id	sid	tid	token	lemma	pos
aiti-819	1	1	advances	advance	NOUN
aiti-819	1	2	in	in	ADP
aiti-819	1	3	technology	technology	NOUN
aiti-819	1	4	innovation	innovation	NOUN
aiti-819	1	5	,	,	PUNCT
aiti-819	1	6	vol	vol	NOUN
aiti-819	1	7	.	.	PROPN
aiti-819	2	1	5	5	NUM
aiti-819	2	2	,	,	PUNCT
aiti-819	2	3	no	no	INTJ
aiti-819	2	4	.	.	NOUN
aiti-819	2	5	2	2	NUM
aiti-819	2	6	,	,	PUNCT
aiti-819	2	7	2020	2020	NUM
aiti-819	2	8	,	,	PUNCT
aiti-819	2	9	pp	pp	ADV
aiti-819	2	10	.	.	PUNCT
aiti-819	3	1	126	126	NUM
aiti-819	3	2	-	-	SYM
aiti-819	3	3	134	134	NUM
aiti-819	3	4	computer	computer	NOUN
aiti-819	3	5	science	science	NOUN
aiti-819	3	6	and	and	CCONJ
aiti-819	3	7	information	information	NOUN
aiti-819	3	8	management	management	NOUN
aiti-819	3	9	,	,	PUNCT
aiti-819	3	10	soochow	soochow	PROPN
aiti-819	3	11	university	university	PROPN
aiti-819	3	12	,	,	PUNCT
aiti-819	3	13	taipei	taipei	PROPN
aiti-819	3	14	,	,	PUNCT
aiti-819	3	15	taiwan	taiwan	PROPN
aiti-819	3	16	received	receive	VERB
aiti-819	3	17	17	17	NUM
aiti-819	3	18	march	march	NOUN
aiti-819	3	19	2019	2019	NUM
aiti-819	3	20	;	;	PUNCT
aiti-819	3	21	received	receive	VERB
aiti-819	3	22	in	in	ADP
aiti-819	3	23	revised	revise	VERB
aiti-819	3	24	form	form	NOUN
aiti-819	3	25	29	29	NUM
aiti-819	3	26	august	august	PROPN
aiti-819	3	27	2019	2019	NUM
aiti-819	3	28	;	;	PUNCT
aiti-819	3	29	accepted	accept	VERB
aiti-819	3	30	02	02	NUM
aiti-819	3	31	october	october	PROPN
aiti-819	3	32	2019	2019	NUM
aiti-819	3	33	doi	doi	NOUN
aiti-819	3	34	:	:	PUNCT
aiti-819	3	35	https://doi.org/10.46604/aiti.2020.819	https://doi.org/10.46604/aiti.2020.819	NOUN
aiti-819	3	36	abstract	abstract	ADJ
aiti-819	3	37	computer	computer	NOUN
aiti-819	3	38	aided	aid	VERB
aiti-819	3	39	geometric	geometric	ADJ
aiti-819	3	40	design	design	NOUN
aiti-819	3	41	employs	employ	VERB
aiti-819	3	42	mathematical	mathematical	ADJ
aiti-819	3	43	and	and	CCONJ
aiti-819	3	44	computational	computational	ADJ
aiti-819	3	45	methods	method	NOUN
aiti-819	3	46	for	for	ADP
aiti-819	3	47	describing	describe	VERB
aiti-819	3	48	geometric	geometric	ADJ
aiti-819	3	49	objects	object	NOUN
aiti-819	3	50	,	,	PUNCT
aiti-819	3	51	such	such	ADJ
aiti-819	3	52	as	as	ADP
aiti-819	3	53	curves	curve	NOUN
aiti-819	3	54	,	,	PUNCT
aiti-819	3	55	areas	area	NOUN
aiti-819	3	56	in	in	ADP
aiti-819	3	57	two	two	NUM
aiti-819	3	58	dimensions	dimension	NOUN
aiti-819	3	59	(	(	PUNCT
aiti-819	3	60	2d	2d	NOUN
aiti-819	3	61	)	)	PUNCT
aiti-819	3	62	and	and	CCONJ
aiti-819	3	63	surfaces	surface	NOUN
aiti-819	3	64	,	,	PUNCT
aiti-819	3	65	and	and	CCONJ
aiti-819	3	66	solids	solid	NOUN
aiti-819	3	67	in	in	ADP
aiti-819	3	68	3d	3d	NUM
aiti-819	3	69	.	.	PUNCT
aiti-819	4	1	an	an	DET
aiti-819	4	2	area	area	NOUN
aiti-819	4	3	can	can	AUX
aiti-819	4	4	be	be	AUX
aiti-819	4	5	represented	represent	VERB
aiti-819	4	6	using	use	VERB
aiti-819	4	7	its	its	PRON
aiti-819	4	8	boundary	boundary	ADJ
aiti-819	4	9	curves	curve	NOUN
aiti-819	4	10	,	,	PUNCT
aiti-819	4	11	and	and	CCONJ
aiti-819	4	12	a	a	DET
aiti-819	4	13	solid	solid	ADJ
aiti-819	4	14	can	can	AUX
aiti-819	4	15	be	be	AUX
aiti-819	4	16	represented	represent	VERB
aiti-819	4	17	using	use	VERB
aiti-819	4	18	its	its	PRON
aiti-819	4	19	boundary	boundary	ADJ
aiti-819	4	20	surfaces	surface	NOUN
aiti-819	4	21	with	with	ADP
aiti-819	4	22	intersection	intersection	NOUN
aiti-819	4	23	curves	curve	NOUN
aiti-819	4	24	among	among	ADP
aiti-819	4	25	these	these	DET
aiti-819	4	26	boundary	boundary	ADJ
aiti-819	4	27	surfaces	surface	NOUN
aiti-819	4	28	.	.	PUNCT
aiti-819	5	1	in	in	ADP
aiti-819	5	2	addition	addition	NOUN
aiti-819	5	3	,	,	PUNCT
aiti-819	5	4	other	other	ADJ
aiti-819	5	5	methods	method	NOUN
aiti-819	5	6	,	,	PUNCT
aiti-819	5	7	such	such	ADJ
aiti-819	5	8	as	as	ADP
aiti-819	5	9	the	the	DET
aiti-819	5	10	medial	medial	ADJ
aiti-819	5	11	-	-	PUNCT
aiti-819	5	12	axis	axis	NOUN
aiti-819	5	13	transform	transform	NOUN
aiti-819	5	14	,	,	PUNCT
aiti-819	5	15	can	can	AUX
aiti-819	5	16	also	also	ADV
aiti-819	5	17	be	be	AUX
aiti-819	5	18	used	use	VERB
aiti-819	5	19	to	to	PART
aiti-819	5	20	represent	represent	VERB
aiti-819	5	21	an	an	DET
aiti-819	5	22	area	area	NOUN
aiti-819	5	23	.	.	PUNCT
aiti-819	6	1	although	although	SCONJ
aiti-819	6	2	most	most	ADJ
aiti-819	6	3	researchers	researcher	NOUN
aiti-819	6	4	have	have	AUX
aiti-819	6	5	presented	present	VERB
aiti-819	6	6	algorithms	algorithm	NOUN
aiti-819	6	7	that	that	PRON
aiti-819	6	8	find	find	VERB
aiti-819	6	9	the	the	DET
aiti-819	6	10	medial	medial	ADJ
aiti-819	6	11	-	-	PUNCT
aiti-819	6	12	axis	axis	NOUN
aiti-819	6	13	transform	transform	NOUN
aiti-819	6	14	from	from	ADP
aiti-819	6	15	an	an	DET
aiti-819	6	16	area	area	NOUN
aiti-819	6	17	,	,	PUNCT
aiti-819	6	18	a	a	DET
aiti-819	6	19	algorithm	algorithm	NOUN
aiti-819	6	20	using	use	VERB
aiti-819	6	21	the	the	DET
aiti-819	6	22	contrasting	contrast	VERB
aiti-819	6	23	approach	approach	NOUN
aiti-819	6	24	is	be	AUX
aiti-819	6	25	proposed	propose	VERB
aiti-819	6	26	;	;	PUNCT
aiti-819	6	27	i.e.	i.e.	X
aiti-819	6	28	,	,	PUNCT
aiti-819	6	29	it	it	PRON
aiti-819	6	30	finds	find	VERB
aiti-819	6	31	an	an	DET
aiti-819	6	32	area	area	NOUN
aiti-819	6	33	using	use	VERB
aiti-819	6	34	a	a	DET
aiti-819	6	35	medial	medial	ADJ
aiti-819	6	36	-	-	PUNCT
aiti-819	6	37	axis	axis	NOUN
aiti-819	6	38	transform	transform	NOUN
aiti-819	6	39	.	.	PUNCT
aiti-819	7	1	the	the	DET
aiti-819	7	2	medial	medial	ADJ
aiti-819	7	3	-	-	PUNCT
aiti-819	7	4	axis	axis	NOUN
aiti-819	7	5	transform	transform	NOUN
aiti-819	7	6	is	be	AUX
aiti-819	7	7	constructed	construct	VERB
aiti-819	7	8	using	use	VERB
aiti-819	7	9	discrete	discrete	ADJ
aiti-819	7	10	points	point	NOUN
aiti-819	7	11	on	on	ADP
aiti-819	7	12	a	a	DET
aiti-819	7	13	curve	curve	NOUN
aiti-819	7	14	and	and	CCONJ
aiti-819	7	15	referred	refer	VERB
aiti-819	7	16	to	to	ADP
aiti-819	7	17	as	as	ADP
aiti-819	7	18	the	the	DET
aiti-819	7	19	skeleton	skeleton	NOUN
aiti-819	7	20	of	of	ADP
aiti-819	7	21	the	the	DET
aiti-819	7	22	area	area	NOUN
aiti-819	7	23	.	.	PUNCT
aiti-819	8	1	subsequently	subsequently	ADV
aiti-819	8	2	,	,	PUNCT
aiti-819	8	3	using	use	VERB
aiti-819	8	4	the	the	DET
aiti-819	8	5	aforementioned	aforementioned	ADJ
aiti-819	8	6	discrete	discrete	ADJ
aiti-819	8	7	points	point	NOUN
aiti-819	8	8	,	,	PUNCT
aiti-819	8	9	medial	medial	ADJ
aiti-819	8	10	-	-	PUNCT
aiti-819	8	11	axis	axis	NOUN
aiti-819	8	12	circles	circle	NOUN
aiti-819	8	13	are	be	AUX
aiti-819	8	14	generated	generate	VERB
aiti-819	8	15	and	and	CCONJ
aiti-819	8	16	referred	refer	VERB
aiti-819	8	17	to	to	ADP
aiti-819	8	18	as	as	ADP
aiti-819	8	19	the	the	DET
aiti-819	8	20	muscles	muscle	NOUN
aiti-819	8	21	of	of	ADP
aiti-819	8	22	the	the	DET
aiti-819	8	23	area	area	NOUN
aiti-819	8	24	.	.	PUNCT
aiti-819	9	1	finally	finally	ADV
aiti-819	9	2	,	,	PUNCT
aiti-819	9	3	these	these	DET
aiti-819	9	4	medial	medial	ADJ
aiti-819	9	5	-	-	PUNCT
aiti-819	9	6	axis	axis	NOUN
aiti-819	9	7	circles	circle	NOUN
aiti-819	9	8	are	be	AUX
aiti-819	9	9	blended	blend	VERB
aiti-819	9	10	and	and	CCONJ
aiti-819	9	11	referred	refer	VERB
aiti-819	9	12	to	to	ADP
aiti-819	9	13	as	as	ADP
aiti-819	9	14	the	the	DET
aiti-819	9	15	blended	blended	ADJ
aiti-819	9	16	boundary	boundary	ADJ
aiti-819	9	17	curves	curve	NOUN
aiti-819	9	18	skin	skin	NOUN
aiti-819	9	19	of	of	ADP
aiti-819	9	20	the	the	DET
aiti-819	9	21	area	area	NOUN
aiti-819	9	22	;	;	PUNCT
aiti-819	9	23	consequently	consequently	ADV
aiti-819	9	24	,	,	PUNCT
aiti-819	9	25	the	the	DET
aiti-819	9	26	boundary	boundary	NOUN
aiti-819	9	27	of	of	ADP
aiti-819	9	28	the	the	DET
aiti-819	9	29	area	area	NOUN
aiti-819	9	30	generated	generate	VERB
aiti-819	9	31	is	be	AUX
aiti-819	9	32	smooth	smooth	ADJ
aiti-819	9	33	.	.	PUNCT
aiti-819	10	1	keywords	keyword	NOUN
aiti-819	10	2	:	:	PUNCT
aiti-819	10	3	medial	medial	ADJ
aiti-819	10	4	-	-	PUNCT
aiti-819	10	5	axis	axis	NOUN
aiti-819	10	6	transform	transform	NOUN
aiti-819	10	7	,	,	PUNCT
aiti-819	10	8	hermite	hermite	ADJ
aiti-819	10	9	curve	curve	NOUN
aiti-819	10	10	,	,	PUNCT
aiti-819	10	11	bezier	bezier	NOUN
aiti-819	10	12	curve	curve	NOUN
aiti-819	10	13	,	,	PUNCT
aiti-819	10	14	computer	computer	NOUN
aiti-819	10	15	-	-	PUNCT
aiti-819	10	16	aided	aid	VERB
aiti-819	10	17	geometric	geometric	ADJ
aiti-819	10	18	design	design	NOUN
aiti-819	10	19	1	1	NUM
aiti-819	10	20	.	.	PUNCT
aiti-819	10	21	introduction	introduction	NOUN
aiti-819	10	22	in	in	ADP
aiti-819	10	23	the	the	DET
aiti-819	10	24	domain	domain	NOUN
aiti-819	10	25	of	of	ADP
aiti-819	10	26	computer	computer	NOUN
aiti-819	10	27	-	-	PUNCT
aiti-819	10	28	aided	aid	VERB
aiti-819	10	29	geometric	geometric	ADJ
aiti-819	10	30	design	design	NOUN
aiti-819	10	31	,	,	PUNCT
aiti-819	10	32	an	an	DET
aiti-819	10	33	area	area	NOUN
aiti-819	10	34	can	can	AUX
aiti-819	10	35	be	be	AUX
aiti-819	10	36	represented	represent	VERB
aiti-819	10	37	using	use	VERB
aiti-819	10	38	various	various	ADJ
aiti-819	10	39	methods	method	NOUN
aiti-819	10	40	,	,	PUNCT
aiti-819	10	41	such	such	ADJ
aiti-819	10	42	as	as	ADP
aiti-819	10	43	via	via	ADP
aiti-819	10	44	its	its	PRON
aiti-819	10	45	boundary	boundary	ADJ
aiti-819	10	46	curves	curve	NOUN
aiti-819	10	47	,	,	PUNCT
aiti-819	10	48	via	via	ADP
aiti-819	10	49	its	its	PRON
aiti-819	10	50	medial	medial	ADJ
aiti-819	10	51	-	-	PUNCT
aiti-819	10	52	axis	axis	NOUN
aiti-819	10	53	transform	transform	NOUN
aiti-819	10	54	[	[	X
aiti-819	10	55	1	1	NUM
aiti-819	10	56	]	]	PUNCT
aiti-819	10	57	,	,	PUNCT
aiti-819	10	58	or	or	CCONJ
aiti-819	10	59	via	via	ADP
aiti-819	10	60	set	set	ADJ
aiti-819	10	61	operations	operation	NOUN
aiti-819	10	62	,	,	PUNCT
aiti-819	10	63	such	such	ADJ
aiti-819	10	64	as	as	ADP
aiti-819	10	65	union	union	NOUN
aiti-819	10	66	,	,	PUNCT
aiti-819	10	67	intersection	intersection	NOUN
aiti-819	10	68	,	,	PUNCT
aiti-819	10	69	and	and	CCONJ
aiti-819	10	70	difference	difference	NOUN
aiti-819	10	71	,	,	PUNCT
aiti-819	10	72	of	of	ADP
aiti-819	10	73	numerous	numerous	ADJ
aiti-819	10	74	primitive	primitive	ADJ
aiti-819	10	75	geometric	geometric	ADJ
aiti-819	10	76	objects	object	NOUN
aiti-819	10	77	.	.	PUNCT
aiti-819	11	1	to	to	PART
aiti-819	11	2	describe	describe	VERB
aiti-819	11	3	a	a	DET
aiti-819	11	4	curve	curve	NOUN
aiti-819	11	5	or	or	CCONJ
aiti-819	11	6	area	area	NOUN
aiti-819	11	7	in	in	ADP
aiti-819	11	8	two	two	NUM
aiti-819	11	9	dimensions	dimension	NOUN
aiti-819	11	10	(	(	PUNCT
aiti-819	11	11	2d	2d	NOUN
aiti-819	11	12	)	)	PUNCT
aiti-819	11	13	,	,	PUNCT
aiti-819	11	14	researchers	researcher	NOUN
aiti-819	11	15	attempted	attempt	VERB
aiti-819	11	16	to	to	PART
aiti-819	11	17	use	use	VERB
aiti-819	11	18	different	different	ADJ
aiti-819	11	19	curve	curve	NOUN
aiti-819	11	20	representations	representation	NOUN
aiti-819	11	21	in	in	ADP
aiti-819	11	22	different	different	ADJ
aiti-819	11	23	applications	application	NOUN
aiti-819	11	24	.	.	PUNCT
aiti-819	12	1	for	for	ADP
aiti-819	12	2	example	example	NOUN
aiti-819	12	3	,	,	PUNCT
aiti-819	12	4	cinque	cinque	NOUN
aiti-819	12	5	,	,	PUNCT
aiti-819	12	6	levialdi	levialdi	NOUN
aiti-819	12	7	,	,	PUNCT
aiti-819	12	8	and	and	CCONJ
aiti-819	12	9	malizia	malizia	PROPN
aiti-819	13	1	[	[	X
aiti-819	13	2	2	2	X
aiti-819	13	3	]	]	PUNCT
aiti-819	13	4	used	use	VERB
aiti-819	13	5	a	a	DET
aiti-819	13	6	cubic	cubic	ADJ
aiti-819	13	7	bezier	bezier	NOUN
aiti-819	13	8	curve	curve	NOUN
aiti-819	13	9	to	to	PART
aiti-819	13	10	describe	describe	VERB
aiti-819	13	11	the	the	DET
aiti-819	13	12	shape	shape	NOUN
aiti-819	13	13	via	via	ADP
aiti-819	13	14	its	its	PRON
aiti-819	13	15	boundary	boundary	ADJ
aiti-819	13	16	curve	curve	NOUN
aiti-819	13	17	with	with	ADP
aiti-819	13	18	orientation	orientation	NOUN
aiti-819	13	19	.	.	PUNCT
aiti-819	14	1	yang	yang	PROPN
aiti-819	14	2	,	,	PUNCT
aiti-819	14	3	lu	lu	PROPN
aiti-819	14	4	,	,	PUNCT
aiti-819	14	5	and	and	CCONJ
aiti-819	14	6	lee	lee	PROPN
aiti-819	15	1	[	[	X
aiti-819	15	2	3	3	X
aiti-819	15	3	]	]	PUNCT
aiti-819	15	4	used	use	VERB
aiti-819	15	5	a	a	DET
aiti-819	15	6	bezier	bezier	ADJ
aiti-819	15	7	curve	curve	NOUN
aiti-819	15	8	to	to	PART
aiti-819	15	9	describe	describe	VERB
aiti-819	15	10	the	the	DET
aiti-819	15	11	shape	shape	NOUN
aiti-819	15	12	of	of	ADP
aiti-819	15	13	chinese	chinese	ADJ
aiti-819	15	14	calligraphy	calligraphy	NOUN
aiti-819	15	15	characters	character	NOUN
aiti-819	15	16	[	[	X
aiti-819	15	17	4	4	NUM
aiti-819	15	18	]	]	PUNCT
aiti-819	15	19	.	.	PUNCT
aiti-819	16	1	chang	chang	PROPN
aiti-819	16	2	and	and	CCONJ
aiti-819	16	3	yan	yan	PROPN
aiti-819	17	1	[	[	X
aiti-819	17	2	5	5	NUM
aiti-819	17	3	]	]	PUNCT
aiti-819	17	4	derived	derive	VERB
aiti-819	17	5	an	an	DET
aiti-819	17	6	algorithm	algorithm	NOUN
aiti-819	17	7	to	to	PART
aiti-819	17	8	simulate	simulate	VERB
aiti-819	17	9	hand	hand	NOUN
aiti-819	17	10	-	-	PUNCT
aiti-819	17	11	drawn	draw	VERB
aiti-819	17	12	images	image	NOUN
aiti-819	17	13	using	use	VERB
aiti-819	17	14	a	a	DET
aiti-819	17	15	cubic	cubic	ADJ
aiti-819	17	16	bezier	bezier	NOUN
aiti-819	17	17	curve	curve	NOUN
aiti-819	17	18	.	.	PUNCT
aiti-819	18	1	cao	cao	PROPN
aiti-819	18	2	and	and	CCONJ
aiti-819	18	3	kot	kot	PROPN
aiti-819	19	1	[	[	X
aiti-819	19	2	6	6	NUM
aiti-819	19	3	]	]	PUNCT
aiti-819	19	4	derived	derive	VERB
aiti-819	19	5	an	an	DET
aiti-819	19	6	algorithm	algorithm	NOUN
aiti-819	19	7	to	to	PART
aiti-819	19	8	embed	embed	VERB
aiti-819	19	9	data	datum	NOUN
aiti-819	19	10	using	use	VERB
aiti-819	19	11	electronic	electronic	ADJ
aiti-819	19	12	inks	ink	NOUN
aiti-819	19	13	without	without	ADP
aiti-819	19	14	the	the	DET
aiti-819	19	15	loss	loss	NOUN
aiti-819	19	16	of	of	ADP
aiti-819	19	17	data	datum	NOUN
aiti-819	19	18	.	.	PUNCT
aiti-819	20	1	furthermore	furthermore	ADV
aiti-819	20	2	,	,	PUNCT
aiti-819	20	3	algorithms	algorithm	NOUN
aiti-819	20	4	were	be	AUX
aiti-819	20	5	proposed	propose	VERB
aiti-819	20	6	to	to	PART
aiti-819	20	7	derive	derive	VERB
aiti-819	20	8	the	the	DET
aiti-819	20	9	interior	interior	ADJ
aiti-819	20	10	/	/	SYM
aiti-819	20	11	exterior	exterior	ADJ
aiti-819	20	12	offset	offset	VERB
aiti-819	20	13	curves	curve	NOUN
aiti-819	20	14	and	and	CCONJ
aiti-819	20	15	medial	medial	ADJ
aiti-819	20	16	axis	axis	NOUN
aiti-819	20	17	of	of	ADP
aiti-819	20	18	an	an	DET
aiti-819	20	19	area	area	NOUN
aiti-819	20	20	using	use	VERB
aiti-819	20	21	the	the	DET
aiti-819	20	22	boundary	boundary	ADJ
aiti-819	20	23	curves	curve	NOUN
aiti-819	20	24	[	[	X
aiti-819	20	25	7	7	NUM
aiti-819	20	26	]	]	PUNCT
aiti-819	20	27	.	.	PUNCT
aiti-819	21	1	in	in	ADP
aiti-819	21	2	3d	3d	NUM
aiti-819	21	3	,	,	PUNCT
aiti-819	21	4	surface	surface	NOUN
aiti-819	21	5	representations	representation	NOUN
aiti-819	21	6	are	be	AUX
aiti-819	21	7	used	use	VERB
aiti-819	21	8	to	to	PART
aiti-819	21	9	simulate	simulate	VERB
aiti-819	21	10	natural	natural	ADJ
aiti-819	21	11	objects	object	NOUN
aiti-819	21	12	,	,	PUNCT
aiti-819	21	13	such	such	ADJ
aiti-819	21	14	as	as	ADP
aiti-819	21	15	flowers	flower	NOUN
aiti-819	21	16	[	[	X
aiti-819	21	17	8	8	NUM
aiti-819	21	18	]	]	PUNCT
aiti-819	21	19	.	.	PUNCT
aiti-819	22	1	in	in	ADP
aiti-819	22	2	addition	addition	NOUN
aiti-819	22	3	,	,	PUNCT
aiti-819	22	4	the	the	DET
aiti-819	22	5	circle	circle	NOUN
aiti-819	22	6	packing	packing	NOUN
aiti-819	22	7	problems	problem	NOUN
aiti-819	22	8	,	,	PUNCT
aiti-819	22	9	i.e.	i.e.	X
aiti-819	22	10	,	,	PUNCT
aiti-819	22	11	the	the	DET
aiti-819	22	12	arrangement	arrangement	NOUN
aiti-819	22	13	of	of	ADP
aiti-819	22	14	circles	circle	NOUN
aiti-819	22	15	with	with	ADP
aiti-819	22	16	same	same	ADJ
aiti-819	22	17	or	or	CCONJ
aiti-819	22	18	different	different	ADJ
aiti-819	22	19	radii	radius	NOUN
aiti-819	22	20	inside	inside	ADP
aiti-819	22	21	a	a	DET
aiti-819	22	22	specified	specified	ADJ
aiti-819	22	23	area	area	NOUN
aiti-819	22	24	,	,	PUNCT
aiti-819	22	25	were	be	AUX
aiti-819	22	26	also	also	ADV
aiti-819	22	27	investigated	investigate	VERB
aiti-819	22	28	by	by	ADP
aiti-819	22	29	researchers	researcher	NOUN
aiti-819	22	30	[	[	X
aiti-819	22	31	9	9	NUM
aiti-819	22	32	-	-	SYM
aiti-819	22	33	11	11	NUM
aiti-819	22	34	]	]	PUNCT
aiti-819	22	35	.	.	PUNCT
aiti-819	23	1	in	in	ADP
aiti-819	23	2	this	this	DET
aiti-819	23	3	study	study	NOUN
aiti-819	23	4	,	,	PUNCT
aiti-819	23	5	methods	method	NOUN
aiti-819	23	6	are	be	AUX
aiti-819	23	7	proposed	propose	VERB
aiti-819	23	8	to	to	PART
aiti-819	23	9	grow	grow	VERB
aiti-819	23	10	an	an	DET
aiti-819	23	11	area	area	NOUN
aiti-819	23	12	.	.	PUNCT
aiti-819	24	1	an	an	DET
aiti-819	24	2	area	area	NOUN
aiti-819	24	3	is	be	AUX
aiti-819	24	4	initialized	initialize	VERB
aiti-819	24	5	using	use	VERB
aiti-819	24	6	two	two	NUM
aiti-819	24	7	approaches	approach	NOUN
aiti-819	24	8	,	,	PUNCT
aiti-819	24	9	one	one	NUM
aiti-819	24	10	with	with	ADP
aiti-819	24	11	the	the	DET
aiti-819	24	12	use	use	NOUN
aiti-819	24	13	of	of	ADP
aiti-819	24	14	medial	medial	ADJ
aiti-819	24	15	-	-	PUNCT
aiti-819	24	16	axis	axis	NOUN
aiti-819	24	17	circles	circle	NOUN
aiti-819	24	18	,	,	PUNCT
aiti-819	24	19	and	and	CCONJ
aiti-819	24	20	the	the	DET
aiti-819	24	21	other	other	ADJ
aiti-819	24	22	via	via	ADP
aiti-819	24	23	points	point	NOUN
aiti-819	24	24	on	on	ADP
aiti-819	24	25	a	a	DET
aiti-819	24	26	curve	curve	NOUN
aiti-819	24	27	.	.	PUNCT
aiti-819	25	1	subsequently	subsequently	ADV
aiti-819	25	2	,	,	PUNCT
aiti-819	25	3	the	the	DET
aiti-819	25	4	algorithms	algorithm	NOUN
aiti-819	25	5	are	be	AUX
aiti-819	25	6	proposed	propose	VERB
aiti-819	25	7	to	to	PART
aiti-819	25	8	grow	grow	VERB
aiti-819	25	9	the	the	DET
aiti-819	25	10	areas	area	NOUN
aiti-819	25	11	using	use	VERB
aiti-819	25	12	the	the	DET
aiti-819	25	13	initialized	initialize	VERB
aiti-819	25	14	area	area	NOUN
aiti-819	25	15	.	.	PUNCT
aiti-819	26	1	given	give	VERB
aiti-819	26	2	a	a	DET
aiti-819	26	3	cubic	cubic	ADJ
aiti-819	26	4	bezier	bezier	NOUN
aiti-819	26	5	curve	curve	NOUN
aiti-819	26	6	with	with	ADP
aiti-819	26	7	n	n	CCONJ
aiti-819	26	8	discrete	discrete	ADJ
aiti-819	26	9	points	point	NOUN
aiti-819	26	10	on	on	ADP
aiti-819	26	11	it	it	PRON
aiti-819	26	12	,	,	PUNCT
aiti-819	26	13	n	n	PRON
aiti-819	26	14	circles	circle	NOUN
aiti-819	26	15	are	be	AUX
aiti-819	26	16	attempted	attempt	VERB
aiti-819	26	17	to	to	PART
aiti-819	26	18	find	find	VERB
aiti-819	26	19	centered	center	VERB
aiti-819	26	20	at	at	ADP
aiti-819	26	21	these	these	PRON
aiti-819	27	1	n	n	NUM
aiti-819	27	2	points	point	NOUN
aiti-819	27	3	with	with	ADP
aiti-819	27	4	different	different	ADJ
aiti-819	27	5	radii	radius	NOUN
aiti-819	27	6	,	,	PUNCT
aiti-819	27	7	such	such	ADJ
aiti-819	27	8	that	that	SCONJ
aiti-819	27	9	the	the	DET
aiti-819	27	10	neighboring	neighboring	NOUN
aiti-819	27	11	circles	circle	NOUN
aiti-819	27	12	are	be	AUX
aiti-819	27	13	tangent	tangent	ADJ
aiti-819	27	14	to	to	ADP
aiti-819	27	15	each	each	DET
aiti-819	27	16	other	other	ADJ
aiti-819	27	17	.	.	PUNCT
aiti-819	28	1	this	this	PRON
aiti-819	28	2	is	be	AUX
aiti-819	28	3	the	the	DET
aiti-819	28	4	initial	initial	ADJ
aiti-819	28	5	area	area	NOUN
aiti-819	28	6	that	that	PRON
aiti-819	28	7	is	be	AUX
aiti-819	28	8	constructed	construct	VERB
aiti-819	28	9	from	from	ADP
aiti-819	28	10	a	a	DET
aiti-819	28	11	curve	curve	NOUN
aiti-819	28	12	that	that	PRON
aiti-819	28	13	has	have	VERB
aiti-819	28	14	points	point	NOUN
aiti-819	28	15	on	on	ADP
aiti-819	28	16	it	it	PRON
aiti-819	28	17	.	.	PUNCT
aiti-819	29	1	next	next	ADV
aiti-819	29	2	,	,	PUNCT
aiti-819	29	3	the	the	DET
aiti-819	29	4	area	area	NOUN
aiti-819	29	5	along	along	ADP
aiti-819	29	6	different	different	ADJ
aiti-819	29	7	directions	direction	NOUN
aiti-819	29	8	is	be	AUX
aiti-819	29	9	grown	grow	VERB
aiti-819	29	10	;	;	PUNCT
aiti-819	29	11	the	the	DET
aiti-819	29	12	first	first	ADJ
aiti-819	29	13	direction	direction	NOUN
aiti-819	29	14	is	be	AUX
aiti-819	29	15	along	along	ADP
aiti-819	29	16	the	the	DET
aiti-819	29	17	two	two	NUM
aiti-819	29	18	end	end	NOUN
aiti-819	29	19	points	point	NOUN
aiti-819	29	20	of	of	ADP
aiti-819	29	21	the	the	DET
aiti-819	29	22	curve	curve	NOUN
aiti-819	29	23	,	,	PUNCT
aiti-819	29	24	as	as	SCONJ
aiti-819	29	25	depicted	depict	VERB
aiti-819	29	26	in	in	ADP
aiti-819	29	27	fig	fig	NOUN
aiti-819	29	28	.	.	PUNCT
aiti-819	30	1	1(a	1(a	NUM
aiti-819	30	2	)	)	PUNCT
aiti-819	30	3	;	;	PUNCT
aiti-819	30	4	the	the	DET
aiti-819	30	5	second	second	ADJ
aiti-819	30	6	direction	direction	NOUN
aiti-819	30	7	is	be	AUX
aiti-819	30	8	along	along	ADP
aiti-819	30	9	the	the	DET
aiti-819	30	10	two	two	NUM
aiti-819	30	11	sides	side	NOUN
aiti-819	30	12	of	of	ADP
aiti-819	30	13	the	the	DET
aiti-819	30	14	curve	curve	NOUN
aiti-819	30	15	,	,	PUNCT
aiti-819	30	16	as	as	SCONJ
aiti-819	30	17	depicted	depict	VERB
aiti-819	30	18	in	in	ADP
aiti-819	30	19	fig	fig	NOUN
aiti-819	30	20	.	.	PUNCT
aiti-819	31	1	1(b	1(b	NUM
aiti-819	31	2	)	)	PUNCT
aiti-819	31	3	.	.	PUNCT
aiti-819	32	1	a	a	DET
aiti-819	32	2	single	single	ADJ
aiti-819	32	3	circle	circle	NOUN
aiti-819	32	4	is	be	AUX
aiti-819	32	5	also	also	ADV
aiti-819	32	6	considered	consider	VERB
aiti-819	32	7	to	to	PART
aiti-819	32	8	be	be	AUX
aiti-819	32	9	an	an	DET
aiti-819	32	10	initial	initial	ADJ
aiti-819	32	11	area	area	NOUN
aiti-819	32	12	,	,	PUNCT
aiti-819	32	13	in	in	ADP
aiti-819	32	14	this	this	DET
aiti-819	32	15	case	case	NOUN
aiti-819	32	16	;	;	PUNCT
aiti-819	32	17	the	the	DET
aiti-819	32	18	area	area	NOUN
aiti-819	32	19	then	then	ADV
aiti-819	32	20	grows	grow	VERB
aiti-819	32	21	along	along	ADP
aiti-819	32	22	different	different	ADJ
aiti-819	32	23	directions	direction	NOUN
aiti-819	32	24	,	,	PUNCT
aiti-819	32	25	as	as	SCONJ
aiti-819	32	26	depicted	depict	VERB
aiti-819	32	27	in	in	ADP
aiti-819	32	28	fig	fig	NOUN
aiti-819	32	29	.	.	PUNCT
aiti-819	33	1	1(c	1(c	NUM
aiti-819	33	2	)	)	PUNCT
aiti-819	33	3	.	.	PUNCT
aiti-819	34	1	*	*	PUNCT
aiti-819	34	2	corresponding	correspond	VERB
aiti-819	34	3	author	author	NOUN
aiti-819	34	4	.	.	PUNCT
aiti-819	35	1	e	e	X
aiti-819	35	2	-	-	NOUN
aiti-819	35	3	mail	mail	NOUN
aiti-819	35	4	address	address	NOUN
aiti-819	35	5	:	:	PUNCT
aiti-819	35	6	chiang@gm.scu.edu.tw	chiang@gm.scu.edu.tw	PROPN
aiti-819	35	7	tel	tel	PROPN
aiti-819	35	8	.	.	PUNCT
aiti-819	35	9	:	:	PUNCT
aiti-819	36	1	+886	+886	NUM
aiti-819	36	2	-	-	SYM
aiti-819	36	3	2	2	NUM
aiti-819	36	4	-	-	PUNCT
aiti-819	36	5	23111531	23111531	NUM
aiti-819	36	6	ext	ext	NOUN
aiti-819	36	7	.	.	PROPN
aiti-819	37	1	3801	3801	NUM
aiti-819	37	2	;	;	PUNCT
aiti-819	37	3	fax	fax	NOUN
aiti-819	37	4	:	:	PUNCT
aiti-819	37	5	+886	+886	NUM
aiti-819	37	6	-	-	PUNCT
aiti-819	37	7	2	2	NUM
aiti-819	37	8	-	-	PUNCT
aiti-819	37	9	23756878	23756878	NUM
aiti-819	37	10	area	area	NOUN
aiti-819	37	11	-	-	PUNCT
aiti-819	37	12	construction	construction	NOUN
aiti-819	37	13	algorithms	algorithm	NOUN
aiti-819	37	14	using	use	VERB
aiti-819	37	15	tangent	tangent	NOUN
aiti-819	37	16	circles	circle	NOUN
aiti-819	37	17	ching	ching	PROPN
aiti-819	37	18	-	-	PUNCT
aiti-819	37	19	shoei	shoei	PROPN
aiti-819	37	20	chiang	chiang	PROPN
aiti-819	37	21	*	*	PUNCT
aiti-819	37	22	,	,	PUNCT
aiti-819	37	23	hung	hung	PROPN
aiti-819	37	24	-	-	PUNCT
aiti-819	37	25	chieh	chieh	PROPN
aiti-819	37	26	li	li	PROPN
