id	sid	tid	token	lemma	pos
aiti-203	1	1	advances	advance	NOUN
aiti-203	1	2	in	in	ADP
aiti-203	1	3	technology	technology	NOUN
aiti-203	1	4	innovation	innovation	NOUN
aiti-203	1	5	,	,	PUNCT
aiti-203	1	6	vol	vol	NOUN
aiti-203	1	7	.	.	PROPN
aiti-203	2	1	2	2	NUM
aiti-203	2	2	,	,	PUNCT
aiti-203	2	3	no	no	INTJ
aiti-203	2	4	.	.	NOUN
aiti-203	2	5	1	1	NUM
aiti-203	2	6	,	,	PUNCT
aiti-203	2	7	2017	2017	NUM
aiti-203	2	8	,	,	PUNCT
aiti-203	2	9	pp	pp	ADV
aiti-203	2	10	.	.	PUNCT
aiti-203	3	1	08	08	NUM
aiti-203	4	1	12	12	NUM
aiti-203	4	2	8	8	NUM
aiti-203	4	3	the	the	DET
aiti-203	4	4	tangent	tangent	ADJ
aiti-203	4	5	medial	medial	ADJ
aiti-203	4	6	circles	circle	NOUN
aiti-203	4	7	inside	inside	ADP
aiti-203	4	8	the	the	DET
aiti-203	4	9	region	region	NOUN
aiti-203	4	10	defined	define	VERB
aiti-203	4	11	by	by	ADP
aiti-203	4	12	hermite	hermite	ADJ
aiti-203	4	13	curve	curve	NOUN
aiti-203	4	14	tangent	tangent	NOUN
aiti-203	4	15	to	to	ADP
aiti-203	4	16	unit	unit	NOUN
aiti-203	4	17	circle	circle	PROPN
aiti-203	4	18	ching	ching	PROPN
aiti-203	4	19	-	-	PUNCT
aiti-203	4	20	shoei	shoei	PROPN
aiti-203	4	21	chiang	chiang	PROPN
aiti-203	4	22	computer	computer	NOUN
aiti-203	4	23	science	science	PROPN
aiti-203	4	24	and	and	CCONJ
aiti-203	4	25	information	information	NOUN
aiti-203	4	26	management	management	NOUN
aiti-203	4	27	,	,	PUNCT
aiti-203	4	28	soochow	soochow	PROPN
aiti-203	4	29	university	university	PROPN
aiti-203	4	30	,	,	PUNCT
aiti-203	4	31	taipei	taipei	PROPN
aiti-203	4	32	,	,	PUNCT
aiti-203	4	33	taiwan	taiwan	PROPN
aiti-203	4	34	.	.	PUNCT
aiti-203	5	1	received	receive	VERB
aiti-203	5	2	19	19	NUM
aiti-203	5	3	february	february	NOUN
aiti-203	5	4	2016	2016	NUM
aiti-203	5	5	;	;	PUNCT
aiti-203	5	6	received	receive	VERB
aiti-203	5	7	in	in	ADP
aiti-203	5	8	revised	revise	VERB
aiti-203	5	9	form	form	NOUN
aiti-203	5	10	08	08	NUM
aiti-203	5	11	april	april	PROPN
aiti-203	5	12	2016	2016	NUM
aiti-203	5	13	;	;	PUNCT
aiti-203	5	14	accepted	accept	VERB
aiti-203	5	15	10	10	NUM
aiti-203	5	16	april	april	PROPN
aiti-203	5	17	2016	2016	NUM
aiti-203	5	18	abstract	abstract	ADJ
aiti-203	5	19	the	the	DET
aiti-203	5	20	design	design	NOUN
aiti-203	5	21	of	of	ADP
aiti-203	5	22	curves	curve	NOUN
aiti-203	5	23	,	,	PUNCT
aiti-203	5	24	surfaces	surface	NOUN
aiti-203	5	25	,	,	PUNCT
aiti-203	5	26	and	and	CCONJ
aiti-203	5	27	solids	solid	NOUN
aiti-203	5	28	are	be	AUX
aiti-203	5	29	important	important	ADJ
aiti-203	5	30	in	in	ADP
aiti-203	5	31	computer	computer	NOUN
aiti-203	5	32	aided	aid	VERB
aiti-203	5	33	geometric	geometric	ADJ
aiti-203	5	34	design	design	NOUN
aiti-203	5	35	(	(	PUNCT
aiti-203	5	36	cagd	cagd	PROPN
aiti-203	5	37	)	)	PUNCT
aiti-203	5	38	.	.	PUNCT
aiti-203	6	1	images	image	NOUN
aiti-203	6	2	,	,	PUNCT
aiti-203	6	3	surround	surround	NOUN
aiti-203	6	4	by	by	ADP
aiti-203	6	5	boundary	boundary	ADJ
aiti-203	6	6	curves	curve	NOUN
aiti-203	6	7	,	,	PUNCT
aiti-203	6	8	are	be	AUX
aiti-203	6	9	also	also	ADV
aiti-203	6	10	investigated	investigate	VERB
aiti-203	6	11	by	by	ADP
aiti-203	6	12	many	many	ADJ
aiti-203	6	13	researchers	researcher	NOUN
aiti-203	6	14	.	.	PUNCT
aiti-203	7	1	one	one	NUM
aiti-203	7	2	way	way	NOUN
aiti-203	7	3	to	to	PART
aiti-203	7	4	describe	describe	VERB
aiti-203	7	5	an	an	DET
aiti-203	7	6	image	image	NOUN
aiti-203	7	7	is	be	AUX
aiti-203	7	8	using	use	VERB
aiti-203	7	9	the	the	DET
aiti-203	7	10	medial	medial	ADJ
aiti-203	7	11	axis	axis	NOUN
aiti-203	7	12	transform	transform	NOUN
aiti-203	7	13	.	.	PUNCT
aiti-203	8	1	under	under	ADP
aiti-203	8	2	this	this	DET
aiti-203	8	3	consideration	consideration	NOUN
aiti-203	8	4	,	,	PUNCT
aiti-203	8	5	the	the	DET
aiti-203	8	6	properties	property	NOUN
aiti-203	8	7	of	of	ADP
aiti-203	8	8	the	the	DET
aiti-203	8	9	boundary	boundary	ADJ
aiti-203	8	10	curves	curve	NOUN
aiti-203	8	11	tangent	tangent	NOUN
aiti-203	8	12	to	to	ADP
aiti-203	8	13	circles	circle	NOUN
aiti-203	8	14	become	become	VERB
aiti-203	8	15	important	important	ADJ
aiti-203	8	16	to	to	PART
aiti-203	8	17	design	design	VERB
aiti-203	8	18	for	for	ADP
aiti-203	8	19	2d	2d	NOUN
aiti-203	8	20	images	image	NOUN
aiti-203	8	21	.	.	PUNCT
aiti-203	9	1	in	in	ADP
aiti-203	9	2	this	this	DET
aiti-203	9	3	paper	paper	NOUN
aiti-203	9	4	,	,	PUNCT
aiti-203	9	5	we	we	PRON
aiti-203	9	6	want	want	VERB
aiti-203	9	7	to	to	PART
aiti-203	9	8	find	find	VERB
aiti-203	9	9	the	the	DET
aiti-203	9	10	medial	medial	ADJ
aiti-203	9	11	axis	axis	NOUN
aiti-203	9	12	transform	transform	NOUN
aiti-203	9	13	(	(	PUNCT
aiti-203	9	14	mat	mat	NOUN
aiti-203	9	15	)	)	PUNCT
aiti-203	9	16	for	for	ADP
aiti-203	9	17	a	a	DET
aiti-203	9	18	special	special	ADJ
aiti-203	9	19	class	class	NOUN
aiti-203	9	20	of	of	ADP
aiti-203	9	21	region	region	NOUN
aiti-203	9	22	,	,	PUNCT
aiti-203	9	23	which	which	PRON
aiti-203	9	24	is	be	AUX
aiti-203	9	25	bounded	bound	VERB
aiti-203	9	26	by	by	ADP
aiti-203	9	27	unit	unit	NOUN
aiti-203	9	28	circle	circle	NOUN
aiti-203	9	29	and	and	CCONJ
aiti-203	9	30	the	the	DET
aiti-203	9	31	curves	curve	NOUN
aiti-203	9	32	whose	whose	DET
aiti-203	9	33	end	end	NOUN
aiti-203	9	34	points	point	NOUN
aiti-203	9	35	is	be	AUX
aiti-203	9	36	on	on	ADP
aiti-203	9	37	a	a	DET
aiti-203	9	38	the	the	DET
aiti-203	9	39	circle	circle	NOUN
aiti-203	9	40	,	,	PUNCT
aiti-203	9	41	and	and	CCONJ
aiti-203	9	42	endpoints	endpoint	NOUN
aiti-203	9	43	tangent	tangent	PROPN
aiti-203	9	44	vectors	vector	NOUN
aiti-203	9	45	are	be	AUX
aiti-203	9	46	parallel	parallel	ADJ
aiti-203	9	47	to	to	ADP
aiti-203	9	48	the	the	DET
aiti-203	9	49	tangent	tangent	NOUN
aiti-203	9	50	of	of	ADP
aiti-203	9	51	circle	circle	NOUN
aiti-203	9	52	at	at	ADP
aiti-203	9	53	the	the	DET
aiti-203	9	54	end	end	NOUN
aiti-203	9	55	points	point	NOUN
aiti-203	9	56	.	.	PUNCT
aiti-203	10	1	during	during	ADP
aiti-203	10	2	the	the	DET
aiti-203	10	3	process	process	NOUN
aiti-203	10	4	,	,	PUNCT
aiti-203	10	5	we	we	PRON
aiti-203	10	6	want	want	AUX
aiti-203	10	7	find	find	VERB
aiti-203	10	8	the	the	DET
aiti-203	10	9	medial	medial	ADJ
aiti-203	10	10	circle	circle	NOUN
aiti-203	10	11	tangent	tangent	NOUN
aiti-203	10	12	to	to	ADP
aiti-203	10	13	other	other	ADJ
aiti-203	10	14	medial	medial	ADJ
aiti-203	10	15	circle	circle	NOUN
aiti-203	10	16	,	,	PUNCT
aiti-203	10	17	until	until	SCONJ
aiti-203	10	18	we	we	PRON
aiti-203	10	19	reach	reach	VERB
aiti-203	10	20	the	the	DET
aiti-203	10	21	medial	medial	ADJ
aiti-203	10	22	circle	circle	NOUN
aiti-203	10	23	whose	whose	DET
aiti-203	10	24	center	center	NOUN
aiti-203	10	25	is	be	AUX
aiti-203	10	26	the	the	DET
aiti-203	10	27	center	center	NOUN
aiti-203	10	28	of	of	ADP
aiti-203	10	29	the	the	DET
aiti-203	10	30	osculating	osculating	NOUN
aiti-203	10	31	circle	circle	NOUN
aiti-203	10	32	for	for	ADP
aiti-203	10	33	the	the	DET
aiti-203	10	34	point	point	NOUN
aiti-203	10	35	with	with	ADP
aiti-203	10	36	local	local	ADJ
aiti-203	10	37	maximum	maximum	ADJ
aiti-203	10	38	curvature	curvature	NOUN
aiti-203	10	39	.	.	PUNCT
aiti-203	11	1	there	there	PRON
aiti-203	11	2	are	be	VERB
aiti-203	11	3	4	4	NUM
aiti-203	11	4	cases	case	NOUN
aiti-203	11	5	,	,	PUNCT
aiti-203	11	6	symmetric	symmetric	ADJ
aiti-203	11	7	/	/	SYM
aiti-203	11	8	non	non	ADJ
aiti-203	11	9	-	-	ADJ
aiti-203	11	10	symmetric	symmetric	ADJ
aiti-203	11	11	region	region	NOUN
aiti-203	11	12	with	with	ADP
aiti-203	11	13	singular	singular	ADJ
aiti-203	11	14	point	point	NOUN
aiti-203	11	15	/	/	SYM
aiti-203	11	16	local	local	ADJ
aiti-203	11	17	maximum	maximum	ADJ
aiti-203	11	18	curvature	curvature	NOUN
aiti-203	11	19	point	point	NOUN
aiti-203	11	20	,	,	PUNCT
aiti-203	11	21	and	and	CCONJ
aiti-203	11	22	proposed	propose	VERB
aiti-203	11	23	algorithm	algorithm	NOUN
aiti-203	11	24	for	for	ADP
aiti-203	11	25	these	these	DET
aiti-203	11	26	4	4	NUM
aiti-203	11	27	cases	case	NOUN
aiti-203	11	28	.	.	PUNCT
aiti-203	12	1	we	we	PRON
aiti-203	12	2	introduced	introduce	VERB
aiti-203	12	3	algorithm	algorithm	NOUN
aiti-203	12	4	for	for	ADP
aiti-203	12	5	this	this	DET
aiti-203	12	6	4	4	NUM
aiti-203	12	7	cases	case	NOUN
aiti-203	12	8	in	in	ADP
aiti-203	12	9	this	this	DET
aiti-203	12	10	paper	paper	NOUN
aiti-203	12	11	.	.	PUNCT
aiti-203	13	1	keywords	keyword	NOUN
aiti-203	13	2	:	:	PUNCT
aiti-203	13	3	medial	medial	ADJ
aiti-203	13	4	axis	axis	NOUN
aiti-203	13	5	transform	transform	NOUN
aiti-203	13	6	,	,	PUNCT
aiti-203	13	7	hermite	hermite	ADJ
aiti-203	13	8	curve	curve	NOUN
aiti-203	13	9	,	,	PUNCT
aiti-203	13	10	computer	computer	NOUN
aiti-203	13	11	geometric	geometric	ADJ
aiti-203	13	12	modeling	modeling	NOUN
aiti-203	13	13	1	1	NUM
aiti-203	13	14	.	.	PUNCT
aiti-203	14	1	introduction	introduction	NOUN
aiti-203	14	2	the	the	DET
aiti-203	14	3	2d	2d	NUM
aiti-203	14	4	image	image	NOUN
aiti-203	14	5	can	can	AUX
aiti-203	14	6	be	be	AUX
aiti-203	14	7	stored	store	VERB
aiti-203	14	8	by	by	ADP
aiti-203	14	9	many	many	ADJ
aiti-203	14	10	different	different	ADJ
aiti-203	14	11	ways	way	NOUN
aiti-203	14	12	,	,	PUNCT
aiti-203	14	13	including	include	VERB
aiti-203	14	14	its	its	PRON
aiti-203	14	15	boundary	boundary	ADJ
aiti-203	14	16	curves	curve	NOUN
aiti-203	14	17	,	,	PUNCT
aiti-203	14	18	a	a	DET
aiti-203	14	19	medial	medial	ADJ
aiti-203	14	20	axis	axis	NOUN
aiti-203	14	21	curves	curve	NOUN
aiti-203	14	22	with	with	ADP
aiti-203	14	23	radius	radius	NOUN
aiti-203	14	24	function	function	NOUN
aiti-203	14	25	,	,	PUNCT
aiti-203	14	26	union	union	NOUN
aiti-203	14	27	of	of	ADP
aiti-203	14	28	many	many	ADJ
aiti-203	14	29	primitive	primitive	ADJ
aiti-203	14	30	figures	figure	NOUN
aiti-203	14	31	,	,	PUNCT
aiti-203	14	32	and	and	CCONJ
aiti-203	14	33	so	so	ADV
aiti-203	14	34	on	on	ADV
aiti-203	14	35	.	.	PUNCT
aiti-203	15	1	there	there	PRON
aiti-203	15	2	are	be	VERB
aiti-203	15	3	many	many	ADJ
aiti-203	15	4	researchers	researcher	NOUN
aiti-203	15	5	use	use	VERB
aiti-203	15	6	different	different	ADJ
aiti-203	15	7	curves	curve	NOUN
aiti-203	15	8	to	to	PART
aiti-203	15	9	simulate	simulate	VERB
aiti-203	15	10	different	different	ADJ
aiti-203	15	11	images	image	NOUN
aiti-203	15	12	.	.	PUNCT
aiti-203	16	1	for	for	ADP
aiti-203	16	2	example	example	NOUN
aiti-203	16	3	,	,	PUNCT
aiti-203	16	4	cinque	cinque	NOUN
aiti-203	16	5	,	,	PUNCT
aiti-203	16	6	levialdi	levialdi	NOUN
aiti-203	16	7	and	and	CCONJ
aiti-203	16	8	malizia	malizia	PROPN
aiti-203	17	1	[	[	X
aiti-203	17	2	1	1	X
aiti-203	17	3	]	]	PUNCT
aiti-203	17	4	uses	use	VERB
aiti-203	17	5	cubic	cubic	ADJ
aiti-203	17	6	bezier	bezier	NOUN
aiti-203	17	7	curve	curve	NOUN
aiti-203	17	8	to	to	PART
aiti-203	17	9	do	do	VERB
aiti-203	17	10	the	the	DET
aiti-203	17	11	shape	shape	NOUN
aiti-203	17	12	description	description	NOUN
aiti-203	17	13	.	.	PUNCT
aiti-203	18	1	yang	yang	PROPN
aiti-203	18	2	,	,	PUNCT
aiti-203	18	3	lu	lu	PROPN
aiti-203	18	4	and	and	CCONJ
aiti-203	18	5	lee[2	lee[2	X
aiti-203	18	6	]	]	PUNCT
aiti-203	18	7	use	use	VERB
aiti-203	18	8	bezier	bezier	NOUN
aiti-203	18	9	curve	curve	NOUN
aiti-203	18	10	to	to	PART
aiti-203	18	11	approach	approach	VERB
aiti-203	18	12	the	the	DET
aiti-203	18	13	shape	shape	NOUN
aiti-203	18	14	description	description	NOUN
aiti-203	18	15	for	for	ADP
aiti-203	18	16	chinese	chinese	ADJ
aiti-203	18	17	calligraphy	calligraphy	NOUN
aiti-203	18	18	characters	character	NOUN
aiti-203	18	19	.	.	PUNCT
aiti-203	19	1	chang	chang	PROPN
aiti-203	19	2	and	and	CCONJ
aiti-203	19	3	yan[3	yan[3	PROPN
aiti-203	19	4	]	]	PUNCT
aiti-203	19	5	derived	derive	VERB
aiti-203	19	6	an	an	DET
aiti-203	19	7	algorithm	algorithm	NOUN
aiti-203	19	8	to	to	PART
aiti-203	19	9	approach	approach	VERB
aiti-203	19	10	the	the	DET
aiti-203	19	11	hand	hand	NOUN
aiti-203	19	12	-	-	PUNCT
aiti-203	19	13	drawn	draw	VERB
aiti-203	19	14	image	image	NOUN
aiti-203	19	15	by	by	ADP
aiti-203	19	16	using	use	VERB
aiti-203	19	17	cubic	cubic	ADJ
aiti-203	19	18	bezier	bezier	NOUN
aiti-203	19	19	curve	curve	NOUN
aiti-203	19	20	.	.	PUNCT
aiti-203	20	1	cao	cao	PROPN
aiti-203	20	2	and	and	CCONJ
aiti-203	20	3	kot[4	kot[4	PROPN
aiti-203	20	4	]	]	PUNCT
aiti-203	20	5	derived	derive	VERB
aiti-203	20	6	an	an	DET
aiti-203	20	7	algorithm	algorithm	NOUN
aiti-203	20	8	to	to	PART
aiti-203	20	9	do	do	VERB
aiti-203	20	10	data	datum	NOUN
aiti-203	20	11	embedding	embed	VERB
aiti-203	20	12	in	in	ADP
aiti-203	20	13	electronic	electronic	ADJ
aiti-203	20	14	inks	ink	NOUN
aiti-203	20	15	without	without	ADP
aiti-203	20	16	losing	lose	VERB
aiti-203	20	17	data	datum	NOUN
aiti-203	20	18	.	.	PUNCT
aiti-203	21	1	the	the	DET
aiti-203	21	2	boundary	boundary	ADJ
aiti-203	21	3	curves	curve	NOUN
aiti-203	21	4	can	can	AUX
aiti-203	21	5	be	be	AUX
aiti-203	21	6	also	also	ADV
aiti-203	21	7	used	use	VERB
aiti-203	21	8	to	to	PART
aiti-203	21	9	derived	derived	VERB
aiti-203	21	10	the	the	DET
aiti-203	21	11	offset	offset	NOUN
aiti-203	21	12	curves	curve	NOUN
aiti-203	21	13	and	and	CCONJ
aiti-203	21	14	medial	medial	ADJ
aiti-203	21	15	axis	axis	NOUN
aiti-203	21	16	of	of	ADP
aiti-203	21	17	an	an	DET
aiti-203	21	18	images[5	images[5	NOUN
aiti-203	21	19	]	]	PUNCT
aiti-203	21	20	,	,	PUNCT
aiti-203	21	21	and	and	CCONJ
aiti-203	21	22	also	also	ADV
aiti-203	21	23	to	to	PART
aiti-203	21	24	simulate	simulate	VERB
aiti-203	21	25	the	the	DET
aiti-203	21	26	nature	nature	NOUN
aiti-203	21	27	objects	object	NOUN
aiti-203	21	28	,	,	PUNCT
aiti-203	21	29	such	such	ADJ
aiti-203	21	30	as	as	ADP
aiti-203	21	31	flowers[6	flowers[6	NUM
aiti-203	21	32	]	]	PUNCT
aiti-203	21	33	.	.	PUNCT
aiti-203	22	1	in	in	ADP
aiti-203	22	2	this	this	DET
aiti-203	22	3	paper	paper	NOUN
aiti-203	22	4	,	,	PUNCT
aiti-203	22	5	we	we	PRON
aiti-203	22	6	would	would	AUX
aiti-203	22	7	like	like	VERB
aiti-203	22	8	to	to	PART
aiti-203	22	9	investigate	investigate	VERB
aiti-203	22	10	the	the	DET
