi-2729	1	13	science	science	NOUN
gi-2729	1	14	,	,	PUNCT
gi-2729	1	15	charles	charles	PROPN
gi-2729	1	16	university	university	PROPN
gi-2729	1	17	in	in	ADP
gi-2729	1	18	prague	prague	PROPN
gi-2729	1	19	bayertom@natur.cuni.cz	bayertom@natur.cuni.cz	ADP
gi-2729	1	20	keywords	keyword	NOUN
gi-2729	1	21	:	:	PUNCT
gi-2729	1	22	computational	computational	ADJ
gi-2729	1	23	geometry	geometry	NOUN
gi-2729	1	24	,	,	PUNCT
gi-2729	1	25	digital	digital	ADJ
gi-2729	1	26	cartography	cartography	NOUN
gi-2729	1	27	,	,	PUNCT
gi-2729	1	28	open	open	ADJ
gi-2729	1	29	source	source	NOUN
gi-2729	1	30	,	,	PUNCT
gi-2729	1	31	gis	gis	PROPN
gi-2729	1	32	,	,	PUNCT
gi-2729	1	33	automated	automate	VERB
gi-2729	1	34	generalization	generalization	NOUN
gi-2729	1	35	,	,	PUNCT
gi-2729	1	36	convex	convex	PROPN
gi-2729	1	37	hull	hull	NOUN
gi-2729	1	38	abstract	abstract	NOUN
gi-2729	1	39	this	this	DET
gi-2729	1	40	paper	paper	NOUN
gi-2729	1	41	describes	describe	VERB
gi-2729	1	42	the	the	DET
gi-2729	1	43	use	use	NOUN
gi-2729	1	44	of	of	ADP
gi-2729	1	45	computational	computational	ADJ
gi-2729	1	46	geometry	geometry	NOUN
gi-2729	1	47	concepts	concept	NOUN
gi-2729	1	48	in	in	ADP
gi-2729	1	49	the	the	DET
gi-2729	1	50	digital	digital	ADJ
gi-2729	1	51	cartography	cartography	NOUN
gi-2729	1	52	.	.	PUNCT
gi-2729	2	1	it	it	PRON
gi-2729	2	2	presents	present	VERB
gi-2729	2	3	an	an	DET
gi-2729	2	4	importance	importance	NOUN
gi-2729	2	5	of	of	ADP
gi-2729	2	6	2d	2d	NUM
gi-2729	2	7	geometric	geometric	ADJ
gi-2729	2	8	structures	structure	NOUN
gi-2729	2	9	,	,	PUNCT
gi-2729	2	10	geometric	geometric	ADJ
gi-2729	2	11	operations	operation	NOUN
gi-2729	2	12	and	and	CCONJ
gi-2729	2	13	procedures	procedure	NOUN
gi-2729	2	14	for	for	ADP
gi-2729	2	15	automated	automated	ADJ
gi-2729	2	16	or	or	CCONJ
gi-2729	2	17	semi	semi	ADV
gi-2729	2	18	automated	automate	VERB
gi-2729	2	19	simplification	simplification	NOUN
gi-2729	2	20	process	process	NOUN
gi-2729	2	21	.	.	PUNCT
gi-2729	3	1	this	this	DET
gi-2729	3	2	article	article	NOUN
gi-2729	3	3	is	be	AUX
gi-2729	3	4	focused	focus	VERB
gi-2729	3	5	on	on	ADP
gi-2729	3	6	automated	automate	VERB
gi-2729	3	7	building	building	NOUN
gi-2729	3	8	simplification	simplification	NOUN
gi-2729	3	9	procedures	procedure	NOUN
gi-2729	3	10	,	,	PUNCT
gi-2729	3	11	some	some	DET
gi-2729	3	12	techniques	technique	NOUN
gi-2729	3	13	are	be	AUX
gi-2729	3	14	illustrated	illustrate	VERB
gi-2729	3	15	and	and	CCONJ
gi-2729	3	16	discussed	discuss	VERB
gi-2729	3	17	.	.	PUNCT
gi-2729	4	1	concrete	concrete	ADJ
gi-2729	4	2	examples	example	NOUN
gi-2729	4	3	with	with	ADP
gi-2729	4	4	the	the	DET
gi-2729	4	5	requirements	requirement	NOUN
gi-2729	4	6	to	to	ADP
gi-2729	4	7	the	the	DET
gi-2729	4	8	lowest	low	ADJ
gi-2729	4	9	time	time	NOUN
gi-2729	4	10	complexity	complexity	NOUN
gi-2729	4	11	,	,	PUNCT
gi-2729	4	12	emphasis	emphasis	NOUN
gi-2729	4	13	on	on	ADP
gi-2729	4	14	the	the	DET
gi-2729	4	15	smallest	small	ADJ
gi-2729	4	16	area	area	NOUN
gi-2729	4	17	enclosing	enclose	VERB
gi-2729	4	18	rectangle	rectangle	NOUN
gi-2729	4	19	,	,	PUNCT
gi-2729	4	20	convex	convex	NOUN
gi-2729	4	21	hull	hull	NOUN
gi-2729	4	22	or	or	CCONJ
gi-2729	4	23	self	self	NOUN
gi-2729	4	24	intersection	intersection	NOUN
gi-2729	4	25	procedures	procedure	NOUN
gi-2729	4	26	,	,	PUNCT
gi-2729	4	27	are	be	AUX
gi-2729	4	28	given	give	VERB
gi-2729	4	29	.	.	PUNCT
gi-2729	5	1	presented	present	VERB
gi-2729	5	2	results	result	NOUN
gi-2729	5	3	illustrate	illustrate	VERB
gi-2729	5	4	the	the	DET
gi-2729	5	5	relationship	relationship	NOUN
gi-2729	5	6	of	of	ADP
gi-2729	5	7	digital	digital	ADJ
gi-2729	5	8	cartography	cartography	NOUN
gi-2729	5	9	and	and	CCONJ
gi-2729	5	10	computational	computational	ADJ
gi-2729	5	11	geometry	geometry	NOUN
gi-2729	5	12	.	.	PUNCT
gi-2729	6	1	introduction	introduction	NOUN
gi-2729	6	2	needs	need	NOUN
gi-2729	6	3	of	of	ADP
gi-2729	6	4	human	human	NOUN
gi-2729	6	5	to	to	PART
gi-2729	6	6	capture	capture	VERB
gi-2729	6	7	and	and	CCONJ
gi-2729	6	8	represent	represent	VERB
gi-2729	6	9	surrounding	surround	VERB
gi-2729	6	10	landscape	landscape	NOUN
gi-2729	6	11	are	be	AUX
gi-2729	6	12	very	very	ADV
gi-2729	6	13	old	old	ADJ
gi-2729	6	14	.	.	PUNCT
gi-2729	7	1	the	the	DET
gi-2729	7	2	first	first	ADJ
gi-2729	7	3	evidences	evidence	NOUN
gi-2729	7	4	can	can	AUX
gi-2729	7	5	be	be	AUX
gi-2729	7	6	found	find	VERB
gi-2729	7	7	on	on	ADP
gi-2729	7	8	the	the	DET
gi-2729	7	9	walls	wall	NOUN
gi-2729	7	10	of	of	ADP
gi-2729	7	11	caves	cave	NOUN
gi-2729	7	12	or	or	CCONJ
gi-2729	7	13	animal	animal	NOUN
gi-2729	7	14	horns	horn	NOUN
gi-2729	7	15	;	;	PUNCT
gi-2729	7	16	they	they	PRON
gi-2729	7	17	are	be	AUX
gi-2729	7	18	associated	associate	VERB
gi-2729	7	19	with	with	ADP
gi-2729	7	20	the	the	DET
gi-2729	7	21	beginnings	beginning	NOUN
gi-2729	7	22	of	of	ADP
gi-2729	7	23	the	the	DET
gi-2729	7	24	cartography	cartography	NOUN
gi-2729	7	25	.	.	PUNCT
gi-2729	8	1	cartography	cartography	NOUN
gi-2729	8	2	is	be	AUX
gi-2729	8	3	over	over	ADP
gi-2729	8	4	two	two	NUM
gi-2729	8	5	milenia	milenia	ADJ
gi-2729	8	6	old	old	ADJ
gi-2729	8	7	science	science	NOUN
gi-2729	8	8	,	,	PUNCT
gi-2729	8	9	but	but	CCONJ
gi-2729	8	10	during	during	ADP
gi-2729	8	11	this	this	DET
gi-2729	8	12	period	period	NOUN
gi-2729	8	13	has	have	AUX
gi-2729	8	14	been	be	AUX
gi-2729	8	15	radically	radically	ADV
gi-2729	8	16	changed	change	VERB
gi-2729	8	17	.	.	PUNCT
gi-2729	9	1	adding	add	VERB
gi-2729	9	2	mathematical	mathematical	ADJ
gi-2729	9	3	fundamental	fundamental	ADJ
gi-2729	9	4	and	and	CCONJ
gi-2729	9	5	analytical	analytical	ADJ
gi-2729	9	6	methods	method	NOUN
gi-2729	9	7	to	to	ADP
gi-2729	9	8	the	the	DET
gi-2729	9	9	process	process	NOUN
gi-2729	9	10	of	of	ADP
gi-2729	9	11	data	datum	NOUN
gi-2729	9	12	acquisition	acquisition	NOUN
gi-2729	9	13	and	and	CCONJ
gi-2729	9	14	mapping	mapping	NOUN
gi-2729	9	15	resulted	result	VERB
gi-2729	9	16	in	in	ADP
gi-2729	9	17	the	the	DET
gi-2729	9	18	birth	birth	NOUN
gi-2729	9	19	of	of	ADP
gi-2729	9	20	earth	earth	NOUN
gi-2729	9	21	sciences	science	NOUN
gi-2729	9	22	.	.	PUNCT
gi-2729	10	1	due	due	ADP
gi-2729	10	2	to	to	ADP
gi-2729	10	3	new	new	ADJ
gi-2729	10	4	knowledge	knowledge	NOUN
gi-2729	10	5	in	in	ADP
gi-2729	10	6	mathematics	mathematic	NOUN
gi-2729	10	7	,	,	PUNCT
gi-2729	10	8	physics	physics	NOUN
gi-2729	10	9	,	,	PUNCT
gi-2729	10	10	computational	computational	ADJ
gi-2729	10	11	geometry	geometry	NOUN
gi-2729	10	12	,	,	PUNCT
gi-2729	10	13	statistics	statistic	NOUN
gi-2729	10	14	and	and	CCONJ
gi-2729	10	15	informatics	informatic	NOUN
gi-2729	10	16	the	the	DET
gi-2729	10	17	methods	method	NOUN
gi-2729	10	18	of	of	ADP
gi-2729	10	19	creating	create	VERB
gi-2729	10	20	maps	map	NOUN
gi-2729	10	21	have	have	AUX
gi-2729	10	22	been	be	AUX
gi-2729	10	23	rapidly	rapidly	ADV
gi-2729	10	24	modified	modify	VERB
gi-2729	10	25	and	and	CCONJ
gi-2729	10	26	enforced	enforce	VERB
gi-2729	10	27	(	(	PUNCT
gi-2729	10	28	kolar	kolar	PROPN
gi-2729	10	29	at	at	ADP
gi-2729	10	30	al	al	PROPN
gi-2729	10	31	,	,	PUNCT
gi-2729	10	32	2008	2008	NUM
gi-2729	10	33	)	)	PUNCT
gi-2729	10	34	.	.	PUNCT
gi-2729	11	1	the	the	DET
gi-2729	11	2	transformation	transformation	NOUN
gi-2729	11	3	process	process	NOUN
gi-2729	11	4	of	of	ADP
gi-2729	11	5	analogue	analogue	NOUN
gi-2729	11	6	maps	map	NOUN
gi-2729	11	7	to	to	ADP
gi-2729	11	8	digital	digital	ADJ
gi-2729	11	9	maps	map	NOUN
gi-2729	11	10	incurred	incur	VERB
gi-2729	11	11	as	as	ADP
gi-2729	11	12	a	a	DET
gi-2729	11	13	result	result	NOUN
gi-2729	11	14	of	of	ADP
gi-2729	11	15	cartographic	cartographic	ADJ
gi-2729	11	16	representation	representation	NOUN
gi-2729	11	17	of	of	ADP
gi-2729	11	18	the	the	DET
gi-2729	11	19	earth	earth	NOUN
gi-2729	11	20	based	base	VERB
gi-2729	11	21	on	on	ADP
gi-2729	11	22	planar	planar	ADJ
gi-2729	11	23	structures	structure	NOUN
gi-2729	11	24	(	(	PUNCT
gi-2729	11	25	eg	eg	NOUN
gi-2729	11	26	.	.	PUNCT
gi-2729	11	27	points	point	NOUN
gi-2729	11	28	,	,	PUNCT
gi-2729	11	29	lines	line	NOUN
gi-2729	11	30	,	,	PUNCT
gi-2729	11	31	polygons	polygon	NOUN
gi-2729	11	32	)	)	PUNCT
gi-2729	11	33	brought	bring	VERB
gi-2729	11	34	some	some	DET
gi-2729	11	35	new	new	ADJ
gi-2729	11	36	problems	problem	NOUN
gi-2729	11	37	that	that	PRON
gi-2729	11	38	can	can	AUX
gi-2729	11	39	be	be	AUX
gi-2729	11	40	effectively	effectively	ADV
gi-2729	11	41	solved	solve	VERB
gi-2729	11	42	using	use	VERB
gi-2729	11	43	computational	computational	ADJ
gi-2729	11	44	geometry	geometry	NOUN
gi-2729	11	45	.	.	PUNCT
gi-2729	12	1	in	in	ADP
gi-2729	12	2	digital	digital	ADJ
gi-2729	12	3	cartography	cartography	NOUN
gi-2729	12	4	are	be	AUX
gi-2729	12	5	some	some	DET
gi-2729	12	6	new	new	ADJ
gi-2729	12	7	geometric	geometric	ADJ
gi-2729	12	8	structures	structure	NOUN
gi-2729	12	9	like	like	ADP
gi-2729	12	10	topological	topological	ADJ
gi-2729	12	11	skeleton	skeleton	NOUN
gi-2729	12	12	,	,	PUNCT
gi-2729	12	13	voronoi	voronoi	NOUN
gi-2729	12	14	diagrams	diagram	NOUN
gi-2729	12	15	,	,	PUNCT
gi-2729	12	16	delaunay	delaunay	PROPN
gi-2729	12	17	triangulation	triangulation	NOUN
gi-2729	12	18	has	have	AUX
gi-2729	12	19	been	be	AUX
gi-2729	12	20	started	start	VERB
gi-2729	12	21	to	to	PART
gi-2729	12	22	use	use	VERB
gi-2729	12	23	.	.	PUNCT
gi-2729	13	1	geinformatics	geinformatic	NOUN
gi-2729	13	2	fce	fce	VERB
gi-2729	13	3	ctu	ctu	NOUN
gi-2729	13	4	2008	2008	NUM
gi-2729	13	5	15	15	NUM
gi-2729	13	6	the	the	DET
gi-2729	13	7	importance	importance	NOUN
gi-2729	13	8	of	of	ADP
gi-2729	13	9	computational	computational	ADJ
gi-2729	13	10	geometry	geometry	NOUN
gi-2729	13	11	for	for	ADP
gi-2729	13	12	digital	digital	ADJ
gi-2729	13	13	cartography	cartography	NOUN
gi-2729	13	14	from	from	ADP
gi-2729	13	15	computational	computational	ADJ
gi-2729	13	16	geometry	geometry	NOUN
gi-2729	13	17	to	to	ADP
gi-2729	13	18	natural	natural	ADJ
gi-2729	13	19	sciences	science	NOUN
gi-2729	13	20	the	the	DET
gi-2729	13	21	beginnings	beginning	NOUN
gi-2729	13	22	of	of	ADP
gi-2729	13	23	the	the	DET
gi-2729	13	24	computational	computational	ADJ
gi-2729	13	25	geometry	geometry	NOUN
gi-2729	13	26	arose	arise	VERB
gi-2729	13	27	as	as	ADP
gi-2729	13	28	a	a	DET
gi-2729	13	29	response	response	NOUN
gi-2729	13	30	to	to	ADP
gi-2729	13	31	data	datum	NOUN
gi-2729	13	32	acquisition	acquisition	NOUN
gi-2729	13	33	and	and	CCONJ
gi-2729	13	34	data	datum	NOUN
gi-2729	13	35	processing	processing	NOUN
gi-2729	13	36	techniques	technique	NOUN
gi-2729	13	37	changes	change	NOUN
gi-2729	13	38	at	at	ADP
gi-2729	13	39	the	the	DET
gi-2729	13	40	60th	60th	NOUN
gi-2729	13	41	of	of	ADP
gi-2729	13	42	20	20	NUM
gi-2729	13	43	century	century	NOUN
gi-2729	13	44	.	.	PUNCT
gi-2729	14	1	their	their	PRON
gi-2729	14	2	transformation	transformation	NOUN
gi-2729	14	3	into	into	ADP
gi-2729	14	4	digital	digital	ADJ
gi-2729	14	5	form	form	NOUN
gi-2729	14	6	brought	bring	VERB
gi-2729	14	7	a	a	DET
gi-2729	14	8	new	new	ADJ
gi-2729	14	9	data	datum	NOUN
gi-2729	14	10	representation	representation	NOUN
gi-2729	14	11	of	of	ADP
gi-2729	14	12	the	the	DET
gi-2729	14	13	landscape	landscape	NOUN
gi-2729	14	14	,	,	PUNCT
gi-2729	14	15	based	base	VERB
gi-2729	14	16	on	on	ADP
gi-2729	14	17	its	its	PRON
gi-2729	14	18	decomposition	decomposition	NOUN
gi-2729	14	19	to	to	ADP
gi-2729	14	20	0d	0d	NUM
gi-2729	14	21	,	,	PUNCT
gi-2729	14	22	1d	1d	NUM
gi-2729	14	23	,	,	PUNCT
gi-2729	14	24	2d	2d	NUM
gi-2729	14	25	,	,	PUNCT
gi-2729	14	26	3d	3d	NUM
gi-2729	14	27	entities	entity	NOUN
gi-2729	14	28	.	.	PUNCT
gi-2729	15	1	the	the	DET
gi-2729	15	2	process	process	NOUN
gi-2729	15	3	of	of	ADP
gi-2729	15	4	creating	create	VERB
gi-2729	15	5	maps	map	NOUN
gi-2729	15	6	was	be	AUX
gi-2729	15	7	associated	associate	VERB
gi-2729	15	8	with	with	ADP
gi-2729	15	9	the	the	DET
gi-2729	15	10	lack	lack	NOUN
gi-2729	15	11	of	of	ADP
gi-2729	15	12	digital	digital	ADJ
gi-2729	15	13	data	datum	NOUN
gi-2729	15	14	analysis	analysis	NOUN
gi-2729	15	15	and	and	CCONJ
gi-2729	15	16	synthesis	synthesis	NOUN
gi-2729	15	17	.	.	PUNCT
gi-2729	16	1	it	it	PRON
gi-2729	16	2	led	lead	VERB
gi-2729	16	3	to	to	ADP
gi-2729	16	4	the	the	DET
gi-2729	16	5	need	need	NOUN
gi-2729	16	6	of	of	ADP
gi-2729	16	7	their	their	PRON
gi-2729	16	8	processing	processing	NOUN
gi-2729	16	9	with	with	ADP
gi-2729	16	10	the	the	DET
gi-2729	16	11	least	least	ADJ
gi-2729	16	12	amount	amount	NOUN
gi-2729	16	13	of	of	ADP
gi-2729	16	14	manual	manual	ADJ
gi-2729	16	15	interventions	intervention	NOUN
gi-2729	16	16	by	by	ADP
gi-2729	16	17	an	an	DET
gi-2729	16	18	operator	operator	NOUN
gi-2729	16	19	.	.	PUNCT
gi-2729	17	1	a	a	DET
gi-2729	17	2	number	number	NOUN
gi-2729	17	3	of	of	ADP
gi-2729	17	4	new	new	ADJ
gi-2729	17	5	techniques	technique	NOUN
gi-2729	17	6	aimed	aim	VERB
gi-2729	17	7	to	to	PART
gi-2729	17	8	planar	planar	VERB
gi-2729	17	9	or	or	CCONJ
gi-2729	17	10	spatial	spatial	ADJ
gi-2729	17	11	data	datum	NOUN
gi-2729	17	12	analysis	analysis	NOUN
gi-2729	17	13	and	and	CCONJ
gi-2729	17	14	their	their	PRON
gi-2729	17	15	relationships	relationship	NOUN
gi-2729	17	16	has	have	AUX
gi-2729	17	17	been	be	AUX
gi-2729	17	18	created	create	VERB
gi-2729	17	19	.	.	PUNCT
gi-2729	18	1	those	those	DET
gi-2729	18	2	exact	exact	ADJ
gi-2729	18	3	methods	method	NOUN
gi-2729	18	4	were	be	AUX
gi-2729	18	5	based	base	VERB
gi-2729	18	6	on	on	ADP
gi-2729	18	7	linear	linear	PROPN
gi-2729	18	8	algebra	algebra	PROPN
gi-2729	18	9	,	,	PUNCT
gi-2729	18	10	geometry	geometry	NOUN
gi-2729	18	11	,	,	PUNCT
gi-2729	18	12	cartography	cartography	NOUN
gi-2729	18	13	,	,	PUNCT
gi-2729	18	14	statistic	statistic	NOUN
gi-2729	18	15	or	or	CCONJ
gi-2729	18	16	adjustment	adjustment	NOUN
gi-2729	18	17	calculus	calculus	NOUN
gi-2729	18	18	.	.	PUNCT
gi-2729	19	1	based	base	VERB
gi-2729	19	2	on	on	ADP
gi-2729	19	3	synthesis	synthesis	NOUN
gi-2729	19	4	of	of	ADP
gi-2729	19	5	these	these	DET
gi-2729	19	6	findings	finding	NOUN
gi-2729	19	7	,	,	PUNCT
gi-2729	19	8	a	a	DET
gi-2729	19	9	new	new	ADJ
gi-2729	19	10	field	field	NOUN
gi-2729	19	11	“	"	PUNCT
gi-2729	19	12	computational	computational	ADJ
gi-2729	19	13	geometry	geometry	NOUN
gi-2729	19	14	”	"	PUNCT
gi-2729	19	15	has	have	AUX
gi-2729	19	16	been	be	AUX
gi-2729	19	17	established	establish	VERB
gi-2729	19	18	.	.	PUNCT
gi-2729	20	1	the	the	DET
gi-2729	20	2	computational	computational	ADJ
gi-2729	20	3	geometry	geometry	NOUN
gi-2729	20	4	studies	study	NOUN
gi-2729	20	5	features	feature	NOUN
gi-2729	20	6	of	of	ADP
gi-2729	20	7	geometry	geometry	NOUN
gi-2729	20	8	algorithms	algorithm	NOUN
gi-2729	20	9	in	in	ADP
gi-2729	20	10	2d	2d	NUM
gi-2729	20	11	or	or	CCONJ
gi-2729	20	12	3d	3d	NUM
gi-2729	20	13	and	and	CCONJ
gi-2729	20	14	tries	try	VERB
gi-2729	20	15	to	to	PART
gi-2729	20	16	find	find	VERB
gi-2729	20	17	an	an	DET
gi-2729	20	18	optimal	optimal	ADJ
gi-2729	20	19	solution	solution	NOUN
gi-2729	20	20	for	for	ADP
gi-2729	20	21	geometry	geometry	NOUN
gi-2729	20	22	problems	problem	NOUN
gi-2729	20	23	due	due	ADJ
gi-2729	20	24	to	to	ADP
gi-2729	20	25	the	the	DET
gi-2729	20	26	time	time	NOUN
gi-2729	20	27	complexity	complexity	NOUN
gi-2729	20	28	.	.	PUNCT
gi-2729	21	1	whereas	whereas	SCONJ
