id	sid	tid	token	lemma	pos
ejpam-6498	1	1	european	european	PROPN
ejpam-6498	1	2	journal	journal	PROPN
ejpam-6498	1	3	of	of	ADP
ejpam-6498	1	4	pure	pure	ADJ
ejpam-6498	1	5	and	and	CCONJ
ejpam-6498	1	6	applied	applied	ADJ
ejpam-6498	1	7	mathematics	mathematic	NOUN
ejpam-6498	1	8	2025	2025	NUM
ejpam-6498	1	9	,	,	PUNCT
ejpam-6498	1	10	vol	vol	NOUN
ejpam-6498	1	11	.	.	PROPN
ejpam-6498	1	12	18	18	NUM
ejpam-6498	1	13	,	,	PUNCT
ejpam-6498	1	14	issue	issue	NOUN
ejpam-6498	1	15	4	4	NUM
ejpam-6498	1	16	,	,	PUNCT
ejpam-6498	1	17	article	article	NOUN
ejpam-6498	1	18	number	number	NOUN
ejpam-6498	1	19	6498	6498	NUM
ejpam-6498	1	20	issn	issn	PROPN
ejpam-6498	1	21	1307	1307	NUM
ejpam-6498	1	22	-	-	SYM
ejpam-6498	1	23	5543	5543	NUM
ejpam-6498	1	24	–	–	PUNCT
ejpam-6498	1	25	ejpam.com	ejpam.com	X
ejpam-6498	1	26	published	publish	VERB
ejpam-6498	1	27	by	by	ADP
ejpam-6498	1	28	new	new	PROPN
ejpam-6498	1	29	york	york	PROPN
ejpam-6498	1	30	business	business	PROPN
ejpam-6498	1	31	global	global	PROPN
ejpam-6498	1	32	a	a	DET
ejpam-6498	1	33	high	high	ADJ
ejpam-6498	1	34	-	-	PUNCT
ejpam-6498	1	35	order	order	NOUN
ejpam-6498	1	36	,	,	PUNCT
ejpam-6498	1	37	optimization	optimization	NOUN
ejpam-6498	1	38	-	-	PUNCT
ejpam-6498	1	39	free	free	ADJ
ejpam-6498	1	40	,	,	PUNCT
ejpam-6498	1	41	tangent	tangent	ADJ
ejpam-6498	1	42	continuous	continuous	ADJ
ejpam-6498	1	43	approximation	approximation	NOUN
ejpam-6498	1	44	of	of	ADP
ejpam-6498	1	45	conic	conic	ADJ
ejpam-6498	1	46	sections	section	NOUN
ejpam-6498	1	47	using	use	VERB
ejpam-6498	1	48	cubic	cubic	ADV
ejpam-6498	1	49	bézier	bézier	ADP
ejpam-6498	1	50	curves	curve	NOUN
ejpam-6498	1	51	maria	maria	NOUN
ejpam-6498	1	52	hussain1	hussain1	NOUN
ejpam-6498	1	53	,	,	PUNCT
ejpam-6498	1	54	hafiz	hafiz	PROPN
ejpam-6498	1	55	abdul	abdul	PROPN
ejpam-6498	1	56	wajid2,∗	wajid2,∗	PROPN
ejpam-6498	1	57	,	,	PUNCT
ejpam-6498	1	58	saira	saira	PROPN
ejpam-6498	1	59	aqeel1	aqeel1	PROPN
ejpam-6498	1	60	1	1	NUM
ejpam-6498	1	61	department	department	NOUN
ejpam-6498	1	62	of	of	ADP
ejpam-6498	1	63	mathematics	mathematic	NOUN
ejpam-6498	1	64	,	,	PUNCT
ejpam-6498	1	65	lahore	lahore	PROPN
ejpam-6498	1	66	college	college	NOUN
ejpam-6498	1	67	for	for	ADP
ejpam-6498	1	68	women	woman	NOUN
ejpam-6498	1	69	university	university	NOUN
ejpam-6498	1	70	,	,	PUNCT
ejpam-6498	1	71	lahore	lahore	PROPN
ejpam-6498	1	72	,	,	PUNCT
ejpam-6498	1	73	pakistan	pakistan	PROPN
ejpam-6498	1	74	2	2	NUM
ejpam-6498	1	75	department	department	NOUN
ejpam-6498	1	76	of	of	ADP
ejpam-6498	1	77	electrical	electrical	ADJ
ejpam-6498	1	78	engineering	engineering	NOUN
ejpam-6498	1	79	,	,	PUNCT
ejpam-6498	1	80	faculty	faculty	NOUN
ejpam-6498	1	81	of	of	ADP
ejpam-6498	1	82	engineering	engineering	PROPN
ejpam-6498	1	83	,	,	PUNCT
ejpam-6498	1	84	islamic	islamic	PROPN
ejpam-6498	1	85	university	university	PROPN
ejpam-6498	1	86	of	of	ADP
ejpam-6498	1	87	madinah	madinah	PROPN
ejpam-6498	1	88	,	,	PUNCT
ejpam-6498	1	89	madinah	madinah	PROPN
ejpam-6498	1	90	42351	42351	NUM
ejpam-6498	1	91	,	,	PUNCT
ejpam-6498	1	92	saudi	saudi	PROPN
ejpam-6498	1	93	arabia	arabia	PROPN
ejpam-6498	1	94	abstract	abstract	NOUN
ejpam-6498	1	95	.	.	PUNCT
ejpam-6498	2	1	this	this	DET
ejpam-6498	2	2	paper	paper	NOUN
ejpam-6498	2	3	presents	present	VERB
ejpam-6498	2	4	a	a	DET
ejpam-6498	2	5	high	high	ADJ
ejpam-6498	2	6	-	-	PUNCT
ejpam-6498	2	7	order	order	NOUN
ejpam-6498	2	8	,	,	PUNCT
ejpam-6498	2	9	optimization	optimization	NOUN
ejpam-6498	2	10	-	-	PUNCT
ejpam-6498	2	11	free	free	ADJ
ejpam-6498	2	12	method	method	NOUN
ejpam-6498	2	13	for	for	ADP
ejpam-6498	2	14	approximating	approximate	VERB
ejpam-6498	2	15	conic	conic	ADJ
ejpam-6498	2	16	sections	section	NOUN
ejpam-6498	2	17	using	use	VERB
ejpam-6498	2	18	cubic	cubic	ADV
ejpam-6498	2	19	bézier	bézier	ADP
ejpam-6498	2	20	curves	curve	NOUN
ejpam-6498	2	21	.	.	PUNCT
ejpam-6498	3	1	by	by	ADP
ejpam-6498	3	2	matching	match	VERB
ejpam-6498	3	3	endpoints	endpoint	NOUN
ejpam-6498	3	4	and	and	CCONJ
ejpam-6498	3	5	tangents	tangent	NOUN
ejpam-6498	3	6	while	while	SCONJ
ejpam-6498	3	7	analytically	analytically	ADV
ejpam-6498	3	8	determining	determine	VERB
ejpam-6498	3	9	free	free	ADJ
ejpam-6498	3	10	parameters	parameter	NOUN
ejpam-6498	3	11	via	via	ADP
ejpam-6498	3	12	midpoint	midpoint	NOUN
ejpam-6498	3	13	interpolation	interpolation	NOUN
ejpam-6498	3	14	,	,	PUNCT
ejpam-6498	3	15	the	the	DET
ejpam-6498	3	16	method	method	NOUN
ejpam-6498	3	17	achieves	achieve	VERB
ejpam-6498	3	18	unprecedented	unprecedented	ADJ
ejpam-6498	3	19	accuracy	accuracy	NOUN
ejpam-6498	3	20	and	and	CCONJ
ejpam-6498	3	21	efficiency	efficiency	NOUN
ejpam-6498	3	22	.	.	PUNCT
ejpam-6498	4	1	for	for	ADP
ejpam-6498	4	2	elliptic	elliptic	ADJ
ejpam-6498	4	3	arcs	arc	NOUN
ejpam-6498	4	4	,	,	PUNCT
ejpam-6498	4	5	it	it	PRON
ejpam-6498	4	6	delivers	deliver	VERB
ejpam-6498	4	7	tenth	tenth	ADJ
ejpam-6498	4	8	-	-	PUNCT
ejpam-6498	4	9	order	order	NOUN
ejpam-6498	4	10	convergence	convergence	NOUN
ejpam-6498	4	11	with	with	ADP
ejpam-6498	4	12	a	a	DET
ejpam-6498	4	13	maximum	maximum	ADJ
ejpam-6498	4	14	absolute	absolute	ADJ
ejpam-6498	4	15	error	error	NOUN
ejpam-6498	4	16	of	of	ADP
ejpam-6498	4	17	just	just	ADV
ejpam-6498	4	18	1.2	1.2	NUM
ejpam-6498	4	19	×	×	NOUN
ejpam-6498	4	20	10−3	10−3	NUM
ejpam-6498	4	21	.	.	PUNCT
ejpam-6498	5	1	parabolic	parabolic	ADJ
ejpam-6498	5	2	arcs	arc	NOUN
ejpam-6498	5	3	are	be	AUX
ejpam-6498	5	4	reconstructed	reconstruct	VERB
ejpam-6498	5	5	exactly	exactly	ADV
ejpam-6498	5	6	with	with	ADP
ejpam-6498	5	7	machine	machine	NOUN
ejpam-6498	5	8	-	-	PUNCT
ejpam-6498	5	9	level	level	NOUN
ejpam-6498	5	10	accuracy	accuracy	NOUN
ejpam-6498	5	11	(	(	PUNCT
ejpam-6498	5	12	3.55×	3.55×	NUM
ejpam-6498	5	13	10−15	10−15	NUM
ejpam-6498	5	14	error	error	NOUN
ejpam-6498	5	15	)	)	PUNCT
ejpam-6498	5	16	.	.	PUNCT
ejpam-6498	6	1	the	the	DET
ejpam-6498	6	2	approach	approach	NOUN
ejpam-6498	6	3	maintains	maintain	VERB
ejpam-6498	6	4	computational	computational	ADJ
ejpam-6498	6	5	efficiency	efficiency	NOUN
ejpam-6498	6	6	,	,	PUNCT
ejpam-6498	6	7	processing	process	VERB
ejpam-6498	6	8	all	all	DET
ejpam-6498	6	9	cases	case	NOUN
ejpam-6498	6	10	in	in	ADP
ejpam-6498	6	11	under	under	ADP
ejpam-6498	6	12	1.5	1.5	NUM
ejpam-6498	6	13	seconds	second	NOUN
ejpam-6498	6	14	without	without	ADP
ejpam-6498	6	15	requiring	require	VERB
ejpam-6498	6	16	optimization	optimization	NOUN
ejpam-6498	6	17	or	or	CCONJ
ejpam-6498	6	18	rational	rational	ADJ
ejpam-6498	6	19	forms	form	NOUN
ejpam-6498	6	20	.	.	PUNCT
ejpam-6498	7	1	its	its	PRON
ejpam-6498	7	2	combination	combination	NOUN
ejpam-6498	7	3	of	of	ADP
ejpam-6498	7	4	mathematical	mathematical	ADJ
ejpam-6498	7	5	simplicity	simplicity	NOUN
ejpam-6498	7	6	,	,	PUNCT
ejpam-6498	7	7	superior	superior	ADJ
ejpam-6498	7	8	accuracy	accuracy	NOUN
ejpam-6498	7	9	,	,	PUNCT
ejpam-6498	7	10	and	and	CCONJ
ejpam-6498	7	11	rapid	rapid	ADJ
ejpam-6498	7	12	execution	execution	NOUN
ejpam-6498	7	13	makes	make	VERB
ejpam-6498	7	14	it	it	PRON
ejpam-6498	7	15	ideal	ideal	ADJ
ejpam-6498	7	16	for	for	ADP
ejpam-6498	7	17	cad	cad	NOUN
ejpam-6498	7	18	applications	application	NOUN
ejpam-6498	7	19	where	where	SCONJ
ejpam-6498	7	20	both	both	DET
ejpam-6498	7	21	precision	precision	NOUN
ejpam-6498	7	22	and	and	CCONJ
ejpam-6498	7	23	performance	performance	NOUN
ejpam-6498	7	24	are	be	AUX
ejpam-6498	7	25	critical	critical	ADJ
ejpam-6498	7	26	.	.	PUNCT
ejpam-6498	8	1	the	the	DET
ejpam-6498	8	2	robustness	robustness	NOUN
ejpam-6498	8	3	of	of	ADP
ejpam-6498	8	4	the	the	DET
ejpam-6498	8	5	proposed	propose	VERB
ejpam-6498	8	6	method	method	NOUN
ejpam-6498	8	7	under	under	ADP
ejpam-6498	8	8	geometric	geometric	ADJ
ejpam-6498	8	9	transformations	transformation	NOUN
ejpam-6498	8	10	and	and	CCONJ
ejpam-6498	8	11	seamless	seamless	ADJ
ejpam-6498	8	12	scalability	scalability	NOUN
ejpam-6498	8	13	to	to	ADP
ejpam-6498	8	14	3d	3d	PROPN
ejpam-6498	8	15	surfaces	surface	NOUN
ejpam-6498	8	16	further	far	ADV
ejpam-6498	8	17	demonstrate	demonstrate	VERB
ejpam-6498	8	18	its	its	PRON
ejpam-6498	8	19	practical	practical	ADJ
ejpam-6498	8	20	value	value	NOUN
ejpam-6498	8	21	for	for	ADP
ejpam-6498	8	22	industrial	industrial	ADJ
ejpam-6498	8	23	applications	application	NOUN
ejpam-6498	8	24	.	.	PUNCT
ejpam-6498	9	1	2020	2020	NUM
ejpam-6498	9	2	mathematics	mathematic	NOUN
ejpam-6498	9	3	subject	subject	NOUN
ejpam-6498	9	4	classifications	classification	NOUN
ejpam-6498	9	5	:	:	PUNCT
ejpam-6498	9	6	65d05	65d05	NUM
ejpam-6498	9	7	,	,	PUNCT
ejpam-6498	9	8	65d07	65d07	NUM
ejpam-6498	9	9	,	,	PUNCT
ejpam-6498	9	10	65d15	65d15	NUM
ejpam-6498	9	11	,	,	PUNCT
ejpam-6498	9	12	65d17	65d17	NUM
ejpam-6498	9	13	,	,	PUNCT
ejpam-6498	9	14	65d18	65d18	NUM
ejpam-6498	9	15	key	key	ADJ
ejpam-6498	9	16	words	word	NOUN
ejpam-6498	9	17	and	and	CCONJ
ejpam-6498	9	18	phrases	phrase	NOUN
ejpam-6498	9	19	:	:	PUNCT
ejpam-6498	9	20	conic	conic	ADJ
ejpam-6498	9	21	section	section	NOUN
ejpam-6498	9	22	approximation	approximation	NOUN
ejpam-6498	9	23	,	,	PUNCT
ejpam-6498	9	24	cubic	cubic	ADJ
ejpam-6498	9	25	bézier	bézier	ADP
ejpam-6498	9	26	curve	curve	NOUN
ejpam-6498	9	27	,	,	PUNCT
ejpam-6498	9	28	tangent	tangent	ADJ
ejpam-6498	9	29	continuity	continuity	NOUN
ejpam-6498	9	30	,	,	PUNCT
ejpam-6498	9	31	absolute	absolute	ADJ
ejpam-6498	9	32	approximation	approximation	NOUN
ejpam-6498	9	33	error	error	NOUN
ejpam-6498	9	34	,	,	PUNCT
ejpam-6498	9	35	approximation	approximation	NOUN
ejpam-6498	9	36	order	order	NOUN
ejpam-6498	9	37	,	,	PUNCT
ejpam-6498	9	38	optimization	optimization	NOUN
ejpam-6498	9	39	-	-	PUNCT
ejpam-6498	9	40	free	free	ADJ
ejpam-6498	9	41	method	method	NOUN
ejpam-6498	9	42	,	,	PUNCT
ejpam-6498	9	43	cad	cad	PROPN
ejpam-6498	9	44	curve	curve	NOUN
ejpam-6498	9	45	fitting	fit	VERB
ejpam-6498	9	46	1	1	NUM
ejpam-6498	9	47	.	.	PUNCT
ejpam-6498	10	1	introduction	introduction	NOUN
ejpam-6498	10	2	conic	conic	ADJ
ejpam-6498	10	3	sections	section	NOUN
ejpam-6498	10	4	are	be	AUX
ejpam-6498	10	5	fundamental	fundamental	ADJ
ejpam-6498	10	6	to	to	ADP
ejpam-6498	10	7	computer	computer	NOUN
ejpam-6498	10	8	-	-	PUNCT
ejpam-6498	10	9	aided	aid	VERB
ejpam-6498	10	10	design	design	NOUN
ejpam-6498	10	11	(	(	PUNCT
ejpam-6498	10	12	cad	cad	NOUN
ejpam-6498	10	13	)	)	PUNCT
ejpam-6498	10	14	due	due	ADP
ejpam-6498	10	15	to	to	ADP
ejpam-6498	10	16	their	their	PRON
ejpam-6498	10	17	wideranging	wideranging	NOUN
ejpam-6498	10	18	applications	application	NOUN
ejpam-6498	10	19	in	in	ADP
ejpam-6498	10	20	mechanical	mechanical	ADJ
ejpam-6498	10	21	component	component	NOUN
ejpam-6498	10	22	modelling	modelling	NOUN
ejpam-6498	10	23	,	,	PUNCT
ejpam-6498	10	24	typography	typography	NOUN
ejpam-6498	10	25	,	,	PUNCT
ejpam-6498	10	26	route	route	NOUN
ejpam-6498	10	27	planning	planning	NOUN
ejpam-6498	10	28	,	,	PUNCT
ejpam-6498	10	29	satellite	satellite	NOUN
ejpam-6498	10	30	navigation	navigation	NOUN
ejpam-6498	10	31	,	,	PUNCT