aiti-819	37	27	advances	advance	NOUN
aiti-819	37	28	in	in	ADP
aiti-819	37	29	technology	technology	NOUN
aiti-819	37	30	innovation	innovation	NOUN
aiti-819	37	31	,	,	PUNCT
aiti-819	37	32	vol	vol	NOUN
aiti-819	37	33	.	.	PROPN
aiti-819	37	34	5	5	NUM
aiti-819	37	35	,	,	PUNCT
aiti-819	37	36	no	no	INTJ
aiti-819	37	37	.	.	NOUN
aiti-819	37	38	2	2	NUM
aiti-819	37	39	,	,	PUNCT
aiti-819	37	40	2020	2020	NUM
aiti-819	37	41	,	,	PUNCT
aiti-819	37	42	pp	pp	ADV
aiti-819	37	43	.	.	PUNCT
aiti-819	38	1	126	126	NUM
aiti-819	38	2	-	-	SYM
aiti-819	38	3	134	134	NUM
aiti-819	38	4	127	127	NUM
aiti-819	38	5	the	the	DET
aiti-819	38	6	initial	initial	ADJ
aiti-819	38	7	area	area	NOUN
aiti-819	38	8	generated	generate	VERB
aiti-819	38	9	by	by	ADP
aiti-819	38	10	the	the	DET
aiti-819	38	11	aforementioned	aforementioned	ADJ
aiti-819	38	12	curve	curve	NOUN
aiti-819	38	13	is	be	AUX
aiti-819	38	14	referred	refer	VERB
aiti-819	38	15	to	to	ADP
aiti-819	38	16	as	as	ADP
aiti-819	38	17	the	the	DET
aiti-819	38	18	skeleton	skeleton	NOUN
aiti-819	38	19	of	of	ADP
aiti-819	38	20	initial	initial	ADJ
aiti-819	38	21	area	area	NOUN
aiti-819	38	22	,	,	PUNCT
aiti-819	38	23	this	this	DET
aiti-819	38	24	curve	curve	NOUN
aiti-819	38	25	is	be	AUX
aiti-819	38	26	referred	refer	VERB
aiti-819	38	27	to	to	ADP
aiti-819	38	28	as	as	ADP
aiti-819	38	29	the	the	DET
aiti-819	38	30	skeleton	skeleton	NOUN
aiti-819	38	31	of	of	ADP
aiti-819	38	32	the	the	DET
aiti-819	38	33	initial	initial	ADJ
aiti-819	38	34	area	area	NOUN
aiti-819	38	35	and	and	CCONJ
aiti-819	38	36	these	these	DET
aiti-819	38	37	circles	circle	NOUN
aiti-819	38	38	as	as	ADP
aiti-819	38	39	the	the	DET
aiti-819	38	40	muscle	muscle	NOUN
aiti-819	38	41	of	of	ADP
aiti-819	38	42	the	the	DET
aiti-819	38	43	initial	initial	ADJ
aiti-819	38	44	area	area	NOUN
aiti-819	38	45	.	.	PUNCT
aiti-819	39	1	the	the	DET
aiti-819	39	2	union	union	NOUN
aiti-819	39	3	of	of	ADP
aiti-819	39	4	all	all	DET
aiti-819	39	5	the	the	DET
aiti-819	39	6	muscles	muscle	NOUN
aiti-819	39	7	is	be	AUX
aiti-819	39	8	referred	refer	VERB
aiti-819	39	9	to	to	ADP
aiti-819	39	10	as	as	ADP
aiti-819	39	11	the	the	DET
aiti-819	39	12	central	central	ADJ
aiti-819	39	13	muscle	muscle	NOUN
aiti-819	39	14	of	of	ADP
aiti-819	39	15	the	the	DET
aiti-819	39	16	area	area	NOUN
aiti-819	39	17	.	.	PUNCT
aiti-819	40	1	upon	upon	SCONJ
aiti-819	40	2	extending	extend	VERB
aiti-819	40	3	the	the	DET
aiti-819	40	4	area	area	NOUN
aiti-819	40	5	along	along	ADP
aiti-819	40	6	different	different	ADJ
aiti-819	40	7	directions	direction	NOUN
aiti-819	40	8	,	,	PUNCT
aiti-819	40	9	the	the	DET
aiti-819	40	10	circular	circular	ADJ
aiti-819	40	11	arc	arc	NOUN
aiti-819	40	12	connecting	connect	VERB
aiti-819	40	13	two	two	NUM
aiti-819	40	14	tangent	tangent	NOUN
aiti-819	40	15	circles	circle	NOUN
aiti-819	40	16	needs	need	VERB
aiti-819	40	17	to	to	PART
aiti-819	40	18	be	be	AUX
aiti-819	40	19	blended	blend	VERB
aiti-819	40	20	such	such	ADJ
aiti-819	40	21	that	that	SCONJ
aiti-819	40	22	the	the	DET
aiti-819	40	23	boundary	boundary	NOUN
aiti-819	40	24	of	of	ADP
aiti-819	40	25	the	the	DET
aiti-819	40	26	extended	extended	ADJ
aiti-819	40	27	area	area	NOUN
aiti-819	40	28	is	be	AUX
aiti-819	40	29	smooth	smooth	ADJ
aiti-819	40	30	.	.	PUNCT
aiti-819	41	1	the	the	DET
aiti-819	41	2	entire	entire	ADJ
aiti-819	41	3	process	process	NOUN
aiti-819	41	4	,	,	PUNCT
aiti-819	41	5	from	from	ADP
aiti-819	41	6	skeleton	skeleton	NOUN
aiti-819	41	7	to	to	ADP
aiti-819	41	8	muscles	muscle	NOUN
aiti-819	41	9	,	,	PUNCT
aiti-819	41	10	and	and	CCONJ
aiti-819	41	11	,	,	PUNCT
aiti-819	41	12	subsequently	subsequently	ADV
aiti-819	41	13	,	,	PUNCT
aiti-819	41	14	from	from	ADP
aiti-819	41	15	muscles	muscle	NOUN
aiti-819	41	16	to	to	ADP
aiti-819	41	17	skins	skin	NOUN
aiti-819	41	18	,	,	PUNCT
aiti-819	41	19	leads	lead	VERB
aiti-819	41	20	to	to	ADP
aiti-819	41	21	the	the	DET
aiti-819	41	22	generation	generation	NOUN
aiti-819	41	23	of	of	ADP
aiti-819	41	24	the	the	DET
aiti-819	41	25	desired	desire	VERB
aiti-819	41	26	area	area	NOUN
aiti-819	41	27	.	.	PUNCT
aiti-819	42	1	the	the	DET
aiti-819	42	2	generation	generation	NOUN
aiti-819	42	3	of	of	ADP
aiti-819	42	4	the	the	DET
aiti-819	42	5	skeleton	skeleton	NOUN
aiti-819	42	6	and	and	CCONJ
aiti-819	42	7	skin	skin	NOUN
aiti-819	42	8	is	be	AUX
aiti-819	42	9	simple	simple	ADJ
aiti-819	42	10	.	.	PUNCT
aiti-819	43	1	therefore	therefore	ADV
aiti-819	43	2	,	,	PUNCT
aiti-819	43	3	the	the	DET
aiti-819	43	4	extension	extension	NOUN
aiti-819	43	5	of	of	ADP
aiti-819	43	6	the	the	DET
aiti-819	43	7	muscles	muscle	NOUN
aiti-819	43	8	is	be	AUX
aiti-819	43	9	mainly	mainly	ADV
aiti-819	43	10	emphasized	emphasize	VERB
aiti-819	43	11	.	.	PUNCT
aiti-819	44	1	in	in	ADP
aiti-819	44	2	the	the	DET
aiti-819	44	3	first	first	ADJ
aiti-819	44	4	section	section	NOUN
aiti-819	44	5	,	,	PUNCT
aiti-819	44	6	the	the	DET
aiti-819	44	7	problem	problem	NOUN
aiti-819	44	8	is	be	AUX
aiti-819	44	9	illustrated	illustrate	VERB
aiti-819	44	10	.	.	PUNCT
aiti-819	45	1	in	in	ADP
aiti-819	45	2	the	the	DET
aiti-819	45	3	second	second	ADJ
aiti-819	45	4	section	section	NOUN
aiti-819	45	5	,	,	PUNCT
aiti-819	45	6	an	an	DET
aiti-819	45	7	algorithm	algorithm	NOUN
aiti-819	45	8	is	be	AUX
aiti-819	45	9	proposed	propose	VERB
aiti-819	45	10	to	to	PART
aiti-819	45	11	generate	generate	VERB
aiti-819	45	12	the	the	DET
aiti-819	45	13	central	central	ADJ
aiti-819	45	14	muscles	muscle	NOUN
aiti-819	45	15	,	,	PUNCT
aiti-819	45	16	and	and	CCONJ
aiti-819	45	17	in	in	ADP
aiti-819	45	18	the	the	DET
aiti-819	45	19	third	third	ADJ
aiti-819	45	20	section	section	NOUN
aiti-819	45	21	,	,	PUNCT
aiti-819	45	22	the	the	DET
aiti-819	45	23	extending	extending	NOUN
aiti-819	45	24	of	of	ADP
aiti-819	45	25	the	the	DET
aiti-819	45	26	muscles	muscle	NOUN
aiti-819	45	27	is	be	AUX
aiti-819	45	28	introduced	introduce	VERB
aiti-819	45	29	from	from	ADP
aiti-819	45	30	one	one	NUM
aiti-819	45	31	side	side	NOUN
aiti-819	45	32	of	of	ADP
aiti-819	45	33	the	the	DET
aiti-819	45	34	skeleton	skeleton	NOUN
aiti-819	45	35	,	,	PUNCT
aiti-819	45	36	or	or	CCONJ
aiti-819	45	37	from	from	ADP
aiti-819	45	38	every	every	DET
aiti-819	45	39	direction	direction	NOUN
aiti-819	45	40	of	of	ADP
aiti-819	45	41	a	a	DET
aiti-819	45	42	circle	circle	NOUN
aiti-819	45	43	muscle	muscle	NOUN
aiti-819	45	44	.	.	PUNCT
aiti-819	46	1	the	the	DET
aiti-819	46	2	conclusions	conclusion	NOUN
aiti-819	46	3	are	be	AUX
aiti-819	46	4	presented	present	VERB
aiti-819	46	5	in	in	ADP
aiti-819	46	6	the	the	DET
aiti-819	46	7	last	last	ADJ
aiti-819	46	8	section	section	NOUN
aiti-819	46	9	.	.	PUNCT
aiti-819	47	1	(	(	PUNCT
aiti-819	47	2	a	a	X
aiti-819	47	3	)	)	PUNCT
aiti-819	47	4	along	along	ADP
aiti-819	47	5	two	two	NUM
aiti-819	47	6	end	end	NOUN
aiti-819	47	7	points	point	NOUN
aiti-819	47	8	of	of	ADP
aiti-819	47	9	the	the	DET
aiti-819	47	10	central	central	ADJ
aiti-819	47	11	muscle	muscle	NOUN
aiti-819	47	12	(	(	PUNCT
aiti-819	47	13	b	b	NOUN
aiti-819	47	14	)	)	PUNCT
aiti-819	47	15	along	along	ADP
aiti-819	47	16	one	one	NUM
aiti-819	47	17	side	side	NOUN
aiti-819	47	18	of	of	ADP
aiti-819	47	19	the	the	DET
aiti-819	47	20	central	central	ADJ
aiti-819	47	21	muscle	muscle	NOUN
aiti-819	47	22	(	(	PUNCT
aiti-819	47	23	c	c	NOUN
aiti-819	47	24	)	)	PUNCT
aiti-819	47	25	along	along	ADP
aiti-819	47	26	multiple	multiple	ADJ
aiti-819	47	27	directions	direction	NOUN
aiti-819	47	28	of	of	ADP
aiti-819	47	29	a	a	DET
aiti-819	47	30	circle	circle	NOUN
aiti-819	47	31	fig	fig	NOUN
aiti-819	47	32	.	.	PUNCT
aiti-819	48	1	1	1	NUM
aiti-819	48	2	muscle	muscle	NOUN
aiti-819	48	3	growth	growth	NOUN
aiti-819	48	4	2	2	NUM
aiti-819	48	5	.	.	PUNCT
aiti-819	48	6	generating	generate	VERB
aiti-819	48	7	central	central	ADJ
aiti-819	48	8	muscles	muscle	NOUN
aiti-819	48	9	consider	consider	VERB
aiti-819	48	10	the	the	DET
aiti-819	48	11	following	follow	VERB
aiti-819	48	12	problem	problem	NOUN
aiti-819	48	13	.	.	PUNCT
aiti-819	49	1	given	give	VERB
aiti-819	49	2	n	n	PRON
aiti-819	49	3	distinct	distinct	ADJ
aiti-819	49	4	ordered	order	VERB
aiti-819	49	5	points	point	NOUN
aiti-819	49	6	pi	pi	NOUN
aiti-819	49	7	,	,	PUNCT
aiti-819	49	8	where	where	SCONJ
aiti-819	49	9	i	i	PRON
aiti-819	49	10	=	=	NOUN
aiti-819	49	11	0	0	NUM
aiti-819	49	12	,	,	PUNCT
aiti-819	49	13	…	…	PUNCT
aiti-819	49	14	,	,	PUNCT
aiti-819	49	15	n	n	CCONJ
aiti-819	49	16	,	,	PUNCT
aiti-819	49	17	a	a	DET
aiti-819	49	18	set	set	NOUN
aiti-819	49	19	of	of	ADP
aiti-819	49	20	circles	circle	NOUN
aiti-819	49	21	has	have	VERB
aiti-819	49	22	to	to	PART
aiti-819	49	23	be	be	AUX
aiti-819	49	24	found	find	VERB
aiti-819	49	25	,	,	PUNCT
aiti-819	49	26	ci	ci	NOUN
aiti-819	49	27	,	,	PUNCT
aiti-819	49	28	whose	whose	DET
aiti-819	49	29	circles	circle	NOUN
aiti-819	49	30	are	be	AUX
aiti-819	49	31	centered	center	VERB
aiti-819	49	32	at	at	ADP
aiti-819	49	33	these	these	DET
aiti-819	49	34	points	point	NOUN
aiti-819	49	35	pi	pi	NOUN
aiti-819	49	36	,	,	PUNCT
aiti-819	49	37	and	and	CCONJ
aiti-819	49	38	each	each	DET
aiti-819	49	39	circle	circle	NOUN
aiti-819	49	40	is	be	AUX
aiti-819	49	41	tangent	tangent	ADJ
aiti-819	49	42	to	to	ADP
aiti-819	49	43	its	its	PRON
aiti-819	49	44	neighboring	neighboring	NOUN
aiti-819	49	45	circles	circle	NOUN
aiti-819	49	46	.	.	PUNCT
aiti-819	50	1	in	in	ADP
aiti-819	50	2	this	this	DET
aiti-819	50	3	problem	problem	NOUN
aiti-819	50	4	,	,	PUNCT
aiti-819	50	5	there	there	PRON
aiti-819	50	6	are	be	VERB
aiti-819	50	7	n+1	n+1	PROPN
aiti-819	50	8	variables	variable	NOUN
aiti-819	50	9	(	(	PUNCT
aiti-819	50	10	ri	ri	NOUN
aiti-819	50	11	,	,	PUNCT
aiti-819	50	12	where	where	SCONJ
aiti-819	50	13	i	i	PRON
aiti-819	50	14	=	=	NOUN
aiti-819	50	15	0	0	NUM
aiti-819	50	16	,	,	PUNCT
aiti-819	50	17	…	…	PUNCT
aiti-819	50	18	,	,	PUNCT
aiti-819	50	19	n	n	CCONJ
aiti-819	50	20	)	)	PUNCT
aiti-819	50	21	with	with	ADP
aiti-819	50	22	only	only	ADV
aiti-819	50	23	n	n	PRON
aiti-819	50	24	constraint	constraint	NOUN
aiti-819	50	25	equations	equation	NOUN
aiti-819	50	26	(	(	PUNCT
aiti-819	50	27	li	li	NOUN
aiti-819	50	28	=	=	SYM
aiti-819	50	29	dist(pi	dist(pi	PROPN
aiti-819	50	30	,	,	PUNCT
aiti-819	50	31	pi+1	pi+1	NUM
aiti-819	50	32	)	)	PUNCT
aiti-819	50	33	,	,	PUNCT
aiti-819	50	34	i	i	NOUN
aiti-819	50	35	=	=	NOUN
aiti-819	50	36	0	0	NUM
aiti-819	50	37	,	,	PUNCT
aiti-819	50	38	…	…	PUNCT
aiti-819	50	39	,	,	PUNCT
aiti-819	50	40	n–1	n–1	PRON
aiti-819	50	41	)	)	PUNCT
aiti-819	50	42	.	.	PUNCT
aiti-819	51	1	therefore	therefore	ADV
aiti-819	51	2	,	,	PUNCT
aiti-819	51	3	one	one	NUM
aiti-819	51	4	more	more	ADJ
aiti-819	51	5	constraint	constraint	NOUN
aiti-819	51	6	equation	equation	NOUN
aiti-819	51	7	needs	need	VERB
aiti-819	51	8	solving	solve	VERB
aiti-819	51	9	the	the	DET
aiti-819	51	10	aforementioned	aforementioned	ADJ
aiti-819	51	11	problem	problem	NOUN
aiti-819	51	12	.	.	PUNCT
aiti-819	52	1	the	the	DET
aiti-819	52	2	following	follow	VERB
aiti-819	52	3	algorithm	algorithm	NOUN
aiti-819	52	4	can	can	AUX
aiti-819	52	5	be	be	AUX
aiti-819	52	6	obtained	obtain	VERB
aiti-819	52	7	by	by	ADP
aiti-819	52	8	inputting	inputte	VERB
aiti-819	52	9	the	the	DET
aiti-819	52	10	value	value	NOUN
aiti-819	52	11	r0	r0	NOUN
aiti-819	52	12	:	:	PUNCT
aiti-819	52	13	algorithm	algorithm	NOUN
aiti-819	52	14	1	1	NUM
aiti-819	52	15	:	:	SYM
aiti-819	52	16	1	1	NUM
aiti-819	52	17	.	.	X
aiti-819	52	18	input	input	VERB
aiti-819	52	19	the	the	DET
aiti-819	52	20	distinct	distinct	ADJ
aiti-819	52	21	ordered	order	VERB
aiti-819	52	22	points	point	NOUN
aiti-819	52	23	,	,	PUNCT
aiti-819	52	24	i.e.	i.e.	X
aiti-819	52	25	,	,	PUNCT
aiti-819	52	26	p0	p0	NOUN
aiti-819	52	27	,	,	PUNCT
aiti-819	52	28	p1	p1	NOUN
aiti-819	52	29	,	,	PUNCT
aiti-819	52	30	…	…	PUNCT
aiti-819	52	31	,	,	PUNCT
aiti-819	52	32	pn	pn	NOUN
aiti-819	52	33	.	.	PROPN
aiti-819	52	34	2	2	NUM
aiti-819	52	35	.	.	X
aiti-819	52	36	input	input	NOUN
aiti-819	52	37	r0	r0	NOUN
aiti-819	52	38	3	3	NUM
aiti-819	52	39	.	.	PUNCT
aiti-819	53	1	for	for	ADP
aiti-819	53	2	i	i	PRON
aiti-819	53	3	in	in	ADP
aiti-819	53	4	0	0	NUM
aiti-819	53	5	,	,	PUNCT
aiti-819	53	6	1	1	NUM
aiti-819	53	7	,	,	PUNCT
aiti-819	53	8	…	…	PUNCT
aiti-819	53	9	,	,	PUNCT
aiti-819	53	10	n–1	n–1	NOUN
aiti-819	53	11	:	:	PUNCT
aiti-819	53	12	4	4	X
aiti-819	53	13	.	.	NUM
aiti-819	53	14	calculate	calculate	NOUN
aiti-819	53	15	ri+1	ri+1	PROPN
aiti-819	53	16	=	=	SYM
aiti-819	53	17	li	li	PROPN
aiti-819	53	18	–	–	PUNCT
aiti-819	53	19	ri	ri	PROPN
aiti-819	53	20	,	,	PUNCT
aiti-819	53	21	where	where	SCONJ
aiti-819	53	22	0	0	X
aiti-819	53	23	<	<	X
aiti-819	53	24	r0	r0	NOUN
aiti-819	53	25	<	<	X
aiti-819	53	26	l0	l0	PROPN
aiti-819	53	27	although	although	SCONJ
aiti-819	53	28	the	the	DET
aiti-819	53	29	neighboring	neighboring	NOUN
aiti-819	53	30	circles	circle	NOUN
aiti-819	53	31	are	be	AUX
aiti-819	53	32	tangents	tangent	NOUN
aiti-819	53	33	to	to	ADP
aiti-819	53	34	each	each	DET
aiti-819	53	35	other	other	ADJ
aiti-819	53	36	,	,	PUNCT
aiti-819	53	37	two	two	NUM
aiti-819	53	38	neighbors	neighbor	NOUN
aiti-819	53	39	of	of	ADP
aiti-819	53	40	the	the	DET
aiti-819	53	41	same	same	ADJ
aiti-819	53	42	circle	circle	NOUN
aiti-819	53	43	can	can	AUX
aiti-819	53	44	not	not	PART
aiti-819	53	45	be	be	AUX
aiti-819	53	46	ensured	ensure	VERB
aiti-819	53	47	that	that	SCONJ
aiti-819	53	48	they	they	PRON
aiti-819	53	49	would	would	AUX
aiti-819	53	50	not	not	PART
aiti-819	53	51	intersect	intersect	VERB
aiti-819	53	52	each	each	DET
aiti-819	53	53	other	other	ADJ
aiti-819	53	54	.	.	PUNCT
aiti-819	54	1	therefore	therefore	ADV
aiti-819	54	2	,	,	PUNCT
aiti-819	54	3	to	to	PART
aiti-819	54	4	avoid	avoid	VERB
aiti-819	54	5	the	the	DET
aiti-819	54	6	aforementioned	aforementioned	ADJ
aiti-819	54	7	intersection	intersection	NOUN
aiti-819	54	8	,	,	PUNCT
aiti-819	54	9	constraints	constraint	NOUN
aiti-819	54	10	are	be	AUX
aiti-819	54	11	placed	place	VERB
aiti-819	54	12	on	on	ADP
aiti-819	54	13	the	the	DET
aiti-819	54	14	radius	radius	NOUN
aiti-819	54	15	of	of	ADP
aiti-819	54	16	each	each	DET
aiti-819	54	17	circle	circle	NOUN
aiti-819	54	18	using	use	VERB
aiti-819	54	19	the	the	DET
aiti-819	54	20	following	follow	VERB
aiti-819	54	21	theorems	theorem	NOUN
aiti-819	54	22	:	:	PUNCT
aiti-819	54	23	theorem	theorem	NOUN
aiti-819	54	24	1	1	NUM
aiti-819	54	25	:	:	PUNCT
aiti-819	54	26	given	give	VERB
aiti-819	54	27	pi	pi	NOUN
aiti-819	54	28	,	,	PUNCT
aiti-819	54	29	where	where	SCONJ
aiti-819	54	30	i	i	PRON
aiti-819	54	31	=	=	NOUN
aiti-819	54	32	0	0	NUM
aiti-819	54	33	,	,	PUNCT
aiti-819	54	34	...	...	PUNCT
aiti-819	54	35	,	,	PUNCT
aiti-819	54	36	n	n	CCONJ
aiti-819	54	37	,	,	PUNCT
aiti-819	54	38	if	if	SCONJ
aiti-819	54	39	ci-1	ci-1	NOUN
aiti-819	54	40	did	do	AUX
aiti-819	54	41	not	not	PART
aiti-819	54	42	intersect	intersect	VERB
aiti-819	54	43	ci+1	ci+1	PROPN
aiti-819	54	44	,	,	PUNCT
aiti-819	54	45	where	where	SCONJ
aiti-819	54	46	i	i	PRON
aiti-819	54	47	=	=	NOUN
aiti-819	54	48	1	1	NUM
aiti-819	54	49	,	,	PUNCT
aiti-819	54	50	..	..	PUNCT
aiti-819	54	51	,	,	PUNCT
aiti-819	54	52	n–1	n–1	PROPN
aiti-819	54	53	,	,	PUNCT
aiti-819	54	54	then	then	ADV
aiti-819	54	55	ri	ri	INTJ
aiti-819	54	56	>	>	X
aiti-819	54	57	(	(	PUNCT
aiti-819	54	58	li-1+li	li-1+li	NOUN
aiti-819	54	59	-	-	PUNCT
aiti-819	54	60	dist(pi+1,pi-1))/2	dist(pi+1,pi-1))/2	NOUN
aiti-819	54	61	.	.	PUNCT
aiti-819	55	1	(	(	PUNCT
aiti-819	55	2	see	see	VERB
aiti-819	55	3	fig	fig	NOUN
aiti-819	55	4	.	.	PUNCT
aiti-819	56	1	2	2	NUM
aiti-819	56	2	)	)	PUNCT
aiti-819	56	3	proof	proof	NOUN
aiti-819	56	4	:	:	PUNCT
aiti-819	56	5	the	the	DET
aiti-819	56	6	result	result	NOUN
aiti-819	56	7	is	be	AUX
aiti-819	56	8	derived	derive	VERB
aiti-819	56	9	directly	directly	ADV
aiti-819	56	10	from	from	ADP
aiti-819	56	11	the	the	DET
aiti-819	56	12	following	follow	VERB
aiti-819	56	13	equation	equation	NOUN
aiti-819	56	14	:	:	PUNCT
aiti-819	56	15	dist	dist	NOUN
aiti-819	56	16	(	(	PUNCT
aiti-819	56	17	pi+1	pi+1	X
aiti-819	56	18	,	,	PUNCT
aiti-819	56	19	pi-1	pi-1	ADJ
aiti-819	56	20	)	)	PUNCT
aiti-819	56	21	>	>	X
aiti-819	57	1	ri-1+ri+1	ri-1+ri+1	PROPN
aiti-819	57	2	,	,	PUNCT
aiti-819	57	3	where	where	SCONJ
aiti-819	57	4	ri-1	ri-1	PRON
aiti-819	57	5	=	=	SYM
aiti-819	57	6	li-1	li-1	X
aiti-819	57	7	–	–	PUNCT
aiti-819	57	8	ri	ri	NOUN
aiti-819	57	9	and	and	CCONJ
aiti-819	57	10	ri+1	ri+1	PROPN
aiti-819	57	11	=	=	SYM
aiti-819	57	12	li	li	X
aiti-819	57	13	–	–	PUNCT
aiti-819	57	14	ri	ri	PROPN
aiti-819	57	15	.	.	PROPN
aiti-819	57	16	advances	advance	NOUN
aiti-819	57	17	in	in	ADP
aiti-819	57	18	technology	technology	NOUN
aiti-819	57	19	innovation	innovation	NOUN
aiti-819	57	20	,	,	PUNCT
aiti-819	57	21	vol	vol	NOUN
aiti-819	57	22	.	.	PROPN
aiti-819	57	23	5	5	NUM
aiti-819	57	24	,	,	PUNCT
aiti-819	57	25	no	no	INTJ
aiti-819	57	26	.	.	NOUN
aiti-819	57	27	2	2	NUM
aiti-819	57	28	,	,	PUNCT
aiti-819	57	29	2020	2020	NUM
aiti-819	57	30	,	,	PUNCT
aiti-819	57	31	pp	pp	ADV
aiti-819	57	32	.	.	PUNCT
aiti-819	58	1	126	126	NUM
aiti-819	58	2	-	-	SYM
aiti-819	58	3	134	134	NUM
aiti-819	58	4	128	128	NUM
aiti-819	58	5	theorem	theorem	NOUN
aiti-819	58	6	1	1	NUM
aiti-819	58	7	is	be	AUX
aiti-819	58	8	used	use	VERB
aiti-819	58	9	to	to	PART
aiti-819	58	10	calculate	calculate	VERB
aiti-819	58	11	the	the	DET
aiti-819	58	12	lower	low	ADJ
aiti-819	58	13	bound	bind	VERB
aiti-819	58	14	of	of	ADP
aiti-819	58	15	the	the	DET
aiti-819	58	16	radius	radius	NOUN
aiti-819	58	17	of	of	ADP
aiti-819	58	18	circle	circle	NOUN
aiti-819	58	19	centered	center	VERB
aiti-819	58	20	at	at	ADP
aiti-819	58	21	pi	pi	NOUN
aiti-819	58	22	,	,	PUNCT
aiti-819	58	23	and	and	CCONJ
aiti-819	58	24	these	these	DET
aiti-819	58	25	radii	radius	NOUN
aiti-819	58	26	are	be	AUX
aiti-819	58	27	denoted	denote	VERB
aiti-819	58	28	by	by	ADP
aiti-819	58	29	mri	mri	NOUN
aiti-819	58	30	,	,	PUNCT
aiti-819	58	31	where	where	SCONJ
aiti-819	58	32	i	i	PRON
aiti-819	58	33	=	=	NOUN
aiti-819	58	34	1	1	NUM
aiti-819	58	35	,	,	PUNCT
aiti-819	58	36	…	…	PUNCT
aiti-819	58	37	,	,	PUNCT
aiti-819	58	38	n–1	n–1	PRON
aiti-819	58	39	.	.	PUNCT
aiti-819	59	1	notably	notably	ADV
aiti-819	59	2	,	,	PUNCT
aiti-819	59	3	li-1+li	li-1+li	NOUN
aiti-819	59	4	-	-	PUNCT
aiti-819	59	5	dist	dist	NOUN
aiti-819	59	6	(	(	PUNCT
aiti-819	59	7	pi+1,pi-1)>0	pi+1,pi-1)>0	NOUN
aiti-819	59	8	by	by	ADP
aiti-819	59	9	triangle	triangle	NOUN
aiti-819	59	10	inequality	inequality	NOUN
aiti-819	59	11	.	.	PUNCT
aiti-819	60	1	consider	consider	VERB
aiti-819	60	2	the	the	DET
aiti-819	60	3	case	case	NOUN
aiti-819	60	4	wherein	wherein	SCONJ
aiti-819	60	5	two	two	NUM
aiti-819	60	6	circles	circle	NOUN
aiti-819	60	7	ci	ci	NOUN
aiti-819	60	8	=	=	SYM
aiti-819	60	9	c	c	PROPN
aiti-819	60	10	(	(	PUNCT
aiti-819	60	11	pi	pi	NOUN
aiti-819	60	12	,	,	PUNCT
aiti-819	60	13	mri	mri	NOUN
aiti-819	60	14	)	)	PUNCT
aiti-819	60	15	and	and	CCONJ
aiti-819	60	16	ci+1	ci+1	PROPN
aiti-819	60	17	=	=	SYM
aiti-819	60	18	c(pi+1	c(pi+1	PROPN
aiti-819	60	19	,	,	PUNCT
aiti-819	60	20	mri+1	mri+1	PROPN
aiti-819	60	21	)	)	PUNCT
aiti-819	60	22	,	,	PUNCT
aiti-819	60	23	where	where	SCONJ
aiti-819	60	24	i	i	PRON
aiti-819	60	25	=	=	NOUN
aiti-819	60	26	1	1	NUM
aiti-819	60	27	,	,	PUNCT
aiti-819	60	28	…	…	PUNCT
aiti-819	60	29	,	,	PUNCT
aiti-819	60	30	n–2	n–2	PROPN
aiti-819	60	31	intersect	intersect	VERB
aiti-819	60	32	each	each	DET
aiti-819	60	33	other	other	ADJ
aiti-819	60	34	;	;	PUNCT
aiti-819	60	35	therefore	therefore	ADV
aiti-819	60	36	,	,	PUNCT
aiti-819	60	37	it	it	PRON
aiti-819	60	38	is	be	AUX
aiti-819	60	39	impossible	impossible	ADJ
aiti-819	60	40	to	to	PART
aiti-819	60	41	find	find	VERB
aiti-819	60	42	a	a	DET
aiti-819	60	43	set	set	NOUN
aiti-819	60	44	of	of	ADP
aiti-819	60	45	circles	circle	NOUN
aiti-819	60	46	that	that	PRON
aiti-819	60	47	are	be	AUX
aiti-819	60	48	tangents	tangent	NOUN
aiti-819	60	49	to	to	ADP
aiti-819	60	50	each	each	DET
aiti-819	60	51	other	other	ADJ
aiti-819	60	52	,	,	PUNCT
aiti-819	60	53	i.e.	i.e.	X
aiti-819	60	54	,	,	PUNCT
aiti-819	60	55	the	the	DET
aiti-819	60	56	circles	circle	NOUN
aiti-819	60	57	do	do	AUX
aiti-819	60	58	not	not	PART
aiti-819	60	59	intersect	intersect	VERB
aiti-819	60	60	each	each	DET
aiti-819	60	61	other	other	ADJ
aiti-819	60	62	.	.	PUNCT
aiti-819	61	1	therefore	therefore	ADV
aiti-819	61	2	,	,	PUNCT
aiti-819	61	3	the	the	DET
aiti-819	61	4	following	follow	VERB
aiti-819	61	5	example	example	NOUN
aiti-819	61	6	is	be	AUX
aiti-819	61	7	provided	provide	VERB
aiti-819	61	8	:	:	PUNCT
aiti-819	61	9	fig	fig	NOUN
aiti-819	61	10	.	.	PUNCT
aiti-819	62	1	2	2	NUM
aiti-819	62	2	intersection	intersection	NOUN
aiti-819	62	3	of	of	ADP
aiti-819	62	4	two	two	NUM
aiti-819	62	5	neighboring	neighboring	NOUN
aiti-819	62	6	circles	circle	NOUN
aiti-819	62	7	(	(	PUNCT
aiti-819	62	8	a	a	PRON
aiti-819	62	9	)	)	PUNCT
aiti-819	62	10	invalid	invalid	ADJ
aiti-819	62	11	input	input	NOUN
aiti-819	62	12	(	(	PUNCT
aiti-819	62	13	b	b	NOUN
aiti-819	62	14	)	)	PUNCT
aiti-819	62	15	minimal	minimal	ADJ
aiti-819	62	16	radius	radius	NOUN
aiti-819	62	17	(	(	PUNCT
aiti-819	62	18	c	c	NOUN
aiti-819	62	19	)	)	PUNCT
aiti-819	62	20	cj-1	cj-1	ADV
aiti-819	62	21	is	be	AUX
aiti-819	62	22	tangent	tangent	ADJ
aiti-819	62	23	to	to	ADP
aiti-819	62	24	cj+1	cj+1	NUM
aiti-819	62	25	(	(	PUNCT
aiti-819	62	26	d	d	NOUN
aiti-819	62	27	)	)	PUNCT
aiti-819	62	28	better	well	ADJ
aiti-819	62	29	result	result	VERB
aiti-819	62	30	fig	fig	NOUN
aiti-819	62	31	.	.	PUNCT
aiti-819	63	1	3	3	NUM
aiti-819	63	2	circles	circle	NOUN
aiti-819	63	3	with	with	ADP
aiti-819	63	4	different	different	ADJ
aiti-819	63	5	radii	radius	NOUN
aiti-819	63	6	example	example	NOUN
aiti-819	63	7	1	1	NUM
aiti-819	63	8	:	:	PUNCT
aiti-819	63	9	given	give	VERB
aiti-819	63	10	four	four	NUM
aiti-819	63	11	points	point	NOUN
aiti-819	63	12	,	,	PUNCT
aiti-819	63	13	namely	namely	ADV
aiti-819	63	14	,	,	PUNCT
aiti-819	63	15	p0	p0	NOUN
aiti-819	63	16	=	=	SYM
aiti-819	63	17	(	(	PUNCT
aiti-819	63	18	0	0	NUM
aiti-819	63	19	,	,	PUNCT
aiti-819	63	20	0	0	NUM
aiti-819	63	21	)	)	PUNCT
aiti-819	63	22	,	,	PUNCT
aiti-819	63	23	p1	p1	NOUN
aiti-819	63	24	=	=	SYM
aiti-819	63	25	(	(	PUNCT
aiti-819	63	26	2	2	NUM
aiti-819	63	27	,	,	PUNCT
aiti-819	63	28	5	5	NUM
aiti-819	63	29	)	)	PUNCT
aiti-819	63	30	,	,	PUNCT
aiti-819	63	31	p2	p2	PROPN
aiti-819	63	32	=	=	SYM
aiti-819	63	33	(	(	PUNCT
aiti-819	63	34	4	4	NUM
aiti-819	63	35	,	,	PUNCT
aiti-819	63	36	–	–	PUNCT
aiti-819	63	37	5	5	NUM
aiti-819	63	38	)	)	PUNCT
aiti-819	63	39	,	,	PUNCT
aiti-819	63	40	and	and	CCONJ
aiti-819	63	41	p3	p3	PROPN
aiti-819	63	42	=	=	SYM
aiti-819	63	43	(	(	PUNCT
aiti-819	63	44	8	8	NUM
aiti-819	63	45	,	,	PUNCT
aiti-819	63	46	2	2	NUM
aiti-819	63	47	)	)	PUNCT
aiti-819	63	48	.	.	PUNCT
aiti-819	64	1	the	the	DET
aiti-819	64	2	minimal	minimal	ADJ
aiti-819	64	3	radius	radius	NOUN
aiti-819	64	4	can	can	AUX
aiti-819	64	5	be	be	AUX
aiti-819	64	6	calculated	calculate	VERB
aiti-819	64	7	,	,	PUNCT
aiti-819	64	8	called	call	VERB
aiti-819	64	9	mri	mri	NOUN
aiti-819	64	10	,	,	PUNCT
aiti-819	64	11	for	for	ADP
aiti-819	64	12	p1	p1	NOUN
aiti-819	64	13	,	,	PUNCT
aiti-819	64	14	p2	p2	NOUN
aiti-819	64	15	,	,	PUNCT
aiti-819	64	16	and	and	CCONJ
aiti-819	64	17	p3	p3	PROPN