aiti-203	22	11	cubic	cubic	ADJ
aiti-203	22	12	hermite	hermite	ADJ
aiti-203	22	13	curves	curve	NOUN
aiti-203	22	14	,	,	PUNCT
aiti-203	22	15	where	where	SCONJ
aiti-203	22	16	the	the	DET
aiti-203	22	17	end	end	NOUN
aiti-203	22	18	points	point	NOUN
aiti-203	22	19	are	be	AUX
aiti-203	22	20	on	on	ADP
aiti-203	22	21	a	a	DET
aiti-203	22	22	unit	unit	NOUN
aiti-203	22	23	circle	circle	NOUN
aiti-203	22	24	,	,	PUNCT
aiti-203	22	25	and	and	CCONJ
aiti-203	22	26	its	its	PRON
aiti-203	22	27	end	end	NOUN
aiti-203	22	28	points	point	NOUN
aiti-203	22	29	tangent	tangent	NOUN
aiti-203	22	30	line	line	NOUN
aiti-203	22	31	is	be	AUX
aiti-203	22	32	parallel	parallel	ADJ
aiti-203	22	33	to	to	ADP
aiti-203	22	34	the	the	DET
aiti-203	22	35	tangent	tangent	ADJ
aiti-203	22	36	line	line	NOUN
aiti-203	22	37	of	of	ADP
aiti-203	22	38	circles	circle	NOUN
aiti-203	22	39	.	.	PUNCT
aiti-203	23	1	using	use	VERB
aiti-203	23	2	these	these	DET
aiti-203	23	3	properties	property	NOUN
aiti-203	23	4	,	,	PUNCT
aiti-203	23	5	with	with	ADP
aiti-203	23	6	more	more	ADJ
aiti-203	23	7	constraints	constraint	NOUN
aiti-203	23	8	on	on	ADP
aiti-203	23	9	the	the	DET
aiti-203	23	10	singular	singular	ADJ
aiti-203	23	11	point	point	NOUN
aiti-203	23	12	or	or	CCONJ
aiti-203	23	13	maximum	maximum	ADJ
aiti-203	23	14	curvature	curvature	NOUN
aiti-203	23	15	at	at	ADP
aiti-203	23	16	specified	specified	ADJ
aiti-203	23	17	parameter	parameter	NOUN
aiti-203	23	18	,	,	PUNCT
aiti-203	23	19	we	we	PRON
aiti-203	23	20	survey	survey	VERB
aiti-203	23	21	the	the	DET
aiti-203	23	22	couture	couture	NOUN
aiti-203	23	23	of	of	ADP
aiti-203	23	24	the	the	DET
aiti-203	23	25	curves	curve	NOUN
aiti-203	23	26	,	,	PUNCT
aiti-203	23	27	so	so	SCONJ
aiti-203	23	28	that	that	SCONJ
aiti-203	23	29	the	the	DET
aiti-203	23	30	design	design	NOUN
aiti-203	23	31	of	of	ADP
aiti-203	23	32	the	the	DET
aiti-203	23	33	curve	curve	NOUN
aiti-203	23	34	may	may	AUX
aiti-203	23	35	be	be	AUX
aiti-203	23	36	simplify	simplify	VERB
aiti-203	23	37	by	by	ADP
aiti-203	23	38	giving	give	VERB
aiti-203	23	39	constraint	constraint	NOUN
aiti-203	23	40	.	.	PUNCT
aiti-203	24	1	2	2	X
aiti-203	24	2	.	.	X
aiti-203	24	3	definition	definition	NOUN
aiti-203	24	4	and	and	CCONJ
aiti-203	24	5	theorem	theorem	NOUN
aiti-203	24	6	let	let	AUX
aiti-203	24	7	introduce	introduce	VERB
aiti-203	24	8	the	the	DET
aiti-203	24	9	hermite	hermite	ADJ
aiti-203	24	10	curve	curve	NOUN
aiti-203	24	11	first	first	ADV
aiti-203	24	12	.	.	PUNCT
aiti-203	25	1	given	give	VERB
aiti-203	25	2	two	two	NUM
aiti-203	25	3	points	point	NOUN
aiti-203	25	4	p0	p0	NOUN
aiti-203	25	5	and	and	CCONJ
aiti-203	25	6	p1	p1	PROPN
aiti-203	25	7	,	,	PUNCT
aiti-203	25	8	with	with	ADP
aiti-203	25	9	two	two	NUM
aiti-203	25	10	associated	associate	VERB
aiti-203	25	11	tangent	tangent	NOUN
aiti-203	25	12	vectors	vector	NOUN
aiti-203	25	13	and	and	CCONJ
aiti-203	25	14	v1	v1	NOUN
aiti-203	25	15	,	,	PUNCT
aiti-203	25	16	the	the	DET
aiti-203	25	17	hermite	hermite	ADJ
aiti-203	25	18	curve	curve	NOUN
aiti-203	25	19	c(t	c(t	PROPN
aiti-203	25	20	)	)	PUNCT
aiti-203	25	21	defined	define	VERB
aiti-203	25	22	as	as	ADP
aiti-203	25	23	(	(	PUNCT
aiti-203	25	24	see	see	VERB
aiti-203	25	25	fig	fig	NOUN
aiti-203	25	26	.	.	PUNCT
aiti-203	26	1	1	1	NUM
aiti-203	26	2	):	):	PUNCT
aiti-203	26	3	fig	fig	NOUN
aiti-203	26	4	.	.	PUNCT
aiti-203	27	1	1	1	NUM
aiti-203	27	2	hermite	hermite	ADJ
aiti-203	27	3	curve	curve	NOUN
aiti-203	27	4	to	to	PART
aiti-203	27	5	simplify	simplify	VERB
aiti-203	27	6	our	our	PRON
aiti-203	27	7	problem	problem	NOUN
aiti-203	27	8	,	,	PUNCT
aiti-203	27	9	we	we	PRON
aiti-203	27	10	assume	assume	VERB
aiti-203	27	11	that	that	SCONJ
aiti-203	27	12	the	the	DET
aiti-203	27	13	end	end	NOUN
aiti-203	27	14	points	point	VERB
aiti-203	27	15	p0	p0	NOUN
aiti-203	27	16	and	and	CCONJ
aiti-203	27	17	p1	p1	NOUN
aiti-203	27	18	are	be	AUX
aiti-203	27	19	on	on	ADP
aiti-203	27	20	the	the	DET
aiti-203	27	21	unit	unit	NOUN
aiti-203	27	22	circle	circle	NOUN
aiti-203	27	23	,	,	PUNCT
aiti-203	27	24	the	the	DET
aiti-203	27	25	first	first	ADJ
aiti-203	27	26	point	point	NOUN
aiti-203	27	27	p0	p0	PROPN
aiti-203	27	28	=(	=(	NOUN
aiti-203	27	29	-1,0	-1,0	PROPN
aiti-203	27	30	)	)	PUNCT
aiti-203	27	31	,	,	PUNCT
aiti-203	27	32	and	and	CCONJ
aiti-203	27	33	the	the	DET
aiti-203	27	34	second	second	ADJ
aiti-203	27	35	point	point	NOUN
aiti-203	27	36	p1	p1	NOUN
aiti-203	27	37	=(	=(	NOUN
aiti-203	27	38	-cosθ	-cosθ	PROPN
aiti-203	27	39	,	,	PUNCT
aiti-203	27	40	sinθ	sinθ	PROPN
aiti-203	27	41	)	)	PUNCT
aiti-203	27	42	.	.	PUNCT
aiti-203	28	1	it	it	PRON
aiti-203	28	2	’s	’	VERB
aiti-203	28	3	associated	associate	VERB
aiti-203	28	4	tangent	tangent	NOUN
aiti-203	28	5	vectors	vector	NOUN
aiti-203	28	6	parallel	parallel	ADJ
aiti-203	28	7	to	to	ADP
aiti-203	28	8	(	(	PUNCT
aiti-203	28	9	0,1	0,1	NUM
aiti-203	28	10	)	)	PUNCT
aiti-203	28	11	and	and	CCONJ
aiti-203	28	12	(	(	PUNCT
aiti-203	28	13	sinθ	sinθ	PROPN
aiti-203	28	14	,	,	PUNCT
aiti-203	28	15	cosθ	cosθ	PROPN
aiti-203	28	16	)	)	PUNCT
aiti-203	28	17	.	.	PUNCT
aiti-203	29	1	we	we	PRON
aiti-203	29	2	have	have	VERB
aiti-203	29	3	the	the	DET
aiti-203	29	4	following	follow	VERB
aiti-203	29	5	definition	definition	NOUN
aiti-203	29	6	for	for	ADP
aiti-203	29	7	this	this	DET
aiti-203	29	8	curve	curve	NOUN
aiti-203	29	9	.	.	PUNCT
aiti-203	30	1	*	*	PUNCT
aiti-203	30	2	corresponding	correspond	VERB
aiti-203	30	3	author	author	NOUN
aiti-203	30	4	,	,	PUNCT
aiti-203	30	5	email	email	NOUN
aiti-203	30	6	:	:	PUNCT
aiti-203	30	7	chiang@scu.edu.tw	chiang@scu.edu.tw	PROPN
aiti-203	30	8	advances	advance	VERB
aiti-203	30	9	in	in	ADP
aiti-203	30	10	technology	technology	NOUN
aiti-203	30	11	innovation	innovation	NOUN
aiti-203	30	12	,	,	PUNCT
aiti-203	30	13	vol	vol	NOUN
aiti-203	30	14	.	.	PROPN
aiti-203	31	1	2	2	NUM
aiti-203	31	2	,	,	PUNCT
aiti-203	31	3	no	no	INTJ
aiti-203	31	4	.	.	NOUN
aiti-203	31	5	1	1	NUM
aiti-203	31	6	,	,	PUNCT
aiti-203	31	7	2017	2017	NUM
aiti-203	31	8	,	,	PUNCT
aiti-203	31	9	pp	pp	ADV
aiti-203	31	10	.	.	PUNCT
aiti-203	32	1	08	08	NUM
aiti-203	32	2	12	12	NUM
aiti-203	32	3	9	9	NUM
aiti-203	32	4	copyright	copyright	NOUN
aiti-203	32	5	©	©	PROPN
aiti-203	32	6	taeti	taeti	PROPN
aiti-203	32	7	definition	definition	NOUN
aiti-203	32	8	1	1	NUM
aiti-203	32	9	:	:	PUNCT
aiti-203	32	10	two	two	NUM
aiti-203	32	11	points	point	NOUN
aiti-203	32	12	p0	p0	NOUN
aiti-203	32	13	=(	=(	PROPN
aiti-203	32	14	-1	-1	PROPN
aiti-203	32	15	,	,	PUNCT
aiti-203	32	16	0	0	NUM
aiti-203	32	17	)	)	PUNCT
aiti-203	32	18	,	,	PUNCT
aiti-203	32	19	p1	p1	NOUN
aiti-203	32	20	=(	=(	NOUN
aiti-203	32	21	-cosθ	-cosθ	PROPN
aiti-203	32	22	,	,	PUNCT
aiti-203	32	23	sinθ	sinθ	PROPN
aiti-203	32	24	)	)	PUNCT
aiti-203	32	25	on	on	ADP
aiti-203	32	26	the	the	DET
aiti-203	32	27	unit	unit	NOUN
aiti-203	32	28	circle	circle	NOUN
aiti-203	32	29	with	with	ADP
aiti-203	32	30	its	its	PRON
aiti-203	32	31	associated	associated	ADJ
aiti-203	32	32	tangent	tangent	NOUN
aiti-203	32	33	vector	vector	PROPN
aiti-203	32	34	v0	v0	PROPN
aiti-203	32	35	=	=	NOUN
aiti-203	32	36	α0(0,1	α0(0,1	NOUN
aiti-203	32	37	)	)	PUNCT
aiti-203	32	38	,	,	PUNCT
aiti-203	32	39	v1	v1	PROPN
aiti-203	32	40	=	=	SYM
aiti-203	32	41	α1(sinθ	α1(sinθ	PROPN
aiti-203	32	42	,	,	PUNCT
aiti-203	32	43	cosθ	cosθ	PROPN
aiti-203	32	44	)	)	PUNCT
aiti-203	32	45	produced	produce	VERB
aiti-203	32	46	a	a	DET
aiti-203	32	47	hermite	hermite	ADJ
aiti-203	32	48	curve	curve	NOUN
aiti-203	32	49	,	,	PUNCT
aiti-203	32	50	we	we	PRON
aiti-203	32	51	call	call	VERB
aiti-203	32	52	it	it	PRON
aiti-203	32	53	unit	unit	NOUN
aiti-203	32	54	circle	circle	PROPN
aiti-203	32	55	hermite	hermite	PROPN
aiti-203	32	56	curve	curve	PROPN
aiti-203	32	57	,	,	PUNCT
aiti-203	32	58	denoted	denote	VERB
aiti-203	32	59	h1(t;θ	h1(t;θ	PROPN
aiti-203	32	60	,	,	PUNCT
aiti-203	32	61	α0,α1	α0,α1	PROPN
aiti-203	32	62	)	)	PUNCT
aiti-203	32	63	,	,	PUNCT
aiti-203	32	64	where	where	SCONJ
aiti-203	32	65	α0>0	α0>0	NOUN
aiti-203	32	66	,	,	PUNCT
aiti-203	32	67	α1>0	α1>0	NOUN
aiti-203	32	68	,	,	PUNCT
aiti-203	32	69	0	0	PUNCT
aiti-203	32	70	<	<	X
aiti-203	32	71	t<1	t<1	PROPN
aiti-203	32	72	,	,	PUNCT
aiti-203	32	73	0	0	NUM
aiti-203	32	74	<	<	X
aiti-203	32	75	θ<2π	θ<2π	PROPN
aiti-203	32	76	.	.	PUNCT
aiti-203	33	1	notice	notice	VERB
aiti-203	33	2	that	that	SCONJ
aiti-203	33	3	for	for	ADP
aiti-203	33	4	the	the	DET
aiti-203	33	5	general	general	ADJ
aiti-203	33	6	case	case	NOUN
aiti-203	33	7	,	,	PUNCT
aiti-203	33	8	we	we	PRON
aiti-203	33	9	can	can	AUX
aiti-203	33	10	always	always	ADV
aiti-203	33	11	convert	convert	VERB
aiti-203	33	12	the	the	DET
aiti-203	33	13	design	design	NOUN
aiti-203	33	14	problem	problem	NOUN
aiti-203	33	15	into	into	ADP
aiti-203	33	16	the	the	DET
aiti-203	33	17	design	design	NOUN
aiti-203	33	18	problem	problem	NOUN
aiti-203	33	19	for	for	ADP
aiti-203	33	20	h1(t;θ	h1(t;θ	PROPN
aiti-203	33	21	,	,	PUNCT
aiti-203	33	22	α0,α1	α0,α1	NUM
aiti-203	33	23	)	)	PUNCT
aiti-203	33	24	.	.	PUNCT
aiti-203	34	1	we	we	PRON
aiti-203	34	2	can	can	AUX
aiti-203	34	3	always	always	ADV
aiti-203	34	4	translate	translate	VERB
aiti-203	34	5	the	the	DET
aiti-203	34	6	center	center	NOUN
aiti-203	34	7	of	of	ADP
aiti-203	34	8	current	current	ADJ
aiti-203	34	9	medial	medial	ADJ
aiti-203	34	10	axis	axis	NOUN
aiti-203	34	11	circle	circle	NOUN
aiti-203	34	12	to	to	ADP
aiti-203	34	13	the	the	DET
aiti-203	34	14	origin	origin	NOUN
aiti-203	34	15	,	,	PUNCT
aiti-203	34	16	scale	scale	VERB
aiti-203	34	17	the	the	DET
aiti-203	34	18	radius	radius	NOUN
aiti-203	34	19	into	into	ADP
aiti-203	34	20	one	one	NUM
aiti-203	34	21	and	and	CCONJ
aiti-203	34	22	rotate	rotate	VERB
aiti-203	34	23	the	the	DET
aiti-203	34	24	circle	circle	NOUN
aiti-203	34	25	so	so	SCONJ
aiti-203	34	26	that	that	SCONJ
aiti-203	34	27	the	the	DET
aiti-203	34	28	first	first	ADJ
aiti-203	34	29	boundary	boundary	ADJ
aiti-203	34	30	point	point	NOUN
aiti-203	34	31	is	be	AUX
aiti-203	34	32	on	on	ADP
aiti-203	34	33	(	(	PUNCT
aiti-203	34	34	-1,0	-1,0	PROPN
aiti-203	34	35	)	)	PUNCT
aiti-203	34	36	.	.	PUNCT
aiti-203	35	1	we	we	PRON
aiti-203	35	2	call	call	VERB
aiti-203	35	3	this	this	DET
aiti-203	35	4	process	process	NOUN
aiti-203	35	5	the	the	DET
aiti-203	35	6	standardization	standardization	NOUN
aiti-203	35	7	of	of	ADP
aiti-203	35	8	the	the	DET
aiti-203	35	9	problem	problem	NOUN
aiti-203	35	10	.	.	PUNCT
aiti-203	36	1	after	after	SCONJ
aiti-203	36	2	we	we	PRON
aiti-203	36	3	solve	solve	VERB
aiti-203	36	4	the	the	DET
aiti-203	36	5	problem	problem	NOUN
aiti-203	36	6	,	,	PUNCT
aiti-203	36	7	produce	produce	VERB
aiti-203	36	8	the	the	DET
aiti-203	36	9	curve	curve	NOUN
aiti-203	36	10	we	we	PRON
aiti-203	36	11	want	want	VERB
aiti-203	36	12	,	,	PUNCT
aiti-203	36	13	we	we	PRON
aiti-203	36	14	can	can	AUX
aiti-203	36	15	always	always	ADV
aiti-203	36	16	inverse	inverse	VERB
aiti-203	36	17	the	the	DET
aiti-203	36	18	rotate	rotate	NOUN
aiti-203	36	19	,	,	PUNCT
aiti-203	36	20	scale	scale	NOUN
aiti-203	36	21	,	,	PUNCT
aiti-203	36	22	and	and	CCONJ
aiti-203	36	23	translate	translate	ADJ
aiti-203	36	24	process	process	NOUN
aiti-203	36	25	,	,	PUNCT
aiti-203	36	26	to	to	PART
aiti-203	36	27	see	see	VERB
aiti-203	36	28	the	the	DET
aiti-203	36	29	designed	design	VERB
aiti-203	36	30	curves	curve	NOUN
aiti-203	36	31	for	for	ADP
aiti-203	36	32	the	the	DET
aiti-203	36	33	original	original	ADJ
aiti-203	36	34	design	design	NOUN
aiti-203	36	35	problem	problem	NOUN
aiti-203	36	36	.	.	PUNCT
aiti-203	37	1	in	in	ADP
aiti-203	37	2	[	[	X
aiti-203	37	3	7	7	NUM
aiti-203	37	4	]	]	PUNCT
aiti-203	37	5	,	,	PUNCT
aiti-203	37	6	we	we	PRON
aiti-203	37	7	have	have	VERB
aiti-203	37	8	the	the	DET
aiti-203	37	9	following	follow	VERB
aiti-203	37	10	two	two	NUM
aiti-203	37	11	theorems	theorem	NOUN
aiti-203	37	12	:	:	PUNCT
aiti-203	37	13	theorm	theorm	NOUN
aiti-203	37	14	1	1	NUM
aiti-203	37	15	:	:	PUNCT
aiti-203	37	16	let	let	VERB
aiti-203	37	17	c(t)=h1(t;θ	c(t)=h1(t;θ	PROPN
aiti-203	37	18	,	,	PUNCT
aiti-203	37	19	α0,α1	α0,α1	NOUN
aiti-203	37	20	)	)	PUNCT
aiti-203	37	21	,	,	PUNCT
aiti-203	37	22	then	then	ADV
aiti-203	37	23	c'(t)=(x′(t),y′(t	c'(t)=(x′(t),y′(t	PROPN
aiti-203	37	24	)	)	PUNCT
aiti-203	37	25	)	)	PUNCT
aiti-203	37	26	=(	=(	NOUN
aiti-203	37	27	0	0	NUM
aiti-203	37	28	,	,	PUNCT
aiti-203	37	29	0	0	NUM
aiti-203	37	30	)	)	PUNCT
aiti-203	37	31	↔	↔	NOUN
aiti-203	37	32	α0b(t)=α1d(t	α0b(t)=α1d(t	NOUN
aiti-203	37	33	)	)	PUNCT
aiti-203	37	34	=	=	SYM
aiti-203	37	35	a(t	a(t	NOUN
aiti-203	37	36	)	)	PUNCT
aiti-203	37	37	tan	tan	NOUN
aiti-203	37	38	(	(	PUNCT
aiti-203	37	39	θ	θ	PROPN
aiti-203	37	40	2	2	NUM
aiti-203	37	41	)	)	PUNCT
aiti-203	37	42	,	,	PUNCT
aiti-203	37	43	where	where	SCONJ
aiti-203	37	44	a(t	a(t	NOUN
aiti-203	37	45	)	)	PUNCT
aiti-203	37	46	=	=	NOUN
aiti-203	37	47	6t(t-1	6t(t-1	NUM
aiti-203	37	48	)	)	PUNCT
aiti-203	37	49	,	,	PUNCT
aiti-203	37	50	b(t)=(3t-1	b(t)=(3t-1	PROPN
aiti-203	37	51	)	)	PUNCT
aiti-203	37	52	(	(	PUNCT
aiti-203	37	53	t-1	t-1	PROPN
aiti-203	37	54	)	)	PUNCT
aiti-203	37	55	,	,	PUNCT
aiti-203	37	56	d(t)=t(3t-2	d(t)=t(3t-2	PROPN
aiti-203	37	57	)	)	PUNCT
aiti-203	37	58	.	.	PUNCT
aiti-203	38	1	we	we	PRON
aiti-203	38	2	would	would	AUX
aiti-203	38	3	like	like	VERB
aiti-203	38	4	to	to	PART
aiti-203	38	5	find	find	VERB
aiti-203	38	6	the	the	DET
aiti-203	38	7	ma	ma	PROPN
aiti-203	38	8	and	and	CCONJ
aiti-203	38	9	mat	mat	NOUN
aiti-203	38	10	for	for	ADP
aiti-203	38	11	the	the	DET
aiti-203	38	12	region	region	NOUN
aiti-203	38	13	bounded	bound	VERB
aiti-203	38	14	by	by	ADP
aiti-203	38	15	the	the	DET
aiti-203	38	16	hermite	hermite	PROPN
aiti-203	38	17	curve	curve	NOUN
aiti-203	38	18	with	with	ADP
aiti-203	38	19	the	the	DET
aiti-203	38	20	circular	circular	ADJ