gi-2729	21	2	there	there	PRON
gi-2729	21	3	is	be	VERB
gi-2729	21	4	a	a	DET
gi-2729	21	5	bigger	big	ADJ
gi-2729	21	6	amount	amount	NOUN
gi-2729	21	7	of	of	ADP
gi-2729	21	8	data	datum	NOUN
gi-2729	21	9	we	we	PRON
gi-2729	21	10	are	be	AUX
gi-2729	21	11	able	able	ADJ
gi-2729	21	12	to	to	PART
gi-2729	21	13	process	process	VERB
gi-2729	21	14	,	,	PUNCT
gi-2729	21	15	it	it	PRON
gi-2729	21	16	is	be	AUX
gi-2729	21	17	necessary	necessary	ADJ
gi-2729	21	18	to	to	PART
gi-2729	21	19	solve	solve	VERB
gi-2729	21	20	problems	problem	NOUN
gi-2729	21	21	effectively	effectively	ADV
gi-2729	21	22	.	.	PUNCT
gi-2729	22	1	due	due	ADP
gi-2729	22	2	to	to	ADP
gi-2729	22	3	the	the	DET
gi-2729	22	4	difference	difference	NOUN
gi-2729	22	5	of	of	ADP
gi-2729	22	6	the	the	DET
gi-2729	22	7	cartographic	cartographic	ADJ
gi-2729	22	8	and	and	CCONJ
gi-2729	22	9	informatic	informatic	ADJ
gi-2729	22	10	look	look	NOUN
gi-2729	22	11	to	to	ADP
gi-2729	22	12	problems	problem	NOUN
gi-2729	22	13	,	,	PUNCT
gi-2729	22	14	this	this	DET
gi-2729	22	15	article	article	NOUN
gi-2729	22	16	tries	try	VERB
gi-2729	22	17	to	to	PART
gi-2729	22	18	find	find	VERB
gi-2729	22	19	unifying	unifying	NOUN
gi-2729	22	20	perspective	perspective	NOUN
gi-2729	22	21	emphasing	emphase	VERB
gi-2729	22	22	importance	importance	NOUN
gi-2729	22	23	of	of	ADP
gi-2729	22	24	the	the	DET
gi-2729	22	25	computational	computational	ADJ
gi-2729	22	26	geometry	geometry	NOUN
gi-2729	22	27	for	for	ADP
gi-2729	22	28	the	the	DET
gi-2729	22	29	cartography	cartography	NOUN
gi-2729	22	30	education	education	NOUN
gi-2729	22	31	.	.	PUNCT
gi-2729	23	1	in	in	ADP
gi-2729	23	2	order	order	NOUN
gi-2729	23	3	to	to	ADP
gi-2729	23	4	the	the	DET
gi-2729	23	5	czech	czech	PROPN
gi-2729	23	6	republic	republic	NOUN
gi-2729	23	7	does	do	AUX
gi-2729	23	8	not	not	PART
gi-2729	23	9	become	become	VERB
gi-2729	23	10	passive	passive	ADJ
gi-2729	23	11	consumers	consumer	NOUN
gi-2729	23	12	of	of	ADP
gi-2729	23	13	information	information	NOUN
gi-2729	23	14	technologies	technology	NOUN
gi-2729	23	15	,	,	PUNCT
gi-2729	23	16	it	it	PRON
gi-2729	23	17	is	be	AUX
gi-2729	23	18	necessary	necessary	ADJ
gi-2729	23	19	to	to	PART
gi-2729	23	20	invest	invest	VERB
gi-2729	23	21	in	in	ADP
gi-2729	23	22	development	development	NOUN
gi-2729	23	23	of	of	ADP
gi-2729	23	24	own	own	ADJ
gi-2729	23	25	geoinformatic	geoinformatic	ADJ
gi-2729	23	26	problems	problem	NOUN
gi-2729	23	27	solutions	solution	NOUN
gi-2729	23	28	.	.	PUNCT
gi-2729	24	1	this	this	DET
gi-2729	24	2	fact	fact	NOUN
gi-2729	24	3	plays	play	VERB
gi-2729	24	4	and	and	CCONJ
gi-2729	24	5	important	important	ADJ
gi-2729	24	6	role	role	NOUN
gi-2729	24	7	and	and	CCONJ
gi-2729	24	8	can	can	AUX
gi-2729	24	9	not	not	PART
gi-2729	24	10	be	be	AUX
gi-2729	24	11	underestimated	underestimate	VERB
gi-2729	24	12	in	in	ADP
gi-2729	24	13	the	the	DET
gi-2729	24	14	long	long	ADJ
gi-2729	24	15	term	term	NOUN
gi-2729	24	16	perspective	perspective	NOUN
gi-2729	24	17	.	.	PUNCT
gi-2729	25	1	the	the	DET
gi-2729	25	2	educational	educational	ADJ
gi-2729	25	3	process	process	NOUN
gi-2729	25	4	must	must	AUX
gi-2729	25	5	be	be	AUX
gi-2729	25	6	adapted	adapt	VERB
gi-2729	25	7	to	to	ADP
gi-2729	25	8	those	those	DET
gi-2729	25	9	facts	fact	NOUN
gi-2729	25	10	.	.	PUNCT
gi-2729	26	1	it	it	PRON
gi-2729	26	2	is	be	AUX
gi-2729	26	3	not	not	PART
gi-2729	26	4	sufficient	sufficient	ADJ
gi-2729	26	5	to	to	PART
gi-2729	26	6	focus	focus	VERB
gi-2729	26	7	only	only	ADV
gi-2729	26	8	on	on	ADP
gi-2729	26	9	practical	practical	ADJ
gi-2729	26	10	solving	solving	NOUN
gi-2729	26	11	of	of	ADP
gi-2729	26	12	problems	problem	NOUN
gi-2729	26	13	.	.	PUNCT
gi-2729	27	1	based	base	VERB
gi-2729	27	2	on	on	ADP
gi-2729	27	3	an	an	DET
gi-2729	27	4	analysis	analysis	NOUN
gi-2729	27	5	,	,	PUNCT
gi-2729	27	6	the	the	DET
gi-2729	27	7	student	student	NOUN
gi-2729	27	8	should	should	AUX
gi-2729	27	9	be	be	AUX
gi-2729	27	10	able	able	ADJ
gi-2729	27	11	to	to	PART
gi-2729	27	12	find	find	VERB
gi-2729	27	13	optimal	optimal	ADJ
gi-2729	27	14	solution	solution	NOUN
gi-2729	27	15	for	for	ADP
gi-2729	27	16	the	the	DET
gi-2729	27	17	problem	problem	NOUN
gi-2729	27	18	.	.	PUNCT
gi-2729	28	1	in	in	ADP
gi-2729	28	2	general	general	ADJ
gi-2729	28	3	terms	term	NOUN
gi-2729	28	4	,	,	PUNCT
gi-2729	28	5	it	it	PRON
gi-2729	28	6	is	be	AUX
gi-2729	28	7	necessary	necessary	ADJ
gi-2729	28	8	to	to	PART
gi-2729	28	9	strengthen	strengthen	VERB
gi-2729	28	10	the	the	DET
gi-2729	28	11	teaching	teaching	NOUN
gi-2729	28	12	of	of	ADP
gi-2729	28	13	natural	natural	ADJ
gi-2729	28	14	sciences	science	NOUN
gi-2729	28	15	.	.	PUNCT
gi-2729	29	1	in	in	ADP
gi-2729	29	2	today´s	today´s	PROPN
gi-2729	29	3	highly	highly	ADV
gi-2729	29	4	over	over	ADP
gi-2729	29	5	-	-	PUNCT
gi-2729	29	6	technized	technize	VERB
gi-2729	29	7	world	world	NOUN
gi-2729	29	8	plays	play	VERB
gi-2729	29	9	the	the	DET
gi-2729	29	10	ability	ability	NOUN
gi-2729	29	11	of	of	ADP
gi-2729	29	12	exact	exact	ADJ
gi-2729	29	13	assessment	assessment	NOUN
gi-2729	29	14	of	of	ADP
gi-2729	29	15	the	the	DET
gi-2729	29	16	problem	problem	NOUN
gi-2729	29	17	an	an	DET
gi-2729	29	18	important	important	ADJ
gi-2729	29	19	role	role	NOUN
gi-2729	29	20	.	.	PUNCT
gi-2729	30	1	it	it	PRON
gi-2729	30	2	allows	allow	VERB
gi-2729	30	3	to	to	PART
gi-2729	30	4	reduce	reduce	VERB
gi-2729	30	5	an	an	DET
gi-2729	30	6	inwardness	inwardness	NOUN
gi-2729	30	7	of	of	ADP
gi-2729	30	8	human	human	ADJ
gi-2729	30	9	decisionmaking	decisionmaking	NOUN
gi-2729	30	10	and	and	CCONJ
gi-2729	30	11	a	a	DET
gi-2729	30	12	dependency	dependency	NOUN
gi-2729	30	13	on	on	ADP
gi-2729	30	14	ideologies	ideology	NOUN
gi-2729	30	15	.	.	PUNCT
gi-2729	31	1	but	but	CCONJ
gi-2729	31	2	this	this	DET
gi-2729	31	3	concept	concept	NOUN
gi-2729	31	4	is	be	AUX
gi-2729	31	5	in	in	ADP
gi-2729	31	6	the	the	DET
gi-2729	31	7	discrepancy	discrepancy	NOUN
gi-2729	31	8	with	with	ADP
gi-2729	31	9	the	the	DET
gi-2729	31	10	requirements	requirement	NOUN
gi-2729	31	11	to	to	ADP
gi-2729	31	12	practical	practical	ADJ
gi-2729	31	13	focus	focus	NOUN
gi-2729	31	14	of	of	ADP
gi-2729	31	15	higher	high	ADJ
gi-2729	31	16	education	education	NOUN
gi-2729	31	17	.	.	PUNCT
gi-2729	32	1	it	it	PRON
gi-2729	32	2	is	be	AUX
gi-2729	32	3	possible	possible	ADJ
gi-2729	32	4	to	to	PART
gi-2729	32	5	illustrate	illustrate	VERB
gi-2729	32	6	those	those	DET
gi-2729	32	7	problems	problem	NOUN
gi-2729	32	8	on	on	ADP
gi-2729	32	9	the	the	DET
gi-2729	32	10	educational	educational	ADJ
gi-2729	32	11	process	process	NOUN
gi-2729	32	12	of	of	ADP
gi-2729	32	13	computational	computational	ADJ
gi-2729	32	14	geometry	geometry	NOUN
gi-2729	32	15	with	with	ADP
gi-2729	32	16	the	the	DET
gi-2729	32	17	focus	focus	NOUN
gi-2729	32	18	on	on	ADP
gi-2729	32	19	interrelationships	interrelationship	NOUN
gi-2729	32	20	and	and	CCONJ
gi-2729	32	21	interdisciplinary	interdisciplinary	ADJ
gi-2729	32	22	links	link	NOUN
gi-2729	32	23	.	.	PUNCT
gi-2729	33	1	students	student	NOUN
gi-2729	33	2	would	would	AUX
gi-2729	33	3	be	be	AUX
gi-2729	33	4	able	able	ADJ
gi-2729	33	5	to	to	PART
gi-2729	33	6	feel	feel	VERB
gi-2729	33	7	the	the	DET
gi-2729	33	8	problem	problem	NOUN
gi-2729	33	9	comprehensively	comprehensively	ADV
gi-2729	33	10	and	and	CCONJ
gi-2729	33	11	solve	solve	VERB
gi-2729	33	12	it	it	PRON
gi-2729	33	13	much	much	ADV
gi-2729	33	14	more	more	ADV
gi-2729	33	15	effectively	effectively	ADV
gi-2729	33	16	.	.	PUNCT
gi-2729	34	1	computational	computational	ADJ
gi-2729	34	2	geometry	geometry	NOUN
gi-2729	34	3	and	and	CCONJ
gi-2729	34	4	building	building	NOUN
gi-2729	34	5	generalization	generalization	NOUN
gi-2729	34	6	a	a	DET
gi-2729	34	7	map	map	NOUN
gi-2729	34	8	represents	represent	VERB
gi-2729	34	9	an	an	DET
gi-2729	34	10	abstract	abstract	ADJ
gi-2729	34	11	expression	expression	NOUN
gi-2729	34	12	of	of	ADP
gi-2729	34	13	the	the	DET
gi-2729	34	14	reality	reality	NOUN
gi-2729	34	15	.	.	PUNCT
gi-2729	35	1	to	to	PART
gi-2729	35	2	maintain	maintain	VERB
gi-2729	35	3	the	the	DET
gi-2729	35	4	basic	basic	ADJ
gi-2729	35	5	characteristics	characteristic	NOUN
gi-2729	35	6	of	of	ADP
gi-2729	35	7	the	the	DET
gi-2729	35	8	cartographic	cartographic	ADJ
gi-2729	35	9	products	product	NOUN
gi-2729	35	10	(	(	PUNCT
gi-2729	35	11	dis	dis	PROPN
gi-2729	35	12	passionateness	passionateness	NOUN
gi-2729	35	13	,	,	PUNCT
gi-2729	35	14	clearness	clearness	NOUN
gi-2729	35	15	,	,	PUNCT
gi-2729	35	16	lucidity	lucidity	NOUN
gi-2729	35	17	...	...	PUNCT
gi-2729	35	18	)	)	PUNCT
gi-2729	35	19	,	,	PUNCT
gi-2729	35	20	a	a	DET
gi-2729	35	21	controlled	control	VERB
gi-2729	35	22	reduction	reduction	NOUN
gi-2729	35	23	of	of	ADP
gi-2729	35	24	information	information	NOUN
gi-2729	35	25	must	must	AUX
gi-2729	35	26	be	be	AUX
gi-2729	35	27	performed	perform	VERB
gi-2729	35	28	.	.	PUNCT
gi-2729	36	1	this	this	DET
gi-2729	36	2	process	process	NOUN
gi-2729	36	3	is	be	AUX
gi-2729	36	4	called	call	VERB
gi-2729	36	5	“	"	PUNCT
gi-2729	36	6	generalization	generalization	NOUN
gi-2729	36	7	”	"	PUNCT
gi-2729	36	8	and	and	CCONJ
gi-2729	36	9	results	result	VERB
gi-2729	36	10	in	in	ADP
gi-2729	36	11	the	the	DET
gi-2729	36	12	simplification	simplification	NOUN
gi-2729	36	13	of	of	ADP
gi-2729	36	14	the	the	DET
gi-2729	36	15	map	map	NOUN
gi-2729	36	16	content	content	NOUN
gi-2729	36	17	.	.	PUNCT
gi-2729	37	1	generalization	generalization	NOUN
gi-2729	37	2	takes	take	VERB
gi-2729	37	3	an	an	DET
gi-2729	37	4	important	important	ADJ
gi-2729	37	5	role	role	NOUN
gi-2729	37	6	in	in	ADP
gi-2729	37	7	computer	computer	NOUN
gi-2729	37	8	graphics	graphic	NOUN
gi-2729	37	9	,	,	PUNCT
gi-2729	37	10	it	it	PRON
gi-2729	37	11	allows	allow	VERB
gi-2729	37	12	to	to	PART
gi-2729	37	13	reduce	reduce	VERB
gi-2729	37	14	the	the	DET
gi-2729	37	15	amount	amount	NOUN
gi-2729	37	16	of	of	ADP
gi-2729	37	17	information	information	NOUN
gi-2729	37	18	and	and	CCONJ
gi-2729	37	19	shorten	shorten	VERB
gi-2729	37	20	the	the	DET
gi-2729	37	21	visualization	visualization	NOUN
gi-2729	37	22	process	process	NOUN
gi-2729	37	23	.	.	PUNCT
gi-2729	38	1	generalization	generalization	NOUN
gi-2729	38	2	is	be	AUX
gi-2729	38	3	a	a	DET
gi-2729	38	4	subjective	subjective	ADJ
gi-2729	38	5	process	process	NOUN
gi-2729	38	6	with	with	ADP
gi-2729	38	7	an	an	DET
gi-2729	38	8	accent	accent	NOUN
gi-2729	38	9	to	to	ADP
gi-2729	38	10	knowledge	knowledge	NOUN
gi-2729	38	11	and	and	CCONJ
gi-2729	38	12	experiences	experience	NOUN
gi-2729	38	13	of	of	ADP
gi-2729	38	14	the	the	DET
gi-2729	38	15	cartographer	cartographer	NOUN
gi-2729	38	16	.	.	PUNCT
gi-2729	39	1	computational	computational	ADJ
gi-2729	39	2	geometry	geometry	NOUN
gi-2729	39	3	makes	make	VERB
gi-2729	39	4	the	the	DET
gi-2729	39	5	process	process	NOUN
gi-2729	39	6	of	of	ADP
gi-2729	39	7	simplification	simplification	NOUN
gi-2729	39	8	less	less	ADV
gi-2729	39	9	dependent	dependent	ADJ
gi-2729	39	10	on	on	ADP
gi-2729	39	11	a	a	DET
gi-2729	39	12	subjective	subjective	ADJ
gi-2729	39	13	view	view	NOUN
gi-2729	39	14	of	of	ADP
gi-2729	39	15	a	a	DET
gi-2729	39	16	cartographer	cartographer	NOUN
gi-2729	39	17	.	.	PUNCT
gi-2729	40	1	an	an	DET
gi-2729	40	2	algoritmization	algoritmization	NOUN
gi-2729	40	3	of	of	ADP
gi-2729	40	4	the	the	DET
gi-2729	40	5	simplification	simplification	NOUN
gi-2729	40	6	process	process	NOUN
gi-2729	40	7	is	be	AUX
gi-2729	40	8	not	not	PART
gi-2729	40	9	unambiguous	unambiguous	ADJ
gi-2729	40	10	.	.	PUNCT
gi-2729	41	1	it	it	PRON
gi-2729	41	2	is	be	AUX
gi-2729	41	3	not	not	PART
gi-2729	41	4	an	an	DET
gi-2729	41	5	easy	easy	ADJ
gi-2729	41	6	task	task	NOUN
gi-2729	41	7	to	to	PART
gi-2729	41	8	find	find	VERB
gi-2729	41	9	and	and	CCONJ
gi-2729	41	10	set	set	VERB
gi-2729	41	11	a	a	DET
gi-2729	41	12	geometric	geometric	ADJ
gi-2729	41	13	criterion	criterion	NOUN
gi-2729	41	14	,	,	PUNCT
gi-2729	41	15	that	that	PRON
gi-2729	41	16	is	be	AUX
gi-2729	41	17	supposed	suppose	VERB
gi-2729	41	18	to	to	PART
gi-2729	41	19	be	be	AUX
gi-2729	41	20	satisfied	satisfy	VERB
gi-2729	41	21	by	by	ADP
gi-2729	41	22	a	a	DET
gi-2729	41	23	simplified	simplified	ADJ
gi-2729	41	24	element	element	NOUN
gi-2729	41	25	.	.	PUNCT
gi-2729	42	1	the	the	DET
gi-2729	42	2	simplification	simplification	NOUN
gi-2729	42	3	represents	represent	VERB
gi-2729	42	4	a	a	DET
gi-2729	42	5	process	process	NOUN
gi-2729	42	6	of	of	ADP
gi-2729	42	7	more	more	ADJ
gi-2729	42	8	interdependent	interdependent	ADJ
gi-2729	42	9	steps	step	NOUN
gi-2729	42	10	,	,	PUNCT
gi-2729	42	11	an	an	DET
gi-2729	42	12	implementation	implementation	NOUN
gi-2729	42	13	of	of	ADP
gi-2729	42	14	one	one	NUM
gi-2729	42	15	step	step	NOUN
gi-2729	42	16	causes	cause	VERB
gi-2729	42	17	the	the	DET
gi-2729	42	18	next	next	ADJ
gi-2729	42	19	step	step	NOUN
gi-2729	42	20	.	.	PUNCT
gi-2729	43	1	this	this	DET
gi-2729	43	2	geinformatics	geinformatic	NOUN
gi-2729	43	3	fce	fce	VERB
gi-2729	43	4	ctu	ctu	NOUN
gi-2729	43	5	2008	2008	NUM
gi-2729	43	6	16	16	NUM
gi-2729	43	7	the	the	DET
gi-2729	43	8	importance	importance	NOUN
gi-2729	43	9	of	of	ADP
gi-2729	43	10	computational	computational	ADJ
gi-2729	43	11	geometry	geometry	NOUN
gi-2729	43	12	for	for	ADP
gi-2729	43	13	digital	digital	ADJ
gi-2729	43	14	cartography	cartography	NOUN
gi-2729	43	15	part	part	NOUN
gi-2729	43	16	of	of	ADP
gi-2729	43	17	the	the	DET
gi-2729	43	18	article	article	NOUN
gi-2729	43	19	uses	use	VERB
gi-2729	43	20	information	information	NOUN
gi-2729	43	21	and	and	CCONJ
gi-2729	43	22	mathematical	mathematical	ADJ
gi-2729	43	23	background	background	NOUN
gi-2729	43	24	from	from	ADP
gi-2729	43	25	a	a	DET
gi-2729	43	26	new	new	ADJ
gi-2729	43	27	simplification	simplification	NOUN
gi-2729	43	28	algorithm	algorithm	NOUN
gi-2729	43	29	proposed	propose	VERB
gi-2729	43	30	by	by	ADP
gi-2729	43	31	the	the	DET
gi-2729	43	32	author	author	NOUN
gi-2729	43	33	.	.	PUNCT
gi-2729	44	1	generalization	generalization	NOUN
gi-2729	44	2	factors	factor	NOUN
gi-2729	44	3	.	.	PUNCT
gi-2729	45	1	the	the	PRON
gi-2729	45	2	are	be	AUX
gi-2729	45	3	several	several	ADJ
gi-2729	45	4	important	important	ADJ
gi-2729	45	5	factors	factor	NOUN
gi-2729	45	6	of	of	ADP
gi-2729	45	7	the	the	DET
gi-2729	45	8	generalization	generalization	NOUN
gi-2729	45	9	that	that	PRON
gi-2729	45	10	affect	affect	VERB
gi-2729	45	11	the	the	DET
gi-2729	45	12	results	result	NOUN
gi-2729	45	13	.	.	PUNCT
gi-2729	46	1	they	they	PRON
gi-2729	46	2	could	could	AUX
gi-2729	46	3	be	be	AUX
gi-2729	46	4	divided	divide	VERB
gi-2729	46	5	into	into	ADP
gi-2729	46	6	four	four	NUM
gi-2729	46	7	categories	category	NOUN
gi-2729	46	8	:	:	PUNCT
gi-2729	46	9	map	map	NOUN
gi-2729	46	10	scale	scale	NOUN
gi-2729	46	11	,	,	PUNCT
gi-2729	46	12	the	the	DET
gi-2729	46	13	purpose	purpose	NOUN
gi-2729	46	14	of	of	ADP
gi-2729	46	15	the	the	DET
gi-2729	46	16	map	map	NOUN
gi-2729	46	17	,	,	PUNCT
gi-2729	46	18	characteristic	characteristic	ADJ
gi-2729	46	19	of	of	ADP
gi-2729	46	20	the	the	DET
gi-2729	46	21	territory	territory	NOUN
gi-2729	46	22	,	,	PUNCT
gi-2729	46	23	used	use	VERB
gi-2729	46	24	cartographic	cartographic	ADJ
gi-2729	46	25	symbols	symbol	NOUN