aiti-819	64	18	as	as	ADP
aiti-819	64	19	mr1	mr1	PROPN
aiti-819	64	20	=	=	PROPN
aiti-819	64	21	4.59	4.59	NUM
aiti-819	64	22	,	,	PUNCT
aiti-819	64	23	mr2	mr2	X
aiti-819	64	24	=	=	SYM
aiti-819	64	25	5.78	5.78	NUM
aiti-819	64	26	,	,	PUNCT
aiti-819	64	27	and	and	CCONJ
aiti-819	64	28	mr1	mr1	PROPN
aiti-819	64	29	+	+	NUM
aiti-819	64	30	mr2	mr2	X
aiti-819	64	31	>	>	X
aiti-819	64	32	l1	l1	PROPN
aiti-819	64	33	=	=	PUNCT
aiti-819	64	34	10.198	10.198	NUM
aiti-819	64	35	,	,	PUNCT
aiti-819	64	36	respectively	respectively	ADV
aiti-819	64	37	(	(	PUNCT
aiti-819	64	38	see	see	VERB
aiti-819	64	39	fig	fig	NOUN
aiti-819	64	40	.	.	PUNCT
aiti-819	65	1	3(a	3(a	NUM
aiti-819	65	2	)	)	PUNCT
aiti-819	65	3	)	)	PUNCT
aiti-819	65	4	.	.	PUNCT
aiti-819	66	1	in	in	ADP
aiti-819	66	2	this	this	DET
aiti-819	66	3	case	case	NOUN
aiti-819	66	4	,	,	PUNCT
aiti-819	66	5	irrespective	irrespective	ADV
aiti-819	66	6	of	of	ADP
aiti-819	66	7	the	the	DET
aiti-819	66	8	values	value	NOUN
aiti-819	66	9	are	be	AUX
aiti-819	66	10	assigned	assign	VERB
aiti-819	66	11	to	to	ADP
aiti-819	66	12	r1	r1	NOUN
aiti-819	66	13	and	and	CCONJ
aiti-819	66	14	r2	r2	PROPN
aiti-819	66	15	,	,	PUNCT
aiti-819	66	16	there	there	PRON
aiti-819	66	17	is	be	VERB
aiti-819	66	18	always	always	ADV
aiti-819	66	19	the	the	DET
aiti-819	66	20	case	case	NOUN
aiti-819	66	21	wherein	wherein	SCONJ
aiti-819	66	22	c0	c0	PROPN
aiti-819	66	23	intersects	intersect	VERB
aiti-819	66	24	c2	c2	PROPN
aiti-819	66	25	or	or	CCONJ
aiti-819	66	26	c1	c1	PROPN
aiti-819	66	27	intersects	intersect	NOUN
aiti-819	66	28	c3	c3	PROPN
aiti-819	66	29	.	.	PUNCT
aiti-819	66	30	example	example	NOUN
aiti-819	66	31	2	2	NUM
aiti-819	66	32	:	:	PUNCT
aiti-819	66	33	using	use	VERB
aiti-819	66	34	the	the	DET
aiti-819	66	35	input	input	NOUN
aiti-819	66	36	p0	p0	NOUN
aiti-819	66	37	=	=	SYM
aiti-819	66	38	(	(	PUNCT
aiti-819	66	39	0	0	NUM
aiti-819	66	40	,	,	PUNCT
aiti-819	66	41	0	0	NUM
aiti-819	66	42	)	)	PUNCT
aiti-819	66	43	,	,	PUNCT
aiti-819	66	44	p1	p1	NOUN
aiti-819	66	45	=	=	SYM
aiti-819	66	46	(	(	PUNCT
aiti-819	66	47	2	2	NUM
aiti-819	66	48	,	,	PUNCT
aiti-819	66	49	1	1	NUM
aiti-819	66	50	)	)	PUNCT
aiti-819	66	51	,	,	PUNCT
aiti-819	66	52	p2	p2	PROPN
aiti-819	66	53	=	=	SYM
aiti-819	66	54	(	(	PUNCT
aiti-819	66	55	4	4	NUM
aiti-819	66	56	,	,	PUNCT
aiti-819	66	57	–	–	PUNCT
aiti-819	66	58	1	1	NUM
aiti-819	66	59	)	)	PUNCT
aiti-819	66	60	,	,	PUNCT
aiti-819	66	61	p3	p3	PROPN
aiti-819	66	62	=	=	SYM
aiti-819	66	63	(	(	PUNCT
aiti-819	66	64	6	6	NUM
aiti-819	66	65	,	,	PUNCT
aiti-819	66	66	1	1	NUM
aiti-819	66	67	)	)	PUNCT
aiti-819	66	68	,	,	PUNCT
aiti-819	66	69	and	and	CCONJ
aiti-819	66	70	p4	p4	ADJ
aiti-819	66	71	=	=	SYM
aiti-819	66	72	(	(	PUNCT
aiti-819	66	73	8	8	NUM
aiti-819	66	74	,	,	PUNCT
aiti-819	66	75	0	0	NUM
aiti-819	66	76	)	)	PUNCT
aiti-819	66	77	,	,	PUNCT
aiti-819	66	78	mr1	mr1	PROPN
aiti-819	66	79	,	,	PUNCT
aiti-819	66	80	mr2	mr2	PROPN
aiti-819	66	81	,	,	PUNCT
aiti-819	66	82	and	and	CCONJ
aiti-819	66	83	mr3	mr3	PROPN
aiti-819	66	84	are	be	AUX
aiti-819	66	85	calculated	calculate	VERB
aiti-819	66	86	as	as	ADP
aiti-819	66	87	0.47	0.47	NUM
aiti-819	66	88	,	,	PUNCT
aiti-819	66	89	0.82	0.82	NUM
aiti-819	66	90	,	,	PUNCT
aiti-819	66	91	and	and	CCONJ
aiti-819	66	92	0.47	0.47	NUM
aiti-819	66	93	,	,	PUNCT
aiti-819	66	94	respectively	respectively	ADV
aiti-819	66	95	,	,	PUNCT
aiti-819	66	96	and	and	CCONJ
aiti-819	66	97	the	the	DET
aiti-819	66	98	circles	circle	NOUN
aiti-819	66	99	centred	centre	VERB
aiti-819	66	100	at	at	ADP
aiti-819	66	101	pi	pi	NOUN
aiti-819	66	102	with	with	ADP
aiti-819	66	103	radius	radius	NOUN
aiti-819	66	104	mri	mri	NOUN
aiti-819	66	105	are	be	AUX
aiti-819	66	106	depicted	depict	VERB
aiti-819	66	107	in	in	ADP
aiti-819	66	108	fig	fig	NOUN
aiti-819	66	109	.	.	PUNCT
aiti-819	67	1	3(b	3(b	NUM
aiti-819	67	2	)	)	PUNCT
aiti-819	67	3	.	.	PUNCT
aiti-819	68	1	assuming	assume	VERB
aiti-819	68	2	j	j	PROPN
aiti-819	68	3	to	to	PART
aiti-819	68	4	be	be	AUX
aiti-819	68	5	the	the	DET
aiti-819	68	6	index	index	NOUN
aiti-819	68	7	of	of	ADP
aiti-819	68	8	the	the	DET
aiti-819	68	9	maximum	maximum	ADJ
aiti-819	68	10	value	value	NOUN
aiti-819	68	11	of	of	ADP
aiti-819	68	12	mri	mri	NOUN
aiti-819	68	13	,	,	PUNCT
aiti-819	68	14	rj	rj	PROPN
aiti-819	68	15	=	=	NOUN
aiti-819	68	16	mrj	mrj	NOUN
aiti-819	68	17	can	can	AUX
aiti-819	68	18	be	be	AUX
aiti-819	68	19	set	set	VERB
aiti-819	68	20	.	.	PUNCT
aiti-819	69	1	consequently	consequently	ADV
aiti-819	69	2	,	,	PUNCT
aiti-819	69	3	other	other	ADJ
aiti-819	69	4	radii	radius	NOUN
aiti-819	69	5	are	be	AUX
aiti-819	69	6	calculated	calculate	VERB
aiti-819	69	7	starting	start	VERB
aiti-819	69	8	from	from	ADP
aiti-819	69	9	rj	rj	PROPN
aiti-819	69	10	,	,	PUNCT
aiti-819	69	11	and	and	CCONJ
aiti-819	69	12	rj+1	rj+1	NOUN
aiti-819	69	13	,	,	PUNCT
aiti-819	69	14	rj+2	rj+2	NOUN
aiti-819	69	15	,	,	PUNCT
aiti-819	69	16	…	…	PUNCT
aiti-819	69	17	,	,	PUNCT
aiti-819	69	18	rn	rn	PROPN
aiti-819	69	19	and	and	CCONJ
aiti-819	69	20	rj-1	rj-1	ADV
aiti-819	69	21	,	,	PUNCT
aiti-819	69	22	rj-1	rj-1	ADV
aiti-819	69	23	,	,	PUNCT
aiti-819	69	24	…	…	PUNCT
aiti-819	69	25	,	,	PUNCT
aiti-819	69	26	r0	r0	NOUN
aiti-819	69	27	are	be	AUX
aiti-819	69	28	also	also	ADV
aiti-819	69	29	calculated	calculate	VERB
aiti-819	69	30	using	use	VERB
aiti-819	69	31	an	an	DET
aiti-819	69	32	approach	approach	NOUN
aiti-819	69	33	similar	similar	ADJ
aiti-819	69	34	to	to	ADP
aiti-819	69	35	that	that	PRON
aiti-819	69	36	used	use	VERB
aiti-819	69	37	in	in	ADP
aiti-819	69	38	algorithm	algorithm	NOUN
aiti-819	69	39	1	1	NUM
aiti-819	69	40	.	.	PUNCT
aiti-819	69	41	accordingly	accordingly	ADV
aiti-819	69	42	,	,	PUNCT
aiti-819	69	43	it	it	PRON
aiti-819	69	44	yields	yield	VERB
aiti-819	69	45	the	the	DET
aiti-819	69	46	following	follow	VERB
aiti-819	69	47	algorithm	algorithm	NOUN
aiti-819	69	48	:	:	PUNCT
aiti-819	69	49	algorithm	algorithm	NOUN
aiti-819	69	50	2	2	NUM
aiti-819	69	51	:	:	SYM
aiti-819	69	52	1	1	NUM
aiti-819	69	53	.	.	X
aiti-819	69	54	input	input	VERB
aiti-819	69	55	the	the	DET
aiti-819	69	56	distinct	distinct	ADJ
aiti-819	69	57	ordered	order	VERB
aiti-819	69	58	points	point	NOUN
aiti-819	69	59	,	,	PUNCT
aiti-819	69	60	i.e.	i.e.	X
aiti-819	69	61	,	,	PUNCT
aiti-819	69	62	p0	p0	NOUN
aiti-819	69	63	,	,	PUNCT
aiti-819	69	64	p1	p1	NOUN
aiti-819	69	65	,	,	PUNCT
aiti-819	69	66	…	…	PUNCT
aiti-819	69	67	,	,	PUNCT
aiti-819	69	68	pn	pn	PROPN
aiti-819	69	69	.	.	PROPN
aiti-819	69	70	check	check	VERB
aiti-819	69	71	whether	whether	SCONJ
aiti-819	69	72	the	the	DET
aiti-819	69	73	input	input	NOUN
aiti-819	69	74	is	be	AUX
aiti-819	69	75	appropriate	appropriate	ADJ
aiti-819	69	76	for	for	ADP
aiti-819	69	77	the	the	DET
aiti-819	69	78	algorithm	algorithm	NOUN
aiti-819	69	79	.	.	PUNCT
aiti-819	70	1	if	if	SCONJ
aiti-819	70	2	the	the	DET
aiti-819	70	3	input	input	NOUN
aiti-819	70	4	is	be	AUX
aiti-819	70	5	inappropriate	inappropriate	ADJ
aiti-819	70	6	,	,	PUNCT
aiti-819	70	7	a	a	DET
aiti-819	70	8	new	new	ADJ
aiti-819	70	9	set	set	NOUN
aiti-819	70	10	of	of	ADP
aiti-819	70	11	points	point	NOUN
aiti-819	70	12	is	be	AUX
aiti-819	70	13	requested	request	VERB
aiti-819	70	14	for	for	ADP
aiti-819	70	15	as	as	ADP
aiti-819	70	16	the	the	DET
aiti-819	70	17	input	input	NOUN
aiti-819	70	18	data	datum	NOUN
aiti-819	70	19	.	.	PUNCT
aiti-819	71	1	2	2	X
aiti-819	71	2	.	.	X
aiti-819	71	3	calculate	calculate	NOUN
aiti-819	71	4	mri	mri	NOUN
aiti-819	71	5	,	,	PUNCT
aiti-819	71	6	where	where	SCONJ
aiti-819	71	7	i	i	PRON
aiti-819	71	8	=	=	NOUN
aiti-819	71	9	1	1	NUM
aiti-819	71	10	,	,	PUNCT
aiti-819	71	11	...	...	PUNCT
aiti-819	71	12	,	,	PUNCT
aiti-819	71	13	n–1	n–1	PROPN
aiti-819	71	14	.	.	PUNCT
aiti-819	71	15	compute	compute	PROPN
aiti-819	71	16	index	index	PROPN
aiti-819	71	17	j	j	PROPN
aiti-819	71	18	for	for	ADP
aiti-819	71	19	max{mri	max{mri	PROPN
aiti-819	71	20	,	,	PUNCT
aiti-819	71	21	where	where	SCONJ
aiti-819	71	22	i	i	PRON
aiti-819	71	23	=	=	NOUN
aiti-819	71	24	1	1	NUM
aiti-819	71	25	,	,	PUNCT
aiti-819	71	26	…	…	PUNCT
aiti-819	71	27	,	,	PUNCT
aiti-819	71	28	n–1	n–1	PRON
aiti-819	71	29	}	}	PUNCT
aiti-819	71	30	.	.	PUNCT
aiti-819	72	1	set	set	VERB
aiti-819	72	2	rj	rj	PROPN
aiti-819	72	3	=	=	SYM
aiti-819	72	4	mrj	mrj	PROPN
aiti-819	72	5	.	.	PROPN
aiti-819	72	6	3	3	NUM
aiti-819	72	7	.	.	X
aiti-819	72	8	from	from	ADP
aiti-819	72	9	rj	rj	PROPN
aiti-819	72	10	,	,	PUNCT
aiti-819	72	11	repeat	repeat	VERB
aiti-819	72	12	rk+1	rk+1	ADP
aiti-819	72	13	=	=	SYM
aiti-819	72	14	lk	lk	X
aiti-819	72	15	–	–	PUNCT
aiti-819	72	16	rk	rk	NOUN
aiti-819	72	17	for	for	ADP
aiti-819	72	18	k	k	PROPN
aiti-819	72	19	=	=	SYM
aiti-819	72	20	j	j	PROPN
aiti-819	72	21	,	,	PUNCT
aiti-819	72	22	…	…	PUNCT
aiti-819	72	23	,	,	PUNCT
aiti-819	72	24	n–1	n–1	X
aiti-819	72	25	.	.	NOUN
aiti-819	73	1	4	4	X
aiti-819	73	2	.	.	X
aiti-819	73	3	from	from	ADP
aiti-819	73	4	rj	rj	PROPN
aiti-819	73	5	,	,	PUNCT
aiti-819	73	6	repeat	repeat	VERB
aiti-819	73	7	rk-1	rk-1	NOUN
aiti-819	73	8	=	=	SYM
aiti-819	73	9	lk-1	lk-1	PUNCT
aiti-819	73	10	–	–	PUNCT
aiti-819	73	11	rk	rk	NOUN
aiti-819	73	12	for	for	ADP
aiti-819	73	13	k	k	PROPN
aiti-819	73	14	=	=	SYM
aiti-819	73	15	j	j	PROPN
aiti-819	73	16	,	,	PUNCT
aiti-819	73	17	…	…	PUNCT
aiti-819	73	18	,	,	PUNCT
aiti-819	73	19	1	1	X
aiti-819	73	20	.	.	PUNCT
aiti-819	74	1	in	in	ADP
aiti-819	74	2	this	this	DET
aiti-819	74	3	case	case	NOUN
aiti-819	74	4	,	,	PUNCT
aiti-819	74	5	the	the	DET
aiti-819	74	6	circles	circle	NOUN
aiti-819	74	7	are	be	AUX
aiti-819	74	8	found	find	VERB
aiti-819	74	9	with	with	ADP
aiti-819	74	10	pj	pj	PROPN
aiti-819	74	11	as	as	ADP
aiti-819	74	12	their	their	PRON
aiti-819	74	13	centers	center	NOUN
aiti-819	74	14	and	and	CCONJ
aiti-819	74	15	mrj	mrj	VERB
aiti-819	74	16	their	their	PRON
aiti-819	74	17	radii	radius	NOUN
aiti-819	74	18	,	,	PUNCT
aiti-819	74	19	where	where	SCONJ
aiti-819	74	20	mrj	mrj	NOUN
aiti-819	74	21	+	+	X
aiti-819	74	22	mrj+1	mrj+1	NOUN
aiti-819	74	23	<	<	X
aiti-819	74	24	lj	lj	PROPN
aiti-819	74	25	.	.	PUNCT
aiti-819	75	1	a	a	DET
aiti-819	75	2	set	set	NOUN
aiti-819	75	3	of	of	ADP
aiti-819	75	4	radius	radius	NOUN
aiti-819	75	5	rk	rk	NOUN
aiti-819	75	6	is	be	AUX
aiti-819	75	7	found	find	VERB
aiti-819	75	8	,	,	PUNCT
aiti-819	75	9	where	where	SCONJ
aiti-819	75	10	k=1,2	k=1,2	PROPN
aiti-819	75	11	,	,	PUNCT
aiti-819	75	12	…	…	PUNCT
aiti-819	75	13	,	,	PUNCT
aiti-819	75	14	j-1	j-1	ADV
aiti-819	75	15	,	,	PUNCT
aiti-819	75	16	j+1	j+1	PROPN
aiti-819	75	17	,	,	PUNCT
aiti-819	75	18	…	…	PUNCT
aiti-819	75	19	n	n	CCONJ
aiti-819	75	20	,	,	PUNCT
aiti-819	75	21	such	such	ADJ
aiti-819	75	22	that	that	SCONJ
aiti-819	75	23	the	the	DET
aiti-819	75	24	circles	circle	NOUN
aiti-819	75	25	will	will	AUX
aiti-819	75	26	not	not	PART
aiti-819	75	27	intersect	intersect	VERB
aiti-819	75	28	locally	locally	ADV
aiti-819	75	29	(	(	PUNCT
aiti-819	75	30	ck-1	ck-1	NOUN
aiti-819	75	31	and	and	CCONJ
aiti-819	75	32	ck	ck	INTJ
aiti-819	75	33	are	be	AUX
aiti-819	75	34	tangent	tangent	ADJ
aiti-819	75	35	to	to	ADP
aiti-819	75	36	each	each	DET
aiti-819	75	37	other	other	ADJ
aiti-819	75	38	,	,	PUNCT
aiti-819	75	39	and	and	CCONJ
aiti-819	76	1	cj	cj	NOUN
aiti-819	76	2	and	and	CCONJ
aiti-819	76	3	ck+1	ck+1	PRON
aiti-819	76	4	are	be	AUX
aiti-819	76	5	also	also	ADV
aiti-819	76	6	tangent	tangent	ADJ
aiti-819	76	7	to	to	ADP
aiti-819	76	8	each	each	DET
aiti-819	76	9	other	other	ADJ
aiti-819	76	10	;	;	PUNCT
aiti-819	76	11	in	in	ADP
aiti-819	76	12	addition	addition	NOUN
aiti-819	76	13	,	,	PUNCT
aiti-819	76	14	ck-1	ck-1	PUNCT
aiti-819	76	15	and	and	CCONJ
aiti-819	76	16	ck+1	ck+1	PRON
aiti-819	76	17	may	may	AUX
aiti-819	76	18	be	be	AUX
aiti-819	76	19	tangent	tangent	ADJ
aiti-819	76	20	to	to	ADP
aiti-819	76	21	each	each	DET
aiti-819	76	22	other	other	ADJ
aiti-819	76	23	but	but	CCONJ
aiti-819	76	24	can	can	AUX
aiti-819	76	25	not	not	PART
aiti-819	76	26	intersect	intersect	VERB
aiti-819	76	27	otherwise	otherwise	ADV
aiti-819	76	28	)	)	PUNCT
aiti-819	76	29	.	.	PUNCT
aiti-819	77	1	for	for	ADP
aiti-819	77	2	the	the	DET
aiti-819	77	3	case	case	NOUN
aiti-819	77	4	rj	rj	PROPN
aiti-819	77	5	=	=	SYM
aiti-819	77	6	mrj	mrj	PROPN
aiti-819	77	7	,	,	PUNCT
aiti-819	77	8	circle	circle	NOUN
aiti-819	77	9	cj-1	cj-1	ADV
aiti-819	77	10	will	will	AUX
aiti-819	77	11	be	be	AUX
aiti-819	77	12	tangent	tangent	ADJ
aiti-819	77	13	to	to	ADP
aiti-819	77	14	cj+1	cj+1	NUM
aiti-819	77	15	,	,	PUNCT
aiti-819	77	16	as	as	SCONJ
aiti-819	77	17	depicted	depict	VERB
aiti-819	77	18	in	in	ADP
aiti-819	77	19	fig	fig	NOUN
aiti-819	77	20	.	.	PUNCT
aiti-819	78	1	3(c	3(c	NUM
aiti-819	78	2	)	)	PUNCT
aiti-819	78	3	.	.	PUNCT
aiti-819	79	1	advances	advance	NOUN
aiti-819	79	2	in	in	ADP
aiti-819	79	3	technology	technology	NOUN
aiti-819	79	4	innovation	innovation	NOUN
aiti-819	79	5	,	,	PUNCT
aiti-819	79	6	vol	vol	NOUN
aiti-819	79	7	.	.	PROPN
aiti-819	79	8	5	5	NUM
aiti-819	79	9	,	,	PUNCT
aiti-819	79	10	no	no	INTJ
aiti-819	79	11	.	.	NOUN
aiti-819	79	12	2	2	NUM
aiti-819	79	13	,	,	PUNCT
aiti-819	79	14	2020	2020	NUM
aiti-819	79	15	,	,	PUNCT
aiti-819	79	16	pp	pp	ADV
aiti-819	79	17	.	.	PUNCT
aiti-819	80	1	126	126	NUM
aiti-819	80	2	-	-	SYM
aiti-819	80	3	134	134	NUM
aiti-819	80	4	129	129	NUM
aiti-819	80	5	example	example	NOUN
aiti-819	80	6	3	3	NUM
aiti-819	80	7	:	:	PUNCT
aiti-819	80	8	using	use	VERB
aiti-819	80	9	the	the	DET
aiti-819	80	10	same	same	ADJ
aiti-819	80	11	input	input	NOUN
aiti-819	80	12	as	as	ADP
aiti-819	80	13	that	that	PRON
aiti-819	80	14	used	use	VERB
aiti-819	80	15	in	in	ADP
aiti-819	80	16	example	example	NOUN
aiti-819	80	17	2	2	NUM
aiti-819	80	18	,	,	PUNCT
aiti-819	80	19	r2	r2	NOUN
aiti-819	80	20	=	=	SYM
aiti-819	80	21	mr2	mr2	PROPN
aiti-819	80	22	=	=	PUNCT
aiti-819	80	23	0.82	0.82	NUM
aiti-819	80	24	was	be	AUX
aiti-819	80	25	fixed	fix	VERB
aiti-819	80	26	and	and	CCONJ
aiti-819	80	27	r3	r3	PROPN
aiti-819	80	28	and	and	CCONJ
aiti-819	80	29	r4	r4	PROPN
aiti-819	80	30	was	be	AUX
aiti-819	80	31	calculated	calculate	VERB
aiti-819	80	32	to	to	PART
aiti-819	80	33	be	be	AUX
aiti-819	80	34	2	2	NUM
aiti-819	80	35	and	and	CCONJ
aiti-819	80	36	0.24	0.24	NUM
aiti-819	80	37	,	,	PUNCT
aiti-819	80	38	respectively	respectively	ADV
aiti-819	80	39	.	.	PUNCT
aiti-819	81	1	in	in	ADP
aiti-819	81	2	addition	addition	NOUN
aiti-819	81	3	,	,	PUNCT
aiti-819	81	4	r1	r1	NOUN
aiti-819	81	5	and	and	CCONJ
aiti-819	81	6	r0	r0	NOUN
aiti-819	81	7	are	be	AUX
aiti-819	81	8	equal	equal	ADJ
aiti-819	81	9	to	to	ADP
aiti-819	81	10	2	2	NUM
aiti-819	81	11	and	and	CCONJ
aiti-819	81	12	0.24	0.24	NUM
aiti-819	81	13	,	,	PUNCT
aiti-819	81	14	respectively	respectively	ADV
aiti-819	81	15	,	,	PUNCT
aiti-819	81	16	as	as	SCONJ
aiti-819	81	17	depicted	depict	VERB
aiti-819	81	18	in	in	ADP
aiti-819	81	19	fig	fig	NOUN
aiti-819	81	20	.	.	PUNCT
aiti-819	82	1	3(c	3(c	NUM
aiti-819	82	2	)	)	PUNCT
aiti-819	82	3	.	.	PUNCT
aiti-819	83	1	the	the	DET
aiti-819	83	2	radius	radius	NOUN
aiti-819	83	3	of	of	ADP
aiti-819	83	4	cj	cj	PROPN
aiti-819	83	5	is	be	AUX
aiti-819	83	6	increased	increase	VERB
aiti-819	83	7	to	to	PART
aiti-819	83	8	avoid	avoid	VERB
aiti-819	83	9	c	c	NOUN
aiti-819	83	10	j-1	j-1	ADV
aiti-819	83	11	and	and	CCONJ
aiti-819	83	12	cj+1	cj+1	NUM
aiti-819	83	13	being	be	AUX
aiti-819	83	14	tangents	tangent	NOUN
aiti-819	83	15	to	to	ADP
aiti-819	83	16	one	one	NUM
aiti-819	83	17	another	another	DET
aiti-819	83	18	,	,	PUNCT
aiti-819	83	19	as	as	SCONJ
aiti-819	83	20	depicted	depict	VERB
aiti-819	83	21	in	in	ADP
aiti-819	83	22	fig	fig	NOUN
aiti-819	83	23	.	.	PUNCT
aiti-819	84	1	3(c	3(c	NUM
aiti-819	84	2	)	)	PUNCT
aiti-819	84	3	.	.	PUNCT
aiti-819	85	1	a	a	DET
aiti-819	85	2	“	"	PUNCT
aiti-819	85	3	better	well	ADJ
aiti-819	85	4	”	"	PUNCT
aiti-819	85	5	chain	chain	NOUN
aiti-819	85	6	of	of	ADP
aiti-819	85	7	circles	circle	NOUN
aiti-819	85	8	must	must	AUX
aiti-819	85	9	be	be	AUX
aiti-819	85	10	produced	produce	VERB
aiti-819	85	11	,	,	PUNCT
aiti-819	85	12	such	such	ADJ
aiti-819	85	13	that	that	SCONJ
aiti-819	85	14	all	all	DET
aiti-819	85	15	circles	circle	NOUN
aiti-819	85	16	ci-1	ci-1	VERB
aiti-819	85	17	and	and	CCONJ
aiti-819	85	18	ci+1	ci+1	NOUN
aiti-819	85	19	on	on	ADP
aiti-819	85	20	the	the	DET
aiti-819	85	21	chain	chain	NOUN
aiti-819	85	22	are	be	AUX
aiti-819	85	23	separated	separate	VERB
aiti-819	85	24	locally	locally	ADV
aiti-819	85	25	.	.	PUNCT
aiti-819	86	1	the	the	DET
aiti-819	86	2	“	"	PUNCT
aiti-819	86	3	better	well	ADJ
aiti-819	86	4	”	"	PUNCT
aiti-819	86	5	chain	chain	NOUN
aiti-819	86	6	of	of	ADP
aiti-819	86	7	circles	circle	NOUN
aiti-819	86	8	may	may	AUX
aiti-819	86	9	be	be	AUX
aiti-819	86	10	the	the	DET
aiti-819	86	11	case	case	NOUN
aiti-819	86	12	wherein	wherein	SCONJ
aiti-819	86	13	the	the	DET
aiti-819	86	14	radii	radius	NOUN
aiti-819	86	15	of	of	ADP
aiti-819	86	16	circles	circle	NOUN
aiti-819	86	17	are	be	AUX
aiti-819	86	18	within	within	ADP
aiti-819	86	19	a	a	DET
aiti-819	86	20	small	small	ADJ
aiti-819	86	21	range	range	NOUN
aiti-819	86	22	.	.	PUNCT
aiti-819	87	1	theoretically	theoretically	ADV
aiti-819	87	2	,	,	PUNCT
aiti-819	87	3	to	to	PART
aiti-819	87	4	minimize	minimize	VERB
aiti-819	87	5	the	the	DET
aiti-819	87	6	value	value	NOUN
aiti-819	87	7	of	of	ADP
aiti-819	87	8	max	max	PROPN
aiti-819	87	9	{	{	PUNCT
aiti-819	87	10	ri	ri	PROPN
aiti-819	87	11	,	,	PUNCT
aiti-819	87	12	i=0	i=0	PROPN
aiti-819	87	13	,	,	PUNCT
aiti-819	87	14	n	n	CCONJ
aiti-819	87	15	}	}	PUNCT
aiti-819	87	16	–	–	PUNCT
aiti-819	87	17	min	min	NOUN
aiti-819	87	18	{	{	PUNCT
aiti-819	87	19	ri	ri	PROPN
aiti-819	87	20	,	,	PUNCT
aiti-819	87	21	i=0	i=0	PROPN
aiti-819	87	22	,	,	PUNCT
aiti-819	87	23	n	n	CCONJ
aiti-819	87	24	}	}	PUNCT
aiti-819	87	25	.	.	PUNCT
aiti-819	88	1	using	use	VERB
aiti-819	88	2	the	the	DET
aiti-819	88	3	algorithm	algorithm	NOUN
aiti-819	88	4	,	,	PUNCT
aiti-819	88	5	all	all	DET
aiti-819	88	6	mri	mri	NOUN
aiti-819	88	7	are	be	AUX
aiti-819	88	8	calculated	calculate	VERB
aiti-819	88	9	,	,	PUNCT
aiti-819	88	10	where	where	SCONJ
aiti-819	88	11	i	i	PRON
aiti-819	88	12	=	=	NOUN
aiti-819	88	13	1	1	NUM
aiti-819	88	14	,	,	PUNCT
aiti-819	88	15	…	…	PUNCT
aiti-819	88	16	,	,	PUNCT
aiti-819	88	17	n–1	n–1	NOUN
aiti-819	88	18	,	,	PUNCT
aiti-819	88	19	and	and	CCONJ
aiti-819	88	20	mci	mci	PROPN
aiti-819	88	21	,	,	PUNCT
aiti-819	88	22	where	where	SCONJ
aiti-819	88	23	mci	mci	PROPN
aiti-819	88	24	are	be	AUX
aiti-819	88	25	the	the	DET
aiti-819	88	26	circles	circle	NOUN
aiti-819	88	27	centered	center	VERB
aiti-819	88	28	at	at	ADP
aiti-819	88	29	pi	pi	NOUN
aiti-819	88	30	with	with	ADP
aiti-819	88	31	radius	radius	NOUN
aiti-819	88	32	mri	mri	NOUN
aiti-819	88	33	.	.	PUNCT
aiti-819	89	1	if	if	SCONJ
aiti-819	89	2	mci-1	mci-1	VERB
aiti-819	89	3	did	do	AUX
aiti-819	89	4	not	not	PART
aiti-819	89	5	intersect	intersect	ADJ
aiti-819	89	6	mci+1	mci+1	PROPN
aiti-819	89	7	,	,	PUNCT
aiti-819	89	8	where	where	SCONJ
aiti-819	89	9	i	i	PRON
aiti-819	89	10	=	=	NOUN
aiti-819	89	11	1	1	NUM
aiti-819	89	12	,	,	PUNCT
aiti-819	89	13	…	…	PUNCT
aiti-819	89	14	,	,	PUNCT
aiti-819	89	15	n–1	n–1	PRON
aiti-819	89	16	,	,	PUNCT
aiti-819	89	17	a	a	DET
aiti-819	89	18	set	set	NOUN
aiti-819	89	19	of	of	ADP
aiti-819	89	20	ri	ri	PROPN
aiti-819	89	21	is	be	AUX
aiti-819	89	22	found	find	VERB
aiti-819	89	23	,	,	PUNCT
aiti-819	89	24	such	such	ADJ
aiti-819	89	25	that	that	DET
aiti-819	89	26	ci	ci	PROPN
aiti-819	89	27	is	be	AUX
aiti-819	89	28	tangent	tangent	ADJ
aiti-819	89	29	to	to	ADP
aiti-819	89	30	ci+1	ci+1	PROPN
aiti-819	89	31	with	with	ADP
aiti-819	89	32	the	the	DET
aiti-819	89	33	property	property	NOUN
aiti-819	89	34	that	that	PRON
aiti-819	89	35	ci-1	ci-1	VERB
aiti-819	89	36	did	do	AUX
aiti-819	89	37	not	not	PART
aiti-819	89	38	intersect	intersect	VERB
aiti-819	89	39	ci+1	ci+1	PROPN
aiti-819	89	40	.	.	PUNCT
aiti-819	90	1	moreover	moreover	ADV
aiti-819	90	2	,	,	PUNCT
aiti-819	90	3	rj	rj	PROPN
aiti-819	90	4	has	have	VERB
aiti-819	90	5	both	both	CCONJ
aiti-819	90	6	a	a	DET
aiti-819	90	7	lower	lower	ADV
aiti-819	90	8	bound	bind	VERB
aiti-819	90	9	,	,	PUNCT
aiti-819	90	10	i.e.	i.e.	X
aiti-819	90	11	,	,	PUNCT
aiti-819	90	12	mrj	mrj	NOUN
aiti-819	90	13	,	,	PUNCT
aiti-819	90	14	and	and	CCONJ
aiti-819	90	15	an	an	DET
aiti-819	90	16	upper	upper	ADJ
aiti-819	90	17	bound	bind	VERB
aiti-819	90	18	,	,	PUNCT
aiti-819	90	19	which	which	PRON
aiti-819	90	20	could	could	AUX
aiti-819	90	21	be	be	AUX
aiti-819	90	22	min{dist(pj	min{dist(pj	ADJ
aiti-819	90	23	,	,	PUNCT
aiti-819	90	24	pj+1)-rj+1	pj+1)-rj+1	PROPN
aiti-819	90	25	,	,	PUNCT
aiti-819	90	26	dist(pj	dist(pj	NOUN
aiti-819	90	27	,	,	PUNCT
aiti-819	90	28	pj-1)-rj-1	pj-1)-rj-1	ADV
aiti-819	90	29	}	}	PUNCT
aiti-819	90	30	;	;	PUNCT
aiti-819	90	31	notably	notably	ADV
aiti-819	90	32	,	,	PUNCT
aiti-819	90	33	upon	upon	SCONJ
aiti-819	90	34	increasing	increase	VERB
aiti-819	90	35	rj	rj	PROPN
aiti-819	90	36	,	,	PUNCT
aiti-819	90	37	circles	circle	NOUN
aiti-819	90	38	mcj-1	mcj-1	ADV
aiti-819	90	39	and	and	CCONJ
aiti-819	90	40	mcj+1	mcj+1	NOUN
aiti-819	90	41	will	will	AUX
aiti-819	90	42	not	not	PART
aiti-819	90	43	intersect	intersect	VERB
aiti-819	90	44	each	each	DET
aiti-819	90	45	other	other	ADJ
aiti-819	90	46	.	.	PUNCT
aiti-819	91	1	the	the	DET
aiti-819	91	2	radius	radius	NOUN
aiti-819	91	3	was	be	AUX
aiti-819	91	4	discretized	discretize	VERB
aiti-819	91	5	from	from	ADP
aiti-819	91	6	its	its	PRON
aiti-819	91	7	lower	low	ADJ
aiti-819	91	8	bound	bind	VERB
aiti-819	91	9	to	to	ADP
aiti-819	91	10	upper	upper	ADJ
aiti-819	91	11	bound	bind	VERB
aiti-819	91	12	and	and	CCONJ
aiti-819	91	13	tried	try	VERB
aiti-819	91	14	each	each	DET
aiti-819	91	15	case	case	NOUN
aiti-819	91	16	and	and	CCONJ
aiti-819	91	17	,	,	PUNCT
aiti-819	91	18	subsequently	subsequently	ADV
aiti-819	91	19	,	,	PUNCT
aiti-819	91	20	produced	produce	VERB
aiti-819	91	21	the	the	DET
aiti-819	91	22	“	"	PUNCT
aiti-819	91	23	better	well	ADJ
aiti-819	91	24	”	"	PUNCT
aiti-819	91	25	chain	chain	NOUN
aiti-819	91	26	of	of	ADP
aiti-819	91	27	circles	circle	NOUN
aiti-819	91	28	satisfying	satisfy	VERB
aiti-819	91	29	the	the	DET
aiti-819	91	30	case	case	NOUN
aiti-819	91	31	wherein	wherein	SCONJ
aiti-819	91	32	max{ri	max{ri	ADV
aiti-819	91	33	,	,	PUNCT
aiti-819	91	34	i=0	i=0	PROPN
aiti-819	91	35	,	,	PUNCT
aiti-819	91	36	n	n	CCONJ
aiti-819	91	37	}	}	PUNCT
aiti-819	91	38	–	–	PUNCT
aiti-819	91	39	min{ri	min{ri	PRON
aiti-819	91	40	,	,	PUNCT
aiti-819	91	41	i=0	i=0	PROPN
aiti-819	91	42	,	,	PUNCT
aiti-819	91	43	n	n	CCONJ
aiti-819	91	44	}	}	PUNCT
aiti-819	91	45	was	be	AUX
aiti-819	91	46	minimum	minimum	ADJ
aiti-819	91	47	.	.	PUNCT
aiti-819	92	1	therefore	therefore	ADV
aiti-819	92	2	,	,	PUNCT
aiti-819	92	3	there	there	PRON
aiti-819	92	4	is	be	VERB
aiti-819	92	5	the	the	DET
aiti-819	92	6	following	follow	VERB
aiti-819	92	7	algorithm	algorithm	NOUN
aiti-819	92	8	can	can	AUX
aiti-819	92	9	be	be	AUX
aiti-819	92	10	found	find	VERB
aiti-819	92	11	:	:	PUNCT
aiti-819	92	12	algorithm	algorithm	NOUN
aiti-819	92	13	3	3	NUM
aiti-819	92	14	:	:	SYM
aiti-819	92	15	1	1	NUM
aiti-819	92	16	.	.	X
aiti-819	92	17	input	input	VERB
aiti-819	92	18	the	the	DET
aiti-819	92	19	distinct	distinct	ADJ
aiti-819	92	20	ordered	order	VERB