ejpam-6498	10	32	optical	optical	ADJ
ejpam-6498	10	33	systems	system	NOUN
ejpam-6498	10	34	,	,	PUNCT
ejpam-6498	10	35	and	and	CCONJ
ejpam-6498	10	36	even	even	ADV
ejpam-6498	10	37	medical	medical	ADJ
ejpam-6498	10	38	technologies	technology	NOUN
ejpam-6498	10	39	such	such	ADJ
ejpam-6498	10	40	as	as	ADP
ejpam-6498	10	41	lithotripsy	lithotripsy	NOUN
ejpam-6498	10	42	[	[	X
ejpam-6498	10	43	1	1	NUM
ejpam-6498	10	44	,	,	PUNCT
ejpam-6498	10	45	2	2	NUM
ejpam-6498	10	46	]	]	PUNCT
ejpam-6498	10	47	.	.	PUNCT
ejpam-6498	11	1	despite	despite	SCONJ
ejpam-6498	11	2	their	their	PRON
ejpam-6498	11	3	geometric	geometric	ADJ
ejpam-6498	11	4	importance	importance	NOUN
ejpam-6498	11	5	,	,	PUNCT
ejpam-6498	11	6	conic	conic	ADJ
ejpam-6498	11	7	sections	section	NOUN
ejpam-6498	11	8	can	can	AUX
ejpam-6498	11	9	not	not	PART
ejpam-6498	11	10	be	be	AUX
ejpam-6498	11	11	directly	directly	ADV
ejpam-6498	11	12	represented	represent	VERB
ejpam-6498	11	13	in	in	ADP
ejpam-6498	11	14	polynomial	polynomial	ADJ
ejpam-6498	11	15	-	-	PUNCT
ejpam-6498	11	16	based	base	VERB
ejpam-6498	11	17	cad	cad	NOUN
ejpam-6498	11	18	systems	system	NOUN
ejpam-6498	11	19	due	due	ADP
ejpam-6498	11	20	to	to	ADP
ejpam-6498	11	21	their	their	PRON
ejpam-6498	11	22	non	non	ADJ
ejpam-6498	11	23	-	-	ADJ
ejpam-6498	11	24	polynomial	polynomial	ADJ
ejpam-6498	11	25	nature	nature	NOUN
ejpam-6498	11	26	.	.	PUNCT
ejpam-6498	12	1	to	to	PART
ejpam-6498	12	2	overcome	overcome	VERB
ejpam-6498	12	3	this	this	DET
ejpam-6498	12	4	limitation	limitation	NOUN
ejpam-6498	12	5	,	,	PUNCT
ejpam-6498	12	6	bézier	bézier	SCONJ
ejpam-6498	12	7	curves	curve	NOUN
ejpam-6498	12	8	widely	widely	ADV
ejpam-6498	12	9	supported	support	VERB
ejpam-6498	12	10	in	in	ADP
ejpam-6498	12	11	cad	cad	PROPN
ejpam-6498	12	12	software	software	NOUN
ejpam-6498	12	13	are	be	AUX
ejpam-6498	12	14	often	often	ADV
ejpam-6498	12	15	used	use	VERB
ejpam-6498	12	16	to	to	PART
ejpam-6498	12	17	approximate	approximate	VERB
ejpam-6498	12	18	conic	conic	ADJ
ejpam-6498	12	19	arcs	arc	NOUN
ejpam-6498	13	1	[	[	X
ejpam-6498	13	2	3–5	3–5	NOUN
ejpam-6498	13	3	]	]	PUNCT
ejpam-6498	13	4	.	.	PUNCT
ejpam-6498	14	1	∗corresponding	∗corresponde	VERB
ejpam-6498	14	2	author	author	NOUN
ejpam-6498	14	3	.	.	PUNCT
ejpam-6498	15	1	doi	doi	NOUN
ejpam-6498	15	2	:	:	PUNCT
ejpam-6498	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6498	https://doi.org/10.29020/nybg.ejpam.v18i4.6498	VERB
ejpam-6498	15	4	email	email	NOUN
ejpam-6498	15	5	address	address	NOUN
ejpam-6498	15	6	:	:	PUNCT
ejpam-6498	15	7	hawajid@iu.edu.sa	hawajid@iu.edu.sa	PROPN
ejpam-6498	15	8	(	(	PUNCT
ejpam-6498	15	9	h.	h.	PROPN
ejpam-6498	15	10	a.	a.	PROPN
ejpam-6498	15	11	wajid	wajid	PROPN
ejpam-6498	15	12	)	)	PUNCT
ejpam-6498	15	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6498	16	1	1	1	NUM
ejpam-6498	16	2	copyright	copyright	NOUN
ejpam-6498	16	3	:	:	PUNCT
ejpam-6498	16	4	©	©	PROPN
ejpam-6498	16	5	2025	2025	NUM
ejpam-6498	16	6	the	the	DET
ejpam-6498	16	7	author(s	author(s	NOUN
ejpam-6498	16	8	)	)	PUNCT
ejpam-6498	16	9	.	.	PUNCT
ejpam-6498	17	1	(	(	PUNCT
ejpam-6498	17	2	cc	cc	NOUN
ejpam-6498	17	3	by	by	ADP
ejpam-6498	17	4	-	-	PUNCT
ejpam-6498	17	5	nc	nc	PROPN
ejpam-6498	17	6	4.0	4.0	NUM
ejpam-6498	17	7	)	)	PUNCT
ejpam-6498	17	8	m.	m.	NOUN
ejpam-6498	17	9	hussain	hussain	PROPN
ejpam-6498	17	10	,	,	PUNCT
ejpam-6498	17	11	h.	h.	PROPN
ejpam-6498	17	12	a.	a.	PROPN
ejpam-6498	17	13	wajid	wajid	PROPN
ejpam-6498	17	14	,	,	PUNCT
ejpam-6498	17	15	s.	s.	PROPN
ejpam-6498	17	16	aqeel	aqeel	PROPN
ejpam-6498	17	17	/	/	SYM
ejpam-6498	17	18	eur	eur	PROPN
ejpam-6498	17	19	.	.	PUNCT
ejpam-6498	18	1	j.	j.	PROPN
ejpam-6498	18	2	pure	pure	PROPN
ejpam-6498	18	3	appl	appl	PROPN
ejpam-6498	18	4	.	.	PROPN
ejpam-6498	18	5	math	math	PROPN
ejpam-6498	18	6	,	,	PUNCT
ejpam-6498	18	7	18	18	NUM
ejpam-6498	18	8	(	(	PUNCT
ejpam-6498	18	9	4	4	NUM
ejpam-6498	18	10	)	)	PUNCT
ejpam-6498	18	11	(	(	PUNCT
ejpam-6498	18	12	2025	2025	NUM
ejpam-6498	18	13	)	)	PUNCT
ejpam-6498	18	14	,	,	PUNCT
ejpam-6498	18	15	6498	6498	NUM
ejpam-6498	18	16	2	2	NUM
ejpam-6498	18	17	of	of	ADP
ejpam-6498	18	18	12	12	NUM
ejpam-6498	18	19	among	among	ADP
ejpam-6498	18	20	the	the	DET
ejpam-6498	18	21	bézier	bézier	PROPN
ejpam-6498	18	22	families	family	NOUN
ejpam-6498	18	23	,	,	PUNCT
ejpam-6498	18	24	rational	rational	ADJ
ejpam-6498	18	25	quadratic	quadratic	ADJ
ejpam-6498	18	26	bézier	bézier	ADP
ejpam-6498	18	27	curves	curve	NOUN
ejpam-6498	18	28	(	(	PUNCT
ejpam-6498	18	29	rqbcs	rqbc	NOUN
ejpam-6498	18	30	)	)	PUNCT
ejpam-6498	18	31	can	can	AUX
ejpam-6498	18	32	represent	represent	VERB
ejpam-6498	18	33	conics	conic	NOUN
ejpam-6498	18	34	exactly	exactly	ADV
ejpam-6498	18	35	by	by	ADP
ejpam-6498	18	36	adjusting	adjust	VERB
ejpam-6498	18	37	control	control	NOUN
ejpam-6498	18	38	point	point	NOUN
ejpam-6498	18	39	weights	weight	NOUN
ejpam-6498	18	40	.	.	PUNCT
ejpam-6498	19	1	existing	exist	VERB
ejpam-6498	19	2	techniques	technique	NOUN
ejpam-6498	19	3	[	[	X
ejpam-6498	19	4	6–8	6–8	X
ejpam-6498	19	5	]	]	X
ejpam-6498	19	6	typically	typically	ADV
ejpam-6498	19	7	follow	follow	VERB
ejpam-6498	19	8	a	a	DET
ejpam-6498	19	9	multi	multi	ADJ
ejpam-6498	19	10	-	-	ADJ
ejpam-6498	19	11	step	step	ADJ
ejpam-6498	19	12	approach	approach	NOUN
ejpam-6498	19	13	:	:	PUNCT
ejpam-6498	19	14	first	first	ADV
ejpam-6498	19	15	reconstructing	reconstruct	VERB
ejpam-6498	19	16	the	the	DET
ejpam-6498	19	17	conic	conic	ADJ
ejpam-6498	19	18	arc	arc	NOUN
ejpam-6498	19	19	using	use	VERB
ejpam-6498	19	20	an	an	DET
ejpam-6498	19	21	rqbc	rqbc	NOUN
ejpam-6498	19	22	,	,	PUNCT
ejpam-6498	19	23	then	then	ADV
ejpam-6498	19	24	applying	apply	VERB
ejpam-6498	19	25	further	further	ADJ
ejpam-6498	19	26	approximation	approximation	NOUN
ejpam-6498	19	27	,	,	PUNCT
ejpam-6498	19	28	and	and	CCONJ
ejpam-6498	19	29	finally	finally	ADV
ejpam-6498	19	30	visualizing	visualize	VERB
ejpam-6498	19	31	the	the	DET
ejpam-6498	19	32	result	result	NOUN
ejpam-6498	19	33	.	.	PUNCT
ejpam-6498	20	1	however	however	ADV
ejpam-6498	20	2	,	,	PUNCT
ejpam-6498	20	3	such	such	ADJ
ejpam-6498	20	4	indirect	indirect	ADJ
ejpam-6498	20	5	methods	method	NOUN
ejpam-6498	20	6	suffer	suffer	VERB
ejpam-6498	20	7	from	from	ADP
ejpam-6498	20	8	non	non	ADJ
ejpam-6498	20	9	-	-	ADJ
ejpam-6498	20	10	uniqueness	uniqueness	ADJ
ejpam-6498	20	11	in	in	ADP
ejpam-6498	20	12	weight	weight	NOUN
ejpam-6498	20	13	selection	selection	NOUN
ejpam-6498	20	14	and	and	CCONJ
ejpam-6498	20	15	often	often	ADV
ejpam-6498	20	16	rely	rely	VERB
ejpam-6498	20	17	on	on	ADP
ejpam-6498	20	18	iterative	iterative	NOUN
ejpam-6498	20	19	tuning	tuning	NOUN
ejpam-6498	20	20	,	,	PUNCT
ejpam-6498	20	21	which	which	PRON
ejpam-6498	20	22	complicates	complicate	VERB
ejpam-6498	20	23	practical	practical	ADJ
ejpam-6498	20	24	implementation	implementation	NOUN
ejpam-6498	20	25	.	.	PUNCT
ejpam-6498	21	1	more	more	ADJ
ejpam-6498	21	2	recent	recent	ADJ
ejpam-6498	21	3	efforts	effort	NOUN
ejpam-6498	21	4	have	have	AUX
ejpam-6498	21	5	been	be	AUX
ejpam-6498	21	6	made	make	VERB
ejpam-6498	21	7	to	to	PART
ejpam-6498	21	8	simplify	simplify	VERB
ejpam-6498	21	9	this	this	DET
ejpam-6498	21	10	process	process	NOUN
ejpam-6498	21	11	.	.	PUNCT
ejpam-6498	22	1	some	some	DET
ejpam-6498	22	2	researchers	researcher	NOUN
ejpam-6498	22	3	have	have	AUX
ejpam-6498	22	4	proposed	propose	VERB
ejpam-6498	22	5	polynomial	polynomial	ADJ
ejpam-6498	22	6	-	-	PUNCT
ejpam-6498	22	7	based	base	VERB
ejpam-6498	22	8	direct	direct	ADJ
ejpam-6498	22	9	approximations	approximation	NOUN
ejpam-6498	22	10	that	that	PRON
ejpam-6498	22	11	bypass	bypass	VERB
ejpam-6498	22	12	the	the	DET
ejpam-6498	22	13	rqbc	rqbc	NOUN
ejpam-6498	22	14	stage	stage	NOUN
ejpam-6498	22	15	[	[	X
ejpam-6498	22	16	1	1	NUM
ejpam-6498	22	17	,	,	PUNCT
ejpam-6498	22	18	9	9	NUM
ejpam-6498	22	19	]	]	PUNCT
ejpam-6498	22	20	,	,	PUNCT
ejpam-6498	22	21	but	but	CCONJ
ejpam-6498	22	22	many	many	ADJ
ejpam-6498	22	23	of	of	ADP
ejpam-6498	22	24	these	these	PRON
ejpam-6498	22	25	still	still	ADV
ejpam-6498	22	26	involve	involve	VERB
ejpam-6498	22	27	optimization	optimization	NOUN
ejpam-6498	22	28	procedures	procedure	NOUN
ejpam-6498	22	29	to	to	PART
ejpam-6498	22	30	determine	determine	VERB
ejpam-6498	22	31	free	free	ADJ
ejpam-6498	22	32	parameters	parameter	NOUN
ejpam-6498	22	33	,	,	PUNCT
ejpam-6498	22	34	limiting	limit	VERB
ejpam-6498	22	35	computational	computational	ADJ
ejpam-6498	22	36	efficiency	efficiency	NOUN
ejpam-6498	22	37	.	.	PUNCT
ejpam-6498	23	1	others	other	NOUN
ejpam-6498	23	2	,	,	PUNCT
ejpam-6498	23	3	such	such	ADJ
ejpam-6498	23	4	as	as	ADP
ejpam-6498	23	5	sánchez	sánchez	PROPN
ejpam-6498	23	6	-	-	PUNCT
ejpam-6498	23	7	reyes	reyes	PROPN
ejpam-6498	23	8	,	,	PUNCT
ejpam-6498	23	9	proposed	propose	VERB
ejpam-6498	23	10	rational	rational	ADJ
ejpam-6498	23	11	cubic	cubic	ADJ
ejpam-6498	23	12	representations	representation	NOUN
ejpam-6498	23	13	[	[	X
ejpam-6498	23	14	10	10	NUM
ejpam-6498	23	15	]	]	PUNCT
ejpam-6498	23	16	,	,	PUNCT
ejpam-6498	23	17	yet	yet	CCONJ
ejpam-6498	23	18	rationality	rationality	NOUN
ejpam-6498	23	19	still	still	ADV
ejpam-6498	23	20	entails	entail	VERB
ejpam-6498	23	21	weight	weight	NOUN
ejpam-6498	23	22	dependency	dependency	NOUN
ejpam-6498	23	23	.	.	PUNCT
ejpam-6498	24	1	nawara	nawara	PROPN
ejpam-6498	25	1	[	[	X
ejpam-6498	25	2	11	11	NUM
ejpam-6498	25	3	]	]	X
ejpam-6498	25	4	determined	determine	VERB
ejpam-6498	25	5	osculating	osculate	VERB
ejpam-6498	25	6	conics	conic	NOUN
ejpam-6498	25	7	and	and	CCONJ
ejpam-6498	25	8	sextactic	sextactic	ADJ
ejpam-6498	25	9	points	point	NOUN
ejpam-6498	25	10	for	for	ADP
ejpam-6498	25	11	cubic	cubic	ADJ
ejpam-6498	25	12	curves	curve	NOUN
ejpam-6498	25	13	known	know	VERB
ejpam-6498	25	14	as	as	ADP
ejpam-6498	25	15	hesse	hesse	PROPN
ejpam-6498	25	16	pencil	pencil	PROPN
ejpam-6498	25	17	.	.	PUNCT
ejpam-6498	26	1	hwang	hwang	PROPN
ejpam-6498	26	2	and	and	CCONJ
ejpam-6498	26	3	li	li	PROPN
ejpam-6498	27	1	[	[	X
ejpam-6498	27	2	12	12	NUM
ejpam-6498	27	3	]	]	PUNCT
ejpam-6498	27	4	formulated	formulate	VERB
ejpam-6498	27	5	the	the	DET
ejpam-6498	27	6	sufficient	sufficient	ADJ
ejpam-6498	27	7	conditions	condition	NOUN
ejpam-6498	27	8	for	for	ADP
ejpam-6498	27	9	which	which	PRON
ejpam-6498	27	10	the	the	DET
ejpam-6498	27	11	existence	existence	NOUN
ejpam-6498	27	12	of	of	ADP
ejpam-6498	27	13	a	a	DET
ejpam-6498	27	14	characteristic	characteristic	ADJ
ejpam-6498	27	15	conic	conic	ADJ
ejpam-6498	27	16	connection	connection	NOUN
ejpam-6498	27	17	implies	imply	VERB
ejpam-6498	27	18	the	the	DET
ejpam-6498	27	19	existence	existence	NOUN
ejpam-6498	27	20	of	of	ADP
ejpam-6498	27	21	a	a	DET
ejpam-6498	27	22	torsion	torsion	NOUN
ejpam-6498	27	23	-	-	PUNCT
ejpam-6498	27	24	free	free	ADJ
ejpam-6498	27	25	principal	principal	ADJ
ejpam-6498	27	26	connection	connection	NOUN
ejpam-6498	27	27	.	.	PUNCT
ejpam-6498	28	1	this	this	DET
ejpam-6498	28	2	study	study	NOUN