aiti-203	38	21	arc	arc	NOUN
aiti-203	38	22	from	from	ADP
aiti-203	38	23	(	(	PUNCT
aiti-203	38	24	-cosθ	-cosθ	X
aiti-203	38	25	,	,	PUNCT
aiti-203	38	26	sinθ	sinθ	PROPN
aiti-203	38	27	)	)	PUNCT
aiti-203	38	28	to	to	ADP
aiti-203	38	29	the	the	DET
aiti-203	38	30	point	point	NOUN
aiti-203	38	31	(	(	PUNCT
aiti-203	38	32	-1,0	-1,0	NUM
aiti-203	38	33	)	)	PUNCT
aiti-203	38	34	rotate	rotate	VERB
aiti-203	38	35	about	about	ADP
aiti-203	38	36	the	the	DET
aiti-203	38	37	origin	origin	NOUN
aiti-203	38	38	clockwise	clockwise	NOUN
aiti-203	38	39	,	,	PUNCT
aiti-203	38	40	we	we	PRON
aiti-203	38	41	call	call	VERB
aiti-203	38	42	this	this	DET
aiti-203	38	43	region	region	NOUN
aiti-203	38	44	r(t;θ	r(t;θ	PROPN
aiti-203	38	45	,	,	PUNCT
aiti-203	38	46	α	α	NOUN
aiti-203	38	47	)	)	PUNCT
aiti-203	38	48	.	.	PUNCT
aiti-203	39	1	theorem	theorem	NOUN
aiti-203	39	2	2	2	NUM
aiti-203	39	3	:	:	PUNCT
aiti-203	39	4	let	let	VERB
aiti-203	39	5	the	the	DET
aiti-203	39	6	hermite	hermite	ADJ
aiti-203	39	7	curve	curve	NOUN
aiti-203	39	8	c(t)=(x(t),y(t))=	c(t)=(x(t),y(t))=	PROPN
aiti-203	39	9	h1(t;θ	h1(t;θ	PROPN
aiti-203	39	10	,	,	PUNCT
aiti-203	39	11	α0,α1	α0,α1	PROPN
aiti-203	39	12	)	)	PUNCT
aiti-203	39	13	,	,	PUNCT
aiti-203	39	14	if	if	SCONJ
aiti-203	39	15	the	the	DET
aiti-203	39	16	local	local	ADJ
aiti-203	39	17	maximum	maximum	ADJ
aiti-203	39	18	curvature	curvature	NOUN
aiti-203	39	19	is	be	AUX
aiti-203	39	20	at	at	ADP
aiti-203	39	21	t0	t0	NOUN
aiti-203	39	22	,	,	PUNCT
aiti-203	39	23	then	then	ADV
aiti-203	39	24	(	(	PUNCT
aiti-203	39	25	x'(t0)y'''(t0)-x'''(t0)y'(t0))(x'(t0)2+y'(t0)2)-3(x'(t0)y	x'(t0)y'''(t0)-x'''(t0)y'(t0))(x'(t0)2+y'(t0)2)-3(x'(t0)y	PROPN
aiti-203	39	26	''	''	PUNCT
aiti-203	39	27	(	(	PUNCT
aiti-203	39	28	t0)-x''(t0)y'(t0))(x'(t0)x''(t0)+y'(t0)y''(t0))=0	t0)-x''(t0)y'(t0))(x'(t0)x''(t0)+y'(t0)y''(t0))=0	X
aiti-203	39	29	.	.	PUNCT
aiti-203	39	30	notice	notice	VERB
aiti-203	39	31	that	that	SCONJ
aiti-203	39	32	this	this	DET
aiti-203	39	33	equation	equation	NOUN
aiti-203	39	34	has	have	VERB
aiti-203	39	35	degree	degree	NOUN
aiti-203	39	36	5	5	NUM
aiti-203	39	37	in	in	ADP
aiti-203	39	38	t	t	PROPN
aiti-203	39	39	,	,	PUNCT
aiti-203	39	40	which	which	PRON
aiti-203	39	41	means	mean	VERB
aiti-203	39	42	there	there	PRON
aiti-203	39	43	are	be	VERB
aiti-203	39	44	5	5	NUM
aiti-203	39	45	local	local	ADJ
aiti-203	39	46	maximum	maximum	ADJ
aiti-203	39	47	/	/	SYM
aiti-203	39	48	minimum	minimum	ADJ
aiti-203	39	49	curvatures	curvature	NOUN
aiti-203	39	50	on	on	ADP
aiti-203	39	51	the	the	DET
aiti-203	39	52	curve	curve	NOUN
aiti-203	39	53	.	.	PUNCT
aiti-203	40	1	the	the	DET
aiti-203	40	2	ma	ma	PROPN
aiti-203	40	3	is	be	AUX
aiti-203	40	4	very	very	ADV
aiti-203	40	5	sensitive	sensitive	ADJ
aiti-203	40	6	to	to	ADP
aiti-203	40	7	its	its	PRON
aiti-203	40	8	boundary	boundary	NOUN
aiti-203	40	9	,	,	PUNCT
aiti-203	40	10	so	so	ADV
aiti-203	40	11	many	many	ADJ
aiti-203	40	12	researcher	researcher	NOUN
aiti-203	40	13	use	use	NOUN
aiti-203	40	14	approximated	approximate	VERB
aiti-203	40	15	ma	ma	PROPN
aiti-203	40	16	instead	instead	ADV
aiti-203	40	17	.	.	PUNCT
aiti-203	41	1	in	in	ADP
aiti-203	41	2	pattern	pattern	NOUN
aiti-203	41	3	recognition	recognition	NOUN
aiti-203	41	4	,	,	PUNCT
aiti-203	41	5	the	the	DET
aiti-203	41	6	important	important	ADJ
aiti-203	41	7	information	information	NOUN
aiti-203	41	8	for	for	ADP
aiti-203	41	9	the	the	DET
aiti-203	41	10	region	region	NOUN
aiti-203	41	11	is	be	AUX
aiti-203	41	12	easier	easy	ADJ
aiti-203	41	13	to	to	PART
aiti-203	41	14	capture	capture	VERB
aiti-203	41	15	by	by	ADP
aiti-203	41	16	using	use	VERB
aiti-203	41	17	approximated	approximate	VERB
aiti-203	41	18	ma	ma	PROPN
aiti-203	41	19	.	.	PROPN
aiti-203	42	1	although	although	SCONJ
aiti-203	42	2	it	it	PRON
aiti-203	42	3	could	could	AUX
aiti-203	42	4	have	have	VERB
aiti-203	42	5	more	more	ADJ
aiti-203	42	6	than	than	ADP
aiti-203	42	7	one	one	NUM
aiti-203	42	8	local	local	ADJ
aiti-203	42	9	maximum	maximum	ADJ
aiti-203	42	10	curvature	curvature	NOUN
aiti-203	42	11	in	in	ADP
aiti-203	42	12	our	our	PRON
aiti-203	42	13	region	region	NOUN
aiti-203	42	14	,	,	PUNCT
aiti-203	42	15	which	which	PRON
aiti-203	42	16	means	mean	VERB
aiti-203	42	17	more	more	ADJ
aiti-203	42	18	than	than	ADP
aiti-203	42	19	one	one	NUM
aiti-203	42	20	end	end	NOUN
aiti-203	42	21	point	point	NOUN
aiti-203	42	22	of	of	ADP
aiti-203	42	23	the	the	DET
aiti-203	42	24	mat	mat	NOUN
aiti-203	42	25	in	in	ADP
aiti-203	42	26	the	the	DET
aiti-203	42	27	region	region	NOUN
aiti-203	42	28	,	,	PUNCT
aiti-203	42	29	we	we	PRON
aiti-203	42	30	would	would	AUX
aiti-203	42	31	like	like	VERB
aiti-203	42	32	to	to	PART
aiti-203	42	33	find	find	VERB
aiti-203	42	34	one	one	NUM
aiti-203	42	35	endpoint	endpoint	NOUN
aiti-203	42	36	in	in	ADP
aiti-203	42	37	the	the	DET
aiti-203	42	38	region	region	NOUN
aiti-203	42	39	,	,	PUNCT
aiti-203	42	40	so	so	SCONJ
aiti-203	42	41	that	that	SCONJ
aiti-203	42	42	the	the	DET
aiti-203	42	43	ma	ma	PROPN
aiti-203	42	44	of	of	ADP
aiti-203	42	45	the	the	DET
aiti-203	42	46	region	region	NOUN
aiti-203	42	47	has	have	VERB
aiti-203	42	48	only	only	ADV
aiti-203	42	49	two	two	NUM
aiti-203	42	50	end	end	NOUN
aiti-203	42	51	points	point	NOUN
aiti-203	42	52	(	(	PUNCT
aiti-203	42	53	one	one	NOUN
aiti-203	42	54	is	be	AUX
aiti-203	42	55	on	on	ADP
aiti-203	42	56	the	the	DET
aiti-203	42	57	singular	singular	ADJ
aiti-203	42	58	point	point	NOUN
aiti-203	42	59	,	,	PUNCT
aiti-203	42	60	or	or	CCONJ
aiti-203	42	61	the	the	DET
aiti-203	42	62	center	center	NOUN
aiti-203	42	63	of	of	ADP
aiti-203	42	64	the	the	DET
aiti-203	42	65	osculating	osculating	NOUN
aiti-203	42	66	circle	circle	NOUN
aiti-203	42	67	associated	associate	VERB
aiti-203	42	68	with	with	ADP
aiti-203	42	69	the	the	DET
aiti-203	42	70	boundary	boundary	ADJ
aiti-203	42	71	curve	curve	NOUN
aiti-203	42	72	with	with	ADP
aiti-203	42	73	local	local	ADJ
aiti-203	42	74	maximum	maximum	ADJ
aiti-203	42	75	curvature	curvature	NOUN
aiti-203	42	76	,	,	PUNCT
aiti-203	42	77	the	the	DET
aiti-203	42	78	other	other	ADJ
aiti-203	42	79	one	one	NOUN
aiti-203	42	80	is	be	AUX
aiti-203	42	81	on	on	ADP
aiti-203	42	82	the	the	DET
aiti-203	42	83	origin	origin	NOUN
aiti-203	42	84	)	)	PUNCT
aiti-203	42	85	.	.	PUNCT
aiti-203	43	1	in	in	ADP
aiti-203	43	2	this	this	DET
aiti-203	43	3	paper	paper	NOUN
aiti-203	43	4	,	,	PUNCT
aiti-203	43	5	we	we	PRON
aiti-203	43	6	use	use	VERB
aiti-203	43	7	ma	ma	PROPN
aiti-203	43	8	to	to	PART
aiti-203	43	9	represent	represent	VERB
aiti-203	43	10	the	the	DET
aiti-203	43	11	approximated	approximate	VERB
aiti-203	43	12	ma	ma	PROPN
aiti-203	43	13	.	.	PUNCT
aiti-203	44	1	we	we	PRON
aiti-203	44	2	start	start	VERB
aiti-203	44	3	simple	simple	ADJ
aiti-203	44	4	case	case	NOUN
aiti-203	44	5	here	here	ADV
aiti-203	44	6	.	.	PUNCT
aiti-203	45	1	let	let	VERB
aiti-203	45	2	’s	’s	PRON
aiti-203	45	3	start	start	VERB
aiti-203	45	4	from	from	ADP
aiti-203	45	5	the	the	DET
aiti-203	45	6	case	case	NOUN
aiti-203	45	7	α0	α0	VERB
aiti-203	45	8	=	=	SYM
aiti-203	45	9	α1	α1	NOUN
aiti-203	45	10	=	=	SYM
aiti-203	46	1	α	α	NOUN
aiti-203	46	2	.	.	PUNCT
aiti-203	47	1	let	let	VERB
aiti-203	47	2	’s	’s	NOUN
aiti-203	47	3	also	also	ADV
aiti-203	47	4	assume	assume	VERB
aiti-203	47	5	that	that	SCONJ
aiti-203	47	6	all	all	DET
aiti-203	47	7	points	point	NOUN
aiti-203	47	8	on	on	ADP
aiti-203	47	9	the	the	DET
aiti-203	47	10	curve	curve	NOUN
aiti-203	47	11	is	be	AUX
aiti-203	47	12	outside	outside	ADP
aiti-203	47	13	the	the	DET
aiti-203	47	14	unit	unit	NOUN
aiti-203	47	15	circle	circle	NOUN
aiti-203	47	16	and	and	CCONJ
aiti-203	47	17	the	the	DET
aiti-203	47	18	curve	curve	NOUN
aiti-203	47	19	has	have	VERB
aiti-203	47	20	no	no	DET
aiti-203	47	21	self	self	NOUN
aiti-203	47	22	-	-	PUNCT
aiti-203	47	23	intersection	intersection	NOUN
aiti-203	47	24	.	.	PUNCT
aiti-203	48	1	the	the	DET
aiti-203	48	2	ma	ma	PROPN
aiti-203	48	3	of	of	ADP
aiti-203	48	4	a	a	DET
aiti-203	48	5	region	region	NOUN
aiti-203	48	6	is	be	AUX
aiti-203	48	7	easy	easy	ADJ
aiti-203	48	8	to	to	PART
aiti-203	48	9	find	find	VERB
aiti-203	48	10	if	if	SCONJ
aiti-203	48	11	we	we	PRON
aiti-203	48	12	know	know	VERB
aiti-203	48	13	the	the	DET
aiti-203	48	14	region	region	NOUN
aiti-203	48	15	is	be	AUX
aiti-203	48	16	symmetric	symmetric	ADJ
aiti-203	48	17	to	to	ADP
aiti-203	48	18	a	a	DET
aiti-203	48	19	line	line	NOUN
aiti-203	48	20	,	,	PUNCT
aiti-203	48	21	so	so	SCONJ
aiti-203	48	22	we	we	PRON
aiti-203	48	23	have	have	VERB
aiti-203	48	24	the	the	DET
aiti-203	48	25	following	follow	VERB
aiti-203	48	26	theorem	theorem	NOUN
aiti-203	48	27	:	:	PUNCT
aiti-203	48	28	theorem	theorem	NOUN
aiti-203	48	29	3	3	NUM
aiti-203	48	30	:	:	PUNCT
aiti-203	48	31	the	the	DET
aiti-203	48	32	curve	curve	NOUN
aiti-203	48	33	c(t)=h1(t;θ	c(t)=h1(t;θ	PROPN
aiti-203	48	34	,	,	PUNCT
aiti-203	48	35	α	α	NOUN
aiti-203	48	36	,	,	PUNCT
aiti-203	48	37	α	α	NOUN
aiti-203	48	38	)	)	PUNCT
aiti-203	48	39	is	be	AUX
aiti-203	48	40	symmetric	symmetric	ADJ
aiti-203	48	41	to	to	ADP
aiti-203	48	42	the	the	DET
aiti-203	48	43	line	line	NOUN
aiti-203	48	44	y=	y=	PRON
aiti-203	48	45	(	(	PUNCT
aiti-203	48	46	−tan	−tan	X
aiti-203	48	47	θ	θ	NOUN
aiti-203	48	48	2	2	NUM
aiti-203	48	49	)	)	PUNCT
aiti-203	48	50	x.	x.	NOUN
aiti-203	49	1	furthermore	furthermore	ADV
aiti-203	49	2	,	,	PUNCT
aiti-203	49	3	c(t	c(t	PROPN
aiti-203	49	4	)	)	PUNCT
aiti-203	49	5	and	and	CCONJ
aiti-203	49	6	c(1	c(1	PROPN
aiti-203	49	7	-	-	PUNCT
aiti-203	49	8	t	t	PROPN
aiti-203	49	9	)	)	PUNCT
aiti-203	49	10	are	be	AUX
aiti-203	49	11	symmetric	symmetric	ADJ
aiti-203	49	12	points	point	NOUN
aiti-203	49	13	.	.	PUNCT
aiti-203	50	1	proof	proof	NOUN
aiti-203	50	2	:	:	PUNCT
aiti-203	50	3	let	let	VERB
aiti-203	50	4	t	t	NOUN
aiti-203	50	5	=	=	PUNCT
aiti-203	50	6	tan	tan	PROPN
aiti-203	50	7	θ	θ	PROPN
aiti-203	50	8	2	2	NUM
aiti-203	50	9	,	,	PUNCT
aiti-203	50	10	we	we	PRON
aiti-203	50	11	have	have	VERB
aiti-203	50	12	c(t)+c(1−t	c(t)+c(1−t	NOUN
aiti-203	50	13	)	)	PUNCT
aiti-203	50	14	2	2	NUM
aiti-203	50	15	=	=	SYM
aiti-203	50	16	αtt(t−1)−1	αtt(t−1)−1	NOUN
aiti-203	50	17	1+t2	1+t2	NUM
aiti-203	50	18	.	.	PUNCT
aiti-203	51	1	obviously	obviously	ADV
aiti-203	51	2	,	,	PUNCT
aiti-203	51	3	this	this	DET
aiti-203	51	4	point	point	NOUN
aiti-203	51	5	is	be	AUX
aiti-203	51	6	on	on	ADP
aiti-203	51	7	the	the	DET
aiti-203	51	8	line	line	NOUN
aiti-203	51	9	y	y	PROPN
aiti-203	51	10	=	=	PROPN
aiti-203	51	11	tx	tx	PROPN
aiti-203	51	12	.	.	PUNCT
aiti-203	52	1	notice	notice	VERB
aiti-203	52	2	that	that	SCONJ
aiti-203	52	3	this	this	DET
aiti-203	52	4	line	line	NOUN
aiti-203	52	5	y	y	PROPN
aiti-203	52	6	=	=	ADJ
aiti-203	52	7	tx	tx	ADP
aiti-203	52	8	passing	pass	VERB
aiti-203	52	9	through	through	ADP
aiti-203	52	10	c(1/2	c(1/2	NOUN
aiti-203	52	11	)	)	PUNCT
aiti-203	52	12	.	.	PUNCT
aiti-203	53	1	notice	notice	VERB
aiti-203	53	2	further	far	ADV
aiti-203	53	3	that	that	SCONJ
aiti-203	53	4	because	because	SCONJ
aiti-203	53	5	c(t	c(t	PROPN
aiti-203	53	6	)	)	PUNCT
aiti-203	53	7	and	and	CCONJ
aiti-203	53	8	c(1	c(1	PROPN
aiti-203	53	9	-	-	PUNCT
aiti-203	53	10	t	t	PROPN
aiti-203	53	11	)	)	PUNCT
aiti-203	53	12	are	be	AUX
aiti-203	53	13	symmetric	symmetric	ADJ
aiti-203	53	14	points	point	NOUN
aiti-203	53	15	,	,	PUNCT
aiti-203	53	16	so	so	SCONJ
aiti-203	53	17	the	the	DET
aiti-203	53	18	point	point	NOUN
aiti-203	53	19	c(1/2	c(1/2	NOUN
aiti-203	53	20	)	)	PUNCT
aiti-203	53	21	is	be	AUX
aiti-203	53	22	a	a	DET
aiti-203	53	23	singular	singular	ADJ
aiti-203	53	24	point	point	NOUN
aiti-203	53	25	,	,	PUNCT
aiti-203	53	26	or	or	CCONJ
aiti-203	53	27	c(t	c(t	PROPN
aiti-203	53	28	)	)	PUNCT
aiti-203	53	29	is	be	AUX
aiti-203	53	30	a	a	DET
aiti-203	53	31	vertex	vertex	NOUN
aiti-203	53	32	of	of	ADP
aiti-203	53	33	the	the	DET
aiti-203	53	34	curve	curve	NOUN
aiti-203	53	35	,	,	PUNCT
aiti-203	53	36	which	which	PRON
aiti-203	53	37	means	mean	VERB
aiti-203	53	38	c(1/2	c(1/2	NOUN
aiti-203	53	39	)	)	PUNCT
aiti-203	53	40	is	be	AUX
aiti-203	53	41	a	a	DET
aiti-203	53	42	singular	singular	ADJ
aiti-203	53	43	point	point	NOUN
aiti-203	53	44	,	,	PUNCT
aiti-203	53	45	or	or	CCONJ
aiti-203	53	46	has	have	VERB
aiti-203	53	47	constant	constant	ADJ
aiti-203	53	48	curvature	curvature	NOUN
aiti-203	53	49	,	,	PUNCT
aiti-203	53	50	or	or	CCONJ
aiti-203	53	51	has	have	VERB
aiti-203	53	52	local	local	ADJ
aiti-203	53	53	maximum	maximum	ADJ
aiti-203	53	54	/	/	SYM
aiti-203	53	55	minimum	minimum	ADJ
aiti-203	53	56	curvature	curvature	NOUN
aiti-203	53	57	.	.	PUNCT
aiti-203	54	1	with	with	ADP
aiti-203	54	2	the	the	DET
aiti-203	54	3	symmetric	symmetric	ADJ
aiti-203	54	4	property	property	NOUN
aiti-203	54	5	,	,	PUNCT
aiti-203	54	6	we	we	PRON
aiti-203	54	7	know	know	VERB
aiti-203	54	8	the	the	DET
aiti-203	54	9	ma	ma	PROPN
aiti-203	54	10	of	of	ADP
aiti-203	54	11	the	the	DET
aiti-203	54	12	region	region	NOUN
aiti-203	54	13	is	be	AUX
aiti-203	54	14	on	on	ADP
aiti-203	54	15	the	the	DET
aiti-203	54	16	line	line	NOUN
aiti-203	54	17	(	(	PUNCT
aiti-203	54	18	−tan	−tan	X
aiti-203	54	19	θ	θ	NOUN
aiti-203	54	20	2	2	NUM
aiti-203	54	21	)	)	PUNCT
aiti-203	54	22	x.	x.	NOUN
aiti-203	55	1	we	we	PRON
aiti-203	55	2	would	would	AUX
aiti-203	55	3	like	like	VERB
aiti-203	55	4	to	to	PART
aiti-203	55	5	find	find	VERB
aiti-203	55	6	the	the	DET
aiti-203	55	7	ma	ma	PROPN
aiti-203	55	8	point	point	NOUN
aiti-203	55	9	from	from	ADP
aiti-203	55	10	its	its	PRON
aiti-203	55	11	footpoint	footpoint	NOUN
aiti-203	55	12	c(t	c(t	NOUN
aiti-203	55	13	)	)	PUNCT
aiti-203	55	14	or	or	CCONJ
aiti-203	55	15	c(1	c(1	PROPN
aiti-203	55	16	-	-	PUNCT
aiti-203	55	17	t	t	PROPN
aiti-203	55	18	)	)	PUNCT
aiti-203	55	19	,	,	PUNCT
aiti-203	55	20	we	we	PRON