aiti-819	92	21	points	point	NOUN
aiti-819	92	22	,	,	PUNCT
aiti-819	92	23	i.e.	i.e.	X
aiti-819	92	24	,	,	PUNCT
aiti-819	92	25	p0	p0	NOUN
aiti-819	92	26	,	,	PUNCT
aiti-819	92	27	p1	p1	NOUN
aiti-819	92	28	,	,	PUNCT
aiti-819	92	29	…	…	PUNCT
aiti-819	92	30	,	,	PUNCT
aiti-819	92	31	pn	pn	PROPN
aiti-819	92	32	.	.	PROPN
aiti-819	92	33	check	check	VERB
aiti-819	92	34	whether	whether	SCONJ
aiti-819	92	35	the	the	DET
aiti-819	92	36	input	input	NOUN
aiti-819	92	37	is	be	AUX
aiti-819	92	38	appropriate	appropriate	ADJ
aiti-819	92	39	for	for	ADP
aiti-819	92	40	the	the	DET
aiti-819	92	41	algorithm	algorithm	NOUN
aiti-819	92	42	.	.	PUNCT
aiti-819	93	1	if	if	SCONJ
aiti-819	93	2	the	the	DET
aiti-819	93	3	input	input	NOUN
aiti-819	93	4	is	be	AUX
aiti-819	93	5	not	not	PART
aiti-819	93	6	appropriate	appropriate	ADJ
aiti-819	93	7	,	,	PUNCT
aiti-819	93	8	ask	ask	VERB
aiti-819	93	9	for	for	ADP
aiti-819	93	10	a	a	DET
aiti-819	93	11	new	new	ADJ
aiti-819	93	12	set	set	NOUN
aiti-819	93	13	of	of	ADP
aiti-819	93	14	points	point	NOUN
aiti-819	93	15	as	as	ADP
aiti-819	93	16	the	the	DET
aiti-819	93	17	input	input	NOUN
aiti-819	93	18	.	.	PUNCT
aiti-819	94	1	2	2	X
aiti-819	94	2	.	.	NUM
aiti-819	94	3	calculate	calculate	NOUN
aiti-819	94	4	mri	mri	NOUN
aiti-819	94	5	,	,	PUNCT
aiti-819	94	6	where	where	SCONJ
aiti-819	94	7	i	i	PRON
aiti-819	94	8	=	=	NOUN
aiti-819	94	9	1	1	NUM
aiti-819	94	10	,	,	PUNCT
aiti-819	94	11	..	..	PUNCT
aiti-819	94	12	,	,	PUNCT
aiti-819	94	13	n–1	n–1	PROPN
aiti-819	94	14	.	.	PUNCT
aiti-819	94	15	compute	compute	PROPN
aiti-819	94	16	index	index	PROPN
aiti-819	94	17	j	j	PROPN
aiti-819	94	18	for	for	ADP
aiti-819	94	19	max{mri	max{mri	PROPN
aiti-819	94	20	,	,	PUNCT
aiti-819	94	21	where	where	SCONJ
aiti-819	94	22	i=1	i=1	X
aiti-819	94	23	,	,	PUNCT
aiti-819	94	24	..	..	PUNCT
aiti-819	94	25	,	,	PUNCT
aiti-819	94	26	n–1	n–1	X
aiti-819	94	27	}	}	PUNCT
aiti-819	94	28	.	.	PUNCT
aiti-819	95	1	set	set	VERB
aiti-819	95	2	upper	upper	ADJ
aiti-819	95	3	=	=	VERB
aiti-819	95	4	min{li	min{li	NOUN
aiti-819	95	5	–	–	PUNCT
aiti-819	95	6	mri+1	mri+1	NOUN
aiti-819	95	7	,	,	PUNCT
aiti-819	95	8	li-1	li-1	NOUN
aiti-819	95	9	–	–	PUNCT
aiti-819	95	10	mri-1	mri-1	ADJ
aiti-819	95	11	}	}	SYM
aiti-819	95	12	3	3	NUM
aiti-819	95	13	.	.	PUNCT
aiti-819	96	1	set	set	VERB
aiti-819	96	2	m	m	VERB
aiti-819	96	3	such	such	ADJ
aiti-819	96	4	that	that	SCONJ
aiti-819	96	5	it	it	PRON
aiti-819	96	6	divides	divide	VERB
aiti-819	96	7	r	r	NOUN
aiti-819	96	8	from	from	ADP
aiti-819	96	9	its	its	PRON
aiti-819	96	10	lower	low	ADJ
aiti-819	96	11	bound	bind	VERB
aiti-819	96	12	to	to	ADP
aiti-819	96	13	upper	upper	ADJ
aiti-819	96	14	bound	bind	VERB
aiti-819	96	15	into	into	ADP
aiti-819	96	16	m+1	m+1	NUM
aiti-819	96	17	values	value	NOUN
aiti-819	96	18	.	.	PUNCT
aiti-819	97	1	4	4	X
aiti-819	97	2	.	.	X
aiti-819	97	3	for	for	ADP
aiti-819	97	4	rj	rj	PROPN
aiti-819	97	5	from	from	ADP
aiti-819	97	6	mrj	mrj	NOUN
aiti-819	97	7	to	to	ADP
aiti-819	97	8	its	its	PRON
aiti-819	97	9	upper	upper	ADJ
aiti-819	97	10	bound	bind	VERB
aiti-819	97	11	with	with	ADP
aiti-819	97	12	step	step	NOUN
aiti-819	97	13	(	(	PUNCT
aiti-819	97	14	upper	upper	ADJ
aiti-819	97	15	–	–	PUNCT
aiti-819	97	16	mrj)/m	mrj)/m	SYM
aiti-819	97	17	4.1	4.1	NUM
aiti-819	97	18	from	from	ADP
aiti-819	97	19	rj	rj	PROPN
aiti-819	97	20	,	,	PUNCT
aiti-819	97	21	repeat	repeat	VERB
aiti-819	97	22	rk+1	rk+1	ADP
aiti-819	97	23	=	=	SYM
aiti-819	97	24	lk	lk	X
aiti-819	97	25	–	–	PUNCT
aiti-819	97	26	rk	rk	NOUN
aiti-819	97	27	for	for	ADP
aiti-819	97	28	k	k	PROPN
aiti-819	97	29	=	=	SYM
aiti-819	97	30	j	j	PROPN
aiti-819	97	31	,	,	PUNCT
aiti-819	97	32	…	…	PUNCT
aiti-819	97	33	,	,	PUNCT
aiti-819	97	34	n–1	n–1	PRON
aiti-819	97	35	.	.	NOUN
aiti-819	97	36	4.2	4.2	NUM
aiti-819	97	37	repeat	repeat	NOUN
aiti-819	97	38	rk-1	rk-1	NOUN
aiti-819	97	39	=	=	SYM
aiti-819	97	40	lk-1	lk-1	PUNCT
aiti-819	97	41	–	–	PUNCT
aiti-819	97	42	rk	rk	NOUN
aiti-819	97	43	for	for	ADP
aiti-819	97	44	k	k	PROPN
aiti-819	97	45	=	=	SYM
aiti-819	97	46	j	j	PROPN
aiti-819	97	47	,	,	PUNCT
aiti-819	97	48	…	…	PUNCT
aiti-819	97	49	,	,	PUNCT
aiti-819	97	50	1	1	X
aiti-819	97	51	.	.	NUM
aiti-819	97	52	4.3	4.3	NUM
aiti-819	97	53	calculate	calculate	NOUN
aiti-819	97	54	max	max	PROPN
aiti-819	97	55	{	{	PUNCT
aiti-819	97	56	rj	rj	PROPN
aiti-819	97	57	}	}	PUNCT
aiti-819	97	58	–	–	PUNCT
aiti-819	97	59	min	min	PROPN
aiti-819	97	60	{	{	PUNCT
aiti-819	97	61	rj	rj	PROPN
aiti-819	97	62	}	}	PUNCT
aiti-819	97	63	for	for	ADP
aiti-819	97	64	j	j	PROPN
aiti-819	97	65	=	=	SYM
aiti-819	97	66	1	1	NUM
aiti-819	97	67	,	,	PUNCT
aiti-819	97	68	…	…	PUNCT
aiti-819	97	69	,	,	PUNCT
aiti-819	97	70	n–1	n–1	PRON
aiti-819	97	71	.	.	PUNCT
aiti-819	98	1	memorize	memorize	VERB
aiti-819	98	2	k	k	PROPN
aiti-819	98	3	when	when	SCONJ
aiti-819	98	4	max	max	PROPN
aiti-819	98	5	{	{	PUNCT
aiti-819	98	6	rk	rk	NOUN
aiti-819	98	7	}	}	PUNCT
aiti-819	98	8	–	–	PUNCT
aiti-819	98	9	min	min	NOUN
aiti-819	98	10	{	{	PUNCT
aiti-819	98	11	rk	rk	PRON
aiti-819	98	12	}	}	PUNCT
aiti-819	98	13	is	be	AUX
aiti-819	98	14	minimum	minimum	ADJ
aiti-819	98	15	.	.	PUNCT
aiti-819	98	16	example	example	NOUN
aiti-819	98	17	4	4	NUM
aiti-819	98	18	:	:	PUNCT
aiti-819	98	19	using	use	VERB
aiti-819	98	20	the	the	DET
aiti-819	98	21	same	same	ADJ
aiti-819	98	22	input	input	NOUN
aiti-819	98	23	as	as	ADP
aiti-819	98	24	that	that	PRON
aiti-819	98	25	used	use	VERB
aiti-819	98	26	in	in	ADP
aiti-819	98	27	example	example	NOUN
aiti-819	98	28	2	2	NUM
aiti-819	98	29	to	to	PART
aiti-819	98	30	have	have	VERB
aiti-819	98	31	the	the	DET
aiti-819	98	32	lower	low	ADJ
aiti-819	98	33	and	and	CCONJ
aiti-819	98	34	upper	upper	ADJ
aiti-819	98	35	bounds	bound	NOUN
aiti-819	98	36	for	for	ADP
aiti-819	98	37	r2	r2	PROPN
aiti-819	98	38	(0.82	(0.82	NOUN
aiti-819	98	39	,	,	PUNCT
aiti-819	98	40	2.36	2.36	NUM
aiti-819	98	41	)	)	PUNCT
aiti-819	98	42	.	.	PUNCT
aiti-819	99	1	this	this	DET
aiti-819	99	2	range	range	NOUN
aiti-819	99	3	linearly	linearly	ADV
aiti-819	99	4	was	be	AUX
aiti-819	99	5	discretized	discretize	VERB
aiti-819	99	6	into	into	ADP
aiti-819	99	7	11	11	NUM
aiti-819	99	8	different	different	ADJ
aiti-819	99	9	radii	radius	NOUN
aiti-819	99	10	and	and	CCONJ
aiti-819	99	11	observed	observe	VERB
aiti-819	99	12	that	that	SCONJ
aiti-819	99	13	when	when	SCONJ
aiti-819	99	14	r2	r2	PROPN
aiti-819	99	15	=	=	PROPN
aiti-819	99	16	1.44	1.44	NUM
aiti-819	99	17	,	,	PUNCT
aiti-819	99	18	a	a	DET
aiti-819	99	19	“	"	PUNCT
aiti-819	99	20	better	well	ADJ
aiti-819	99	21	”	"	PUNCT
aiti-819	99	22	chain	chain	NOUN
aiti-819	99	23	of	of	ADP
aiti-819	99	24	circles	circle	NOUN
aiti-819	99	25	was	be	AUX
aiti-819	99	26	produced	produce	VERB
aiti-819	99	27	.	.	PUNCT
aiti-819	100	1	the	the	DET
aiti-819	100	2	result	result	NOUN
aiti-819	100	3	is	be	AUX
aiti-819	100	4	depicted	depict	VERB
aiti-819	100	5	in	in	ADP
aiti-819	100	6	fig	fig	NOUN
aiti-819	100	7	.	.	PUNCT
aiti-819	101	1	3(d	3(d	NUM
aiti-819	101	2	)	)	PUNCT
aiti-819	101	3	.	.	PUNCT
aiti-819	102	1	a	a	DET
aiti-819	102	2	sequence	sequence	NOUN
aiti-819	102	3	of	of	ADP
aiti-819	102	4	points	point	NOUN
aiti-819	102	5	,	,	PUNCT
aiti-819	102	6	p	p	X
aiti-819	102	7	=	=	PUNCT
aiti-819	103	1	[	[	X
aiti-819	103	2	p0	p0	NOUN
aiti-819	103	3	,	,	PUNCT
aiti-819	103	4	p1	p1	NOUN
aiti-819	103	5	,	,	PUNCT
aiti-819	103	6	…	…	PUNCT
aiti-819	103	7	,	,	PUNCT
aiti-819	103	8	pn	pn	X
aiti-819	103	9	]	]	X
aiti-819	103	10	is	be	AUX
aiti-819	103	11	used	use	VERB
aiti-819	103	12	to	to	PART
aiti-819	103	13	produce	produce	VERB
aiti-819	103	14	the	the	DET
aiti-819	103	15	associated	associate	VERB
aiti-819	103	16	radii	radius	NOUN
aiti-819	103	17	for	for	ADP
aiti-819	103	18	point	point	NOUN
aiti-819	103	19	pi	pi	NOUN
aiti-819	103	20	using	use	VERB
aiti-819	103	21	the	the	DET
aiti-819	103	22	above	above	ADJ
aiti-819	103	23	algorithm	algorithm	NOUN
aiti-819	103	24	.	.	PUNCT
aiti-819	104	1	p	p	PROPN
aiti-819	104	2	is	be	AUX
aiti-819	104	3	called	call	VERB
aiti-819	104	4	the	the	DET
aiti-819	104	5	skeleton	skeleton	NOUN
aiti-819	104	6	/	/	SYM
aiti-819	104	7	bone	bone	NOUN
aiti-819	104	8	of	of	ADP
aiti-819	104	9	the	the	DET
aiti-819	104	10	area	area	NOUN
aiti-819	104	11	.	.	PUNCT
aiti-819	105	1	the	the	DET
aiti-819	105	2	produced	produce	VERB
aiti-819	105	3	circles	circle	NOUN
aiti-819	105	4	are	be	AUX
aiti-819	105	5	referred	refer	VERB
aiti-819	105	6	to	to	ADP
aiti-819	105	7	as	as	ADP
aiti-819	105	8	the	the	DET
aiti-819	105	9	muscles	muscle	NOUN
aiti-819	105	10	of	of	ADP
aiti-819	105	11	the	the	DET
aiti-819	105	12	area	area	NOUN
aiti-819	105	13	.	.	PUNCT
aiti-819	106	1	if	if	SCONJ
aiti-819	106	2	the	the	DET
aiti-819	106	3	path	path	NOUN
aiti-819	106	4	that	that	PRON
aiti-819	106	5	connects	connect	VERB
aiti-819	106	6	these	these	DET
aiti-819	106	7	ordered	order	VERB
aiti-819	106	8	points	point	NOUN
aiti-819	106	9	pi	pi	NOUN
aiti-819	106	10	has	have	VERB
aiti-819	106	11	a	a	DET
aiti-819	106	12	sharp	sharp	ADJ
aiti-819	106	13	angle	angle	NOUN
aiti-819	106	14	,	,	PUNCT
aiti-819	106	15	it	it	PRON
aiti-819	106	16	is	be	AUX
aiti-819	106	17	highly	highly	ADV
aiti-819	106	18	probable	probable	ADJ
aiti-819	106	19	that	that	SCONJ
aiti-819	106	20	the	the	DET
aiti-819	106	21	circles	circle	NOUN
aiti-819	106	22	generated	generate	VERB
aiti-819	106	23	using	use	VERB
aiti-819	106	24	algorithm	algorithm	NOUN
aiti-819	106	25	3	3	NUM
aiti-819	106	26	intersect	intersect	ADJ
aiti-819	106	27	other	other	ADJ
aiti-819	106	28	circles	circle	NOUN
aiti-819	106	29	locally	locally	ADV
aiti-819	106	30	.	.	PUNCT
aiti-819	107	1	to	to	PART
aiti-819	107	2	avoid	avoid	VERB
aiti-819	107	3	the	the	DET
aiti-819	107	4	aforementioned	aforementioned	ADJ
aiti-819	107	5	situation	situation	NOUN
aiti-819	107	6	,	,	PUNCT
aiti-819	107	7	skeleton	skeleton	NOUN
aiti-819	107	8	must	must	AUX
aiti-819	107	9	be	be	AUX
aiti-819	107	10	constructed	construct	VERB
aiti-819	107	11	using	use	VERB
aiti-819	107	12	points	point	NOUN
aiti-819	107	13	on	on	ADP
aiti-819	107	14	bezier	bezier	NOUN
aiti-819	107	15	or	or	CCONJ
aiti-819	107	16	hermite	hermite	ADJ
aiti-819	107	17	curve	curve	NOUN
aiti-819	107	18	.	.	PUNCT
aiti-819	108	1	consider	consider	VERB
aiti-819	108	2	the	the	DET
aiti-819	108	3	case	case	NOUN
aiti-819	108	4	wherein	wherein	ADJ
aiti-819	108	5	points	point	NOUN
aiti-819	108	6	lie	lie	VERB
aiti-819	108	7	on	on	ADP
aiti-819	108	8	a	a	DET
aiti-819	108	9	bezier	bezier	ADJ
aiti-819	108	10	curve	curve	NOUN
aiti-819	108	11	b(t	b(t	PROPN
aiti-819	108	12	)	)	PUNCT
aiti-819	108	13	,	,	PUNCT
aiti-819	108	14	where	where	SCONJ
aiti-819	108	15	t	t	PROPN
aiti-819	108	16	is	be	AUX
aiti-819	108	17	equal	equal	ADJ
aiti-819	108	18	to	to	ADP
aiti-819	108	19	0	0	NUM
aiti-819	108	20	,	,	PUNCT
aiti-819	108	21	0.25	0.25	NUM
aiti-819	108	22	,	,	PUNCT
aiti-819	108	23	0.5	0.5	NUM
aiti-819	108	24	,	,	PUNCT
aiti-819	108	25	0.75	0.75	NUM
aiti-819	108	26	,	,	PUNCT
aiti-819	108	27	and	and	CCONJ
aiti-819	108	28	1.0	1.0	NUM
aiti-819	108	29	.	.	PUNCT
aiti-819	109	1	the	the	DET
aiti-819	109	2	points	point	NOUN
aiti-819	109	3	are	be	AUX
aiti-819	109	4	used	use	VERB
aiti-819	109	5	on	on	ADP
aiti-819	109	6	the	the	DET
aiti-819	109	7	curve	curve	NOUN
aiti-819	109	8	as	as	ADP
aiti-819	109	9	the	the	DET
aiti-819	109	10	input	input	NOUN
aiti-819	109	11	for	for	ADP
aiti-819	109	12	algorithm	algorithm	NOUN
aiti-819	109	13	3	3	NUM
aiti-819	109	14	.	.	PUNCT
aiti-819	109	15	example	example	NOUN
aiti-819	109	16	5	5	NUM
aiti-819	109	17	:	:	PUNCT
aiti-819	109	18	consider	consider	VERB
aiti-819	109	19	the	the	DET
aiti-819	109	20	bezier	bezi	ADJ
aiti-819	109	21	curve	curve	NOUN
aiti-819	109	22	whose	whose	DET
aiti-819	109	23	control	control	NOUN
aiti-819	109	24	polygon	polygon	NOUN
aiti-819	109	25	is	be	AUX
aiti-819	109	26	denoted	denote	VERB
aiti-819	109	27	by	by	ADP
aiti-819	109	28	[	[	PUNCT
aiti-819	109	29	p0	p0	NOUN
aiti-819	109	30	,	,	PUNCT
aiti-819	109	31	p1	p1	NOUN
aiti-819	109	32	,	,	PUNCT
aiti-819	109	33	p2	p2	NOUN
aiti-819	109	34	,	,	PUNCT
aiti-819	109	35	p3	p3	PROPN
aiti-819	109	36	]	]	PUNCT
aiti-819	109	37	,	,	PUNCT
aiti-819	109	38	where	where	SCONJ
aiti-819	109	39	p0	p0	NOUN
aiti-819	109	40	=	=	PUNCT
aiti-819	110	1	[	[	X
aiti-819	110	2	0	0	NUM
aiti-819	110	3	,	,	PUNCT
aiti-819	110	4	0	0	NUM
aiti-819	110	5	]	]	PUNCT
aiti-819	110	6	,	,	PUNCT
aiti-819	110	7	p1	p1	PROPN
aiti-819	110	8	=	=	PUNCT
aiti-819	111	1	[	[	X
aiti-819	111	2	2	2	NUM
aiti-819	111	3	,	,	PUNCT
aiti-819	111	4	6	6	NUM
aiti-819	111	5	]	]	PUNCT
aiti-819	111	6	,	,	PUNCT
aiti-819	111	7	p2	p2	PROPN
aiti-819	111	8	=	=	PUNCT
aiti-819	112	1	[	[	X
aiti-819	112	2	7	7	NUM
aiti-819	112	3	,	,	PUNCT
aiti-819	112	4	–	–	PUNCT
aiti-819	112	5	1	1	NUM
aiti-819	112	6	]	]	PUNCT
aiti-819	112	7	,	,	PUNCT
aiti-819	112	8	and	and	CCONJ
aiti-819	112	9	p3	p3	PROPN
aiti-819	112	10	=	=	PUNCT
aiti-819	113	1	[	[	X
aiti-819	113	2	9	9	NUM
aiti-819	113	3	,	,	PUNCT
aiti-819	113	4	3	3	NUM
aiti-819	113	5	]	]	PUNCT
aiti-819	113	6	.	.	PUNCT
aiti-819	114	1	the	the	DET
aiti-819	114	2	control	control	NOUN
aiti-819	114	3	polygon	polygon	PROPN
aiti-819	114	4	and	and	CCONJ
aiti-819	114	5	bezier	bezier	NOUN
aiti-819	114	6	curve	curve	NOUN
aiti-819	114	7	are	be	AUX
aiti-819	114	8	depicted	depict	VERB
aiti-819	114	9	using	use	VERB
aiti-819	114	10	gray	gray	ADJ
aiti-819	114	11	line	line	NOUN
aiti-819	114	12	and	and	CCONJ
aiti-819	114	13	red	red	ADJ
aiti-819	114	14	curve	curve	NOUN
aiti-819	114	15	,	,	PUNCT
aiti-819	114	16	respectively	respectively	ADV
aiti-819	114	17	,	,	PUNCT
aiti-819	114	18	in	in	ADP
aiti-819	114	19	fig	fig	NOUN
aiti-819	114	20	.	.	PUNCT
aiti-819	115	1	4	4	X
aiti-819	115	2	.	.	X
aiti-819	115	3	using	use	VERB
aiti-819	115	4	algorithm	algorithm	NOUN
aiti-819	115	5	3	3	NUM
aiti-819	115	6	,	,	PUNCT
aiti-819	115	7	the	the	DET
aiti-819	115	8	muscles	muscle	NOUN
aiti-819	115	9	are	be	AUX
aiti-819	115	10	calculated	calculate	VERB
aiti-819	115	11	to	to	PART
aiti-819	115	12	be	be	AUX
aiti-819	115	13	c(0	c(0	PROPN
aiti-819	115	14	,	,	PUNCT
aiti-819	115	15	0	0	NUM
aiti-819	115	16	,	,	PUNCT
aiti-819	115	17	1.969	1.969	NUM
aiti-819	115	18	)	)	PUNCT
aiti-819	115	19	,	,	PUNCT
aiti-819	115	20	c(1.969	c(1.969	PROPN
aiti-819	115	21	,	,	PUNCT
aiti-819	115	22	2.438	2.438	NUM
aiti-819	115	23	,	,	PUNCT
aiti-819	115	24	1.164	1.164	NUM
aiti-819	115	25	)	)	PUNCT
aiti-819	115	26	,	,	PUNCT
aiti-819	115	27	c(4.5	c(4.5	PROPN
aiti-819	115	28	,	,	PUNCT
aiti-819	115	29	2.25	2.25	NUM
aiti-819	115	30	,	,	PUNCT
aiti-819	115	31	1.374	1.374	NUM
aiti-819	115	32	)	)	PUNCT
aiti-819	115	33	,	,	PUNCT
aiti-819	115	34	c(7.03	c(7.03	PROPN
aiti-819	115	35	,	,	PUNCT
aiti-819	115	36	1.688	1.688	NUM
aiti-819	115	37	,	,	PUNCT
aiti-819	115	38	1.219	1.219	NUM
aiti-819	115	39	)	)	PUNCT
aiti-819	115	40	,	,	PUNCT
aiti-819	115	41	and	and	CCONJ
aiti-819	115	42	c(9.0	c(9.0	PROPN
aiti-819	115	43	,	,	PUNCT
aiti-819	115	44	3.0	3.0	NUM
aiti-819	115	45	,	,	PUNCT
aiti-819	115	46	1.147	1.147	NUM
aiti-819	115	47	)	)	PUNCT
aiti-819	115	48	,	,	PUNCT
aiti-819	115	49	as	as	SCONJ
aiti-819	115	50	depicted	depict	VERB
aiti-819	115	51	using	use	VERB
aiti-819	115	52	green	green	ADJ
aiti-819	115	53	circles	circle	NOUN
aiti-819	115	54	in	in	ADP
aiti-819	115	55	fig	fig	NOUN
aiti-819	115	56	.	.	PUNCT
aiti-819	116	1	4	4	X
aiti-819	116	2	.	.	PUNCT
aiti-819	116	3	the	the	DET
aiti-819	116	4	case	case	NOUN
aiti-819	116	5	is	be	AUX
aiti-819	116	6	selected	select	VERB
aiti-819	116	7	wherein	wherein	SCONJ
aiti-819	116	8	the	the	DET
aiti-819	116	9	difference	difference	NOUN
aiti-819	116	10	between	between	ADP
aiti-819	116	11	the	the	DET
aiti-819	116	12	maximum	maximum	ADJ
aiti-819	116	13	radius	radius	NOUN
aiti-819	116	14	and	and	CCONJ
aiti-819	116	15	minimum	minimum	NOUN
aiti-819	116	16	radius	radius	NOUN
aiti-819	116	17	is	be	AUX
aiti-819	116	18	minimum	minimum	ADJ
aiti-819	116	19	.	.	PUNCT
aiti-819	117	1	notably	notably	ADV
aiti-819	117	2	,	,	PUNCT
aiti-819	117	3	the	the	DET
aiti-819	117	4	polygon	polygon	NOUN
aiti-819	117	5	that	that	PRON
aiti-819	117	6	connects	connect	VERB
aiti-819	117	7	points	point	NOUN
aiti-819	117	8	b(0	b(0	NOUN
aiti-819	117	9	)	)	PUNCT
aiti-819	117	10	,	,	PUNCT
aiti-819	117	11	b(0.25	b(0.25	NOUN
aiti-819	117	12	)	)	PUNCT
aiti-819	117	13	,	,	PUNCT
aiti-819	117	14	b(0.5	b(0.5	PROPN
aiti-819	117	15	)	)	PUNCT
aiti-819	117	16	,	,	PUNCT
aiti-819	117	17	b(0.75	b(0.75	PROPN
aiti-819	117	18	)	)	PUNCT
aiti-819	117	19	,	,	PUNCT
aiti-819	117	20	and	and	CCONJ
aiti-819	117	21	b(1.0	b(1.0	PROPN
aiti-819	117	22	)	)	PUNCT
aiti-819	117	23	did	do	AUX
aiti-819	117	24	not	not	PART
aiti-819	117	25	have	have	VERB
aiti-819	117	26	sharp	sharp	ADJ
aiti-819	117	27	angles	angle	NOUN
aiti-819	117	28	,	,	PUNCT
aiti-819	117	29	and	and	CCONJ
aiti-819	117	30	the	the	DET
aiti-819	117	31	values	value	NOUN
aiti-819	117	32	of	of	ADP
aiti-819	117	33	mri	mri	NOUN
aiti-819	117	34	,	,	PUNCT
aiti-819	117	35	where	where	SCONJ
aiti-819	117	36	i	i	PRON
aiti-819	117	37	=	=	NOUN
aiti-819	117	38	1	1	NUM
aiti-819	117	39	,	,	PUNCT
aiti-819	117	40	2	2	NUM
aiti-819	117	41	,	,	PUNCT
aiti-819	117	42	and	and	CCONJ
aiti-819	117	43	3	3	NUM
aiti-819	117	44	,	,	PUNCT
aiti-819	117	45	are	be	AUX
aiti-819	117	46	considerably	considerably	ADV
aiti-819	117	47	small	small	ADJ
aiti-819	117	48	,	,	PUNCT
aiti-819	117	49	i.e.	i.e.	X
aiti-819	117	50	,	,	PUNCT
aiti-819	117	51	0.32	0.32	NUM
aiti-819	117	52	,	,	PUNCT
aiti-819	117	53	0.007	0.007	NUM
aiti-819	117	54	,	,	PUNCT
aiti-819	117	55	and	and	CCONJ
aiti-819	117	56	0.199	0.199	NUM
aiti-819	117	57	,	,	PUNCT
aiti-819	117	58	respectively	respectively	ADV
aiti-819	117	59	.	.	PUNCT
aiti-819	118	1	mc1	mc1	PROPN
aiti-819	118	2	and	and	CCONJ
aiti-819	118	3	mc3	mc3	PROPN
aiti-819	118	4	are	be	AUX
aiti-819	118	5	depicted	depict	VERB
aiti-819	118	6	as	as	ADP
aiti-819	118	7	left	left	ADJ
aiti-819	118	8	and	and	CCONJ
aiti-819	118	9	right	right	ADJ
aiti-819	118	10	red	red	ADJ
aiti-819	118	11	circles	circle	NOUN
aiti-819	118	12	in	in	ADP
aiti-819	118	13	fig	fig	NOUN
aiti-819	118	14	.	.	PUNCT
aiti-819	119	1	4	4	X
aiti-819	119	2	.	.	X
aiti-819	119	3	advances	advance	NOUN
aiti-819	119	4	in	in	ADP
aiti-819	119	5	technology	technology	NOUN
aiti-819	119	6	innovation	innovation	NOUN
aiti-819	119	7	,	,	PUNCT
aiti-819	119	8	vol	vol	NOUN
aiti-819	119	9	.	.	PROPN
aiti-819	119	10	5	5	NUM
aiti-819	119	11	,	,	PUNCT
aiti-819	119	12	no	no	INTJ
aiti-819	119	13	.	.	NOUN
aiti-819	119	14	2	2	NUM
aiti-819	119	15	,	,	PUNCT
aiti-819	119	16	2020	2020	NUM
aiti-819	119	17	,	,	PUNCT
aiti-819	119	18	pp	pp	ADV
aiti-819	119	19	.	.	PUNCT
aiti-819	120	1	126	126	NUM
aiti-819	120	2	-	-	SYM
aiti-819	120	3	134	134	NUM
aiti-819	120	4	130	130	NUM
aiti-819	120	5	fig	fig	NOUN
aiti-819	120	6	.	.	PUNCT
aiti-819	121	1	4	4	NUM
aiti-819	121	2	skeleton	skeleton	NOUN
aiti-819	121	3	on	on	ADP
aiti-819	121	4	bezier	bezi	ADJ
aiti-819	121	5	curve	curve	NOUN
aiti-819	121	6	3	3	NUM
aiti-819	121	7	.	.	PUNCT
aiti-819	122	1	generating	generate	VERB
aiti-819	122	2	external	external	ADJ
aiti-819	122	3	muscles	muscle	NOUN
aiti-819	122	4	after	after	ADP
aiti-819	122	5	generating	generate	VERB
aiti-819	122	6	the	the	DET
aiti-819	122	7	central	central	ADJ
aiti-819	122	8	muscles	muscle	NOUN
aiti-819	122	9	the	the	DET
aiti-819	122	10	generation	generation	NOUN
aiti-819	122	11	of	of	ADP
aiti-819	122	12	external	external	ADJ
aiti-819	122	13	muscles	muscle	NOUN
aiti-819	122	14	is	be	AUX
aiti-819	122	15	launched	launch	VERB
aiti-819	122	16	.	.	PUNCT
aiti-819	123	1	for	for	ADP
aiti-819	123	2	this	this	PRON
aiti-819	123	3	,	,	PUNCT
aiti-819	123	4	continuous	continuous	ADJ
aiti-819	123	5	circles	circle	NOUN
aiti-819	123	6	that	that	PRON
aiti-819	123	7	are	be	AUX
aiti-819	123	8	tangents	tangent	NOUN
aiti-819	123	9	to	to	ADP
aiti-819	123	10	one	one	NUM
aiti-819	123	11	side	side	NOUN
aiti-819	123	12	of	of	ADP
aiti-819	123	13	the	the	DET
aiti-819	123	14	central	central	ADJ
aiti-819	123	15	muscle	muscle	NOUN
aiti-819	123	16	must	must	AUX
aiti-819	123	17	be	be	AUX
aiti-819	123	18	produce	produce	ADJ
aiti-819	123	19	,	,	PUNCT
aiti-819	123	20	as	as	SCONJ
aiti-819	123	21	depicted	depict	VERB
aiti-819	123	22	in	in	ADP
aiti-819	123	23	fig	fig	NOUN
aiti-819	123	24	.	.	PUNCT
aiti-819	124	1	1(b	1(b	NUM
aiti-819	124	2	)	)	PUNCT
aiti-819	124	3	.	.	PUNCT
aiti-819	125	1	consider	consider	VERB
aiti-819	125	2	3	3	NUM
aiti-819	125	3	circles	circle	NOUN
aiti-819	125	4	c0	c0	NOUN
aiti-819	125	5	,	,	PUNCT
aiti-819	125	6	c1	c1	PROPN
aiti-819	125	7	,	,	PUNCT
aiti-819	125	8	and	and	CCONJ
aiti-819	125	9	c2	c2	PROPN
aiti-819	125	10	,	,	PUNCT
aiti-819	125	11	as	as	SCONJ
aiti-819	125	12	depicted	depict	VERB
aiti-819	125	13	in	in	ADP
aiti-819	125	14	fig	fig	NOUN
aiti-819	125	15	.	.	PUNCT
aiti-819	126	1	5	5	X
aiti-819	126	2	.	.	X
aiti-819	126	3	a	a	DET
aiti-819	126	4	sequence	sequence	NOUN
aiti-819	126	5	of	of	ADP
aiti-819	126	6	circles	circle	NOUN
aiti-819	126	7	wants	want	VERB
aiti-819	126	8	finding	find	VERB
aiti-819	126	9	,	,	PUNCT
aiti-819	126	10	such	such	ADJ
aiti-819	126	11	that	that	SCONJ
aiti-819	126	12	the	the	DET
aiti-819	126	13	following	follow	VERB
aiti-819	126	14	conditions	condition	NOUN
aiti-819	126	15	are	be	AUX
aiti-819	126	16	satisfied	satisfied	ADJ
aiti-819	126	17	:	:	PUNCT
aiti-819	126	18	the	the	DET
aiti-819	126	19	first	first	ADJ
aiti-819	126	20	circle	circle	NOUN
aiti-819	126	21	c0	c0	PROPN
aiti-819	126	22	is	be	AUX
aiti-819	126	23	tangent	tangent	ADJ
aiti-819	126	24	to	to	ADP
aiti-819	126	25	c0	c0	PROPN
aiti-819	126	26	and	and	CCONJ
aiti-819	126	27	c1	c1	PROPN
aiti-819	126	28	;	;	PUNCT
aiti-819	126	29	the	the	DET
aiti-819	126	30	last	last	ADJ
aiti-819	126	31	circle	circle	NOUN
aiti-819	126	32	cn	cn	PROPN
aiti-819	126	33	is	be	AUX
aiti-819	126	34	tangent	tangent	NOUN
aiti-819	126	35	to	to	ADP
aiti-819	126	36	c1	c1	PROPN
aiti-819	126	37	and	and	CCONJ
aiti-819	126	38	c2	c2	PROPN
aiti-819	126	39	;	;	PUNCT
aiti-819	126	40	circle	circle	NOUN
aiti-819	126	41	ci	ci	PROPN
aiti-819	126	42	between	between	ADP
aiti-819	126	43	c0	c0	PROPN
aiti-819	126	44	and	and	CCONJ
aiti-819	126	45	cn	cn	PROPN
aiti-819	126	46	is	be	AUX
aiti-819	126	47	tangent	tangent	NOUN
aiti-819	126	48	to	to	ADP
aiti-819	126	49	c1	c1	PROPN
aiti-819	126	50	and	and	CCONJ
aiti-819	126	51	its	its	PRON
aiti-819	126	52	neighbors	neighbor	NOUN
aiti-819	126	53	ci-1	ci-1	NOUN
aiti-819	126	54	and	and	CCONJ
aiti-819	126	55	ci+1	ci+1	NOUN
aiti-819	126	56	,	,	PUNCT
aiti-819	126	57	as	as	SCONJ
aiti-819	126	58	depicted	depict	VERB
aiti-819	126	59	in	in	ADP
aiti-819	126	60	fig	fig	NOUN
aiti-819	126	61	.	.	PUNCT
aiti-819	127	1	5(a	5(a	NUM
aiti-819	127	2	)	)	PUNCT
aiti-819	127	3	.	.	PUNCT
aiti-819	128	1	fig	fig	NOUN
aiti-819	128	2	.	.	PUNCT
aiti-819	129	1	5(b	5(b	NUM
aiti-819	129	2	)	)	PUNCT
aiti-819	129	3	and	and	CCONJ
aiti-819	129	4	fig	fig	NOUN
aiti-819	129	5	.	.	PUNCT
aiti-819	130	1	5(c	5(c	NUM
aiti-819	130	2	)	)	PUNCT
aiti-819	130	3	depicts	depict	VERB
aiti-819	130	4	the	the	DET
aiti-819	130	5	cases	case	NOUN
aiti-819	130	6	for	for	ADP
aiti-819	130	7	n	n	NOUN
aiti-819	130	8	=	=	SYM
aiti-819	130	9	0	0	NUM