ejpam-6498	28	3	introduces	introduce	VERB
ejpam-6498	28	4	a	a	DET
ejpam-6498	28	5	direct	direct	ADJ
ejpam-6498	28	6	,	,	PUNCT
ejpam-6498	28	7	optimization	optimization	NOUN
ejpam-6498	28	8	-	-	PUNCT
ejpam-6498	28	9	free	free	ADJ
ejpam-6498	28	10	approximation	approximation	NOUN
ejpam-6498	28	11	method	method	NOUN
ejpam-6498	28	12	using	use	VERB
ejpam-6498	28	13	cubic	cubic	ADV
ejpam-6498	28	14	bézier	bézier	ADP
ejpam-6498	28	15	curves	curve	NOUN
ejpam-6498	28	16	which	which	PRON
ejpam-6498	28	17	are	be	AUX
ejpam-6498	28	18	the	the	DET
ejpam-6498	28	19	lowest	low	ADJ
ejpam-6498	28	20	-	-	PUNCT
ejpam-6498	28	21	degree	degree	NOUN
ejpam-6498	28	22	polynomial	polynomial	NOUN
ejpam-6498	28	23	bézier	bézier	ADP
ejpam-6498	28	24	curves	curve	NOUN
ejpam-6498	28	25	capable	capable	ADJ
ejpam-6498	28	26	of	of	ADP
ejpam-6498	28	27	ensuring	ensure	VERB
ejpam-6498	28	28	tangent	tangent	NOUN
ejpam-6498	28	29	continuity	continuity	NOUN
ejpam-6498	28	30	.	.	PUNCT
ejpam-6498	29	1	the	the	DET
ejpam-6498	29	2	method	method	NOUN
ejpam-6498	29	3	constructs	construct	VERB
ejpam-6498	29	4	the	the	DET
ejpam-6498	29	5	curve	curve	NOUN
ejpam-6498	29	6	by	by	ADP
ejpam-6498	29	7	matching	match	VERB
ejpam-6498	29	8	endpoint	endpoint	NOUN
ejpam-6498	29	9	positions	position	NOUN
ejpam-6498	29	10	and	and	CCONJ
ejpam-6498	29	11	tangents	tangent	NOUN
ejpam-6498	29	12	and	and	CCONJ
ejpam-6498	29	13	computes	compute	VERB
ejpam-6498	29	14	the	the	DET
ejpam-6498	29	15	two	two	NUM
ejpam-6498	29	16	free	free	ADJ
ejpam-6498	29	17	parameters	parameter	NOUN
ejpam-6498	29	18	using	use	VERB
ejpam-6498	29	19	a	a	DET
ejpam-6498	29	20	midpoint	midpoint	NOUN
ejpam-6498	29	21	interpolation	interpolation	NOUN
ejpam-6498	29	22	condition	condition	NOUN
ejpam-6498	29	23	.	.	PUNCT
ejpam-6498	30	1	this	this	DET
ejpam-6498	30	2	approach	approach	NOUN
ejpam-6498	30	3	not	not	PART
ejpam-6498	30	4	only	only	ADV
ejpam-6498	30	5	simplifies	simplify	VERB
ejpam-6498	30	6	the	the	DET
ejpam-6498	30	7	control	control	NOUN
ejpam-6498	30	8	point	point	NOUN
ejpam-6498	30	9	calculation	calculation	NOUN
ejpam-6498	30	10	but	but	CCONJ
ejpam-6498	30	11	also	also	ADV
ejpam-6498	30	12	yields	yield	VERB
ejpam-6498	30	13	a	a	DET
ejpam-6498	30	14	high	high	ADJ
ejpam-6498	30	15	approximation	approximation	NOUN
ejpam-6498	30	16	order	order	NOUN
ejpam-6498	30	17	(	(	PUNCT
ejpam-6498	30	18	ten	ten	NUM
ejpam-6498	30	19	for	for	ADP
ejpam-6498	30	20	elliptic	elliptic	ADJ
ejpam-6498	30	21	arcs	arc	NOUN
ejpam-6498	30	22	)	)	PUNCT
ejpam-6498	30	23	and	and	CCONJ
ejpam-6498	30	24	exact	exact	ADJ
ejpam-6498	30	25	reconstruction	reconstruction	NOUN
ejpam-6498	30	26	for	for	ADP
ejpam-6498	30	27	parabolic	parabolic	ADJ
ejpam-6498	30	28	arcs	arc	NOUN
ejpam-6498	30	29	.	.	PUNCT
ejpam-6498	31	1	compared	compare	VERB
ejpam-6498	31	2	to	to	ADP
ejpam-6498	31	3	existing	exist	VERB
ejpam-6498	31	4	methods	method	NOUN
ejpam-6498	31	5	,	,	PUNCT
ejpam-6498	31	6	the	the	DET
ejpam-6498	31	7	proposed	propose	VERB
ejpam-6498	31	8	method	method	NOUN
ejpam-6498	31	9	offers	offer	VERB
ejpam-6498	31	10	three	three	NUM
ejpam-6498	31	11	key	key	ADJ
ejpam-6498	31	12	advantages	advantage	NOUN
ejpam-6498	31	13	:	:	PUNCT
ejpam-6498	31	14	(	(	PUNCT
ejpam-6498	31	15	i	i	NOUN
ejpam-6498	31	16	)	)	PUNCT
ejpam-6498	31	17	it	it	PRON
ejpam-6498	31	18	avoids	avoid	VERB
ejpam-6498	31	19	weight	weight	NOUN
ejpam-6498	31	20	tuning	tuning	NOUN
ejpam-6498	31	21	and	and	CCONJ
ejpam-6498	31	22	guarantees	guarantee	VERB
ejpam-6498	31	23	a	a	DET
ejpam-6498	31	24	unique	unique	ADJ
ejpam-6498	31	25	control	control	NOUN
ejpam-6498	31	26	point	point	NOUN
ejpam-6498	31	27	configuration	configuration	NOUN
ejpam-6498	31	28	unlike	unlike	ADP
ejpam-6498	31	29	rqbc	rqbc	NOUN
ejpam-6498	31	30	-	-	PUNCT
ejpam-6498	31	31	based	base	VERB
ejpam-6498	31	32	techniques	technique	NOUN
ejpam-6498	31	33	[	[	X
ejpam-6498	31	34	6–8	6–8	X
ejpam-6498	31	35	]	]	X
ejpam-6498	31	36	.	.	PUNCT
ejpam-6498	32	1	(	(	PUNCT
ejpam-6498	32	2	ii	ii	X
ejpam-6498	32	3	)	)	PUNCT
ejpam-6498	32	4	it	it	PRON
ejpam-6498	32	5	has	have	VERB
ejpam-6498	32	6	lower	low	ADJ
ejpam-6498	32	7	computational	computational	ADJ
ejpam-6498	32	8	overhead	overhead	NOUN
ejpam-6498	32	9	,	,	PUNCT
ejpam-6498	32	10	making	make	VERB
ejpam-6498	32	11	it	it	PRON
ejpam-6498	32	12	more	more	ADV
ejpam-6498	32	13	suitable	suitable	ADJ
ejpam-6498	32	14	for	for	ADP
ejpam-6498	32	15	real	real	ADJ
ejpam-6498	32	16	-	-	PUNCT
ejpam-6498	32	17	time	time	NOUN
ejpam-6498	32	18	cad	cad	PROPN
ejpam-6498	32	19	applications	application	NOUN
ejpam-6498	32	20	unlike	unlike	ADP
ejpam-6498	32	21	optimization	optimization	NOUN
ejpam-6498	32	22	-	-	PUNCT
ejpam-6498	32	23	based	base	VERB
ejpam-6498	32	24	methods	method	NOUN
ejpam-6498	32	25	[	[	X
ejpam-6498	32	26	9	9	NUM
ejpam-6498	32	27	,	,	PUNCT
ejpam-6498	32	28	10	10	NUM
ejpam-6498	32	29	]	]	PUNCT
ejpam-6498	32	30	.	.	PUNCT
ejpam-6498	33	1	(	(	PUNCT
ejpam-6498	33	2	iii	iii	X
ejpam-6498	33	3	)	)	PUNCT
ejpam-6498	33	4	it	it	PRON
ejpam-6498	33	5	outperforms	outperform	VERB
ejpam-6498	33	6	several	several	ADJ
ejpam-6498	33	7	established	establish	VERB
ejpam-6498	33	8	methods	method	NOUN
ejpam-6498	33	9	[	[	X
ejpam-6498	33	10	4	4	NUM
ejpam-6498	33	11	,	,	PUNCT
ejpam-6498	33	12	6	6	NUM
ejpam-6498	33	13	,	,	PUNCT
ejpam-6498	33	14	9	9	NUM
ejpam-6498	33	15	,	,	PUNCT
ejpam-6498	33	16	10	10	NUM
ejpam-6498	33	17	]	]	PUNCT
ejpam-6498	33	18	in	in	ADP
ejpam-6498	33	19	terms	term	NOUN
ejpam-6498	33	20	of	of	ADP
ejpam-6498	33	21	approximation	approximation	NOUN
ejpam-6498	33	22	error	error	NOUN
ejpam-6498	33	23	.	.	PUNCT
ejpam-6498	34	1	in	in	ADP
ejpam-6498	34	2	summary	summary	NOUN
ejpam-6498	34	3	,	,	PUNCT
ejpam-6498	34	4	the	the	DET
ejpam-6498	34	5	proposed	propose	VERB
ejpam-6498	34	6	method	method	NOUN
ejpam-6498	34	7	addresses	address	NOUN
ejpam-6498	34	8	both	both	CCONJ
ejpam-6498	34	9	theoretical	theoretical	ADJ
ejpam-6498	34	10	and	and	CCONJ
ejpam-6498	34	11	practical	practical	ADJ
ejpam-6498	34	12	challenges	challenge	NOUN
ejpam-6498	34	13	in	in	ADP
ejpam-6498	34	14	conic	conic	ADJ
ejpam-6498	34	15	approximation	approximation	NOUN
ejpam-6498	34	16	.	.	PUNCT
ejpam-6498	35	1	it	it	PRON
ejpam-6498	35	2	enhances	enhance	VERB
ejpam-6498	35	3	computational	computational	ADJ
ejpam-6498	35	4	simplicity	simplicity	NOUN
ejpam-6498	35	5	without	without	ADP
ejpam-6498	35	6	sacrificing	sacrifice	VERB
ejpam-6498	35	7	accuracy	accuracy	NOUN
ejpam-6498	35	8	,	,	PUNCT
ejpam-6498	35	9	making	make	VERB
ejpam-6498	35	10	it	it	PRON
ejpam-6498	35	11	highly	highly	ADV
ejpam-6498	35	12	suitable	suitable	ADJ
ejpam-6498	35	13	for	for	ADP
ejpam-6498	35	14	integration	integration	NOUN
ejpam-6498	35	15	into	into	ADP
ejpam-6498	35	16	modern	modern	ADJ
ejpam-6498	35	17	geometric	geometric	ADJ
ejpam-6498	35	18	design	design	NOUN
ejpam-6498	35	19	systems	system	NOUN
ejpam-6498	35	20	.	.	PUNCT
ejpam-6498	36	1	this	this	DET
ejpam-6498	36	2	contribution	contribution	NOUN
ejpam-6498	36	3	provides	provide	VERB
ejpam-6498	36	4	a	a	DET
ejpam-6498	36	5	robust	robust	ADJ
ejpam-6498	36	6	and	and	CCONJ
ejpam-6498	36	7	lightweight	lightweight	ADJ
ejpam-6498	36	8	alternative	alternative	NOUN
ejpam-6498	36	9	to	to	ADP
ejpam-6498	36	10	rational	rational	ADJ
ejpam-6498	36	11	or	or	CCONJ
ejpam-6498	36	12	optimization	optimization	NOUN
ejpam-6498	36	13	-	-	PUNCT
ejpam-6498	36	14	based	base	VERB
ejpam-6498	36	15	approximations	approximation	NOUN
ejpam-6498	36	16	,	,	PUNCT
ejpam-6498	36	17	with	with	ADP
ejpam-6498	36	18	potential	potential	ADJ
ejpam-6498	36	19	implications	implication	NOUN
ejpam-6498	36	20	for	for	ADP
ejpam-6498	36	21	precision	precision	NOUN
ejpam-6498	36	22	-	-	PUNCT
ejpam-6498	36	23	critical	critical	ADJ
ejpam-6498	36	24	cad	cad	NOUN
ejpam-6498	36	25	environments	environment	NOUN
ejpam-6498	36	26	.	.	PUNCT
ejpam-6498	37	1	the	the	DET
ejpam-6498	37	2	rest	rest	NOUN
ejpam-6498	37	3	of	of	ADP
ejpam-6498	37	4	the	the	DET
ejpam-6498	37	5	paper	paper	NOUN
ejpam-6498	37	6	is	be	AUX
ejpam-6498	37	7	organized	organize	VERB
ejpam-6498	37	8	as	as	SCONJ
ejpam-6498	37	9	follows	follow	VERB
ejpam-6498	37	10	.	.	PUNCT
ejpam-6498	38	1	section	section	NOUN
ejpam-6498	38	2	2	2	NUM
ejpam-6498	38	3	introduces	introduce	NOUN
ejpam-6498	38	4	cubic	cubic	ADJ
ejpam-6498	38	5	bézier	bézier	ADP
ejpam-6498	38	6	approximation	approximation	NOUN
ejpam-6498	38	7	method	method	NOUN
ejpam-6498	38	8	for	for	ADP
ejpam-6498	38	9	conic	conic	ADJ
ejpam-6498	38	10	sections	section	NOUN
ejpam-6498	38	11	.	.	PUNCT
ejpam-6498	39	1	in	in	ADP
ejpam-6498	39	2	section	section	NOUN
ejpam-6498	39	3	3	3	NUM
ejpam-6498	39	4	,	,	PUNCT
ejpam-6498	39	5	results	result	NOUN
ejpam-6498	39	6	are	be	AUX
ejpam-6498	39	7	presented	present	VERB
ejpam-6498	39	8	solving	solve	VERB
ejpam-6498	39	9	a	a	DET
ejpam-6498	39	10	range	range	NOUN
ejpam-6498	39	11	of	of	ADP
ejpam-6498	39	12	problems	problem	NOUN
ejpam-6498	39	13	followed	follow	VERB
ejpam-6498	39	14	by	by	ADP
ejpam-6498	39	15	conclusion	conclusion	NOUN
ejpam-6498	39	16	section	section	NOUN
ejpam-6498	39	17	4	4	NUM
ejpam-6498	39	18	presenting	present	VERB
ejpam-6498	39	19	key	key	ADJ
ejpam-6498	39	20	insights	insight	NOUN
ejpam-6498	39	21	.	.	PUNCT
ejpam-6498	40	1	2	2	X
ejpam-6498	40	2	.	.	X
ejpam-6498	40	3	cubic	cubic	ADJ
ejpam-6498	40	4	bézier	bézier	ADP
ejpam-6498	40	5	approximation	approximation	NOUN
ejpam-6498	40	6	method	method	NOUN
ejpam-6498	40	7	for	for	ADP
ejpam-6498	40	8	conic	conic	ADJ
ejpam-6498	40	9	sections	section	NOUN
ejpam-6498	40	10	in	in	ADP
ejpam-6498	40	11	this	this	DET
ejpam-6498	40	12	section	section	NOUN
ejpam-6498	40	13	,	,	PUNCT
ejpam-6498	40	14	a	a	DET
ejpam-6498	40	15	new	new	ADJ
ejpam-6498	40	16	approximation	approximation	NOUN
ejpam-6498	40	17	method	method	NOUN
ejpam-6498	40	18	is	be	AUX
ejpam-6498	40	19	derived	derive	VERB
ejpam-6498	40	20	to	to	PART
ejpam-6498	40	21	approximate	approximate	ADJ
ejpam-6498	40	22	conic	conic	ADJ
ejpam-6498	40	23	sections	section	NOUN
ejpam-6498	40	24	(	(	PUNCT
ejpam-6498	40	25	ellipse	ellipse	NOUN
ejpam-6498	40	26	and	and	CCONJ
ejpam-6498	40	27	parabola	parabola	PROPN
ejpam-6498	40	28	)	)	PUNCT
ejpam-6498	40	29	by	by	ADP
ejpam-6498	40	30	the	the	DET
ejpam-6498	40	31	famous	famous	ADJ
ejpam-6498	40	32	cubic	cubic	NOUN
ejpam-6498	41	1	bézier	bézier	ADP
ejpam-6498	41	2	curve	curve	NOUN
ejpam-6498	41	3	.	.	PUNCT
ejpam-6498	42	1	the	the	DET
ejpam-6498	42	2	outline	outline	NOUN
ejpam-6498	42	3	of	of	ADP
ejpam-6498	42	4	the	the	DET
ejpam-6498	42	5	proposed	propose	VERB
ejpam-6498	42	6	m.	m.	NOUN
ejpam-6498	42	7	hussain	hussain	PROPN
ejpam-6498	42	8	,	,	PUNCT
ejpam-6498	42	9	h.	h.	PROPN
ejpam-6498	42	10	a.	a.	PROPN
ejpam-6498	42	11	wajid	wajid	PROPN
ejpam-6498	42	12	,	,	PUNCT
ejpam-6498	42	13	s.	s.	PROPN
ejpam-6498	42	14	aqeel	aqeel	PROPN
ejpam-6498	42	15	/	/	SYM
ejpam-6498	42	16	eur	eur	PROPN
ejpam-6498	42	17	.	.	PUNCT