gi-2729	46	26	.	.	PUNCT
gi-2729	47	1	geometric	geometric	ADJ
gi-2729	47	2	generalization	generalization	NOUN
gi-2729	47	3	of	of	ADP
gi-2729	47	4	the	the	DET
gi-2729	47	5	building	building	NOUN
gi-2729	47	6	.	.	PUNCT
gi-2729	48	1	the	the	DET
gi-2729	48	2	geometric	geometric	ADJ
gi-2729	48	3	generalization	generalization	NOUN
gi-2729	48	4	carries	carry	VERB
gi-2729	48	5	out	out	ADP
gi-2729	48	6	a	a	DET
gi-2729	48	7	controlled	control	VERB
gi-2729	48	8	reduction	reduction	NOUN
gi-2729	48	9	of	of	ADP
gi-2729	48	10	the	the	DET
gi-2729	48	11	map	map	NOUN
gi-2729	48	12	content	content	NOUN
gi-2729	48	13	based	base	VERB
gi-2729	48	14	on	on	ADP
gi-2729	48	15	analysis	analysis	NOUN
gi-2729	48	16	of	of	ADP
gi-2729	48	17	the	the	DET
gi-2729	48	18	geometric	geometric	ADJ
gi-2729	48	19	properties	property	NOUN
gi-2729	48	20	of	of	ADP
gi-2729	48	21	the	the	DET
gi-2729	48	22	elements	element	NOUN
gi-2729	48	23	.	.	PUNCT
gi-2729	49	1	it	it	PRON
gi-2729	49	2	tries	try	VERB
gi-2729	49	3	to	to	PART
gi-2729	49	4	remove	remove	VERB
gi-2729	49	5	those	those	DET
gi-2729	49	6	elements	element	NOUN
gi-2729	49	7	,	,	PUNCT
gi-2729	49	8	that	that	PRON
gi-2729	49	9	are	be	AUX
gi-2729	49	10	not	not	PART
gi-2729	49	11	significant	significant	ADJ
gi-2729	49	12	in	in	ADP
gi-2729	49	13	the	the	DET
gi-2729	49	14	map	map	NOUN
gi-2729	49	15	context	context	NOUN
gi-2729	49	16	.	.	PUNCT
gi-2729	50	1	some	some	DET
gi-2729	50	2	geometric	geometric	ADJ
gi-2729	50	3	structures	structure	NOUN
gi-2729	50	4	like	like	ADP
gi-2729	50	5	voronoi	voronoi	ADJ
gi-2729	50	6	tessellation	tessellation	NOUN
gi-2729	50	7	or	or	CCONJ
gi-2729	50	8	delaunay	delaunay	PROPN
gi-2729	50	9	triangulation	triangulation	NOUN
gi-2729	50	10	can	can	AUX
gi-2729	50	11	be	be	AUX
gi-2729	50	12	used	use	VERB
gi-2729	50	13	.	.	PUNCT
gi-2729	51	1	automated	automate	VERB
gi-2729	51	2	or	or	CCONJ
gi-2729	51	3	semi	semi	ADV
gi-2729	51	4	automated	automate	VERB
gi-2729	51	5	generalization	generalization	NOUN
gi-2729	51	6	of	of	ADP
gi-2729	51	7	the	the	DET
gi-2729	51	8	building	building	NOUN
gi-2729	51	9	represents	represent	VERB
gi-2729	51	10	a	a	DET
gi-2729	51	11	problem	problem	NOUN
gi-2729	51	12	solved	solve	VERB
gi-2729	51	13	in	in	ADP
gi-2729	51	14	many	many	ADJ
gi-2729	51	15	ways	way	NOUN
gi-2729	51	16	.	.	PUNCT
gi-2729	52	1	commonly	commonly	ADV
gi-2729	52	2	used	use	VERB
gi-2729	52	3	simplifying	simplify	VERB
gi-2729	52	4	algorithms	algorithm	NOUN
gi-2729	52	5	can	can	AUX
gi-2729	52	6	not	not	PART
gi-2729	52	7	be	be	AUX
gi-2729	52	8	applied	apply	VERB
gi-2729	52	9	,	,	PUNCT
gi-2729	52	10	they	they	PRON
gi-2729	52	11	do	do	AUX
gi-2729	52	12	not	not	PART
gi-2729	52	13	maintain	maintain	VERB
gi-2729	52	14	internal	internal	ADJ
gi-2729	52	15	angles	angle	NOUN
gi-2729	52	16	of	of	ADP
gi-2729	52	17	the	the	DET
gi-2729	52	18	polygon	polygon	NOUN
gi-2729	52	19	edges	edge	NOUN
gi-2729	52	20	(	(	PUNCT
gi-2729	52	21	±π	±π	X
gi-2729	52	22	2	2	NUM
gi-2729	52	23	)	)	PUNCT
gi-2729	52	24	representing	represent	VERB
gi-2729	52	25	the	the	DET
gi-2729	52	26	building	building	NOUN
gi-2729	52	27	,	,	PUNCT
gi-2729	52	28	see	see	VERB
gi-2729	52	29	fig	fig	NOUN
gi-2729	52	30	.	.	PUNCT
gi-2729	53	1	1	1	X
gi-2729	53	2	.	.	X
gi-2729	53	3	building	building	NOUN
gi-2729	53	4	simplification	simplification	NOUN
gi-2729	53	5	has	have	VERB
gi-2729	53	6	the	the	DET
gi-2729	53	7	constrain	constrain	NOUN
gi-2729	53	8	that	that	PRON
gi-2729	53	9	makes	make	VERB
gi-2729	53	10	this	this	DET
gi-2729	53	11	process	process	NOUN
gi-2729	53	12	more	more	ADV
gi-2729	53	13	difficult	difficult	ADJ
gi-2729	53	14	.	.	PUNCT
gi-2729	54	1	figure	figure	NOUN
gi-2729	54	2	1	1	NUM
gi-2729	54	3	:	:	PUNCT
gi-2729	54	4	building	build	VERB
gi-2729	54	5	generalization	generalization	NOUN
gi-2729	54	6	without	without	ADP
gi-2729	54	7	internal	internal	ADJ
gi-2729	54	8	angles	angle	NOUN
gi-2729	54	9	maintaining	maintain	VERB
gi-2729	54	10	.	.	PUNCT
gi-2729	55	1	requirements	requirement	NOUN
gi-2729	55	2	for	for	ADP
gi-2729	55	3	the	the	DET
gi-2729	55	4	algorithm	algorithm	NOUN
gi-2729	55	5	.	.	PUNCT
gi-2729	56	1	a	a	DET
gi-2729	56	2	design	design	NOUN
gi-2729	56	3	of	of	ADP
gi-2729	56	4	the	the	DET
gi-2729	56	5	algorithm	algorithm	NOUN
gi-2729	56	6	with	with	ADP
gi-2729	56	7	the	the	DET
gi-2729	56	8	reasonable	reasonable	ADJ
gi-2729	56	9	time	time	NOUN
gi-2729	56	10	complexity	complexity	NOUN
gi-2729	56	11	(	(	PUNCT
gi-2729	56	12	quadratic	quadratic	ADJ
gi-2729	56	13	or	or	CCONJ
gi-2729	56	14	better	well	ADJ
gi-2729	56	15	)	)	PUNCT
gi-2729	56	16	providing	provide	VERB
gi-2729	56	17	appropriate	appropriate	ADJ
gi-2729	56	18	cartographic	cartographic	ADJ
gi-2729	56	19	results	result	NOUN
gi-2729	56	20	with	with	ADP
gi-2729	56	21	minimizing	minimize	VERB
gi-2729	56	22	the	the	DET
gi-2729	56	23	needs	need	NOUN
gi-2729	56	24	of	of	ADP
gi-2729	56	25	manual	manual	ADJ
gi-2729	56	26	corrections	correction	NOUN
gi-2729	56	27	seems	seem	VERB
gi-2729	56	28	to	to	PART
gi-2729	56	29	be	be	AUX
gi-2729	56	30	a	a	DET
gi-2729	56	31	hard	hard	ADJ
gi-2729	56	32	problem	problem	NOUN
gi-2729	56	33	.	.	PUNCT
gi-2729	57	1	in	in	ADP
gi-2729	57	2	addition	addition	NOUN
gi-2729	57	3	,	,	PUNCT
gi-2729	57	4	we	we	PRON
gi-2729	57	5	have	have	VERB
gi-2729	57	6	the	the	DET
gi-2729	57	7	following	follow	VERB
gi-2729	57	8	requirements	requirement	NOUN
gi-2729	57	9	for	for	ADP
gi-2729	57	10	the	the	DET
gi-2729	57	11	simplification	simplification	NOUN
gi-2729	57	12	algorithm	algorithm	NOUN
gi-2729	57	13	:	:	PUNCT
gi-2729	57	14	�	�	PROPN
gi-2729	57	15	ability	ability	NOUN
gi-2729	57	16	of	of	ADP
gi-2729	57	17	building	build	VERB
gi-2729	57	18	detection	detection	NOUN
gi-2729	57	19	and	and	CCONJ
gi-2729	57	20	simplification	simplification	NOUN
gi-2729	57	21	in	in	ADP
gi-2729	57	22	any	any	DET
gi-2729	57	23	position	position	NOUN
gi-2729	57	24	,	,	PUNCT
gi-2729	57	25	�	�	PROPN
gi-2729	57	26	self	self	NOUN
gi-2729	57	27	intersections	intersection	NOUN
gi-2729	57	28	removing	remove	VERB
gi-2729	57	29	,	,	PUNCT
gi-2729	57	30	�	�	PROPN
gi-2729	57	31	ability	ability	NOUN
gi-2729	57	32	to	to	PART
gi-2729	57	33	keep	keep	VERB
gi-2729	57	34	the	the	DET
gi-2729	57	35	area	area	NOUN
gi-2729	57	36	(	(	PUNCT
gi-2729	57	37	equal	equal	ADJ
gi-2729	57	38	area	area	NOUN
gi-2729	57	39	or	or	CCONJ
gi-2729	57	40	near	near	ADP
gi-2729	57	41	o	o	NOUN
gi-2729	57	42	equal	equal	ADJ
gi-2729	57	43	area	area	NOUN
gi-2729	57	44	algorithm	algorithm	NOUN
gi-2729	57	45	)	)	PUNCT
gi-2729	57	46	,	,	PUNCT
gi-2729	57	47	�	�	PROPN
gi-2729	57	48	regulation	regulation	NOUN
gi-2729	57	49	of	of	ADP
gi-2729	57	50	the	the	DET
gi-2729	57	51	simplification	simplification	NOUN
gi-2729	57	52	factor	factor	NOUN
gi-2729	57	53	by	by	ADP
gi-2729	57	54	user	user	NOUN
gi-2729	57	55	,	,	PUNCT
gi-2729	57	56	�	�	PROPN
gi-2729	57	57	ability	ability	NOUN
gi-2729	57	58	to	to	PART
gi-2729	57	59	simplify	simplify	VERB
gi-2729	57	60	complex	complex	ADJ
gi-2729	57	61	and	and	CCONJ
gi-2729	57	62	non	non	ADJ
gi-2729	57	63	-	-	ADJ
gi-2729	57	64	convex	convex	ADJ
gi-2729	57	65	shapes	shape	NOUN
gi-2729	57	66	.	.	PUNCT
gi-2729	58	1	in	in	ADP
gi-2729	58	2	terms	term	NOUN
gi-2729	58	3	of	of	ADP
gi-2729	58	4	computational	computational	ADJ
gi-2729	58	5	geometry	geometry	NOUN
gi-2729	58	6	we	we	PRON
gi-2729	58	7	explain	explain	VERB
gi-2729	58	8	more	more	ADV
gi-2729	58	9	detailed	detailed	ADJ
gi-2729	58	10	the	the	DET
gi-2729	58	11	first	first	ADJ
gi-2729	58	12	and	and	CCONJ
gi-2729	58	13	second	second	ADJ
gi-2729	58	14	points	point	NOUN
gi-2729	58	15	.	.	PUNCT
gi-2729	59	1	scheme	scheme	NOUN
gi-2729	59	2	of	of	ADP
gi-2729	59	3	the	the	DET
gi-2729	59	4	simplification	simplification	NOUN
gi-2729	59	5	process	process	NOUN
gi-2729	59	6	an	an	DET
gi-2729	59	7	automated	automate	VERB
gi-2729	59	8	or	or	CCONJ
gi-2729	59	9	semi	semi	ADV
gi-2729	59	10	automated	automate	VERB
gi-2729	59	11	simplification	simplification	NOUN
gi-2729	59	12	of	of	ADP
gi-2729	59	13	buildings	building	NOUN
gi-2729	59	14	based	base	VERB
gi-2729	59	15	on	on	ADP
gi-2729	59	16	the	the	DET
gi-2729	59	17	least	least	ADJ
gi-2729	59	18	square	square	ADJ
gi-2729	59	19	method	method	NOUN
gi-2729	59	20	is	be	AUX
gi-2729	59	21	currently	currently	ADV
gi-2729	59	22	being	be	AUX
gi-2729	59	23	solved	solve	VERB
gi-2729	59	24	in	in	ADP
gi-2729	59	25	many	many	ADJ
gi-2729	59	26	ways	way	NOUN
gi-2729	59	27	.	.	PUNCT
gi-2729	60	1	from	from	ADP
gi-2729	60	2	the	the	DET
gi-2729	60	3	cartographic	cartographic	ADJ
gi-2729	60	4	perspective	perspective	NOUN
gi-2729	60	5	it	it	PRON
gi-2729	60	6	provides	provide	VERB
gi-2729	60	7	relatively	relatively	ADV
gi-2729	60	8	good	good	ADJ
gi-2729	60	9	results	result	NOUN
gi-2729	60	10	.	.	PUNCT
gi-2729	61	1	the	the	DET
gi-2729	61	2	simplification	simplification	NOUN
gi-2729	61	3	process	process	NOUN
gi-2729	61	4	can	can	AUX
gi-2729	61	5	be	be	AUX
gi-2729	61	6	shortly	shortly	ADV
gi-2729	61	7	described	describe	VERB
gi-2729	61	8	using	use	VERB
gi-2729	61	9	the	the	DET
gi-2729	61	10	following	follow	VERB
gi-2729	61	11	geinformatics	geinformatic	NOUN
gi-2729	61	12	fce	fce	VERB
gi-2729	61	13	ctu	ctu	NOUN
gi-2729	61	14	2008	2008	NUM
gi-2729	61	15	17	17	NUM
gi-2729	61	16	the	the	DET
gi-2729	61	17	importance	importance	NOUN
gi-2729	61	18	of	of	ADP
gi-2729	61	19	computational	computational	ADJ
gi-2729	61	20	geometry	geometry	NOUN
gi-2729	61	21	for	for	ADP
gi-2729	61	22	digital	digital	ADJ
gi-2729	61	23	cartography	cartography	NOUN
gi-2729	61	24	steps	step	NOUN
gi-2729	61	25	:	:	PUNCT
gi-2729	61	26	1	1	X
gi-2729	61	27	.	.	X
gi-2729	61	28	detection	detection	NOUN
gi-2729	61	29	of	of	ADP
gi-2729	61	30	the	the	DET
gi-2729	61	31	angle	angle	NOUN
gi-2729	61	32	of	of	ADP
gi-2729	61	33	rotation	rotation	PROPN
gi-2729	61	34	ϕ	ϕ	PROPN
gi-2729	61	35	of	of	ADP
gi-2729	61	36	the	the	DET
gi-2729	61	37	building	building	NOUN
gi-2729	61	38	:	:	PUNCT
gi-2729	61	39	�	�	PROPN
gi-2729	61	40	construction	construction	NOUN
gi-2729	61	41	of	of	ADP
gi-2729	61	42	the	the	DET
gi-2729	61	43	convex	convex	PROPN
gi-2729	61	44	hull	hull	NOUN
gi-2729	61	45	of	of	ADP
gi-2729	61	46	a	a	DET
gi-2729	61	47	set	set	NOUN
gi-2729	61	48	of	of	ADP
gi-2729	61	49	points	point	NOUN
gi-2729	61	50	,	,	PUNCT
gi-2729	61	51	�	�	PROPN
gi-2729	61	52	construction	construction	NOUN
gi-2729	61	53	of	of	ADP
gi-2729	61	54	the	the	DET
gi-2729	61	55	smallest	small	ADJ
gi-2729	61	56	area	area	NOUN
gi-2729	61	57	enclosing	enclose	VERB
gi-2729	61	58	rectangle	rectangle	NOUN
gi-2729	61	59	of	of	ADP
gi-2729	61	60	a	a	DET
gi-2729	61	61	set	set	NOUN
gi-2729	61	62	of	of	ADP
gi-2729	61	63	points	point	NOUN
gi-2729	61	64	.	.	PUNCT
gi-2729	62	1	2	2	X
gi-2729	62	2	.	.	X
gi-2729	62	3	set	set	VERB
gi-2729	62	4	rotation	rotation	NOUN
gi-2729	62	5	of	of	ADP
gi-2729	62	6	the	the	DET
gi-2729	62	7	building	building	NOUN
gi-2729	62	8	:	:	PUNCT
gi-2729	62	9	the	the	DET
gi-2729	62	10	angle	angle	NOUN
gi-2729	62	11	of	of	ADP
gi-2729	62	12	rotation	rotation	NOUN
gi-2729	62	13	−ϕ.	−ϕ.	ADV
gi-2729	62	14	3	3	NUM
gi-2729	62	15	.	.	X
gi-2729	63	1	detection	detection	NOUN
gi-2729	63	2	of	of	ADP
gi-2729	63	3	the	the	DET
gi-2729	63	4	vertices	vertex	NOUN
gi-2729	63	5	and	and	CCONJ
gi-2729	63	6	edges	edge	NOUN
gi-2729	63	7	of	of	ADP
gi-2729	63	8	the	the	DET
gi-2729	63	9	building	building	NOUN
gi-2729	63	10	based	base	VERB
gi-2729	63	11	on	on	ADP
gi-2729	63	12	the	the	DET
gi-2729	63	13	recursion	recursion	NOUN
gi-2729	63	14	:	:	PUNCT
gi-2729	63	15	�	�	PROPN
gi-2729	63	16	calculation	calculation	NOUN
gi-2729	63	17	of	of	ADP
gi-2729	63	18	the	the	DET
gi-2729	63	19	splitting	splitting	NOUN
gi-2729	63	20	criterion	criterion	NOUN
gi-2729	63	21	σ	σ	PROPN
gi-2729	63	22	,	,	PUNCT
gi-2729	63	23	�	�	PROPN
gi-2729	63	24	recursive	recursive	ADJ
gi-2729	63	25	decomposition	decomposition	NOUN
gi-2729	63	26	of	of	ADP
gi-2729	63	27	the	the	DET
gi-2729	63	28	edge	edge	NOUN
gi-2729	63	29	to	to	ADP
gi-2729	63	30	the	the	DET
gi-2729	63	31	set	set	NOUN
gi-2729	63	32	of	of	ADP
gi-2729	63	33	new	new	ADJ
gi-2729	63	34	edges	edge	NOUN
gi-2729	63	35	.	.	PUNCT
gi-2729	64	1	4	4	X
gi-2729	64	2	.	.	X
gi-2729	64	3	set	set	VERB
gi-2729	64	4	rotation	rotation	NOUN
gi-2729	64	5	of	of	ADP
gi-2729	64	6	the	the	DET
gi-2729	64	7	building	building	NOUN
gi-2729	64	8	:	:	PUNCT
gi-2729	64	9	angle	angle	NOUN
gi-2729	64	10	of	of	ADP
gi-2729	64	11	rotation	rotation	NOUN
gi-2729	64	12	ϕ.	ϕ.	PROPN
gi-2729	64	13	in	in	ADP
gi-2729	64	14	order	order	NOUN
gi-2729	64	15	to	to	PART
gi-2729	64	16	simplify	simplify	VERB
gi-2729	64	17	mathematical	mathematical	ADJ
gi-2729	64	18	calculations	calculation	NOUN
gi-2729	64	19	,	,	PUNCT
gi-2729	64	20	generalized	generalized	ADJ
gi-2729	64	21	building	building	NOUN
gi-2729	64	22	is	be	AUX
gi-2729	64	23	rotated	rotate	VERB
gi-2729	64	24	by	by	ADP
gi-2729	64	25	the	the	DET
gi-2729	64	26	angle	angle	NOUN
gi-2729	64	27	of	of	ADP
gi-2729	64	28	−ϕ.	−ϕ.	NOUN
gi-2729	64	29	the	the	DET
gi-2729	64	30	building	building	NOUN
gi-2729	64	31	is	be	AUX
gi-2729	64	32	rotated	rotate	VERB
gi-2729	64	33	so	so	SCONJ
gi-2729	64	34	that	that	SCONJ
gi-2729	64	35	its	its	PRON
gi-2729	64	36	edges	edge	NOUN
gi-2729	64	37	are	be	AUX
gi-2729	64	38	parallel	parallel	ADJ
gi-2729	64	39	to	to	ADP
gi-2729	64	40	the	the	DET
gi-2729	64	41	axes	axis	NOUN
gi-2729	64	42	of	of	ADP
gi-2729	64	43	x	x	PRON
gi-2729	64	44	,	,	PUNCT
gi-2729	64	45	y.	y.	NOUN
gi-2729	64	46	detection	detection	NOUN
gi-2729	64	47	of	of	ADP
gi-2729	64	48	the	the	DET
gi-2729	64	49	building	building	NOUN
gi-2729	64	50	rotation	rotation	NOUN
gi-2729	64	51	we	we	PRON
gi-2729	64	52	will	will	AUX
gi-2729	64	53	consider	consider	VERB
gi-2729	64	54	a	a	DET
gi-2729	64	55	non	non	ADJ
gi-2729	64	56	convex	convex	VERB
gi-2729	64	57	rectangular	rectangular	ADJ
gi-2729	64	58	polygon	polygon	NOUN
gi-2729	64	59	in	in	ADP
gi-2729	64	60	the	the	DET
gi-2729	64	61	plane	plane	NOUN
gi-2729	64	62	to	to	PART
gi-2729	64	63	be	be	AUX
gi-2729	64	64	a	a	DET
gi-2729	64	65	building	building	NOUN
gi-2729	64	66	.	.	PUNCT
gi-2729	65	1	the	the	DET
gi-2729	65	2	building	building	NOUN
gi-2729	65	3	usually	usually	ADV
gi-2729	65	4	does	do	AUX
gi-2729	65	5	not	not	PART
gi-2729	65	6	have	have	VERB
gi-2729	65	7	to	to	PART
gi-2729	65	8	be	be	AUX
gi-2729	65	9	oriented	orient	VERB
gi-2729	65	10	in	in	ADP
gi-2729	65	11	the	the	DET
gi-2729	65	12	basic	basic	ADJ
gi-2729	65	13	position	position	NOUN
gi-2729	65	14	,	,	PUNCT
gi-2729	65	15	when	when	SCONJ
gi-2729	65	16	all	all	DET
gi-2729	65	17	edges	edge	NOUN
gi-2729	65	18	are	be	AUX
gi-2729	65	19	parallel	parallel	ADJ
gi-2729	65	20	to	to	ADP
gi-2729	65	21	axis	axis	NOUN
gi-2729	65	22	x	x	X
gi-2729	65	23	,	,	PUNCT
gi-2729	65	24	y	y	PROPN
gi-2729	65	25	of	of	ADP
gi-2729	65	26	the	the	DET
gi-2729	65	27	coordinate	coordinate	NOUN
gi-2729	65	28	system	system	NOUN
gi-2729	65	29	.	.	PUNCT
gi-2729	66	1	in	in	ADP
gi-2729	66	2	general	general	ADJ
gi-2729	66	3	position	position	NOUN
gi-2729	66	4	the	the	DET
gi-2729	66	5	building	building	NOUN
gi-2729	66	6	is	be	AUX
gi-2729	66	7	rotated	rotate	VERB