aiti-819	130	10	and	and	CCONJ
aiti-819	130	11	n	n	CCONJ
aiti-819	131	1	=	=	NOUN
aiti-819	131	2	1	1	X
aiti-819	131	3	.	.	X
aiti-819	132	1	algorithms	algorithm	NOUN
aiti-819	132	2	are	be	AUX
aiti-819	132	3	developed	develop	VERB
aiti-819	132	4	for	for	ADP
aiti-819	132	5	this	this	DET
aiti-819	132	6	case	case	NOUN
aiti-819	132	7	in	in	ADP
aiti-819	132	8	this	this	DET
aiti-819	132	9	section	section	NOUN
aiti-819	132	10	.	.	PUNCT
aiti-819	133	1	two	two	NUM
aiti-819	133	2	subcases	subcase	NOUN
aiti-819	133	3	are	be	AUX
aiti-819	133	4	considered	consider	VERB
aiti-819	133	5	,	,	PUNCT
aiti-819	133	6	the	the	DET
aiti-819	133	7	first	first	ADJ
aiti-819	133	8	case	case	NOUN
aiti-819	133	9	wherein	wherein	SCONJ
aiti-819	133	10	circles	circle	NOUN
aiti-819	133	11	ci	ci	VERB
aiti-819	133	12	,	,	PUNCT
aiti-819	133	13	where	where	SCONJ
aiti-819	133	14	i	i	PRON
aiti-819	133	15	=	=	NOUN
aiti-819	133	16	0	0	NUM
aiti-819	133	17	,	,	PUNCT
aiti-819	133	18	…	…	PUNCT
aiti-819	133	19	,	,	PUNCT
aiti-819	133	20	n	n	CCONJ
aiti-819	133	21	,	,	PUNCT
aiti-819	133	22	have	have	VERB
aiti-819	133	23	the	the	DET
aiti-819	133	24	same	same	ADJ
aiti-819	133	25	radius	radius	NOUN
aiti-819	133	26	,	,	PUNCT
aiti-819	133	27	and	and	CCONJ
aiti-819	133	28	the	the	DET
aiti-819	133	29	second	second	ADJ
aiti-819	133	30	case	case	NOUN
aiti-819	133	31	wherein	wherein	SCONJ
aiti-819	133	32	the	the	DET
aiti-819	133	33	radii	radius	NOUN
aiti-819	133	34	of	of	ADP
aiti-819	133	35	these	these	DET
aiti-819	133	36	circles	circle	NOUN
aiti-819	133	37	have	have	VERB
aiti-819	133	38	the	the	DET
aiti-819	133	39	arithmetic	arithmetic	ADJ
aiti-819	133	40	progression	progression	NOUN
aiti-819	133	41	property	property	NOUN
aiti-819	133	42	.	.	PUNCT
aiti-819	134	1	the	the	DET
aiti-819	134	2	first	first	ADJ
aiti-819	134	3	case	case	NOUN
aiti-819	134	4	is	be	AUX
aiti-819	134	5	started	start	VERB
aiti-819	134	6	from	from	ADP
aiti-819	134	7	considering	consider	VERB
aiti-819	134	8	the	the	DET
aiti-819	134	9	case	case	NOUN
aiti-819	134	10	wherein	wherein	SCONJ
aiti-819	134	11	a	a	DET
aiti-819	134	12	circle	circle	NOUN
aiti-819	134	13	is	be	AUX
aiti-819	134	14	tangent	tangent	ADJ
aiti-819	134	15	to	to	ADP
aiti-819	134	16	3	3	NUM
aiti-819	134	17	circles	circle	NOUN
aiti-819	134	18	,	,	PUNCT
aiti-819	134	19	as	as	SCONJ
aiti-819	134	20	depicted	depict	VERB
aiti-819	134	21	in	in	ADP
aiti-819	134	22	fig	fig	NOUN
aiti-819	134	23	.	.	PUNCT
aiti-819	135	1	5(a	5(a	NUM
aiti-819	135	2	)	)	PUNCT
aiti-819	135	3	;	;	PUNCT
aiti-819	135	4	this	this	DET
aiti-819	135	5	case	case	NOUN
aiti-819	135	6	comprises	comprise	VERB
aiti-819	135	7	a	a	DET
aiti-819	135	8	well	well	ADV
aiti-819	135	9	-	-	PUNCT
aiti-819	135	10	known	know	VERB
aiti-819	135	11	problem	problem	NOUN
aiti-819	135	12	called	call	VERB
aiti-819	135	13	apollonius	apollonius	NOUN
aiti-819	135	14	’s	’s	PART
aiti-819	135	15	problem	problem	NOUN
aiti-819	135	16	,	,	PUNCT
aiti-819	135	17	which	which	PRON
aiti-819	135	18	has	have	VERB
aiti-819	135	19	8	8	NUM
aiti-819	135	20	solutions	solution	NOUN
aiti-819	135	21	.	.	PUNCT
aiti-819	136	1	on	on	ADP
aiti-819	136	2	the	the	DET
aiti-819	136	3	basis	basis	NOUN
aiti-819	136	4	of	of	ADP
aiti-819	136	5	the	the	DET
aiti-819	136	6	orientation	orientation	NOUN
aiti-819	136	7	of	of	ADP
aiti-819	136	8	circles	circle	NOUN
aiti-819	136	9	(	(	PUNCT
aiti-819	136	10	a	a	DET
aiti-819	136	11	circle	circle	NOUN
aiti-819	136	12	oriented	orient	VERB
aiti-819	136	13	clockwise	clockwise	NOUN
aiti-819	136	14	has	have	VERB
aiti-819	136	15	positive	positive	ADJ
aiti-819	136	16	radius	radius	NOUN
aiti-819	136	17	,	,	PUNCT
aiti-819	136	18	and	and	CCONJ
aiti-819	136	19	that	that	DET
aiti-819	136	20	oriented	orient	VERB
aiti-819	136	21	counter	counter	NOUN
aiti-819	136	22	-	-	NOUN
aiti-819	136	23	clockwise	clockwise	NOUN
aiti-819	136	24	has	have	VERB
aiti-819	136	25	negative	negative	ADJ
aiti-819	136	26	radius	radius	NOUN
aiti-819	136	27	)	)	PUNCT
aiti-819	136	28	,	,	PUNCT
aiti-819	136	29	the	the	DET
aiti-819	136	30	problem	problem	NOUN
aiti-819	136	31	can	can	AUX
aiti-819	136	32	be	be	AUX
aiti-819	136	33	simplified	simplify	VERB
aiti-819	136	34	by	by	ADP
aiti-819	136	35	solving	solve	VERB
aiti-819	136	36	a	a	DET
aiti-819	136	37	quadratic	quadratic	ADJ
aiti-819	136	38	equation	equation	NOUN
aiti-819	136	39	.	.	PUNCT
aiti-819	137	1	after	after	ADP
aiti-819	137	2	solving	solve	VERB
aiti-819	137	3	the	the	DET
aiti-819	137	4	equation	equation	NOUN
aiti-819	137	5	,	,	PUNCT
aiti-819	137	6	two	two	NUM
aiti-819	137	7	circles	circle	NOUN
aiti-819	137	8	are	be	AUX
aiti-819	137	9	founded	found	VERB
aiti-819	137	10	,	,	PUNCT
aiti-819	137	11	one	one	NUM
aiti-819	137	12	contains	contain	VERB
aiti-819	137	13	all	all	DET
aiti-819	137	14	the	the	DET
aiti-819	137	15	three	three	NUM
aiti-819	137	16	circles	circle	NOUN
aiti-819	137	17	,	,	PUNCT
aiti-819	137	18	and	and	CCONJ
aiti-819	137	19	the	the	DET
aiti-819	137	20	other	other	ADJ
aiti-819	137	21	contains	contain	VERB
aiti-819	137	22	none	none	NOUN
aiti-819	137	23	of	of	ADP
aiti-819	137	24	the	the	DET
aiti-819	137	25	three	three	NUM
aiti-819	137	26	circles	circle	NOUN
aiti-819	137	27	.	.	PUNCT
aiti-819	138	1	the	the	DET
aiti-819	138	2	wanted	want	VERB
aiti-819	138	3	circle	circle	NOUN
aiti-819	138	4	,	,	PUNCT
aiti-819	138	5	in	in	ADP
aiti-819	138	6	this	this	DET
aiti-819	138	7	case	case	NOUN
aiti-819	138	8	,	,	PUNCT
aiti-819	138	9	is	be	AUX
aiti-819	138	10	the	the	DET
aiti-819	138	11	one	one	NOUN
aiti-819	138	12	that	that	PRON
aiti-819	138	13	contains	contain	VERB
aiti-819	138	14	none	none	NOUN
aiti-819	138	15	of	of	ADP
aiti-819	138	16	the	the	DET
aiti-819	138	17	three	three	NUM
aiti-819	138	18	circles	circle	NOUN
aiti-819	138	19	.	.	PUNCT
aiti-819	139	1	(	(	PUNCT
aiti-819	139	2	a	a	X
aiti-819	139	3	)	)	PUNCT
aiti-819	139	4	n+1	n+1	NUM
aiti-819	139	5	circles	circle	NOUN
aiti-819	139	6	(	(	PUNCT
aiti-819	139	7	b	b	NOUN
aiti-819	139	8	)	)	PUNCT
aiti-819	139	9	one	one	NUM
aiti-819	139	10	circle	circle	NOUN
aiti-819	139	11	(	(	PUNCT
aiti-819	139	12	c	c	NOUN
aiti-819	139	13	)	)	PUNCT
aiti-819	139	14	two	two	NUM
aiti-819	139	15	circles	circle	NOUN
aiti-819	139	16	fig	fig	NOUN
aiti-819	139	17	.	.	PUNCT
aiti-819	140	1	5	5	NUM
aiti-819	140	2	construction	construction	NOUN
aiti-819	140	3	of	of	ADP
aiti-819	140	4	circles	circle	NOUN
aiti-819	140	5	along	along	ADP
aiti-819	140	6	one	one	NUM
aiti-819	140	7	side	side	NOUN
aiti-819	140	8	for	for	ADP
aiti-819	140	9	finding	find	VERB
aiti-819	140	10	a	a	DET
aiti-819	140	11	circle	circle	NOUN
aiti-819	140	12	that	that	PRON
aiti-819	140	13	is	be	AUX
aiti-819	140	14	tangent	tangent	NOUN
aiti-819	140	15	to	to	ADP
aiti-819	140	16	the	the	DET
aiti-819	140	17	three	three	NUM
aiti-819	140	18	circles	circle	NOUN
aiti-819	140	19	,	,	PUNCT
aiti-819	140	20	the	the	DET
aiti-819	140	21	problem	problem	NOUN
aiti-819	140	22	can	can	AUX
aiti-819	140	23	be	be	AUX
aiti-819	140	24	solved	solve	VERB
aiti-819	140	25	algebraically	algebraically	ADV
aiti-819	140	26	.	.	PUNCT
aiti-819	141	1	assume	assume	VERB
aiti-819	141	2	that	that	SCONJ
aiti-819	141	3	the	the	DET
aiti-819	141	4	three	three	NUM
aiti-819	141	5	circles	circle	NOUN
aiti-819	141	6	have	have	VERB
aiti-819	141	7	(	(	PUNCT
aiti-819	141	8	xi	xi	PROPN
aiti-819	141	9	,	,	PUNCT
aiti-819	141	10	yi	yi	PROPN
aiti-819	141	11	)	)	PUNCT
aiti-819	141	12	as	as	ADP
aiti-819	141	13	their	their	PRON
aiti-819	141	14	centers	center	NOUN
aiti-819	141	15	and	and	CCONJ
aiti-819	141	16	ri	ri	NOUN
aiti-819	141	17	as	as	ADP
aiti-819	141	18	their	their	PRON
aiti-819	141	19	radii	radius	NOUN
aiti-819	141	20	,	,	PUNCT
aiti-819	141	21	where	where	SCONJ
aiti-819	141	22	i	i	PRON
aiti-819	141	23	=	=	NOUN
aiti-819	141	24	1	1	NUM
aiti-819	141	25	,	,	PUNCT
aiti-819	141	26	2	2	NUM
aiti-819	141	27	,	,	PUNCT
aiti-819	141	28	and	and	CCONJ
aiti-819	142	1	3	3	X
aiti-819	142	2	.	.	X
aiti-819	142	3	the	the	DET
aiti-819	142	4	circle	circle	NOUN
aiti-819	142	5	centered	center	VERB
aiti-819	142	6	at	at	ADP
aiti-819	142	7	(	(	PUNCT
aiti-819	142	8	x	x	NOUN
aiti-819	142	9	,	,	PUNCT
aiti-819	142	10	y	y	PROPN
aiti-819	142	11	)	)	PUNCT
aiti-819	142	12	with	with	ADP
aiti-819	142	13	radius	radius	NOUN
aiti-819	142	14	r	r	NOUN
aiti-819	142	15	is	be	AUX
aiti-819	142	16	tangent	tangent	NOUN
aiti-819	142	17	to	to	ADP
aiti-819	142	18	these	these	DET
aiti-819	142	19	three	three	NUM
aiti-819	142	20	circles	circle	NOUN
aiti-819	142	21	.	.	PUNCT
aiti-819	143	1	therefore	therefore	ADV
aiti-819	143	2	,	,	PUNCT
aiti-819	143	3	there	there	PRON
aiti-819	143	4	are	be	VERB
aiti-819	143	5	three	three	NUM
aiti-819	143	6	equations	equation	NOUN
aiti-819	143	7	as	as	ADP
aiti-819	143	8	(	(	PUNCT
aiti-819	143	9	x	x	X
aiti-819	143	10	–	–	PUNCT
aiti-819	143	11	xi	xi	NUM
aiti-819	143	12	)	)	PUNCT
aiti-819	143	13	2	2	NUM
aiti-819	144	1	+	+	CCONJ
aiti-819	144	2	(	(	PUNCT
aiti-819	144	3	y	y	PROPN
aiti-819	144	4	–	–	PUNCT
aiti-819	144	5	yi	yi	NOUN
aiti-819	144	6	)	)	PUNCT
aiti-819	144	7	2	2	NUM
aiti-819	144	8	=	=	SYM
aiti-819	144	9	(	(	PUNCT
aiti-819	144	10	r	r	PROPN
aiti-819	144	11	–	–	PUNCT
aiti-819	144	12	ri	ri	NOUN
aiti-819	144	13	)	)	PUNCT
aiti-819	144	14	2	2	NUM
aiti-819	144	15	,	,	PUNCT
aiti-819	144	16	where	where	SCONJ
aiti-819	144	17	i	i	PRON
aiti-819	144	18	=	=	NOUN
aiti-819	144	19	0	0	NUM
aiti-819	144	20	,	,	PUNCT
aiti-819	144	21	1	1	NUM
aiti-819	144	22	,	,	PUNCT
aiti-819	144	23	and	and	CCONJ
aiti-819	144	24	2	2	NUM
aiti-819	144	25	,	,	PUNCT
aiti-819	144	26	with	with	ADP
aiti-819	144	27	three	three	NUM
aiti-819	144	28	variables	variable	NOUN
aiti-819	144	29	x	x	NOUN
aiti-819	144	30	,	,	PUNCT
aiti-819	144	31	y	y	PROPN
aiti-819	144	32	,	,	PUNCT
aiti-819	144	33	and	and	CCONJ
aiti-819	144	34	r.	r.	PROPN
aiti-819	144	35	because	because	SCONJ
aiti-819	144	36	each	each	PRON
aiti-819	144	37	of	of	ADP
aiti-819	144	38	the	the	DET
aiti-819	144	39	aforementioned	aforementioned	ADJ
aiti-819	144	40	three	three	NUM
aiti-819	144	41	equations	equation	NOUN
aiti-819	144	42	are	be	AUX
aiti-819	144	43	of	of	ADP
aiti-819	144	44	degree	degree	NOUN
aiti-819	144	45	two	two	NUM
aiti-819	144	46	,	,	PUNCT
aiti-819	144	47	they	they	PRON
aiti-819	144	48	should	should	AUX
aiti-819	144	49	have	have	VERB
aiti-819	144	50	eight	eight	NUM
aiti-819	144	51	solutions	solution	NOUN
aiti-819	144	52	in	in	ADP
aiti-819	144	53	total	total	NOUN
aiti-819	144	54	.	.	PUNCT
aiti-819	145	1	these	these	DET
aiti-819	145	2	three	three	NUM
aiti-819	145	3	equations	equation	NOUN
aiti-819	145	4	are	be	AUX
aiti-819	145	5	referred	refer	VERB
aiti-819	145	6	to	to	ADP
aiti-819	145	7	as	as	ADP
aiti-819	145	8	eq0	eq0	X
aiti-819	145	9	,	,	PUNCT
aiti-819	145	10	eq1	eq1	PROPN
aiti-819	145	11	,	,	PUNCT
aiti-819	145	12	and	and	CCONJ
aiti-819	145	13	eq2	eq2	NOUN
aiti-819	145	14	.	.	PUNCT
aiti-819	146	1	notably	notably	ADV
aiti-819	146	2	,	,	PUNCT
aiti-819	146	3	by	by	ADP
aiti-819	146	4	performing	perform	VERB
aiti-819	146	5	eq0	eq0	NOUN
aiti-819	146	6	–	–	PUNCT
aiti-819	146	7	eq1	eq1	PROPN
aiti-819	146	8	,	,	PUNCT
aiti-819	146	9	the	the	DET
aiti-819	146	10	terms	term	NOUN
aiti-819	146	11	with	with	ADP
aiti-819	146	12	degree	degree	NOUN
aiti-819	146	13	two	two	NUM
aiti-819	146	14	are	be	AUX
aiti-819	146	15	eliminated	eliminate	VERB
aiti-819	146	16	,	,	PUNCT
aiti-819	146	17	and	and	CCONJ
aiti-819	146	18	,	,	PUNCT
aiti-819	146	19	accordingly	accordingly	ADV
aiti-819	146	20	,	,	PUNCT
aiti-819	146	21	the	the	DET
aiti-819	146	22	equation	equation	NOUN
aiti-819	146	23	obtained	obtain	VERB
aiti-819	146	24	is	be	AUX
aiti-819	146	25	a	a	DET
aiti-819	146	26	linear	linear	ADJ
aiti-819	146	27	equation	equation	NOUN
aiti-819	146	28	.	.	PUNCT
aiti-819	147	1	the	the	DET
aiti-819	147	2	system	system	NOUN
aiti-819	147	3	of	of	ADP
aiti-819	147	4	equation	equation	NOUN
aiti-819	147	5	can	can	AUX
aiti-819	147	6	be	be	AUX
aiti-819	147	7	simplified	simplify	VERB
aiti-819	147	8	{	{	PUNCT
aiti-819	147	9	eqn0	eqn0	NOUN
aiti-819	147	10	,	,	PUNCT
aiti-819	147	11	eqn1	eqn1	NOUN
aiti-819	147	12	,	,	PUNCT
aiti-819	147	13	eqn2	eqn2	NOUN
aiti-819	147	14	}	}	PUNCT
aiti-819	147	15	into	into	ADP
aiti-819	147	16	{	{	PUNCT
aiti-819	147	17	eqn0	eqn0	NOUN
aiti-819	147	18	,	,	PUNCT
aiti-819	147	19	eqn0	eqn0	NOUN
aiti-819	147	20	–	–	PUNCT
aiti-819	147	21	eqn1	eqn1	NOUN
aiti-819	147	22	,	,	PUNCT
aiti-819	147	23	eqn0	eqn0	NOUN
aiti-819	147	24	–	–	PUNCT
aiti-819	147	25	eqn2	eqn2	PROPN
aiti-819	147	26	}	}	PUNCT
aiti-819	147	27	,	,	PUNCT
aiti-819	147	28	where	where	SCONJ
aiti-819	147	29	the	the	DET
aiti-819	147	30	new	new	ADJ
aiti-819	147	31	system	system	NOUN
aiti-819	147	32	of	of	ADP
aiti-819	147	33	equation	equation	NOUN
aiti-819	147	34	is	be	AUX
aiti-819	147	35	of	of	ADP
aiti-819	147	36	degrees	degree	NOUN
aiti-819	147	37	two	two	NUM
aiti-819	147	38	,	,	PUNCT
aiti-819	147	39	one	one	NUM
aiti-819	147	40	,	,	PUNCT
aiti-819	147	41	and	and	CCONJ
aiti-819	147	42	one	one	NUM
aiti-819	147	43	,	,	PUNCT
aiti-819	147	44	respectively	respectively	ADV
aiti-819	147	45	;	;	PUNCT
aiti-819	147	46	therefore	therefore	ADV
aiti-819	147	47	,	,	PUNCT
aiti-819	147	48	the	the	DET
aiti-819	147	49	number	number	NOUN
aiti-819	147	50	of	of	ADP
aiti-819	147	51	solutions	solution	NOUN
aiti-819	147	52	becomes	become	VERB
aiti-819	147	53	two	two	NUM
aiti-819	147	54	.	.	PUNCT
aiti-819	148	1	in	in	ADP
aiti-819	148	2	the	the	DET
aiti-819	148	3	algorithm	algorithm	NOUN
aiti-819	148	4	,	,	PUNCT
aiti-819	148	5	the	the	DET
aiti-819	148	6	binary	binary	ADJ
aiti-819	148	7	approach	approach	NOUN
aiti-819	148	8	is	be	AUX
aiti-819	148	9	used	use	VERB
aiti-819	148	10	to	to	PART
aiti-819	148	11	find	find	VERB
aiti-819	148	12	the	the	DET
aiti-819	148	13	radius	radius	NOUN
aiti-819	148	14	of	of	ADP
aiti-819	148	15	the	the	DET
aiti-819	148	16	tangent	tangent	ADJ
aiti-819	148	17	circle	circle	NOUN
aiti-819	148	18	.	.	PUNCT
aiti-819	149	1	this	this	DET
aiti-819	149	2	algorithm	algorithm	NOUN
aiti-819	149	3	is	be	AUX
aiti-819	149	4	introduced	introduce	VERB
aiti-819	149	5	because	because	SCONJ
aiti-819	149	6	it	it	PRON
aiti-819	149	7	can	can	AUX
aiti-819	149	8	be	be	AUX
aiti-819	149	9	easily	easily	ADV
aiti-819	149	10	extended	extend	VERB
aiti-819	149	11	to	to	ADP
aiti-819	149	12	the	the	DET
aiti-819	149	13	case	case	NOUN
aiti-819	149	14	with	with	ADP
aiti-819	149	15	more	more	ADJ
aiti-819	149	16	circles	circle	NOUN
aiti-819	149	17	,	,	PUNCT
aiti-819	149	18	as	as	SCONJ
aiti-819	149	19	depicted	depict	VERB
aiti-819	149	20	in	in	ADP
aiti-819	149	21	fig	fig	NOUN
aiti-819	149	22	.	.	PUNCT
aiti-819	150	1	5(b	5(b	NUM
aiti-819	150	2	)	)	PUNCT
aiti-819	150	3	and	and	CCONJ
aiti-819	150	4	5(c	5(c	NUM
aiti-819	150	5	)	)	PUNCT
aiti-819	150	6	.	.	PUNCT
aiti-819	151	1	before	before	ADP
aiti-819	151	2	the	the	DET
aiti-819	151	3	algorithm	algorithm	NOUN
aiti-819	151	4	,	,	PUNCT
aiti-819	151	5	there	there	PRON
aiti-819	151	6	are	be	VERB
aiti-819	151	7	the	the	DET
aiti-819	151	8	following	follow	VERB
aiti-819	151	9	theorems	theorem	NOUN
aiti-819	151	10	.	.	PUNCT
aiti-819	152	1	theorem	theorem	NOUN
aiti-819	152	2	2	2	NUM
aiti-819	152	3	:	:	PUNCT
aiti-819	152	4	three	three	NUM
aiti-819	152	5	circles	circle	NOUN
aiti-819	152	6	are	be	AUX
aiti-819	152	7	tangent	tangent	ADJ
aiti-819	152	8	to	to	ADP
aiti-819	152	9	each	each	DET
aiti-819	152	10	other	other	ADJ
aiti-819	152	11	,	,	PUNCT
aiti-819	152	12	and	and	CCONJ
aiti-819	152	13	their	their	PRON
aiti-819	152	14	radii	radius	NOUN
aiti-819	152	15	are	be	AUX
aiti-819	152	16	x	x	X
aiti-819	152	17	,	,	PUNCT
aiti-819	152	18	y	y	PROPN
aiti-819	152	19	,	,	PUNCT
aiti-819	152	20	and	and	CCONJ
aiti-819	152	21	z.	z.	PROPN
aiti-819	152	22	furthermore	furthermore	ADV
aiti-819	152	23	,	,	PUNCT
aiti-819	152	24	the	the	DET
aiti-819	152	25	angle	angle	NOUN
aiti-819	152	26			NOUN
aiti-819	152	27	of	of	ADP
aiti-819	152	28	the	the	DET
aiti-819	152	29	triangle	triangle	NOUN
aiti-819	152	30	that	that	PRON
aiti-819	152	31	is	be	AUX
aiti-819	152	32	formed	form	VERB
aiti-819	152	33	by	by	ADP
aiti-819	152	34	connecting	connect	VERB
aiti-819	152	35	their	their	PRON
aiti-819	152	36	centers	center	NOUN
aiti-819	152	37	has	have	VERB
aiti-819	152	38	the	the	DET
aiti-819	152	39	opposite	opposite	ADJ
aiti-819	152	40	side	side	NOUN
aiti-819	152	41	of	of	ADP
aiti-819	152	42	length	length	NOUN
aiti-819	152	43	y	y	PROPN
aiti-819	153	1	+	+	PROPN
aiti-819	153	2	z	z	PROPN
aiti-819	153	3	,	,	PUNCT
aiti-819	153	4	as	as	SCONJ
aiti-819	153	5	depicted	depict	VERB
aiti-819	153	6	in	in	ADP
aiti-819	153	7	fig	fig	NOUN
aiti-819	153	8	.	.	PUNCT
aiti-819	154	1	6(a	6(a	NUM
aiti-819	154	2	)	)	PUNCT
aiti-819	154	3	.	.	PUNCT
aiti-819	155	1	then	then	ADV
aiti-819	155	2	:	:	PUNCT
aiti-819	155	3	advances	advance	NOUN
aiti-819	155	4	in	in	ADP
aiti-819	155	5	technology	technology	NOUN
aiti-819	155	6	innovation	innovation	NOUN
aiti-819	155	7	,	,	PUNCT
aiti-819	155	8	vol	vol	NOUN
aiti-819	155	9	.	.	PROPN
aiti-819	155	10	5	5	NUM
aiti-819	155	11	,	,	PUNCT
aiti-819	155	12	no	no	INTJ
aiti-819	155	13	.	.	NOUN
aiti-819	155	14	2	2	NUM
aiti-819	155	15	,	,	PUNCT
aiti-819	155	16	2020	2020	NUM
aiti-819	155	17	,	,	PUNCT
aiti-819	155	18	pp	pp	ADV
aiti-819	155	19	.	.	PUNCT
aiti-819	156	1	126	126	NUM
aiti-819	156	2	-	-	SYM
aiti-819	156	3	134	134	NUM
aiti-819	156	4	131	131	NUM
aiti-819	156	5	2	2	NUM
aiti-819	156	6	2	2	NUM
aiti-819	156	7	cos	cos	PROPN
aiti-819	156	8	(	(	PUNCT
aiti-819	156	9	)	)	PUNCT
aiti-819	156	10	x	x	PUNCT
aiti-819	156	11	xy	xy	PROPN
aiti-819	156	12	xz	xz	PROPN
aiti-819	156	13	yz	yz	INTJ
aiti-819	157	1	a	a	DET
aiti-819	157	2	x	x	X
aiti-819	157	3	xy	xy	PROPN
aiti-819	157	4	xz	xz	PROPN
aiti-819	157	5	yz	yz	PROPN
aiti-819	157	6			PROPN
aiti-819	157	7			VERB
aiti-819	157	8			PROPN
aiti-819	157	9			PROPN
aiti-819	157	10			PROPN
aiti-819	157	11			PUNCT
aiti-819	157	12			X
aiti-819	157	13	(	(	PUNCT
aiti-819	157	14	1	1	X
aiti-819	157	15	)	)	PUNCT
aiti-819	157	16	proof	proof	NOUN
aiti-819	157	17	:	:	PUNCT
aiti-819	157	18	the	the	DET
aiti-819	157	19	result	result	NOUN
aiti-819	157	20	is	be	AUX
aiti-819	157	21	derived	derive	VERB
aiti-819	157	22	directly	directly	ADV
aiti-819	157	23	from	from	ADP
aiti-819	157	24	the	the	DET
aiti-819	157	25	cosine	cosine	NOUN
aiti-819	157	26	theorem	theorem	NOUN
aiti-819	157	27	,	,	PUNCT
aiti-819	157	28	that	that	ADV
aiti-819	157	29	is	is	ADV
aiti-819	157	30	,	,	PUNCT
aiti-819	157	31	(	(	PUNCT
aiti-819	157	32	y	y	PROPN
aiti-819	157	33	+	+	PROPN
aiti-819	157	34	z	z	X
aiti-819	157	35	)	)	PUNCT
aiti-819	157	36	2	2	NUM
aiti-819	157	37	=	=	SYM
aiti-819	157	38	(	(	PUNCT
aiti-819	157	39	x	x	PROPN
aiti-819	157	40	+	+	NUM
aiti-819	157	41	y	y	NOUN
aiti-819	157	42	)	)	PUNCT
aiti-819	157	43	2	2	NUM
aiti-819	158	1	+	+	CCONJ
aiti-819	158	2	(	(	PUNCT
aiti-819	158	3	x	x	X
aiti-819	158	4	+	+	NUM
aiti-819	158	5	z	z	NOUN
aiti-819	158	6	)	)	PUNCT
aiti-819	158	7	2	2	NUM
aiti-819	158	8	–	–	PUNCT
aiti-819	158	9	2(x	2(x	NUM
aiti-819	159	1	+	+	CCONJ
aiti-819	159	2	y)(x	y)(x	PROPN
aiti-819	159	3	+	+	CCONJ
aiti-819	159	4	z)cos(	z)cos(	PROPN
aiti-819	159	5	)	)	PUNCT
aiti-819	159	6	.	.	PUNCT
aiti-819	160	1	using	use	VERB
aiti-819	160	2	the	the	DET
aiti-819	160	3	equation	equation	NOUN
aiti-819	160	4	in	in	ADP
aiti-819	160	5	theorem	theorem	NOUN
aiti-819	160	6	2	2	NUM
aiti-819	160	7	,	,	PUNCT
aiti-819	160	8	there	there	PRON
aiti-819	160	9	are	be	VERB
aiti-819	160	10	four	four	NUM
aiti-819	160	11	variables	variable	NOUN
aiti-819	160	12	,	,	PUNCT
aiti-819	160	13	namely	namely	ADV
aiti-819	160	14	,	,	PUNCT
aiti-819	160	15	x	x	X
aiti-819	160	16	,	,	PUNCT
aiti-819	160	17	y	y	PROPN
aiti-819	160	18	,	,	PUNCT
aiti-819	160	19	z	z	NOUN
aiti-819	160	20	,	,	PUNCT
aiti-819	160	21	and	and	CCONJ
aiti-819	160	22			NOUN
aiti-819	160	23	,	,	PUNCT
aiti-819	160	24	with	with	ADP
aiti-819	160	25	one	one	NUM
aiti-819	160	26	equation	equation	NOUN
aiti-819	160	27	.	.	PUNCT
aiti-819	161	1	given	give	VERB
aiti-819	161	2	any	any	DET
aiti-819	161	3	three	three	NUM
aiti-819	161	4	variables	variable	NOUN
aiti-819	161	5	,	,	PUNCT
aiti-819	161	6	the	the	DET
aiti-819	161	7	fourth	fourth	ADJ
aiti-819	161	8	one	one	NOUN
aiti-819	161	9	can	can	AUX
aiti-819	161	10	be	be	AUX
aiti-819	161	11	calculated	calculate	VERB
aiti-819	161	12	.	.	PUNCT
aiti-819	162	1	assume	assume	VERB
aiti-819	162	2	that	that	SCONJ
aiti-819	162	3	there	there	PRON
aiti-819	162	4	are	be	VERB
aiti-819	162	5	two	two	NUM
aiti-819	162	6	circles	circle	NOUN
aiti-819	162	7	with	with	ADP
aiti-819	162	8	radii	radius	NOUN
aiti-819	162	9	x	x	PUNCT
aiti-819	162	10	and	and	CCONJ
aiti-819	162	11	y	y	PROPN
aiti-819	162	12	,	,	PUNCT
aiti-819	162	13	and	and	CCONJ
aiti-819	162	14	angle	angle	NOUN
aiti-819	162	15	.	.	NOUN
aiti-819	162	16	accordingly	accordingly	ADV
aiti-819	162	17	,	,	PUNCT
aiti-819	162	18	radius	radius	NOUN
aiti-819	162	19	z	z	PROPN
aiti-819	162	20	can	can	AUX
aiti-819	162	21	be	be	AUX
aiti-819	162	22	calculated	calculate	VERB
aiti-819	162	23	.	.	PUNCT
aiti-819	163	1	besides	besides	SCONJ
aiti-819	163	2	,	,	PUNCT
aiti-819	163	3	if	if	SCONJ
aiti-819	163	4	x	x	PRON
aiti-819	163	5	and	and	CCONJ
aiti-819	163	6	y	y	PROPN
aiti-819	163	7	are	be	AUX
aiti-819	163	8	known	know	VERB
aiti-819	163	9	,	,	PUNCT
aiti-819	163	10	and	and	CCONJ
aiti-819	163	11	assumed	assume	VERB
aiti-819	163	12	radius	radius	PROPN
aiti-819	163	13	z	z	PROPN
aiti-819	163	14	,	,	PUNCT
aiti-819	163	15			X
aiti-819	163	16	can	can	AUX
aiti-819	163	17	be	be	AUX
aiti-819	163	18	calculated	calculate	VERB
aiti-819	163	19	as	as	ADV
aiti-819	163	20	well	well	ADV
aiti-819	163	21	.	.	PUNCT
aiti-819	164	1	(	(	PUNCT
aiti-819	164	2	a	a	X
aiti-819	164	3	)	)	PUNCT
aiti-819	164	4	one	one	NUM
aiti-819	164	5	circle	circle	NOUN
aiti-819	164	6	tangent	tangent	NOUN
aiti-819	164	7	to	to	ADP
aiti-819	164	8	two	two	NUM
aiti-819	164	9	circles	circle	NOUN
aiti-819	164	10	(	(	PUNCT
aiti-819	164	11	b	b	NOUN
aiti-819	164	12	)	)	PUNCT
aiti-819	164	13	one	one	NUM
aiti-819	164	14	circle	circle	NOUN
aiti-819	164	15	tangent	tangent	NOUN
aiti-819	164	16	to	to	ADP
aiti-819	164	17	three	three	NUM
aiti-819	164	18	circles	circle	NOUN
aiti-819	164	19	fig	fig	NOUN
aiti-819	164	20	.	.	PUNCT
aiti-819	165	1	6	6	NUM
aiti-819	165	2	relation	relation	NOUN
aiti-819	165	3	between	between	ADP
aiti-819	165	4	radii	radius	NOUN
aiti-819	165	5	and	and	CCONJ
aiti-819	165	6	angles	angle	NOUN
aiti-819	165	7	now	now	ADV
aiti-819	165	8	,	,	PUNCT
aiti-819	165	9	consider	consider	VERB
aiti-819	165	10	3	3	NUM
aiti-819	165	11	circles	circle	NOUN
aiti-819	165	12	ci	ci	NOUN
aiti-819	165	13	,	,	PUNCT
aiti-819	165	14	where	where	SCONJ
aiti-819	165	15	i	i	PRON
aiti-819	165	16	=	=	NOUN
aiti-819	165	17	0	0	NUM
aiti-819	165	18	,	,	PUNCT
aiti-819	165	19	1	1	NUM
aiti-819	165	20	,	,	PUNCT
aiti-819	165	21	and	and	CCONJ
aiti-819	165	22	2	2	X
aiti-819	165	23	.	.	X
aiti-819	165	24	assume	assume	VERB
aiti-819	165	25	that	that	SCONJ
aiti-819	165	26	c0	c0	PROPN
aiti-819	165	27	is	be	AUX
aiti-819	165	28	tangent	tangent	ADJ
aiti-819	165	29	to	to	ADP
aiti-819	165	30	c1	c1	PROPN
aiti-819	165	31	and	and	CCONJ