aiti-203	55	21	have	have	VERB
aiti-203	55	22	the	the	DET
aiti-203	55	23	following	follow	VERB
aiti-203	55	24	theorem	theorem	NOUN
aiti-203	55	25	:	:	PUNCT
aiti-203	55	26	theorem	theorem	NOUN
aiti-203	55	27	4	4	NUM
aiti-203	55	28	:	:	PUNCT
aiti-203	55	29	the	the	DET
aiti-203	55	30	medial	medial	ADJ
aiti-203	55	31	axis	axis	NOUN
aiti-203	55	32	(	(	PUNCT
aiti-203	55	33	xm	xm	PROPN
aiti-203	55	34	,	,	PUNCT
aiti-203	55	35	ym	ym	PROPN
aiti-203	55	36	)	)	PUNCT
aiti-203	55	37	associated	associate	VERB
aiti-203	55	38	with	with	ADP
aiti-203	55	39	c(t)=(x(t),y(t	c(t)=(x(t),y(t	NOUN
aiti-203	55	40	)	)	PUNCT
aiti-203	55	41	)	)	PUNCT
aiti-203	55	42	,	,	PUNCT
aiti-203	55	43	where	where	SCONJ
aiti-203	55	44	0	0	X
aiti-203	55	45	<	<	X
aiti-203	55	46	t<1/2	t<1/2	X
aiti-203	55	47	is	be	AUX
aiti-203	55	48	(	(	PUNCT
aiti-203	55	49	to	to	PART
aiti-203	55	50	simplify	simplify	VERB
aiti-203	55	51	the	the	DET
aiti-203	55	52	representation	representation	NOUN
aiti-203	55	53	of	of	ADP
aiti-203	55	54	the	the	DET
aiti-203	55	55	equation	equation	NOUN
aiti-203	55	56	,	,	PUNCT
aiti-203	55	57	we	we	PRON
aiti-203	55	58	eliminate	eliminate	VERB
aiti-203	55	59	the	the	DET
aiti-203	55	60	parameter	parameter	NOUN
aiti-203	55	61	t	t	PROPN
aiti-203	55	62	for	for	ADP
aiti-203	55	63	x	x	PROPN
aiti-203	55	64	,	,	PUNCT
aiti-203	55	65	y	y	PROPN
aiti-203	55	66	,	,	PUNCT
aiti-203	55	67	x′	x′	NUM
aiti-203	55	68	,	,	PUNCT
aiti-203	55	69	y′	y′	NUM
aiti-203	55	70	,	,	PUNCT
aiti-203	55	71	xm	xm	PROPN
aiti-203	55	72	,	,	PUNCT
aiti-203	55	73	ym	ym	PROPN
aiti-203	55	74	and	and	CCONJ
aiti-203	55	75	rm	rm	PROPN
aiti-203	55	76	):	):	PUNCT
aiti-203	55	77	(	(	PUNCT
aiti-203	55	78	xm	xm	PROPN
aiti-203	55	79	,	,	PUNCT
aiti-203	55	80	ym	ym	PROPN
aiti-203	55	81	)	)	PUNCT
aiti-203	55	82	=	=	SYM
aiti-203	55	83	(	(	PUNCT
aiti-203	55	84	x	x	X
aiti-203	55	85	,	,	PUNCT
aiti-203	55	86	y)∙(x′,y′	y)∙(x′,y′	NUM
aiti-203	55	87	)	)	PUNCT
aiti-203	55	88	(	(	PUNCT
aiti-203	55	89	1,t)∙(x′,y′	1,t)∙(x′,y′	NUM
aiti-203	55	90	)	)	PUNCT
aiti-203	55	91	(	(	PUNCT
aiti-203	55	92	1,t	1,t	NOUN
aiti-203	55	93	)	)	PUNCT
aiti-203	55	94	and	and	CCONJ
aiti-203	55	95	rm	rm	NOUN
aiti-203	55	96	=	=	SYM
aiti-203	56	1	|	|	INTJ
aiti-203	56	2	(	(	PUNCT
aiti-203	56	3	1,t)∙(−y	1,t)∙(−y	NUM
aiti-203	56	4	,	,	PUNCT
aiti-203	56	5	x	x	X
aiti-203	56	6	)	)	PUNCT
aiti-203	56	7	(	(	PUNCT
aiti-203	56	8	1,t)∙(x′,y′	1,t)∙(x′,y′	NUM
aiti-203	56	9	)	)	PUNCT
aiti-203	56	10	|	|	ADV
aiti-203	56	11	‖(x′	‖(x′	ADV
aiti-203	56	12	,	,	PUNCT
aiti-203	56	13	y′)‖	y′)‖	NUM
aiti-203	56	14	where	where	SCONJ
aiti-203	56	15	∙	∙	PROPN
aiti-203	56	16	is	be	AUX
aiti-203	56	17	the	the	DET
aiti-203	56	18	inner	inner	ADJ
aiti-203	56	19	product	product	NOUN
aiti-203	56	20	of	of	ADP
aiti-203	56	21	two	two	NUM
aiti-203	56	22	vectors	vector	NOUN
aiti-203	56	23	,	,	PUNCT
aiti-203	56	24	|a|	|a|	PROPN
aiti-203	56	25	is	be	AUX
aiti-203	56	26	the	the	DET
aiti-203	56	27	absolute	absolute	ADJ
aiti-203	56	28	value	value	NOUN
aiti-203	56	29	of	of	ADP
aiti-203	56	30	a	a	PRON
aiti-203	56	31	,	,	PUNCT
aiti-203	56	32	and	and	CCONJ
aiti-203	56	33	||(x	||(x	NOUN
aiti-203	56	34	,	,	PUNCT
aiti-203	56	35	y)||	y)||	PROPN
aiti-203	56	36	is	be	AUX
aiti-203	56	37	the	the	DET
aiti-203	56	38	norm	norm	NOUN
aiti-203	56	39	of	of	ADP
aiti-203	56	40	the	the	DET
aiti-203	56	41	vector	vector	NOUN
aiti-203	56	42	,	,	PUNCT
aiti-203	56	43	t=−tan	t=−tan	PUNCT
aiti-203	56	44	θ	θ	NOUN
aiti-203	56	45	2	2	NUM
aiti-203	56	46	.	.	PUNCT
aiti-203	57	1	with	with	ADP
aiti-203	57	2	the	the	DET
aiti-203	57	3	ma	ma	PROPN
aiti-203	57	4	point	point	NOUN
aiti-203	57	5	and	and	CCONJ
aiti-203	57	6	its	its	PRON
aiti-203	57	7	distance	distance	NOUN
aiti-203	57	8	to	to	ADP
aiti-203	57	9	its	its	PRON
aiti-203	57	10	footpoint	footpoint	NOUN
aiti-203	57	11	,	,	PUNCT
aiti-203	57	12	we	we	PRON
aiti-203	57	13	find	find	VERB
aiti-203	57	14	mat	mat	NOUN
aiti-203	57	15	of	of	ADP
aiti-203	57	16	the	the	DET
aiti-203	57	17	region	region	NOUN
aiti-203	57	18	.	.	PUNCT
aiti-203	58	1	we	we	PRON
aiti-203	58	2	also	also	ADV
aiti-203	58	3	call	call	VERB
aiti-203	58	4	mat	mat	NOUN
aiti-203	58	5	the	the	DET
aiti-203	58	6	medial	medial	ADJ
aiti-203	58	7	axis	axis	NOUN
aiti-203	58	8	circles	circle	NOUN
aiti-203	58	9	in	in	ADP
aiti-203	58	10	this	this	DET
aiti-203	58	11	paper	paper	NOUN
aiti-203	58	12	.	.	PUNCT
aiti-203	59	1	notice	notice	VERB
aiti-203	59	2	that	that	SCONJ
aiti-203	59	3	(	(	PUNCT
aiti-203	59	4	xm(0	xm(0	NOUN
aiti-203	59	5	)	)	PUNCT
aiti-203	59	6	,	,	PUNCT
aiti-203	59	7	ym(0	ym(0	NOUN
aiti-203	59	8	)	)	PUNCT
aiti-203	59	9	)	)	PUNCT
aiti-203	60	1	=	=	SYM
aiti-203	60	2	(	(	PUNCT
aiti-203	60	3	xm(1	xm(1	PROPN
aiti-203	60	4	)	)	PUNCT
aiti-203	60	5	,	,	PUNCT
aiti-203	60	6	ym(1))=(0,0	ym(1))=(0,0	NOUN
aiti-203	60	7	)	)	PUNCT
aiti-203	60	8	.	.	PUNCT
aiti-203	61	1	3	3	X
aiti-203	61	2	.	.	X
aiti-203	61	3	algorithm	algorithm	NOUN
aiti-203	61	4	and	and	CCONJ
aiti-203	61	5	experimental	experimental	ADJ
aiti-203	61	6	result	result	NOUN
aiti-203	61	7	in	in	ADP
aiti-203	61	8	this	this	DET
aiti-203	61	9	paper	paper	NOUN
aiti-203	61	10	,	,	PUNCT
aiti-203	61	11	we	we	PRON
aiti-203	61	12	want	want	AUX
aiti-203	61	13	find	find	VERB
aiti-203	61	14	the	the	DET
aiti-203	61	15	medial	medial	ADJ
aiti-203	61	16	axis	axis	NOUN
aiti-203	61	17	circles	circle	NOUN
aiti-203	61	18	inside	inside	ADP
aiti-203	61	19	the	the	DET
aiti-203	61	20	region	region	NOUN
aiti-203	61	21	,	,	PUNCT
aiti-203	61	22	and	and	CCONJ
aiti-203	61	23	all	all	DET
aiti-203	61	24	medial	medial	ADJ
aiti-203	61	25	axis	axis	NOUN
aiti-203	61	26	advances	advance	NOUN
aiti-203	61	27	in	in	ADP
aiti-203	61	28	technology	technology	NOUN
aiti-203	61	29	innovation	innovation	NOUN
aiti-203	61	30	,	,	PUNCT
aiti-203	61	31	vol	vol	NOUN
aiti-203	61	32	.	.	PROPN
aiti-203	62	1	2	2	NUM
aiti-203	62	2	,	,	PUNCT
aiti-203	62	3	no	no	INTJ
aiti-203	62	4	.	.	NOUN
aiti-203	62	5	1	1	NUM
aiti-203	62	6	,	,	PUNCT
aiti-203	62	7	2017	2017	NUM
aiti-203	62	8	,	,	PUNCT
aiti-203	62	9	pp	pp	ADV
aiti-203	62	10	.	.	PUNCT
aiti-203	63	1	08	08	NUM
aiti-203	63	2	12	12	NUM
aiti-203	63	3	10	10	NUM
aiti-203	63	4	copyright	copyright	NOUN
aiti-203	63	5	©	©	PROPN
aiti-203	63	6	taeti	taeti	PROPN
aiti-203	63	7	circles	circle	NOUN
aiti-203	63	8	tangent	tangent	VERB
aiti-203	63	9	with	with	ADP
aiti-203	63	10	its	its	PRON
aiti-203	63	11	neighbors	neighbor	NOUN
aiti-203	63	12	.	.	PUNCT
aiti-203	64	1	in	in	ADP
aiti-203	64	2	our	our	PRON
aiti-203	64	3	assumption	assumption	NOUN
aiti-203	64	4	,	,	PUNCT
aiti-203	64	5	we	we	PRON
aiti-203	64	6	can	can	AUX
aiti-203	64	7	always	always	ADV
aiti-203	64	8	find	find	VERB
aiti-203	64	9	one	one	NUM
aiti-203	64	10	end	end	NOUN
aiti-203	64	11	points	point	NOUN
aiti-203	64	12	of	of	ADP
aiti-203	64	13	the	the	DET
aiti-203	64	14	mat	mat	NOUN
aiti-203	64	15	.	.	PUNCT
aiti-203	65	1	in	in	ADP
aiti-203	65	2	some	some	DET
aiti-203	65	3	case	case	NOUN
aiti-203	65	4	,	,	PUNCT
aiti-203	65	5	there	there	PRON
aiti-203	65	6	is	be	VERB
aiti-203	65	7	singular	singular	ADJ
aiti-203	65	8	point	point	NOUN
aiti-203	65	9	exist	exist	VERB
aiti-203	65	10	,	,	PUNCT
aiti-203	65	11	the	the	DET
aiti-203	65	12	singular	singular	ADJ
aiti-203	65	13	point	point	NOUN
aiti-203	65	14	is	be	AUX
aiti-203	65	15	the	the	DET
aiti-203	65	16	end	end	NOUN
aiti-203	65	17	point	point	NOUN
aiti-203	65	18	of	of	ADP
aiti-203	65	19	the	the	DET
aiti-203	65	20	mat	mat	NOUN
aiti-203	65	21	branch	branch	NOUN
aiti-203	65	22	(	(	PUNCT
aiti-203	65	23	the	the	DET
aiti-203	65	24	other	other	ADJ
aiti-203	65	25	one	one	NOUN
aiti-203	65	26	is	be	AUX
aiti-203	65	27	on	on	ADP
aiti-203	65	28	the	the	DET
aiti-203	65	29	origin	origin	NOUN
aiti-203	65	30	)	)	PUNCT
aiti-203	65	31	.	.	PUNCT
aiti-203	66	1	on	on	ADP
aiti-203	66	2	the	the	DET
aiti-203	66	3	other	other	ADJ
aiti-203	66	4	case	case	NOUN
aiti-203	66	5	,	,	PUNCT
aiti-203	66	6	we	we	PRON
aiti-203	66	7	can	can	AUX
aiti-203	66	8	always	always	ADV
aiti-203	66	9	find	find	VERB
aiti-203	66	10	a	a	DET
aiti-203	66	11	point	point	NOUN
aiti-203	66	12	with	with	ADP
aiti-203	66	13	local	local	ADJ
aiti-203	66	14	maximum	maximum	ADJ
aiti-203	66	15	curvature	curvature	NOUN
aiti-203	66	16	;	;	PUNCT
aiti-203	66	17	we	we	PRON
aiti-203	66	18	use	use	VERB
aiti-203	66	19	the	the	DET
aiti-203	66	20	center	center	NOUN
aiti-203	66	21	of	of	ADP
aiti-203	66	22	its	its	PRON
aiti-203	66	23	osculating	osculating	NOUN
aiti-203	66	24	circle	circle	NOUN
aiti-203	66	25	as	as	ADP
aiti-203	66	26	the	the	DET
aiti-203	66	27	end	end	NOUN
aiti-203	66	28	point	point	NOUN
aiti-203	66	29	of	of	ADP
aiti-203	66	30	the	the	DET
aiti-203	66	31	mat	mat	NOUN
aiti-203	66	32	branch	branch	NOUN
aiti-203	66	33	.	.	PUNCT
aiti-203	67	1	how	how	SCONJ
aiti-203	67	2	to	to	PART
aiti-203	67	3	find	find	VERB
aiti-203	67	4	normal	normal	ADJ
aiti-203	67	5	point	point	NOUN
aiti-203	67	6	of	of	ADP
aiti-203	67	7	the	the	DET
aiti-203	67	8	mat	mat	NOUN
aiti-203	67	9	?	?	PUNCT
aiti-203	67	10	consider	consider	VERB
aiti-203	67	11	the	the	DET
aiti-203	67	12	end	end	NOUN
aiti-203	67	13	ma	ma	PROPN
aiti-203	67	14	point	point	NOUN
aiti-203	67	15	we	we	PRON
aiti-203	67	16	find	find	VERB
aiti-203	67	17	,	,	PUNCT
aiti-203	67	18	either	either	CCONJ
aiti-203	67	19	singular	singular	ADJ
aiti-203	67	20	point	point	NOUN
aiti-203	67	21	or	or	CCONJ
aiti-203	67	22	points	point	NOUN
aiti-203	67	23	with	with	ADP
aiti-203	67	24	local	local	ADJ
aiti-203	67	25	maximum	maximum	ADJ
aiti-203	67	26	curvature	curvature	NOUN
aiti-203	67	27	.	.	PUNCT
aiti-203	68	1	assume	assume	VERB
aiti-203	68	2	it	it	PRON
aiti-203	68	3	has	have	VERB
aiti-203	68	4	parameter	parameter	NOUN
aiti-203	68	5	tend	tend	NOUN
aiti-203	68	6	,	,	PUNCT
aiti-203	69	1	0	0	NUM
aiti-203	69	2	<	<	X
aiti-203	69	3	tend<1	tend<1	NOUN
aiti-203	69	4	,	,	PUNCT
aiti-203	69	5	c(t)=(x(t),y(t	c(t)=(x(t),y(t	NOUN
aiti-203	69	6	)	)	PUNCT
aiti-203	69	7	)	)	PUNCT
aiti-203	70	1	and	and	CCONJ
aiti-203	70	2	we	we	PRON
aiti-203	70	3	want	want	AUX
aiti-203	70	4	find	find	VERB
aiti-203	70	5	t1	t1	NOUN
aiti-203	70	6	and	and	CCONJ
aiti-203	70	7	t2	t2	NOUN
aiti-203	70	8	,	,	PUNCT
aiti-203	70	9	0	0	NUM
aiti-203	70	10	<	<	X
aiti-203	70	11	t0	t0	NOUN
aiti-203	70	12	<	<	X
aiti-203	70	13	tend	tend	VERB
aiti-203	70	14	and	and	CCONJ
aiti-203	70	15	tend	tend	VERB
aiti-203	70	16	<	<	X
aiti-203	70	17	t1<1	t1<1	PROPN
aiti-203	70	18	,	,	PUNCT
aiti-203	70	19	so	so	SCONJ
aiti-203	70	20	that	that	PRON
aiti-203	70	21	c(t1	c(t1	NOUN
aiti-203	70	22	)	)	PUNCT
aiti-203	70	23	and	and	CCONJ
aiti-203	70	24	c(t2	c(t2	NOUN
aiti-203	70	25	)	)	PUNCT
aiti-203	70	26	are	be	AUX
aiti-203	70	27	footpoints	footpoint	NOUN
aiti-203	70	28	of	of	ADP
aiti-203	70	29	a	a	DET
aiti-203	70	30	ma	ma	PROPN
aiti-203	70	31	point	point	NOUN
aiti-203	70	32	(	(	PUNCT
aiti-203	70	33	x	x	X
aiti-203	70	34	,	,	PUNCT
aiti-203	70	35	y	y	PROPN
aiti-203	70	36	)	)	PUNCT
aiti-203	70	37	,	,	PUNCT
aiti-203	70	38	from	from	ADP
aiti-203	70	39	the	the	DET
aiti-203	70	40	property	property	NOUN
aiti-203	70	41	of	of	ADP
aiti-203	70	42	ma	ma	PROPN
aiti-203	70	43	point	point	NOUN
aiti-203	70	44	,	,	PUNCT
aiti-203	70	45	we	we	PRON
aiti-203	70	46	have	have	VERB
aiti-203	70	47	:	:	PUNCT
aiti-203	70	48	(	(	PUNCT
aiti-203	70	49	x	x	X
aiti-203	70	50	-	-	NOUN
aiti-203	70	51	x(t0),y	x(t0),y	NOUN
aiti-203	70	52	-	-	PUNCT
aiti-203	70	53	y(t0))․(x′(t0),y′(t0))=0	y(t0))․(x′(t0),y′(t0))=0	PROPN
aiti-203	70	54	(	(	PUNCT
aiti-203	70	55	x	x	NOUN
aiti-203	70	56	-	-	NOUN
aiti-203	70	57	x(t1),y	x(t1),y	NOUN
aiti-203	70	58	-	-	PUNCT
aiti-203	70	59	y(t1	y(t1	NOUN
aiti-203	70	60	)	)	PUNCT
aiti-203	70	61	)	)	PUNCT
aiti-203	71	1	․	․	VERB
aiti-203	71	2	(	(	PUNCT
aiti-203	71	3	x′(t1),y′(t1))=0	x′(t1),y′(t1))=0	PROPN
aiti-203	71	4	(	(	PUNCT
aiti-203	71	5	(	(	PUNCT
aiti-203	71	6	x	x	NOUN
aiti-203	71	7	-	-	NOUN
aiti-203	71	8	x(t0	x(t0	NOUN
aiti-203	71	9	)	)	PUNCT
aiti-203	71	10	)	)	PUNCT
aiti-203	71	11	2	2	NUM
aiti-203	72	1	+	+	ADJ
aiti-203	72	2	(	(	PUNCT
aiti-203	72	3	y	y	PROPN
aiti-203	72	4	-	-	PROPN
aiti-203	72	5	y(t0	y(t0	PROPN
aiti-203	72	6	)	)	PUNCT
aiti-203	72	7	)	)	PUNCT
aiti-203	72	8	2	2	NUM
aiti-203	72	9	=(	=(	NOUN
aiti-203	72	10	x	x	X
aiti-203	72	11	-	-	NOUN
aiti-203	72	12	x(t1	x(t1	X
aiti-203	72	13	)	)	PUNCT
aiti-203	72	14	)	)	PUNCT
aiti-203	72	15	2	2	NUM
aiti-203	73	1	+	+	ADJ
aiti-203	73	2	(	(	PUNCT
aiti-203	73	3	y	y	NOUN
aiti-203	73	4	-	-	PUNCT
aiti-203	73	5	y(t1	y(t1	NOUN
aiti-203	73	6	)	)	PUNCT
aiti-203	73	7	)	)	PUNCT
aiti-203	73	8	2	2	NUM
aiti-203	73	9	the	the	DET
aiti-203	73	10	first	first	ADJ
aiti-203	73	11	two	two	NUM
aiti-203	73	12	equations	equation	NOUN
aiti-203	73	13	indicates	indicate	VERB
aiti-203	73	14	that	that	SCONJ
aiti-203	73	15	the	the	DET
aiti-203	73	16	line	line	NOUN
aiti-203	73	17	through	through	ADP
aiti-203	73	18	ma	ma	PROPN
aiti-203	73	19	point	point	NOUN
aiti-203	73	20	and	and	CCONJ
aiti-203	73	21	its	its	PRON
aiti-203	73	22	footpoints	footpoint	NOUN
aiti-203	73	23	perpendicular	perpendicular	ADJ
aiti-203	73	24	to	to	ADP
aiti-203	73	25	tangent	tangent	NOUN
aiti-203	73	26	of	of	ADP
aiti-203	73	27	the	the	DET
aiti-203	73	28	footpoint	footpoint	NOUN
aiti-203	73	29	on	on	ADP
aiti-203	73	30	the	the	DET
aiti-203	73	31	curve	curve	NOUN
aiti-203	73	32	.	.	PUNCT
aiti-203	74	1	the	the	DET
aiti-203	74	2	third	third	ADJ
aiti-203	74	3	equation	equation	NOUN
aiti-203	74	4	indicates	indicate	VERB
aiti-203	74	5	that	that	SCONJ
aiti-203	74	6	the	the	DET
aiti-203	74	7	distances	distance	NOUN
aiti-203	74	8	from	from	ADP
aiti-203	74	9	ma	ma	PROPN
aiti-203	74	10	point	point	NOUN
aiti-203	74	11	to	to	ADP
aiti-203	74	12	its	its	PRON
aiti-203	74	13	two	two	NUM
aiti-203	74	14	footpoints	footpoint	NOUN