ejpam-6498	43	1	j.	j.	PROPN
ejpam-6498	43	2	pure	pure	PROPN
ejpam-6498	43	3	appl	appl	PROPN
ejpam-6498	43	4	.	.	PROPN
ejpam-6498	43	5	math	math	PROPN
ejpam-6498	43	6	,	,	PUNCT
ejpam-6498	43	7	18	18	NUM
ejpam-6498	43	8	(	(	PUNCT
ejpam-6498	43	9	4	4	NUM
ejpam-6498	43	10	)	)	PUNCT
ejpam-6498	43	11	(	(	PUNCT
ejpam-6498	43	12	2025	2025	NUM
ejpam-6498	43	13	)	)	PUNCT
ejpam-6498	43	14	,	,	PUNCT
ejpam-6498	43	15	6498	6498	NUM
ejpam-6498	43	16	3	3	NUM
ejpam-6498	43	17	of	of	ADP
ejpam-6498	43	18	12	12	NUM
ejpam-6498	43	19	method	method	NOUN
ejpam-6498	43	20	for	for	ADP
ejpam-6498	43	21	both	both	CCONJ
ejpam-6498	43	22	elliptic	elliptic	ADJ
ejpam-6498	43	23	and	and	CCONJ
ejpam-6498	43	24	parabolic	parabolic	ADJ
ejpam-6498	43	25	arc	arc	NOUN
ejpam-6498	43	26	is	be	AUX
ejpam-6498	43	27	the	the	DET
ejpam-6498	43	28	same	same	ADJ
ejpam-6498	43	29	.	.	PUNCT
ejpam-6498	44	1	however	however	ADV
ejpam-6498	44	2	,	,	PUNCT
ejpam-6498	44	3	due	due	ADP
ejpam-6498	44	4	to	to	ADP
ejpam-6498	44	5	different	different	ADJ
ejpam-6498	44	6	tangent	tangent	NOUN
ejpam-6498	44	7	continuity	continuity	NOUN
ejpam-6498	44	8	approximation	approximation	NOUN
ejpam-6498	44	9	constraints	constraint	VERB
ejpam-6498	44	10	the	the	DET
ejpam-6498	44	11	evaluated	evaluated	ADJ
ejpam-6498	44	12	control	control	NOUN
ejpam-6498	44	13	points	point	NOUN
ejpam-6498	44	14	and	and	CCONJ
ejpam-6498	44	15	free	free	ADJ
ejpam-6498	44	16	parameters	parameter	NOUN
ejpam-6498	44	17	for	for	ADP
ejpam-6498	44	18	these	these	DET
ejpam-6498	44	19	conic	conic	ADJ
ejpam-6498	44	20	sections	section	NOUN
ejpam-6498	44	21	are	be	AUX
ejpam-6498	44	22	different	different	ADJ
ejpam-6498	44	23	.	.	PUNCT
ejpam-6498	45	1	the	the	DET
ejpam-6498	45	2	derived	derive	VERB
ejpam-6498	45	3	results	result	NOUN
ejpam-6498	45	4	for	for	ADP
ejpam-6498	45	5	the	the	DET
ejpam-6498	45	6	approximation	approximation	NOUN
ejpam-6498	45	7	of	of	ADP
ejpam-6498	45	8	elliptic	elliptic	ADJ
ejpam-6498	45	9	and	and	CCONJ
ejpam-6498	45	10	parabolic	parabolic	ADJ
ejpam-6498	45	11	arcs	arc	NOUN
ejpam-6498	45	12	are	be	AUX
ejpam-6498	45	13	stated	state	VERB
ejpam-6498	45	14	separately	separately	ADV
ejpam-6498	45	15	in	in	ADP
ejpam-6498	45	16	theorem	theorem	ADJ
ejpam-6498	45	17	1	1	NUM
ejpam-6498	45	18	and	and	CCONJ
ejpam-6498	45	19	theorem	theorem	VERB
ejpam-6498	45	20	3	3	NUM
ejpam-6498	45	21	respectively	respectively	ADV
ejpam-6498	45	22	.	.	PUNCT
ejpam-6498	46	1	computed	compute	VERB
ejpam-6498	46	2	approximation	approximation	NOUN
ejpam-6498	46	3	order	order	NOUN
ejpam-6498	46	4	of	of	ADP
ejpam-6498	46	5	these	these	DET
ejpam-6498	46	6	methods	method	NOUN
ejpam-6498	46	7	are	be	AUX
ejpam-6498	46	8	stated	state	VERB
ejpam-6498	46	9	in	in	ADP
ejpam-6498	46	10	theorem	theorem	ADJ
ejpam-6498	46	11	2	2	NUM
ejpam-6498	46	12	and	and	CCONJ
ejpam-6498	46	13	theorem	theorem	VERB
ejpam-6498	46	14	4	4	NUM
ejpam-6498	46	15	respectively	respectively	ADV
ejpam-6498	46	16	.	.	PUNCT
ejpam-6498	47	1	the	the	DET
ejpam-6498	47	2	cubic	cubic	ADJ
ejpam-6498	47	3	bézier	bézier	PROPN
ejpam-6498	47	4	curve	curve	NOUN
ejpam-6498	47	5	b(t	b(t	PROPN
ejpam-6498	47	6	)	)	PUNCT
ejpam-6498	47	7	is	be	AUX
ejpam-6498	47	8	defined	define	VERB
ejpam-6498	47	9	by	by	ADP
ejpam-6498	47	10	[	[	X
ejpam-6498	47	11	10	10	NUM
ejpam-6498	47	12	]	]	NOUN
ejpam-6498	47	13	:	:	PUNCT
ejpam-6498	47	14	b(t	b(t	NOUN
ejpam-6498	47	15	)	)	PUNCT
ejpam-6498	47	16	=	=	PUNCT
ejpam-6498	47	17	3∑	3∑	NUM
ejpam-6498	47	18	k=0	k=0	PROPN
ejpam-6498	47	19	b3	b3	PROPN
ejpam-6498	47	20	k(t)bk	k(t)bk	PROPN
ejpam-6498	47	21	,	,	PUNCT
ejpam-6498	47	22	t	t	PROPN
ejpam-6498	47	23	∈	∈	PROPN
ejpam-6498	48	1	[	[	X
ejpam-6498	48	2	0	0	NUM
ejpam-6498	48	3	,	,	PUNCT
ejpam-6498	48	4	1	1	NUM
ejpam-6498	48	5	]	]	PUNCT
ejpam-6498	48	6	.	.	PUNCT
ejpam-6498	49	1	(	(	PUNCT
ejpam-6498	49	2	1	1	X
ejpam-6498	49	3	)	)	PUNCT
ejpam-6498	49	4	here	here	ADV
ejpam-6498	49	5	b3	b3	PROPN
ejpam-6498	49	6	k(t	k(t	PROPN
ejpam-6498	49	7	)	)	PUNCT
ejpam-6498	49	8	=	=	PUNCT
ejpam-6498	49	9	(	(	PUNCT
ejpam-6498	49	10	3	3	NUM
ejpam-6498	49	11	k	k	NOUN
ejpam-6498	49	12	)	)	PUNCT
ejpam-6498	49	13	(	(	PUNCT
ejpam-6498	49	14	1−	1−	NUM
ejpam-6498	49	15	t)3−ktk	t)3−ktk	PROPN
ejpam-6498	49	16	are	be	AUX
ejpam-6498	49	17	the	the	DET
ejpam-6498	49	18	bernstein	bernstein	PROPN
ejpam-6498	49	19	polynomials	polynomial	NOUN
ejpam-6498	49	20	,	,	PUNCT
ejpam-6498	49	21	well	well	ADV
ejpam-6498	49	22	known	know	VERB
ejpam-6498	49	23	as	as	ADP
ejpam-6498	49	24	bernstein	bernstein	PROPN
ejpam-6498	49	25	basis	basis	NOUN
ejpam-6498	49	26	functions	function	NOUN
ejpam-6498	49	27	and	and	CCONJ
ejpam-6498	49	28	bk	bk	NOUN
ejpam-6498	49	29	are	be	VERB
ejpam-6498	49	30	control	control	NOUN
ejpam-6498	49	31	points	point	NOUN
ejpam-6498	49	32	of	of	ADP
ejpam-6498	49	33	the	the	DET
ejpam-6498	49	34	cubic	cubic	ADJ
ejpam-6498	50	1	bézier	bézier	ADP
ejpam-6498	50	2	curve	curve	NOUN
ejpam-6498	50	3	.	.	PUNCT
ejpam-6498	51	1	theorem	theorem	NOUN
ejpam-6498	51	2	1	1	NUM
ejpam-6498	51	3	.	.	PUNCT
ejpam-6498	52	1	if	if	SCONJ
ejpam-6498	52	2	the	the	DET
ejpam-6498	52	3	cubic	cubic	ADJ
ejpam-6498	52	4	bézier	bézier	ADP
ejpam-6498	52	5	curve	curve	NOUN
ejpam-6498	52	6	(	(	PUNCT
ejpam-6498	52	7	1	1	X
ejpam-6498	52	8	)	)	PUNCT
ejpam-6498	52	9	has	have	VERB
ejpam-6498	52	10	control	control	NOUN
ejpam-6498	52	11	points	point	NOUN
ejpam-6498	52	12	b0	b0	NOUN
ejpam-6498	52	13	=	=	SYM
ejpam-6498	52	14	(	(	PUNCT
ejpam-6498	52	15	a	a	PRON
ejpam-6498	52	16	,	,	PUNCT
ejpam-6498	52	17	0	0	NUM
ejpam-6498	52	18	)	)	PUNCT
ejpam-6498	52	19	,	,	PUNCT
ejpam-6498	52	20	b1	b1	NOUN
ejpam-6498	52	21	=	=	SYM
ejpam-6498	52	22	(	(	PUNCT
ejpam-6498	52	23	a	a	DET
ejpam-6498	52	24	,	,	PUNCT
ejpam-6498	52	25	r1	r1	PROPN
ejpam-6498	52	26	)	)	PUNCT
ejpam-6498	52	27	,	,	PUNCT
ejpam-6498	52	28	b2	b2	NOUN
ejpam-6498	52	29	=	=	SYM
ejpam-6498	52	30	(	(	PUNCT
ejpam-6498	52	31	a	a	DET
ejpam-6498	52	32	cosφ+	cosφ+	X
ejpam-6498	52	33	ar2	ar2	PROPN
ejpam-6498	52	34	sinφ√	sinφ√	VERB
ejpam-6498	52	35	u	u	PROPN
ejpam-6498	52	36	,	,	PUNCT
ejpam-6498	52	37	b	b	PROPN
ejpam-6498	52	38	sinφ−	sinφ−	NOUN
ejpam-6498	52	39	br2	br2	PROPN
ejpam-6498	52	40	cosφ√	cosφ√	PROPN
ejpam-6498	52	41	u	u	PROPN
ejpam-6498	52	42	)	)	PUNCT
ejpam-6498	52	43	,	,	PUNCT
ejpam-6498	52	44	b3	b3	PROPN
ejpam-6498	52	45	=	=	SYM
ejpam-6498	52	46	(	(	PUNCT
ejpam-6498	52	47	a	a	DET
ejpam-6498	52	48	cosφ	cosφ	NOUN
ejpam-6498	52	49	,	,	PUNCT
ejpam-6498	52	50	b	b	NOUN
ejpam-6498	52	51	sinφ	sinφ	NOUN
ejpam-6498	52	52	)	)	PUNCT
ejpam-6498	52	53	,	,	PUNCT
ejpam-6498	52	54	with	with	ADP
ejpam-6498	52	55	r1	r1	PROPN
ejpam-6498	52	56	=	=	PUNCT
ejpam-6498	52	57	4b(1−cosφ1	4b(1−cosφ1	NUM
ejpam-6498	52	58	)	)	PUNCT
ejpam-6498	52	59	3	3	NUM
ejpam-6498	52	60	sinφ1	sinφ1	NOUN
ejpam-6498	52	61	,	,	PUNCT
ejpam-6498	53	1	r2	r2	PROPN
ejpam-6498	53	2	=	=	PROPN
ejpam-6498	53	3	r1	r1	PROPN
ejpam-6498	53	4	b	b	PROPN
ejpam-6498	53	5	√	√	NUM
ejpam-6498	53	6	u	u	NOUN
ejpam-6498	53	7	,	,	PUNCT
ejpam-6498	53	8	φ1	φ1	NOUN
ejpam-6498	53	9	=	=	SYM
ejpam-6498	53	10	0.5φ	0.5φ	NOUN
ejpam-6498	53	11	,	,	PUNCT
ejpam-6498	53	12	and	and	CCONJ
ejpam-6498	53	13	u	u	NOUN
ejpam-6498	53	14	=	=	PROPN
ejpam-6498	53	15	a2	a2	PROPN
ejpam-6498	53	16	sin2	sin2	PROPN
ejpam-6498	53	17	φ	φ	PROPN
ejpam-6498	53	18	+	+	CCONJ
ejpam-6498	53	19	b2	b2	NOUN
ejpam-6498	53	20	cos2	cos2	NOUN
ejpam-6498	53	21	φ	φ	NOUN
ejpam-6498	53	22	,	,	PUNCT
ejpam-6498	53	23	then	then	ADV
ejpam-6498	53	24	the	the	DET
ejpam-6498	53	25	approximation	approximation	NOUN
ejpam-6498	53	26	of	of	ADP
ejpam-6498	53	27	the	the	DET
ejpam-6498	53	28	elliptic	elliptic	ADJ
ejpam-6498	53	29	arc	arc	NOUN
ejpam-6498	53	30	p̂0p1	p̂0p1	NOUN
ejpam-6498	53	31	by	by	ADP
ejpam-6498	53	32	the	the	DET
ejpam-6498	53	33	cubic	cubic	ADJ
ejpam-6498	53	34	bézier	bézier	PROPN
ejpam-6498	53	35	curve	curve	NOUN
ejpam-6498	53	36	(	(	PUNCT
ejpam-6498	53	37	1	1	X
ejpam-6498	53	38	)	)	PUNCT
ejpam-6498	53	39	is	be	AUX
ejpam-6498	53	40	unique	unique	ADJ
ejpam-6498	53	41	.	.	PUNCT
ejpam-6498	54	1	proof	proof	NOUN
ejpam-6498	54	2	.	.	PUNCT
ejpam-6498	55	1	let	let	VERB
ejpam-6498	55	2	the	the	DET
ejpam-6498	55	3	elliptic	elliptic	ADJ
ejpam-6498	55	4	arc	arc	NOUN
ejpam-6498	55	5	be	be	AUX
ejpam-6498	55	6	starting	start	VERB
ejpam-6498	55	7	at	at	ADP
ejpam-6498	55	8	the	the	DET
ejpam-6498	55	9	point	point	NOUN
ejpam-6498	55	10	p0(a	p0(a	PROPN
ejpam-6498	55	11	,	,	PUNCT
ejpam-6498	55	12	0	0	NUM
ejpam-6498	55	13	)	)	PUNCT
ejpam-6498	55	14	and	and	CCONJ
ejpam-6498	55	15	its	its	PRON
ejpam-6498	55	16	final	final	ADJ
ejpam-6498	55	17	point	point	NOUN
ejpam-6498	55	18	be	be	AUX
ejpam-6498	55	19	p1(a	p1(a	PROPN
ejpam-6498	55	20	cosφ	cosφ	NOUN
ejpam-6498	55	21	,	,	PUNCT
ejpam-6498	55	22	b	b	NOUN
ejpam-6498	55	23	sinφ	sinφ	NOUN
ejpam-6498	55	24	)	)	PUNCT
ejpam-6498	55	25	,	,	PUNCT
ejpam-6498	55	26	making	make	VERB
ejpam-6498	55	27	angle	angle	NOUN
ejpam-6498	55	28	0	0	NUM
ejpam-6498	55	29	<	<	X
ejpam-6498	55	30	φ	φ	PROPN
ejpam-6498	55	31	≤	≤	PROPN
ejpam-6498	55	32	π	π	PROPN
ejpam-6498	55	33	2	2	NUM
ejpam-6498	55	34	with	with	ADP
ejpam-6498	55	35	horizontal	horizontal	ADJ
ejpam-6498	55	36	axis	axis	NOUN
ejpam-6498	55	37	.	.	PUNCT
ejpam-6498	56	1	any	any	DET
ejpam-6498	56	2	elliptic	elliptic	ADJ
ejpam-6498	56	3	arc	arc	NOUN
ejpam-6498	56	4	can	can	AUX
ejpam-6498	56	5	be	be	AUX
ejpam-6498	56	6	shifted	shift	VERB
ejpam-6498	56	7	to	to	ADP
ejpam-6498	56	8	this	this	DET
ejpam-6498	56	9	position	position	NOUN
ejpam-6498	56	10	by	by	ADP
ejpam-6498	56	11	using	use	VERB
ejpam-6498	56	12	affine	affine	NOUN
ejpam-6498	56	13	transformations	transformation	NOUN
ejpam-6498	56	14	.	.	PUNCT
ejpam-6498	57	1	the	the	DET
ejpam-6498	57	2	approximation	approximation	NOUN
ejpam-6498	57	3	constraints	constraint	NOUN
ejpam-6498	57	4	used	use	VERB
ejpam-6498	57	5	are	be	AUX
ejpam-6498	57	6	as	as	SCONJ
ejpam-6498	57	7	follows	follow	VERB
ejpam-6498	57	8	:	:	PUNCT
ejpam-6498	57	9	b(t)|t=0	b(t)|t=0	PROPN
ejpam-6498	57	10	=	=	SYM
ejpam-6498	57	11	p0	p0	NOUN
ejpam-6498	57	12	,	,	PUNCT
ejpam-6498	57	13	b(t)|t=1	b(t)|t=1	PROPN
ejpam-6498	57	14	=	=	SYM
ejpam-6498	57	15	p1	p1	PROPN
ejpam-6498	57	16	.	.	PUNCT
ejpam-6498	58	1	(	(	PUNCT
ejpam-6498	58	2	2	2	X
ejpam-6498	58	3	)	)	PUNCT
ejpam-6498	58	4	t0	t0	NOUN
ejpam-6498	58	5	=	=	SYM
ejpam-6498	58	6	t0	t0	PROPN
ejpam-6498	58	7	,	,	PUNCT
ejpam-6498	58	8	t1	t1	NOUN
ejpam-6498	58	9	=	=	PUNCT
ejpam-6498	58	10	t1	t1	PROPN
ejpam-6498	58	11	.	.	PUNCT
ejpam-6498	59	1	(	(	PUNCT
ejpam-6498	59	2	3	3	X
ejpam-6498	59	3	)	)	PUNCT
ejpam-6498	59	4	the	the	DET
ejpam-6498	59	5	end	end	NOUN
ejpam-6498	59	6	unit	unit	NOUN
ejpam-6498	59	7	tangent	tangent	PROPN
ejpam-6498	59	8	vectors	vector	NOUN
ejpam-6498	59	9	of	of	ADP
ejpam-6498	59	10	the	the	DET
ejpam-6498	59	11	cubic	cubic	NOUN
ejpam-6498	59	12	bézier	bézier	ADP
ejpam-6498	59	13	curve	curve	NOUN
ejpam-6498	59	14	are	be	AUX
ejpam-6498	59	15	tm	tm	NOUN