aiti-819	165	32	that	that	SCONJ
aiti-819	165	33	c1	c1	PROPN
aiti-819	165	34	is	be	AUX
aiti-819	165	35	tangent	tangent	NOUN
aiti-819	165	36	to	to	ADP
aiti-819	165	37	c2	c2	PROPN
aiti-819	165	38	.	.	PUNCT
aiti-819	166	1	in	in	ADP
aiti-819	166	2	addition	addition	NOUN
aiti-819	166	3	,	,	PUNCT
aiti-819	166	4	assume	assume	VERB
aiti-819	166	5	that	that	SCONJ
aiti-819	166	6	the	the	DET
aiti-819	166	7	circle	circle	NOUN
aiti-819	166	8	that	that	PRON
aiti-819	166	9	is	be	AUX
aiti-819	166	10	tangent	tangent	NOUN
aiti-819	166	11	to	to	ADP
aiti-819	166	12	c0	c0	PROPN
aiti-819	166	13	,	,	PUNCT
aiti-819	166	14	c1	c1	PROPN
aiti-819	166	15	,	,	PUNCT
aiti-819	166	16	and	and	CCONJ
aiti-819	166	17	c2	c2	PROPN
aiti-819	166	18	has	have	VERB
aiti-819	166	19	radius	radius	PROPN
aiti-819	166	20	r.	r.	PROPN
aiti-819	166	21	from	from	ADP
aiti-819	166	22	this	this	DET
aiti-819	166	23	assumption	assumption	NOUN
aiti-819	166	24	and	and	CCONJ
aiti-819	166	25	considering	consider	VERB
aiti-819	166	26	fig	fig	NOUN
aiti-819	166	27	.	.	PUNCT
aiti-819	167	1	6(b	6(b	NUM
aiti-819	167	2	)	)	PUNCT
aiti-819	167	3	,	,	PUNCT
aiti-819	167	4	angles	angle	VERB
aiti-819	167	5	1	1	PUNCT
aiti-819	167	6	and	and	CCONJ
aiti-819	167	7	2	2	PROPN
aiti-819	167	8	can	can	AUX
aiti-819	167	9	be	be	AUX
aiti-819	167	10	calculated	calculate	VERB
aiti-819	167	11	using	use	VERB
aiti-819	167	12	the	the	DET
aiti-819	167	13	equation	equation	NOUN
aiti-819	167	14	in	in	ADP
aiti-819	167	15	theorem	theorem	NOUN
aiti-819	167	16	2	2	NUM
aiti-819	167	17	,	,	PUNCT
aiti-819	167	18	and	and	CCONJ
aiti-819	167	19	,	,	PUNCT
aiti-819	167	20	subsequently	subsequently	ADV
aiti-819	167	21	,	,	PUNCT
aiti-819	167	22	their	their	PRON
aiti-819	167	23	sum	sum	NOUN
aiti-819	167	24	is	be	AUX
aiti-819	167	25	compared	compare	VERB
aiti-819	167	26	with	with	ADP
aiti-819	167	27	the	the	DET
aiti-819	167	28	angle	angle	NOUN
aiti-819	167	29	between	between	ADP
aiti-819	167	30	vectors	vector	NOUN
aiti-819	167	31	p0	p0	NOUN
aiti-819	167	32	–	–	PUNCT
aiti-819	167	33	p1	p1	NOUN
aiti-819	167	34	and	and	CCONJ
aiti-819	167	35	p2	p2	PROPN
aiti-819	167	36	–	–	PUNCT
aiti-819	167	37	p1	p1	NOUN
aiti-819	167	38	.	.	PUNCT
aiti-819	168	1	if	if	SCONJ
aiti-819	168	2	the	the	DET
aiti-819	168	3	sum	sum	NOUN
aiti-819	168	4	is	be	AUX
aiti-819	168	5	less	less	ADJ
aiti-819	168	6	than	than	ADP
aiti-819	168	7	the	the	DET
aiti-819	168	8	angle	angle	NOUN
aiti-819	168	9	between	between	ADP
aiti-819	168	10	the	the	DET
aiti-819	168	11	vectors	vector	NOUN
aiti-819	168	12	,	,	PUNCT
aiti-819	168	13	radius	radius	NOUN
aiti-819	168	14	r	r	NOUN
aiti-819	168	15	enlarged	enlarge	VERB
aiti-819	168	16	,	,	PUNCT
aiti-819	168	17	and	and	CCONJ
aiti-819	168	18	if	if	SCONJ
aiti-819	168	19	the	the	DET
aiti-819	168	20	sum	sum	NOUN
aiti-819	168	21	is	be	AUX
aiti-819	168	22	greater	great	ADJ
aiti-819	168	23	than	than	ADP
aiti-819	168	24	the	the	DET
aiti-819	168	25	angle	angle	NOUN
aiti-819	168	26	between	between	ADP
aiti-819	168	27	the	the	DET
aiti-819	168	28	vectors	vector	NOUN
aiti-819	168	29	,	,	PUNCT
aiti-819	168	30	radius	radius	NOUN
aiti-819	168	31	r	r	NOUN
aiti-819	168	32	reduced	reduce	VERB
aiti-819	168	33	,	,	PUNCT
aiti-819	168	34	until	until	SCONJ
aiti-819	168	35	the	the	DET
aiti-819	168	36	solution	solution	NOUN
aiti-819	168	37	is	be	AUX
aiti-819	168	38	found	find	VERB
aiti-819	168	39	within	within	ADP
aiti-819	168	40	a	a	DET
aiti-819	168	41	tolerance	tolerance	NOUN
aiti-819	168	42	.	.	PUNCT
aiti-819	169	1	this	this	DET
aiti-819	169	2	aforementioned	aforementione	VERB
aiti-819	169	3	idea	idea	NOUN
aiti-819	169	4	can	can	AUX
aiti-819	169	5	be	be	AUX
aiti-819	169	6	implemented	implement	VERB
aiti-819	169	7	using	use	VERB
aiti-819	169	8	the	the	DET
aiti-819	169	9	following	follow	VERB
aiti-819	169	10	algorithm	algorithm	NOUN
aiti-819	169	11	:	:	PUNCT
aiti-819	169	12	algorithm	algorithm	NOUN
aiti-819	169	13	4	4	NUM
aiti-819	169	14	:	:	SYM
aiti-819	169	15	1	1	NUM
aiti-819	169	16	.	.	X
aiti-819	169	17	input	input	NOUN
aiti-819	169	18	three	three	NUM
aiti-819	169	19	circles	circle	NOUN
aiti-819	169	20	c0	c0	NOUN
aiti-819	169	21	,	,	PUNCT
aiti-819	169	22	c1	c1	PROPN
aiti-819	169	23	,	,	PUNCT
aiti-819	169	24	and	and	CCONJ
aiti-819	169	25	c2	c2	PROPN
aiti-819	169	26	.	.	PUNCT
aiti-819	170	1	#	#	NOUN
aiti-819	170	2	assume	assume	VERB
aiti-819	170	3	that	that	SCONJ
aiti-819	170	4	c0	c0	PROPN
aiti-819	170	5	is	be	AUX
aiti-819	170	6	tangent	tangent	ADJ
aiti-819	170	7	to	to	ADP
aiti-819	170	8	c1	c1	PROPN
aiti-819	170	9	and	and	CCONJ
aiti-819	170	10	that	that	SCONJ
aiti-819	170	11	c1	c1	PROPN
aiti-819	170	12	is	be	AUX
aiti-819	170	13	tangent	tangent	NOUN
aiti-819	170	14	to	to	ADP
aiti-819	170	15	c2	c2	PROPN
aiti-819	170	16	.	.	PUNCT
aiti-819	171	1	2	2	X
aiti-819	171	2	.	.	X
aiti-819	171	3	calculate	calculate	VERB
aiti-819	171	4	the	the	DET
aiti-819	171	5	angle	angle	NOUN
aiti-819	171	6	between	between	ADP
aiti-819	171	7	vectors	vector	NOUN
aiti-819	171	8	p0	p0	NOUN
aiti-819	171	9	-	-	PUNCT
aiti-819	171	10	p1	p1	NOUN
aiti-819	171	11	and	and	CCONJ
aiti-819	171	12	p2	p2	NOUN
aiti-819	171	13	-	-	PUNCT
aiti-819	171	14	p1	p1	NOUN
aiti-819	171	15	,	,	PUNCT
aiti-819	171	16	and	and	CCONJ
aiti-819	171	17	refer	refer	VERB
aiti-819	171	18	to	to	ADP
aiti-819	171	19	it	it	PRON
aiti-819	171	20	as	as	ADP
aiti-819	171	21	.	.	NOUN
aiti-819	171	22	3	3	NUM
aiti-819	171	23	.	.	X
aiti-819	171	24	set	set	VERB
aiti-819	171	25	r	r	NOUN
aiti-819	171	26	,	,	PUNCT
aiti-819	171	27	rmin	rmin	NOUN
aiti-819	171	28	,	,	PUNCT
aiti-819	171	29	and	and	CCONJ
aiti-819	171	30	rmax	rmax	ADJ
aiti-819	171	31	as	as	ADP
aiti-819	171	32	1	1	NUM
aiti-819	171	33	,	,	PUNCT
aiti-819	171	34	0	0	NUM
aiti-819	171	35	,	,	PUNCT
aiti-819	171	36	and	and	CCONJ
aiti-819	171	37	999	999	NUM
aiti-819	171	38	,	,	PUNCT
aiti-819	171	39	respectively	respectively	ADV
aiti-819	171	40	.	.	PUNCT
aiti-819	172	1	4	4	X
aiti-819	172	2	.	.	X
aiti-819	172	3	set	set	VERB
aiti-819	172	4	eps	eps	PROPN
aiti-819	172	5	=	=	PROPN
aiti-819	172	6	0.001	0.001	NUM
aiti-819	172	7	5	5	NUM
aiti-819	172	8	.	.	PUNCT
aiti-819	172	9	calculate	calculate	NOUN
aiti-819	172	10	angles	angle	NOUN
aiti-819	172	11	1	1	PUNCT
aiti-819	172	12	and	and	CCONJ
aiti-819	172	13	2	2	NOUN
aiti-819	172	14	using	use	VERB
aiti-819	172	15	the	the	DET
aiti-819	172	16	assumed	assumed	ADJ
aiti-819	172	17	radius	radius	PROPN
aiti-819	172	18	r.	r.	PROPN
aiti-819	172	19	6	6	NUM
aiti-819	172	20	.	.	PUNCT
aiti-819	173	1	while	while	SCONJ
aiti-819	173	2	|1	|1	ADP
aiti-819	173	3	+	+	CCONJ
aiti-819	173	4	2	2	NOUN
aiti-819	173	5	–	–	PUNCT
aiti-819	173	6	|	|	ADJ
aiti-819	173	7	>	>	X
aiti-819	173	8	eps	eps	PROPN
aiti-819	173	9	:	:	PUNCT
aiti-819	173	10	if	if	SCONJ
aiti-819	173	11	1	1	PUNCT
aiti-819	173	12	+	+	PUNCT
aiti-819	173	13	2	2	NOUN
aiti-819	173	14	>	>	PRON
aiti-819	173	15			NOUN
aiti-819	173	16	:	:	PUNCT
aiti-819	173	17	rmax	rmax	ADJ
aiti-819	173	18	=	=	NOUN
aiti-819	173	19	r	r	NOUN
aiti-819	173	20	r	r	NOUN
aiti-819	173	21	=	=	PUNCT
aiti-819	173	22	(	(	PUNCT
aiti-819	173	23	rmax	rmax	ADJ
aiti-819	173	24	+	+	NUM
aiti-819	173	25	rmin)/2	rmin)/2	NOUN
aiti-819	173	26	else	else	ADV
aiti-819	173	27	:	:	PUNCT
aiti-819	173	28	rmin	rmin	NOUN
aiti-819	173	29	=	=	SYM
aiti-819	173	30	r	r	NOUN
aiti-819	173	31	r	r	NOUN
aiti-819	173	32	=	=	PUNCT
aiti-819	173	33	(	(	PUNCT
aiti-819	173	34	rmax	rmax	ADJ
aiti-819	173	35	+	+	CCONJ
aiti-819	173	36	rmin)/2	rmin)/2	NOUN
aiti-819	173	37	7	7	NUM
aiti-819	173	38	.	.	PUNCT
aiti-819	173	39	display	display	VERB
aiti-819	173	40	the	the	DET
aiti-819	173	41	result	result	NOUN
aiti-819	173	42	.	.	PUNCT
aiti-819	174	1	advances	advance	NOUN
aiti-819	174	2	in	in	ADP
aiti-819	174	3	technology	technology	NOUN
aiti-819	174	4	innovation	innovation	NOUN
aiti-819	174	5	,	,	PUNCT
aiti-819	174	6	vol	vol	NOUN
aiti-819	174	7	.	.	PROPN
aiti-819	174	8	5	5	NUM
aiti-819	174	9	,	,	PUNCT
aiti-819	174	10	no	no	INTJ
aiti-819	174	11	.	.	NOUN
aiti-819	174	12	2	2	NUM
aiti-819	174	13	,	,	PUNCT
aiti-819	174	14	2020	2020	NUM
aiti-819	174	15	,	,	PUNCT
aiti-819	174	16	pp	pp	ADV
aiti-819	174	17	.	.	PUNCT
aiti-819	175	1	126	126	NUM
aiti-819	175	2	-	-	SYM
aiti-819	175	3	134	134	NUM
aiti-819	175	4	132	132	NUM
aiti-819	175	5	example	example	NOUN
aiti-819	175	6	5	5	NUM
aiti-819	175	7	:	:	PUNCT
aiti-819	175	8	consider	consider	VERB
aiti-819	175	9	three	three	NUM
aiti-819	175	10	circles	circle	NOUN
aiti-819	175	11	c0	c0	NOUN
aiti-819	175	12	(	(	PUNCT
aiti-819	175	13	–	–	PUNCT
aiti-819	175	14	4	4	NUM
aiti-819	175	15	,	,	PUNCT
aiti-819	175	16	3	3	NUM
aiti-819	175	17	,	,	PUNCT
aiti-819	175	18	3	3	NUM
aiti-819	175	19	)	)	PUNCT
aiti-819	175	20	,	,	PUNCT
aiti-819	175	21	c1	c1	PROPN
aiti-819	175	22	(	(	PUNCT
aiti-819	175	23	0	0	NUM
aiti-819	175	24	,	,	PUNCT
aiti-819	175	25	0	0	NUM
aiti-819	175	26	,	,	PUNCT
aiti-819	175	27	2	2	NUM
aiti-819	175	28	)	)	PUNCT
aiti-819	175	29	,	,	PUNCT
aiti-819	175	30	and	and	CCONJ
aiti-819	175	31	c2	c2	PROPN
aiti-819	175	32	(	(	PUNCT
aiti-819	175	33	4	4	NUM
aiti-819	175	34	,	,	PUNCT
aiti-819	175	35	0	0	NUM
aiti-819	175	36	,	,	PUNCT
aiti-819	175	37	2	2	NUM
aiti-819	175	38	)	)	PUNCT
aiti-819	175	39	.	.	PUNCT
aiti-819	176	1	notably	notably	ADV
aiti-819	176	2	,	,	PUNCT
aiti-819	176	3	c0	c0	PROPN
aiti-819	176	4	is	be	AUX
aiti-819	176	5	tangent	tangent	ADJ
aiti-819	176	6	to	to	ADP
aiti-819	176	7	c1	c1	PROPN
aiti-819	176	8	and	and	CCONJ
aiti-819	176	9	c1	c1	PROPN
aiti-819	176	10	is	be	AUX
aiti-819	176	11	tangent	tangent	NOUN
aiti-819	176	12	to	to	ADP
aiti-819	176	13	c2	c2	PROPN
aiti-819	176	14	.	.	PUNCT
aiti-819	177	1	circle	circle	PROPN
aiti-819	177	2	c0	c0	PROPN
aiti-819	177	3	(	(	PUNCT
aiti-819	177	4	2	2	NUM
aiti-819	177	5	,	,	PUNCT
aiti-819	177	6	6.60	6.60	NUM
aiti-819	177	7	,	,	PUNCT
aiti-819	177	8	4.90	4.90	NUM
aiti-819	177	9	)	)	PUNCT
aiti-819	177	10	is	be	AUX
aiti-819	177	11	found	find	VERB
aiti-819	177	12	,	,	PUNCT
aiti-819	177	13	as	as	SCONJ
aiti-819	177	14	depicted	depict	VERB
aiti-819	177	15	in	in	ADP
aiti-819	177	16	fig	fig	NOUN
aiti-819	177	17	.	.	PUNCT
aiti-819	178	1	7(a	7(a	NUM
aiti-819	178	2	)	)	PUNCT
aiti-819	178	3	.	.	PUNCT
aiti-819	179	1	now	now	ADV
aiti-819	179	2	consider	consider	VERB
aiti-819	179	3	the	the	DET
aiti-819	179	4	case	case	NOUN
aiti-819	179	5	wherein	wherein	SCONJ
aiti-819	179	6	n+1	n+1	PROPN
aiti-819	179	7	circles	circle	NOUN
aiti-819	179	8	want	want	VERB
aiti-819	179	9	adding	add	VERB
aiti-819	179	10	.	.	PUNCT
aiti-819	180	1	in	in	ADP
aiti-819	180	2	this	this	DET
aiti-819	180	3	case	case	NOUN
aiti-819	180	4	,	,	PUNCT
aiti-819	180	5	the	the	DET
aiti-819	180	6	first	first	ADJ
aiti-819	180	7	circle	circle	NOUN
aiti-819	180	8	c0	c0	PROPN
aiti-819	180	9	is	be	AUX
aiti-819	180	10	tangent	tangent	ADJ
aiti-819	180	11	to	to	ADP
aiti-819	180	12	c0	c0	PROPN
aiti-819	180	13	and	and	CCONJ
aiti-819	180	14	c1	c1	PROPN
aiti-819	180	15	;	;	PUNCT
aiti-819	180	16	the	the	DET
aiti-819	180	17	last	last	ADJ
aiti-819	180	18	circle	circle	NOUN
aiti-819	180	19	cn	cn	PROPN
aiti-819	180	20	is	be	AUX
aiti-819	180	21	tangent	tangent	NOUN
aiti-819	180	22	to	to	ADP
aiti-819	180	23	c1	c1	PROPN
aiti-819	180	24	and	and	CCONJ
aiti-819	180	25	c2	c2	PROPN
aiti-819	180	26	;	;	PUNCT
aiti-819	180	27	circle	circle	NOUN
aiti-819	180	28	ci	ci	PROPN
aiti-819	180	29	between	between	ADP
aiti-819	180	30	c0	c0	PROPN
aiti-819	180	31	and	and	CCONJ
aiti-819	180	32	cn	cn	PROPN
aiti-819	180	33	is	be	AUX
aiti-819	180	34	tangent	tangent	NOUN
aiti-819	180	35	to	to	ADP
aiti-819	180	36	both	both	DET
aiti-819	180	37	c1	c1	PROPN
aiti-819	180	38	and	and	CCONJ
aiti-819	180	39	its	its	PRON
aiti-819	180	40	neighbors	neighbor	NOUN
aiti-819	180	41	ci-1	ci-1	NOUN
aiti-819	180	42	and	and	CCONJ
aiti-819	180	43	ci+1	ci+1	NOUN
aiti-819	180	44	,	,	PUNCT
aiti-819	180	45	as	as	SCONJ
aiti-819	180	46	depicted	depict	VERB
aiti-819	180	47	in	in	ADP
aiti-819	180	48	fig	fig	NOUN
aiti-819	180	49	.	.	PUNCT
aiti-819	181	1	5(c	5(c	NUM
aiti-819	181	2	)	)	PUNCT
aiti-819	181	3	.	.	PUNCT
aiti-819	182	1	a	a	DET
aiti-819	182	2	similar	similar	ADJ
aiti-819	182	3	idea	idea	NOUN
aiti-819	182	4	as	as	ADP
aiti-819	182	5	that	that	PRON
aiti-819	182	6	for	for	ADP
aiti-819	182	7	algorithm	algorithm	NOUN
aiti-819	182	8	4	4	NUM
aiti-819	182	9	can	can	AUX
aiti-819	182	10	be	be	AUX
aiti-819	182	11	applied	apply	VERB
aiti-819	182	12	.	.	PUNCT
aiti-819	183	1	in	in	ADP
aiti-819	183	2	algorithm	algorithm	NOUN
aiti-819	183	3	4	4	NUM
aiti-819	183	4	,	,	PUNCT
aiti-819	183	5	the	the	DET
aiti-819	183	6	sum	sum	NOUN
aiti-819	183	7	of	of	ADP
aiti-819	183	8	two	two	NUM
aiti-819	183	9	angles	angle	NOUN
aiti-819	183	10	,	,	PUNCT
aiti-819	183	11	1	1	PUNCT
aiti-819	183	12	and	and	CCONJ
aiti-819	183	13	2	2	PROPN
aiti-819	183	14	,	,	PUNCT
aiti-819	183	15	are	be	AUX
aiti-819	183	16	compared	compare	VERB
aiti-819	183	17	with	with	ADP
aiti-819	183	18	angle	angle	NOUN
aiti-819	183	19			NOUN
aiti-819	183	20	,	,	PUNCT
aiti-819	183	21	and	and	CCONJ
aiti-819	183	22	now	now	ADV
aiti-819	183	23	the	the	DET
aiti-819	183	24	sum	sum	NOUN
aiti-819	183	25	of	of	ADP
aiti-819	183	26	n	n	PROPN
aiti-819	183	27	+	+	CCONJ
aiti-819	183	28	2	2	NUM
aiti-819	183	29	angles	angle	NOUN
aiti-819	183	30	is	be	AUX
aiti-819	183	31	compared	compare	VERB
aiti-819	183	32	with	with	ADP
aiti-819	183	33	angle	angle	NOUN
aiti-819	183	34	.	.	NOUN
aiti-819	183	35	it	it	PRON
aiti-819	183	36	is	be	AUX
aiti-819	183	37	referred	refer	VERB
aiti-819	183	38	to	to	ADP
aiti-819	183	39	as	as	ADP
aiti-819	183	40	the	the	DET
aiti-819	183	41	extended	extended	ADJ
aiti-819	183	42	algorithm	algorithm	NOUN
aiti-819	183	43	4	4	NUM
aiti-819	183	44	.	.	NOUN
aiti-819	183	45	example	example	NOUN
aiti-819	183	46	6	6	NUM
aiti-819	183	47	:	:	PUNCT
aiti-819	183	48	using	use	VERB
aiti-819	183	49	the	the	DET
aiti-819	183	50	same	same	ADJ
aiti-819	183	51	input	input	NOUN
aiti-819	183	52	as	as	ADP
aiti-819	183	53	that	that	PRON
aiti-819	183	54	used	use	VERB
aiti-819	183	55	in	in	ADP
aiti-819	183	56	example	example	NOUN
aiti-819	183	57	5	5	NUM
aiti-819	183	58	,	,	PUNCT
aiti-819	183	59	2	2	NUM
aiti-819	183	60	circles	circle	NOUN
aiti-819	183	61	that	that	PRON
aiti-819	183	62	are	be	AUX
aiti-819	183	63	tangent	tangent	ADJ
aiti-819	183	64	to	to	ADP
aiti-819	183	65	each	each	DET
aiti-819	183	66	other	other	ADJ
aiti-819	183	67	want	want	VERB
aiti-819	183	68	finding	find	VERB
aiti-819	183	69	,	,	PUNCT
aiti-819	183	70	where	where	SCONJ
aiti-819	183	71	the	the	DET
aiti-819	183	72	first	first	ADJ
aiti-819	183	73	circle	circle	NOUN
aiti-819	183	74	is	be	AUX
aiti-819	183	75	tangent	tangent	ADJ
aiti-819	183	76	to	to	ADP
aiti-819	183	77	c0	c0	PROPN
aiti-819	183	78	and	and	CCONJ
aiti-819	183	79	c1	c1	PROPN
aiti-819	183	80	and	and	CCONJ
aiti-819	183	81	the	the	DET
aiti-819	183	82	second	second	ADJ
aiti-819	183	83	circle	circle	NOUN
aiti-819	183	84	is	be	AUX
aiti-819	183	85	tangent	tangent	NOUN
aiti-819	183	86	to	to	ADP
aiti-819	183	87	c1	c1	PROPN
aiti-819	183	88	and	and	CCONJ
aiti-819	183	89	c2	c2	PROPN
aiti-819	183	90	.	.	PUNCT
aiti-819	184	1	using	use	VERB
aiti-819	184	2	the	the	DET
aiti-819	184	3	extended	extended	ADJ
aiti-819	184	4	algorithm	algorithm	NOUN
aiti-819	184	5	4	4	NUM
aiti-819	184	6	,	,	PUNCT
aiti-819	184	7	these	these	DET
aiti-819	184	8	two	two	NUM
aiti-819	184	9	circles	circle	NOUN
aiti-819	184	10	are	be	AUX
aiti-819	184	11	found	find	VERB
aiti-819	184	12	centered	center	VERB
aiti-819	184	13	at	at	ADP
aiti-819	184	14	(	(	PUNCT
aiti-819	184	15	0.047	0.047	NUM
aiti-819	184	16	,	,	PUNCT
aiti-819	184	17	3.045	3.045	NUM
aiti-819	184	18	)	)	PUNCT
aiti-819	184	19	and	and	CCONJ
aiti-819	184	20	(	(	PUNCT
aiti-819	184	21	2	2	NUM
aiti-819	184	22	,	,	PUNCT
aiti-819	184	23	2	2	NUM
aiti-819	184	24	,	,	PUNCT
aiti-819	184	25	97	97	NUM
aiti-819	184	26	)	)	PUNCT
aiti-819	184	27	each	each	PRON
aiti-819	184	28	of	of	ADP
aiti-819	184	29	radius	radius	NOUN
aiti-819	184	30	r	r	NOUN
aiti-819	184	31	=	=	PUNCT
aiti-819	184	32	1.046	1.046	NUM
aiti-819	184	33	,	,	PUNCT
aiti-819	184	34	as	as	SCONJ
aiti-819	184	35	depicted	depict	VERB
aiti-819	184	36	in	in	ADP
aiti-819	184	37	fig	fig	NOUN
aiti-819	184	38	.	.	PUNCT
aiti-819	185	1	7(b	7(b	X
aiti-819	185	2	)	)	PUNCT
aiti-819	185	3	.	.	PUNCT
aiti-819	186	1	example	example	NOUN
aiti-819	186	2	7	7	NUM
aiti-819	186	3	:	:	PUNCT
aiti-819	186	4	given	give	VERB
aiti-819	186	5	three	three	NUM
aiti-819	186	6	circles	circle	NOUN
aiti-819	186	7	c0	c0	NOUN
aiti-819	186	8	(	(	PUNCT
aiti-819	186	9	–	–	PUNCT
aiti-819	186	10	4	4	NUM
aiti-819	186	11	,	,	PUNCT
aiti-819	186	12	–	–	PUNCT
aiti-819	186	13	3	3	NUM
aiti-819	186	14	,	,	PUNCT
aiti-819	186	15	3	3	NUM
aiti-819	186	16	)	)	PUNCT
aiti-819	186	17	,	,	PUNCT
aiti-819	186	18	c1	c1	PROPN
aiti-819	186	19	(	(	PUNCT
aiti-819	186	20	0	0	NUM
aiti-819	186	21	,	,	PUNCT
aiti-819	186	22	0	0	NUM
aiti-819	186	23	,	,	PUNCT
aiti-819	186	24	2	2	NUM
aiti-819	186	25	)	)	PUNCT
aiti-819	186	26	,	,	PUNCT
aiti-819	186	27	and	and	CCONJ
aiti-819	186	28	c2	c2	PROPN
aiti-819	186	29	(	(	PUNCT
aiti-819	186	30	4	4	NUM
aiti-819	186	31	,	,	PUNCT
aiti-819	186	32	0	0	NUM
aiti-819	186	33	,	,	PUNCT
aiti-819	186	34	2	2	NUM
aiti-819	186	35	)	)	PUNCT
aiti-819	186	36	.	.	PUNCT
aiti-819	187	1	using	use	VERB
aiti-819	187	2	the	the	DET
aiti-819	187	3	extended	extended	ADJ
aiti-819	187	4	algorithm	algorithm	NOUN
aiti-819	187	5	4	4	NUM
aiti-819	187	6	,	,	PUNCT
aiti-819	187	7	5	5	NUM
aiti-819	187	8	circles	circle	NOUN
aiti-819	187	9	are	be	AUX
aiti-819	187	10	found	find	VERB
aiti-819	187	11	between	between	ADP
aiti-819	187	12	c0	c0	PROPN
aiti-819	187	13	and	and	CCONJ
aiti-819	187	14	c2	c2	PROPN
aiti-819	187	15	,	,	PUNCT
aiti-819	187	16	such	such	ADJ
aiti-819	187	17	that	that	SCONJ
aiti-819	187	18	these	these	DET
aiti-819	187	19	5	5	NUM
aiti-819	187	20	circles	circle	NOUN
aiti-819	187	21	are	be	AUX
aiti-819	187	22	tangent	tangent	ADJ
aiti-819	187	23	to	to	ADP
aiti-819	187	24	c1	c1	PROPN
aiti-819	187	25	.	.	PUNCT
aiti-819	188	1	the	the	DET
aiti-819	188	2	circles	circle	NOUN
aiti-819	188	3	are	be	AUX
aiti-819	188	4	found	find	VERB
aiti-819	188	5	centered	center	VERB
aiti-819	188	6	at	at	ADP
aiti-819	188	7	(	(	PUNCT
aiti-819	188	8	–	–	PUNCT
aiti-819	188	9	2.697	2.697	NUM
aiti-819	188	10	,	,	PUNCT
aiti-819	188	11	0.513	0.513	NUM
aiti-819	188	12	)	)	PUNCT
aiti-819	188	13	,	,	PUNCT
aiti-819	188	14	(	(	PUNCT
aiti-819	188	15	–	–	PUNCT
aiti-819	188	16	2.031	2.031	NUM
aiti-819	188	17	,	,	PUNCT
aiti-819	188	18	1.846	1.846	NUM
aiti-819	188	19	)	)	PUNCT
aiti-819	188	20	,	,	PUNCT
aiti-819	188	21	(	(	PUNCT
aiti-819	188	22	–	–	PUNCT
aiti-819	188	23	0.767	0.767	NUM
aiti-819	188	24	,	,	PUNCT
aiti-819	188	25	2.636	2.636	NUM
aiti-819	188	26	)	)	PUNCT
aiti-819	188	27	,	,	PUNCT
aiti-819	188	28	(	(	PUNCT
aiti-819	188	29	0.723	0.723	NUM
aiti-819	188	30	,	,	PUNCT
aiti-819	188	31	2.648	2.648	NUM
aiti-819	188	32	)	)	PUNCT
aiti-819	188	33	,	,	PUNCT
aiti-819	188	34	and	and	CCONJ
aiti-819	188	35	(	(	PUNCT
aiti-819	188	36	2.0	2.0	NUM
aiti-819	188	37	,	,	PUNCT
aiti-819	188	38	1.88	1.88	NUM
aiti-819	188	39	)	)	PUNCT
aiti-819	188	40	each	each	PRON
aiti-819	188	41	of	of	ADP
aiti-819	188	42	radius	radius	NOUN
aiti-819	188	43	0.745	0.745	NUM
aiti-819	188	44	,	,	PUNCT
aiti-819	188	45	as	as	SCONJ
aiti-819	188	46	depicted	depict	VERB
aiti-819	188	47	in	in	ADP
aiti-819	188	48	fig	fig	NOUN
aiti-819	188	49	.	.	PUNCT
aiti-819	189	1	7(c	7(c	NUM
aiti-819	189	2	)	)	PUNCT
aiti-819	189	3	.	.	PUNCT
aiti-819	190	1	(	(	PUNCT
aiti-819	190	2	a	a	X
aiti-819	190	3	)	)	PUNCT
aiti-819	190	4	one	one	NUM
aiti-819	190	5	circle	circle	NOUN
aiti-819	190	6	(	(	PUNCT
aiti-819	190	7	b	b	NOUN
aiti-819	190	8	)	)	PUNCT
aiti-819	190	9	two	two	NUM
aiti-819	190	10	circles	circle	NOUN
aiti-819	190	11	(	(	PUNCT
aiti-819	190	12	c	c	NOUN
aiti-819	190	13	)	)	PUNCT
aiti-819	190	14	five	five	NUM
aiti-819	190	15	circles	circle	NOUN
aiti-819	190	16	fig	fig	NOUN
aiti-819	190	17	.	.	PUNCT
aiti-819	191	1	7	7	NUM
aiti-819	191	2	tangent	tangent	ADJ
aiti-819	191	3	circles	circle	NOUN
aiti-819	191	4	with	with	ADP
aiti-819	191	5	similar	similar	ADJ
aiti-819	191	6	radii	radius	NOUN
aiti-819	191	7	(	(	PUNCT
aiti-819	191	8	a	a	X
aiti-819	191	9	)	)	PUNCT
aiti-819	191	10	2	2	NUM
aiti-819	191	11	circles	circle	NOUN
aiti-819	191	12	with	with	ADP
aiti-819	191	13	dr	dr	PROPN
aiti-819	191	14	=	=	PROPN
aiti-819	191	15	0.5	0.5	NUM
aiti-819	191	16	(	(	PUNCT
aiti-819	191	17	b	b	NOUN
aiti-819	191	18	)	)	PUNCT
aiti-819	191	19	5	5	NUM
aiti-819	191	20	circles	circle	NOUN
aiti-819	191	21	with	with	ADP
aiti-819	191	22	dr	dr	PROPN
aiti-819	191	23	=	=	PROPN
aiti-819	191	24	0.2	0.2	NUM
aiti-819	191	25	(	(	PUNCT
aiti-819	191	26	c	c	NOUN
aiti-819	191	27	)	)	PUNCT
aiti-819	191	28	5	5	NUM
aiti-819	191	29	circles	circle	NOUN
aiti-819	191	30	with	with	ADP
aiti-819	191	31	dr	dr	PROPN
aiti-819	191	32	=	=	PROPN
aiti-819	191	33	0.25	0.25	NUM
aiti-819	191	34	fig	fig	NOUN
aiti-819	191	35	.	.	PUNCT
aiti-819	191	36	8	8	NUM
aiti-819	191	37	tangent	tangent	NOUN
aiti-819	191	38	circles	circle	NOUN
aiti-819	191	39	with	with	ADP
aiti-819	191	40	different	different	ADJ
aiti-819	191	41	radii	radius	NOUN
aiti-819	191	42	let	let	VERB
aiti-819	191	43	people	people	NOUN
aiti-819	191	44	consider	consider	VERB
aiti-819	191	45	the	the	DET
aiti-819	191	46	case	case	NOUN
aiti-819	191	47	wherein	wherein	SCONJ
aiti-819	191	48	the	the	DET
aiti-819	191	49	radii	radius	NOUN
aiti-819	191	50	of	of	ADP
aiti-819	191	51	the	the	DET
aiti-819	191	52	circles	circle	NOUN
aiti-819	191	53	along	along	ADP
aiti-819	191	54	one	one	NUM
aiti-819	191	55	side	side	NOUN
aiti-819	191	56	of	of	ADP
aiti-819	191	57	initial	initial	ADJ
aiti-819	191	58	area	area	NOUN
aiti-819	191	59	are	be	AUX
aiti-819	191	60	in	in	ADP
aiti-819	191	61	an	an	DET
aiti-819	191	62	arithmetic	arithmetic	ADJ
aiti-819	191	63	progression	progression	NOUN
aiti-819	191	64	.	.	PUNCT
aiti-819	192	1	assume	assume	VERB
aiti-819	192	2	that	that	SCONJ
aiti-819	192	3	dr	dr	PROPN
aiti-819	192	4	is	be	AUX
aiti-819	192	5	the	the	DET
aiti-819	192	6	common	common	ADJ
aiti-819	192	7	difference	difference	NOUN
aiti-819	192	8	.	.	PUNCT
aiti-819	193	1	accordingly	accordingly	ADV
aiti-819	193	2	,	,	PUNCT
aiti-819	193	3	the	the	DET
aiti-819	193	4	first	first	ADJ
aiti-819	193	5	circle	circle	NOUN
aiti-819	193	6	has	have	VERB
aiti-819	193	7	radius	radius	NOUN
aiti-819	193	8	r	r	NOUN
aiti-819	193	9	;	;	PUNCT
aiti-819	193	10	the	the	DET
aiti-819	193	11	second	second	ADJ
aiti-819	193	12	circle	circle	NOUN
aiti-819	193	13	has	have	VERB
aiti-819	193	14	radius	radius	NOUN
aiti-819	193	15	r	r	NOUN
aiti-819	193	16	–	–	PUNCT
aiti-819	193	17	dr	dr	PROPN
aiti-819	193	18	;	;	PUNCT
aiti-819	193	19	the	the	DET
aiti-819	193	20	third	third	ADJ
aiti-819	193	21	circle	circle	NOUN
aiti-819	193	22	has	have	VERB
aiti-819	193	23	radius	radius	NOUN
aiti-819	193	24	r	r	NOUN
aiti-819	193	25	–	–	PUNCT
aiti-819	193	26	2*dr	2*dr	NUM
aiti-819	193	27	,	,	PUNCT
aiti-819	193	28	…	…	PUNCT
aiti-819	193	29	,	,	PUNCT
aiti-819	193	30	and	and	CCONJ
aiti-819	193	31	so	so	ADV
aiti-819	193	32	on	on	ADV