aiti-203	74	15	are	be	AUX
aiti-203	74	16	equal	equal	ADJ
aiti-203	74	17	.	.	PUNCT
aiti-203	75	1	now	now	ADV
aiti-203	75	2	we	we	PRON
aiti-203	75	3	have	have	VERB
aiti-203	75	4	3	3	NUM
aiti-203	75	5	equations	equation	NOUN
aiti-203	75	6	,	,	PUNCT
aiti-203	75	7	and	and	CCONJ
aiti-203	75	8	4	4	NUM
aiti-203	75	9	variables	variable	NOUN
aiti-203	75	10	,	,	PUNCT
aiti-203	75	11	which	which	PRON
aiti-203	75	12	are	be	AUX
aiti-203	75	13	x	x	X
aiti-203	75	14	,	,	PUNCT
aiti-203	75	15	y	y	PROPN
aiti-203	75	16	,	,	PUNCT
aiti-203	75	17	t0	t0	PROPN
aiti-203	75	18	and	and	CCONJ
aiti-203	75	19	t1	t1	NOUN
aiti-203	75	20	.	.	PUNCT
aiti-203	76	1	given	give	VERB
aiti-203	76	2	t0	t0	PROPN
aiti-203	76	3	,	,	PUNCT
aiti-203	76	4	we	we	PRON
aiti-203	76	5	can	can	AUX
aiti-203	76	6	find	find	VERB
aiti-203	76	7	the	the	DET
aiti-203	76	8	ma	ma	PROPN
aiti-203	76	9	point	point	NOUN
aiti-203	76	10	(	(	PUNCT
aiti-203	76	11	x	x	NOUN
aiti-203	76	12	,	,	PUNCT
aiti-203	76	13	y	y	PROPN
aiti-203	76	14	)	)	PUNCT
aiti-203	76	15	and	and	CCONJ
aiti-203	76	16	t1	t1	NOUN
aiti-203	76	17	.	.	PUNCT
aiti-203	77	1	the	the	DET
aiti-203	77	2	idea	idea	NOUN
aiti-203	77	3	to	to	PART
aiti-203	77	4	solve	solve	VERB
aiti-203	77	5	the	the	DET
aiti-203	77	6	system	system	NOUN
aiti-203	77	7	of	of	ADP
aiti-203	77	8	equation	equation	NOUN
aiti-203	77	9	is	be	AUX
aiti-203	77	10	:	:	PUNCT
aiti-203	77	11	algorithm	algorithm	NOUN
aiti-203	77	12	1	1	NUM
aiti-203	77	13	:	:	PUNCT
aiti-203	77	14	finding	find	VERB
aiti-203	77	15	one	one	NUM
aiti-203	77	16	ma	ma	PROPN
aiti-203	77	17	point	point	NOUN
aiti-203	77	18	.	.	PUNCT
aiti-203	78	1	1	1	X
aiti-203	78	2	.	.	X
aiti-203	78	3	solve	solve	VERB
aiti-203	78	4	(	(	PUNCT
aiti-203	78	5	x	x	NOUN
aiti-203	78	6	,	,	PUNCT
aiti-203	78	7	y	y	PROPN
aiti-203	78	8	)	)	PUNCT
aiti-203	78	9	by	by	ADP
aiti-203	78	10	cramer	cramer	PROPN
aiti-203	78	11	’s	’s	PART
aiti-203	78	12	rule	rule	NOUN
aiti-203	78	13	from	from	ADP
aiti-203	78	14	the	the	DET
aiti-203	78	15	first	first	ADJ
aiti-203	78	16	2	2	NUM
aiti-203	78	17	equations	equation	NOUN
aiti-203	78	18	,	,	PUNCT
aiti-203	78	19	and	and	CCONJ
aiti-203	78	20	x	x	X
aiti-203	78	21	,	,	PUNCT
aiti-203	78	22	y	y	PROPN
aiti-203	78	23	has	have	VERB
aiti-203	78	24	two	two	NUM
aiti-203	78	25	variables	variable	NOUN
aiti-203	78	26	t0	t0	PROPN
aiti-203	78	27	and	and	CCONJ
aiti-203	78	28	t1	t1	NOUN
aiti-203	78	29	.	.	PUNCT
aiti-203	79	1	2	2	X
aiti-203	79	2	.	.	X
aiti-203	79	3	substitute	substitute	VERB
aiti-203	79	4	the	the	DET
aiti-203	79	5	value	value	NOUN
aiti-203	79	6	x	x	NOUN
aiti-203	79	7	,	,	PUNCT
aiti-203	79	8	y	y	PROPN
aiti-203	79	9	into	into	ADP
aiti-203	79	10	the	the	DET
aiti-203	79	11	third	third	ADJ
aiti-203	79	12	equations	equation	NOUN
aiti-203	79	13	,	,	PUNCT
aiti-203	79	14	and	and	CCONJ
aiti-203	79	15	leave	leave	VERB
aiti-203	79	16	one	one	NUM
aiti-203	79	17	equation	equation	NOUN
aiti-203	79	18	with	with	ADP
aiti-203	79	19	2	2	NUM
aiti-203	79	20	variables	variable	NOUN
aiti-203	79	21	t0	t0	PROPN
aiti-203	79	22	and	and	CCONJ
aiti-203	79	23	t1	t1	NOUN
aiti-203	79	24	.	.	PUNCT
aiti-203	80	1	3	3	X
aiti-203	80	2	.	.	PUNCT
aiti-203	80	3	given	give	VERB
aiti-203	80	4	t0	t0	PRON
aiti-203	80	5	,	,	PUNCT
aiti-203	80	6	we	we	PRON
aiti-203	80	7	have	have	VERB
aiti-203	80	8	one	one	NUM
aiti-203	80	9	equation	equation	NOUN
aiti-203	80	10	with	with	ADP
aiti-203	80	11	one	one	NUM
aiti-203	80	12	variable	variable	NOUN
aiti-203	80	13	t1	t1	NOUN
aiti-203	80	14	,	,	PUNCT
aiti-203	80	15	so	so	SCONJ
aiti-203	80	16	we	we	PRON
aiti-203	80	17	can	can	AUX
aiti-203	80	18	find	find	VERB
aiti-203	80	19	solutions	solution	NOUN
aiti-203	80	20	for	for	ADP
aiti-203	80	21	t1	t1	PROPN
aiti-203	80	22	.	.	PUNCT
aiti-203	81	1	with	with	ADP
aiti-203	81	2	careful	careful	ADJ
aiti-203	81	3	selection	selection	NOUN
aiti-203	81	4	of	of	ADP
aiti-203	81	5	t1	t1	NOUN
aiti-203	81	6	,	,	PUNCT
aiti-203	81	7	we	we	PRON
aiti-203	81	8	find	find	VERB
aiti-203	81	9	the	the	DET
aiti-203	81	10	ma	ma	PROPN
aiti-203	81	11	points	point	NOUN
aiti-203	81	12	with	with	ADP
aiti-203	81	13	its	its	PRON
aiti-203	81	14	two	two	NUM
aiti-203	81	15	footpoints	footpoint	NOUN
aiti-203	81	16	.	.	PUNCT
aiti-203	82	1	the	the	DET
aiti-203	82	2	above	above	ADJ
aiti-203	82	3	idea	idea	NOUN
aiti-203	82	4	solves	solve	VERB
aiti-203	82	5	the	the	DET
aiti-203	82	6	mat	mat	NOUN
aiti-203	82	7	(	(	PUNCT
aiti-203	82	8	ma	ma	PROPN
aiti-203	82	9	with	with	ADP
aiti-203	82	10	radius	radius	NOUN
aiti-203	82	11	function	function	NOUN
aiti-203	82	12	)	)	PUNCT
aiti-203	82	13	for	for	ADP
aiti-203	82	14	one	one	NUM
aiti-203	82	15	specified	specified	ADJ
aiti-203	82	16	point	point	NOUN
aiti-203	82	17	.	.	PUNCT
aiti-203	83	1	as	as	ADV
aiti-203	83	2	long	long	ADV
aiti-203	83	3	as	as	SCONJ
aiti-203	83	4	we	we	PRON
aiti-203	83	5	know	know	VERB
aiti-203	83	6	the	the	DET
aiti-203	83	7	parameter	parameter	NOUN
aiti-203	83	8	for	for	ADP
aiti-203	83	9	the	the	DET
aiti-203	83	10	end	end	NOUN
aiti-203	83	11	point	point	NOUN
aiti-203	83	12	,	,	PUNCT
aiti-203	83	13	we	we	PRON
aiti-203	83	14	can	can	AUX
aiti-203	83	15	always	always	ADV
aiti-203	83	16	find	find	VERB
aiti-203	83	17	all	all	DET
aiti-203	83	18	mat	mat	NOUN
aiti-203	83	19	for	for	ADP
aiti-203	83	20	parameter	parameter	NOUN
aiti-203	83	21	from	from	ADP
aiti-203	83	22	0	0	NUM
aiti-203	83	23	to	to	PART
aiti-203	83	24	tend	tend	VERB
aiti-203	83	25	.	.	PUNCT
aiti-203	84	1	we	we	PRON
aiti-203	84	2	would	would	AUX
aiti-203	84	3	like	like	VERB
aiti-203	84	4	to	to	PART
aiti-203	84	5	find	find	VERB
aiti-203	84	6	not	not	PART
aiti-203	84	7	only	only	ADV
aiti-203	84	8	one	one	NUM
aiti-203	84	9	ma	ma	PROPN
aiti-203	84	10	point	point	NOUN
aiti-203	84	11	,	,	PUNCT
aiti-203	84	12	but	but	CCONJ
aiti-203	84	13	also	also	ADV
aiti-203	84	14	its	its	PRON
aiti-203	84	15	ma	ma	PROPN
aiti-203	84	16	circle	circle	PROPN
aiti-203	84	17	tangent	tangent	NOUN
aiti-203	84	18	to	to	ADP
aiti-203	84	19	current	current	ADJ
aiti-203	84	20	ma	ma	PROPN
aiti-203	84	21	circles	circle	NOUN
aiti-203	84	22	.	.	PUNCT
aiti-203	85	1	we	we	PRON
aiti-203	85	2	proposed	propose	VERB
aiti-203	85	3	two	two	NUM
aiti-203	85	4	methods	method	NOUN
aiti-203	85	5	to	to	PART
aiti-203	85	6	find	find	VERB
aiti-203	85	7	next	next	ADJ
aiti-203	85	8	ma	ma	PROPN
aiti-203	85	9	circle	circle	PROPN
aiti-203	85	10	.	.	PUNCT
aiti-203	86	1	one	one	NUM
aiti-203	86	2	method	method	NOUN
aiti-203	86	3	solve	solve	VERB
aiti-203	86	4	the	the	DET
aiti-203	86	5	problem	problem	NOUN
aiti-203	86	6	algebraically	algebraically	ADV
aiti-203	86	7	,	,	PUNCT
aiti-203	86	8	and	and	CCONJ
aiti-203	86	9	the	the	DET
aiti-203	86	10	other	other	ADJ
aiti-203	86	11	method	method	NOUN
aiti-203	86	12	using	use	VERB
aiti-203	86	13	an	an	DET
aiti-203	86	14	algorithm	algorithm	NOUN
aiti-203	86	15	with	with	ADP
aiti-203	86	16	binary	binary	ADJ
aiti-203	86	17	search	search	NOUN
aiti-203	86	18	to	to	PART
aiti-203	86	19	approach	approach	VERB
aiti-203	86	20	the	the	DET
aiti-203	86	21	result	result	NOUN
aiti-203	86	22	.	.	PUNCT
aiti-203	87	1	the	the	DET
aiti-203	87	2	first	first	ADJ
aiti-203	87	3	method	method	NOUN
aiti-203	87	4	only	only	ADV
aiti-203	87	5	suitable	suitable	ADJ
aiti-203	87	6	for	for	ADP
aiti-203	87	7	the	the	DET
aiti-203	87	8	symmetric	symmetric	ADJ
aiti-203	87	9	case	case	NOUN
aiti-203	87	10	,	,	PUNCT
aiti-203	87	11	which	which	PRON
aiti-203	87	12	means	mean	VERB
aiti-203	87	13	the	the	DET
aiti-203	87	14	case	case	NOUN
aiti-203	87	15	with	with	ADP
aiti-203	87	16	α0	α0	ADJ
aiti-203	87	17	=	=	SYM
aiti-203	87	18	α1	α1	PROPN
aiti-203	87	19	.	.	PUNCT
aiti-203	88	1	on	on	ADP
aiti-203	88	2	the	the	DET
aiti-203	88	3	case	case	NOUN
aiti-203	88	4	that	that	SCONJ
aiti-203	88	5	α0	α0	ADJ
aiti-203	88	6	=	=	SYM
aiti-203	88	7	α1	α1	NOUN
aiti-203	88	8	=	=	SYM
aiti-203	88	9	α	α	NOUN
aiti-203	88	10	,	,	PUNCT
aiti-203	88	11	we	we	PRON
aiti-203	88	12	want	want	AUX
aiti-203	88	13	find	find	VERB
aiti-203	88	14	the	the	DET
aiti-203	88	15	next	next	ADJ
aiti-203	88	16	circle	circle	NOUN
aiti-203	88	17	tangent	tangent	NOUN
aiti-203	88	18	to	to	ADP
aiti-203	88	19	the	the	DET
aiti-203	88	20	first	first	ADJ
aiti-203	88	21	circle	circle	NOUN
aiti-203	88	22	,	,	PUNCT
aiti-203	88	23	which	which	PRON
aiti-203	88	24	centered	center	VERB
aiti-203	88	25	at	at	ADP
aiti-203	88	26	(	(	PUNCT
aiti-203	88	27	0,0	0,0	NOUN
aiti-203	88	28	)	)	PUNCT
aiti-203	88	29	with	with	ADP
aiti-203	88	30	radius	radius	NOUN
aiti-203	88	31	1	1	NUM
aiti-203	88	32	in	in	ADP
aiti-203	88	33	the	the	DET
aiti-203	88	34	very	very	ADJ
aiti-203	88	35	beginning	beginning	NOUN
aiti-203	88	36	.	.	PUNCT
aiti-203	89	1	from	from	ADP
aiti-203	89	2	theorem	theorem	ADJ
aiti-203	89	3	4	4	NUM
aiti-203	89	4	,	,	PUNCT
aiti-203	89	5	we	we	PRON
aiti-203	89	6	know	know	VERB
aiti-203	89	7	the	the	DET
aiti-203	89	8	curve	curve	NOUN
aiti-203	89	9	whose	whose	DET
aiti-203	89	10	parameter	parameter	NOUN
aiti-203	89	11	t	t	PROPN
aiti-203	89	12	associate	associate	VERB
aiti-203	89	13	a	a	DET
aiti-203	89	14	mat	mat	NOUN
aiti-203	89	15	circle	circle	NOUN
aiti-203	89	16	(	(	PUNCT
aiti-203	89	17	xm	xm	PROPN
aiti-203	89	18	,	,	PUNCT
aiti-203	89	19	ym	ym	PROPN
aiti-203	89	20	,	,	PUNCT
aiti-203	89	21	rm	rm	PROPN
aiti-203	89	22	)	)	PUNCT
aiti-203	89	23	,	,	PUNCT
aiti-203	89	24	we	we	PRON
aiti-203	89	25	assume	assume	VERB
aiti-203	89	26	the	the	DET
aiti-203	89	27	next	next	ADJ
aiti-203	89	28	circle	circle	NOUN
aiti-203	89	29	whose	whose	DET
aiti-203	89	30	associated	associate	VERB
aiti-203	89	31	boundary	boundary	ADJ
aiti-203	89	32	parameter	parameter	NOUN
aiti-203	89	33	is	be	AUX
aiti-203	89	34	t	t	PROPN
aiti-203	89	35	,	,	PUNCT
aiti-203	89	36	so	so	ADV
aiti-203	89	37	we	we	PRON
aiti-203	89	38	want	want	VERB
aiti-203	89	39	to	to	PART
aiti-203	89	40	find	find	VERB
aiti-203	89	41	the	the	DET
aiti-203	89	42	circle	circle	NOUN
aiti-203	89	43	tangent	tangent	NOUN
aiti-203	89	44	to	to	ADP
aiti-203	89	45	the	the	DET
aiti-203	89	46	unit	unit	NOUN
aiti-203	89	47	circle	circle	NOUN
aiti-203	89	48	centered	center	VERB
aiti-203	89	49	at	at	ADP
aiti-203	89	50	the	the	DET
aiti-203	89	51	origin	origin	NOUN
aiti-203	89	52	.	.	PUNCT
aiti-203	90	1	the	the	DET
aiti-203	90	2	constraints	constraint	NOUN
aiti-203	90	3	we	we	PRON
aiti-203	90	4	give	give	VERB
aiti-203	90	5	is	be	AUX
aiti-203	90	6	the	the	DET
aiti-203	90	7	distance	distance	NOUN
aiti-203	90	8	between	between	ADP
aiti-203	90	9	the	the	DET
aiti-203	90	10	centers	center	NOUN
aiti-203	90	11	of	of	ADP
aiti-203	90	12	two	two	NUM
aiti-203	90	13	circle	circle	NOUN
aiti-203	90	14	is	be	AUX
aiti-203	90	15	equal	equal	ADJ
aiti-203	90	16	to	to	ADP
aiti-203	90	17	the	the	DET
aiti-203	90	18	sum	sum	NOUN
aiti-203	90	19	of	of	ADP
aiti-203	90	20	the	the	DET
aiti-203	90	21	radius	radius	NOUN
aiti-203	90	22	of	of	ADP
aiti-203	90	23	two	two	NUM
aiti-203	90	24	circles	circle	NOUN
aiti-203	90	25	.	.	PUNCT
aiti-203	91	1	that	that	PRON
aiti-203	91	2	is	be	AUX
aiti-203	91	3	,	,	PUNCT
aiti-203	91	4	‖	‖	PROPN
aiti-203	91	5	(	(	PUNCT
aiti-203	91	6	x𝑚	x𝑚	ADP
aiti-203	91	7	,	,	PUNCT
aiti-203	91	8	y𝑚)‖	y𝑚)‖	PROPN
aiti-203	91	9	=	=	SYM
aiti-203	91	10	rm	rm	NOUN
aiti-203	91	11	+	+	NOUN
aiti-203	91	12	1	1	X
aiti-203	91	13	.	.	PUNCT
aiti-203	91	14	to	to	PART
aiti-203	91	15	find	find	VERB
aiti-203	91	16	the	the	DET
aiti-203	91	17	medial	medial	ADJ
aiti-203	91	18	axis	axis	NOUN
aiti-203	91	19	circle	circle	NOUN
aiti-203	91	20	(	(	PUNCT
aiti-203	91	21	xm	xm	PROPN
aiti-203	91	22	,	,	PUNCT
aiti-203	91	23	ym	ym	PROPN
aiti-203	91	24	,	,	PUNCT
aiti-203	91	25	rm	rm	PROPN
aiti-203	91	26	)	)	PUNCT
aiti-203	91	27	associated	associate	VERB
aiti-203	91	28	with	with	ADP
aiti-203	91	29	c(t)=(x(t),y(t	c(t)=(x(t),y(t	NOUN
aiti-203	91	30	)	)	PUNCT
aiti-203	91	31	)	)	PUNCT
aiti-203	91	32	,	,	PUNCT
aiti-203	91	33	where	where	SCONJ
aiti-203	91	34	0	0	NUM
aiti-203	91	35	<	<	X
aiti-203	91	36	t<1/2	t<1/2	PROPN
aiti-203	91	37	,	,	PUNCT
aiti-203	91	38	tangents	tangent	NOUN
aiti-203	91	39	to	to	ADP
aiti-203	91	40	the	the	DET
aiti-203	91	41	unit	unit	NOUN
aiti-203	91	42	circle	circle	NOUN
aiti-203	91	43	centered	center	VERB
aiti-203	91	44	at	at	ADP
aiti-203	91	45	the	the	DET
aiti-203	91	46	origin	origin	NOUN
aiti-203	91	47	,	,	PUNCT
aiti-203	91	48	we	we	PRON
aiti-203	91	49	have	have	VERB
aiti-203	91	50	to	to	PART
aiti-203	91	51	solve	solve	VERB
aiti-203	91	52	a	a	DET
aiti-203	91	53	one	one	NUM
aiti-203	91	54	parameter	parameter	NOUN
aiti-203	91	55	equation	equation	NOUN
aiti-203	91	56	with	with	ADP
aiti-203	91	57	degree	degree	NOUN
aiti-203	91	58	10	10	NUM
aiti-203	91	59	.	.	PUNCT
aiti-203	92	1	because	because	SCONJ
aiti-203	92	2	the	the	DET
aiti-203	92	3	solutions	solution	NOUN
aiti-203	92	4	for	for	ADP
aiti-203	92	5	this	this	DET
aiti-203	92	6	equation	equation	NOUN
aiti-203	92	7	are	be	AUX
aiti-203	92	8	sensitive	sensitive	ADJ
aiti-203	92	9	to	to	ADP
aiti-203	92	10	its	its	PRON
aiti-203	92	11	coefficient	coefficient	NOUN
aiti-203	92	12	,	,	PUNCT
aiti-203	92	13	we	we	PRON
aiti-203	92	14	did	do	AUX
aiti-203	92	15	not	not	PART
aiti-203	92	16	implement	implement	VERB
aiti-203	92	17	this	this	DET
aiti-203	92	18	method	method	NOUN
aiti-203	92	19	.	.	PUNCT
aiti-203	93	1	we	we	PRON
aiti-203	93	2	use	use	VERB
aiti-203	93	3	the	the	DET
aiti-203	93	4	binary	binary	ADJ
aiti-203	93	5	search	search	NOUN
aiti-203	93	6	strategy	strategy	NOUN
aiti-203	93	7	instead	instead	ADV
aiti-203	93	8	.	.	PUNCT
aiti-203	94	1	algorithm	algorithm	PROPN
aiti-203	94	2	2	2	NUM
aiti-203	94	3	:	:	PUNCT
aiti-203	94	4	finding	find	VERB
aiti-203	94	5	the	the	DET
aiti-203	94	6	next	next	ADJ
aiti-203	94	7	ma	ma	PROPN
aiti-203	94	8	point	point	NOUN