gi-2729	66	8	,	,	PUNCT
gi-2729	66	9	the	the	DET
gi-2729	66	10	rotation	rotation	NOUN
gi-2729	66	11	angle	angle	NOUN
gi-2729	66	12	ϕ	ϕ	PROPN
gi-2729	66	13	must	must	AUX
gi-2729	66	14	be	be	AUX
gi-2729	66	15	detected	detect	VERB
gi-2729	66	16	as	as	ADP
gi-2729	66	17	a	a	DET
gi-2729	66	18	first	first	ADJ
gi-2729	66	19	step	step	NOUN
gi-2729	66	20	of	of	ADP
gi-2729	66	21	the	the	DET
gi-2729	66	22	simplification	simplification	NOUN
gi-2729	66	23	algorithm	algorithm	NOUN
gi-2729	66	24	.	.	PUNCT
gi-2729	67	1	an	an	DET
gi-2729	67	2	accuracy	accuracy	NOUN
gi-2729	67	3	of	of	ADP
gi-2729	67	4	determining	determine	VERB
gi-2729	67	5	the	the	DET
gi-2729	67	6	angle	angle	NOUN
gi-2729	67	7	of	of	ADP
gi-2729	67	8	rotation	rotation	PROPN
gi-2729	67	9	ϕ	ϕ	PROPN
gi-2729	67	10	significantly	significantly	ADV
gi-2729	67	11	affects	affect	VERB
gi-2729	67	12	an	an	DET
gi-2729	67	13	effectiveness	effectiveness	NOUN
gi-2729	67	14	of	of	ADP
gi-2729	67	15	the	the	DET
gi-2729	67	16	algorithm	algorithm	NOUN
gi-2729	67	17	.	.	PUNCT
gi-2729	68	1	the	the	DET
gi-2729	68	2	most	most	ADV
gi-2729	68	3	common	common	ADJ
gi-2729	68	4	method	method	NOUN
gi-2729	68	5	of	of	ADP
gi-2729	68	6	detecting	detect	VERB
gi-2729	68	7	the	the	DET
gi-2729	68	8	angle	angle	NOUN
gi-2729	68	9	of	of	ADP
gi-2729	68	10	rotation	rotation	PROPN
gi-2729	68	11	ϕ	ϕ	PROPN
gi-2729	68	12	formed	form	VERB
gi-2729	68	13	by	by	ADP
gi-2729	68	14	x	x	SYM
gi-2729	68	15	axis	axis	NOUN
gi-2729	68	16	and	and	CCONJ
gi-2729	68	17	the	the	DET
gi-2729	68	18	longer	long	ADJ
gi-2729	68	19	edge	edge	NOUN
gi-2729	68	20	of	of	ADP
gi-2729	68	21	the	the	DET
gi-2729	68	22	rectangle	rectangle	NOUN
gi-2729	68	23	,	,	PUNCT
gi-2729	68	24	is	be	AUX
gi-2729	68	25	based	base	VERB
gi-2729	68	26	on	on	ADP
gi-2729	68	27	construction	construction	NOUN
gi-2729	68	28	of	of	ADP
gi-2729	68	29	the	the	DET
gi-2729	68	30	minimum	minimum	ADJ
gi-2729	68	31	bounding	bounding	NOUN
gi-2729	68	32	box	box	NOUN
gi-2729	68	33	(	(	PUNCT
gi-2729	68	34	rectangle	rectangle	NOUN
gi-2729	68	35	enclosing	enclose	VERB
gi-2729	68	36	all	all	DET
gi-2729	68	37	points	point	NOUN
gi-2729	68	38	with	with	ADP
gi-2729	68	39	the	the	DET
gi-2729	68	40	minimum	minimum	ADJ
gi-2729	68	41	area	area	NOUN
gi-2729	68	42	)	)	PUNCT
gi-2729	68	43	,	,	PUNCT
gi-2729	68	44	and	and	CCONJ
gi-2729	68	45	follows	follow	VERB
gi-2729	68	46	with	with	ADP
gi-2729	68	47	the	the	DET
gi-2729	68	48	detection	detection	NOUN
gi-2729	68	49	of	of	ADP
gi-2729	68	50	the	the	DET
gi-2729	68	51	angle	angle	NOUN
gi-2729	68	52	formed	form	VERB
gi-2729	68	53	by	by	ADP
gi-2729	68	54	the	the	DET
gi-2729	68	55	x	x	NOUN
gi-2729	68	56	axis	axis	NOUN
gi-2729	68	57	and	and	CCONJ
gi-2729	68	58	the	the	DET
gi-2729	68	59	longer	long	ADJ
gi-2729	68	60	edge	edge	NOUN
gi-2729	68	61	of	of	ADP
gi-2729	68	62	the	the	DET
gi-2729	68	63	rectangle	rectangle	NOUN
gi-2729	68	64	,	,	PUNCT
gi-2729	68	65	see	see	VERB
gi-2729	68	66	fig	fig	NOUN
gi-2729	68	67	.	.	PUNCT
gi-2729	69	1	2	2	NUM
gi-2729	69	2	.	.	PUNCT
gi-2729	70	1	whereas	whereas	SCONJ
gi-2729	70	2	,	,	PUNCT
gi-2729	70	3	the	the	DET
gi-2729	70	4	calculation	calculation	NOUN
gi-2729	70	5	is	be	AUX
gi-2729	70	6	carried	carry	VERB
gi-2729	70	7	out	out	ADP
gi-2729	70	8	over	over	ADP
gi-2729	70	9	a	a	DET
gi-2729	70	10	large	large	ADJ
gi-2729	70	11	set	set	NOUN
gi-2729	70	12	of	of	ADP
gi-2729	70	13	points	point	NOUN
gi-2729	70	14	,	,	PUNCT
gi-2729	70	15	it	it	PRON
gi-2729	70	16	is	be	AUX
gi-2729	70	17	necessary	necessary	ADJ
gi-2729	70	18	to	to	PART
gi-2729	70	19	choose	choose	VERB
gi-2729	70	20	the	the	DET
gi-2729	70	21	procedure	procedure	NOUN
gi-2729	70	22	with	with	ADP
gi-2729	70	23	the	the	DET
gi-2729	70	24	lowest	low	ADJ
gi-2729	70	25	time	time	NOUN
gi-2729	70	26	complexity	complexity	NOUN
gi-2729	70	27	.	.	PUNCT
gi-2729	71	1	the	the	DET
gi-2729	71	2	procedure	procedure	NOUN
gi-2729	71	3	runs	run	VERB
gi-2729	71	4	over	over	ADP
gi-2729	71	5	non	non	ADJ
gi-2729	71	6	-	-	ADJ
gi-2729	71	7	convex	convex	ADJ
gi-2729	71	8	polygon	polygon	NOUN
gi-2729	71	9	,	,	PUNCT
gi-2729	71	10	this	this	DET
gi-2729	71	11	feature	feature	NOUN
gi-2729	71	12	makes	make	VERB
gi-2729	71	13	the	the	DET
gi-2729	71	14	process	process	NOUN
gi-2729	71	15	more	more	ADV
gi-2729	71	16	complex	complex	ADJ
gi-2729	71	17	.	.	PUNCT
gi-2729	72	1	commonly	commonly	ADV
gi-2729	72	2	available	available	ADJ
gi-2729	72	3	algorithms	algorithm	NOUN
gi-2729	72	4	achieve	achieve	VERB
gi-2729	72	5	quadratic	quadratic	ADJ
gi-2729	72	6	time	time	NOUN
gi-2729	72	7	complexity	complexity	NOUN
gi-2729	72	8	o(n2	o(n2	ADV
gi-2729	72	9	)	)	PUNCT
gi-2729	72	10	for	for	ADP
gi-2729	72	11	this	this	DET
gi-2729	72	12	operation	operation	NOUN
gi-2729	72	13	.	.	PUNCT
gi-2729	73	1	using	use	VERB
gi-2729	73	2	rotating	rotate	VERB
gi-2729	73	3	calipers	caliper	NOUN
gi-2729	73	4	method	method	NOUN
gi-2729	73	5	published	publish	VERB
gi-2729	73	6	in	in	ADP
gi-2729	73	7	[	[	X
gi-2729	73	8	2	2	X
gi-2729	73	9	]	]	PUNCT
gi-2729	73	10	we	we	PRON
gi-2729	73	11	can	can	AUX
gi-2729	73	12	perform	perform	VERB
gi-2729	73	13	this	this	DET
gi-2729	73	14	step	step	NOUN
gi-2729	73	15	in	in	ADP
gi-2729	73	16	linear	linear	ADJ
gi-2729	73	17	time	time	NOUN
gi-2729	73	18	.	.	PUNCT
gi-2729	74	1	this	this	DET
gi-2729	74	2	procedure	procedure	NOUN
gi-2729	74	3	is	be	AUX
gi-2729	74	4	usable	usable	ADJ
gi-2729	74	5	only	only	ADV
gi-2729	74	6	for	for	ADP
gi-2729	74	7	convex	convex	ADJ
gi-2729	74	8	polygons	polygon	NOUN
gi-2729	74	9	,	,	PUNCT
gi-2729	74	10	first	first	ADJ
gi-2729	74	11	step	step	NOUN
gi-2729	74	12	represents	represent	VERB
gi-2729	74	13	transformation	transformation	NOUN
gi-2729	74	14	of	of	ADP
gi-2729	74	15	the	the	DET
gi-2729	74	16	non	non	ADJ
gi-2729	74	17	-	-	ADJ
gi-2729	74	18	convex	convex	ADJ
gi-2729	74	19	polygon	polygon	NOUN
gi-2729	74	20	to	to	PART
gi-2729	74	21	convex	convex	VERB
gi-2729	74	22	hull	hull	NOUN
gi-2729	74	23	.	.	PUNCT
gi-2729	75	1	which	which	PRON
gi-2729	75	2	method	method	VERB
gi-2729	75	3	for	for	ADP
gi-2729	75	4	the	the	DET
gi-2729	75	5	convex	convex	PROPN
gi-2729	75	6	hull	hull	NOUN
gi-2729	75	7	construction	construction	NOUN
gi-2729	75	8	is	be	AUX
gi-2729	75	9	the	the	DET
gi-2729	75	10	best	good	ADJ
gi-2729	75	11	to	to	PART
gi-2729	75	12	choose	choose	VERB
gi-2729	75	13	:	:	PUNCT
gi-2729	75	14	jarvis	jarvis	PROPN
gi-2729	75	15	scan	scan	PROPN
gi-2729	75	16	,	,	PUNCT
gi-2729	75	17	graham	graham	PROPN
gi-2729	75	18	scan	scan	PROPN
gi-2729	75	19	or	or	CCONJ
gi-2729	75	20	quickhull	quickhull	VERB
gi-2729	75	21	?	?	PUNCT
gi-2729	76	1	given	give	VERB
gi-2729	76	2	the	the	DET
gi-2729	76	3	time	time	NOUN
gi-2729	76	4	complexity	complexity	NOUN
gi-2729	76	5	requirements	requirement	NOUN
gi-2729	76	6	as	as	SCONJ
gi-2729	76	7	the	the	DET
gi-2729	76	8	best	good	ADJ
gi-2729	76	9	variant	variant	NOUN
gi-2729	76	10	appears	appear	VERB
gi-2729	76	11	the	the	DET
gi-2729	76	12	graham	graham	PROPN
gi-2729	76	13	scan	scan	PROPN
gi-2729	76	14	.	.	PUNCT
gi-2729	77	1	an	an	DET
gi-2729	77	2	interesting	interesting	ADJ
gi-2729	77	3	fact	fact	NOUN
gi-2729	77	4	may	may	AUX
gi-2729	77	5	be	be	AUX
gi-2729	77	6	a	a	DET
gi-2729	77	7	comparison	comparison	NOUN
gi-2729	77	8	of	of	ADP
gi-2729	77	9	the	the	DET
gi-2729	77	10	detected	detect	VERB
gi-2729	77	11	angle	angle	NOUN
gi-2729	77	12	ϕ	ϕ	PROPN
gi-2729	77	13	to	to	ADP
gi-2729	77	14	street	street	NOUN
gi-2729	77	15	line	line	NOUN
gi-2729	77	16	angle	angle	NOUN
gi-2729	77	17	constructed	construct	VERB
gi-2729	77	18	using	use	VERB
gi-2729	77	19	the	the	DET
gi-2729	77	20	topological	topological	ADJ
gi-2729	77	21	skeleton	skeleton	NOUN
gi-2729	77	22	(	(	PUNCT
gi-2729	77	23	eg	eg	NOUN
gi-2729	77	24	straight	straight	PROPN
gi-2729	77	25	skeleton	skeleton	PROPN
gi-2729	77	26	)	)	PUNCT
gi-2729	77	27	.	.	PUNCT
gi-2729	78	1	this	this	DET
gi-2729	78	2	technique	technique	NOUN
gi-2729	78	3	is	be	AUX
gi-2729	78	4	currently	currently	ADV
gi-2729	78	5	at	at	ADP
gi-2729	78	6	the	the	DET
gi-2729	78	7	research	research	NOUN
gi-2729	78	8	stage	stage	NOUN
gi-2729	78	9	.	.	PUNCT
gi-2729	79	1	graham	graham	PROPN
gi-2729	79	2	scan	scan	PROPN
gi-2729	79	3	graham	graham	PROPN
gi-2729	79	4	scan	scan	PROPN
gi-2729	79	5	enables	enable	VERB
gi-2729	79	6	constructioning	constructione	VERB
gi-2729	79	7	the	the	DET
gi-2729	79	8	convex	convex	PROPN
gi-2729	79	9	hull	hull	NOUN
gi-2729	79	10	in	in	ADP
gi-2729	79	11	sub	sub	NOUN
gi-2729	79	12	quadratic	quadratic	ADJ
gi-2729	79	13	time	time	NOUN
gi-2729	79	14	with	with	ADP
gi-2729	79	15	o(n	o(n	PROPN
gi-2729	79	16	·	·	SYM
gi-2729	79	17	lgn	lgn	PROPN
gi-2729	79	18	)	)	PUNCT
gi-2729	79	19	complexity	complexity	NOUN
gi-2729	79	20	.	.	PUNCT
gi-2729	80	1	it	it	PRON
gi-2729	80	2	assumes	assume	VERB
gi-2729	80	3	,	,	PUNCT
gi-2729	80	4	there	there	PRON
gi-2729	80	5	are	be	VERB
gi-2729	80	6	no	no	DET
gi-2729	80	7	three	three	NUM
gi-2729	80	8	collinear	collinear	ADJ
gi-2729	80	9	points	point	NOUN
gi-2729	80	10	in	in	ADP
gi-2729	80	11	the	the	DET
gi-2729	80	12	set	set	NOUN
gi-2729	80	13	.	.	PUNCT
gi-2729	81	1	algorithm	algorithm	PROPN
gi-2729	81	2	is	be	AUX
gi-2729	81	3	based	base	VERB
gi-2729	81	4	on	on	ADP
gi-2729	81	5	the	the	DET
gi-2729	81	6	idea	idea	NOUN
gi-2729	81	7	of	of	ADP
gi-2729	81	8	right	right	ADJ
gi-2729	81	9	turn	turn	NOUN
gi-2729	81	10	.	.	PUNCT
gi-2729	82	1	for	for	ADP
gi-2729	82	2	each	each	DET
gi-2729	82	3	triplet	triplet	NOUN
gi-2729	82	4	pi	pi	NOUN
gi-2729	82	5	,	,	PUNCT
gi-2729	82	6	pi+1	pi+1	X
gi-2729	82	7	,	,	PUNCT
gi-2729	82	8	pi+2	pi+2	NUM
gi-2729	82	9	,	,	PUNCT
gi-2729	82	10	i	i	PRON
gi-2729	82	11	∈	∈	PROPN
gi-2729	82	12	1	1	NUM
gi-2729	82	13	,	,	PUNCT
gi-2729	82	14	..	..	PUNCT
gi-2729	82	15	,	,	PUNCT
gi-2729	82	16	n	n	CCONJ
gi-2729	82	17	−	−	PROPN
gi-2729	82	18	2	2	NUM
gi-2729	82	19	,	,	PUNCT
gi-2729	82	20	we	we	PRON
gi-2729	82	21	analyze	analyze	VERB
gi-2729	82	22	relative	relative	ADJ
gi-2729	82	23	geinformatics	geinformatic	NOUN
gi-2729	82	24	fce	fce	VERB
gi-2729	82	25	ctu	ctu	NOUN
gi-2729	82	26	2008	2008	NUM
gi-2729	82	27	18	18	NUM
gi-2729	82	28	the	the	DET
gi-2729	82	29	importance	importance	NOUN
gi-2729	82	30	of	of	ADP
gi-2729	82	31	computational	computational	ADJ
gi-2729	82	32	geometry	geometry	NOUN
gi-2729	82	33	for	for	ADP
gi-2729	82	34	digital	digital	ADJ
gi-2729	82	35	cartography	cartography	NOUN
gi-2729	82	36	figure	figure	NOUN
gi-2729	82	37	2	2	NUM
gi-2729	82	38	:	:	PUNCT
gi-2729	82	39	a	a	DET
gi-2729	82	40	detection	detection	NOUN
gi-2729	82	41	of	of	ADP
gi-2729	82	42	the	the	DET
gi-2729	82	43	building	building	NOUN
gi-2729	82	44	rotation	rotation	NOUN
gi-2729	82	45	using	use	VERB
gi-2729	82	46	convex	convex	PROPN
gi-2729	82	47	hull	hull	NOUN
gi-2729	82	48	and	and	CCONJ
gi-2729	82	49	the	the	DET
gi-2729	82	50	smallest	small	ADJ
gi-2729	82	51	area	area	NOUN
gi-2729	82	52	enclosing	enclose	VERB
gi-2729	82	53	rectangle	rectangle	NOUN
gi-2729	82	54	.	.	PUNCT
gi-2729	83	1	position	position	NOUN
gi-2729	83	2	of	of	ADP
gi-2729	83	3	pi+2	pi+2	PROPN
gi-2729	83	4	and	and	CCONJ
gi-2729	83	5	the	the	DET
gi-2729	83	6	segment	segment	NOUN
gi-2729	83	7	consisting	consist	VERB
gi-2729	83	8	of	of	ADP
gi-2729	83	9	pi	pi	NOUN
gi-2729	83	10	,	,	PUNCT
gi-2729	83	11	pi+1	pi+1	X
gi-2729	83	12	(	(	PUNCT
gi-2729	83	13	left	left	ADJ
gi-2729	83	14	or	or	CCONJ
gi-2729	83	15	right	right	ADJ
gi-2729	83	16	turn	turn	NOUN
gi-2729	83	17	)	)	PUNCT
gi-2729	83	18	.	.	PUNCT
gi-2729	84	1	let	let	VERB
gi-2729	84	2	us	we	PRON
gi-2729	84	3	denote	denote	VERB
gi-2729	84	4	−→u	−→u	ADP
gi-2729	84	5	=	=	SYM
gi-2729	84	6	pi	pi	NOUN
gi-2729	84	7	−	−	PROPN
gi-2729	84	8	pi+1	pi+1	INTJ
gi-2729	84	9	and	and	CCONJ
gi-2729	84	10	−→v	−→v	ADV
gi-2729	84	11	=	=	NOUN
gi-2729	85	1	pi+1	pi+1	NUM
gi-2729	85	2	−	−	PROPN
gi-2729	85	3	pi+2	pi+2	NOUN
gi-2729	85	4	.	.	PUNCT
gi-2729	86	1	right	right	ADJ
gi-2729	86	2	turn	turn	NOUN
gi-2729	86	3	criterion	criterion	NOUN
gi-2729	86	4	we	we	PRON
gi-2729	86	5	can	can	AUX
gi-2729	86	6	write	write	VERB
gi-2729	86	7	as∣∣∣∣	as∣∣∣∣	PROPN
gi-2729	87	1	ux	ux	PROPN
gi-2729	87	2	uy	uy	PROPN
gi-2729	87	3	vx	vx	PROPN
gi-2729	87	4	vy	vy	PROPN
gi-2729	87	5	∣∣∣∣	∣∣∣∣	PROPN
gi-2729	87	6	v	v	NUM
gi-2729	87	7	5	5	NUM
gi-2729	87	8	0	0	NUM
gi-2729	87	9	.	.	PUNCT
gi-2729	88	1	the	the	DET
gi-2729	88	2	first	first	ADJ
gi-2729	88	3	step	step	NOUN
gi-2729	88	4	consists	consist	VERB
gi-2729	88	5	of	of	ADP
gi-2729	88	6	finding	find	VERB
gi-2729	88	7	a	a	DET
gi-2729	88	8	point	point	NOUN
gi-2729	88	9	q	q	NOUN
gi-2729	88	10	with	with	ADP
gi-2729	88	11	extreme	extreme	ADJ
gi-2729	88	12	x	x	SYM
gi-2729	88	13	coordinate	coordinate	NOUN
gi-2729	88	14	(	(	PUNCT
gi-2729	88	15	xmax	xmax	PROPN
gi-2729	88	16	)	)	PUNCT
gi-2729	88	17	.	.	PUNCT
gi-2729	89	1	it	it	PRON
gi-2729	89	2	follows	follow	VERB
gi-2729	89	3	with	with	ADP
gi-2729	89	4	sorting	sorting	NOUN
gi-2729	89	5	of	of	ADP
gi-2729	89	6	points	point	NOUN
gi-2729	89	7	according	accord	VERB
gi-2729	89	8	to	to	ADP
gi-2729	89	9	the	the	DET
gi-2729	89	10	angle	angle	NOUN
gi-2729	89	11	ω	ω	PROPN
gi-2729	89	12	measured	measure	VERB
gi-2729	89	13	between	between	ADP
gi-2729	89	14	‖	‖	PROPN
gi-2729	89	15	x	x	PROPN
gi-2729	89	16	and	and	CCONJ
gi-2729	89	17	q	q	NOUN
gi-2729	89	18	,	,	PUNCT
gi-2729	89	19	p	p	X
gi-2729	89	20	.	.	PUNCT
gi-2729	90	1	when	when	SCONJ
gi-2729	90	2	calculating	calculate	VERB
gi-2729	90	3	the	the	DET
gi-2729	90	4	angle	angle	NOUN
gi-2729	90	5	,	,	PUNCT
gi-2729	90	6	it	it	PRON
gi-2729	90	7	is	be	AUX
gi-2729	90	8	necessary	necessary	ADJ
gi-2729	90	9	to	to	PART
gi-2729	90	10	determine	determine	VERB
gi-2729	90	11	ω	ω	PROPN
gi-2729	90	12	at	at	ADP
gi-2729	90	13	interval	interval	NOUN
gi-2729	90	14	(	(	PUNCT
gi-2729	90	15	0	0	NUM
gi-2729	90	16	,	,	PUNCT
gi-2729	90	17	2π	2π	NOUN
gi-2729	90	18	)	)	PUNCT
gi-2729	90	19	.	.	PUNCT
gi-2729	91	1	notify	notify	VERB
gi-2729	91	2	,	,	PUNCT
gi-2729	91	3	that	that	SCONJ
gi-2729	91	4	computing	compute	VERB
gi-2729	91	5	angle	angle	NOUN
gi-2729	91	6	ω	ω	PROPN
gi-2729	91	7	from	from	ADP
gi-2729	91	8	ω	ω	PROPN
gi-2729	91	9	=	=	SYM
gi-2729	91	10	arccos	arccos	X
gi-2729	91	11	(	(	PUNCT
gi-2729	91	12	(	(	PUNCT
gi-2729	91	13	x2−x1)(x3−x2)+(y2−y1)(y3−y2)√	x2−x1)(x3−x2)+(y2−y1)(y3−y2)√	PROPN
gi-2729	91	14	(	(	PUNCT
gi-2729	91	15	x2−x1)2+(y2−y1)2	x2−x1)2+(y2−y1)2	NOUN
gi-2729	91	16	√	√	PROPN
gi-2729	91	17	(	(	PUNCT
gi-2729	91	18	x3−x2)2+(y3−y2)2	x3−x2)2+(y3−y2)2	PUNCT
gi-2729	91	19	)	)	PUNCT
gi-2729	91	20	brings	bring	VERB
gi-2729	91	21	numerical	numerical	ADJ
gi-2729	91	22	troubles	trouble	NOUN
gi-2729	91	23	.	.	PUNCT
gi-2729	92	1	sorting	sort	VERB
gi-2729	92	2	algorithm	algorithm	NOUN
gi-2729	92	3	.	.	PUNCT
gi-2729	93	1	the	the	DET
gi-2729	93	2	relationship	relationship	NOUN
gi-2729	93	3	computational	computational	ADJ
gi-2729	93	4	geometry	geometry	NOUN
gi-2729	93	5	and	and	CCONJ
gi-2729	93	6	informatics	informatic	NOUN
gi-2729	93	7	can	can	AUX
gi-2729	93	8	be	be	AUX
gi-2729	93	9	illustrated	illustrate	VERB
gi-2729	93	10	by	by	ADP
gi-2729	93	11	a	a	DET
gi-2729	93	12	sorting	sort	VERB
gi-2729	93	13	algorithm	algorithm	NOUN
gi-2729	93	14	.	.	PUNCT