aiti-819	193	33	.	.	PUNCT
aiti-819	194	1	using	use	VERB
aiti-819	194	2	the	the	DET
aiti-819	194	3	binary	binary	ADJ
aiti-819	194	4	approach	approach	NOUN
aiti-819	194	5	as	as	ADP
aiti-819	194	6	that	that	PRON
aiti-819	194	7	employed	employ	VERB
aiti-819	194	8	in	in	ADP
aiti-819	194	9	algorithm	algorithm	NOUN
aiti-819	194	10	4	4	NUM
aiti-819	194	11	,	,	PUNCT
aiti-819	194	12	to	to	PART
aiti-819	194	13	find	find	VERB
aiti-819	194	14	2	2	NUM
aiti-819	194	15	or	or	CCONJ
aiti-819	194	16	5	5	NUM
aiti-819	194	17	tangent	tangent	ADJ
aiti-819	194	18	circles	circle	NOUN
aiti-819	194	19	,	,	PUNCT
aiti-819	194	20	examples	example	NOUN
aiti-819	194	21	8	8	NUM
aiti-819	194	22	and	and	CCONJ
aiti-819	194	23	9	9	NUM
aiti-819	194	24	are	be	AUX
aiti-819	194	25	referred	refer	VERB
aiti-819	194	26	to	to	ADP
aiti-819	194	27	as	as	SCONJ
aiti-819	194	28	depicted	depict	VERB
aiti-819	194	29	in	in	ADP
aiti-819	194	30	fig	fig	NOUN
aiti-819	194	31	.	.	PUNCT
aiti-819	195	1	8(a	8(a	NUM
aiti-819	195	2	)	)	PUNCT
aiti-819	195	3	and	and	CCONJ
aiti-819	195	4	(	(	PUNCT
aiti-819	195	5	b	b	NOUN
aiti-819	195	6	)	)	PUNCT
aiti-819	195	7	,	,	PUNCT
aiti-819	195	8	respectively	respectively	ADV
aiti-819	195	9	.	.	PUNCT
aiti-819	195	10	example	example	NOUN
aiti-819	195	11	8	8	NUM
aiti-819	195	12	:	:	PUNCT
aiti-819	195	13	using	use	VERB
aiti-819	195	14	the	the	DET
aiti-819	195	15	same	same	ADJ
aiti-819	195	16	input	input	NOUN
aiti-819	195	17	data	datum	NOUN
aiti-819	195	18	as	as	ADP
aiti-819	195	19	those	those	PRON
aiti-819	195	20	used	use	VERB
aiti-819	195	21	in	in	ADP
aiti-819	195	22	example	example	NOUN
aiti-819	195	23	5	5	NUM
aiti-819	195	24	and	and	CCONJ
aiti-819	195	25	setting	set	VERB
aiti-819	195	26	dr	dr	PROPN
aiti-819	195	27	=	=	PROPN
aiti-819	195	28	0.5	0.5	NUM
aiti-819	195	29	,	,	PUNCT
aiti-819	195	30	two	two	NUM
aiti-819	195	31	circles	circle	NOUN
aiti-819	195	32	are	be	AUX
aiti-819	195	33	found	find	VERB
aiti-819	195	34	:	:	PUNCT
aiti-819	196	1	c0	c0	X
aiti-819	196	2	(	(	PUNCT
aiti-819	196	3	0.31	0.31	NUM
aiti-819	196	4	,	,	PUNCT
aiti-819	196	5	3.31	3.31	NUM
aiti-819	196	6	,	,	PUNCT
aiti-819	196	7	1.32	1.32	NUM
aiti-819	196	8	)	)	PUNCT
aiti-819	196	9	and	and	CCONJ
aiti-819	196	10	c1	c1	PROPN
aiti-819	196	11	(	(	PUNCT
aiti-819	196	12	2.0	2.0	NUM
aiti-819	196	13	,	,	PUNCT
aiti-819	196	14	1.99	1.99	NUM
aiti-819	196	15	,	,	PUNCT
aiti-819	196	16	0.82	0.82	NUM
aiti-819	196	17	)	)	PUNCT
aiti-819	196	18	,	,	PUNCT
aiti-819	196	19	as	as	SCONJ
aiti-819	196	20	depicted	depict	VERB
aiti-819	196	21	in	in	ADP
aiti-819	196	22	fig	fig	NOUN
aiti-819	196	23	.	.	PUNCT
aiti-819	197	1	8(a	8(a	NUM
aiti-819	197	2	)	)	PUNCT
aiti-819	197	3	.	.	PUNCT
aiti-819	198	1	example	example	NOUN
aiti-819	198	2	9	9	NUM
aiti-819	198	3	:	:	PUNCT
aiti-819	198	4	using	use	VERB
aiti-819	198	5	the	the	DET
aiti-819	198	6	same	same	ADJ
aiti-819	198	7	input	input	NOUN
aiti-819	198	8	data	datum	NOUN
aiti-819	198	9	as	as	ADP
aiti-819	198	10	those	those	PRON
aiti-819	198	11	used	use	VERB
aiti-819	198	12	in	in	ADP
aiti-819	198	13	example	example	NOUN
aiti-819	198	14	7	7	NUM
aiti-819	198	15	and	and	CCONJ
aiti-819	198	16	setting	set	VERB
aiti-819	198	17	dr	dr	PROPN
aiti-819	198	18	=	=	PROPN
aiti-819	198	19	0.2	0.2	NUM
aiti-819	198	20	,	,	PUNCT
aiti-819	198	21	5	5	NUM
aiti-819	198	22	circles	circle	NOUN
aiti-819	198	23	are	be	AUX
aiti-819	198	24	found	find	VERB
aiti-819	198	25	:	:	PUNCT
aiti-819	198	26	c0	c0	X
aiti-819	198	27	(	(	PUNCT
aiti-819	198	28	–	–	PUNCT
aiti-819	198	29	3.03	3.03	NUM
aiti-819	198	30	,	,	PUNCT
aiti-819	198	31	1.09	1.09	NUM
aiti-819	198	32	,	,	PUNCT
aiti-819	198	33	1.22	1.22	NUM
aiti-819	198	34	)	)	PUNCT
aiti-819	198	35	,	,	PUNCT
aiti-819	198	36	c1	c1	X
aiti-819	198	37	(	(	PUNCT
aiti-819	198	38	–	–	PUNCT
aiti-819	198	39	1.43	1.43	NUM
aiti-819	198	40	,	,	PUNCT
aiti-819	198	41	2.66	2.66	NUM
aiti-819	198	42	,	,	PUNCT
aiti-819	198	43	1.02	1.02	NUM
aiti-819	198	44	)	)	PUNCT
aiti-819	198	45	,	,	PUNCT
aiti-819	199	1	c2	c2	PROPN
aiti-819	199	2	(	(	PUNCT
aiti-819	199	3	0.41	0.41	NUM
aiti-819	199	4	,	,	PUNCT
aiti-819	199	5	2.79	2.79	NUM
aiti-819	199	6	,	,	PUNCT
aiti-819	199	7	0.82	0.82	NUM
aiti-819	199	8	)	)	PUNCT
aiti-819	199	9	,	,	PUNCT
aiti-819	199	10	c3	c3	PROPN
aiti-819	199	11	(	(	PUNCT
aiti-819	199	12	1.64	1.64	NUM
aiti-819	199	13	,	,	PUNCT
aiti-819	199	14	2.04	2.04	NUM
aiti-819	199	15	,	,	PUNCT
aiti-819	199	16	0.62	0.62	NUM
aiti-819	199	17	)	)	PUNCT
aiti-819	199	18	,	,	PUNCT
aiti-819	199	19	and	and	CCONJ
aiti-819	199	20	c4	c4	PROPN
aiti-819	199	21	(	(	PUNCT
aiti-819	199	22	2.14	2.14	NUM
aiti-819	199	23	,	,	PUNCT
aiti-819	199	24	1.13	1.13	NUM
aiti-819	199	25	,	,	PUNCT
aiti-819	199	26	0.42	0.42	NUM
aiti-819	199	27	)	)	PUNCT
aiti-819	199	28	,	,	PUNCT
aiti-819	199	29	as	as	SCONJ
aiti-819	199	30	depicted	depict	VERB
aiti-819	199	31	in	in	ADP
aiti-819	199	32	fig	fig	NOUN
aiti-819	199	33	.	.	PUNCT
aiti-819	200	1	8(b	8(b	NUM
aiti-819	200	2	)	)	PUNCT
aiti-819	200	3	.	.	PUNCT
aiti-819	201	1	upon	upon	SCONJ
aiti-819	201	2	increasing	increase	VERB
aiti-819	201	3	dr	dr	PROPN
aiti-819	201	4	,	,	PUNCT
aiti-819	201	5	the	the	DET
aiti-819	201	6	difference	difference	NOUN
aiti-819	201	7	between	between	ADP
aiti-819	201	8	the	the	DET
aiti-819	201	9	radii	radius	NOUN
aiti-819	201	10	of	of	ADP
aiti-819	201	11	c0	c0	NOUN
aiti-819	201	12	and	and	CCONJ
aiti-819	201	13	c4	c4	PROPN
aiti-819	201	14	is	be	AUX
aiti-819	201	15	also	also	ADV
aiti-819	201	16	increased	increase	VERB
aiti-819	201	17	.	.	PUNCT
aiti-819	202	1	the	the	DET
aiti-819	202	2	difference	difference	NOUN
aiti-819	202	3	can	can	AUX
aiti-819	202	4	be	be	AUX
aiti-819	202	5	seen	see	VERB
aiti-819	202	6	in	in	ADP
aiti-819	202	7	radii	radius	NOUN
aiti-819	202	8	by	by	ADP
aiti-819	202	9	comparing	compare	VERB
aiti-819	202	10	fig	fig	NOUN
aiti-819	202	11	.	.	PUNCT
aiti-819	203	1	8(c	8(c	NUM
aiti-819	203	2	)	)	PUNCT
aiti-819	203	3	,	,	PUNCT
aiti-819	203	4	where	where	SCONJ
aiti-819	203	5	dr	dr	PROPN
aiti-819	203	6	=	=	PROPN
aiti-819	203	7	0.25	0.25	NUM
aiti-819	203	8	,	,	PUNCT
aiti-819	203	9	with	with	ADP
aiti-819	203	10	fig	fig	NOUN
aiti-819	203	11	.	.	PUNCT
aiti-819	204	1	8(b	8(b	NUM
aiti-819	204	2	)	)	PUNCT
aiti-819	204	3	,	,	PUNCT
aiti-819	204	4	where	where	SCONJ
aiti-819	204	5	dr	dr	PROPN
aiti-819	204	6	=	=	PROPN
aiti-819	204	7	0.2	0.2	NUM
aiti-819	204	8	.	.	PUNCT
aiti-819	205	1	now	now	ADV
aiti-819	205	2	,	,	PUNCT
aiti-819	205	3	consider	consider	VERB
aiti-819	205	4	the	the	DET
aiti-819	205	5	case	case	NOUN
aiti-819	205	6	wherein	wherein	SCONJ
aiti-819	205	7	the	the	DET
aiti-819	205	8	external	external	ADJ
aiti-819	205	9	muscle	muscle	NOUN
aiti-819	205	10	/	/	SYM
aiti-819	205	11	circle	circle	NOUN
aiti-819	205	12	grows	grow	VERB
aiti-819	205	13	along	along	ADP
aiti-819	205	14	every	every	DET
aiti-819	205	15	direction	direction	NOUN
aiti-819	205	16	of	of	ADP
aiti-819	205	17	a	a	DET
aiti-819	205	18	muscle	muscle	NOUN
aiti-819	205	19	/	/	SYM
aiti-819	205	20	circle	circle	NOUN
aiti-819	205	21	,	,	PUNCT
aiti-819	205	22	as	as	SCONJ
aiti-819	205	23	depicted	depict	VERB
aiti-819	205	24	in	in	ADP
aiti-819	205	25	figs	fig	NOUN
aiti-819	205	26	.	.	PUNCT
aiti-819	206	1	1(c	1(c	NUM
aiti-819	206	2	)	)	PUNCT
aiti-819	206	3	and	and	CCONJ
aiti-819	206	4	fig	fig	NOUN
aiti-819	206	5	.	.	PUNCT
aiti-819	207	1	9	9	X
aiti-819	207	2	.	.	X
aiti-819	207	3	in	in	ADP
aiti-819	207	4	this	this	DET
aiti-819	207	5	case	case	NOUN
aiti-819	207	6	,	,	PUNCT
aiti-819	207	7	a	a	DET
aiti-819	207	8	list	list	NOUN
aiti-819	207	9	of	of	ADP
aiti-819	207	10	angles	angle	NOUN
aiti-819	207	11	is	be	AUX
aiti-819	207	12	needed	need	VERB
aiti-819	207	13	;	;	PUNCT
aiti-819	207	14	the	the	DET
aiti-819	207	15	list	list	NOUN
aiti-819	207	16	indicates	indicate	VERB
aiti-819	207	17	the	the	DET
aiti-819	207	18	direction	direction	NOUN
aiti-819	207	19	along	along	ADP
aiti-819	207	20	which	which	PRON
aiti-819	207	21	new	new	ADJ
aiti-819	207	22	circles	circle	NOUN
aiti-819	207	23	want	want	VERB
aiti-819	207	24	advances	advance	NOUN
aiti-819	207	25	in	in	ADP
aiti-819	207	26	technology	technology	NOUN
aiti-819	207	27	innovation	innovation	NOUN
aiti-819	207	28	,	,	PUNCT
aiti-819	207	29	vol	vol	NOUN
aiti-819	207	30	.	.	PROPN
aiti-819	208	1	5	5	NUM
aiti-819	208	2	,	,	PUNCT
aiti-819	208	3	no	no	INTJ
aiti-819	208	4	.	.	NOUN
aiti-819	208	5	2	2	NUM
aiti-819	208	6	,	,	PUNCT
aiti-819	208	7	2020	2020	NUM
aiti-819	208	8	,	,	PUNCT
aiti-819	208	9	pp	pp	ADV
aiti-819	208	10	.	.	PUNCT
aiti-819	209	1	126	126	NUM
aiti-819	209	2	-	-	SYM
aiti-819	209	3	134	134	NUM
aiti-819	209	4	133	133	NUM
aiti-819	209	5	extending	extending	NOUN
aiti-819	209	6	.	.	PUNCT
aiti-819	210	1	the	the	DET
aiti-819	210	2	extension	extension	NOUN
aiti-819	210	3	might	might	AUX
aiti-819	210	4	have	have	VERB
aiti-819	210	5	no	no	DET
aiti-819	210	6	solution	solution	NOUN
aiti-819	210	7	.	.	PUNCT
aiti-819	211	1	consider	consider	VERB
aiti-819	211	2	a	a	DET
aiti-819	211	3	unit	unit	NOUN
aiti-819	211	4	circle	circle	NOUN
aiti-819	211	5	centered	center	VERB
aiti-819	211	6	at	at	ADP
aiti-819	211	7	the	the	DET
aiti-819	211	8	origin	origin	NOUN
aiti-819	211	9	,	,	PUNCT
aiti-819	211	10	with	with	ADP
aiti-819	211	11	the	the	DET
aiti-819	211	12	list	list	NOUN
aiti-819	211	13	of	of	ADP
aiti-819	211	14	angles	angle	NOUN
aiti-819	211	15	,	,	PUNCT
aiti-819	211	16	alist	alist	NOUN
aiti-819	211	17	,	,	PUNCT
aiti-819	211	18	where	where	SCONJ
aiti-819	211	19	the	the	DET
aiti-819	211	20	first	first	ADJ
aiti-819	211	21	element	element	NOUN
aiti-819	211	22	in	in	ADP
aiti-819	211	23	alist	alist	NOUN
aiti-819	211	24	is	be	AUX
aiti-819	211	25	0	0	NUM
aiti-819	211	26	.	.	PUNCT
aiti-819	212	1	other	other	ADJ
aiti-819	212	2	cases	case	NOUN
aiti-819	212	3	can	can	AUX
aiti-819	212	4	be	be	AUX
aiti-819	212	5	converted	convert	VERB
aiti-819	212	6	into	into	ADP
aiti-819	212	7	this	this	DET
aiti-819	212	8	situation	situation	NOUN
aiti-819	212	9	by	by	ADP
aiti-819	212	10	translating	translate	VERB
aiti-819	212	11	,	,	PUNCT
aiti-819	212	12	rotating	rotating	NOUN
aiti-819	212	13	,	,	PUNCT
aiti-819	212	14	and	and	CCONJ
aiti-819	212	15	scaling	scale	VERB
aiti-819	212	16	the	the	DET
aiti-819	212	17	circles	circle	NOUN
aiti-819	212	18	in	in	ADP
aiti-819	212	19	the	the	DET
aiti-819	212	20	problem	problem	NOUN
aiti-819	212	21	.	.	PUNCT
aiti-819	213	1	with	with	ADP
aiti-819	213	2	this	this	DET
aiti-819	213	3	initial	initial	ADJ
aiti-819	213	4	condition	condition	NOUN
aiti-819	213	5	,	,	PUNCT
aiti-819	213	6	it	it	PRON
aiti-819	213	7	yields	yield	VERB
aiti-819	213	8	the	the	DET
aiti-819	213	9	following	follow	VERB
aiti-819	213	10	algorithm	algorithm	NOUN
aiti-819	213	11	:	:	PUNCT
aiti-819	213	12	fig	fig	NOUN
aiti-819	213	13	.	.	PUNCT
aiti-819	214	1	9	9	NUM
aiti-819	214	2	growth	growth	NOUN
aiti-819	214	3	direction	direction	NOUN
aiti-819	214	4	of	of	ADP
aiti-819	214	5	circles	circle	NOUN
aiti-819	214	6	algorithm	algorithm	NOUN
aiti-819	214	7	5	5	NUM
aiti-819	214	8	:	:	PUNCT
aiti-819	214	9	(	(	PUNCT
aiti-819	214	10	eps	eps	X
aiti-819	214	11	is	be	AUX
aiti-819	214	12	a	a	DET
aiti-819	214	13	considerably	considerably	ADV
aiti-819	214	14	small	small	ADJ
aiti-819	214	15	number	number	NOUN
aiti-819	214	16	)	)	PUNCT
aiti-819	214	17	1	1	NUM
aiti-819	214	18	.	.	PUNCT
aiti-819	214	19	input	input	NOUN
aiti-819	214	20	c(0,0,1	c(0,0,1	ADV
aiti-819	214	21	)	)	PUNCT
aiti-819	214	22	and	and	CCONJ
aiti-819	214	23	a	a	DET
aiti-819	214	24	list	list	NOUN
aiti-819	214	25	of	of	ADP
aiti-819	214	26	angles	angle	NOUN
aiti-819	214	27	,	,	PUNCT
aiti-819	214	28	alist	alist	NOUN
aiti-819	214	29	.	.	PUNCT
aiti-819	215	1	the	the	DET
aiti-819	215	2	length	length	NOUN
aiti-819	215	3	of	of	ADP
aiti-819	215	4	alist	alist	NOUN
aiti-819	215	5	denotes	denote	NOUN
aiti-819	215	6	len(alist	len(alist	NOUN
aiti-819	215	7	)	)	PUNCT
aiti-819	215	8	2	2	NUM
aiti-819	215	9	.	.	X
aiti-819	215	10	assume	assume	VERB
aiti-819	215	11	the	the	DET
aiti-819	215	12	initial	initial	ADJ
aiti-819	215	13	radius	radius	NOUN
aiti-819	215	14	of	of	ADP
aiti-819	215	15	the	the	DET
aiti-819	215	16	first	first	ADJ
aiti-819	215	17	circle	circle	NOUN
aiti-819	215	18	along	along	ADP
aiti-819	215	19	the	the	DET
aiti-819	215	20	x+	x+	ADJ
aiti-819	215	21	axis	axis	NOUN
aiti-819	215	22	,	,	PUNCT
aiti-819	215	23	and	and	CCONJ
aiti-819	215	24	refer	refer	VERB
aiti-819	215	25	to	to	ADP
aiti-819	215	26	it	it	PRON
aiti-819	215	27	as	as	ADP
aiti-819	215	28	r0	r0	NOUN
aiti-819	215	29	.	.	PUNCT
aiti-819	216	1	3	3	X
aiti-819	216	2	.	.	NOUN
aiti-819	216	3	calculate	calculate	NOUN
aiti-819	216	4	r1	r1	PROPN
aiti-819	216	5	using	use	VERB
aiti-819	216	6	the	the	DET
aiti-819	216	7	equation	equation	NOUN
aiti-819	216	8	in	in	ADP
aiti-819	216	9	theorem	theorem	NOUN
aiti-819	216	10	2	2	NUM
aiti-819	216	11	with	with	ADP
aiti-819	216	12	the	the	DET
aiti-819	216	13	angle	angle	NOUN
aiti-819	216	14	data	datum	NOUN
aiti-819	216	15	provided	provide	VERB
aiti-819	216	16	by	by	ADP
aiti-819	216	17	alist	alist	NOUN
aiti-819	216	18	.	.	PUNCT
aiti-819	216	19	continue	continue	VERB
aiti-819	216	20	this	this	DET
aiti-819	216	21	process	process	NOUN
aiti-819	216	22	until	until	ADP
aiti-819	216	23	all	all	DET
aiti-819	216	24	r	r	NOUN
aiti-819	216	25	i	i	PRON
aiti-819	216	26	,	,	PUNCT
aiti-819	216	27	where	where	SCONJ
aiti-819	216	28	i	i	PRON
aiti-819	216	29	=	=	NOUN
aiti-819	216	30	1	1	NUM
aiti-819	216	31	,	,	PUNCT
aiti-819	216	32	2	2	NUM
aiti-819	216	33	,	,	PUNCT
aiti-819	216	34	…	…	PUNCT
aiti-819	216	35	,	,	PUNCT
aiti-819	216	36	len(alist	len(alist	NOUN
aiti-819	216	37	)	)	PUNCT
aiti-819	216	38	–	–	PUNCT
aiti-819	216	39	1	1	NUM
aiti-819	216	40	have	have	AUX
aiti-819	216	41	been	be	AUX
aiti-819	216	42	calculated	calculate	VERB
aiti-819	216	43	.	.	PUNCT
aiti-819	217	1	4	4	X
aiti-819	217	2	.	.	X
aiti-819	217	3	calculate	calculate	VERB
aiti-819	217	4	the	the	DET
aiti-819	217	5	sum	sum	NOUN
aiti-819	217	6	of	of	ADP
aiti-819	217	7	the	the	DET
aiti-819	217	8	angles	angle	NOUN
aiti-819	217	9	between	between	ADP
aiti-819	217	10	the	the	DET
aiti-819	217	11	angle	angle	NOUN
aiti-819	217	12	generated	generate	VERB
aiti-819	217	13	by	by	ADP
aiti-819	217	14	connecting	connect	VERB
aiti-819	217	15	the	the	DET
aiti-819	217	16	center	center	NOUN
aiti-819	217	17	of	of	ADP
aiti-819	217	18	three	three	NUM
aiti-819	217	19	circles	circle	NOUN
aiti-819	217	20	as	as	ADP
aiti-819	217	21	c0cc1	c0cc1	NOUN
aiti-819	217	22	,	,	PUNCT
aiti-819	217	23	c1cc2	c1cc2	NOUN
aiti-819	217	24	,	,	PUNCT
aiti-819	217	25	…	…	PUNCT
aiti-819	217	26	,	,	PUNCT
aiti-819	217	27	cncc0	cncc0	NOUN
aiti-819	217	28	,	,	PUNCT
aiti-819	217	29	and	and	CCONJ
aiti-819	217	30	refer	refer	VERB
aiti-819	217	31	to	to	ADP
aiti-819	217	32	it	it	PRON
aiti-819	217	33	as	as	ADP
aiti-819	217	34	rsum	rsum	NOUN
aiti-819	217	35	.	.	PUNCT
aiti-819	218	1	5	5	NUM
aiti-819	218	2	.	.	X
aiti-819	218	3	while	while	SCONJ
aiti-819	218	4	abs(rsum	abs(rsum	INTJ
aiti-819	218	5	–	–	PUNCT
aiti-819	218	6	2)>eps	2)>eps	NUM
aiti-819	218	7	:	:	PUNCT
aiti-819	218	8	if	if	SCONJ
aiti-819	218	9	rsum	rsum	VERB
aiti-819	218	10	>	>	X
aiti-819	218	11	2	2	NUM
aiti-819	218	12	:	:	PUNCT
aiti-819	218	13	reduce	reduce	VERB
aiti-819	218	14	the	the	DET
aiti-819	218	15	assumed	assumed	ADJ
aiti-819	218	16	radius	radius	NOUN
aiti-819	218	17	r0	r0	NOUN
aiti-819	218	18	else	else	ADV
aiti-819	218	19	:	:	PUNCT
aiti-819	218	20	increase	increase	VERB
aiti-819	218	21	the	the	DET
aiti-819	218	22	assumed	assumed	ADJ
aiti-819	218	23	radius	radius	NOUN
aiti-819	218	24	r0	r0	NOUN
aiti-819	218	25	.	.	PUNCT
aiti-819	218	26	example	example	NOUN
aiti-819	218	27	10	10	NUM
aiti-819	218	28	:	:	PUNCT
aiti-819	218	29	assuming	assume	VERB
aiti-819	218	30	the	the	DET
aiti-819	218	31	input	input	NOUN
aiti-819	218	32	as	as	ADP
aiti-819	218	33	alist=[0	alist=[0	NOUN
aiti-819	218	34	,	,	PUNCT
aiti-819	218	35	90	90	NUM
aiti-819	218	36	,	,	PUNCT
aiti-819	218	37	180	180	NUM
aiti-819	218	38	,	,	PUNCT
aiti-819	218	39	270	270	NUM
aiti-819	218	40	]	]	PUNCT
aiti-819	218	41	,	,	PUNCT
aiti-819	218	42	the	the	DET
aiti-819	218	43	four	four	NUM
aiti-819	218	44	circles	circle	NOUN
aiti-819	218	45	obtained	obtain	VERB
aiti-819	218	46	are	be	AUX
aiti-819	218	47	c(4	c(4	PROPN
aiti-819	218	48	,	,	PUNCT
aiti-819	218	49	0	0	NUM
aiti-819	218	50	,	,	PUNCT
aiti-819	218	51	3	3	NUM
aiti-819	218	52	)	)	PUNCT
aiti-819	218	53	,	,	PUNCT
aiti-819	218	54	c(0,3,2	c(0,3,2	NOUN
aiti-819	218	55	)	)	PUNCT
aiti-819	218	56	,	,	PUNCT
aiti-819	218	57	c(–4	c(–4	NOUN
aiti-819	218	58	,	,	PUNCT
aiti-819	218	59	0,3	0,3	NUM
aiti-819	218	60	)	)	PUNCT
aiti-819	218	61	,	,	PUNCT
aiti-819	218	62	and	and	CCONJ
aiti-819	218	63	c(0	c(0	PROPN
aiti-819	218	64	,	,	PUNCT
aiti-819	218	65	–	–	PUNCT
aiti-819	218	66	3	3	NUM
aiti-819	218	67	,	,	PUNCT
aiti-819	218	68	2	2	NUM
aiti-819	218	69	)	)	PUNCT
aiti-819	218	70	,	,	PUNCT
aiti-819	218	71	as	as	SCONJ
aiti-819	218	72	depicted	depict	VERB
aiti-819	218	73	in	in	ADP
aiti-819	218	74	fig	fig	NOUN
aiti-819	218	75	.	.	PUNCT
aiti-819	219	1	10(a	10(a	NUM
aiti-819	219	2	)	)	PUNCT
aiti-819	219	3	.	.	PUNCT
aiti-819	220	1	notably	notably	ADV
aiti-819	220	2	,	,	PUNCT
aiti-819	220	3	the	the	DET
aiti-819	220	4	radii	radius	NOUN
aiti-819	220	5	of	of	ADP
aiti-819	220	6	these	these	DET
aiti-819	220	7	circles	circle	NOUN
aiti-819	220	8	are	be	AUX
aiti-819	220	9	not	not	PART
aiti-819	220	10	the	the	DET
aiti-819	220	11	same	same	ADJ
aiti-819	220	12	,	,	PUNCT
aiti-819	220	13	although	although	SCONJ
aiti-819	220	14	their	their	PRON
aiti-819	220	15	directions	direction	NOUN
aiti-819	220	16	of	of	ADP
aiti-819	220	17	extension	extension	NOUN
aiti-819	220	18	are	be	AUX
aiti-819	220	19	east	east	ADJ
aiti-819	220	20	,	,	PUNCT
aiti-819	220	21	north	north	NOUN
aiti-819	220	22	,	,	PUNCT
aiti-819	220	23	west	west	NOUN
aiti-819	220	24	,	,	PUNCT
aiti-819	220	25	and	and	CCONJ
aiti-819	220	26	south	south	NOUN
aiti-819	220	27	,	,	PUNCT
aiti-819	220	28	respectively	respectively	ADV
aiti-819	220	29	.	.	PUNCT
aiti-819	221	1	there	there	PRON
aiti-819	221	2	are	be	VERB
aiti-819	221	3	more	more	ADJ
aiti-819	221	4	than	than	ADP
aiti-819	221	5	one	one	NUM
aiti-819	221	6	solution	solution	NOUN
aiti-819	221	7	,	,	PUNCT
aiti-819	221	8	and	and	CCONJ
aiti-819	221	9	the	the	DET
aiti-819	221	10	algorithm	algorithm	NOUN
aiti-819	221	11	finds	find	VERB
aiti-819	221	12	an	an	DET
aiti-819	221	13	appropriate	appropriate	ADJ
aiti-819	221	14	one	one	NUM
aiti-819	221	15	.	.	PUNCT
aiti-819	222	1	(	(	PUNCT
aiti-819	222	2	a	a	X
aiti-819	222	3	)	)	PUNCT
aiti-819	222	4	four	four	NUM
aiti-819	222	5	directions	direction	NOUN
aiti-819	222	6	(	(	PUNCT
aiti-819	222	7	b	b	NOUN
aiti-819	222	8	)	)	PUNCT
aiti-819	222	9	five	five	NUM
aiti-819	222	10	directions	direction	NOUN
aiti-819	222	11	fig	fig	NOUN
aiti-819	222	12	.	.	PUNCT
aiti-819	223	1	10	10	NUM
aiti-819	223	2	grow	grow	VERB
aiti-819	223	3	external	external	ADJ
aiti-819	223	4	muscle	muscle	NOUN
aiti-819	223	5	example	example	NOUN
aiti-819	223	6	11	11	NUM
aiti-819	223	7	:	:	PUNCT
aiti-819	223	8	assuming	assume	VERB
aiti-819	223	9	the	the	DET
aiti-819	223	10	input	input	NOUN
aiti-819	223	11	as	as	ADP
aiti-819	223	12	alist=[0	alist=[0	NOUN
aiti-819	223	13	,	,	PUNCT
aiti-819	223	14	72	72	NUM
aiti-819	223	15	,	,	PUNCT
aiti-819	223	16	144	144	NUM
aiti-819	223	17	,	,	PUNCT
aiti-819	223	18	216	216	NUM
aiti-819	223	19	,	,	PUNCT
aiti-819	223	20	288	288	NUM
aiti-819	223	21	]	]	PUNCT
aiti-819	223	22	,	,	PUNCT
aiti-819	223	23	the	the	DET
aiti-819	223	24	five	five	NUM
aiti-819	223	25	circles	circle	NOUN
aiti-819	223	26	obtained	obtain	VERB
aiti-819	223	27	are	be	AUX
aiti-819	223	28	c(2.5	c(2.5	NOUN
aiti-819	223	29	,	,	PUNCT
aiti-819	223	30	0	0	NUM
aiti-819	223	31	,	,	PUNCT
aiti-819	223	32	1.5	1.5	NUM
aiti-819	223	33	)	)	PUNCT
aiti-819	223	34	,	,	PUNCT
aiti-819	223	35	c(0.73	c(0.73	PROPN
aiti-819	223	36	,	,	PUNCT
aiti-819	223	37	2.42	2.42	NUM
aiti-819	223	38	,	,	PUNCT
aiti-819	223	39	1.36	1.36	NUM
aiti-819	223	40	)	)	PUNCT
aiti-819	223	41	,	,	PUNCT
aiti-819	223	42	c(–2.02	c(–2.02	PROPN
aiti-819	223	43	,	,	PUNCT
aiti-819	223	44	1.47	1.47	NUM
aiti-819	223	45	,	,	PUNCT
aiti-819	223	46	1.5	1.5	NUM
aiti-819	223	47	)	)	PUNCT
aiti-819	223	48	,	,	PUNCT
aiti-819	223	49	c(–1.91	c(–1.91	PROPN
aiti-819	223	50	,	,	PUNCT
aiti-819	223	51	–	–	PUNCT
aiti-819	223	52	1.39	1.39	NUM
aiti-819	223	53	,	,	PUNCT
aiti-819	223	54	1.36	1.36	NUM
aiti-819	223	55	)	)	PUNCT
aiti-819	223	56	,	,	PUNCT
aiti-819	223	57	and	and	CCONJ
aiti-819	223	58	c(0.77	c(0.77	PROPN
aiti-819	223	59	,	,	PUNCT
aiti-819	223	60	–	–	PUNCT
aiti-819	223	61	2.38	2.38	NUM
aiti-819	223	62	,	,	PUNCT
aiti-819	223	63	1.5	1.5	NUM
aiti-819	223	64	)	)	PUNCT
aiti-819	223	65	.	.	PUNCT
aiti-819	224	1	to	to	PART
aiti-819	224	2	generate	generate	VERB
aiti-819	224	3	skin	skin	NOUN
aiti-819	224	4	to	to	PART
aiti-819	224	5	wrap	wrap	VERB
aiti-819	224	6	an	an	DET
aiti-819	224	7	area	area	NOUN
aiti-819	224	8	,	,	PUNCT
aiti-819	224	9	such	such	ADJ
aiti-819	224	10	as	as	ADP
aiti-819	224	11	the	the	DET
aiti-819	224	12	area	area	NOUN
aiti-819	224	13	in	in	ADP
aiti-819	224	14	figs	fig	NOUN
aiti-819	224	15	.	.	PUNCT
aiti-819	225	1	(	(	PUNCT
aiti-819	225	2	7)-(10	7)-(10	NOUN
aiti-819	225	3	)	)	PUNCT
aiti-819	225	4	,	,	PUNCT
aiti-819	225	5	the	the	DET
aiti-819	225	6	interior	interior	ADJ
aiti-819	225	7	and	and	CCONJ
aiti-819	225	8	exterior	exterior	ADJ
aiti-819	225	9	circle	circle	NOUN
aiti-819	225	10	muscles	muscle	NOUN
aiti-819	225	11	must	must	AUX
aiti-819	225	12	be	be	AUX
aiti-819	225	13	identified	identify	VERB
aiti-819	225	14	.	.	PUNCT
aiti-819	226	1	for	for	ADP
aiti-819	226	2	two	two	NUM
aiti-819	226	3	exterior	exterior	ADJ
aiti-819	226	4	muscles	muscle	NOUN
aiti-819	226	5	tangents	tangent	NOUN
aiti-819	226	6	to	to	ADP
aiti-819	226	7	one	one	NUM
aiti-819	226	8	another	another	DET
aiti-819	226	9	,	,	PUNCT
aiti-819	226	10	the	the	DET
aiti-819	226	11	skin	skin	NOUN
aiti-819	226	12	to	to	PART
aiti-819	226	13	connect	connect	VERB
aiti-819	226	14	these	these	DET
aiti-819	226	15	two	two	NUM
aiti-819	226	16	circles	circle	NOUN
aiti-819	226	17	can	can	AUX
aiti-819	226	18	be	be	AUX
aiti-819	226	19	easily	easily	ADV
aiti-819	226	20	produced	produce	VERB
aiti-819	226	21	.	.	PUNCT
aiti-819	227	1	a	a	DET
aiti-819	227	2	advances	advance	NOUN
aiti-819	227	3	in	in	ADP
aiti-819	227	4	technology	technology	NOUN
aiti-819	227	5	innovation	innovation	NOUN
aiti-819	227	6	,	,	PUNCT
aiti-819	227	7	vol	vol	NOUN
aiti-819	227	8	.	.	PROPN
aiti-819	227	9	5	5	NUM
aiti-819	227	10	,	,	PUNCT
aiti-819	227	11	no	no	INTJ
aiti-819	227	12	.	.	NOUN
aiti-819	227	13	2	2	NUM
aiti-819	227	14	,	,	PUNCT
aiti-819	227	15	2020	2020	NUM
aiti-819	227	16	,	,	PUNCT
aiti-819	227	17	pp	pp	ADV
aiti-819	227	18	.	.	PUNCT
aiti-819	228	1	126	126	NUM
aiti-819	228	2	-	-	SYM
aiti-819	228	3	134	134	NUM
aiti-819	228	4	134	134	NUM
aiti-819	228	5	circular	circular	ADJ
aiti-819	228	6	arc	arc	NOUN
aiti-819	228	7	is	be	AUX
aiti-819	228	8	an	an	DET
aiti-819	228	9	appropriate	appropriate	ADJ
aiti-819	228	10	choice	choice	NOUN
aiti-819	228	11	to	to	PART