aiti-203	94	9	(	(	PUNCT
aiti-203	94	10	eps	eps	PROPN
aiti-203	94	11	is	be	AUX
aiti-203	94	12	a	a	DET
aiti-203	94	13	small	small	ADJ
aiti-203	94	14	number	number	NOUN
aiti-203	94	15	):	):	PUNCT
aiti-203	94	16	#	#	NOUN
aiti-203	94	17	current	current	ADJ
aiti-203	94	18	ma	ma	PROPN
aiti-203	94	19	circle	circle	PROPN
aiti-203	94	20	is	be	AUX
aiti-203	94	21	(	(	PUNCT
aiti-203	94	22	x	x	NOUN
aiti-203	94	23	,	,	PUNCT
aiti-203	94	24	y	y	PROPN
aiti-203	94	25	,	,	PUNCT
aiti-203	94	26	r	r	NOUN
aiti-203	94	27	)	)	PUNCT
aiti-203	94	28	with	with	ADP
aiti-203	94	29	parameter	parameter	NOUN
aiti-203	94	30	t.	t.	PROPN
aiti-203	94	31	the	the	DET
aiti-203	94	32	return	return	NOUN
aiti-203	94	33	value	value	NOUN
aiti-203	94	34	is	be	AUX
aiti-203	94	35	next	next	ADJ
aiti-203	94	36	ma	ma	PROPN
aiti-203	94	37	circle	circle	PROPN
aiti-203	94	38	(	(	PUNCT
aiti-203	94	39	x1	x1	PROPN
aiti-203	94	40	,	,	PUNCT
aiti-203	94	41	y1	y1	NOUN
aiti-203	94	42	,	,	PUNCT
aiti-203	94	43	r1	r1	PROPN
aiti-203	94	44	)	)	PUNCT
aiti-203	94	45	and	and	CCONJ
aiti-203	94	46	t1	t1	NOUN
aiti-203	94	47	1	1	NUM
aiti-203	94	48	.	.	PUNCT
aiti-203	95	1	set	set	VERB
aiti-203	95	2	the	the	DET
aiti-203	95	3	tmin	tmin	NOUN
aiti-203	95	4	=	=	PROPN
aiti-203	95	5	t	t	PROPN
aiti-203	95	6	,	,	PUNCT
aiti-203	95	7	the	the	DET
aiti-203	95	8	current	current	ADJ
aiti-203	95	9	parameter	parameter	NOUN
aiti-203	95	10	value	value	NOUN
aiti-203	95	11	,	,	PUNCT
aiti-203	95	12	and	and	CCONJ
aiti-203	95	13	tmax	tmax	ADV
aiti-203	95	14	is	be	AUX
aiti-203	95	15	the	the	DET
aiti-203	95	16	parameter	parameter	NOUN
aiti-203	95	17	value	value	NOUN
aiti-203	95	18	for	for	ADP
aiti-203	95	19	the	the	DET
aiti-203	95	20	end	end	NOUN
aiti-203	95	21	ma	ma	PROPN
aiti-203	95	22	point	point	NOUN
aiti-203	95	23	.	.	PUNCT
aiti-203	96	1	2	2	X
aiti-203	96	2	.	.	X
aiti-203	96	3	let	let	VERB
aiti-203	96	4	dist	dist	NOUN
aiti-203	96	5	(	(	PUNCT
aiti-203	96	6	distance	distance	NOUN
aiti-203	96	7	between	between	ADP
aiti-203	96	8	two	two	NUM
aiti-203	96	9	centers	center	NOUN
aiti-203	96	10	)	)	PUNCT
aiti-203	96	11	be	be	VERB
aiti-203	96	12	2	2	NUM
aiti-203	96	13	,	,	PUNCT
aiti-203	96	14	and	and	CCONJ
aiti-203	96	15	srad	srad	PROPN
aiti-203	96	16	(	(	PUNCT
aiti-203	96	17	the	the	DET
aiti-203	96	18	sum	sum	NOUN
aiti-203	96	19	of	of	ADP
aiti-203	96	20	the	the	DET
aiti-203	96	21	radius	radius	NOUN
aiti-203	96	22	of	of	ADP
aiti-203	96	23	two	two	NUM
aiti-203	96	24	circles	circle	NOUN
aiti-203	96	25	)	)	PUNCT
aiti-203	96	26	be	be	VERB
aiti-203	96	27	1	1	NUM
aiti-203	96	28	.	.	ADP
aiti-203	97	1	3	3	NUM
aiti-203	97	2	.	.	PUNCT
aiti-203	98	1	while	while	SCONJ
aiti-203	98	2	|dist	|dist	NOUN
aiti-203	98	3	–	–	PUNCT
aiti-203	98	4	srad|	srad|	X
aiti-203	98	5	>	>	X
aiti-203	98	6	eps	eps	PROPN
aiti-203	98	7	and	and	CCONJ
aiti-203	98	8	|tmax	|tmax	NOUN
aiti-203	98	9	-	-	PUNCT
aiti-203	98	10	tmin|	tmin|	NUM
aiti-203	98	11	<	<	X
aiti-203	98	12	eps	eps	PROPN
aiti-203	98	13	:	:	PUNCT
aiti-203	98	14	tt	tt	PROPN
aiti-203	98	15	=	=	PUNCT
aiti-203	98	16	(	(	PUNCT
aiti-203	98	17	tmin+tmax)/2	tmin+tmax)/2	PROPN
aiti-203	98	18	find	find	VERB
aiti-203	98	19	the	the	DET
aiti-203	98	20	mat	mat	NOUN
aiti-203	98	21	(	(	PUNCT
aiti-203	98	22	x1	x1	PROPN
aiti-203	98	23	,	,	PUNCT
aiti-203	98	24	y1	y1	NOUN
aiti-203	98	25	,	,	PUNCT
aiti-203	98	26	r1	r1	PROPN
aiti-203	98	27	)	)	PUNCT
aiti-203	98	28	for	for	ADP
aiti-203	98	29	the	the	DET
aiti-203	98	30	parameter	parameter	NOUN
aiti-203	98	31	tt	tt	PROPN
aiti-203	98	32	#	#	NOUN
aiti-203	98	33	(	(	PUNCT
aiti-203	98	34	from	from	ADP
aiti-203	98	35	algorithm	algorithm	NOUN
aiti-203	98	36	1	1	NUM
aiti-203	98	37	)	)	PUNCT
aiti-203	98	38	.	.	PUNCT
aiti-203	99	1	find	find	VERB
aiti-203	99	2	dist	dist	NOUN
aiti-203	99	3	,	,	PUNCT
aiti-203	99	4	srad	srad	PROPN
aiti-203	99	5	from	from	ADP
aiti-203	99	6	these	these	DET
aiti-203	99	7	two	two	NUM
aiti-203	99	8	circles	circle	NOUN
aiti-203	99	9	.	.	PUNCT
aiti-203	100	1	if	if	SCONJ
aiti-203	100	2	dist	dist	PROPN
aiti-203	100	3	srad	srad	PROPN
aiti-203	100	4	>	>	X
aiti-203	100	5	eps	eps	PROPN
aiti-203	100	6	,	,	PUNCT
aiti-203	100	7	then	then	ADV
aiti-203	100	8	tmax	tmax	ADP
aiti-203	100	9	=	=	PUNCT
aiti-203	100	10	tt	tt	PROPN
aiti-203	100	11	if	if	SCONJ
aiti-203	100	12	dist	dist	PROPN
aiti-203	100	13	srad	srad	PROPN
aiti-203	100	14	<	<	X
aiti-203	100	15	-eps	-ep	NOUN
aiti-203	100	16	,	,	PUNCT
aiti-203	100	17	then	then	ADV
aiti-203	100	18	tmin	tmin	NOUN
aiti-203	100	19	=	=	PUNCT
aiti-203	100	20	tt	tt	PROPN
aiti-203	100	21	4	4	NUM
aiti-203	100	22	.	.	PUNCT
aiti-203	101	1	the	the	DET
aiti-203	101	2	value	value	NOUN
aiti-203	101	3	x1	x1	PROPN
aiti-203	101	4	,	,	PUNCT
aiti-203	101	5	y1	y1	PROPN
aiti-203	101	6	,	,	PUNCT
aiti-203	101	7	r1	r1	PROPN
aiti-203	101	8	is	be	AUX
aiti-203	101	9	the	the	DET
aiti-203	101	10	ma	ma	PROPN
aiti-203	101	11	circle	circle	NOUN
aiti-203	101	12	we	we	PRON
aiti-203	101	13	find	find	VERB
aiti-203	101	14	.	.	PUNCT
aiti-203	102	1	from	from	ADP
aiti-203	102	2	the	the	DET
aiti-203	102	3	above	above	ADJ
aiti-203	102	4	algorithm	algorithm	NOUN
aiti-203	102	5	,	,	PUNCT
aiti-203	102	6	we	we	PRON
aiti-203	102	7	can	can	AUX
aiti-203	102	8	find	find	VERB
aiti-203	102	9	the	the	DET
aiti-203	102	10	next	next	ADJ
aiti-203	102	11	ma	ma	PROPN
aiti-203	102	12	circles	circle	NOUN
aiti-203	102	13	for	for	ADP
aiti-203	102	14	the	the	DET
aiti-203	102	15	parameter	parameter	NOUN
aiti-203	102	16	t.	t.	PROPN
aiti-203	102	17	however	however	ADV
aiti-203	102	18	,	,	PUNCT
aiti-203	102	19	when	when	SCONJ
aiti-203	102	20	the	the	DET
aiti-203	102	21	parameter	parameter	NOUN
aiti-203	102	22	t	t	PROPN
aiti-203	102	23	value	value	NOUN
aiti-203	102	24	close	close	ADV
aiti-203	102	25	to	to	ADP
aiti-203	102	26	the	the	DET
aiti-203	102	27	parameter	parameter	NOUN
aiti-203	102	28	associate	associate	NOUN
aiti-203	102	29	with	with	ADP
aiti-203	102	30	the	the	DET
aiti-203	102	31	local	local	ADJ
aiti-203	102	32	maximum	maximum	ADJ
aiti-203	102	33	curvature	curvature	NOUN
aiti-203	102	34	,	,	PUNCT
aiti-203	102	35	it	it	PRON
aiti-203	102	36	can	can	AUX
aiti-203	102	37	only	only	ADV
aiti-203	102	38	produce	produce	VERB
aiti-203	102	39	circles	circle	NOUN
aiti-203	102	40	intersect	intersect	ADJ
aiti-203	102	41	with	with	ADP
aiti-203	102	42	previadvances	previadvance	NOUN
aiti-203	102	43	in	in	ADP
aiti-203	102	44	technology	technology	NOUN
aiti-203	102	45	innovation	innovation	NOUN
aiti-203	102	46	,	,	PUNCT
aiti-203	102	47	vol	vol	NOUN
aiti-203	102	48	.	.	PROPN
aiti-203	103	1	2	2	NUM
aiti-203	103	2	,	,	PUNCT
aiti-203	103	3	no	no	INTJ
aiti-203	103	4	.	.	NOUN
aiti-203	103	5	1	1	NUM
aiti-203	103	6	,	,	PUNCT
aiti-203	103	7	2017	2017	NUM
aiti-203	103	8	,	,	PUNCT
aiti-203	103	9	pp	pp	ADV
aiti-203	103	10	.	.	PUNCT
aiti-203	104	1	08	08	NUM
aiti-203	104	2	12	12	NUM
aiti-203	104	3	11	11	NUM
aiti-203	104	4	copyright	copyright	NOUN
aiti-203	104	5	©	©	PROPN
aiti-203	104	6	taeti	taeti	PROPN
aiti-203	104	7	ous	ous	PROPN
aiti-203	104	8	circle	circle	PROPN
aiti-203	104	9	,	,	PUNCT
aiti-203	104	10	which	which	PRON
aiti-203	104	11	means	mean	VERB
aiti-203	104	12	it	it	PRON
aiti-203	104	13	can	can	AUX
aiti-203	104	14	not	not	PART
aiti-203	104	15	find	find	VERB
aiti-203	104	16	more	more	ADJ
aiti-203	104	17	circle	circle	NOUN
aiti-203	104	18	tangent	tangent	NOUN
aiti-203	104	19	to	to	ADP
aiti-203	104	20	current	current	ADJ
aiti-203	104	21	circle	circle	NOUN
aiti-203	104	22	,	,	PUNCT
aiti-203	104	23	and	and	CCONJ
aiti-203	104	24	"	"	PUNCT
aiti-203	104	25	inside	inside	ADV
aiti-203	104	26	"	"	PUNCT
aiti-203	104	27	the	the	DET
aiti-203	104	28	hermite	hermite	ADJ
aiti-203	104	29	curve	curve	NOUN
aiti-203	104	30	.	.	PUNCT
aiti-203	105	1	from	from	ADP
aiti-203	105	2	the	the	DET
aiti-203	105	3	theorem	theorem	NOUN
aiti-203	105	4	describes	describe	NOUN
aiti-203	105	5	in	in	ADP
aiti-203	105	6	the	the	DET
aiti-203	105	7	last	last	ADJ
aiti-203	105	8	section	section	NOUN
aiti-203	105	9	,	,	PUNCT
aiti-203	105	10	with	with	ADP
aiti-203	105	11	the	the	DET
aiti-203	105	12	idea	idea	NOUN
aiti-203	105	13	mentioned	mention	VERB
aiti-203	105	14	above	above	ADV
aiti-203	105	15	,	,	PUNCT
aiti-203	105	16	we	we	PRON
aiti-203	105	17	give	give	VERB
aiti-203	105	18	4	4	NUM
aiti-203	105	19	examples	example	NOUN
aiti-203	105	20	in	in	ADP
aiti-203	105	21	this	this	DET
aiti-203	105	22	section	section	NOUN
aiti-203	105	23	.	.	PUNCT
aiti-203	106	1	the	the	DET
aiti-203	106	2	first	first	ADJ
aiti-203	106	3	two	two	NUM
aiti-203	106	4	examples	example	NOUN
aiti-203	106	5	is	be	AUX
aiti-203	106	6	for	for	ADP
aiti-203	106	7	the	the	DET
aiti-203	106	8	symmetric	symmetric	ADJ
aiti-203	106	9	boundary	boundary	ADJ
aiti-203	106	10	curve	curve	NOUN
aiti-203	106	11	where	where	SCONJ
aiti-203	106	12	α0	α0	ADJ
aiti-203	106	13	=	=	SYM
aiti-203	106	14	α1	α1	NOUN
aiti-203	106	15	=	=	SYM
aiti-203	106	16	α	α	NOUN
aiti-203	106	17	,	,	PUNCT
aiti-203	106	18	for	for	ADP
aiti-203	106	19	boundary	boundary	ADJ
aiti-203	106	20	curve	curve	NOUN
aiti-203	106	21	with	with	ADP
aiti-203	106	22	singular	singular	ADJ
aiti-203	106	23	point	point	NOUN
aiti-203	106	24	and	and	CCONJ
aiti-203	106	25	with	with	ADP
aiti-203	106	26	local	local	ADJ
aiti-203	106	27	maximum	maximum	ADJ
aiti-203	106	28	curvature	curvature	NOUN
aiti-203	106	29	respectively	respectively	ADV
aiti-203	106	30	.	.	PUNCT
aiti-203	107	1	the	the	DET
aiti-203	107	2	third	third	ADJ
aiti-203	107	3	and	and	CCONJ
aiti-203	107	4	fourth	fourth	ADJ
aiti-203	107	5	cases	case	NOUN
aiti-203	107	6	are	be	AUX
aiti-203	107	7	for	for	ADP
aiti-203	107	8	the	the	DET
aiti-203	107	9	non	non	ADJ
aiti-203	107	10	-	-	ADJ
aiti-203	107	11	symmetric	symmetric	ADJ
aiti-203	107	12	boundary	boundary	ADJ
aiti-203	107	13	curve	curve	NOUN
aiti-203	107	14	,	,	PUNCT
aiti-203	107	15	also	also	ADV
aiti-203	107	16	for	for	ADP
aiti-203	107	17	boundary	boundary	ADJ
aiti-203	107	18	curve	curve	NOUN
aiti-203	107	19	with	with	ADP
aiti-203	107	20	singular	singular	ADJ
aiti-203	107	21	point	point	NOUN
aiti-203	107	22	and	and	CCONJ
aiti-203	107	23	with	with	ADP
aiti-203	107	24	local	local	ADJ
aiti-203	107	25	maximum	maximum	ADJ
aiti-203	107	26	curvature	curvature	NOUN
aiti-203	107	27	respectively	respectively	ADV
aiti-203	107	28	.	.	PUNCT
aiti-203	107	29	example	example	NOUN
aiti-203	108	1	1	1	NUM
aiti-203	108	2	:	:	PUNCT
aiti-203	108	3	(	(	PUNCT
aiti-203	108	4	symmetric	symmetric	ADJ
aiti-203	108	5	curve	curve	NOUN
aiti-203	108	6	with	with	ADP
aiti-203	108	7	singular	singular	ADJ
aiti-203	108	8	point	point	NOUN
aiti-203	108	9	):	):	PUNCT
aiti-203	108	10	given	give	VERB
aiti-203	108	11	θ=5/9	θ=5/9	PROPN
aiti-203	108	12	,	,	PUNCT
aiti-203	108	13	t=0.5	t=0.5	NOUN
aiti-203	108	14	,	,	PUNCT
aiti-203	108	15	we	we	PRON
aiti-203	108	16	can	can	AUX
aiti-203	108	17	find	find	VERB
aiti-203	108	18	α0	α0	ADJ
aiti-203	108	19	=	=	SYM
aiti-203	108	20	α1=7.15025	α1=7.15025	NUM
aiti-203	108	21	.	.	PUNCT
aiti-203	109	1	the	the	DET
aiti-203	109	2	associated	associated	ADJ
aiti-203	109	3	mat	mat	NOUN
aiti-203	109	4	is	be	AUX
aiti-203	109	5	shown	show	VERB
aiti-203	109	6	in	in	ADP
aiti-203	109	7	fig	fig	NOUN
aiti-203	109	8	.	.	PUNCT
aiti-203	110	1	2	2	X
aiti-203	110	2	.	.	X
aiti-203	110	3	fig	fig	NOUN
aiti-203	110	4	.	.	PUNCT
aiti-203	111	1	2	2	NUM
aiti-203	111	2	symmetric	symmetric	ADJ
aiti-203	111	3	region	region	NOUN
aiti-203	111	4	with	with	ADP
aiti-203	111	5	singular	singular	PROPN
aiti-203	111	6	point	point	NOUN
aiti-203	111	7	example	example	NOUN
aiti-203	111	8	2	2	NUM
aiti-203	111	9	:	:	PUNCT
aiti-203	111	10	(	(	PUNCT
aiti-203	111	11	symmetric	symmetric	ADJ
aiti-203	111	12	curve	curve	NOUN
aiti-203	111	13	with	with	ADP
aiti-203	111	14	local	local	ADJ
aiti-203	111	15	maximum	maximum	ADJ
aiti-203	111	16	curvature	curvature	NOUN
aiti-203	111	17	):	):	PUNCT
aiti-203	111	18	given	give	VERB
aiti-203	111	19	θ=5/6	θ=5/6	NOUN
aiti-203	111	20	,	,	PUNCT
aiti-203	111	21	α0	α0	PROPN
aiti-203	111	22	=	=	SYM
aiti-203	111	23	α1=8	α1=8	PROPN
aiti-203	111	24	,	,	PUNCT
aiti-203	111	25	the	the	DET
aiti-203	111	26	associated	associated	ADJ
aiti-203	111	27	mat	mat	NOUN
aiti-203	111	28	is	be	AUX
aiti-203	111	29	shown	show	VERB
aiti-203	111	30	in	in	ADP
aiti-203	111	31	fig	fig	NOUN
aiti-203	111	32	.	.	PUNCT
aiti-203	112	1	3	3	X
aiti-203	112	2	.	.	X
aiti-203	112	3	fig	fig	NOUN
aiti-203	112	4	.	.	PUNCT
aiti-203	113	1	3	3	NUM
aiti-203	113	2	symm	symm	NOUN
aiti-203	113	3	.	.	PUNCT
aiti-203	113	4	region	region	NOUN
aiti-203	113	5	with	with	ADP
aiti-203	113	6	localmaximum	localmaximum	ADJ
aiti-203	113	7	curvature	curvature	NOUN
aiti-203	113	8	in	in	ADP
aiti-203	113	9	fig	fig	NOUN
aiti-203	113	10	.	.	PUNCT
aiti-203	114	1	3(a	3(a	NUM
aiti-203	114	2	)	)	PUNCT
aiti-203	114	3	,	,	PUNCT
aiti-203	114	4	we	we	PRON
aiti-203	114	5	find	find	VERB
aiti-203	114	6	one	one	NUM
aiti-203	114	7	ma	ma	PROPN
aiti-203	114	8	circle	circle	PROPN
aiti-203	114	9	tangent	tangent	NOUN
aiti-203	114	10	to	to	ADP
aiti-203	114	11	the	the	DET
aiti-203	114	12	original	original	ADJ
aiti-203	114	13	one	one	NUM
aiti-203	114	14	.	.	PUNCT
aiti-203	115	1	we	we	PRON
aiti-203	115	2	can	can	AUX
aiti-203	115	3	find	find	VERB
aiti-203	115	4	the	the	DET
aiti-203	115	5	next	next	ADJ
aiti-203	115	6	circle	circle	NOUN
aiti-203	115	7	tangent	tangent	NOUN
aiti-203	115	8	to	to	ADP
aiti-203	115	9	the	the	DET
aiti-203	115	10	red	red	ADJ
aiti-203	115	11	curve	curve	NOUN
aiti-203	115	12	and	and	CCONJ
aiti-203	115	13	the	the	DET
aiti-203	115	14	hermite	hermite	ADJ
aiti-203	115	15	cuve	cuve	NOUN
aiti-203	115	16	,	,	PUNCT
aiti-203	115	17	however	however	ADV
aiti-203	115	18	,	,	PUNCT
aiti-203	115	19	this	this	DET
aiti-203	115	20	circle	circle	NOUN