gi-2729	94	1	what	what	PRON
gi-2729	94	2	algorithm	algorithm	NOUN
gi-2729	94	3	seems	seem	VERB
gi-2729	94	4	to	to	PART
gi-2729	94	5	be	be	AUX
gi-2729	94	6	appropriate	appropriate	ADJ
gi-2729	94	7	for	for	ADP
gi-2729	94	8	sorting	sort	VERB
gi-2729	94	9	the	the	DET
gi-2729	94	10	set	set	NOUN
gi-2729	94	11	of	of	ADP
gi-2729	94	12	points	point	NOUN
gi-2729	94	13	because	because	SCONJ
gi-2729	94	14	of	of	ADP
gi-2729	94	15	the	the	DET
gi-2729	94	16	time	time	NOUN
gi-2729	94	17	complexity	complexity	NOUN
gi-2729	94	18	?	?	PUNCT
gi-2729	95	1	given	give	VERB
gi-2729	95	2	the	the	DET
gi-2729	95	3	fact	fact	NOUN
gi-2729	95	4	,	,	PUNCT
gi-2729	95	5	that	that	SCONJ
gi-2729	95	6	the	the	DET
gi-2729	95	7	set	set	NOUN
gi-2729	95	8	of	of	ADP
gi-2729	95	9	points	point	NOUN
gi-2729	95	10	forming	form	VERB
gi-2729	95	11	a	a	DET
gi-2729	95	12	building	building	NOUN
gi-2729	95	13	is	be	AUX
gi-2729	95	14	not	not	PART
gi-2729	95	15	too	too	ADV
gi-2729	95	16	large	large	ADJ
gi-2729	95	17	,	,	PUNCT
gi-2729	95	18	the	the	DET
gi-2729	95	19	choice	choice	NOUN
gi-2729	95	20	of	of	ADP
gi-2729	95	21	sorting	sort	VERB
gi-2729	95	22	algorithm	algorithm	NOUN
gi-2729	95	23	does	do	AUX
gi-2729	95	24	not	not	PART
gi-2729	95	25	play	play	VERB
gi-2729	95	26	an	an	DET
gi-2729	95	27	important	important	ADJ
gi-2729	95	28	role	role	NOUN
gi-2729	95	29	.	.	PUNCT
gi-2729	96	1	given	give	VERB
gi-2729	96	2	the	the	DET
gi-2729	96	3	fact	fact	NOUN
gi-2729	96	4	that	that	SCONJ
gi-2729	96	5	sorting	sort	VERB
gi-2729	96	6	procedure	procedure	NOUN
gi-2729	96	7	could	could	AUX
gi-2729	96	8	be	be	AUX
gi-2729	96	9	repeated	repeat	VERB
gi-2729	96	10	for	for	ADP
gi-2729	96	11	the	the	DET
gi-2729	96	12	data	datum	NOUN
gi-2729	96	13	made	make	VERB
gi-2729	96	14	of	of	ADP
gi-2729	96	15	thousands	thousand	NOUN
gi-2729	96	16	of	of	ADP
gi-2729	96	17	buildings	building	NOUN
gi-2729	96	18	,	,	PUNCT
gi-2729	96	19	it	it	PRON
gi-2729	96	20	is	be	AUX
gi-2729	96	21	efficient	efficient	ADJ
gi-2729	96	22	,	,	PUNCT
gi-2729	96	23	in	in	ADP
gi-2729	96	24	terms	term	NOUN
gi-2729	96	25	of	of	ADP
gi-2729	96	26	overall	overall	ADJ
gi-2729	96	27	approach	approach	NOUN
gi-2729	96	28	to	to	ADP
gi-2729	96	29	the	the	DET
gi-2729	96	30	problem	problem	NOUN
gi-2729	96	31	,	,	PUNCT
gi-2729	96	32	to	to	PART
gi-2729	96	33	use	use	VERB
gi-2729	96	34	quicksort	quicksort	NOUN
gi-2729	96	35	.	.	PUNCT
gi-2729	97	1	the	the	DET
gi-2729	97	2	quicksort	quicksort	NOUN
gi-2729	97	3	implementation	implementation	NOUN
gi-2729	97	4	is	be	AUX
gi-2729	97	5	available	available	ADJ
gi-2729	97	6	in	in	ADP
gi-2729	97	7	many	many	ADJ
gi-2729	97	8	programming	programming	NOUN
gi-2729	97	9	languages	language	NOUN
gi-2729	97	10	as	as	ADP
gi-2729	97	11	a	a	DET
gi-2729	97	12	standard	standard	ADJ
gi-2729	97	13	sorting	sort	VERB
gi-2729	97	14	procedure	procedure	NOUN
gi-2729	97	15	.	.	PUNCT
gi-2729	98	1	data	datum	NOUN
gi-2729	98	2	structure	structure	NOUN
gi-2729	98	3	and	and	CCONJ
gi-2729	98	4	implementation	implementation	NOUN
gi-2729	98	5	.	.	PUNCT
gi-2729	99	1	a	a	DET
gi-2729	99	2	concept	concept	NOUN
gi-2729	99	3	of	of	ADP
gi-2729	99	4	the	the	DET
gi-2729	99	5	data	data	NOUN
gi-2729	99	6	representation	representation	NOUN
gi-2729	99	7	also	also	ADV
gi-2729	99	8	plays	play	VERB
gi-2729	99	9	an	an	DET
gi-2729	99	10	important	important	ADJ
gi-2729	99	11	role	role	NOUN
gi-2729	99	12	.	.	PUNCT
gi-2729	100	1	one	one	NUM
gi-2729	100	2	possible	possible	ADJ
gi-2729	100	3	solution	solution	NOUN
gi-2729	100	4	using	use	VERB
gi-2729	100	5	the	the	DET
gi-2729	100	6	stack	stack	NOUN
gi-2729	100	7	can	can	AUX
gi-2729	100	8	be	be	AUX
gi-2729	100	9	found	find	VERB
gi-2729	100	10	in	in	ADP
gi-2729	100	11	[	[	X
gi-2729	100	12	3	3	NUM
gi-2729	100	13	]	]	PUNCT
gi-2729	100	14	.	.	PUNCT
gi-2729	101	1	every	every	DET
gi-2729	101	2	point	point	NOUN
gi-2729	101	3	is	be	AUX
gi-2729	101	4	represented	represent	VERB
gi-2729	101	5	by	by	ADP
gi-2729	101	6	its	its	PRON
gi-2729	101	7	unique	unique	ADJ
gi-2729	101	8	identifying	identifying	NOUN
gi-2729	101	9	number	number	NOUN
gi-2729	101	10	,	,	PUNCT
gi-2729	101	11	coordinates	coordinate	NOUN
gi-2729	101	12	x	x	NOUN
gi-2729	101	13	,	,	PUNCT
gi-2729	101	14	y	y	PROPN
gi-2729	101	15	,	,	PUNCT
gi-2729	101	16	and	and	CCONJ
gi-2729	101	17	flag	flag	NOUN
gi-2729	101	18	illustrates	illustrate	VERB
gi-2729	101	19	the	the	DET
gi-2729	101	20	deletion	deletion	NOUN
gi-2729	101	21	of	of	ADP
gi-2729	101	22	point	point	NOUN
gi-2729	101	23	from	from	ADP
gi-2729	101	24	the	the	DET
gi-2729	101	25	hull	hull	NOUN
gi-2729	101	26	.	.	PUNCT
gi-2729	102	1	a	a	DET
gi-2729	102	2	correct	correct	ADJ
gi-2729	102	3	definition	definition	NOUN
gi-2729	102	4	of	of	ADP
gi-2729	102	5	copy	copy	NOUN
gi-2729	102	6	constructors	constructor	NOUN
gi-2729	102	7	and	and	CCONJ
gi-2729	102	8	casting	cast	VERB
gi-2729	102	9	operators	operator	NOUN
gi-2729	102	10	is	be	AUX
gi-2729	102	11	important	important	ADJ
gi-2729	102	12	.	.	PUNCT
gi-2729	103	1	look	look	VERB
gi-2729	103	2	to	to	ADP
gi-2729	103	3	the	the	DET
gi-2729	103	4	following	follow	VERB
gi-2729	103	5	source	source	NOUN
gi-2729	103	6	code	code	NOUN
gi-2729	103	7	sample	sample	NOUN
gi-2729	103	8	:	:	PUNCT
gi-2729	103	9	geinformatics	geinformatics	PROPN
gi-2729	103	10	fce	fce	VERB
gi-2729	103	11	ctu	ctu	NOUN
gi-2729	103	12	2008	2008	NUM
gi-2729	103	13	19	19	NUM
gi-2729	103	14	the	the	DET
gi-2729	103	15	importance	importance	NOUN
gi-2729	103	16	of	of	ADP
gi-2729	103	17	computational	computational	ADJ
gi-2729	103	18	geometry	geometry	NOUN
gi-2729	103	19	for	for	ADP
gi-2729	103	20	digital	digital	ADJ
gi-2729	103	21	cartography	cartography	NOUN
gi-2729	103	22	class	class	NOUN
gi-2729	103	23	point	point	NOUN
gi-2729	103	24	{	{	PUNCT
gi-2729	103	25	private	private	ADJ
gi-2729	103	26	:	:	PUNCT
gi-2729	103	27	int	int	NOUN
gi-2729	103	28	num	num	ADJ
gi-2729	103	29	;	;	PUNCT
gi-2729	103	30	bool	bool	PROPN
gi-2729	103	31	del	del	PROPN
gi-2729	103	32	;	;	PUNCT
gi-2729	103	33	double	double	ADJ
gi-2729	103	34	x	x	NOUN
gi-2729	103	35	,	,	PUNCT
gi-2729	103	36	y	y	PROPN
gi-2729	103	37	;	;	PUNCT
gi-2729	103	38	...	...	PUNCT
gi-2729	104	1	public	public	ADJ
gi-2729	104	2	:	:	PUNCT
gi-2729	104	3	point::point	point::point	NOUN
gi-2729	104	4	(	(	PUNCT
gi-2729	104	5	const	const	NOUN
gi-2729	104	6	point	point	NOUN
gi-2729	104	7	&	&	CCONJ
gi-2729	104	8	point	point	NOUN
gi-2729	104	9	)	)	PUNCT
gi-2729	104	10	{	{	PUNCT
gi-2729	104	11	num	num	PROPN
gi-2729	104	12	=	=	SYM
gi-2729	104	13	point.num	point.num	X
gi-2729	104	14	;	;	PUNCT
gi-2729	104	15	del	del	X
gi-2729	104	16	=	=	NOUN
gi-2729	104	17	point.del	point.del	X
gi-2729	104	18	;	;	PUNCT
gi-2729	104	19	x	x	SYM
gi-2729	104	20	=	=	NOUN
gi-2729	104	21	point.x	point.x	X
gi-2729	104	22	;	;	PUNCT
gi-2729	104	23	y	y	PROPN
gi-2729	104	24	=	=	PROPN
gi-2729	104	25	point.y	point.y	PROPN
gi-2729	104	26	;	;	PUNCT
gi-2729	104	27	}	}	PUNCT
gi-2729	104	28	bool	bool	NOUN
gi-2729	104	29	point::operator	point::operator	NOUN
gi-2729	104	30	<	<	X
gi-2729	104	31	(	(	PUNCT
gi-2729	104	32	const	const	NOUN
gi-2729	104	33	point	point	NOUN
gi-2729	104	34	&	&	CCONJ
gi-2729	104	35	point	point	NOUN
gi-2729	104	36	)	)	PUNCT
gi-2729	104	37	{	{	PUNCT
gi-2729	104	38	return	return	NOUN
gi-2729	104	39	(	(	PUNCT
gi-2729	104	40	y	y	NOUN
gi-2729	104	41	<	<	X
gi-2729	104	42	point.y)||(x	point.y)||(x	PROPN
gi-2729	104	43	>	>	X
gi-2729	104	44	point.x)&&(y==point.y	point.x)&&(y==point.y	PROPN
gi-2729	104	45	)	)	PUNCT
gi-2729	104	46	;	;	PUNCT
gi-2729	104	47	}	}	PUNCT
gi-2729	104	48	;	;	PUNCT
gi-2729	104	49	bool	bool	NOUN
gi-2729	104	50	point::operator	point::operator	NOUN
gi-2729	104	51	=	=	PROPN
gi-2729	104	52	=	=	X
gi-2729	104	53	(	(	PUNCT
gi-2729	104	54	const	const	NOUN
gi-2729	104	55	point	point	NOUN
gi-2729	104	56	&	&	CCONJ
gi-2729	104	57	point	point	NOUN
gi-2729	104	58	)	)	PUNCT
gi-2729	104	59	{	{	PUNCT
gi-2729	104	60	return	return	NOUN
gi-2729	104	61	(	(	PUNCT
gi-2729	104	62	x==point.x)&&(y==point.y	x==point.x)&&(y==point.y	PROPN
gi-2729	104	63	)	)	PUNCT
gi-2729	104	64	;	;	PUNCT
gi-2729	104	65	}	}	PUNCT
gi-2729	104	66	;	;	PUNCT
gi-2729	104	67	point	point	NOUN
gi-2729	104	68	point	point	NOUN
gi-2729	104	69	:	:	PUNCT
gi-2729	104	70	:	:	PUNCT
gi-2729	104	71	operator	operator	NOUN
gi-2729	104	72	=	=	SYM
gi-2729	104	73	(	(	PUNCT
gi-2729	104	74	const	const	NOUN
gi-2729	104	75	point	point	NOUN
gi-2729	104	76	&	&	CCONJ
gi-2729	104	77	point	point	NOUN
gi-2729	104	78	)	)	PUNCT
gi-2729	104	79	{	{	PUNCT
gi-2729	104	80	num	num	PROPN
gi-2729	104	81	=	=	SYM
gi-2729	104	82	point.num	point.num	X
gi-2729	104	83	;	;	PUNCT
gi-2729	104	84	del	del	X
gi-2729	104	85	=	=	NOUN
gi-2729	104	86	point.del	point.del	X
gi-2729	104	87	;	;	PUNCT
gi-2729	104	88	x	x	SYM
gi-2729	104	89	=	=	NOUN
gi-2729	104	90	point.x	point.x	X
gi-2729	104	91	;	;	PUNCT
gi-2729	104	92	y	y	PROPN
gi-2729	104	93	=	=	PROPN
gi-2729	104	94	point.y	point.y	PROPN
gi-2729	104	95	;	;	PUNCT
gi-2729	104	96	return	return	NOUN
gi-2729	104	97	*	*	PUNCT
gi-2729	104	98	this	this	PRON
gi-2729	104	99	;	;	PUNCT
gi-2729	104	100	}	}	PUNCT
gi-2729	104	101	...	...	PUNCT
gi-2729	104	102	}	}	PUNCT
gi-2729	104	103	collinerity	collinerity	NOUN
gi-2729	104	104	problem	problem	NOUN
gi-2729	104	105	.	.	PUNCT
gi-2729	105	1	the	the	DET
gi-2729	105	2	collinearity	collinearity	NOUN
gi-2729	105	3	problem	problem	NOUN
gi-2729	105	4	negatively	negatively	ADV
gi-2729	105	5	affects	affect	VERB
gi-2729	105	6	the	the	DET
gi-2729	105	7	process	process	NOUN
gi-2729	105	8	of	of	ADP
gi-2729	105	9	convex	convex	PROPN
gi-2729	105	10	hull	hull	NOUN
gi-2729	105	11	construction	construction	NOUN
gi-2729	105	12	.	.	PUNCT
gi-2729	106	1	collinear	collinear	ADJ
gi-2729	106	2	points	point	NOUN
gi-2729	106	3	have	have	VERB
gi-2729	106	4	the	the	DET
gi-2729	106	5	same	same	ADJ
gi-2729	106	6	angle	angle	NOUN
gi-2729	106	7	,	,	PUNCT
gi-2729	106	8	how	how	SCONJ
gi-2729	106	9	to	to	PART
gi-2729	106	10	sort	sort	VERB
gi-2729	106	11	those	those	DET
gi-2729	106	12	points	point	NOUN
gi-2729	106	13	?	?	PUNCT
gi-2729	107	1	let	let	VERB
gi-2729	107	2	us	we	PRON
gi-2729	107	3	denote	denote	VERB
gi-2729	107	4	two	two	NUM
gi-2729	107	5	colinear	colinear	ADJ
gi-2729	107	6	points	point	NOUN
gi-2729	107	7	pi	pi	NOUN
gi-2729	107	8	,	,	PUNCT
gi-2729	107	9	pj	pj	PROPN
gi-2729	107	10	and	and	CCONJ
gi-2729	107	11	si	si	PROPN
gi-2729	107	12	,	,	PUNCT
gi-2729	107	13	sj	sj	PROPN
gi-2729	107	14	euclidean	euclidean	ADJ
gi-2729	107	15	distances	distance	NOUN
gi-2729	107	16	from	from	ADP
gi-2729	107	17	those	those	DET
gi-2729	107	18	points	point	NOUN
gi-2729	107	19	to	to	ADP
gi-2729	107	20	the	the	DET
gi-2729	107	21	q.	q.	NOUN
gi-2729	107	22	we	we	PRON
gi-2729	107	23	define	define	VERB
gi-2729	107	24	a	a	DET
gi-2729	107	25	new	new	ADJ
gi-2729	107	26	sorting	sort	VERB
gi-2729	107	27	rule	rule	NOUN
gi-2729	107	28	:	:	PUNCT
gi-2729	107	29	if	if	SCONJ
gi-2729	107	30	(	(	PUNCT
gi-2729	107	31	ωi	ωi	X
gi-2729	107	32	=	=	SYM
gi-2729	107	33	ωj	ωj	CCONJ
gi-2729	107	34	)	)	PUNCT
gi-2729	107	35	than	than	ADP
gi-2729	107	36	closer	close	ADJ
gi-2729	107	37	point	point	NOUN
gi-2729	107	38	min(si	min(si	PROPN
gi-2729	107	39	,	,	PUNCT
gi-2729	107	40	sj	sj	INTJ
gi-2729	107	41	)	)	PUNCT
gi-2729	107	42	is	be	AUX
gi-2729	107	43	considered	consider	VERB
gi-2729	107	44	as	as	ADP
gi-2729	107	45	earlier	early	ADV
gi-2729	107	46	.	.	PUNCT
gi-2729	108	1	coincident	coincident	ADJ
gi-2729	108	2	points	point	NOUN
gi-2729	108	3	represent	represent	VERB
gi-2729	108	4	a	a	DET
gi-2729	108	5	special	special	ADJ
gi-2729	108	6	case	case	NOUN
gi-2729	108	7	of	of	ADP
gi-2729	108	8	the	the	DET
gi-2729	108	9	collinearity	collinearity	NOUN
gi-2729	108	10	problem	problem	NOUN
gi-2729	108	11	.	.	PUNCT
gi-2729	109	1	for	for	ADP
gi-2729	109	2	gis	gis	PROPN
gi-2729	109	3	data	datum	NOUN
gi-2729	109	4	this	this	DET
gi-2729	109	5	problem	problem	NOUN
gi-2729	109	6	is	be	AUX
gi-2729	109	7	not	not	PART
gi-2729	109	8	so	so	ADV
gi-2729	109	9	important	important	ADJ
gi-2729	109	10	,	,	PUNCT
gi-2729	109	11	they	they	PRON
gi-2729	109	12	are	be	AUX
gi-2729	109	13	topologically	topologically	ADV
gi-2729	109	14	valid	valid	ADJ
gi-2729	109	15	(	(	PUNCT
gi-2729	109	16	it	it	PRON
gi-2729	109	17	means	mean	VERB
gi-2729	109	18	also	also	ADV
gi-2729	109	19	without	without	ADP
gi-2729	109	20	duplicated	duplicate	VERB
gi-2729	109	21	points	point	NOUN
gi-2729	109	22	)	)	PUNCT
gi-2729	109	23	.	.	PUNCT
gi-2729	110	1	smallest	small	ADJ
gi-2729	110	2	area	area	NOUN
gi-2729	110	3	enclosing	enclose	VERB
gi-2729	110	4	rectangle	rectangle	NOUN
gi-2729	110	5	problem	problem	NOUN
gi-2729	110	6	of	of	ADP
gi-2729	110	7	the	the	DET
gi-2729	110	8	smallest	small	ADJ
gi-2729	110	9	area	area	NOUN
gi-2729	110	10	enclosing	enclose	VERB
gi-2729	110	11	rectangle	rectangle	NOUN
gi-2729	110	12	construction	construction	NOUN
gi-2729	110	13	was	be	AUX
gi-2729	110	14	solved	solve	VERB
gi-2729	110	15	in	in	ADP
gi-2729	110	16	many	many	ADJ
gi-2729	110	17	ways	way	NOUN
gi-2729	110	18	.	.	PUNCT
gi-2729	111	1	presented	present	VERB
gi-2729	111	2	solution	solution	NOUN
gi-2729	111	3	described	describe	VERB
gi-2729	111	4	in	in	ADP
gi-2729	111	5	[	[	X
gi-2729	111	6	5	5	NUM
gi-2729	111	7	]	]	PUNCT
gi-2729	111	8	solves	solve	VERB
gi-2729	111	9	the	the	DET
gi-2729	111	10	problem	problem	NOUN
gi-2729	111	11	in	in	ADP
gi-2729	111	12	linear	linear	ADJ
gi-2729	111	13	time	time	NOUN
gi-2729	111	14	using	use	VERB
gi-2729	111	15	two	two	NUM
gi-2729	111	16	calipers	caliper	NOUN
gi-2729	111	17	orthogonal	orthogonal	ADJ
gi-2729	111	18	to	to	ADP
gi-2729	111	19	each	each	DET
gi-2729	111	20	other	other	ADJ
gi-2729	111	21	.	.	PUNCT
gi-2729	112	1	the	the	DET
gi-2729	112	2	following	follow	VERB
gi-2729	112	3	procedure	procedure	NOUN
gi-2729	112	4	is	be	AUX
gi-2729	112	5	called	call	VERB
gi-2729	112	6	rotating	rotate	VERB
gi-2729	112	7	calipers	caliper	NOUN
gi-2729	112	8	.	.	PUNCT
gi-2729	113	1	the	the	DET
gi-2729	113	2	idea	idea	NOUN
gi-2729	113	3	of	of	ADP
gi-2729	113	4	construction	construction	NOUN
gi-2729	113	5	is	be	AUX
gi-2729	113	6	based	base	VERB
gi-2729	113	7	on	on	ADP
gi-2729	113	8	the	the	DET
gi-2729	113	9	repeated	repeat	VERB
gi-2729	113	10	rotation	rotation	NOUN
gi-2729	113	11	of	of	ADP
gi-2729	113	12	rectangle	rectangle	NOUN
gi-2729	113	13	,	,	PUNCT
gi-2729	113	14	the	the	DET
gi-2729	113	15	rectangle	rectangle	NOUN
gi-2729	113	16	is	be	AUX
gi-2729	113	17	gradually	gradually	ADV
gi-2729	113	18	improved	improve	VERB
gi-2729	113	19	and	and	CCONJ
gi-2729	113	20	becomes	become	VERB
gi-2729	113	21	an	an	DET
gi-2729	113	22	approximation	approximation	NOUN
gi-2729	113	23	of	of	ADP
gi-2729	113	24	smallest	small	ADJ
gi-2729	113	25	enclosing	enclosing	NOUN
gi-2729	113	26	area	area	NOUN
gi-2729	113	27	in	in	ADP
gi-2729	113	28	the	the	DET
gi-2729	113	29	next	next	ADJ
gi-2729	113	30	step	step	NOUN
gi-2729	113	31	.	.	PUNCT
gi-2729	114	1	one	one	NUM
gi-2729	114	2	edge	edge	NOUN
gi-2729	114	3	of	of	ADP
gi-2729	114	4	the	the	DET
gi-2729	114	5	smallest	small	ADJ
gi-2729	114	6	enclosing	enclosing	NOUN
gi-2729	114	7	box	box	NOUN