aiti-819	228	12	blend	blend	VERB
aiti-819	228	13	these	these	DET
aiti-819	228	14	two	two	NUM
aiti-819	228	15	circles	circle	NOUN
aiti-819	228	16	,	,	PUNCT
aiti-819	228	17	provided	provide	VERB
aiti-819	228	18	the	the	DET
aiti-819	228	19	radii	radius	NOUN
aiti-819	228	20	of	of	ADP
aiti-819	228	21	the	the	DET
aiti-819	228	22	circles	circle	NOUN
aiti-819	228	23	contain	contain	VERB
aiti-819	228	24	the	the	DET
aiti-819	228	25	circular	circular	ADJ
aiti-819	228	26	arc	arc	NOUN
aiti-819	228	27	.	.	PUNCT
aiti-819	229	1	using	use	VERB
aiti-819	229	2	the	the	DET
aiti-819	229	3	chosen	choose	VERB
aiti-819	229	4	radius	radius	NOUN
aiti-819	229	5	,	,	PUNCT
aiti-819	229	6	both	both	CCONJ
aiti-819	229	7	the	the	DET
aiti-819	229	8	center	center	NOUN
aiti-819	229	9	of	of	ADP
aiti-819	229	10	the	the	DET
aiti-819	229	11	circle	circle	NOUN
aiti-819	229	12	and	and	CCONJ
aiti-819	229	13	the	the	DET
aiti-819	229	14	start	start	NOUN
aiti-819	229	15	/	/	SYM
aiti-819	229	16	end	end	NOUN
aiti-819	229	17	angle	angle	NOUN
aiti-819	229	18	of	of	ADP
aiti-819	229	19	the	the	DET
aiti-819	229	20	circular	circular	ADJ
aiti-819	229	21	arc	arc	NOUN
aiti-819	229	22	can	can	AUX
aiti-819	229	23	be	be	AUX
aiti-819	229	24	easily	easily	ADV
aiti-819	229	25	obtained	obtain	VERB
aiti-819	229	26	.	.	PUNCT
aiti-819	230	1	4	4	X
aiti-819	230	2	.	.	NOUN
aiti-819	230	3	conclusion	conclusion	NOUN
aiti-819	230	4	and	and	CCONJ
aiti-819	230	5	future	future	ADJ
aiti-819	230	6	research	research	NOUN
aiti-819	230	7	tangency	tangency	NOUN
aiti-819	230	8	among	among	ADP
aiti-819	230	9	circles	circle	NOUN
aiti-819	230	10	has	have	VERB
aiti-819	230	11	numerous	numerous	ADJ
aiti-819	230	12	important	important	ADJ
aiti-819	230	13	applications	application	NOUN
aiti-819	230	14	,	,	PUNCT
aiti-819	230	15	such	such	ADJ
aiti-819	230	16	as	as	ADP
aiti-819	230	17	in	in	ADP
aiti-819	230	18	packing	packing	NOUN
aiti-819	230	19	problems	problem	NOUN
aiti-819	230	20	.	.	PUNCT
aiti-819	231	1	although	although	SCONJ
aiti-819	231	2	most	most	ADJ
aiti-819	231	3	researchers	researcher	NOUN
aiti-819	231	4	concentrate	concentrate	VERB
aiti-819	231	5	on	on	ADP
aiti-819	231	6	finding	find	VERB
aiti-819	231	7	circles	circle	NOUN
aiti-819	231	8	inside	inside	ADP
aiti-819	231	9	an	an	DET
aiti-819	231	10	area	area	NOUN
aiti-819	231	11	,	,	PUNCT
aiti-819	231	12	a	a	DET
aiti-819	231	13	contrasting	contrast	VERB
aiti-819	231	14	approach	approach	NOUN
aiti-819	231	15	is	be	AUX
aiti-819	231	16	employed	employ	VERB
aiti-819	231	17	by	by	ADP
aiti-819	231	18	constructing	construct	VERB
aiti-819	231	19	the	the	DET
aiti-819	231	20	area	area	NOUN
aiti-819	231	21	inside	inside	ADP
aiti-819	231	22	out	out	ADV
aiti-819	231	23	,	,	PUNCT
aiti-819	231	24	from	from	ADP
aiti-819	231	25	a	a	DET
aiti-819	231	26	1d	1d	NUM
aiti-819	231	27	curve	curve	NOUN
aiti-819	231	28	(	(	PUNCT
aiti-819	231	29	skeleton	skeleton	NOUN
aiti-819	231	30	)	)	PUNCT
aiti-819	231	31	to	to	ADP
aiti-819	231	32	2d	2d	PROPN
aiti-819	231	33	area	area	NOUN
aiti-819	231	34	(	(	PUNCT
aiti-819	231	35	union	union	NOUN
aiti-819	231	36	of	of	ADP
aiti-819	231	37	circles	circle	NOUN
aiti-819	231	38	/	/	SYM
aiti-819	231	39	muscles	muscle	NOUN
aiti-819	231	40	)	)	PUNCT
aiti-819	231	41	,	,	PUNCT
aiti-819	231	42	in	in	ADP
aiti-819	231	43	order	order	NOUN
aiti-819	231	44	to	to	PART
aiti-819	231	45	ensure	ensure	VERB
aiti-819	231	46	a	a	DET
aiti-819	231	47	smooth	smooth	ADJ
aiti-819	231	48	boundary	boundary	ADJ
aiti-819	231	49	area	area	NOUN
aiti-819	231	50	(	(	PUNCT
aiti-819	231	51	g	g	NOUN
aiti-819	231	52	1	1	NUM
aiti-819	231	53	-continuity	-continuity	PROPN
aiti-819	231	54	boundary	boundary	ADJ
aiti-819	231	55	curve	curve	NOUN
aiti-819	231	56	)	)	PUNCT
aiti-819	231	57	.	.	PUNCT
aiti-819	232	1	the	the	DET
aiti-819	232	2	algorithm	algorithm	NOUN
aiti-819	232	3	used	use	VERB
aiti-819	232	4	to	to	PART
aiti-819	232	5	extend	extend	VERB
aiti-819	232	6	the	the	DET
aiti-819	232	7	area	area	NOUN
aiti-819	232	8	is	be	AUX
aiti-819	232	9	based	base	VERB
aiti-819	232	10	on	on	ADP
aiti-819	232	11	the	the	DET
aiti-819	232	12	binary	binary	ADJ
aiti-819	232	13	approach	approach	NOUN
aiti-819	232	14	,	,	PUNCT
aiti-819	232	15	and	and	CCONJ
aiti-819	232	16	it	it	PRON
aiti-819	232	17	can	can	AUX
aiti-819	232	18	be	be	AUX
aiti-819	232	19	easily	easily	ADV
aiti-819	232	20	used	use	VERB
aiti-819	232	21	for	for	ADP
aiti-819	232	22	growing	grow	VERB
aiti-819	232	23	areas	area	NOUN
aiti-819	232	24	.	.	PUNCT
aiti-819	233	1	future	future	ADJ
aiti-819	233	2	research	research	NOUN
aiti-819	233	3	will	will	AUX
aiti-819	233	4	emphasize	emphasize	VERB
aiti-819	233	5	on	on	ADP
aiti-819	233	6	the	the	DET
aiti-819	233	7	design	design	NOUN
aiti-819	233	8	of	of	ADP
aiti-819	233	9	area	area	NOUN
aiti-819	233	10	-	-	PUNCT
aiti-819	233	11	growth	growth	NOUN
aiti-819	233	12	directions	direction	NOUN
aiti-819	233	13	.	.	PUNCT
aiti-819	234	1	for	for	ADP
aiti-819	234	2	example	example	NOUN
aiti-819	234	3	,	,	PUNCT
aiti-819	234	4	the	the	DET
aiti-819	234	5	area	area	NOUN
aiti-819	234	6	generated	generate	VERB
aiti-819	234	7	from	from	ADP
aiti-819	234	8	piecewise	piecewise	PROPN
aiti-819	234	9	cubic	cubic	ADJ
aiti-819	234	10	bezier	bezier	NOUN
aiti-819	234	11	curve	curve	NOUN
aiti-819	234	12	,	,	PUNCT
aiti-819	234	13	so	so	SCONJ
aiti-819	234	14	that	that	SCONJ
aiti-819	234	15	the	the	DET
aiti-819	234	16	whole	whole	ADJ
aiti-819	234	17	area	area	NOUN
aiti-819	234	18	is	be	AUX
aiti-819	234	19	extended	extend	VERB
aiti-819	234	20	to	to	PART
aiti-819	234	21	produce	produce	VERB
aiti-819	234	22	an	an	DET
aiti-819	234	23	elongated	elongate	VERB
aiti-819	234	24	area	area	NOUN
aiti-819	234	25	,	,	PUNCT
aiti-819	234	26	certain	certain	ADJ
aiti-819	234	27	data	data	NOUN
aiti-819	234	28	structures	structure	NOUN
aiti-819	234	29	,	,	PUNCT
aiti-819	234	30	such	such	ADJ
aiti-819	234	31	as	as	ADP
aiti-819	234	32	medial	medial	ADJ
aiti-819	234	33	-	-	PUNCT
aiti-819	234	34	axis	axis	NOUN
aiti-819	234	35	transforms	transform	NOUN
aiti-819	234	36	,	,	PUNCT
aiti-819	234	37	can	can	AUX
aiti-819	234	38	be	be	AUX
aiti-819	234	39	easily	easily	ADV
aiti-819	234	40	generated	generate	VERB
aiti-819	234	41	.	.	PUNCT
aiti-819	235	1	the	the	DET
aiti-819	235	2	other	other	ADJ
aiti-819	235	3	example	example	NOUN
aiti-819	235	4	is	be	AUX
aiti-819	235	5	to	to	PART
aiti-819	235	6	automatically	automatically	ADV
aiti-819	235	7	grow	grow	VERB
aiti-819	235	8	an	an	DET
aiti-819	235	9	area	area	NOUN
aiti-819	235	10	to	to	PART
aiti-819	235	11	approach	approach	VERB
aiti-819	235	12	a	a	DET
aiti-819	235	13	bounded	bounded	ADJ
aiti-819	235	14	one	one	NUM
aiti-819	235	15	.	.	PUNCT
aiti-819	236	1	acknowledgment	acknowledgment	NOUN
aiti-819	236	2	this	this	DET
aiti-819	236	3	work	work	NOUN
aiti-819	236	4	was	be	AUX
aiti-819	236	5	supported	support	VERB
aiti-819	236	6	in	in	ADP
aiti-819	236	7	part	part	NOUN
aiti-819	236	8	by	by	ADP
aiti-819	236	9	the	the	DET
aiti-819	236	10	national	national	PROPN
aiti-819	236	11	science	science	PROPN
aiti-819	236	12	council	council	PROPN
aiti-819	236	13	in	in	ADP
aiti-819	236	14	taiwan	taiwan	PROPN
aiti-819	236	15	under	under	ADP
aiti-819	236	16	grant	grant	NOUN
aiti-819	236	17	most	most	ADJ
aiti-819	236	18	104	104	NUM
aiti-819	236	19	-	-	SYM
aiti-819	236	20	2221e-031	2221e-031	NUM
aiti-819	236	21	-	-	PUNCT
aiti-819	236	22	005	005	NUM
aiti-819	236	23	.	.	PUNCT
aiti-819	237	1	conflicts	conflict	NOUN
aiti-819	237	2	of	of	ADP
aiti-819	237	3	interest	interest	NOUN
aiti-819	237	4	the	the	DET
aiti-819	237	5	authors	author	NOUN
aiti-819	237	6	declare	declare	VERB
aiti-819	237	7	no	no	DET
aiti-819	237	8	conflict	conflict	NOUN
aiti-819	237	9	of	of	ADP
aiti-819	237	10	interest	interest	NOUN
aiti-819	237	11	.	.	PUNCT
aiti-819	238	1	references	reference	NOUN
aiti-819	238	2	[	[	X
aiti-819	238	3	1	1	NUM
aiti-819	238	4	]	]	PUNCT
aiti-819	238	5	c.	c.	PROPN
aiti-819	238	6	s.	s.	PROPN
aiti-819	238	7	chiang	chiang	PROPN
aiti-819	238	8	,	,	PUNCT
aiti-819	238	9	“	"	PUNCT
aiti-819	238	10	the	the	DET
aiti-819	238	11	medial	medial	ADJ
aiti-819	238	12	axis	axis	NOUN
aiti-819	238	13	transform	transform	NOUN
aiti-819	238	14	of	of	ADP
aiti-819	238	15	the	the	DET
aiti-819	238	16	region	region	NOUN
aiti-819	238	17	defined	define	VERB
aiti-819	238	18	by	by	ADP
aiti-819	238	19	circles	circle	NOUN
aiti-819	238	20	and	and	CCONJ
aiti-819	238	21	hermit	hermit	ADJ
aiti-819	238	22	curve	curve	NOUN
aiti-819	238	23	,	,	PUNCT
aiti-819	238	24	”	"	PUNCT
aiti-819	238	25	international	international	ADJ
aiti-819	238	26	conference	conference	NOUN
aiti-819	238	27	on	on	ADP
aiti-819	238	28	computer	computer	NOUN
aiti-819	238	29	science	science	NOUN
aiti-819	238	30	and	and	CCONJ
aiti-819	238	31	engineering	engineering	NOUN
aiti-819	238	32	(	(	PUNCT
aiti-819	238	33	iccse	iccse	NOUN
aiti-819	238	34	)	)	PUNCT
aiti-819	238	35	,	,	PUNCT
aiti-819	238	36	july	july	PROPN
aiti-819	238	37	22	22	NUM
aiti-819	238	38	-	-	SYM
aiti-819	238	39	24	24	NUM
aiti-819	238	40	2015	2015	NUM
aiti-819	238	41	.	.	PUNCT
aiti-819	239	1	[	[	X
aiti-819	239	2	2	2	NUM
aiti-819	239	3	]	]	X
aiti-819	239	4	l.	l.	NOUN
aiti-819	239	5	cinque	cinque	PROPN
aiti-819	239	6	,	,	PUNCT
aiti-819	239	7	s.	s.	PROPN
aiti-819	239	8	levialdi	levialdi	PROPN
aiti-819	239	9	,	,	PUNCT
aiti-819	239	10	and	and	CCONJ
aiti-819	239	11	a.	a.	PROPN
aiti-819	239	12	malizia	malizia	PROPN
aiti-819	239	13	,	,	PUNCT
aiti-819	239	14	“	"	PUNCT
aiti-819	239	15	shape	shape	NOUN
aiti-819	239	16	description	description	NOUN
aiti-819	239	17	using	use	VERB
aiti-819	239	18	cubic	cubic	ADJ
aiti-819	239	19	polynomial	polynomial	ADJ
aiti-819	239	20	bezier	bezier	NOUN
aiti-819	239	21	curves	curve	NOUN
aiti-819	239	22	,	,	PUNCT
aiti-819	239	23	”	"	PUNCT
aiti-819	239	24	pattern	pattern	NOUN
aiti-819	239	25	recognition	recognition	NOUN
aiti-819	239	26	letters	letter	NOUN
aiti-819	239	27	,	,	PUNCT
aiti-819	239	28	vol	vol	NOUN
aiti-819	239	29	.	.	PROPN
aiti-819	239	30	19	19	NUM
aiti-819	239	31	,	,	PUNCT
aiti-819	239	32	pp	pp	ADJ
aiti-819	239	33	.	.	PUNCT
aiti-819	240	1	821	821	NUM
aiti-819	240	2	-	-	SYM
aiti-819	240	3	828	828	NUM
aiti-819	240	4	,	,	PUNCT
aiti-819	240	5	1998	1998	NUM
aiti-819	240	6	.	.	PUNCT
aiti-819	241	1	[	[	X
aiti-819	241	2	3	3	X
aiti-819	241	3	]	]	X
aiti-819	241	4	h.	h.	PROPN
aiti-819	241	5	m.	m.	PROPN
aiti-819	241	6	yang	yang	PROPN
aiti-819	241	7	,	,	PUNCT
aiti-819	241	8	j.	j.	PROPN
aiti-819	241	9	j.	j.	PROPN
aiti-819	241	10	lu	lu	PROPN
aiti-819	241	11	,	,	PUNCT
aiti-819	241	12	and	and	CCONJ
aiti-819	241	13	h.	h.	PROPN
aiti-819	241	14	j.	j.	PROPN
aiti-819	241	15	lee	lee	PROPN
aiti-819	241	16	,	,	PUNCT
aiti-819	241	17	“	"	PUNCT
aiti-819	241	18	a	a	DET
aiti-819	241	19	bezier	bezier	ADJ
aiti-819	241	20	curve	curve	NOUN
aiti-819	241	21	-	-	PUNCT
aiti-819	241	22	based	base	VERB
aiti-819	241	23	approach	approach	NOUN
aiti-819	241	24	to	to	PART
aiti-819	241	25	shape	shape	VERB
aiti-819	241	26	description	description	NOUN
aiti-819	241	27	for	for	ADP
aiti-819	241	28	chinese	chinese	ADJ
aiti-819	241	29	calligraphy	calligraphy	NOUN
aiti-819	241	30	characters	character	NOUN
aiti-819	241	31	,	,	PUNCT
aiti-819	241	32	”	"	PUNCT
aiti-819	241	33	proceedings	proceeding	NOUN
aiti-819	241	34	of	of	ADP
aiti-819	241	35	the	the	DET
aiti-819	241	36	sixth	sixth	ADJ
aiti-819	241	37	international	international	ADJ
aiti-819	241	38	conference	conference	NOUN
aiti-819	241	39	on	on	ADP
aiti-819	241	40	document	document	NOUN
aiti-819	241	41	analysis	analysis	NOUN
aiti-819	241	42	and	and	CCONJ
aiti-819	241	43	recognition	recognition	NOUN
aiti-819	241	44	,	,	PUNCT
aiti-819	241	45	pp	pp	ADP
aiti-819	241	46	.	.	PUNCT
aiti-819	241	47	276	276	NUM
aiti-819	241	48	-	-	SYM
aiti-819	241	49	280	280	NUM
aiti-819	241	50	,	,	PUNCT
aiti-819	241	51	2001	2001	NUM
aiti-819	241	52	.	.	PUNCT
aiti-819	242	1	[	[	X
aiti-819	242	2	4	4	X
aiti-819	242	3	]	]	PUNCT
aiti-819	242	4	c.	c.	PROPN
aiti-819	242	5	s.	s.	PROPN
aiti-819	242	6	chiang	chiang	PROPN
aiti-819	242	7	and	and	CCONJ
aiti-819	242	8	l.	l.	PROPN
aiti-819	242	9	y.	y.	PROPN
aiti-819	242	10	hsu	hsu	PROPN
aiti-819	242	11	,	,	PUNCT
aiti-819	242	12	“	"	PUNCT
aiti-819	242	13	describing	describe	VERB
aiti-819	242	14	the	the	DET
aiti-819	242	15	edge	edge	NOUN
aiti-819	242	16	contour	contour	NOUN
aiti-819	242	17	of	of	ADP
aiti-819	242	18	chinese	chinese	ADJ
aiti-819	242	19	calligraphy	calligraphy	NOUN
aiti-819	242	20	with	with	ADP
aiti-819	242	21	circle	circle	NOUN
aiti-819	242	22	and	and	CCONJ
aiti-819	242	23	cubic	cubic	ADJ
aiti-819	242	24	hermite	hermite	ADJ
aiti-819	242	25	curve	curve	NOUN
aiti-819	242	26	,	,	PUNCT
aiti-819	242	27	”	"	PUNCT
aiti-819	242	28	2013	2013	NUM
aiti-819	242	29	computer	computer	NOUN
aiti-819	242	30	graphics	graphic	NOUN
aiti-819	242	31	workshop	workshop	NOUN
aiti-819	242	32	,	,	PUNCT
aiti-819	242	33	july	july	PROPN
aiti-819	242	34	2013	2013	NUM
aiti-819	242	35	.	.	PUNCT
aiti-819	243	1	[	[	X
aiti-819	243	2	5	5	X
aiti-819	243	3	]	]	PUNCT
aiti-819	243	4	h.	h.	PROPN
aiti-819	243	5	h.	h.	PROPN
aiti-819	243	6	chang	chang	PROPN
aiti-819	243	7	and	and	CCONJ
aiti-819	243	8	h.	h.	PROPN
aiti-819	243	9	yan	yan	PROPN
aiti-819	243	10	,	,	PUNCT
aiti-819	243	11	“	"	PUNCT
aiti-819	243	12	vectorization	vectorization	NOUN
aiti-819	243	13	of	of	ADP
aiti-819	243	14	hand	hand	NOUN
aiti-819	243	15	-	-	PUNCT
aiti-819	243	16	drawn	draw	VERB
aiti-819	243	17	image	image	NOUN
aiti-819	243	18	using	use	VERB
aiti-819	243	19	piecewise	piecewise	NOUN
aiti-819	243	20	cubic	cubic	ADJ
aiti-819	243	21	bezier	bezier	NOUN
aiti-819	243	22	curves	curve	NOUN
aiti-819	243	23	fitting	fitting	ADJ
aiti-819	243	24	,	,	PUNCT
aiti-819	243	25	”	"	PUNCT
aiti-819	243	26	pattern	pattern	NOUN
aiti-819	243	27	recognition	recognition	NOUN
aiti-819	243	28	,	,	PUNCT
aiti-819	243	29	vol	vol	NOUN
aiti-819	243	30	.	.	PROPN
aiti-819	243	31	31	31	NUM
aiti-819	243	32	,	,	PUNCT
aiti-819	243	33	no	no	INTJ
aiti-819	243	34	.	.	NOUN
aiti-819	243	35	11	11	NUM
aiti-819	243	36	,	,	PUNCT
aiti-819	243	37	pp	pp	ADJ
aiti-819	243	38	.	.	PUNCT
aiti-819	244	1	1747	1747	NUM
aiti-819	244	2	-	-	SYM
aiti-819	244	3	1755	1755	NUM
aiti-819	244	4	,	,	PUNCT
aiti-819	244	5	1998	1998	NUM
aiti-819	244	6	.	.	PUNCT
aiti-819	245	1	[	[	X
aiti-819	245	2	6	6	NUM
aiti-819	245	3	]	]	PUNCT
aiti-819	245	4	h.	h.	PROPN
aiti-819	245	5	cao	cao	PROPN
aiti-819	245	6	and	and	CCONJ
aiti-819	245	7	a.	a.	PROPN
aiti-819	245	8	c.	c.	PROPN
aiti-819	245	9	kot	kot	PROPN
aiti-819	245	10	,	,	PUNCT
aiti-819	245	11	“	"	PUNCT
aiti-819	245	12	lossless	lossless	NOUN
aiti-819	245	13	data	datum	NOUN
aiti-819	245	14	embedding	embed	VERB
aiti-819	245	15	in	in	ADP
aiti-819	245	16	electronic	electronic	ADJ
aiti-819	245	17	inks	ink	NOUN
aiti-819	245	18	,	,	PUNCT
aiti-819	245	19	”	"	PUNCT
aiti-819	245	20	ieee	ieee	NOUN
aiti-819	245	21	transactions	transaction	NOUN
aiti-819	245	22	on	on	ADP
aiti-819	245	23	information	information	NOUN
aiti-819	245	24	forensics	forensic	NOUN
aiti-819	245	25	and	and	CCONJ
aiti-819	245	26	security	security	NOUN
aiti-819	245	27	,	,	PUNCT
aiti-819	245	28	vol	vol	NOUN
aiti-819	245	29	.	.	PROPN
aiti-819	245	30	5	5	NUM
aiti-819	245	31	,	,	PUNCT
aiti-819	245	32	no	no	INTJ
aiti-819	245	33	.	.	NOUN
aiti-819	245	34	2	2	NUM
aiti-819	245	35	,	,	PUNCT
aiti-819	245	36	pp	pp	ADJ
aiti-819	245	37	.	.	PUNCT
aiti-819	245	38	314	314	NUM
aiti-819	245	39	-	-	SYM
aiti-819	245	40	323	323	NUM
aiti-819	245	41	,	,	PUNCT
aiti-819	245	42	2010	2010	NUM
aiti-819	245	43	.	.	PUNCT
aiti-819	246	1	[	[	X
aiti-819	246	2	7	7	X
aiti-819	246	3	]	]	X
aiti-819	246	4	l.	l.	PROPN
aiti-819	246	5	cao	cao	PROPN
aiti-819	246	6	,	,	PUNCT
aiti-819	246	7	z.	z.	PROPN
aiti-819	246	8	jia	jia	PROPN
aiti-819	246	9	,	,	PUNCT
aiti-819	246	10	and	and	CCONJ
aiti-819	246	11	j.	j.	PROPN
aiti-819	246	12	liu	liu	PROPN
aiti-819	246	13	,	,	PUNCT
aiti-819	246	14	“	"	PUNCT
aiti-819	246	15	computation	computation	NOUN
aiti-819	246	16	of	of	ADP
aiti-819	246	17	medial	medial	ADJ
aiti-819	246	18	axis	axis	NOUN
aiti-819	246	19	and	and	CCONJ
aiti-819	246	20	offset	offset	VERB
aiti-819	246	21	curves	curve	NOUN
aiti-819	246	22	of	of	ADP
aiti-819	246	23	curved	curved	ADJ
aiti-819	246	24	boundaries	boundary	NOUN
aiti-819	246	25	in	in	ADP
aiti-819	246	26	planar	planar	ADJ
aiti-819	246	27	domains	domain	NOUN
aiti-819	246	28	based	base	VERB
aiti-819	246	29	on	on	ADP
aiti-819	246	30	the	the	DET
aiti-819	246	31	cesaro	cesaro	NOUN
aiti-819	246	32	’s	’s	PART
aiti-819	246	33	approach	approach	NOUN
aiti-819	246	34	,	,	PUNCT
aiti-819	246	35	”	"	PUNCT
aiti-819	246	36	computer	computer	NOUN
aiti-819	246	37	aided	aid	VERB
aiti-819	246	38	geometric	geometric	ADJ
aiti-819	246	39	design	design	NOUN
aiti-819	246	40	,	,	PUNCT
aiti-819	246	41	vol	vol	NOUN
aiti-819	246	42	.	.	PROPN
aiti-819	247	1	26	26	NUM
aiti-819	247	2	,	,	PUNCT
aiti-819	247	3	no	no	INTJ
aiti-819	247	4	.	.	NOUN
aiti-819	247	5	4	4	NUM
aiti-819	247	6	,	,	PUNCT
aiti-819	247	7	pp	pp	ADJ
aiti-819	247	8	.	.	PUNCT
aiti-819	248	1	444	444	NUM
aiti-819	248	2	-	-	SYM
aiti-819	248	3	454	454	NUM
aiti-819	248	4	,	,	PUNCT
aiti-819	248	5	2009	2009	NUM
aiti-819	248	6	.	.	PUNCT
aiti-819	249	1	[	[	X
aiti-819	249	2	8	8	X
aiti-819	249	3	]	]	PUNCT
aiti-819	249	4	p.	p.	NOUN
aiti-819	249	5	qin	qin	PROPN
aiti-819	249	6	and	and	CCONJ
aiti-819	249	7	c.	c.	PROPN
aiti-819	249	8	chen	chen	PROPN
aiti-819	249	9	,	,	PUNCT
aiti-819	249	10	“	"	PUNCT
aiti-819	249	11	simulation	simulation	NOUN
aiti-819	249	12	model	model	NOUN
aiti-819	249	13	of	of	ADP
aiti-819	249	14	flower	flower	NOUN
aiti-819	249	15	using	use	VERB
aiti-819	249	16	the	the	DET
aiti-819	249	17	integration	integration	NOUN
aiti-819	249	18	of	of	ADP
aiti-819	249	19	l	l	NOUN
aiti-819	249	20	-	-	NOUN
aiti-819	249	21	systems	system	NOUN
aiti-819	249	22	with	with	ADP
aiti-819	249	23	bezier	bezier	ADJ
aiti-819	249	24	surfaces	surface	NOUN
aiti-819	249	25	,	,	PUNCT
aiti-819	249	26	”	"	PUNCT
aiti-819	249	27	international	international	ADJ
aiti-819	249	28	journal	journal	NOUN
aiti-819	249	29	of	of	ADP
aiti-819	249	30	computer	computer	NOUN
aiti-819	249	31	science	science	NOUN
aiti-819	249	32	and	and	CCONJ
aiti-819	249	33	network	network	NOUN
aiti-819	249	34	security	security	NOUN
aiti-819	249	35	,	,	PUNCT
aiti-819	249	36	vol	vol	NOUN
aiti-819	249	37	.	.	PROPN
aiti-819	250	1	6	6	NUM
aiti-819	250	2	,	,	PUNCT
aiti-819	250	3	no	no	INTJ
aiti-819	250	4	.	.	NOUN
aiti-819	250	5	2	2	NUM
aiti-819	250	6	,	,	PUNCT
aiti-819	250	7	pp	pp	ADJ
aiti-819	250	8	.	.	PUNCT
aiti-819	251	1	65	65	NUM
aiti-819	251	2	-	-	SYM
aiti-819	251	3	68	68	NUM
aiti-819	251	4	,	,	PUNCT
aiti-819	251	5	2006	2006	NUM
aiti-819	251	6	.	.	PUNCT
aiti-819	252	1	[	[	X
aiti-819	252	2	9	9	NUM
aiti-819	252	3	]	]	X
aiti-819	252	4	g.	g.	PROPN
aiti-819	252	5	l.	l.	PROPN
aiti-819	252	6	orick	orick	PROPN
aiti-819	252	7	,	,	PUNCT
aiti-819	252	8	k.	k.	PROPN
aiti-819	252	9	stephenson	stephenson	PROPN
aiti-819	252	10	,	,	PUNCT
aiti-819	252	11	and	and	CCONJ
aiti-819	252	12	c.	c.	PROPN
aiti-819	252	13	collins	collins	PROPN
aiti-819	252	14	,	,	PUNCT
aiti-819	252	15	“	"	PUNCT
aiti-819	252	16	a	a	DET
aiti-819	252	17	linearized	linearize	VERB
aiti-819	252	18	circle	circle	NOUN
aiti-819	252	19	packing	packing	NOUN
aiti-819	252	20	algorithm	algorithm	NOUN
aiti-819	252	21	,	,	PUNCT
aiti-819	252	22	”	"	PUNCT
aiti-819	252	23	computational	computational	ADJ
aiti-819	252	24	geometry	geometry	NOUN
aiti-819	252	25	64	64	NUM
aiti-819	252	26	,	,	PUNCT
aiti-819	252	27	pp	pp	ADJ
aiti-819	252	28	.	.	PUNCT
aiti-819	252	29	13	13	NUM
aiti-819	252	30	-	-	SYM
aiti-819	252	31	29	29	NUM
aiti-819	252	32	,	,	PUNCT
aiti-819	252	33	2017	2017	NUM
aiti-819	252	34	.	.	PUNCT
aiti-819	253	1	[	[	X
aiti-819	253	2	10	10	NUM
aiti-819	253	3	]	]	X
aiti-819	253	4	o.	o.	NOUN
aiti-819	253	5	angel	angel	NOUN
aiti-819	253	6	,	,	PUNCT
aiti-819	253	7	t.	t.	PROPN
aiti-819	253	8	hutchcroft	hutchcroft	PROPN
aiti-819	253	9	,	,	PUNCT
aiti-819	253	10	a.	a.	NOUN
aiti-819	253	11	nachmias	nachmias	PROPN
aiti-819	253	12	,	,	PUNCT
aiti-819	253	13	and	and	CCONJ
aiti-819	253	14	g.	g.	PROPN
aiti-819	253	15	ray	ray	PROPN
aiti-819	253	16	,	,	PUNCT
aiti-819	253	17	“	"	PUNCT
aiti-819	253	18	unimodular	unimodular	ADJ
aiti-819	253	19	hyperbolic	hyperbolic	ADJ
aiti-819	253	20	triangulations	triangulation	NOUN
aiti-819	253	21	:	:	PUNCT
aiti-819	253	22	circle	circle	NOUN
aiti-819	253	23	packing	packing	NOUN
aiti-819	253	24	and	and	CCONJ
aiti-819	253	25	random	random	ADJ
aiti-819	253	26	walk	walk	NOUN
aiti-819	253	27	,	,	PUNCT
aiti-819	253	28	”	"	PUNCT
aiti-819	253	29	inventiones	inventione	NOUN
aiti-819	253	30	mathematicae	mathematicae	VERB
aiti-819	253	31	206.1	206.1	NUM
aiti-819	253	32	,	,	PUNCT
aiti-819	253	33	pp	pp	ADJ
aiti-819	253	34	.	.	PUNCT
aiti-819	254	1	229	229	NUM
aiti-819	254	2	-	-	SYM
aiti-819	254	3	268	268	NUM
aiti-819	254	4	,	,	PUNCT
aiti-819	254	5	2016	2016	NUM
aiti-819	254	6	.	.	PUNCT
aiti-819	255	1	[	[	X
aiti-819	255	2	11	11	NUM
aiti-819	255	3	]	]	PUNCT
aiti-819	255	4	k.	k.	PROPN
aiti-819	255	5	e.	e.	PROPN
aiti-819	255	6	stange	stange	PROPN
aiti-819	255	7	,	,	PUNCT
aiti-819	255	8	“	"	PUNCT
aiti-819	255	9	the	the	DET
aiti-819	255	10	sensual	sensual	ADJ
aiti-819	255	11	apollonian	apollonian	ADJ
aiti-819	255	12	circle	circle	NOUN
aiti-819	255	13	packing	packing	NOUN
aiti-819	255	14	,	,	PUNCT
aiti-819	255	15	”	"	PUNCT
aiti-819	255	16	expositiones	expositione	NOUN
aiti-819	255	17	mathematicae	mathematicae	VERB
aiti-819	255	18	34.4	34.4	NUM
aiti-819	255	19	,	,	PUNCT
aiti-819	255	20	pp	pp	ADJ
aiti-819	255	21	.	.	PUNCT
aiti-819	256	1	364	364	NUM
aiti-819	256	2	-	-	SYM
aiti-819	256	3	395	395	NUM
aiti-819	256	4	,	,	PUNCT
aiti-819	256	5	2016	2016	NUM
aiti-819	256	6	.	.	PUNCT
aiti-819	257	1	copyright	copyright	NOUN
aiti-819	257	2	©	©	PROPN
aiti-819	257	3	by	by	ADP
aiti-819	257	4	the	the	DET
aiti-819	257	5	authors	author	NOUN
aiti-819	257	6	.	.	PUNCT
aiti-819	258	1	licensee	licensee	PROPN
aiti-819	258	2	taeti	taeti	PROPN
aiti-819	258	3	,	,	PUNCT
aiti-819	258	4	taiwan	taiwan	PROPN
aiti-819	258	5	.	.	PUNCT
aiti-819	259	1	this	this	DET
aiti-819	259	2	article	article	NOUN
aiti-819	259	3	is	be	AUX
aiti-819	259	4	an	an	DET
aiti-819	259	5	open	open	ADJ
aiti-819	259	6	access	access	NOUN
aiti-819	259	7	article	article	NOUN
aiti-819	259	8	distributed	distribute	VERB
aiti-819	259	9	under	under	ADP
aiti-819	259	10	the	the	DET
aiti-819	259	11	terms	term	NOUN
aiti-819	259	12	and	and	CCONJ
aiti-819	259	13	conditions	condition	NOUN
aiti-819	259	14	of	of	ADP
aiti-819	259	15	the	the	DET
aiti-819	259	16	creative	creative	ADJ
aiti-819	259	17	commons	common	NOUN
aiti-819	259	18	attribution	attribution	NOUN
aiti-819	259	19	(	(	PUNCT
aiti-819	259	20	cc	cc	NOUN
aiti-819	259	21	by	by	ADP
aiti-819	259	22	-	-	PUNCT
aiti-819	259	23	nc	nc	NOUN
aiti-819	259	24	)	)	PUNCT
aiti-819	259	25	license	license	NOUN
aiti-819	259	26	(	(	PUNCT
aiti-819	259	27	https://creativecommons.org/licenses/by-nc/4.0/	https://creativecommons.org/licenses/by-nc/4.0/	NOUN
aiti-819	259	28	)	)	PUNCT
aiti-819	259	29	.	.	PUNCT