aiti-203	115	21	is	be	AUX
aiti-203	115	22	not	not	PART
aiti-203	115	23	totally	totally	ADV
aiti-203	115	24	“	"	PUNCT
aiti-203	115	25	inside	inside	ADV
aiti-203	115	26	”	"	PUNCT
aiti-203	115	27	the	the	DET
aiti-203	115	28	hermit	hermit	ADJ
aiti-203	115	29	curve	curve	NOUN
aiti-203	115	30	.	.	PUNCT
aiti-203	116	1	on	on	ADP
aiti-203	116	2	this	this	DET
aiti-203	116	3	case	case	NOUN
aiti-203	116	4	,	,	PUNCT
aiti-203	116	5	we	we	PRON
aiti-203	116	6	draw	draw	VERB
aiti-203	116	7	the	the	DET
aiti-203	116	8	osculating	osculating	NOUN
aiti-203	116	9	circle	circle	NOUN
aiti-203	116	10	associated	associate	VERB
aiti-203	116	11	with	with	ADP
aiti-203	116	12	the	the	DET
aiti-203	116	13	hermite	hermite	ADJ
aiti-203	116	14	curve	curve	NOUN
aiti-203	116	15	at	at	ADP
aiti-203	116	16	local	local	ADJ
aiti-203	116	17	maximum	maximum	ADJ
aiti-203	116	18	curvature	curvature	NOUN
aiti-203	116	19	(	(	PUNCT
aiti-203	116	20	see	see	VERB
aiti-203	116	21	figure	figure	NOUN
aiti-203	116	22	3(b	3(b	NUM
aiti-203	116	23	)	)	PUNCT
aiti-203	116	24	)	)	PUNCT
aiti-203	116	25	.	.	PUNCT
aiti-203	117	1	notice	notice	VERB
aiti-203	117	2	that	that	SCONJ
aiti-203	117	3	the	the	DET
aiti-203	117	4	above	above	ADJ
aiti-203	117	5	two	two	NUM
aiti-203	117	6	examples	example	NOUN
aiti-203	117	7	has	have	VERB
aiti-203	117	8	the	the	DET
aiti-203	117	9	properties	property	NOUN
aiti-203	117	10	that	that	PRON
aiti-203	117	11	the	the	DET
aiti-203	117	12	ma	ma	PROPN
aiti-203	117	13	points	point	NOUN
aiti-203	117	14	are	be	AUX
aiti-203	117	15	on	on	ADP
aiti-203	117	16	one	one	NUM
aiti-203	117	17	straight	straight	ADJ
aiti-203	117	18	line.the	line.the	DET
aiti-203	117	19	design	design	NOUN
aiti-203	117	20	requirements	requirement	NOUN
aiti-203	117	21	and	and	CCONJ
aiti-203	117	22	design	design	NOUN
aiti-203	117	23	constraints	constraint	NOUN
aiti-203	117	24	are	be	AUX
aiti-203	117	25	summarized	summarize	VERB
aiti-203	117	26	based	base	VERB
aiti-203	117	27	on	on	ADP
aiti-203	117	28	the	the	DET
aiti-203	117	29	characteristics	characteristic	NOUN
aiti-203	117	30	of	of	ADP
aiti-203	117	31	the	the	DET
aiti-203	117	32	mechanism	mechanism	NOUN
aiti-203	117	33	.	.	PUNCT
aiti-203	118	1	example	example	NOUN
aiti-203	118	2	3	3	NUM
aiti-203	118	3	:	:	PUNCT
aiti-203	118	4	(	(	PUNCT
aiti-203	118	5	non	non	ADJ
aiti-203	118	6	-	-	ADJ
aiti-203	118	7	symmetric	symmetric	ADJ
aiti-203	118	8	curve	curve	NOUN
aiti-203	118	9	with	with	ADP
aiti-203	118	10	singular	singular	ADJ
aiti-203	118	11	point	point	NOUN
aiti-203	118	12	):	):	PUNCT
aiti-203	119	1	given	give	VERB
aiti-203	119	2	θ	θ	PROPN
aiti-203	119	3	=	=	SYM
aiti-203	119	4	5/6	5/6	NUM
aiti-203	119	5	,	,	PUNCT
aiti-203	119	6	t=0.4	t=0.4	ADJ
aiti-203	119	7	,	,	PUNCT
aiti-203	119	8	we	we	PRON
aiti-203	119	9	find	find	VERB
aiti-203	119	10	α0=44.78461	α0=44.78461	ADP
aiti-203	119	11	,	,	PUNCT
aiti-203	119	12	α1=16.79423	α1=16.79423	NOUN
aiti-203	119	13	.	.	PUNCT
aiti-203	120	1	the	the	DET
aiti-203	120	2	associated	associated	ADJ
aiti-203	120	3	mat	mat	NOUN
aiti-203	120	4	is	be	AUX
aiti-203	120	5	shown	show	VERB
aiti-203	120	6	in	in	ADP
aiti-203	120	7	fig	fig	NOUN
aiti-203	120	8	.	.	PUNCT
aiti-203	121	1	4	4	X
aiti-203	121	2	.	.	X
aiti-203	121	3	fig	fig	NOUN
aiti-203	121	4	.	.	PUNCT
aiti-203	122	1	4	4	NUM
aiti-203	122	2	non	non	ADJ
aiti-203	122	3	-	-	NOUN
aiti-203	122	4	symm	symm	NOUN
aiti-203	122	5	.	.	PUNCT
aiti-203	122	6	region	region	NOUN
aiti-203	122	7	with	with	ADP
aiti-203	122	8	singular	singular	PROPN
aiti-203	122	9	point	point	NOUN
aiti-203	122	10	example	example	NOUN
aiti-203	122	11	4	4	NUM
aiti-203	122	12	:	:	PUNCT
aiti-203	122	13	(	(	PUNCT
aiti-203	122	14	non	non	ADJ
aiti-203	122	15	-	-	ADJ
aiti-203	122	16	symmetric	symmetric	ADJ
aiti-203	122	17	with	with	ADP
aiti-203	122	18	local	local	ADJ
aiti-203	122	19	maximum	maximum	ADJ
aiti-203	122	20	curvature	curvature	NOUN
aiti-203	122	21	):	):	PUNCT
aiti-203	122	22	given	give	VERB
aiti-203	122	23	θ=7/6	θ=7/6	NOUN
aiti-203	122	24	,	,	PUNCT
aiti-203	122	25	α0=18	α0=18	NOUN
aiti-203	122	26	,	,	PUNCT
aiti-203	122	27	α1=6	α1=6	PROPN
aiti-203	122	28	,	,	PUNCT
aiti-203	122	29	the	the	DET
aiti-203	122	30	associated	associated	ADJ
aiti-203	122	31	mat	mat	NOUN
aiti-203	122	32	is	be	AUX
aiti-203	122	33	shown	show	VERB
aiti-203	122	34	in	in	ADP
aiti-203	122	35	fig	fig	NOUN
aiti-203	122	36	.	.	PUNCT
aiti-203	123	1	5	5	NUM
aiti-203	123	2	.	.	X
aiti-203	123	3	fig	fig	NOUN
aiti-203	123	4	.	.	PUNCT
aiti-203	124	1	5	5	NUM
aiti-203	124	2	non	non	ADJ
aiti-203	124	3	-	-	NOUN
aiti-203	124	4	symm	symm	NOUN
aiti-203	124	5	.	.	PUNCT
aiti-203	124	6	region	region	NOUN
aiti-203	124	7	with	with	ADP
aiti-203	124	8	maximum	maximum	ADJ
aiti-203	124	9	curvature	curvature	NOUN
aiti-203	124	10	in	in	ADP
aiti-203	124	11	fig	fig	NOUN
aiti-203	124	12	.	.	PUNCT
aiti-203	125	1	5	5	NUM
aiti-203	125	2	,	,	PUNCT
aiti-203	125	3	the	the	DET
aiti-203	125	4	same	same	ADJ
aiti-203	125	5	as	as	ADP
aiti-203	125	6	fig	fig	NOUN
aiti-203	125	7	3	3	NUM
aiti-203	125	8	,	,	PUNCT
aiti-203	125	9	the	the	DET
aiti-203	125	10	last	last	ADJ
aiti-203	125	11	circle	circle	NOUN
aiti-203	125	12	is	be	AUX
aiti-203	125	13	associated	associate	VERB
aiti-203	125	14	with	with	ADP
aiti-203	125	15	the	the	DET
aiti-203	125	16	hermite	hermite	ADJ
aiti-203	125	17	curve	curve	NOUN
aiti-203	125	18	at	at	ADP
aiti-203	125	19	local	local	ADJ
aiti-203	125	20	maximum	maximum	ADJ
aiti-203	125	21	curvature	curvature	NOUN
aiti-203	125	22	.	.	PUNCT
aiti-203	126	1	4	4	X
aiti-203	126	2	.	.	X
aiti-203	126	3	conclusions	conclusion	NOUN
aiti-203	126	4	the	the	DET
aiti-203	126	5	unit	unit	NOUN
aiti-203	126	6	circle	circle	PROPN
aiti-203	126	7	hermite	hermite	PROPN
aiti-203	126	8	curve	curve	PROPN
aiti-203	126	9	,	,	PUNCT
aiti-203	126	10	h1(t;θ	h1(t;θ	PROPN
aiti-203	126	11	,	,	PUNCT
aiti-203	126	12	α0,α1	α0,α1	PROPN
aiti-203	126	13	)	)	PUNCT
aiti-203	126	14	,	,	PUNCT
aiti-203	126	15	can	can	AUX
aiti-203	126	16	be	be	AUX
aiti-203	126	17	used	use	VERB
aiti-203	126	18	to	to	PART
aiti-203	126	19	design	design	VERB
aiti-203	126	20	curves	curve	NOUN
aiti-203	126	21	and	and	CCONJ
aiti-203	126	22	images	image	NOUN
aiti-203	126	23	.	.	PUNCT
aiti-203	127	1	on	on	ADP
aiti-203	127	2	many	many	ADJ
aiti-203	127	3	cases	case	NOUN
aiti-203	127	4	,	,	PUNCT
aiti-203	127	5	the	the	DET
aiti-203	127	6	singular	singular	ADJ
aiti-203	127	7	point	point	NOUN
aiti-203	127	8	may	may	AUX
aiti-203	127	9	be	be	AUX
aiti-203	127	10	needed	need	VERB
aiti-203	127	11	to	to	PART
aiti-203	127	12	be	be	AUX
aiti-203	127	13	considered	consider	VERB
aiti-203	127	14	.	.	PUNCT
aiti-203	128	1	for	for	ADP
aiti-203	128	2	example	example	NOUN
aiti-203	128	3	,	,	PUNCT
aiti-203	128	4	the	the	DET
aiti-203	128	5	chinese	chinese	ADJ
aiti-203	128	6	characters	character	NOUN
aiti-203	128	7	may	may	AUX
aiti-203	128	8	have	have	VERB
aiti-203	128	9	cusp	cusp	NOUN
aiti-203	128	10	on	on	ADP
aiti-203	128	11	the	the	DET
aiti-203	128	12	boundary	boundary	NOUN
aiti-203	128	13	.	.	PUNCT
aiti-203	129	1	before	before	ADP
aiti-203	129	2	the	the	DET
aiti-203	129	3	design	design	NOUN
aiti-203	129	4	of	of	ADP
aiti-203	129	5	the	the	DET
aiti-203	129	6	character	character	NOUN
aiti-203	129	7	,	,	PUNCT
aiti-203	129	8	the	the	DET
aiti-203	129	9	relationship	relationship	NOUN
aiti-203	129	10	between	between	ADP
aiti-203	129	11	the	the	DET
aiti-203	129	12	parameter	parameter	NOUN
aiti-203	129	13	value	value	NOUN
aiti-203	129	14	and	and	CCONJ
aiti-203	129	15	the	the	DET
aiti-203	129	16	contour	contour	NOUN
aiti-203	129	17	of	of	ADP
aiti-203	129	18	the	the	DET
aiti-203	129	19	boundary	boundary	ADJ
aiti-203	129	20	curve	curve	NOUN
aiti-203	129	21	is	be	AUX
aiti-203	129	22	important	important	ADJ
aiti-203	129	23	.	.	PUNCT
aiti-203	130	1	when	when	SCONJ
aiti-203	130	2	we	we	PRON
aiti-203	130	3	give	give	VERB
aiti-203	130	4	two	two	NUM
aiti-203	130	5	values	value	NOUN
aiti-203	130	6	of	of	ADP
aiti-203	130	7	the	the	DET
aiti-203	130	8	parameters	parameter	NOUN
aiti-203	130	9	for	for	ADP
aiti-203	130	10	h1(t;θ	h1(t;θ	PROPN
aiti-203	130	11	,	,	PUNCT
aiti-203	130	12	α0,α1	α0,α1	PROPN
aiti-203	130	13	)	)	PUNCT
aiti-203	130	14	curve	curve	NOUN
aiti-203	130	15	,	,	PUNCT
aiti-203	130	16	the	the	PRON
aiti-203	130	17	can	can	AUX
aiti-203	130	18	find	find	VERB
aiti-203	130	19	the	the	DET
aiti-203	130	20	other	other	ADJ
aiti-203	130	21	two	two	NUM
aiti-203	130	22	values	value	NOUN
aiti-203	130	23	with	with	ADP
aiti-203	130	24	simple	simple	ADJ
aiti-203	130	25	computation	computation	NOUN
aiti-203	130	26	.	.	PUNCT
aiti-203	131	1	when	when	SCONJ
aiti-203	131	2	we	we	PRON
aiti-203	131	3	define	define	VERB
aiti-203	131	4	a	a	DET
aiti-203	131	5	curve	curve	NOUN
aiti-203	131	6	,	,	PUNCT
aiti-203	131	7	the	the	DET
aiti-203	131	8	only	only	ADJ
aiti-203	131	9	memory	memory	NOUN
aiti-203	131	10	we	we	PRON
aiti-203	131	11	need	need	VERB
aiti-203	131	12	is	be	AUX
aiti-203	131	13	7	7	NUM
aiti-203	131	14	locations	location	NOUN
aiti-203	131	15	to	to	PART
aiti-203	131	16	store	store	VERB
aiti-203	131	17	these	these	DET
aiti-203	131	18	4	4	NUM
aiti-203	131	19	parameters	parameter	NOUN
aiti-203	131	20	,	,	PUNCT
aiti-203	131	21	and	and	CCONJ
aiti-203	131	22	other	other	ADJ
aiti-203	131	23	3	3	NUM
aiti-203	131	24	parameters	parameter	NOUN
aiti-203	131	25	for	for	ADP
aiti-203	131	26	the	the	DET
aiti-203	131	27	standardization	standardization	NOUN
aiti-203	131	28	process	process	NOUN
aiti-203	131	29	.	.	PUNCT
aiti-203	132	1	so	so	ADV
aiti-203	132	2	,	,	PUNCT
aiti-203	132	3	the	the	DET
aiti-203	132	4	design	design	NOUN
aiti-203	132	5	process	process	NOUN
aiti-203	132	6	advances	advance	VERB
aiti-203	132	7	in	in	ADP
aiti-203	132	8	technology	technology	NOUN
aiti-203	132	9	innovation	innovation	NOUN
aiti-203	132	10	,	,	PUNCT
aiti-203	132	11	vol	vol	NOUN
aiti-203	132	12	.	.	PROPN
aiti-203	133	1	2	2	NUM
aiti-203	133	2	,	,	PUNCT
aiti-203	133	3	no	no	INTJ
aiti-203	133	4	.	.	NOUN
aiti-203	133	5	1	1	NUM
aiti-203	133	6	,	,	PUNCT
aiti-203	133	7	2017	2017	NUM
aiti-203	133	8	,	,	PUNCT
aiti-203	133	9	pp	pp	ADV
aiti-203	133	10	.	.	PUNCT
aiti-203	134	1	08	08	NUM
aiti-203	134	2	12	12	NUM
aiti-203	134	3	12	12	NUM
aiti-203	134	4	copyright	copyright	NOUN
aiti-203	134	5	©	©	PROPN
aiti-203	134	6	taeti	taeti	PROPN
aiti-203	134	7	saved	save	VERB
aiti-203	134	8	not	not	PART
aiti-203	134	9	only	only	ADV
aiti-203	134	10	the	the	DET
aiti-203	134	11	time	time	NOUN
aiti-203	134	12	,	,	PUNCT
aiti-203	134	13	but	but	CCONJ
aiti-203	134	14	also	also	ADV
aiti-203	134	15	the	the	DET
aiti-203	134	16	memory	memory	NOUN
aiti-203	134	17	.	.	PUNCT
aiti-203	135	1	when	when	SCONJ
aiti-203	135	2	we	we	PRON
aiti-203	135	3	find	find	VERB
aiti-203	135	4	the	the	DET
aiti-203	135	5	ma	ma	PROPN
aiti-203	135	6	circles	circle	NOUN
aiti-203	135	7	inside	inside	ADP
aiti-203	135	8	the	the	DET
aiti-203	135	9	region	region	NOUN
aiti-203	135	10	bounded	bound	VERB
aiti-203	135	11	by	by	ADP
aiti-203	135	12	unit	unit	NOUN
aiti-203	135	13	circle	circle	PROPN
aiti-203	135	14	and	and	CCONJ
aiti-203	135	15	h1(t;θ	h1(t;θ	PROPN
aiti-203	135	16	,	,	PUNCT
aiti-203	135	17	α0,α1	α0,α1	PROPN
aiti-203	135	18	)	)	PUNCT
aiti-203	135	19	,	,	PUNCT
aiti-203	135	20	it	it	PRON
aiti-203	135	21	is	be	AUX
aiti-203	135	22	possible	possible	ADJ
aiti-203	135	23	that	that	SCONJ
aiti-203	135	24	the	the	DET
aiti-203	135	25	last	last	ADJ
aiti-203	135	26	circle	circle	NOUN
aiti-203	135	27	intersects	intersect	VERB
aiti-203	135	28	the	the	DET
aiti-203	135	29	osculating	osculating	NOUN
aiti-203	135	30	circle	circle	NOUN
aiti-203	135	31	at	at	ADP
aiti-203	135	32	the	the	DET
aiti-203	135	33	local	local	ADJ
aiti-203	135	34	maximum	maximum	ADJ
aiti-203	135	35	curvature	curvature	NOUN
aiti-203	135	36	.	.	PUNCT
aiti-203	136	1	the	the	DET
aiti-203	136	2	osculating	osculating	NOUN
aiti-203	136	3	circle	circle	NOUN
aiti-203	136	4	associated	associate	VERB
aiti-203	136	5	with	with	ADP
aiti-203	136	6	end	end	NOUN
aiti-203	136	7	mat	mat	NOUN
aiti-203	136	8	point	point	NOUN
aiti-203	136	9	of	of	ADP
aiti-203	136	10	the	the	DET
aiti-203	136	11	region	region	NOUN
aiti-203	136	12	,	,	PUNCT
aiti-203	136	13	so	so	CCONJ
aiti-203	136	14	it	it	PRON
aiti-203	136	15	is	be	AUX
aiti-203	136	16	better	well	ADJ
aiti-203	136	17	to	to	PART
aiti-203	136	18	show	show	VERB
aiti-203	136	19	this	this	DET
aiti-203	136	20	circle	circle	NOUN
aiti-203	136	21	,	,	PUNCT
aiti-203	136	22	so	so	SCONJ
aiti-203	136	23	that	that	SCONJ
aiti-203	136	24	the	the	DET
aiti-203	136	25	mat	mat	NOUN
aiti-203	136	26	of	of	ADP
aiti-203	136	27	the	the	DET
aiti-203	136	28	region	region	NOUN
aiti-203	136	29	also	also	ADV
aiti-203	136	30	contains	contain	VERB
aiti-203	136	31	the	the	DET
aiti-203	136	32	end	end	NOUN
aiti-203	136	33	mat	mat	NOUN
aiti-203	136	34	point	point	NOUN
aiti-203	136	35	.	.	PUNCT
aiti-203	137	1	there	there	PRON
aiti-203	137	2	are	be	VERB
aiti-203	137	3	more	more	ADJ
aiti-203	137	4	constraints	constraint	NOUN
aiti-203	137	5	we	we	PRON
aiti-203	137	6	can	can	AUX
aiti-203	137	7	used	use	VERB
aiti-203	137	8	to	to	PART
aiti-203	137	9	design	design	VERB
aiti-203	137	10	the	the	DET
aiti-203	137	11	curves	curve	NOUN
aiti-203	137	12	.	.	PUNCT
aiti-203	138	1	for	for	ADP
aiti-203	138	2	example	example	NOUN
aiti-203	138	3	,	,	PUNCT
aiti-203	138	4	the	the	DET
aiti-203	138	5	maximum	maximum	ADJ
aiti-203	138	6	curvature	curvature	NOUN
aiti-203	138	7	happened	happen	VERB
aiti-203	138	8	at	at	ADP
aiti-203	138	9	t0	t0	NOUN
aiti-203	138	10	,	,	PUNCT
aiti-203	138	11	the	the	DET
aiti-203	138	12	curve	curve	NOUN
aiti-203	138	13	passing	pass	VERB
aiti-203	138	14	through	through	ADP
aiti-203	138	15	a	a	DET