ejpam-6498	59	16	’s	’s	NOUN
ejpam-6498	59	17	,	,	PUNCT
ejpam-6498	59	18	where	where	SCONJ
ejpam-6498	59	19	t0	t0	NOUN
ejpam-6498	59	20	=	=	PUNCT
ejpam-6498	60	1	b1−b0	b1−b0	PROPN
ejpam-6498	60	2	r1	r1	NOUN
ejpam-6498	60	3	and	and	CCONJ
ejpam-6498	60	4	t2	t2	NOUN
ejpam-6498	60	5	=	=	SYM
ejpam-6498	60	6	b3−b2	b3−b2	NUM
ejpam-6498	60	7	r2	r2	NOUN
ejpam-6498	60	8	,	,	PUNCT
ejpam-6498	60	9	with	with	ADP
ejpam-6498	60	10	r1	r1	NOUN
ejpam-6498	60	11	=	=	SYM
ejpam-6498	60	12	∥b1	∥b1	VERB
ejpam-6498	60	13	−	−	PROPN
ejpam-6498	60	14	b0∥	b0∥	NOUN
ejpam-6498	60	15	and	and	CCONJ
ejpam-6498	60	16	r2	r2	PROPN
ejpam-6498	60	17	=	=	SYM
ejpam-6498	60	18	∥b3	∥b3	NOUN
ejpam-6498	61	1	−	−	PROPN
ejpam-6498	61	2	b2∥.	b2∥.	NOUN
ejpam-6498	61	3	here	here	ADV
ejpam-6498	61	4	r1	r1	PROPN
ejpam-6498	61	5	and	and	CCONJ
ejpam-6498	61	6	r2	r2	PROPN
ejpam-6498	61	7	are	be	AUX
ejpam-6498	61	8	also	also	ADV
ejpam-6498	61	9	unknown	unknown	ADJ
ejpam-6498	61	10	by	by	ADP
ejpam-6498	61	11	construction	construction	NOUN
ejpam-6498	61	12	.	.	PUNCT
ejpam-6498	62	1	the	the	DET
ejpam-6498	62	2	tm	tm	PROPN
ejpam-6498	62	3	’s	’s	PART
ejpam-6498	62	4	are	be	AUX
ejpam-6498	62	5	computed	compute	VERB
ejpam-6498	62	6	by	by	ADP
ejpam-6498	62	7	formula	formula	NOUN
ejpam-6498	62	8	tm	tm	NOUN
ejpam-6498	62	9	=	=	PUNCT
ejpam-6498	62	10	db(t	db(t	PROPN
ejpam-6498	62	11	)	)	PUNCT
ejpam-6498	62	12	dt	dt	PUNCT
ejpam-6498	62	13	∥∥∥db(t	∥∥∥db(t	PUNCT
ejpam-6498	62	14	)	)	PUNCT
ejpam-6498	63	1	dt	dt	PROPN
ejpam-6498	63	2	∥∥∥−1	∥∥∥−1	PROPN
ejpam-6498	63	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6498	63	4	t	t	PROPN
ejpam-6498	63	5	=	=	PROPN
ejpam-6498	63	6	m	m	PROPN
ejpam-6498	63	7	,	,	PUNCT
ejpam-6498	63	8	for	for	ADP
ejpam-6498	63	9	m	m	PROPN
ejpam-6498	63	10	=	=	SYM
ejpam-6498	63	11	0	0	NUM
ejpam-6498	63	12	,	,	PUNCT
ejpam-6498	63	13	1	1	NUM
ejpam-6498	63	14	.	.	X
ejpam-6498	64	1	here	here	ADV
ejpam-6498	64	2	∥∥∥db(t	∥∥∥db(t	PUNCT
ejpam-6498	64	3	)	)	PUNCT
ejpam-6498	64	4	dt	dt	PART
ejpam-6498	64	5	∥∥∥	∥∥∥	PROPN
ejpam-6498	64	6	is	be	AUX
ejpam-6498	64	7	the	the	DET
ejpam-6498	64	8	euclidean	euclidean	ADJ
ejpam-6498	64	9	norm	norm	NOUN
ejpam-6498	64	10	in	in	ADP
ejpam-6498	64	11	r2	r2	PROPN
ejpam-6498	64	12	.	.	PUNCT
ejpam-6498	65	1	the	the	DET
ejpam-6498	65	2	end	end	NOUN
ejpam-6498	65	3	unit	unit	NOUN
ejpam-6498	65	4	tangents	tangent	NOUN
ejpam-6498	65	5	of	of	ADP
ejpam-6498	65	6	the	the	DET
ejpam-6498	65	7	elliptic	elliptic	ADJ
ejpam-6498	65	8	arc	arc	NOUN
ejpam-6498	65	9	are	be	AUX
ejpam-6498	65	10	t0	t0	NOUN
ejpam-6498	65	11	=	=	SYM
ejpam-6498	65	12	(	(	PUNCT
ejpam-6498	65	13	0	0	NUM
ejpam-6498	65	14	,	,	PUNCT
ejpam-6498	65	15	1	1	NUM
ejpam-6498	65	16	)	)	PUNCT
ejpam-6498	65	17	and	and	CCONJ
ejpam-6498	65	18	t1	t1	NUM
ejpam-6498	65	19	=	=	PUNCT
ejpam-6498	65	20	(	(	PUNCT
ejpam-6498	65	21	−a	−a	ADV
ejpam-6498	65	22	sinφ	sinφ	NOUN
ejpam-6498	65	23	,	,	PUNCT
ejpam-6498	65	24	b	b	PROPN
ejpam-6498	65	25	cosφ)√	cosφ)√	NOUN
ejpam-6498	65	26	u	u	NOUN
ejpam-6498	65	27	,	,	PUNCT
ejpam-6498	65	28	where	where	SCONJ
ejpam-6498	65	29	u	u	PROPN
ejpam-6498	65	30	=	=	PROPN
ejpam-6498	65	31	a2	a2	PROPN
ejpam-6498	65	32	sin2	sin2	PROPN
ejpam-6498	65	33	φ+	φ+	NOUN
ejpam-6498	65	34	b2	b2	NOUN
ejpam-6498	65	35	cos2	cos2	PROPN
ejpam-6498	65	36	φ	φ	X
ejpam-6498	65	37	.	.	PUNCT
ejpam-6498	66	1	the	the	DET
ejpam-6498	66	2	formulae	formulae	ADJ
ejpam-6498	66	3	(	(	PUNCT
ejpam-6498	66	4	2	2	NUM
ejpam-6498	66	5	)	)	PUNCT
ejpam-6498	66	6	and	and	CCONJ
ejpam-6498	66	7	(	(	PUNCT
ejpam-6498	66	8	3	3	X
ejpam-6498	66	9	)	)	PUNCT
ejpam-6498	66	10	confirm	confirm	VERB
ejpam-6498	66	11	that	that	SCONJ
ejpam-6498	66	12	the	the	DET
ejpam-6498	66	13	cubic	cubic	ADJ
ejpam-6498	66	14	bézier	bézier	PROPN
ejpam-6498	66	15	curve	curve	NOUN
ejpam-6498	66	16	(	(	PUNCT
ejpam-6498	66	17	1	1	NUM
ejpam-6498	66	18	)	)	PUNCT
ejpam-6498	66	19	and	and	CCONJ
ejpam-6498	66	20	the	the	DET
ejpam-6498	66	21	elliptic	elliptic	ADJ
ejpam-6498	66	22	arc	arc	NOUN
ejpam-6498	66	23	share	share	VERB
ejpam-6498	66	24	same	same	ADJ
ejpam-6498	66	25	end	end	NOUN
ejpam-6498	66	26	points	point	NOUN
ejpam-6498	66	27	and	and	CCONJ
ejpam-6498	66	28	the	the	DET
ejpam-6498	66	29	end	end	NOUN
ejpam-6498	66	30	unit	unit	NOUN
ejpam-6498	66	31	tangents	tangent	NOUN
ejpam-6498	66	32	.	.	PUNCT
ejpam-6498	67	1	using	use	VERB
ejpam-6498	67	2	(	(	PUNCT
ejpam-6498	67	3	1	1	NUM
ejpam-6498	67	4	)	)	PUNCT
ejpam-6498	67	5	,	,	PUNCT
ejpam-6498	67	6	(	(	PUNCT
ejpam-6498	67	7	2	2	X
ejpam-6498	67	8	)	)	PUNCT
ejpam-6498	67	9	and	and	CCONJ
ejpam-6498	67	10	(	(	PUNCT
ejpam-6498	67	11	3	3	NUM
ejpam-6498	67	12	)	)	PUNCT
ejpam-6498	67	13	,	,	PUNCT
ejpam-6498	67	14	the	the	DET
ejpam-6498	67	15	control	control	NOUN
ejpam-6498	67	16	points	point	NOUN
ejpam-6498	67	17	of	of	ADP
ejpam-6498	67	18	the	the	DET
ejpam-6498	67	19	cubic	cubic	ADJ
ejpam-6498	67	20	bézier	bézier	ADP
ejpam-6498	67	21	curve	curve	NOUN
ejpam-6498	67	22	are	be	AUX
ejpam-6498	67	23	calculated	calculate	VERB
ejpam-6498	67	24	as	as	ADP
ejpam-6498	67	25	:	:	PUNCT
ejpam-6498	67	26	b0	b0	NOUN
ejpam-6498	67	27	=	=	SYM
ejpam-6498	67	28	(	(	PUNCT
ejpam-6498	67	29	a	a	PRON
ejpam-6498	67	30	,	,	PUNCT
ejpam-6498	67	31	0	0	NUM
ejpam-6498	67	32	)	)	PUNCT
ejpam-6498	67	33	,	,	PUNCT
ejpam-6498	67	34	m.	m.	NOUN
ejpam-6498	67	35	hussain	hussain	PROPN
ejpam-6498	67	36	,	,	PUNCT
ejpam-6498	67	37	h.	h.	PROPN
ejpam-6498	67	38	a.	a.	PROPN
ejpam-6498	67	39	wajid	wajid	PROPN
ejpam-6498	67	40	,	,	PUNCT
ejpam-6498	67	41	s.	s.	PROPN
ejpam-6498	67	42	aqeel	aqeel	PROPN
ejpam-6498	67	43	/	/	SYM
ejpam-6498	67	44	eur	eur	PROPN
ejpam-6498	67	45	.	.	PUNCT
ejpam-6498	68	1	j.	j.	PROPN
ejpam-6498	68	2	pure	pure	PROPN
ejpam-6498	68	3	appl	appl	PROPN
ejpam-6498	68	4	.	.	PROPN
ejpam-6498	68	5	math	math	PROPN
ejpam-6498	68	6	,	,	PUNCT
ejpam-6498	68	7	18	18	NUM
ejpam-6498	68	8	(	(	PUNCT
ejpam-6498	68	9	4	4	NUM
ejpam-6498	68	10	)	)	PUNCT
ejpam-6498	68	11	(	(	PUNCT
ejpam-6498	68	12	2025	2025	NUM
ejpam-6498	68	13	)	)	PUNCT
ejpam-6498	68	14	,	,	PUNCT
ejpam-6498	68	15	6498	6498	NUM
ejpam-6498	68	16	4	4	NUM
ejpam-6498	68	17	of	of	ADP
ejpam-6498	68	18	12	12	NUM
ejpam-6498	68	19	b1	b1	NOUN
ejpam-6498	68	20	=	=	SYM
ejpam-6498	68	21	(	(	PUNCT
ejpam-6498	68	22	a	a	PRON
ejpam-6498	68	23	,	,	PUNCT
ejpam-6498	68	24	r1	r1	PROPN
ejpam-6498	68	25	)	)	PUNCT
ejpam-6498	68	26	,	,	PUNCT
ejpam-6498	68	27	b2	b2	NOUN
ejpam-6498	68	28	=	=	SYM
ejpam-6498	68	29	(	(	PUNCT
ejpam-6498	68	30	a	a	DET
ejpam-6498	68	31	cosφ+	cosφ+	X
ejpam-6498	68	32	ar2	ar2	PROPN
ejpam-6498	68	33	sinφ√	sinφ√	VERB
ejpam-6498	68	34	u	u	PROPN
ejpam-6498	68	35	,	,	PUNCT
ejpam-6498	68	36	b	b	PROPN
ejpam-6498	68	37	sinφ−	sinφ−	NOUN
ejpam-6498	68	38	br2	br2	PROPN
ejpam-6498	68	39	cosφ√	cosφ√	PROPN
ejpam-6498	68	40	u	u	PROPN
ejpam-6498	68	41	)	)	PUNCT
ejpam-6498	68	42	,	,	PUNCT
ejpam-6498	68	43	b3	b3	PROPN
ejpam-6498	68	44	=	=	SYM
ejpam-6498	68	45	(	(	PUNCT
ejpam-6498	68	46	a	a	DET
ejpam-6498	68	47	cosφ	cosφ	NOUN
ejpam-6498	68	48	,	,	PUNCT
ejpam-6498	68	49	b	b	NOUN
ejpam-6498	68	50	sinφ	sinφ	NOUN
ejpam-6498	68	51	)	)	PUNCT
ejpam-6498	68	52	.	.	PUNCT
ejpam-6498	69	1	using	use	VERB
ejpam-6498	69	2	these	these	DET
ejpam-6498	69	3	control	control	NOUN
ejpam-6498	69	4	points	point	NOUN
ejpam-6498	69	5	the	the	DET
ejpam-6498	69	6	parametric	parametric	ADJ
ejpam-6498	69	7	equations	equation	NOUN
ejpam-6498	69	8	of	of	ADP
ejpam-6498	69	9	the	the	DET
ejpam-6498	69	10	cubic	cubic	ADJ
ejpam-6498	69	11	bézier	bézier	ADP
ejpam-6498	69	12	curve	curve	NOUN
ejpam-6498	69	13	are	be	AUX
ejpam-6498	69	14	the	the	DET
ejpam-6498	69	15	following	following	NOUN
ejpam-6498	69	16	:	:	PUNCT
ejpam-6498	69	17	x(t	x(t	X
ejpam-6498	69	18	)	)	PUNCT
ejpam-6498	70	1	=	=	SYM
ejpam-6498	70	2	3∑	3∑	NUM
ejpam-6498	70	3	k=0	k=0	PROPN
ejpam-6498	70	4	(	(	PUNCT
ejpam-6498	70	5	3	3	NUM
ejpam-6498	70	6	k	k	NOUN
ejpam-6498	70	7	)	)	PUNCT
ejpam-6498	70	8	(	(	PUNCT
ejpam-6498	70	9	1−	1−	NUM
ejpam-6498	70	10	t)3−ktkxk	t)3−ktkxk	NUM
ejpam-6498	70	11	,	,	PUNCT
ejpam-6498	70	12	(	(	PUNCT
ejpam-6498	70	13	4	4	NUM
ejpam-6498	70	14	)	)	PUNCT
ejpam-6498	70	15	y(t	y(t	NUM
ejpam-6498	70	16	)	)	PUNCT
ejpam-6498	71	1	=	=	PUNCT
ejpam-6498	71	2	3∑	3∑	NUM
ejpam-6498	71	3	k=0	k=0	PROPN
ejpam-6498	71	4	(	(	PUNCT
ejpam-6498	71	5	3	3	NUM
ejpam-6498	71	6	k	k	NOUN
ejpam-6498	71	7	)	)	PUNCT
ejpam-6498	71	8	(	(	PUNCT
ejpam-6498	71	9	1−	1−	NUM
ejpam-6498	71	10	t)3−ktkyk	t)3−ktkyk	NOUN
ejpam-6498	71	11	,	,	PUNCT
ejpam-6498	71	12	(	(	PUNCT
ejpam-6498	71	13	5	5	NUM
ejpam-6498	71	14	)	)	PUNCT
ejpam-6498	72	1	where	where	SCONJ
ejpam-6498	72	2	x0	x0	PROPN
ejpam-6498	72	3	=	=	PUNCT
ejpam-6498	73	1	a	a	X
ejpam-6498	73	2	,	,	PUNCT
ejpam-6498	73	3	x1	x1	PROPN
ejpam-6498	73	4	=	=	PUNCT
ejpam-6498	74	1	a	a	PROPN
ejpam-6498	74	2	,	,	PUNCT
ejpam-6498	74	3	x2	x2	NOUN
ejpam-6498	74	4	=	=	PUNCT
ejpam-6498	75	1	a	a	DET
ejpam-6498	75	2	cosφ+	cosφ+	X
ejpam-6498	75	3	ar2	ar2	PROPN
ejpam-6498	75	4	sinφ√	sinφ√	VERB
ejpam-6498	75	5	u	u	NOUN
ejpam-6498	75	6	,	,	PUNCT
ejpam-6498	75	7	x3	x3	PROPN
ejpam-6498	75	8	=	=	PUNCT
ejpam-6498	75	9	a	a	DET
ejpam-6498	75	10	cosφ	cosφ	NOUN
ejpam-6498	75	11	,	,	PUNCT
ejpam-6498	75	12	y0	y0	NOUN
ejpam-6498	75	13	=	=	SYM
ejpam-6498	75	14	0	0	NUM
ejpam-6498	75	15	,	,	PUNCT
ejpam-6498	75	16	y1	y1	NOUN
ejpam-6498	75	17	=	=	SYM
ejpam-6498	75	18	r1	r1	PROPN
ejpam-6498	75	19	,	,	PUNCT
ejpam-6498	75	20	y2	y2	PROPN
ejpam-6498	76	1	=	=	SYM
ejpam-6498	76	2	b	b	PROPN
ejpam-6498	76	3	sinφ−	sinφ−	NOUN
ejpam-6498	76	4	br2	br2	PROPN
ejpam-6498	76	5	cosφ√	cosφ√	PROPN
ejpam-6498	76	6	u	u	PROPN
ejpam-6498	76	7	,	,	PUNCT
ejpam-6498	76	8	y3	y3	NOUN
ejpam-6498	76	9	=	=	SYM
ejpam-6498	76	10	b	b	NOUN
ejpam-6498	76	11	sinφ	sinφ	NOUN
ejpam-6498	76	12	.	.	PUNCT
ejpam-6498	77	1	first	first	ADV
ejpam-6498	77	2	the	the	DET
ejpam-6498	77	3	arc	arc	NOUN
ejpam-6498	77	4	of	of	ADP
ejpam-6498	77	5	an	an	DET
ejpam-6498	77	6	ellipse	ellipse	NOUN
ejpam-6498	77	7	in	in	ADP
ejpam-6498	77	8	first	first	ADJ
ejpam-6498	77	9	quadrant	quadrant	NOUN
ejpam-6498	77	10	is	be	AUX
ejpam-6498	77	11	approximated	approximate	VERB
ejpam-6498	77	12	and	and	CCONJ
ejpam-6498	77	13	the	the	DET
ejpam-6498	77	14	whole	whole	ADJ
ejpam-6498	77	15	ellipse	ellipse	NOUN
ejpam-6498	77	16	is	be	AUX
ejpam-6498	77	17	generated	generate	VERB
ejpam-6498	77	18	by	by	ADP
ejpam-6498	77	19	applying	apply	VERB
ejpam-6498	77	20	affine	affine	NOUN
ejpam-6498	77	21	transformations	transformation	NOUN
ejpam-6498	77	22	.	.	PUNCT
ejpam-6498	78	1	theorem	theorem	NOUN
ejpam-6498	78	2	2	2	NUM
ejpam-6498	78	3	.	.	PUNCT
ejpam-6498	79	1	if	if	SCONJ
ejpam-6498	79	2	r1	r1	PROPN
ejpam-6498	79	3	=	=	PUNCT
ejpam-6498	79	4	4b(1−cosφ1	4b(1−cosφ1	NUM
ejpam-6498	79	5	)	)	PUNCT
ejpam-6498	79	6	3	3	NUM
ejpam-6498	79	7	sinφ1	sinφ1	NOUN
ejpam-6498	79	8	and	and	CCONJ
ejpam-6498	79	9	r2	r2	PROPN
ejpam-6498	79	10	=	=	PROPN
ejpam-6498	79	11	r1	r1	PROPN
ejpam-6498	79	12	b	b	PROPN