gi-2729	114	8	must	must	AUX
gi-2729	114	9	be	be	AUX
gi-2729	114	10	collinear	collinear	VERB
gi-2729	114	11	with	with	ADP
gi-2729	114	12	one	one	NUM
gi-2729	114	13	segment	segment	NOUN
gi-2729	114	14	of	of	ADP
gi-2729	114	15	the	the	DET
gi-2729	114	16	convex	convex	PROPN
gi-2729	114	17	hull	hull	NOUN
gi-2729	114	18	.	.	PUNCT
gi-2729	115	1	let	let	VERB
gi-2729	115	2	us	we	PRON
gi-2729	115	3	denote	denote	VERB
gi-2729	115	4	ϕj	ϕj	INTJ
gi-2729	115	5	,	,	PUNCT
gi-2729	115	6	j	j	PROPN
gi-2729	115	7	∈	∈	PROPN
gi-2729	115	8	〈	〈	PROPN
gi-2729	115	9	1	1	NUM
gi-2729	115	10	,	,	PUNCT
gi-2729	115	11	4	4	NUM
gi-2729	115	12	〉	〉	NUM
gi-2729	115	13	,	,	PUNCT
gi-2729	115	14	four	four	NUM
gi-2729	115	15	angles	angle	NOUN
gi-2729	115	16	formed	form	VERB
gi-2729	115	17	by	by	ADP
gi-2729	115	18	the	the	DET
gi-2729	115	19	four	four	NUM
gi-2729	115	20	smallest	small	ADJ
gi-2729	115	21	area	area	NOUN
gi-2729	115	22	enclosing	enclose	VERB
gi-2729	115	23	box	box	NOUN
gi-2729	115	24	edges	edge	NOUN
gi-2729	115	25	and	and	CCONJ
gi-2729	115	26	four	four	NUM
gi-2729	115	27	edges	edge	NOUN
gi-2729	115	28	of	of	ADP
gi-2729	115	29	the	the	DET
gi-2729	115	30	convex	convex	NOUN
gi-2729	115	31	hull	hull	NOUN
gi-2729	115	32	in	in	ADP
gi-2729	115	33	points	point	NOUN
gi-2729	115	34	of	of	ADP
gi-2729	115	35	contact	contact	NOUN
gi-2729	115	36	vj	vj	INTJ
gi-2729	115	37	.	.	PUNCT
gi-2729	116	1	let	let	VERB
gi-2729	116	2	v	v	NOUN
gi-2729	116	3	′j	′j	NOUN
gi-2729	116	4	represents	represent	VERB
gi-2729	116	5	a	a	DET
gi-2729	116	6	point	point	NOUN
gi-2729	116	7	,	,	PUNCT
gi-2729	116	8	that	that	PRON
gi-2729	116	9	is	be	AUX
gi-2729	116	10	a	a	DET
gi-2729	116	11	successor	successor	NOUN
gi-2729	116	12	of	of	ADP
gi-2729	116	13	the	the	DET
gi-2729	116	14	point	point	NOUN
gi-2729	116	15	vj	vj	INTJ
gi-2729	116	16	,	,	PUNCT
gi-2729	116	17	and	and	CCONJ
gi-2729	116	18	mj	mj	PROPN
gi-2729	116	19	represents	represent	VERB
gi-2729	116	20	a	a	DET
gi-2729	116	21	vertex	vertex	NOUN
gi-2729	116	22	of	of	ADP
gi-2729	116	23	the	the	DET
gi-2729	116	24	smallest	small	ADJ
gi-2729	116	25	area	area	NOUN
gi-2729	116	26	enclosing	enclose	VERB
gi-2729	116	27	box	box	PROPN
gi-2729	116	28	.	.	PUNCT
gi-2729	117	1	vertices	vertex	NOUN
gi-2729	117	2	of	of	ADP
gi-2729	117	3	the	the	DET
gi-2729	117	4	smallest	small	ADJ
gi-2729	117	5	area	area	NOUN
gi-2729	117	6	(	(	PUNCT
gi-2729	117	7	and	and	CCONJ
gi-2729	117	8	thus	thus	ADV
gi-2729	117	9	edges	edge	NOUN
gi-2729	117	10	)	)	PUNCT
gi-2729	117	11	are	be	AUX
gi-2729	117	12	clockwise	clockwise	NOUN
gi-2729	117	13	oriented	orient	VERB
gi-2729	117	14	.	.	PUNCT
gi-2729	118	1	geinformatics	geinformatic	NOUN
gi-2729	118	2	fce	fce	VERB
gi-2729	118	3	ctu	ctu	NOUN
gi-2729	118	4	2008	2008	NUM
gi-2729	118	5	20	20	NUM
gi-2729	118	6	the	the	DET
gi-2729	118	7	importance	importance	NOUN
gi-2729	118	8	of	of	ADP
gi-2729	118	9	computational	computational	ADJ
gi-2729	118	10	geometry	geometry	NOUN
gi-2729	118	11	for	for	ADP
gi-2729	118	12	digital	digital	ADJ
gi-2729	118	13	cartography	cartography	NOUN
gi-2729	118	14	we	we	PRON
gi-2729	118	15	find	find	VERB
gi-2729	118	16	the	the	DET
gi-2729	118	17	minimum	minimum	ADJ
gi-2729	118	18	angle	angle	NOUN
gi-2729	118	19	ϕmin	ϕmin	NOUN
gi-2729	118	20	=	=	NOUN
gi-2729	118	21	min(ϕj	min(ϕj	NOUN
gi-2729	118	22	)	)	PUNCT
gi-2729	118	23	and	and	CCONJ
gi-2729	118	24	rotate	rotate	VERB
gi-2729	118	25	the	the	DET
gi-2729	118	26	rectangle	rectangle	NOUN
gi-2729	118	27	by	by	ADP
gi-2729	118	28	an	an	DET
gi-2729	118	29	angle	angle	NOUN
gi-2729	118	30	ϕmin	ϕmin	NOUN
gi-2729	118	31	.	.	PUNCT
gi-2729	119	1	another	another	DET
gi-2729	119	2	edge	edge	NOUN
gi-2729	119	3	of	of	ADP
gi-2729	119	4	the	the	DET
gi-2729	119	5	rectangle	rectangle	NOUN
gi-2729	119	6	becomes	become	VERB
gi-2729	119	7	collinear	collinear	ADJ
gi-2729	119	8	with	with	ADP
gi-2729	119	9	some	some	DET
gi-2729	119	10	segment	segment	NOUN
gi-2729	119	11	of	of	ADP
gi-2729	119	12	the	the	DET
gi-2729	119	13	convex	convex	PROPN
gi-2729	119	14	hull	hull	NOUN
gi-2729	119	15	.	.	PUNCT
gi-2729	120	1	three	three	NUM
gi-2729	120	2	points	point	NOUN
gi-2729	120	3	of	of	ADP
gi-2729	120	4	contacts	contact	NOUN
gi-2729	120	5	will	will	AUX
gi-2729	120	6	not	not	PART
gi-2729	120	7	change	change	VERB
gi-2729	120	8	.	.	PUNCT
gi-2729	121	1	however	however	ADV
gi-2729	121	2	one	one	NUM
gi-2729	121	3	point	point	NOUN
gi-2729	121	4	vj	vj	INTJ
gi-2729	121	5	,	,	PUNCT
gi-2729	121	6	represented	represent	VERB
gi-2729	121	7	by	by	ADP
gi-2729	121	8	the	the	DET
gi-2729	121	9	start	start	NOUN
gi-2729	121	10	point	point	NOUN
gi-2729	121	11	of	of	ADP
gi-2729	121	12	the	the	DET
gi-2729	121	13	collinear	collinear	ADJ
gi-2729	121	14	segments	segment	NOUN
gi-2729	121	15	,	,	PUNCT
gi-2729	121	16	changes	change	NOUN
gi-2729	121	17	to	to	ADP
gi-2729	121	18	its	its	PRON
gi-2729	121	19	successor	successor	NOUN
gi-2729	121	20	v	v	NOUN
gi-2729	121	21	′j	′j	NOUN
gi-2729	121	22	.	.	PUNCT
gi-2729	122	1	we	we	PRON
gi-2729	122	2	calculate	calculate	VERB
gi-2729	122	3	an	an	DET
gi-2729	122	4	area	area	NOUN
gi-2729	122	5	s	s	X
gi-2729	122	6	of	of	ADP
gi-2729	122	7	the	the	DET
gi-2729	122	8	rectangle	rectangle	NOUN
gi-2729	122	9	,	,	PUNCT
gi-2729	122	10	compare	compare	VERB
gi-2729	122	11	it	it	PRON
gi-2729	122	12	with	with	ADP
gi-2729	122	13	a	a	DET
gi-2729	122	14	minimum	minimum	ADJ
gi-2729	122	15	area	area	NOUN
gi-2729	122	16	smin	smin	PROPN
gi-2729	122	17	initialized	initialize	VERB
gi-2729	122	18	during	during	ADP
gi-2729	122	19	the	the	DET
gi-2729	122	20	first	first	ADJ
gi-2729	122	21	step	step	NOUN
gi-2729	122	22	to	to	ADP
gi-2729	122	23	∞.	∞.	PROPN
gi-2729	122	24	if	if	SCONJ
gi-2729	122	25	s	s	VERB
gi-2729	122	26	<	<	X
gi-2729	122	27	smin	smin	X
gi-2729	122	28	,	,	PUNCT
gi-2729	122	29	we	we	PRON
gi-2729	122	30	store	store	VERB
gi-2729	122	31	smin	smin	NOUN
gi-2729	122	32	=	=	PROPN
gi-2729	122	33	s.	s.	PROPN
gi-2729	122	34	repeat	repeat	VERB
gi-2729	122	35	those	those	DET
gi-2729	122	36	steps	step	NOUN
gi-2729	122	37	until	until	SCONJ
gi-2729	122	38	∑	∑	PROPN
gi-2729	122	39	ϕmin	ϕmin	NOUN
gi-2729	122	40	<	<	X
gi-2729	122	41	π	π	PROPN
gi-2729	122	42	2	2	NUM
gi-2729	122	43	leads	lead	VERB
gi-2729	122	44	to	to	PART
gi-2729	122	45	result	result	VERB
gi-2729	122	46	∑	∑	PROPN
gi-2729	122	47	ϕmin	ϕmin	NOUN
gi-2729	122	48	=	=	PROPN
gi-2729	122	49	ϕ.	ϕ.	PROPN
gi-2729	122	50	due	due	ADP
gi-2729	122	51	to	to	ADP
gi-2729	122	52	the	the	DET
gi-2729	122	53	fact	fact	NOUN
gi-2729	122	54	,	,	PUNCT
gi-2729	122	55	that	that	SCONJ
gi-2729	122	56	buildings	building	NOUN
gi-2729	122	57	are	be	AUX
gi-2729	122	58	represented	represent	VERB
gi-2729	122	59	by	by	ADP
gi-2729	122	60	rectangular	rectangular	ADJ
gi-2729	122	61	polygons	polygon	NOUN
gi-2729	122	62	,	,	PUNCT
gi-2729	122	63	more	more	ADJ
gi-2729	122	64	than	than	ADP
gi-2729	122	65	one	one	NUM
gi-2729	122	66	edge	edge	NOUN
gi-2729	122	67	of	of	ADP
gi-2729	122	68	rectangle	rectangle	NOUN
gi-2729	122	69	with	with	ADP
gi-2729	122	70	more	more	ADJ
gi-2729	122	71	segments	segment	NOUN
gi-2729	122	72	of	of	ADP
gi-2729	122	73	the	the	DET
gi-2729	122	74	convex	convex	NOUN
gi-2729	122	75	hull	hull	NOUN
gi-2729	122	76	.	.	PUNCT
gi-2729	123	1	because	because	SCONJ
gi-2729	123	2	of	of	ADP
gi-2729	123	3	errors	error	NOUN
gi-2729	123	4	cumulation	cumulation	VERB
gi-2729	123	5	the	the	DET
gi-2729	123	6	numerical	numerical	ADJ
gi-2729	123	7	inaccuracy	inaccuracy	NOUN
gi-2729	123	8	is	be	AUX
gi-2729	123	9	the	the	DET
gi-2729	123	10	problem	problem	NOUN
gi-2729	123	11	of	of	ADP
gi-2729	123	12	presented	present	VERB
gi-2729	123	13	algorithm	algorithm	NOUN
gi-2729	123	14	.	.	PUNCT
gi-2729	124	1	figure	figure	VERB
gi-2729	124	2	3	3	NUM
gi-2729	124	3	:	:	PUNCT
gi-2729	124	4	problem	problem	NOUN
gi-2729	124	5	of	of	ADP
gi-2729	124	6	smallest	small	ADJ
gi-2729	124	7	area	area	NOUN
gi-2729	124	8	enclosing	enclose	VERB
gi-2729	124	9	rectangle	rectangle	NOUN
gi-2729	124	10	construction	construction	NOUN
gi-2729	124	11	lead	lead	NOUN
gi-2729	124	12	to	to	ADP
gi-2729	124	13	inappropriate	inappropriate	ADJ
gi-2729	124	14	simplification	simplification	NOUN
gi-2729	124	15	.	.	PUNCT
gi-2729	125	1	for	for	ADP
gi-2729	125	2	our	our	PRON
gi-2729	125	3	purposes	purpose	NOUN
gi-2729	125	4	it	it	PRON
gi-2729	125	5	is	be	AUX
gi-2729	125	6	sufficient	sufficient	ADJ
gi-2729	125	7	to	to	PART
gi-2729	125	8	determine	determine	VERB
gi-2729	125	9	the	the	DET
gi-2729	125	10	angle	angle	NOUN
gi-2729	125	11	ϕ	ϕ	NOUN
gi-2729	125	12	with	with	ADP
gi-2729	125	13	the	the	DET
gi-2729	125	14	accuracy	accuracy	NOUN
gi-2729	125	15	of	of	ADP
gi-2729	125	16	one	one	NUM
gi-2729	125	17	degree	degree	NOUN
gi-2729	125	18	,	,	PUNCT
gi-2729	125	19	therefore	therefore	ADV
gi-2729	125	20	we	we	PRON
gi-2729	125	21	do	do	AUX
gi-2729	125	22	not	not	PART
gi-2729	125	23	have	have	VERB
gi-2729	125	24	to	to	PART
gi-2729	125	25	deal	deal	VERB
gi-2729	125	26	with	with	ADP
gi-2729	125	27	this	this	DET
gi-2729	125	28	problem	problem	NOUN
gi-2729	125	29	in	in	ADP
gi-2729	125	30	more	more	ADJ
gi-2729	125	31	detail	detail	NOUN
gi-2729	125	32	.	.	PUNCT
gi-2729	126	1	for	for	ADP
gi-2729	126	2	some	some	DET
gi-2729	126	3	specific	specific	ADJ
gi-2729	126	4	shapes	shape	NOUN
gi-2729	126	5	the	the	DET
gi-2729	126	6	smallest	small	ADJ
gi-2729	126	7	area	area	NOUN
gi-2729	126	8	enclosing	enclose	VERB
gi-2729	126	9	rectangle	rectangle	NOUN
gi-2729	126	10	do	do	AUX
gi-2729	126	11	not	not	PART
gi-2729	126	12	have	have	VERB
gi-2729	126	13	to	to	PART
gi-2729	126	14	be	be	AUX
gi-2729	126	15	the	the	DET
gi-2729	126	16	best	good	ADJ
gi-2729	126	17	way	way	NOUN
gi-2729	126	18	how	how	SCONJ
gi-2729	126	19	to	to	PART
gi-2729	126	20	detect	detect	VERB
gi-2729	126	21	the	the	DET
gi-2729	126	22	rotation	rotation	NOUN
gi-2729	126	23	of	of	ADP
gi-2729	126	24	the	the	DET
gi-2729	126	25	building	building	NOUN
gi-2729	126	26	.	.	PUNCT
gi-2729	127	1	this	this	DET
gi-2729	127	2	situation	situation	NOUN
gi-2729	127	3	is	be	AUX
gi-2729	127	4	typical	typical	ADJ
gi-2729	127	5	for	for	ADP
gi-2729	127	6	z	z	NOUN
gi-2729	127	7	or	or	CCONJ
gi-2729	127	8	l	l	NOUN
gi-2729	127	9	segment	segment	NOUN
gi-2729	127	10	,	,	PUNCT
gi-2729	127	11	when	when	SCONJ
gi-2729	127	12	the	the	DET
gi-2729	127	13	deviation	deviation	NOUN
gi-2729	127	14	between	between	ADP
gi-2729	127	15	calculated	calculated	ADJ
gi-2729	127	16	angle	angle	NOUN
gi-2729	127	17	ϕ	ϕ	NOUN
gi-2729	127	18	and	and	CCONJ
gi-2729	127	19	true	true	ADJ
gi-2729	127	20	value	value	NOUN
gi-2729	127	21	of	of	ADP
gi-2729	127	22	the	the	DET
gi-2729	127	23	angle	angle	NOUN
gi-2729	127	24	may	may	AUX
gi-2729	127	25	be	be	AUX
gi-2729	127	26	of	of	ADP
gi-2729	127	27	up	up	ADP
gi-2729	127	28	to	to	ADP
gi-2729	127	29	several	several	ADJ
gi-2729	127	30	tens	ten	NOUN
gi-2729	127	31	of	of	ADP
gi-2729	127	32	degrees	degree	NOUN
gi-2729	127	33	,	,	PUNCT
gi-2729	127	34	see	see	VERB
gi-2729	127	35	fig	fig	NOUN
gi-2729	127	36	.	.	PUNCT
gi-2729	128	1	3	3	X
gi-2729	128	2	.	.	X
gi-2729	129	1	it	it	PRON
gi-2729	129	2	is	be	AUX
gi-2729	129	3	important	important	ADJ
gi-2729	129	4	to	to	PART
gi-2729	129	5	note	note	VERB
gi-2729	129	6	,	,	PUNCT
gi-2729	129	7	that	that	SCONJ
gi-2729	129	8	the	the	DET
gi-2729	129	9	steps	step	NOUN
gi-2729	129	10	above	above	ADV
gi-2729	129	11	represent	represent	VERB
gi-2729	129	12	only	only	ADV
gi-2729	129	13	auxiliary	auxiliary	ADJ
gi-2729	129	14	geometric	geometric	ADJ
gi-2729	129	15	construction	construction	NOUN
gi-2729	129	16	with	with	ADP
gi-2729	129	17	a	a	DET
gi-2729	129	18	certain	certain	ADJ
gi-2729	129	19	percentage	percentage	NOUN
gi-2729	129	20	of	of	ADP
gi-2729	129	21	errors	error	NOUN
gi-2729	129	22	.	.	PUNCT
gi-2729	130	1	the	the	DET
gi-2729	130	2	detection	detection	NOUN
gi-2729	130	3	of	of	ADP
gi-2729	130	4	self	self	NOUN
gi-2729	130	5	intersections	intersection	NOUN
gi-2729	130	6	during	during	ADP
gi-2729	130	7	the	the	DET
gi-2729	130	8	process	process	NOUN
gi-2729	130	9	of	of	ADP
gi-2729	130	10	the	the	DET
gi-2729	130	11	cartographic	cartographic	ADJ
gi-2729	130	12	generalization	generalization	NOUN
gi-2729	130	13	we	we	PRON
gi-2729	130	14	can	can	AUX
gi-2729	130	15	be	be	AUX
gi-2729	130	16	encountered	encounter	VERB
gi-2729	130	17	with	with	ADP
gi-2729	130	18	the	the	DET
gi-2729	130	19	problem	problem	NOUN
gi-2729	130	20	of	of	ADP
gi-2729	130	21	self	self	NOUN
gi-2729	130	22	intersections	intersection	NOUN
gi-2729	130	23	.	.	PUNCT
gi-2729	131	1	they	they	PRON
gi-2729	131	2	represent	represent	VERB
gi-2729	131	3	such	such	ADJ
gi-2729	131	4	situations	situation	NOUN
gi-2729	131	5	,	,	PUNCT
gi-2729	131	6	in	in	ADP
gi-2729	131	7	which	which	PRON
gi-2729	131	8	some	some	DET
gi-2729	131	9	undesirable	undesirable	ADJ
gi-2729	131	10	forms	form	NOUN
gi-2729	131	11	as	as	ADP
gi-2729	131	12	a	a	DET
gi-2729	131	13	results	result	NOUN
gi-2729	131	14	of	of	ADP
gi-2729	131	15	the	the	DET
gi-2729	131	16	generalization	generalization	NOUN
gi-2729	131	17	process	process	NOUN
gi-2729	131	18	have	have	AUX
gi-2729	131	19	been	be	AUX
gi-2729	131	20	created	create	VERB
gi-2729	131	21	.	.	PUNCT
gi-2729	132	1	due	due	ADP
gi-2729	132	2	to	to	ADP
gi-2729	132	3	the	the	DET
gi-2729	132	4	topological	topological	ADJ
gi-2729	132	5	incorrectness	incorrectness	NOUN
gi-2729	132	6	of	of	ADP
gi-2729	132	7	such	such	ADJ
gi-2729	132	8	data	datum	NOUN
gi-2729	132	9	,	,	PUNCT
gi-2729	132	10	this	this	DET
gi-2729	132	11	error	error	NOUN
gi-2729	132	12	is	be	AUX
gi-2729	132	13	very	very	ADV
gi-2729	132	14	dangerous	dangerous	ADJ
gi-2729	132	15	.	.	PUNCT
gi-2729	133	1	closed	closed	ADJ
gi-2729	133	2	“	"	PUNCT
gi-2729	133	3	pseudoregion	pseudoregion	NOUN
gi-2729	133	4	”	"	PUNCT
gi-2729	133	5	is	be	AUX
gi-2729	133	6	the	the	DET
gi-2729	133	7	result	result	NOUN
gi-2729	133	8	of	of	ADP
gi-2729	133	9	crossing	crossing	NOUN
gi-2729	133	10	of	of	ADP
gi-2729	133	11	two	two	NUM
gi-2729	133	12	or	or	CCONJ
gi-2729	133	13	more	more	ADJ
gi-2729	133	14	line	line	NOUN
gi-2729	133	15	segments	segment	NOUN
gi-2729	133	16	.	.	PUNCT
gi-2729	134	1	in	in	ADP
gi-2729	134	2	the	the	DET
gi-2729	134	3	locus	locus	NOUN
gi-2729	134	4	of	of	ADP
gi-2729	134	5	the	the	DET
gi-2729	134	6	intersection	intersection	NOUN
gi-2729	134	7	there	there	PRON
gi-2729	134	8	is	be	VERB
gi-2729	134	9	no	no	DET
gi-2729	134	10	vertex	vertex	NOUN
gi-2729	134	11	inserted	insert	VERB
gi-2729	134	12	.	.	PUNCT
gi-2729	135	1	using	use	VERB
gi-2729	135	2	gis	gis	PROPN
gi-2729	135	3	software	software	NOUN
gi-2729	135	4	this	this	DET
gi-2729	135	5	pseudoregion	pseudoregion	NOUN
gi-2729	135	6	will	will	AUX
gi-2729	135	7	be	be	AUX
gi-2729	135	8	considered	consider	VERB
gi-2729	135	9	as	as	ADP
gi-2729	135	10	topologically	topologically	ADV
gi-2729	135	11	incorrect	incorrect	ADJ
gi-2729	135	12	,	,	PUNCT
gi-2729	135	13	see	see	VERB
gi-2729	135	14	fig	fig	NOUN
gi-2729	135	15	.	.	PUNCT
gi-2729	136	1	4	4	X
gi-2729	136	2	.	.	X
gi-2729	136	3	one	one	NUM
gi-2729	136	4	of	of	ADP
gi-2729	136	5	the	the	DET
gi-2729	136	6	possible	possible	ADJ
gi-2729	136	7	solution	solution	NOUN