aiti-203	138	16	point	point	NOUN
aiti-203	138	17	p0	p0	NOUN
aiti-203	138	18	,	,	PUNCT
aiti-203	138	19	the	the	DET
aiti-203	138	20	curve	curve	NOUN
aiti-203	138	21	tangent	tangent	NOUN
aiti-203	138	22	to	to	ADP
aiti-203	138	23	a	a	DET
aiti-203	138	24	line	line	NOUN
aiti-203	138	25	l0	l0	NOUN
aiti-203	138	26	,	,	PUNCT
aiti-203	138	27	and	and	CCONJ
aiti-203	138	28	so	so	ADV
aiti-203	138	29	on	on	ADV
aiti-203	138	30	.	.	PUNCT
aiti-203	139	1	we	we	PRON
aiti-203	139	2	believe	believe	VERB
aiti-203	139	3	the	the	DET
aiti-203	139	4	result	result	NOUN
aiti-203	139	5	will	will	AUX
aiti-203	139	6	as	as	ADV
aiti-203	139	7	simple	simple	ADJ
aiti-203	139	8	as	as	ADP
aiti-203	139	9	the	the	DET
aiti-203	139	10	case	case	NOUN
aiti-203	139	11	we	we	PRON
aiti-203	139	12	introduced	introduce	VERB
aiti-203	139	13	here	here	ADV
aiti-203	139	14	.	.	PUNCT
aiti-203	140	1	we	we	PRON
aiti-203	140	2	can	can	AUX
aiti-203	140	3	also	also	ADV
aiti-203	140	4	consider	consider	VERB
aiti-203	140	5	the	the	DET
aiti-203	140	6	inverse	inverse	NOUN
aiti-203	140	7	process	process	NOUN
aiti-203	140	8	,	,	PUNCT
aiti-203	140	9	that	that	ADV
aiti-203	140	10	is	is	ADV
aiti-203	140	11	,	,	PUNCT
aiti-203	140	12	from	from	ADP
aiti-203	140	13	circles	circle	NOUN
aiti-203	140	14	tangents	tangent	NOUN
aiti-203	140	15	to	to	ADP
aiti-203	140	16	each	each	DET
aiti-203	140	17	other	other	ADJ
aiti-203	140	18	,	,	PUNCT
aiti-203	140	19	and	and	CCONJ
aiti-203	140	20	find	find	VERB
aiti-203	140	21	its	its	PRON
aiti-203	140	22	boundary	boundary	ADJ
aiti-203	140	23	hermite	hermite	ADJ
aiti-203	140	24	curve	curve	NOUN
aiti-203	140	25	.	.	PUNCT
aiti-203	141	1	we	we	PRON
aiti-203	141	2	will	will	AUX
aiti-203	141	3	leave	leave	VERB
aiti-203	141	4	this	this	PRON
aiti-203	141	5	for	for	ADP
aiti-203	141	6	further	further	ADJ
aiti-203	141	7	research	research	NOUN
aiti-203	141	8	.	.	PUNCT
aiti-203	142	1	acknowledgement	acknowledgement	NOUN
aiti-203	142	2	this	this	DET
aiti-203	142	3	work	work	NOUN
aiti-203	142	4	was	be	AUX
aiti-203	142	5	supported	support	VERB
aiti-203	142	6	in	in	ADP
aiti-203	142	7	part	part	NOUN
aiti-203	142	8	by	by	ADP
aiti-203	142	9	the	the	DET
aiti-203	142	10	national	national	PROPN
aiti-203	142	11	science	science	PROPN
aiti-203	142	12	council	council	PROPN
aiti-203	142	13	in	in	ADP
aiti-203	142	14	taiwan	taiwan	PROPN
aiti-203	142	15	under	under	ADP
aiti-203	142	16	grants	grant	NOUN
aiti-203	142	17	most	most	ADJ
aiti-203	142	18	104	104	NUM
aiti-203	142	19	-	-	PUNCT
aiti-203	142	20	2221	2221	NUM
aiti-203	142	21	-	-	PUNCT
aiti-203	142	22	e-031	e-031	NOUN
aiti-203	142	23	-	-	PUNCT
aiti-203	142	24	001	001	NOUN
aiti-203	142	25	.	.	PUNCT
aiti-203	143	1	references	reference	NOUN
aiti-203	143	2	[	[	X
aiti-203	143	3	1	1	NUM
aiti-203	143	4	]	]	X
aiti-203	143	5	l.	l.	NOUN
aiti-203	143	6	cinque	cinque	PROPN
aiti-203	143	7	,	,	PUNCT
aiti-203	143	8	s.	s.	PROPN
aiti-203	143	9	levialdi	levialdi	PROPN
aiti-203	143	10	,	,	PUNCT
aiti-203	143	11	and	and	CCONJ
aiti-203	143	12	a.	a.	PROPN
aiti-203	143	13	malizia	malizia	PROPN
aiti-203	143	14	,	,	PUNCT
aiti-203	143	15	“	"	PUNCT
aiti-203	143	16	shape	shape	NOUN
aiti-203	143	17	description	description	NOUN
aiti-203	143	18	using	use	VERB
aiti-203	143	19	cubic	cubic	ADJ
aiti-203	143	20	polynomial	polynomial	ADJ
aiti-203	143	21	bezier	bezier	NOUN
aiti-203	143	22	curves	curve	NOUN
aiti-203	143	23	,	,	PUNCT
aiti-203	143	24	”	"	PUNCT
aiti-203	143	25	pattern	pattern	NOUN
aiti-203	143	26	recognition	recognition	NOUN
aiti-203	143	27	letters	letter	NOUN
aiti-203	143	28	,	,	PUNCT
aiti-203	143	29	vol	vol	NOUN
aiti-203	143	30	.	.	PROPN
aiti-203	143	31	19	19	NUM
aiti-203	143	32	,	,	PUNCT
aiti-203	143	33	pp	pp	ADJ
aiti-203	143	34	.	.	PUNCT
aiti-203	144	1	821	821	NUM
aiti-203	144	2	-	-	SYM
aiti-203	144	3	828	828	NUM
aiti-203	144	4	,	,	PUNCT
aiti-203	144	5	1998	1998	NUM
aiti-203	144	6	.	.	PUNCT
aiti-203	145	1	[	[	X
aiti-203	145	2	2	2	X
aiti-203	145	3	]	]	PUNCT
aiti-203	145	4	h.	h.	PROPN
aiti-203	145	5	m.	m.	PROPN
aiti-203	145	6	yang	yang	PROPN
aiti-203	145	7	,	,	PUNCT
aiti-203	145	8	j.	j.	PROPN
aiti-203	145	9	j.	j.	PROPN
aiti-203	145	10	lu	lu	PROPN
aiti-203	145	11	,	,	PUNCT
aiti-203	145	12	and	and	CCONJ
aiti-203	145	13	h.	h.	PROPN
aiti-203	145	14	j.	j.	PROPN
aiti-203	145	15	lee	lee	PROPN
aiti-203	145	16	,	,	PUNCT
aiti-203	145	17	“	"	PUNCT
aiti-203	145	18	a	a	DET
aiti-203	145	19	bezier	bezier	ADJ
aiti-203	145	20	curve	curve	NOUN
aiti-203	145	21	-	-	PUNCT
aiti-203	145	22	based	base	VERB
aiti-203	145	23	approach	approach	NOUN
aiti-203	145	24	to	to	PART
aiti-203	145	25	shape	shape	VERB
aiti-203	145	26	description	description	NOUN
aiti-203	145	27	for	for	ADP
aiti-203	145	28	chinese	chinese	ADJ
aiti-203	145	29	calligraphy	calligraphy	NOUN
aiti-203	145	30	characters	character	NOUN
aiti-203	145	31	,	,	PUNCT
aiti-203	145	32	”	"	PUNCT
aiti-203	145	33	proceedings	proceeding	NOUN
aiti-203	145	34	of	of	ADP
aiti-203	145	35	the	the	DET
aiti-203	145	36	sixth	sixth	ADJ
aiti-203	145	37	international	international	ADJ
aiti-203	145	38	conference	conference	NOUN
aiti-203	145	39	on	on	ADP
aiti-203	145	40	document	document	NOUN
aiti-203	145	41	analysis	analysis	NOUN
aiti-203	145	42	and	and	CCONJ
aiti-203	145	43	recognition	recognition	NOUN
aiti-203	145	44	,	,	PUNCT
aiti-203	145	45	pp	pp	ADP
aiti-203	145	46	.	.	PUNCT
aiti-203	145	47	276	276	NUM
aiti-203	145	48	-	-	SYM
aiti-203	145	49	280	280	NUM
aiti-203	145	50	,	,	PUNCT
aiti-203	145	51	2001	2001	NUM
aiti-203	145	52	.	.	PUNCT
aiti-203	146	1	[	[	X
aiti-203	146	2	3	3	X
aiti-203	146	3	]	]	X
aiti-203	146	4	h.	h.	PROPN
aiti-203	146	5	h.	h.	PROPN
aiti-203	146	6	chang	chang	PROPN
aiti-203	146	7	and	and	CCONJ
aiti-203	146	8	h.	h.	PROPN
aiti-203	146	9	yan	yan	PROPN
aiti-203	146	10	,	,	PUNCT
aiti-203	146	11	“	"	PUNCT
aiti-203	146	12	vectorization	vectorization	NOUN
aiti-203	146	13	of	of	ADP
aiti-203	146	14	hand	hand	NOUN
aiti-203	146	15	-	-	PUNCT
aiti-203	146	16	drawn	draw	VERB
aiti-203	146	17	image	image	NOUN
aiti-203	146	18	using	use	VERB
aiti-203	146	19	piecewise	piecewise	NOUN
aiti-203	146	20	cubic	cubic	ADJ
aiti-203	146	21	bezier	bezier	NOUN
aiti-203	146	22	curves	curve	NOUN
aiti-203	146	23	fitting	fitting	ADJ
aiti-203	146	24	,	,	PUNCT
aiti-203	146	25	”	"	PUNCT
aiti-203	146	26	pattern	pattern	NOUN
aiti-203	146	27	recognition	recognition	NOUN
aiti-203	146	28	,	,	PUNCT
aiti-203	146	29	vol	vol	NOUN
aiti-203	146	30	.	.	PROPN
aiti-203	146	31	31	31	NUM
aiti-203	146	32	,	,	PUNCT
aiti-203	146	33	no	no	INTJ
aiti-203	146	34	.	.	NOUN
aiti-203	146	35	11	11	NUM
aiti-203	146	36	,	,	PUNCT
aiti-203	146	37	pp	pp	ADJ
aiti-203	146	38	.	.	PUNCT
aiti-203	146	39	1747	1747	NUM
aiti-203	146	40	-	-	SYM
aiti-203	146	41	1755	1755	NUM
aiti-203	146	42	,	,	PUNCT
aiti-203	146	43	1998	1998	NUM
aiti-203	146	44	.	.	PUNCT
aiti-203	147	1	[	[	X
aiti-203	147	2	4	4	X
aiti-203	147	3	]	]	PUNCT
aiti-203	147	4	h.	h.	PROPN
aiti-203	147	5	cao	cao	PROPN
aiti-203	147	6	and	and	CCONJ
aiti-203	147	7	a.	a.	PROPN
aiti-203	147	8	c.	c.	PROPN
aiti-203	147	9	kot	kot	PROPN
aiti-203	147	10	,	,	PUNCT
aiti-203	147	11	“	"	PUNCT
aiti-203	147	12	lossless	lossless	NOUN
aiti-203	147	13	data	datum	NOUN
aiti-203	147	14	embedding	embed	VERB
aiti-203	147	15	in	in	ADP
aiti-203	147	16	electronic	electronic	ADJ
aiti-203	147	17	inks	ink	NOUN
aiti-203	147	18	,	,	PUNCT
aiti-203	147	19	”	"	PUNCT
aiti-203	147	20	ieee	ieee	NOUN
aiti-203	147	21	transactions	transaction	NOUN
aiti-203	147	22	on	on	ADP
aiti-203	147	23	information	information	NOUN
aiti-203	147	24	forensics	forensic	NOUN
aiti-203	147	25	and	and	CCONJ
aiti-203	147	26	security	security	NOUN
aiti-203	147	27	,	,	PUNCT
aiti-203	147	28	vol	vol	NOUN
aiti-203	147	29	.	.	PROPN
aiti-203	147	30	5	5	NUM
aiti-203	147	31	,	,	PUNCT
aiti-203	147	32	no	no	INTJ
aiti-203	147	33	.	.	NOUN
aiti-203	147	34	2	2	NUM
aiti-203	147	35	,	,	PUNCT
aiti-203	147	36	pp	pp	ADJ
aiti-203	147	37	.	.	PUNCT
aiti-203	147	38	314	314	NUM
aiti-203	147	39	-	-	SYM
aiti-203	147	40	323	323	NUM
aiti-203	147	41	,	,	PUNCT
aiti-203	147	42	2010	2010	NUM
aiti-203	147	43	.	.	PUNCT
aiti-203	148	1	[	[	X
aiti-203	148	2	5	5	X
aiti-203	148	3	]	]	PUNCT
aiti-203	148	4	l.	l.	PROPN
aiti-203	148	5	cao	cao	PROPN
aiti-203	148	6	,	,	PUNCT
aiti-203	148	7	z.	z.	PROPN
aiti-203	148	8	jia	jia	PROPN
aiti-203	148	9	,	,	PUNCT
aiti-203	148	10	and	and	CCONJ
aiti-203	148	11	j.	j.	PROPN
aiti-203	148	12	liu	liu	PROPN
aiti-203	148	13	,	,	PUNCT
aiti-203	148	14	“	"	PUNCT
aiti-203	148	15	computation	computation	NOUN
aiti-203	148	16	of	of	ADP
aiti-203	148	17	medial	medial	ADJ
aiti-203	148	18	axis	axis	NOUN
aiti-203	148	19	and	and	CCONJ
aiti-203	148	20	offset	offset	VERB
aiti-203	148	21	curves	curve	NOUN
aiti-203	148	22	of	of	ADP
aiti-203	148	23	curved	curved	ADJ
aiti-203	148	24	boundaries	boundary	NOUN
aiti-203	148	25	in	in	ADP
aiti-203	148	26	planar	planar	ADJ
aiti-203	148	27	domains	domain	NOUN
aiti-203	148	28	based	base	VERB
aiti-203	148	29	on	on	ADP
aiti-203	148	30	the	the	DET
aiti-203	148	31	cesaro	cesaro	NOUN
aiti-203	148	32	’s	’s	PART
aiti-203	148	33	approach	approach	NOUN
aiti-203	148	34	,	,	PUNCT
aiti-203	148	35	”	"	PUNCT
aiti-203	148	36	computer	computer	NOUN
aiti-203	148	37	aided	aid	VERB
aiti-203	148	38	geometric	geometric	ADJ
aiti-203	148	39	design	design	NOUN
aiti-203	148	40	,	,	PUNCT
aiti-203	148	41	vol	vol	NOUN
aiti-203	148	42	.	.	PROPN
aiti-203	149	1	26	26	NUM
aiti-203	149	2	,	,	PUNCT
aiti-203	149	3	no	no	INTJ
aiti-203	149	4	.	.	NOUN
aiti-203	149	5	4	4	NUM
aiti-203	149	6	,	,	PUNCT
aiti-203	149	7	pp	pp	ADJ
aiti-203	149	8	.	.	PUNCT
aiti-203	150	1	444	444	NUM
aiti-203	150	2	-	-	SYM
aiti-203	150	3	454	454	NUM
aiti-203	150	4	,	,	PUNCT
aiti-203	150	5	2009	2009	NUM
aiti-203	150	6	.	.	PUNCT
aiti-203	151	1	[	[	X
aiti-203	151	2	6	6	NUM
aiti-203	151	3	]	]	PUNCT
aiti-203	151	4	p.	p.	NOUN
aiti-203	151	5	qin	qin	PROPN
aiti-203	151	6	,	,	PUNCT
aiti-203	151	7	and	and	CCONJ
aiti-203	151	8	c.	c.	PROPN
aiti-203	151	9	chen	chen	PROPN
aiti-203	151	10	,	,	PUNCT
aiti-203	151	11	“	"	PUNCT
aiti-203	151	12	simulation	simulation	NOUN
aiti-203	151	13	model	model	NOUN
aiti-203	151	14	of	of	ADP
aiti-203	151	15	flower	flower	NOUN
aiti-203	151	16	using	use	VERB
aiti-203	151	17	the	the	DET
aiti-203	151	18	integration	integration	NOUN
aiti-203	151	19	of	of	ADP
aiti-203	151	20	l	l	NOUN
aiti-203	151	21	-	-	NOUN
aiti-203	151	22	systems	system	NOUN
aiti-203	151	23	with	with	ADP
aiti-203	151	24	bezier	bezier	ADJ
aiti-203	151	25	surfaces	surface	NOUN
aiti-203	151	26	,	,	PUNCT
aiti-203	151	27	”	"	PUNCT
aiti-203	151	28	international	international	ADJ
aiti-203	151	29	journal	journal	NOUN
aiti-203	151	30	of	of	ADP
aiti-203	151	31	computer	computer	NOUN
aiti-203	151	32	science	science	NOUN
aiti-203	151	33	and	and	CCONJ
aiti-203	151	34	network	network	NOUN
aiti-203	151	35	security	security	NOUN
aiti-203	151	36	,	,	PUNCT
aiti-203	151	37	vol	vol	NOUN
aiti-203	151	38	.	.	PROPN
aiti-203	152	1	6	6	NUM
aiti-203	152	2	,	,	PUNCT
aiti-203	152	3	no	no	INTJ
aiti-203	152	4	.	.	NOUN
aiti-203	152	5	2	2	NUM
aiti-203	152	6	,	,	PUNCT
aiti-203	152	7	pp	pp	ADJ
aiti-203	152	8	.	.	PUNCT
aiti-203	153	1	65	65	NUM
aiti-203	153	2	-	-	SYM
aiti-203	153	3	68	68	NUM
aiti-203	153	4	,	,	PUNCT
aiti-203	153	5	2006	2006	NUM
aiti-203	153	6	.	.	PUNCT
aiti-203	154	1	[	[	X
aiti-203	154	2	7	7	X
aiti-203	154	3	]	]	X
aiti-203	154	4	c.	c.	PROPN
aiti-203	154	5	s.	s.	PROPN
aiti-203	154	6	chiang	chiang	PROPN
aiti-203	154	7	and	and	CCONJ
aiti-203	154	8	l.	l.	PROPN
aiti-203	154	9	y.	y.	PROPN
aiti-203	154	10	hsu	hsu	PROPN
aiti-203	154	11	,	,	PUNCT
aiti-203	154	12	“	"	PUNCT
aiti-203	154	13	describing	describe	VERB
aiti-203	154	14	the	the	DET
aiti-203	154	15	edge	edge	NOUN
aiti-203	154	16	contour	contour	NOUN
aiti-203	154	17	of	of	ADP
aiti-203	154	18	chinese	chinese	ADJ
aiti-203	154	19	calligraphy	calligraphy	NOUN
aiti-203	154	20	with	with	ADP
aiti-203	154	21	circle	circle	NOUN
aiti-203	154	22	and	and	CCONJ
aiti-203	154	23	cubic	cubic	ADJ
aiti-203	154	24	hermit	hermit	NOUN
aiti-203	154	25	curve	curve	NOUN
aiti-203	154	26	,	,	PUNCT
aiti-203	154	27	”	"	PUNCT
aiti-203	154	28	computer	computer	NOUN
aiti-203	154	29	graphics	graphic	NOUN
aiti-203	154	30	workshop	workshop	NOUN
aiti-203	154	31	,	,	PUNCT
aiti-203	154	32	july	july	PROPN
aiti-203	154	33	2013	2013	NUM
aiti-203	154	34	.	.	PUNCT
aiti-203	155	1	[	[	X
aiti-203	155	2	8	8	NUM
aiti-203	155	3	]	]	X
aiti-203	155	4	c.	c.	PROPN
aiti-203	155	5	s.	s.	PROPN
aiti-203	155	6	chiang	chiang	PROPN
aiti-203	155	7	,	,	PUNCT
aiti-203	155	8	“	"	PUNCT
aiti-203	155	9	the	the	DET
aiti-203	155	10	medial	medial	ADJ
aiti-203	155	11	axis	axis	NOUN
aiti-203	155	12	transform	transform	NOUN
aiti-203	155	13	of	of	ADP
aiti-203	155	14	the	the	DET
aiti-203	155	15	region	region	NOUN
aiti-203	155	16	defined	define	VERB
aiti-203	155	17	by	by	ADP
aiti-203	155	18	circles	circle	NOUN
aiti-203	155	19	and	and	CCONJ
aiti-203	155	20	hermit	hermit	ADJ
aiti-203	155	21	curve	curve	NOUN
aiti-203	155	22	,	,	PUNCT
aiti-203	155	23	”	"	PUNCT
aiti-203	155	24	international	international	ADJ
aiti-203	155	25	conference	conference	NOUN
aiti-203	155	26	on	on	ADP
aiti-203	155	27	computer	computer	NOUN
aiti-203	155	28	science	science	NOUN
aiti-203	155	29	and	and	CCONJ
aiti-203	155	30	engineering	engineering	NOUN
aiti-203	155	31	(	(	PUNCT
aiti-203	155	32	iccse	iccse	NOUN
aiti-203	155	33	)	)	PUNCT
aiti-203	155	34	,	,	PUNCT
aiti-203	155	35	pp	pp	ADP
aiti-203	155	36	.	.	PUNCT
aiti-203	156	1	22	22	NUM
aiti-203	156	2	-	-	SYM
aiti-203	156	3	24	24	NUM
aiti-203	156	4	,	,	PUNCT
aiti-203	156	5	july	july	PROPN
aiti-203	156	6	,	,	PUNCT
aiti-203	156	7	2015	2015	NUM
aiti-203	156	8	.	.	PUNCT