ejpam-6498	79	13	√	√	NUM
ejpam-6498	79	14	u	u	NOUN
ejpam-6498	79	15	,	,	PUNCT
ejpam-6498	79	16	where	where	SCONJ
ejpam-6498	79	17	φ1	φ1	NOUN
ejpam-6498	79	18	=	=	SYM
ejpam-6498	79	19	0.5φ	0.5φ	NOUN
ejpam-6498	79	20	and	and	CCONJ
ejpam-6498	79	21	u	u	NOUN
ejpam-6498	79	22	=	=	PROPN
ejpam-6498	79	23	a2	a2	PROPN
ejpam-6498	79	24	sin2	sin2	PROPN
ejpam-6498	79	25	φ	φ	PROPN
ejpam-6498	79	26	+	+	CCONJ
ejpam-6498	79	27	b2	b2	NOUN
ejpam-6498	79	28	cos2	cos2	NOUN
ejpam-6498	79	29	φ	φ	NOUN
ejpam-6498	79	30	,	,	PUNCT
ejpam-6498	79	31	then	then	ADV
ejpam-6498	79	32	the	the	DET
ejpam-6498	79	33	hausdorff	hausdorff	NOUN
ejpam-6498	79	34	distance	distance	NOUN
ejpam-6498	79	35	between	between	ADP
ejpam-6498	79	36	the	the	DET
ejpam-6498	79	37	elliptic	elliptic	ADJ
ejpam-6498	79	38	arc	arc	NOUN
ejpam-6498	79	39	and	and	CCONJ
ejpam-6498	79	40	its	its	PRON
ejpam-6498	79	41	approximating	approximate	VERB
ejpam-6498	79	42	cubic	cubic	NOUN
ejpam-6498	79	43	bézier	bézier	ADP
ejpam-6498	79	44	curve	curve	NOUN
ejpam-6498	79	45	is	be	AUX
ejpam-6498	79	46	dh(p̂0p1	dh(p̂0p1	PROPN
ejpam-6498	79	47	,	,	PUNCT
ejpam-6498	79	48	b(t	b(t	NOUN
ejpam-6498	79	49	)	)	PUNCT
ejpam-6498	79	50	)	)	PUNCT
ejpam-6498	80	1	=	=	PUNCT
ejpam-6498	80	2	a2b2(3.6168981×	a2b2(3.6168981×	X
ejpam-6498	81	1	10−5)φ6	10−5)φ6	NUM
ejpam-6498	81	2	+	+	NOUN
ejpam-6498	81	3	o(φ10	o(φ10	NOUN
ejpam-6498	81	4	)	)	PUNCT
ejpam-6498	81	5	.	.	PUNCT
ejpam-6498	82	1	proof	proof	NOUN
ejpam-6498	82	2	.	.	PUNCT
ejpam-6498	83	1	let	let	VERB
ejpam-6498	83	2	the	the	DET
ejpam-6498	83	3	error	error	NOUN
ejpam-6498	83	4	function	function	NOUN
ejpam-6498	83	5	w(t	w(t	PROPN
ejpam-6498	83	6	)	)	PUNCT
ejpam-6498	83	7	for	for	ADP
ejpam-6498	83	8	the	the	DET
ejpam-6498	83	9	proposed	propose	VERB
ejpam-6498	83	10	elliptic	elliptic	ADJ
ejpam-6498	83	11	arc	arc	NOUN
ejpam-6498	83	12	approximation	approximation	NOUN
ejpam-6498	83	13	method	method	NOUN
ejpam-6498	83	14	be	be	AUX
ejpam-6498	83	15	defined	define	VERB
ejpam-6498	83	16	as	as	SCONJ
ejpam-6498	83	17	follows	follow	VERB
ejpam-6498	83	18	:	:	PUNCT
ejpam-6498	83	19	w(t	w(t	X
ejpam-6498	83	20	)	)	PUNCT
ejpam-6498	84	1	=	=	SYM
ejpam-6498	84	2	b2x2(t	b2x2(t	NOUN
ejpam-6498	84	3	)	)	PUNCT
ejpam-6498	85	1	+	+	CCONJ
ejpam-6498	85	2	a2y2(t)−	a2y2(t)−	PROPN
ejpam-6498	85	3	a2b2	a2b2	PUNCT
ejpam-6498	85	4	.	.	PUNCT
ejpam-6498	85	5	(	(	PUNCT
ejpam-6498	85	6	6	6	NUM
ejpam-6498	85	7	)	)	PUNCT
ejpam-6498	85	8	as	as	ADP
ejpam-6498	85	9	x(t	x(t	PROPN
ejpam-6498	85	10	)	)	PUNCT
ejpam-6498	85	11	and	and	CCONJ
ejpam-6498	85	12	y(t	y(t	NUM
ejpam-6498	85	13	)	)	PUNCT
ejpam-6498	85	14	are	be	AUX
ejpam-6498	85	15	cubic	cubic	ADJ
ejpam-6498	85	16	polynomials	polynomial	NOUN
ejpam-6498	85	17	,	,	PUNCT
ejpam-6498	85	18	the	the	DET
ejpam-6498	85	19	function	function	NOUN
ejpam-6498	85	20	w(t	w(t	PROPN
ejpam-6498	85	21	)	)	PUNCT
ejpam-6498	85	22	is	be	AUX
ejpam-6498	85	23	a	a	DET
ejpam-6498	85	24	polynomial	polynomial	NOUN
ejpam-6498	85	25	of	of	ADP
ejpam-6498	85	26	degree	degree	NOUN
ejpam-6498	85	27	6	6	NUM
ejpam-6498	85	28	.	.	PUNCT
ejpam-6498	86	1	using	use	VERB
ejpam-6498	86	2	(	(	PUNCT
ejpam-6498	86	3	4	4	NUM
ejpam-6498	86	4	)	)	PUNCT
ejpam-6498	86	5	,	,	PUNCT
ejpam-6498	86	6	(	(	PUNCT
ejpam-6498	86	7	5	5	NUM
ejpam-6498	86	8	)	)	PUNCT
ejpam-6498	86	9	and	and	CCONJ
ejpam-6498	86	10	(	(	PUNCT
ejpam-6498	86	11	6	6	X
ejpam-6498	86	12	)	)	PUNCT
ejpam-6498	86	13	we	we	PRON
ejpam-6498	86	14	get	get	VERB
ejpam-6498	86	15	w(0	w(0	PROPN
ejpam-6498	86	16	)	)	PUNCT
ejpam-6498	86	17	=	=	SYM
ejpam-6498	86	18	0	0	NUM
ejpam-6498	86	19	and	and	CCONJ
ejpam-6498	86	20	w(1	w(1	PROPN
ejpam-6498	86	21	)	)	PUNCT
ejpam-6498	86	22	=	=	SYM
ejpam-6498	86	23	0	0	X
ejpam-6498	86	24	.	.	PUNCT
ejpam-6498	86	25	assume	assume	VERB
ejpam-6498	86	26	that	that	SCONJ
ejpam-6498	86	27	w(t)|t=0.5	w(t)|t=0.5	NOUN
ejpam-6498	86	28	=	=	SYM
ejpam-6498	86	29	0	0	NUM
ejpam-6498	86	30	,	,	PUNCT
ejpam-6498	86	31	then	then	ADV
ejpam-6498	86	32	by	by	ADP
ejpam-6498	86	33	the	the	DET
ejpam-6498	86	34	symmetry	symmetry	NOUN
ejpam-6498	86	35	of	of	ADP
ejpam-6498	86	36	w(t	w(t	PROPN
ejpam-6498	86	37	)	)	PUNCT
ejpam-6498	86	38	,	,	PUNCT
ejpam-6498	86	39	we	we	PRON
ejpam-6498	86	40	have	have	VERB
ejpam-6498	86	41	dw(t	dw(t	NOUN
ejpam-6498	86	42	)	)	PUNCT
ejpam-6498	86	43	dt	dt	X
ejpam-6498	87	1	∣∣∣	∣∣∣	ADJ
ejpam-6498	87	2	t=0.5	t=0.5	NOUN
ejpam-6498	87	3	=	=	NOUN
ejpam-6498	87	4	0	0	NUM
ejpam-6498	87	5	.	.	PUNCT
ejpam-6498	88	1	the	the	DET
ejpam-6498	88	2	assumed	assumed	ADJ
ejpam-6498	88	3	midpoint	midpoint	NOUN
ejpam-6498	88	4	interpolation	interpolation	NOUN
ejpam-6498	88	5	condition	condition	NOUN
ejpam-6498	88	6	of	of	ADP
ejpam-6498	88	7	w(t	w(t	PROPN
ejpam-6498	88	8	)	)	PUNCT
ejpam-6498	88	9	and	and	CCONJ
ejpam-6498	88	10	its	its	PRON
ejpam-6498	88	11	derivative	derivative	NOUN
ejpam-6498	88	12	at	at	ADP
ejpam-6498	88	13	t	t	NOUN
ejpam-6498	88	14	=	=	SYM
ejpam-6498	88	15	0.5	0.5	NUM
ejpam-6498	88	16	gives	give	VERB
ejpam-6498	88	17	the	the	DET
ejpam-6498	88	18	following	follow	VERB
ejpam-6498	88	19	set	set	NOUN
ejpam-6498	88	20	of	of	ADP
ejpam-6498	88	21	simultaneous	simultaneous	ADJ
ejpam-6498	88	22	equations	equation	NOUN
ejpam-6498	88	23	in	in	ADP
ejpam-6498	88	24	r1	r1	PROPN
ejpam-6498	88	25	and	and	CCONJ
ejpam-6498	88	26	r2	r2	PROPN
ejpam-6498	88	27	:	:	PUNCT
ejpam-6498	88	28	−	−	PROPN
ejpam-6498	88	29	1	1	NUM
ejpam-6498	88	30	2	2	NUM
ejpam-6498	88	31	a2b2	a2b2	ADP
ejpam-6498	88	32	+	+	NOUN
ejpam-6498	88	33	9	9	NUM
ejpam-6498	88	34	64	64	NUM
ejpam-6498	88	35	a2b2r22	a2b2r22	ADJ
ejpam-6498	88	36	u	u	NOUN
ejpam-6498	88	37	+	+	CCONJ
ejpam-6498	88	38	a2b2	a2b2	NOUN
ejpam-6498	88	39	cosφ	cosφ	NOUN
ejpam-6498	88	40	2	2	NUM
ejpam-6498	88	41	+	+	CCONJ
ejpam-6498	88	42	3	3	NUM
ejpam-6498	88	43	8	8	NUM
ejpam-6498	88	44	a2b2r2	a2b2r2	NOUN
ejpam-6498	88	45	sinφ√	sinφ√	VERB
ejpam-6498	88	46	u	u	NOUN
ejpam-6498	88	47	+	+	NOUN
ejpam-6498	88	48	9	9	NUM
ejpam-6498	88	49	64	64	NUM
ejpam-6498	88	50	a2r21	a2r21	NUM
ejpam-6498	89	1	+	+	CCONJ
ejpam-6498	89	2	3	3	NUM
ejpam-6498	89	3	8	8	NUM
ejpam-6498	89	4	r1a	r1a	VERB
ejpam-6498	89	5	2b	2b	NUM
ejpam-6498	89	6	sinφ−	sinφ−	X
ejpam-6498	89	7	9	9	NUM
ejpam-6498	89	8	32	32	NUM
ejpam-6498	89	9	a2br1r2	a2br1r2	NUM
ejpam-6498	89	10	cosφ√	cosφ√	NOUN
ejpam-6498	89	11	u	u	NOUN
ejpam-6498	89	12	=	=	SYM
ejpam-6498	89	13	0	0	NUM
ejpam-6498	89	14	(	(	PUNCT
ejpam-6498	89	15	7	7	NUM
ejpam-6498	89	16	)	)	PUNCT
ejpam-6498	89	17	m.	m.	NOUN
ejpam-6498	89	18	hussain	hussain	PROPN
ejpam-6498	89	19	,	,	PUNCT
ejpam-6498	89	20	h.	h.	PROPN
ejpam-6498	89	21	a.	a.	PROPN
ejpam-6498	89	22	wajid	wajid	PROPN
ejpam-6498	89	23	,	,	PUNCT
ejpam-6498	89	24	s.	s.	PROPN
ejpam-6498	89	25	aqeel	aqeel	PROPN
ejpam-6498	89	26	/	/	SYM
ejpam-6498	89	27	eur	eur	PROPN
ejpam-6498	89	28	.	.	PUNCT
ejpam-6498	90	1	j.	j.	PROPN
ejpam-6498	90	2	pure	pure	PROPN
ejpam-6498	90	3	appl	appl	PROPN
ejpam-6498	90	4	.	.	PROPN
ejpam-6498	90	5	math	math	PROPN
ejpam-6498	90	6	,	,	PUNCT
ejpam-6498	90	7	18	18	NUM
ejpam-6498	90	8	(	(	PUNCT
ejpam-6498	90	9	4	4	NUM
ejpam-6498	90	10	)	)	PUNCT
ejpam-6498	90	11	(	(	PUNCT
ejpam-6498	90	12	2025	2025	NUM
ejpam-6498	90	13	)	)	PUNCT
ejpam-6498	90	14	,	,	PUNCT
ejpam-6498	90	15	6498	6498	NUM
ejpam-6498	90	16	5	5	NUM
ejpam-6498	90	17	of	of	ADP
ejpam-6498	90	18	12	12	NUM
ejpam-6498	90	19	3b2r22	3b2r22	NUM
ejpam-6498	90	20	−	−	NUM
ejpam-6498	90	21	2b2r2	2b2r2	NUM
ejpam-6498	91	1	√	√	PROPN
ejpam-6498	92	1	u	u	PROPN
ejpam-6498	92	2	sinφ−	sinφ−	NOUN
ejpam-6498	92	3	3r21u+	3r21u+	NUM
ejpam-6498	92	4	2r1bu	2r1bu	NUM
ejpam-6498	92	5	sinφ	sinφ	NOUN
ejpam-6498	92	6	=	=	PUNCT
ejpam-6498	92	7	0	0	X
ejpam-6498	92	8	.	.	PUNCT
ejpam-6498	93	1	(	(	PUNCT
ejpam-6498	93	2	8)	8)	NUM
ejpam-6498	93	3	as	as	ADP
ejpam-6498	93	4	r1	r1	PROPN
ejpam-6498	93	5	>	>	X
ejpam-6498	93	6	0	0	PUNCT
ejpam-6498	93	7	and	and	CCONJ
ejpam-6498	93	8	r2	r2	PROPN
ejpam-6498	93	9	>	>	X
ejpam-6498	93	10	0	0	NUM
ejpam-6498	93	11	by	by	ADP
ejpam-6498	93	12	construction	construction	NOUN
ejpam-6498	93	13	,	,	PUNCT
ejpam-6498	93	14	the	the	DET
ejpam-6498	93	15	only	only	ADJ
ejpam-6498	93	16	acceptable	acceptable	ADJ
ejpam-6498	93	17	solution	solution	NOUN
ejpam-6498	93	18	of	of	ADP
ejpam-6498	93	19	the	the	DET
ejpam-6498	93	20	above	above	ADJ
ejpam-6498	93	21	set	set	NOUN
ejpam-6498	93	22	of	of	ADP
ejpam-6498	93	23	simultaneous	simultaneous	ADJ
ejpam-6498	93	24	equations	equation	NOUN
ejpam-6498	93	25	is	be	AUX
ejpam-6498	93	26	:	:	PUNCT
ejpam-6498	93	27	r1	r1	PROPN
ejpam-6498	93	28	=	=	PUNCT
ejpam-6498	93	29	4b(1−	4b(1−	PROPN
ejpam-6498	93	30	cosφ1	cosφ1	NOUN
ejpam-6498	93	31	)	)	PUNCT
ejpam-6498	93	32	3	3	NUM
ejpam-6498	93	33	sinφ1	sinφ1	NOUN
ejpam-6498	93	34	and	and	CCONJ
ejpam-6498	93	35	r2	r2	PROPN
ejpam-6498	93	36	=	=	PROPN
ejpam-6498	93	37	r1	r1	PROPN
ejpam-6498	93	38	b	b	PROPN
ejpam-6498	93	39	√	√	NUM
ejpam-6498	93	40	u	u	NOUN
ejpam-6498	93	41	,	,	PUNCT
ejpam-6498	93	42	φ1	φ1	NOUN
ejpam-6498	93	43	=	=	SYM
ejpam-6498	93	44	0.5φ	0.5φ	NOUN
ejpam-6498	93	45	.	.	PUNCT
ejpam-6498	94	1	as	as	SCONJ
ejpam-6498	94	2	the	the	DET
ejpam-6498	94	3	approximation	approximation	NOUN
ejpam-6498	94	4	curve	curve	NOUN
ejpam-6498	94	5	touches	touch	VERB
ejpam-6498	94	6	the	the	DET
ejpam-6498	94	7	elliptic	elliptic	ADJ
ejpam-6498	94	8	arc	arc	NOUN
ejpam-6498	94	9	at	at	ADP
ejpam-6498	94	10	points	point	NOUN
ejpam-6498	94	11	t	t	NOUN
ejpam-6498	94	12	=	=	SYM
ejpam-6498	94	13	0	0	NUM
ejpam-6498	94	14	,	,	PUNCT
ejpam-6498	94	15	0.5	0.5	NUM
ejpam-6498	94	16	,	,	PUNCT
ejpam-6498	94	17	1	1	NUM
ejpam-6498	94	18	,	,	PUNCT
ejpam-6498	94	19	with	with	ADP
ejpam-6498	94	20	multiplicity	multiplicity	NOUN
ejpam-6498	94	21	2	2	NUM
ejpam-6498	94	22	,	,	PUNCT
ejpam-6498	94	23	2	2	NUM
ejpam-6498	94	24	,	,	PUNCT
ejpam-6498	94	25	2	2	NUM
ejpam-6498	94	26	,	,	PUNCT
ejpam-6498	94	27	the	the	DET
ejpam-6498	94	28	function	function	NOUN
ejpam-6498	94	29	w(t	w(t	PROPN
ejpam-6498	94	30	)	)	PUNCT
ejpam-6498	94	31	can	can	AUX
ejpam-6498	94	32	be	be	AUX
ejpam-6498	94	33	written	write	VERB
ejpam-6498	94	34	as	as	ADP
ejpam-6498	94	35	w(t	w(t	PROPN
ejpam-6498	94	36	)	)	PUNCT
ejpam-6498	94	37	=	=	SYM
ejpam-6498	94	38	lf(t	lf(t	NOUN
ejpam-6498	94	39	)	)	PUNCT
ejpam-6498	94	40	,	,	PUNCT
ejpam-6498	94	41	where	where	SCONJ
ejpam-6498	94	42	l	l	NOUN
ejpam-6498	94	43	is	be	AUX
ejpam-6498	94	44	the	the	DET
ejpam-6498	94	45	leading	lead	VERB
ejpam-6498	94	46	coefficient	coefficient	NOUN
ejpam-6498	94	47	of	of	ADP
ejpam-6498	94	48	polynomial	polynomial	ADJ
ejpam-6498	94	49	w(t	w(t	PROPN
ejpam-6498	94	50	)	)	PUNCT
ejpam-6498	94	51	and	and	CCONJ
ejpam-6498	94	52	f(t	f(t	NOUN
ejpam-6498	94	53	)	)	PUNCT
ejpam-6498	95	1	=	=	SYM
ejpam-6498	95	2	t2(t−	t2(t−	NUM
ejpam-6498	96	1	1)2(t−	1)2(t−	NUM
ejpam-6498	96	2	0.5)2	0.5)2	NOUN
ejpam-6498	96	3	.	.	PUNCT
ejpam-6498	97	1	using	use	VERB
ejpam-6498	97	2	(	(	PUNCT
ejpam-6498	97	3	6	6	NUM
ejpam-6498	97	4	)	)	PUNCT