gi-2729	136	8	may	may	AUX
gi-2729	136	9	be	be	AUX
gi-2729	136	10	a	a	DET
gi-2729	136	11	test	test	NOUN
gi-2729	136	12	,	,	PUNCT
gi-2729	136	13	which	which	PRON
gi-2729	136	14	verifies	verify	VERB
gi-2729	136	15	an	an	DET
gi-2729	136	16	existence	existence	NOUN
gi-2729	136	17	of	of	ADP
gi-2729	136	18	self	self	NOUN
gi-2729	136	19	intersections	intersection	NOUN
gi-2729	136	20	.	.	PUNCT
gi-2729	137	1	before	before	ADP
gi-2729	137	2	an	an	DET
gi-2729	137	3	edge	edge	NOUN
gi-2729	137	4	removing	remove	VERB
gi-2729	137	5	or	or	CCONJ
gi-2729	137	6	edge	edge	NOUN
gi-2729	137	7	splitting	splitting	NOUN
gi-2729	137	8	procedure	procedure	NOUN
gi-2729	137	9	it	it	PRON
gi-2729	137	10	is	be	AUX
gi-2729	137	11	verified	verify	VERB
gi-2729	137	12	,	,	PUNCT
gi-2729	137	13	whether	whether	SCONJ
gi-2729	137	14	this	this	DET
gi-2729	137	15	edge	edge	NOUN
gi-2729	137	16	does	do	AUX
gi-2729	137	17	not	not	PART
gi-2729	137	18	intersect	intersect	VERB
gi-2729	137	19	any	any	DET
gi-2729	137	20	other	other	ADJ
gi-2729	137	21	edge	edge	NOUN
gi-2729	137	22	of	of	ADP
gi-2729	137	23	the	the	DET
gi-2729	137	24	building	building	NOUN
gi-2729	137	25	.	.	PUNCT
gi-2729	138	1	if	if	SCONJ
gi-2729	138	2	so	so	ADV
gi-2729	138	3	,	,	PUNCT
gi-2729	138	4	a	a	DET
gi-2729	138	5	procedure	procedure	NOUN
gi-2729	138	6	for	for	ADP
gi-2729	138	7	the	the	DET
gi-2729	138	8	edge	edge	NOUN
gi-2729	138	9	simplification	simplification	NOUN
gi-2729	138	10	will	will	AUX
gi-2729	138	11	be	be	AUX
gi-2729	138	12	geinformatics	geinformatic	NOUN
gi-2729	138	13	fce	fce	ADP
gi-2729	138	14	ctu	ctu	NOUN
gi-2729	138	15	2008	2008	NUM
gi-2729	138	16	21	21	NUM
gi-2729	138	17	the	the	DET
gi-2729	138	18	importance	importance	NOUN
gi-2729	138	19	of	of	ADP
gi-2729	138	20	computational	computational	ADJ
gi-2729	138	21	geometry	geometry	NOUN
gi-2729	138	22	for	for	ADP
gi-2729	138	23	digital	digital	ADJ
gi-2729	138	24	cartography	cartography	NOUN
gi-2729	138	25	canceled	cancel	VERB
gi-2729	138	26	.	.	PUNCT
gi-2729	139	1	unfortunately	unfortunately	ADV
gi-2729	139	2	,	,	PUNCT
gi-2729	139	3	this	this	DET
gi-2729	139	4	step	step	NOUN
gi-2729	139	5	will	will	AUX
gi-2729	139	6	contribute	contribute	VERB
gi-2729	139	7	to	to	ADP
gi-2729	139	8	a	a	DET
gi-2729	139	9	significant	significant	ADJ
gi-2729	139	10	slowdown	slowdown	NOUN
gi-2729	139	11	of	of	ADP
gi-2729	139	12	the	the	DET
gi-2729	139	13	algorithm	algorithm	NOUN
gi-2729	139	14	.	.	PUNCT
gi-2729	140	1	how	how	SCONJ
gi-2729	140	2	to	to	PART
gi-2729	140	3	perform	perform	VERB
gi-2729	140	4	the	the	DET
gi-2729	140	5	effective	effective	ADJ
gi-2729	140	6	detection	detection	NOUN
gi-2729	140	7	of	of	ADP
gi-2729	140	8	self	self	NOUN
gi-2729	140	9	intersections	intersection	NOUN
gi-2729	140	10	with	with	ADP
gi-2729	140	11	better	well	ADJ
gi-2729	140	12	than	than	ADP
gi-2729	140	13	quadratic	quadratic	ADJ
gi-2729	140	14	time	time	NOUN
gi-2729	140	15	complexity	complexity	NOUN
gi-2729	140	16	?	?	PUNCT
gi-2729	141	1	bentley&ottman	bentley&ottman	NOUN
gi-2729	141	2	algorithm	algorithm	NOUN
gi-2729	141	3	brings	bring	VERB
gi-2729	141	4	one	one	NUM
gi-2729	141	5	of	of	ADP
gi-2729	141	6	possible	possible	ADJ
gi-2729	141	7	solutions	solution	NOUN
gi-2729	141	8	.	.	PUNCT
gi-2729	142	1	figure	figure	VERB
gi-2729	142	2	4	4	NUM
gi-2729	142	3	:	:	PUNCT
gi-2729	142	4	problem	problem	NOUN
gi-2729	142	5	of	of	ADP
gi-2729	142	6	self	self	NOUN
gi-2729	142	7	intersection	intersection	NOUN
gi-2729	142	8	after	after	ADP
gi-2729	142	9	the	the	DET
gi-2729	142	10	splitting	splitting	NOUN
gi-2729	142	11	procedure	procedure	NOUN
gi-2729	142	12	.	.	PUNCT
gi-2729	143	1	bentley&ottman	bentley&ottman	NOUN
gi-2729	143	2	algorithm	algorithm	NOUN
gi-2729	143	3	bentley&ottman	bentley&ottman	NOUN
gi-2729	143	4	algorithm	algorithm	NOUN
gi-2729	143	5	,	,	PUNCT
gi-2729	143	6	published	publish	VERB
gi-2729	143	7	in	in	ADP
gi-2729	143	8	1979	1979	NUM
gi-2729	143	9	,	,	PUNCT
gi-2729	143	10	is	be	AUX
gi-2729	143	11	able	able	ADJ
gi-2729	143	12	to	to	PART
gi-2729	143	13	find	find	VERB
gi-2729	143	14	intersections	intersection	NOUN
gi-2729	143	15	of	of	ADP
gi-2729	143	16	sets	set	NOUN
gi-2729	143	17	of	of	ADP
gi-2729	143	18	lines	line	NOUN
gi-2729	143	19	with	with	ADP
gi-2729	143	20	o(n	o(n	PROPN
gi-2729	143	21	lgn	lgn	NOUN
gi-2729	143	22	)	)	PUNCT
gi-2729	143	23	time	time	NOUN
gi-2729	143	24	complexity	complexity	NOUN
gi-2729	143	25	.	.	PUNCT
gi-2729	144	1	a	a	DET
gi-2729	144	2	brute	brute	ADJ
gi-2729	144	3	force	force	NOUN
gi-2729	144	4	algorithm	algorithm	NOUN
gi-2729	144	5	,	,	PUNCT
gi-2729	144	6	based	base	VERB
gi-2729	144	7	on	on	ADP
gi-2729	144	8	checking	checking	NOUN
gi-2729	144	9	of	of	ADP
gi-2729	144	10	all	all	DET
gi-2729	144	11	possible	possible	ADJ
gi-2729	144	12	intersection	intersection	NOUN
gi-2729	144	13	,	,	PUNCT
gi-2729	144	14	is	be	AUX
gi-2729	144	15	working	work	VERB
gi-2729	144	16	only	only	ADV
gi-2729	144	17	with	with	ADP
gi-2729	144	18	the	the	DET
gi-2729	144	19	quadratic	quadratic	ADJ
gi-2729	144	20	time	time	NOUN
gi-2729	144	21	complexity	complexity	NOUN
gi-2729	144	22	.	.	PUNCT
gi-2729	145	1	bentley&ottman	bentley&ottman	NOUN
gi-2729	145	2	algorithm	algorithm	NOUN
gi-2729	145	3	represents	represent	VERB
gi-2729	145	4	an	an	DET
gi-2729	145	5	application	application	NOUN
gi-2729	145	6	of	of	ADP
gi-2729	145	7	the	the	DET
gi-2729	145	8	sweep	sweep	NOUN
gi-2729	145	9	line	line	NOUN
gi-2729	145	10	,	,	PUNCT
gi-2729	145	11	moving	move	VERB
gi-2729	145	12	over	over	ADP
gi-2729	145	13	the	the	DET
gi-2729	145	14	lines	line	NOUN
gi-2729	145	15	from	from	ADP
gi-2729	145	16	left	left	ADJ
gi-2729	145	17	to	to	ADP
gi-2729	145	18	right	right	NOUN
gi-2729	145	19	.	.	PUNCT
gi-2729	146	1	the	the	DET
gi-2729	146	2	sweep	sweep	NOUN
gi-2729	146	3	line	line	NOUN
gi-2729	146	4	parallel	parallel	NOUN
gi-2729	146	5	to	to	ADP
gi-2729	146	6	y	y	PROPN
gi-2729	146	7	axis	axis	NOUN
gi-2729	146	8	divides	divide	VERB
gi-2729	146	9	the	the	DET
gi-2729	146	10	set	set	NOUN
gi-2729	146	11	into	into	ADP
gi-2729	146	12	processed	process	VERB
gi-2729	146	13	part	part	NOUN
gi-2729	146	14	and	and	CCONJ
gi-2729	146	15	unprocessed	unprocesse	VERB
gi-2729	146	16	part	part	NOUN
gi-2729	146	17	.	.	PUNCT
gi-2729	147	1	it	it	PRON
gi-2729	147	2	calculates	calculate	VERB
gi-2729	147	3	intersections	intersection	NOUN
gi-2729	147	4	only	only	ADV
gi-2729	147	5	with	with	ADP
gi-2729	147	6	those	those	DET
gi-2729	147	7	lines	line	NOUN
gi-2729	147	8	,	,	PUNCT
gi-2729	147	9	that	that	PRON
gi-2729	147	10	are	be	AUX
gi-2729	147	11	cut	cut	VERB
gi-2729	147	12	by	by	ADP
gi-2729	147	13	the	the	DET
gi-2729	147	14	sweep	sweep	NOUN
gi-2729	147	15	line	line	NOUN
gi-2729	147	16	.	.	PUNCT
gi-2729	148	1	data	datum	NOUN
gi-2729	148	2	structures	structure	NOUN
gi-2729	148	3	.	.	PUNCT
gi-2729	149	1	the	the	DET
gi-2729	149	2	proposed	propose	VERB
gi-2729	149	3	algorithm	algorithm	NOUN
gi-2729	149	4	is	be	AUX
gi-2729	149	5	an	an	DET
gi-2729	149	6	example	example	NOUN
gi-2729	149	7	of	of	ADP
gi-2729	149	8	the	the	DET
gi-2729	149	9	use	use	NOUN
gi-2729	149	10	of	of	ADP
gi-2729	149	11	the	the	DET
gi-2729	149	12	priority	priority	NOUN
gi-2729	149	13	queue	queue	NOUN
gi-2729	149	14	.	.	PUNCT
gi-2729	150	1	the	the	DET
gi-2729	150	2	proposal	proposal	NOUN
gi-2729	150	3	of	of	ADP
gi-2729	150	4	data	datum	NOUN
gi-2729	150	5	structures	structure	NOUN
gi-2729	150	6	plays	play	VERB
gi-2729	150	7	an	an	DET
gi-2729	150	8	important	important	ADJ
gi-2729	150	9	role	role	NOUN
gi-2729	150	10	.	.	PUNCT
gi-2729	151	1	the	the	DET
gi-2729	151	2	first	first	ADJ
gi-2729	151	3	data	data	NOUN
gi-2729	151	4	structure	structure	NOUN
gi-2729	151	5	is	be	AUX
gi-2729	151	6	represented	represent	VERB
gi-2729	151	7	by	by	ADP
gi-2729	151	8	the	the	DET
gi-2729	151	9	priority	priority	NOUN
gi-2729	151	10	queue	queue	NOUN
gi-2729	151	11	,	,	PUNCT
gi-2729	151	12	points	point	NOUN
gi-2729	151	13	are	be	AUX
gi-2729	151	14	sorted	sort	VERB
gi-2729	151	15	according	accord	VERB
gi-2729	151	16	to	to	ADP
gi-2729	151	17	x	x	PART
gi-2729	151	18	coordinate	coordinate	NOUN
gi-2729	151	19	.	.	PUNCT
gi-2729	152	1	information	information	NOUN
gi-2729	152	2	whether	whether	SCONJ
gi-2729	152	3	this	this	DET
gi-2729	152	4	point	point	NOUN
gi-2729	152	5	is	be	AUX
gi-2729	152	6	a	a	DET
gi-2729	152	7	start	start	NOUN
gi-2729	152	8	point	point	NOUN
gi-2729	152	9	,	,	PUNCT
gi-2729	152	10	an	an	DET
gi-2729	152	11	end	end	NOUN
gi-2729	152	12	point	point	NOUN
gi-2729	152	13	or	or	CCONJ
gi-2729	152	14	an	an	DET
gi-2729	152	15	intersection	intersection	NOUN
gi-2729	152	16	,	,	PUNCT
gi-2729	152	17	are	be	AUX
gi-2729	152	18	stored	store	VERB
gi-2729	152	19	for	for	ADP
gi-2729	152	20	each	each	DET
gi-2729	152	21	point	point	NOUN
gi-2729	152	22	.	.	PUNCT
gi-2729	153	1	if	if	SCONJ
gi-2729	153	2	sweep	sweep	VERB
gi-2729	153	3	line	line	NOUN
gi-2729	153	4	moves	move	NOUN
gi-2729	153	5	to	to	PART
gi-2729	153	6	point	point	VERB
gi-2729	153	7	,	,	PUNCT
gi-2729	153	8	an	an	DET
gi-2729	153	9	event	event	NOUN
gi-2729	153	10	is	be	AUX
gi-2729	153	11	called	call	VERB
gi-2729	153	12	.	.	PUNCT
gi-2729	154	1	the	the	DET
gi-2729	154	2	second	second	ADJ
gi-2729	154	3	data	data	NOUN
gi-2729	154	4	structure	structure	NOUN
gi-2729	154	5	,	,	PUNCT
gi-2729	154	6	often	often	ADV
gi-2729	154	7	represented	represent	VERB
gi-2729	154	8	by	by	ADP
gi-2729	154	9	the	the	DET
gi-2729	154	10	tree	tree	NOUN
gi-2729	154	11	,	,	PUNCT
gi-2729	154	12	stores	store	NOUN
gi-2729	154	13	lines	line	NOUN
gi-2729	154	14	in	in	ADP
gi-2729	154	15	the	the	DET
gi-2729	154	16	order	order	NOUN
gi-2729	154	17	in	in	ADP
gi-2729	154	18	which	which	PRON
gi-2729	154	19	they	they	PRON
gi-2729	154	20	intersect	intersect	VERB
gi-2729	154	21	the	the	DET
gi-2729	154	22	sweep	sweep	NOUN
gi-2729	154	23	line	line	NOUN
gi-2729	154	24	.	.	PUNCT
gi-2729	155	1	lines	line	NOUN
gi-2729	155	2	intersection	intersection	NOUN
gi-2729	155	3	.	.	PUNCT
gi-2729	156	1	finding	find	VERB
gi-2729	156	2	the	the	DET
gi-2729	156	3	intersection	intersection	NOUN
gi-2729	156	4	of	of	ADP
gi-2729	156	5	two	two	NUM
gi-2729	156	6	lines	line	NOUN
gi-2729	156	7	is	be	AUX
gi-2729	156	8	possible	possible	ADJ
gi-2729	156	9	from	from	ADP
gi-2729	156	10	parametric	parametric	ADJ
gi-2729	156	11	equations	equation	NOUN
gi-2729	156	12	.	.	PUNCT
gi-2729	157	1	using	use	VERB
gi-2729	157	2	general	general	ADJ
gi-2729	157	3	equation	equation	NOUN
gi-2729	157	4	for	for	ADP
gi-2729	157	5	lines	line	NOUN
gi-2729	157	6	parallel	parallel	ADJ
gi-2729	157	7	to	to	ADP
gi-2729	157	8	x	x	PART
gi-2729	157	9	bring	bring	VERB
gi-2729	157	10	problems	problem	NOUN
gi-2729	157	11	.	.	PUNCT
gi-2729	158	1	let	let	VERB
gi-2729	158	2	us	we	PRON
gi-2729	158	3	denote	denote	VERB
gi-2729	158	4	the	the	DET
gi-2729	158	5	first	first	ADJ
gi-2729	158	6	line	line	NOUN
gi-2729	158	7	l1	l1	PROPN
gi-2729	158	8	given	give	VERB
gi-2729	158	9	by	by	ADP
gi-2729	158	10	two	two	NUM
gi-2729	158	11	points	point	NOUN
gi-2729	158	12	p1	p1	NOUN
gi-2729	158	13	=	=	PUNCT
gi-2729	159	1	[	[	X
gi-2729	159	2	x1	x1	PROPN
gi-2729	159	3	,	,	PUNCT
gi-2729	159	4	y1	y1	NOUN
gi-2729	159	5	]	]	PUNCT
gi-2729	159	6	,	,	PUNCT
gi-2729	159	7	p2	p2	PROPN
gi-2729	159	8	=	=	PUNCT
gi-2729	160	1	[	[	X
gi-2729	160	2	x2	x2	PROPN
gi-2729	160	3	,	,	PUNCT
gi-2729	160	4	y2	y2	PROPN
gi-2729	160	5	]	]	PUNCT
gi-2729	160	6	,	,	PUNCT
gi-2729	160	7	the	the	DET
gi-2729	160	8	second	second	ADJ
gi-2729	160	9	line	line	NOUN
gi-2729	160	10	l2	l2	NOUN
gi-2729	160	11	given	give	VERB
gi-2729	160	12	by	by	ADP
gi-2729	160	13	two	two	NUM
gi-2729	160	14	pints	pint	NOUN
gi-2729	160	15	p3	p3	NOUN
gi-2729	160	16	=	=	PUNCT
gi-2729	161	1	[	[	X
gi-2729	161	2	x3	x3	ADJ
gi-2729	161	3	,	,	PUNCT
gi-2729	161	4	y3	y3	NOUN
gi-2729	161	5	]	]	PUNCT
gi-2729	161	6	,	,	PUNCT
gi-2729	161	7	p4	p4	ADJ
gi-2729	161	8	=	=	PUNCT
gi-2729	162	1	[	[	X
gi-2729	162	2	x4	x4	PROPN
gi-2729	162	3	,	,	PUNCT
gi-2729	162	4	y4	y4	X
gi-2729	162	5	]	]	PUNCT
gi-2729	162	6	,	,	PUNCT
gi-2729	162	7	and	and	CCONJ
gi-2729	162	8	intersection	intersection	NOUN
gi-2729	162	9	q	q	NOUN
gi-2729	163	1	=	=	PUNCT
gi-2729	163	2	[	[	X
gi-2729	163	3	xq	xq	PROPN
gi-2729	163	4	,	,	PUNCT
gi-2729	163	5	yq	yq	PROPN
gi-2729	163	6	]	]	PUNCT
gi-2729	163	7	.	.	PUNCT
gi-2729	164	1	parametric	parametric	ADJ
gi-2729	164	2	equation	equation	NOUN
gi-2729	164	3	for	for	ADP
gi-2729	164	4	the	the	DET
gi-2729	164	5	line	line	NOUN
gi-2729	164	6	we	we	PRON
gi-2729	164	7	can	can	AUX
gi-2729	164	8	write	write	VERB
gi-2729	164	9	(	(	PUNCT
gi-2729	164	10	xq	xq	PROPN
gi-2729	164	11	yq	yq	PROPN
gi-2729	164	12	)	)	PUNCT
gi-2729	165	1	=	=	PRON
gi-2729	165	2	(	(	PUNCT
gi-2729	165	3	x1	x1	PROPN
gi-2729	165	4	y1	y1	PROPN
gi-2729	165	5	)	)	PUNCT
gi-2729	166	1	+	+	SYM
gi-2729	166	2	s	s	X
gi-2729	166	3	(	(	PUNCT
gi-2729	166	4	x2	x2	INTJ
gi-2729	166	5	−	−	PROPN
gi-2729	167	1	x1	x1	PROPN
gi-2729	167	2	y2	y2	PROPN
gi-2729	167	3	−	−	PROPN
gi-2729	167	4	y1	y1	NOUN
gi-2729	167	5	)	)	PUNCT
gi-2729	167	6	=	=	PUNCT
gi-2729	168	1	(	(	PUNCT
gi-2729	168	2	x3	x3	NOUN
gi-2729	168	3	y3	y3	NOUN
gi-2729	168	4	)	)	PUNCT
gi-2729	169	1	+	+	CCONJ
gi-2729	169	2	t	t	X
gi-2729	169	3	(	(	PUNCT
gi-2729	169	4	x4	x4	ADV
gi-2729	169	5	−	−	PROPN
gi-2729	169	6	x3	x3	PROPN
gi-2729	169	7	y4	y4	PROPN
gi-2729	169	8	−	−	PROPN
gi-2729	169	9	y3	y3	PROPN
gi-2729	169	10	)	)	PUNCT
gi-2729	169	11	,	,	PUNCT
gi-2729	169	12	where	where	SCONJ
gi-2729	169	13	s	s	AUX
gi-2729	169	14	=	=	SYM
gi-2729	169	15	y1(x3−x4)+y3(x4−x1)+y4(x1−x3	y1(x3−x4)+y3(x4−x1)+y4(x1−x3	PROPN
gi-2729	169	16	)	)	PUNCT
gi-2729	169	17	(	(	PUNCT
gi-2729	169	18	x2−x1)(y3−y4)−(y2−y1)(x3−x4	x2−x1)(y3−y4)−(y2−y1)(x3−x4	PROPN
gi-2729	169	19	)	)	PUNCT
gi-2729	169	20	,	,	PUNCT
gi-2729	169	21	t	t	NOUN
gi-2729	169	22	=	=	SYM
gi-2729	169	23	y1(x3−x2)+y2(x1−x3)+y3(x2−x1	y1(x3−x2)+y2(x1−x3)+y3(x2−x1	PROPN
gi-2729	169	24	)	)	PUNCT
gi-2729	169	25	(	(	PUNCT
gi-2729	169	26	x2−x1)(y3−y4)−(y2−y1)(x3−x4	x2−x1)(y3−y4)−(y2−y1)(x3−x4	PROPN
gi-2729	169	27	)	)	PUNCT
gi-2729	169	28	.	.	PUNCT
gi-2729	170	1	for	for	ADP
gi-2729	170	2	s	s	PROPN
gi-2729	170	3	∈	∈	PROPN
gi-2729	170	4	(	(	PUNCT
gi-2729	170	5	0	0	NUM
gi-2729	170	6	,	,	PUNCT
gi-2729	170	7	1	1	NUM
gi-2729	170	8	)	)	PUNCT
gi-2729	170	9	∩	∩	NOUN
gi-2729	170	10	t	t	PROPN
gi-2729	170	11	∈	∈	PROPN
gi-2729	170	12	(	(	PUNCT
gi-2729	170	13	0	0	NUM
gi-2729	170	14	,	,	PUNCT
gi-2729	170	15	1	1	NUM
gi-2729	170	16	)	)	PUNCT
gi-2729	170	17	the	the	DET
gi-2729	170	18	intersection	intersection	NOUN
gi-2729	170	19	could	could	AUX
gi-2729	170	20	be	be	AUX
gi-2729	170	21	found	find	VERB
gi-2729	170	22	from	from	ADP
gi-2729	170	23	previous	previous	ADJ
gi-2729	170	24	formulas	formula	NOUN
gi-2729	170	25	.	.	PUNCT
gi-2729	171	1	intersection	intersection	NOUN
gi-2729	171	2	of	of	ADP
gi-2729	171	3	segments	segment	NOUN
gi-2729	171	4	.	.	PUNCT
gi-2729	172	1	the	the	DET
gi-2729	172	2	sweep	sweep	NOUN
gi-2729	172	3	line	line	NOUN
gi-2729	172	4	moves	move	NOUN
gi-2729	172	5	over	over	ADP
gi-2729	172	6	the	the	DET
gi-2729	172	7	segments	segment	NOUN
gi-2729	172	8	and	and	CCONJ
gi-2729	172	9	stops	stop	VERB