ejpam-6498	97	5	the	the	DET
ejpam-6498	97	6	leading	lead	VERB
ejpam-6498	97	7	coefficient	coefficient	NOUN
ejpam-6498	97	8	l	l	NOUN
ejpam-6498	97	9	of	of	ADP
ejpam-6498	97	10	w(t	w(t	PROPN
ejpam-6498	97	11	)	)	PUNCT
ejpam-6498	97	12	is	be	AUX
ejpam-6498	97	13	computed	compute	VERB
ejpam-6498	97	14	and	and	CCONJ
ejpam-6498	97	15	its	its	PRON
ejpam-6498	97	16	value	value	NOUN
ejpam-6498	97	17	is	be	AUX
ejpam-6498	97	18	:	:	PUNCT
ejpam-6498	98	1	l	l	X
ejpam-6498	98	2	=	=	SYM
ejpam-6498	98	3	a2b2	a2b2	X
ejpam-6498	98	4	(	(	PUNCT
ejpam-6498	98	5	1	1	NUM
ejpam-6498	98	6	+	+	CCONJ
ejpam-6498	98	7	cosφ1	cosφ1	X
ejpam-6498	98	8	)	)	PUNCT
ejpam-6498	98	9	(	(	PUNCT
ejpam-6498	98	10	128−	128−	NUM
ejpam-6498	98	11	64	64	NUM
ejpam-6498	98	12	sin2	sin2	NOUN
ejpam-6498	98	13	φ1	φ1	PROPN
ejpam-6498	98	14	−	−	PROPN
ejpam-6498	98	15	64(1	64(1	NUM
ejpam-6498	98	16	+	+	CCONJ
ejpam-6498	98	17	cosφ1)(1−	cosφ1)(1−	ADJ
ejpam-6498	98	18	sin2	sin2	NOUN
ejpam-6498	98	19	φ1	φ1	PROPN
ejpam-6498	98	20	)	)	PUNCT
ejpam-6498	98	21	)	)	PUNCT
ejpam-6498	98	22	.	.	PUNCT
ejpam-6498	99	1	simplifying	simplify	VERB
ejpam-6498	99	2	the	the	DET
ejpam-6498	99	3	above	above	ADJ
ejpam-6498	99	4	equation	equation	NOUN
ejpam-6498	99	5	we	we	PRON
ejpam-6498	99	6	get	get	VERB
ejpam-6498	99	7	the	the	DET
ejpam-6498	99	8	leading	lead	VERB
ejpam-6498	99	9	coefficient	coefficient	NOUN
ejpam-6498	99	10	l	l	NOUN
ejpam-6498	99	11	of	of	ADP
ejpam-6498	99	12	w(t	w(t	PROPN
ejpam-6498	99	13	)	)	PUNCT
ejpam-6498	99	14	.	.	PUNCT
ejpam-6498	100	1	the	the	DET
ejpam-6498	100	2	hausdorff	hausdorff	PROPN
ejpam-6498	100	3	distance	distance	PROPN
ejpam-6498	100	4	dh(p̂0p1	dh(p̂0p1	PROPN
ejpam-6498	100	5	,	,	PUNCT
ejpam-6498	100	6	b(t	b(t	NOUN
ejpam-6498	100	7	)	)	PUNCT
ejpam-6498	100	8	)	)	PUNCT
ejpam-6498	100	9	between	between	ADP
ejpam-6498	100	10	the	the	DET
ejpam-6498	100	11	elliptic	elliptic	ADJ
ejpam-6498	100	12	arc	arc	NOUN
ejpam-6498	100	13	and	and	CCONJ
ejpam-6498	100	14	the	the	DET
ejpam-6498	100	15	cubic	cubic	ADJ
ejpam-6498	100	16	bézier	bézier	ADP
ejpam-6498	100	17	curve	curve	NOUN
ejpam-6498	100	18	is	be	AUX
ejpam-6498	100	19	defined	define	VERB
ejpam-6498	100	20	as	as	ADP
ejpam-6498	100	21	:	:	PUNCT
ejpam-6498	100	22	dh(p̂0p1	dh(p̂0p1	PROPN
ejpam-6498	100	23	,	,	PUNCT
ejpam-6498	100	24	b(t	b(t	NOUN
ejpam-6498	100	25	)	)	PUNCT
ejpam-6498	100	26	)	)	PUNCT
ejpam-6498	101	1	=	=	PUNCT
ejpam-6498	101	2	|l|	|l|	NOUN
ejpam-6498	101	3	max	max	PROPN
ejpam-6498	101	4	t∈[0,1	t∈[0,1	PROPN
ejpam-6498	101	5	]	]	X
ejpam-6498	101	6	|w(t)|	|w(t)|	PROPN
ejpam-6498	101	7	.	.	PUNCT
ejpam-6498	102	1	the	the	DET
ejpam-6498	102	2	zeros	zero	NOUN
ejpam-6498	102	3	of	of	ADP
ejpam-6498	102	4	dw(t	dw(t	NOUN
ejpam-6498	102	5	)	)	PUNCT
ejpam-6498	102	6	dt	dt	X
ejpam-6498	102	7	are	be	AUX
ejpam-6498	102	8	t	t	PROPN
ejpam-6498	102	9	=	=	SYM
ejpam-6498	102	10	0	0	NUM
ejpam-6498	102	11	,	,	PUNCT
ejpam-6498	102	12	1	1	NUM
ejpam-6498	102	13	,	,	PUNCT
ejpam-6498	102	14	12	12	NUM
ejpam-6498	102	15	±	±	NOUN
ejpam-6498	102	16	√	√	ADV
ejpam-6498	102	17	3	3	NUM
ejpam-6498	102	18	6	6	NUM
ejpam-6498	102	19	and	and	CCONJ
ejpam-6498	102	20	the	the	DET
ejpam-6498	102	21	points	point	NOUN
ejpam-6498	102	22	of	of	ADP
ejpam-6498	102	23	relative	relative	ADJ
ejpam-6498	102	24	maxima	maxima	NOUN
ejpam-6498	102	25	of	of	ADP
ejpam-6498	102	26	w(t	w(t	PROPN
ejpam-6498	102	27	)	)	PUNCT
ejpam-6498	102	28	in	in	ADP
ejpam-6498	102	29	the	the	DET
ejpam-6498	102	30	interval	interval	NOUN
ejpam-6498	102	31	[	[	X
ejpam-6498	102	32	0	0	NUM
ejpam-6498	102	33	,	,	PUNCT
ejpam-6498	102	34	1	1	NUM
ejpam-6498	102	35	]	]	PUNCT
ejpam-6498	102	36	is	be	AUX
ejpam-6498	102	37	t	t	NOUN
ejpam-6498	102	38	=	=	SYM
ejpam-6498	102	39	1	1	NUM
ejpam-6498	102	40	2	2	NUM
ejpam-6498	102	41	+	+	CCONJ
ejpam-6498	102	42	√	√	NUM
ejpam-6498	102	43	3	3	NUM
ejpam-6498	102	44	6	6	NUM
ejpam-6498	102	45	.	.	PUNCT
ejpam-6498	103	1	the	the	DET
ejpam-6498	103	2	maximum	maximum	ADJ
ejpam-6498	103	3	value	value	NOUN
ejpam-6498	103	4	of	of	ADP
ejpam-6498	103	5	w(t	w(t	PROPN
ejpam-6498	103	6	)	)	PUNCT
ejpam-6498	103	7	is	be	AUX
ejpam-6498	103	8	1	1	NUM
ejpam-6498	103	9	432	432	NUM
ejpam-6498	103	10	.	.	PUNCT
ejpam-6498	104	1	it	it	PRON
ejpam-6498	104	2	follows	follow	VERB
ejpam-6498	104	3	from	from	ADP
ejpam-6498	104	4	the	the	DET
ejpam-6498	104	5	above	above	ADJ
ejpam-6498	104	6	discussion	discussion	NOUN
ejpam-6498	104	7	that	that	SCONJ
ejpam-6498	104	8	:	:	PUNCT
ejpam-6498	104	9	dh(p̂0p1	dh(p̂0p1	INTJ
ejpam-6498	104	10	,	,	PUNCT
ejpam-6498	104	11	b(t	b(t	NOUN
ejpam-6498	104	12	)	)	PUNCT
ejpam-6498	104	13	)	)	PUNCT
ejpam-6498	105	1	=	=	PUNCT
ejpam-6498	105	2	|l|	|l|	NOUN
ejpam-6498	105	3	1	1	NUM
ejpam-6498	105	4	432	432	NUM
ejpam-6498	105	5	.	.	PUNCT
ejpam-6498	106	1	(	(	PUNCT
ejpam-6498	106	2	9	9	NUM
ejpam-6498	106	3	)	)	PUNCT
ejpam-6498	106	4	by	by	ADP
ejpam-6498	106	5	the	the	DET
ejpam-6498	106	6	taylor	taylor	PROPN
ejpam-6498	106	7	series	series	PROPN
ejpam-6498	106	8	expansion	expansion	NOUN
ejpam-6498	106	9	of	of	ADP
ejpam-6498	106	10	l	l	PROPN
ejpam-6498	106	11	at	at	ADP
ejpam-6498	106	12	φ	φ	PROPN
ejpam-6498	106	13	=	=	SYM
ejpam-6498	106	14	0	0	PROPN
ejpam-6498	106	15	,	,	PUNCT
ejpam-6498	106	16	we	we	PRON
ejpam-6498	106	17	have	have	VERB
ejpam-6498	106	18	:	:	PUNCT
ejpam-6498	106	19	l	l	NOUN
ejpam-6498	106	20	=	=	SYM
ejpam-6498	106	21	l(φ	l(φ	NOUN
ejpam-6498	106	22	)	)	PUNCT
ejpam-6498	107	1	=	=	SYM
ejpam-6498	107	2	l(0	l(0	PROPN
ejpam-6498	107	3	)	)	PUNCT
ejpam-6498	108	1	+	+	CCONJ
ejpam-6498	109	1	φl′(0	φl′(0	NOUN
ejpam-6498	109	2	)	)	PUNCT
ejpam-6498	109	3	+	+	NUM
ejpam-6498	109	4	φ2	φ2	PROPN
ejpam-6498	109	5	2	2	NUM
ejpam-6498	109	6	!	!	PUNCT
ejpam-6498	109	7	l′′(0	l′′(0	PROPN
ejpam-6498	109	8	)	)	PUNCT
ejpam-6498	110	1	+	+	CCONJ
ejpam-6498	110	2	φ3	φ3	PROPN
ejpam-6498	110	3	3	3	NUM
ejpam-6498	110	4	!	!	PUNCT
ejpam-6498	110	5	l′′′(0	l′′′(0	NOUN
ejpam-6498	110	6	)	)	PUNCT
ejpam-6498	111	1	+	+	CCONJ
ejpam-6498	111	2	φ4	φ4	NOUN
ejpam-6498	111	3	4	4	NUM
ejpam-6498	111	4	!	!	PUNCT
ejpam-6498	111	5	l(iv)(0	l(iv)(0	NOUN
ejpam-6498	111	6	)	)	PUNCT
ejpam-6498	112	1	+	+	CCONJ
ejpam-6498	112	2	φ5	φ5	ADJ
ejpam-6498	112	3	5	5	NUM
ejpam-6498	112	4	!	!	PUNCT
ejpam-6498	112	5	l(v)(0	l(v)(0	NUM
ejpam-6498	112	6	)	)	PUNCT
ejpam-6498	113	1	+	+	NUM
ejpam-6498	113	2	φ6	φ6	NOUN
ejpam-6498	113	3	6	6	NUM
ejpam-6498	113	4	!	!	PUNCT
ejpam-6498	113	5	l(vi)(0	l(vi)(0	ADJ
ejpam-6498	113	6	)	)	PUNCT
ejpam-6498	114	1	+	+	NUM
ejpam-6498	114	2	φ7	φ7	PROPN
ejpam-6498	114	3	7	7	NUM
ejpam-6498	114	4	!	!	PUNCT
ejpam-6498	114	5	l(vii)(0	l(vii)(0	NOUN
ejpam-6498	114	6	)	)	PUNCT
ejpam-6498	115	1	+	+	CCONJ
ejpam-6498	115	2	φ8	φ8	ADJ
ejpam-6498	115	3	8	8	NUM
ejpam-6498	115	4	!	!	PUNCT
ejpam-6498	116	1	l(viii)(0	l(viii)(0	ADV
ejpam-6498	116	2	)	)	PUNCT
ejpam-6498	117	1	+	+	CCONJ
ejpam-6498	117	2	φ9	φ9	NOUN
ejpam-6498	117	3	9	9	NUM
ejpam-6498	117	4	!	!	PUNCT
ejpam-6498	118	1	l(ix)(0	l(ix)(0	ADJ
ejpam-6498	118	2	)	)	PUNCT
ejpam-6498	119	1	+	+	NUM
ejpam-6498	119	2	φ10	φ10	NOUN
ejpam-6498	119	3	10	10	NUM
ejpam-6498	119	4	!	!	PUNCT
ejpam-6498	119	5	l(x)(0	l(x)(0	PROPN
ejpam-6498	119	6	)	)	PUNCT
ejpam-6498	120	1	+	+	CCONJ
ejpam-6498	120	2	·	·	PUNCT
ejpam-6498	120	3	·	·	PUNCT
ejpam-6498	120	4	·	·	PUNCT
ejpam-6498	120	5	substituting	substitute	VERB
ejpam-6498	120	6	the	the	DET
ejpam-6498	120	7	values	value	NOUN
ejpam-6498	120	8	of	of	ADP
ejpam-6498	120	9	l(φ	l(φ	NOUN
ejpam-6498	120	10	)	)	PUNCT
ejpam-6498	120	11	and	and	CCONJ
ejpam-6498	120	12	its	its	PRON
ejpam-6498	120	13	derivatives	derivative	NOUN
ejpam-6498	120	14	at	at	ADP
ejpam-6498	120	15	φ	φ	PROPN
ejpam-6498	120	16	=	=	SYM
ejpam-6498	120	17	0	0	NUM
ejpam-6498	120	18	in	in	ADP
ejpam-6498	120	19	the	the	DET
ejpam-6498	120	20	above	above	ADJ
ejpam-6498	120	21	relation	relation	NOUN
ejpam-6498	120	22	,	,	PUNCT
ejpam-6498	120	23	the	the	DET
ejpam-6498	120	24	expression	expression	NOUN
ejpam-6498	120	25	reduces	reduce	VERB
ejpam-6498	120	26	to	to	ADP
ejpam-6498	120	27	:	:	PUNCT
ejpam-6498	120	28	l	l	NOUN
ejpam-6498	120	29	=	=	PUNCT
ejpam-6498	120	30	a2b2φ6	a2b2φ6	ADP
ejpam-6498	120	31	6	6	NUM
ejpam-6498	120	32	!	!	PUNCT
ejpam-6498	121	1	(	(	PUNCT
ejpam-6498	121	2	45	45	NUM
ejpam-6498	121	3	4	4	NUM
ejpam-6498	121	4	)	)	PUNCT
ejpam-6498	122	1	+	+	NOUN
ejpam-6498	122	2	o(φ10	o(φ10	NOUN
ejpam-6498	122	3	)	)	PUNCT
ejpam-6498	122	4	.	.	PUNCT
ejpam-6498	123	1	(	(	PUNCT
ejpam-6498	123	2	10	10	NUM
ejpam-6498	123	3	)	)	PUNCT
ejpam-6498	123	4	thus	thus	ADV
ejpam-6498	123	5	the	the	DET
ejpam-6498	123	6	approximation	approximation	NOUN
ejpam-6498	123	7	order	order	NOUN
ejpam-6498	123	8	of	of	ADP
ejpam-6498	123	9	the	the	DET
ejpam-6498	123	10	proposed	propose	VERB
ejpam-6498	123	11	elliptic	elliptic	ADJ
ejpam-6498	123	12	arc	arc	NOUN
ejpam-6498	123	13	approximation	approximation	NOUN
ejpam-6498	123	14	scheme	scheme	NOUN
ejpam-6498	123	15	is	be	AUX
ejpam-6498	123	16	10	10	NUM
ejpam-6498	123	17	.	.	PUNCT
ejpam-6498	124	1	using	use	VERB
ejpam-6498	124	2	(	(	PUNCT
ejpam-6498	124	3	9	9	NUM
ejpam-6498	124	4	)	)	PUNCT
ejpam-6498	124	5	and	and	CCONJ
ejpam-6498	124	6	(	(	PUNCT
ejpam-6498	124	7	10	10	NUM
ejpam-6498	124	8	)	)	PUNCT
ejpam-6498	124	9	we	we	PRON
ejpam-6498	124	10	get	get	VERB
ejpam-6498	124	11	:	:	PUNCT
ejpam-6498	124	12	dh(p̂0p1	dh(p̂0p1	PROPN
ejpam-6498	124	13	,	,	PUNCT
ejpam-6498	124	14	b(t	b(t	NOUN
ejpam-6498	124	15	)	)	PUNCT
ejpam-6498	124	16	)	)	PUNCT
ejpam-6498	125	1	=	=	PUNCT
ejpam-6498	125	2	a2b2(3.6168981×	a2b2(3.6168981×	X
ejpam-6498	126	1	10−5)φ6	10−5)φ6	NUM
ejpam-6498	126	2	+	+	NOUN
ejpam-6498	126	3	o(φ10	o(φ10	NOUN
ejpam-6498	126	4	)	)	PUNCT
ejpam-6498	126	5	.	.	PUNCT
ejpam-6498	127	1	m.	m.	PROPN
ejpam-6498	127	2	hussain	hussain	PROPN
ejpam-6498	127	3	,	,	PUNCT
ejpam-6498	127	4	h.	h.	PROPN
ejpam-6498	127	5	a.	a.	PROPN
ejpam-6498	127	6	wajid	wajid	PROPN
ejpam-6498	127	7	,	,	PUNCT
ejpam-6498	127	8	s.	s.	PROPN
ejpam-6498	127	9	aqeel	aqeel	PROPN
ejpam-6498	127	10	/	/	SYM
ejpam-6498	127	11	eur	eur	PROPN
ejpam-6498	127	12	.	.	PUNCT
ejpam-6498	128	1	j.	j.	PROPN
ejpam-6498	128	2	pure	pure	PROPN
ejpam-6498	128	3	appl	appl	PROPN
ejpam-6498	128	4	.	.	PROPN
ejpam-6498	128	5	math	math	PROPN
ejpam-6498	128	6	,	,	PUNCT
ejpam-6498	128	7	18	18	NUM
ejpam-6498	128	8	(	(	PUNCT
ejpam-6498	128	9	4	4	NUM
ejpam-6498	128	10	)	)	PUNCT
ejpam-6498	128	11	(	(	PUNCT
ejpam-6498	128	12	2025	2025	NUM
ejpam-6498	128	13	)	)	PUNCT
ejpam-6498	128	14	,	,	PUNCT
ejpam-6498	128	15	6498	6498	NUM
ejpam-6498	128	16	6	6	NUM
ejpam-6498	128	17	of	of	ADP
ejpam-6498	128	18	12	12	NUM
ejpam-6498	128	19	theorem	theorem	NOUN
ejpam-6498	128	20	3	3	NUM
ejpam-6498	128	21	.	.	PUNCT
ejpam-6498	129	1	if	if	SCONJ
ejpam-6498	129	2	the	the	DET
ejpam-6498	129	3	cubic	cubic	ADJ
ejpam-6498	129	4	bézier	bézier	ADP
ejpam-6498	129	5	curve	curve	NOUN
ejpam-6498	129	6	(	(	PUNCT
ejpam-6498	129	7	1	1	X
ejpam-6498	129	8	)	)	PUNCT
ejpam-6498	129	9	has	have	VERB