gi-2729	172	10	at	at	ADP
gi-2729	172	11	events	event	NOUN
gi-2729	172	12	of	of	ADP
gi-2729	172	13	three	three	NUM
gi-2729	172	14	types	type	NOUN
gi-2729	172	15	:	:	PUNCT
gi-2729	172	16	(	(	PUNCT
gi-2729	172	17	1	1	X
gi-2729	172	18	)	)	PUNCT
gi-2729	172	19	start	start	VERB
gi-2729	172	20	point	point	NOUN
gi-2729	172	21	of	of	ADP
gi-2729	172	22	the	the	DET
gi-2729	172	23	segment	segment	NOUN
gi-2729	172	24	,	,	PUNCT
gi-2729	172	25	(	(	PUNCT
gi-2729	172	26	2	2	X
gi-2729	172	27	)	)	PUNCT
gi-2729	172	28	intersection	intersection	NOUN
gi-2729	172	29	point	point	NOUN
gi-2729	172	30	between	between	ADP
gi-2729	172	31	two	two	NUM
gi-2729	172	32	segments	segment	NOUN
gi-2729	172	33	,	,	PUNCT
gi-2729	172	34	(	(	PUNCT
gi-2729	172	35	3	3	X
gi-2729	172	36	)	)	PUNCT
gi-2729	172	37	end	end	NOUN
gi-2729	172	38	point	point	NOUN
gi-2729	172	39	of	of	ADP
gi-2729	172	40	the	the	DET
gi-2729	172	41	segment	segment	NOUN
gi-2729	172	42	,	,	PUNCT
gi-2729	172	43	see	see	VERB
gi-2729	172	44	fig	fig	NOUN
gi-2729	172	45	.	.	PUNCT
gi-2729	173	1	5	5	X
gi-2729	173	2	.	.	X
gi-2729	173	3	if	if	SCONJ
gi-2729	173	4	the	the	DET
gi-2729	173	5	event	event	NOUN
gi-2729	173	6	point	point	NOUN
gi-2729	173	7	represents	represent	VERB
gi-2729	173	8	start	start	NOUN
gi-2729	173	9	point	point	NOUN
gi-2729	173	10	,	,	PUNCT
gi-2729	173	11	we	we	PRON
gi-2729	173	12	test	test	VERB
gi-2729	173	13	segment	segment	NOUN
gi-2729	173	14	against	against	ADP
gi-2729	173	15	two	two	NUM
gi-2729	173	16	neighbors	neighbor	NOUN
gi-2729	173	17	along	along	ADP
gi-2729	173	18	the	the	DET
gi-2729	173	19	sweep	sweep	NOUN
gi-2729	173	20	line	line	NOUN
gi-2729	173	21	.	.	PUNCT
gi-2729	174	1	if	if	SCONJ
gi-2729	174	2	the	the	DET
gi-2729	174	3	event	event	NOUN
gi-2729	174	4	point	point	NOUN
gi-2729	174	5	represents	represent	VERB
gi-2729	174	6	end	end	NOUN
gi-2729	174	7	point	point	NOUN
gi-2729	174	8	,	,	PUNCT
gi-2729	174	9	point	point	NOUN
gi-2729	174	10	is	be	AUX
gi-2729	174	11	removed	remove	VERB
gi-2729	174	12	from	from	ADP
gi-2729	174	13	the	the	DET
gi-2729	174	14	list	list	NOUN
gi-2729	174	15	.	.	PUNCT
gi-2729	175	1	if	if	SCONJ
gi-2729	175	2	we	we	PRON
gi-2729	175	3	found	find	VERB
gi-2729	175	4	an	an	DET
gi-2729	175	5	intersection	intersection	NOUN
gi-2729	175	6	of	of	ADP
gi-2729	175	7	those	those	DET
gi-2729	175	8	segments	segment	NOUN
gi-2729	175	9	,	,	PUNCT
gi-2729	175	10	it	it	PRON
gi-2729	175	11	becomes	become	VERB
gi-2729	175	12	a	a	DET
gi-2729	175	13	new	new	ADJ
gi-2729	175	14	event	event	NOUN
gi-2729	175	15	point	point	NOUN
gi-2729	175	16	.	.	PUNCT
gi-2729	176	1	if	if	SCONJ
gi-2729	176	2	the	the	DET
gi-2729	176	3	event	event	NOUN
gi-2729	176	4	point	point	NOUN
gi-2729	176	5	represents	represent	VERB
gi-2729	176	6	an	an	DET
gi-2729	176	7	intersection	intersection	NOUN
gi-2729	176	8	of	of	ADP
gi-2729	176	9	two	two	NUM
gi-2729	176	10	lines	line	NOUN
gi-2729	176	11	,	,	PUNCT
gi-2729	176	12	we	we	PRON
gi-2729	176	13	change	change	VERB
gi-2729	176	14	their	their	PRON
gi-2729	176	15	geinformatics	geinformatic	NOUN
gi-2729	176	16	fce	fce	VERB
gi-2729	176	17	ctu	ctu	NOUN
gi-2729	176	18	2008	2008	NUM
gi-2729	176	19	22	22	NUM
gi-2729	176	20	the	the	DET
gi-2729	176	21	importance	importance	NOUN
gi-2729	176	22	of	of	ADP
gi-2729	176	23	computational	computational	ADJ
gi-2729	176	24	geometry	geometry	NOUN
gi-2729	176	25	for	for	ADP
gi-2729	176	26	digital	digital	ADJ
gi-2729	176	27	cartography	cartography	NOUN
gi-2729	176	28	order	order	NOUN
gi-2729	176	29	.	.	PUNCT
gi-2729	177	1	each	each	PRON
gi-2729	177	2	of	of	ADP
gi-2729	177	3	both	both	DET
gi-2729	177	4	segments	segment	NOUN
gi-2729	177	5	has	have	VERB
gi-2729	177	6	adjacent	adjacent	ADJ
gi-2729	177	7	segments	segment	NOUN
gi-2729	177	8	along	along	ADP
gi-2729	177	9	the	the	DET
gi-2729	177	10	sweep	sweep	NOUN
gi-2729	177	11	line	line	NOUN
gi-2729	177	12	,	,	PUNCT
gi-2729	177	13	that	that	PRON
gi-2729	177	14	must	must	AUX
gi-2729	177	15	be	be	AUX
gi-2729	177	16	tested	test	VERB
gi-2729	177	17	for	for	ADP
gi-2729	177	18	intersections	intersection	NOUN
gi-2729	177	19	.	.	PUNCT
gi-2729	178	1	if	if	SCONJ
gi-2729	178	2	the	the	DET
gi-2729	178	3	point	point	NOUN
gi-2729	178	4	represents	represent	VERB
gi-2729	178	5	an	an	DET
gi-2729	178	6	end	end	NOUN
gi-2729	178	7	point	point	NOUN
gi-2729	178	8	,	,	PUNCT
gi-2729	178	9	adjacent	adjacent	ADJ
gi-2729	178	10	segments	segment	NOUN
gi-2729	178	11	are	be	AUX
gi-2729	178	12	tested	test	VERB
gi-2729	178	13	for	for	SCONJ
gi-2729	178	14	intersection	intersection	NOUN
gi-2729	178	15	and	and	CCONJ
gi-2729	178	16	event	event	NOUN
gi-2729	178	17	point	point	NOUN
gi-2729	178	18	is	be	AUX
gi-2729	178	19	removed	remove	VERB
gi-2729	178	20	.	.	PUNCT
gi-2729	179	1	bentley&ottman	bentley&ottman	NOUN
gi-2729	179	2	algorithm	algorithm	NOUN
gi-2729	179	3	is	be	AUX
gi-2729	179	4	based	base	VERB
gi-2729	179	5	on	on	ADP
gi-2729	179	6	assumption	assumption	NOUN
gi-2729	179	7	,	,	PUNCT
gi-2729	179	8	that	that	SCONJ
gi-2729	179	9	no	no	DET
gi-2729	179	10	segment	segment	NOUN
gi-2729	179	11	is	be	AUX
gi-2729	179	12	parallel	parallel	ADJ
gi-2729	179	13	to	to	PART
gi-2729	179	14	sweep	sweep	VERB
gi-2729	179	15	line	line	NOUN
gi-2729	179	16	and	and	CCONJ
gi-2729	179	17	no	no	DET
gi-2729	179	18	three	three	NUM
gi-2729	179	19	segments	segment	NOUN
gi-2729	179	20	pass	pass	VERB
gi-2729	179	21	through	through	ADP
gi-2729	179	22	one	one	NUM
gi-2729	179	23	point	point	NOUN
gi-2729	179	24	.	.	PUNCT
gi-2729	180	1	figure	figure	NOUN
gi-2729	180	2	5	5	NUM
gi-2729	180	3	:	:	PUNCT
gi-2729	180	4	bentley&ottman	bentley&ottman	NOUN
gi-2729	180	5	algorithm	algorithm	NOUN
gi-2729	180	6	with	with	ADP
gi-2729	180	7	positions	position	NOUN
gi-2729	180	8	of	of	ADP
gi-2729	180	9	sweep	sweep	NOUN
gi-2729	180	10	line	line	NOUN
gi-2729	180	11	.	.	PUNCT
gi-2729	181	1	history	history	NOUN
gi-2729	181	2	of	of	ADP
gi-2729	181	3	segments	segment	NOUN
gi-2729	181	4	intersecting	intersect	VERB
gi-2729	181	5	the	the	DET
gi-2729	181	6	sweep	sweep	NOUN
gi-2729	181	7	line	line	NOUN
gi-2729	181	8	is	be	AUX
gi-2729	181	9	stored	store	VERB
gi-2729	181	10	in	in	ADP
gi-2729	181	11	balanced	balanced	ADJ
gi-2729	181	12	binary	binary	ADJ
gi-2729	181	13	tree	tree	NOUN
gi-2729	181	14	.	.	PUNCT
gi-2729	182	1	this	this	DET
gi-2729	182	2	data	data	NOUN
gi-2729	182	3	structure	structure	NOUN
gi-2729	182	4	is	be	AUX
gi-2729	182	5	very	very	ADV
gi-2729	182	6	efficient	efficient	ADJ
gi-2729	182	7	and	and	CCONJ
gi-2729	182	8	enables	enable	VERB
gi-2729	182	9	update	update	NOUN
gi-2729	182	10	operations	operation	NOUN
gi-2729	182	11	in	in	ADP
gi-2729	182	12	o(lg(n	o(lg(n	NOUN
gi-2729	182	13	)	)	PUNCT
gi-2729	182	14	)	)	PUNCT
gi-2729	182	15	time	time	NOUN
gi-2729	182	16	.	.	PUNCT
gi-2729	183	1	so	so	ADV
gi-2729	183	2	,	,	PUNCT
gi-2729	183	3	it	it	PRON
gi-2729	183	4	is	be	AUX
gi-2729	183	5	apparent	apparent	ADJ
gi-2729	183	6	,	,	PUNCT
gi-2729	183	7	that	that	SCONJ
gi-2729	183	8	the	the	DET
gi-2729	183	9	implementation	implementation	NOUN
gi-2729	183	10	of	of	ADP
gi-2729	183	11	bentley&ottman	bentley&ottman	NOUN
gi-2729	183	12	algorithm	algorithm	NOUN
gi-2729	183	13	looks	look	VERB
gi-2729	183	14	quite	quite	ADV
gi-2729	183	15	difficult	difficult	ADJ
gi-2729	183	16	,	,	PUNCT
gi-2729	183	17	and	and	CCONJ
gi-2729	183	18	uses	use	VERB
gi-2729	183	19	a	a	DET
gi-2729	183	20	combination	combination	NOUN
gi-2729	183	21	of	of	ADP
gi-2729	183	22	several	several	ADJ
gi-2729	183	23	dynamic	dynamic	ADJ
gi-2729	183	24	data	datum	NOUN
gi-2729	183	25	structures	structure	NOUN
gi-2729	183	26	.	.	PUNCT
gi-2729	184	1	conclusion	conclusion	NOUN
gi-2729	184	2	this	this	DET
gi-2729	184	3	paper	paper	NOUN
gi-2729	184	4	presents	present	VERB
gi-2729	184	5	the	the	DET
gi-2729	184	6	use	use	NOUN
gi-2729	184	7	of	of	ADP
gi-2729	184	8	computational	computational	ADJ
gi-2729	184	9	geometry	geometry	NOUN
gi-2729	184	10	in	in	ADP
gi-2729	184	11	digital	digital	ADJ
gi-2729	184	12	cartography	cartography	NOUN
gi-2729	184	13	.	.	PUNCT
gi-2729	185	1	as	as	ADP
gi-2729	185	2	an	an	DET
gi-2729	185	3	illustrative	illustrative	ADJ
gi-2729	185	4	example	example	NOUN
gi-2729	185	5	the	the	DET
gi-2729	185	6	process	process	NOUN
gi-2729	185	7	of	of	ADP
gi-2729	185	8	automated	automate	VERB
gi-2729	185	9	or	or	CCONJ
gi-2729	185	10	semi	semi	ADV
gi-2729	185	11	automated	automate	VERB
gi-2729	185	12	building	building	NOUN
gi-2729	185	13	simplification	simplification	NOUN
gi-2729	185	14	was	be	AUX
gi-2729	185	15	chosen	choose	VERB
gi-2729	185	16	,	,	PUNCT
gi-2729	185	17	several	several	ADJ
gi-2729	185	18	examples	example	NOUN
gi-2729	185	19	were	be	AUX
gi-2729	185	20	given	give	VERB
gi-2729	185	21	and	and	CCONJ
gi-2729	185	22	discussed	discuss	VERB
gi-2729	185	23	.	.	PUNCT
gi-2729	186	1	it	it	PRON
gi-2729	186	2	was	be	AUX
gi-2729	186	3	focused	focus	VERB
gi-2729	186	4	on	on	ADP
gi-2729	186	5	the	the	DET
gi-2729	186	6	idea	idea	NOUN
gi-2729	186	7	of	of	ADP
gi-2729	186	8	possibility	possibility	NOUN
gi-2729	186	9	of	of	ADP
gi-2729	186	10	more	more	ADV
gi-2729	186	11	intensive	intensive	ADJ
gi-2729	186	12	computational	computational	ADJ
gi-2729	186	13	geometry	geometry	NOUN
gi-2729	186	14	teaching	teaching	NOUN
gi-2729	186	15	.	.	PUNCT
gi-2729	187	1	this	this	DET
gi-2729	187	2	article	article	NOUN
gi-2729	187	3	tries	try	VERB
gi-2729	187	4	to	to	PART
gi-2729	187	5	find	find	VERB
gi-2729	187	6	unifying	unify	VERB
gi-2729	187	7	perspective	perspective	NOUN
gi-2729	187	8	emphasis	emphasis	NOUN
gi-2729	187	9	importance	importance	NOUN
gi-2729	187	10	of	of	ADP
gi-2729	187	11	the	the	DET
gi-2729	187	12	computational	computational	ADJ
gi-2729	187	13	geometry	geometry	NOUN
gi-2729	187	14	for	for	ADP
gi-2729	187	15	cartography	cartography	NOUN
gi-2729	187	16	education	education	NOUN
gi-2729	187	17	.	.	PUNCT
gi-2729	188	1	not	not	PART
gi-2729	188	2	to	to	PART
gi-2729	188	3	become	become	VERB
gi-2729	188	4	only	only	ADV
gi-2729	188	5	passive	passive	ADJ
gi-2729	188	6	consumers	consumer	NOUN
gi-2729	188	7	of	of	ADP
gi-2729	188	8	information	information	NOUN
gi-2729	188	9	technologies	technology	NOUN
gi-2729	188	10	,	,	PUNCT
gi-2729	188	11	it	it	PRON
gi-2729	188	12	is	be	AUX
gi-2729	188	13	necessary	necessary	ADJ
gi-2729	188	14	to	to	PART
gi-2729	188	15	invest	invest	VERB
gi-2729	188	16	in	in	ADP
gi-2729	188	17	the	the	DET
gi-2729	188	18	development	development	NOUN
gi-2729	188	19	of	of	ADP
gi-2729	188	20	own	own	ADJ
gi-2729	188	21	geoinformatic	geoinformatic	ADJ
gi-2729	188	22	solutions	solution	NOUN
gi-2729	188	23	.	.	PUNCT
gi-2729	189	1	this	this	DET
gi-2729	189	2	fact	fact	NOUN
gi-2729	189	3	plays	play	VERB
gi-2729	189	4	and	and	CCONJ
gi-2729	189	5	important	important	ADJ
gi-2729	189	6	role	role	NOUN
gi-2729	189	7	and	and	CCONJ
gi-2729	189	8	can	can	AUX
gi-2729	189	9	not	not	PART
gi-2729	189	10	be	be	AUX
gi-2729	189	11	,	,	PUNCT
gi-2729	189	12	as	as	SCONJ
gi-2729	189	13	mentioned	mention	VERB
gi-2729	189	14	above	above	ADV
gi-2729	189	15	,	,	PUNCT
gi-2729	189	16	underestimated	underestimate	VERB
gi-2729	189	17	in	in	ADP
gi-2729	189	18	the	the	DET
gi-2729	189	19	long	long	ADJ
gi-2729	189	20	term	term	NOUN
gi-2729	189	21	perspective	perspective	NOUN
gi-2729	189	22	.	.	PUNCT
gi-2729	190	1	references	reference	NOUN
gi-2729	190	2	1	1	NUM
gi-2729	190	3	.	.	X
gi-2729	190	4	de	de	PROPN
gi-2729	190	5	berg	berg	PROPN
gi-2729	190	6	m.	m.	PROPN
gi-2729	190	7	,	,	PUNCT
gi-2729	190	8	schwarzkopf	schwarzkopf	PROPN
gi-2729	190	9	o.	o.	PROPN
gi-2729	190	10	,	,	PUNCT
gi-2729	190	11	kreveld	kreveld	VERB
gi-2729	190	12	m.	m.	NOUN
gi-2729	190	13	,	,	PUNCT
gi-2729	190	14	overmars	overmar	NOUN
gi-2729	190	15	m.	m.	NOUN
gi-2729	190	16	:	:	PUNCT
gi-2729	190	17	computational	computational	ADJ
gi-2729	190	18	geometry	geometry	NOUN
gi-2729	190	19	:	:	PUNCT
gi-2729	190	20	algorithms	algorithm	NOUN
gi-2729	190	21	and	and	CCONJ
gi-2729	190	22	applications	application	NOUN
gi-2729	190	23	,	,	PUNCT
gi-2729	190	24	2000	2000	NUM
gi-2729	190	25	,	,	PUNCT
gi-2729	190	26	springer	springer	NOUN
gi-2729	190	27	-	-	PUNCT
gi-2729	190	28	verlag	verlag	NOUN
gi-2729	190	29	.	.	PUNCT
gi-2729	191	1	2	2	X
gi-2729	191	2	.	.	X
gi-2729	191	3	dutter	dutter	NOUN
gi-2729	191	4	m.	m.	NOUN
gi-2729	191	5	:	:	PUNCT
gi-2729	191	6	generalization	generalization	NOUN
gi-2729	191	7	of	of	ADP
gi-2729	191	8	buildings	building	NOUN
gi-2729	191	9	derived	derive	VERB
gi-2729	191	10	from	from	ADP
gi-2729	191	11	high	high	ADJ
gi-2729	191	12	resolution	resolution	NOUN
gi-2729	191	13	remote	remote	ADJ
gi-2729	191	14	sensing	sense	VERB
gi-2729	191	15	data	datum	NOUN
gi-2729	191	16	,	,	PUNCT
gi-2729	191	17	2007	2007	NUM
gi-2729	191	18	.	.	PUNCT
gi-2729	192	1	3	3	X
gi-2729	192	2	.	.	X
gi-2729	192	3	rourke	rourke	PROPN
gi-2729	192	4	o.	o.	PROPN
gi-2729	192	5	j.	j.	PROPN
gi-2729	192	6	:	:	PUNCT
gi-2729	192	7	computational	computational	ADJ
gi-2729	192	8	geometry	geometry	NOUN
gi-2729	192	9	in	in	ADP
gi-2729	192	10	c	c	PROPN
gi-2729	192	11	,	,	PUNCT
gi-2729	192	12	2005	2005	NUM
gi-2729	192	13	,	,	PUNCT
gi-2729	192	14	cambridge	cambridge	PROPN
gi-2729	192	15	university	university	PROPN
gi-2729	192	16	press	press	NOUN
gi-2729	192	17	.	.	PUNCT
gi-2729	193	1	4	4	X
gi-2729	193	2	.	.	X
gi-2729	193	3	sester	sester	NOUN
gi-2729	193	4	m.	m.	NOUN
gi-2729	193	5	:	:	PUNCT
gi-2729	193	6	generalization	generalization	NOUN
gi-2729	193	7	based	base	VERB
gi-2729	193	8	on	on	ADP
gi-2729	193	9	least	least	ADJ
gi-2729	193	10	square	square	ADJ
gi-2729	193	11	adjustment	adjustment	NOUN
gi-2729	193	12	,	,	PUNCT
gi-2729	193	13	international	international	ADJ
gi-2729	193	14	archieves	archieve	NOUN
gi-2729	193	15	of	of	ADP
gi-2729	193	16	photogrammetry	photogrammetry	NOUN
gi-2729	193	17	and	and	CCONJ
gi-2729	193	18	remote	remote	ADJ
gi-2729	193	19	sensing	sensing	NOUN
gi-2729	193	20	,	,	PUNCT
gi-2729	193	21	2000	2000	NUM
gi-2729	193	22	.	.	PUNCT
gi-2729	194	1	geinformatics	geinformatic	NOUN
gi-2729	194	2	fce	fce	VERB
gi-2729	194	3	ctu	ctu	NOUN
gi-2729	194	4	2008	2008	NUM
gi-2729	194	5	23	23	NUM
gi-2729	194	6	the	the	DET
gi-2729	194	7	importance	importance	NOUN
gi-2729	194	8	of	of	ADP
gi-2729	194	9	computational	computational	ADJ
gi-2729	194	10	geometry	geometry	NOUN
gi-2729	194	11	for	for	ADP
gi-2729	194	12	digital	digital	ADJ
gi-2729	194	13	cartography	cartography	NOUN
gi-2729	194	14	5	5	NUM
gi-2729	194	15	.	.	PUNCT
gi-2729	195	1	toussand	toussand	NOUN
gi-2729	195	2	g.	g.	PROPN
gi-2729	195	3	,	,	PUNCT
gi-2729	195	4	solving	solve	VERB
gi-2729	195	5	geometric	geometric	ADJ
gi-2729	195	6	problems	problem	NOUN
gi-2729	195	7	with	with	ADP
gi-2729	195	8	the	the	DET
gi-2729	195	9	rotating	rotate	VERB
gi-2729	195	10	calipers	caliper	NOUN
gi-2729	195	11	,	,	PUNCT
gi-2729	195	12	mcgill	mcgill	PROPN
gi-2729	195	13	university	university	PROPN
gi-2729	195	14	montreal	montreal	PROPN
gi-2729	195	15	,	,	PUNCT
gi-2729	195	16	1983	1983	NUM
gi-2729	195	17	geinformatics	geinformatic	NOUN
gi-2729	195	18	fce	fce	VERB
gi-2729	195	19	ctu	ctu	NOUN
gi-2729	195	20	2008	2008	NUM
gi-2729	195	21	24	24	NUM