ejpam-6498	129	10	control	control	NOUN
ejpam-6498	129	11	points	point	NOUN
ejpam-6498	129	12	b0	b0	NOUN
ejpam-6498	129	13	=	=	SYM
ejpam-6498	129	14	(	(	PUNCT
ejpam-6498	129	15	0	0	NUM
ejpam-6498	129	16	,	,	PUNCT
ejpam-6498	129	17	0	0	NUM
ejpam-6498	129	18	)	)	PUNCT
ejpam-6498	129	19	,	,	PUNCT
ejpam-6498	129	20	b1	b1	NOUN
ejpam-6498	129	21	=	=	SYM
ejpam-6498	129	22	(	(	PUNCT
ejpam-6498	129	23	0	0	NUM
ejpam-6498	129	24	,	,	PUNCT
ejpam-6498	129	25	r1	r1	PROPN
ejpam-6498	129	26	)	)	PUNCT
ejpam-6498	129	27	,	,	PUNCT
ejpam-6498	129	28	b2	b2	NOUN
ejpam-6498	129	29	=	=	SYM
ejpam-6498	129	30	(	(	PUNCT
ejpam-6498	129	31	aϑ2	aϑ2	NOUN
ejpam-6498	129	32	−	−	ADP
ejpam-6498	129	33	ϑr2√	ϑr2√	ADJ
ejpam-6498	129	34	ϑ2	ϑ2	NOUN
ejpam-6498	129	35	+	+	CCONJ
ejpam-6498	129	36	1	1	NUM
ejpam-6498	129	37	,	,	PUNCT
ejpam-6498	129	38	2aϑ−	2aϑ−	NUM
ejpam-6498	129	39	r2√	r2√	ADJ
ejpam-6498	129	40	ϑ2	ϑ2	NOUN
ejpam-6498	129	41	+	+	CCONJ
ejpam-6498	129	42	1	1	NUM
ejpam-6498	129	43	)	)	PUNCT
ejpam-6498	129	44	,	,	PUNCT
ejpam-6498	129	45	b3	b3	PROPN
ejpam-6498	129	46	=	=	SYM
ejpam-6498	129	47	(	(	PUNCT
ejpam-6498	129	48	aϑ2	aϑ2	PROPN
ejpam-6498	129	49	,	,	PUNCT
ejpam-6498	129	50	2aϑ	2aϑ	ADJ
ejpam-6498	129	51	)	)	PUNCT
ejpam-6498	129	52	,	,	PUNCT
ejpam-6498	129	53	with	with	ADP
ejpam-6498	129	54	r1	r1	PROPN
ejpam-6498	129	55	=	=	PUNCT
ejpam-6498	129	56	r2√	r2√	PROPN
ejpam-6498	129	57	ϑ2	ϑ2	NOUN
ejpam-6498	129	58	+	+	PROPN
ejpam-6498	129	59	1	1	NUM
ejpam-6498	129	60	and	and	CCONJ
ejpam-6498	129	61	r2	r2	PROPN
ejpam-6498	129	62	=	=	SYM
ejpam-6498	129	63	2aϑ	2aϑ	ADJ
ejpam-6498	129	64	√	√	NUM
ejpam-6498	129	65	ϑ2	ϑ2	NOUN
ejpam-6498	129	66	+	+	PROPN
ejpam-6498	129	67	1	1	NUM
ejpam-6498	129	68	3	3	NUM
ejpam-6498	129	69	,	,	PUNCT
ejpam-6498	129	70	then	then	ADV
ejpam-6498	129	71	the	the	DET
ejpam-6498	129	72	approximation	approximation	NOUN
ejpam-6498	129	73	of	of	ADP
ejpam-6498	129	74	the	the	DET
ejpam-6498	129	75	parabolic	parabolic	ADJ
ejpam-6498	129	76	arc	arc	NOUN
ejpam-6498	129	77	ôq	ôq	NUM
ejpam-6498	129	78	by	by	ADP
ejpam-6498	129	79	the	the	DET
ejpam-6498	129	80	cubic	cubic	ADJ
ejpam-6498	129	81	bézier	bézier	PROPN
ejpam-6498	129	82	curve	curve	NOUN
ejpam-6498	129	83	(	(	PUNCT
ejpam-6498	129	84	1	1	X
ejpam-6498	129	85	)	)	PUNCT
ejpam-6498	129	86	is	be	AUX
ejpam-6498	129	87	unique	unique	ADJ
ejpam-6498	129	88	.	.	PUNCT
ejpam-6498	130	1	proof	proof	NOUN
ejpam-6498	130	2	.	.	PUNCT
ejpam-6498	131	1	let	let	VERB
ejpam-6498	131	2	the	the	DET
ejpam-6498	131	3	parabolic	parabolic	ADJ
ejpam-6498	131	4	arc	arc	NOUN
ejpam-6498	131	5	be	be	AUX
ejpam-6498	131	6	ôq	ôq	NUM
ejpam-6498	131	7	where	where	SCONJ
ejpam-6498	131	8	o(0	o(0	NOUN
ejpam-6498	131	9	,	,	PUNCT
ejpam-6498	131	10	0	0	NUM
ejpam-6498	131	11	)	)	PUNCT
ejpam-6498	131	12	and	and	CCONJ
ejpam-6498	131	13	q(aϑ2	q(aϑ2	PROPN
ejpam-6498	131	14	,	,	PUNCT
ejpam-6498	131	15	2aϑ	2aϑ	ADJ
ejpam-6498	131	16	)	)	PUNCT
ejpam-6498	131	17	,	,	PUNCT
ejpam-6498	132	1	0	0	NUM
ejpam-6498	132	2	≤	≤	NOUN
ejpam-6498	132	3	ϑ	ϑ	X
ejpam-6498	132	4	<	<	X
ejpam-6498	132	5	∞.	∞.	PROPN
ejpam-6498	132	6	the	the	DET
ejpam-6498	132	7	cubic	cubic	ADJ
ejpam-6498	132	8	bézier	bézier	ADP
ejpam-6498	132	9	curve	curve	NOUN
ejpam-6498	132	10	approximation	approximation	NOUN
ejpam-6498	132	11	of	of	ADP
ejpam-6498	132	12	parabolic	parabolic	ADJ
ejpam-6498	132	13	arc	arc	NOUN
ejpam-6498	132	14	is	be	AUX
ejpam-6498	132	15	carried	carry	VERB
ejpam-6498	132	16	out	out	ADP
ejpam-6498	132	17	by	by	ADP
ejpam-6498	132	18	the	the	DET
ejpam-6498	132	19	tangent	tangent	NOUN
ejpam-6498	132	20	continuity	continuity	NOUN
ejpam-6498	132	21	approximation	approximation	NOUN
ejpam-6498	132	22	constraints	constraint	NOUN
ejpam-6498	132	23	.	.	PUNCT
ejpam-6498	133	1	any	any	DET
ejpam-6498	133	2	parabolic	parabolic	ADJ
ejpam-6498	133	3	arc	arc	NOUN
ejpam-6498	133	4	can	can	AUX
ejpam-6498	133	5	be	be	AUX
ejpam-6498	133	6	transformed	transform	VERB
ejpam-6498	133	7	to	to	ADP
ejpam-6498	133	8	this	this	DET
ejpam-6498	133	9	position	position	NOUN
ejpam-6498	133	10	by	by	ADP
ejpam-6498	133	11	using	use	VERB
ejpam-6498	133	12	affine	affine	NOUN
ejpam-6498	133	13	transformations	transformation	NOUN
ejpam-6498	133	14	.	.	PUNCT
ejpam-6498	134	1	the	the	DET
ejpam-6498	134	2	approximation	approximation	NOUN
ejpam-6498	134	3	constraints	constraint	NOUN
ejpam-6498	134	4	used	use	VERB
ejpam-6498	134	5	for	for	ADP
ejpam-6498	134	6	the	the	DET
ejpam-6498	134	7	approximation	approximation	NOUN
ejpam-6498	134	8	of	of	ADP
ejpam-6498	134	9	parabolic	parabolic	ADJ
ejpam-6498	134	10	arc	arc	NOUN
ejpam-6498	134	11	are	be	AUX
ejpam-6498	134	12	as	as	SCONJ
ejpam-6498	134	13	follows	follow	VERB
ejpam-6498	134	14	:	:	PUNCT
ejpam-6498	135	1	b(t)|t=0	b(t)|t=0	PROPN
ejpam-6498	135	2	=	=	SYM
ejpam-6498	135	3	o(0	o(0	PROPN
ejpam-6498	135	4	,	,	PUNCT
ejpam-6498	135	5	0	0	NUM
ejpam-6498	135	6	)	)	PUNCT
ejpam-6498	135	7	,	,	PUNCT
ejpam-6498	135	8	b(t)|t=1	b(t)|t=1	PROPN
ejpam-6498	135	9	=	=	SYM
ejpam-6498	135	10	q(aϑ2	q(aϑ2	PROPN
ejpam-6498	135	11	,	,	PUNCT
ejpam-6498	135	12	2aϑ	2aϑ	ADJ
ejpam-6498	135	13	)	)	PUNCT
ejpam-6498	135	14	.	.	PUNCT
ejpam-6498	136	1	(	(	PUNCT
ejpam-6498	136	2	11	11	X
ejpam-6498	136	3	)	)	PUNCT
ejpam-6498	136	4	t0	t0	NOUN
ejpam-6498	136	5	=	=	SYM
ejpam-6498	136	6	t̃0	t̃0	PROPN
ejpam-6498	136	7	,	,	PUNCT
ejpam-6498	136	8	t1	t1	NOUN
ejpam-6498	136	9	=	=	PUNCT
ejpam-6498	136	10	t̃1	t̃1	PROPN
ejpam-6498	136	11	.	.	PUNCT
ejpam-6498	137	1	(	(	PUNCT
ejpam-6498	137	2	12	12	NUM
ejpam-6498	137	3	)	)	PUNCT
ejpam-6498	137	4	here	here	ADV
ejpam-6498	137	5	tm	tm	PROPN
ejpam-6498	137	6	’s	’s	PART
ejpam-6498	137	7	,	,	PUNCT
ejpam-6498	137	8	m	m	VERB
ejpam-6498	137	9	=	=	NOUN
ejpam-6498	137	10	0	0	NUM
ejpam-6498	137	11	,	,	PUNCT
ejpam-6498	137	12	1	1	NUM
ejpam-6498	137	13	,	,	PUNCT
ejpam-6498	137	14	are	be	AUX
ejpam-6498	137	15	the	the	DET
ejpam-6498	137	16	end	end	NOUN
ejpam-6498	137	17	unit	unit	NOUN
ejpam-6498	137	18	tangents	tangent	NOUN
ejpam-6498	137	19	of	of	ADP
ejpam-6498	137	20	the	the	DET
ejpam-6498	137	21	cubic	cubic	ADJ
ejpam-6498	138	1	bézier	bézier	PROPN
ejpam-6498	138	2	curve	curve	NOUN
ejpam-6498	138	3	and	and	CCONJ
ejpam-6498	138	4	t̃m	t̃m	NOUN
ejpam-6498	138	5	’s	’s	PART
ejpam-6498	138	6	are	be	AUX
ejpam-6498	138	7	the	the	DET
ejpam-6498	138	8	end	end	NOUN
ejpam-6498	138	9	unit	unit	NOUN
ejpam-6498	138	10	tangents	tangent	NOUN
ejpam-6498	138	11	of	of	ADP
ejpam-6498	138	12	the	the	DET
ejpam-6498	138	13	parabolic	parabolic	ADJ
ejpam-6498	138	14	arc	arc	NOUN
ejpam-6498	138	15	ôq	ôq	NUM
ejpam-6498	138	16	.	.	PUNCT
ejpam-6498	139	1	here	here	ADV
ejpam-6498	139	2	,	,	PUNCT
ejpam-6498	139	3	t0	t0	X
ejpam-6498	139	4	=	=	PUNCT
ejpam-6498	140	1	b1−b0	b1−b0	PROPN
ejpam-6498	140	2	r1	r1	PROPN
ejpam-6498	140	3	and	and	CCONJ
ejpam-6498	140	4	t1	t1	NOUN
ejpam-6498	140	5	=	=	PUNCT
ejpam-6498	140	6	b3−b2	b3−b2	NUM
ejpam-6498	140	7	r2	r2	NOUN
ejpam-6498	140	8	,	,	PUNCT
ejpam-6498	140	9	with	with	ADP
ejpam-6498	140	10	r1	r1	NOUN
ejpam-6498	140	11	=	=	SYM
ejpam-6498	140	12	∥b1	∥b1	VERB
ejpam-6498	140	13	−	−	PROPN
ejpam-6498	140	14	b0∥	b0∥	NOUN
ejpam-6498	140	15	and	and	CCONJ
ejpam-6498	140	16	r2	r2	PROPN
ejpam-6498	140	17	=	=	SYM
ejpam-6498	140	18	∥b3	∥b3	NOUN
ejpam-6498	140	19	−	−	PROPN
ejpam-6498	140	20	b2∥.	b2∥.	NOUN
ejpam-6498	140	21	here	here	ADV
ejpam-6498	140	22	r1	r1	PROPN
ejpam-6498	140	23	and	and	CCONJ
ejpam-6498	140	24	r2	r2	PROPN
ejpam-6498	140	25	are	be	AUX
ejpam-6498	140	26	unknowns	unknown	NOUN
ejpam-6498	140	27	.	.	PUNCT
ejpam-6498	141	1	the	the	DET
ejpam-6498	141	2	end	end	NOUN
ejpam-6498	141	3	unit	unit	NOUN
ejpam-6498	141	4	tangents	tangent	NOUN
ejpam-6498	141	5	of	of	ADP
ejpam-6498	141	6	the	the	DET
ejpam-6498	141	7	parabolic	parabolic	ADJ
ejpam-6498	141	8	arc	arc	NOUN
ejpam-6498	141	9	ôq	ôq	PRON
ejpam-6498	141	10	are	be	AUX
ejpam-6498	141	11	t̃0	t̃0	PROPN
ejpam-6498	141	12	=	=	SYM
ejpam-6498	141	13	(	(	PUNCT
ejpam-6498	141	14	0	0	NUM
ejpam-6498	141	15	,	,	PUNCT
ejpam-6498	141	16	1	1	NUM
ejpam-6498	141	17	)	)	PUNCT
ejpam-6498	141	18	and	and	CCONJ
ejpam-6498	141	19	t̃1	t̃1	PROPN
ejpam-6498	141	20	=	=	SYM
ejpam-6498	141	21	(	(	PUNCT
ejpam-6498	141	22	ϑ,1)√	ϑ,1)√	X
ejpam-6498	141	23	ϑ2	ϑ2	NOUN
ejpam-6498	141	24	+	+	PROPN
ejpam-6498	141	25	1	1	NUM
ejpam-6498	141	26	.	.	PUNCT
ejpam-6498	142	1	formulae	formulae	NOUN
ejpam-6498	142	2	(	(	PUNCT
ejpam-6498	142	3	11	11	NUM
ejpam-6498	142	4	)	)	PUNCT
ejpam-6498	142	5	and	and	CCONJ
ejpam-6498	142	6	(	(	PUNCT
ejpam-6498	142	7	12	12	NUM
ejpam-6498	142	8	)	)	PUNCT
ejpam-6498	142	9	tell	tell	VERB
ejpam-6498	142	10	us	we	PRON
ejpam-6498	142	11	that	that	SCONJ
ejpam-6498	142	12	the	the	DET
ejpam-6498	142	13	cubic	cubic	ADJ
ejpam-6498	142	14	bézier	bézier	PROPN
ejpam-6498	142	15	curve	curve	NOUN
ejpam-6498	142	16	(	(	PUNCT
ejpam-6498	142	17	1	1	X
ejpam-6498	142	18	)	)	PUNCT
ejpam-6498	142	19	approximates	approximate	VERB
ejpam-6498	142	20	the	the	DET
ejpam-6498	142	21	parabolic	parabolic	ADJ
ejpam-6498	142	22	arc	arc	NOUN
ejpam-6498	142	23	using	use	VERB
ejpam-6498	142	24	g1	g1	PROPN
ejpam-6498	142	25	continuity	continuity	NOUN
ejpam-6498	142	26	conditions	condition	NOUN
ejpam-6498	142	27	.	.	PUNCT
ejpam-6498	143	1	using	use	VERB
ejpam-6498	143	2	(	(	PUNCT
ejpam-6498	143	3	1	1	NUM
ejpam-6498	143	4	)	)	PUNCT
ejpam-6498	143	5	,	,	PUNCT
ejpam-6498	143	6	(	(	PUNCT
ejpam-6498	143	7	11	11	NUM
ejpam-6498	143	8	)	)	PUNCT
ejpam-6498	143	9	and	and	CCONJ
ejpam-6498	143	10	(	(	PUNCT
ejpam-6498	143	11	12	12	NUM
ejpam-6498	143	12	)	)	PUNCT
ejpam-6498	143	13	,	,	PUNCT
ejpam-6498	143	14	the	the	DET
ejpam-6498	143	15	control	control	NOUN
ejpam-6498	143	16	points	point	NOUN
ejpam-6498	143	17	(	(	PUNCT
ejpam-6498	143	18	b0	b0	NOUN
ejpam-6498	143	19	,	,	PUNCT
ejpam-6498	143	20	b1	b1	NOUN
ejpam-6498	143	21	,	,	PUNCT
ejpam-6498	143	22	b2	b2	NOUN
ejpam-6498	143	23	,	,	PUNCT
ejpam-6498	143	24	b3	b3	PROPN
ejpam-6498	143	25	)	)	PUNCT
ejpam-6498	143	26	of	of	ADP
ejpam-6498	143	27	the	the	DET
ejpam-6498	143	28	cubic	cubic	ADJ
ejpam-6498	143	29	bézier	bézier	ADP
ejpam-6498	143	30	curve	curve	NOUN
ejpam-6498	143	31	approximation	approximation	NOUN
ejpam-6498	143	32	of	of	ADP
ejpam-6498	143	33	parabolic	parabolic	ADJ
ejpam-6498	143	34	arc	arc	NOUN
ejpam-6498	143	35	ôq	ôq	NUM
ejpam-6498	143	36	are	be	AUX
ejpam-6498	143	37	evaluated	evaluate	VERB
ejpam-6498	143	38	as	as	ADP
ejpam-6498	143	39	:	:	PUNCT
ejpam-6498	143	40	b0	b0	NOUN
ejpam-6498	143	41	=	=	SYM
ejpam-6498	143	42	(	(	PUNCT
ejpam-6498	143	43	0	0	NUM
ejpam-6498	143	44	,	,	PUNCT
ejpam-6498	143	45	0	0	NUM
ejpam-6498	143	46	)	)	PUNCT
ejpam-6498	143	47	,	,	PUNCT
ejpam-6498	143	48	b1	b1	NOUN
ejpam-6498	143	49	=	=	SYM
ejpam-6498	143	50	(	(	PUNCT
ejpam-6498	143	51	0	0	NUM
ejpam-6498	143	52	,	,	PUNCT
ejpam-6498	143	53	r1	r1	PROPN
ejpam-6498	143	54	)	)	PUNCT
ejpam-6498	143	55	,	,	PUNCT
ejpam-6498	143	56	b2	b2	NOUN
ejpam-6498	143	57	=	=	SYM
ejpam-6498	143	58	(	(	PUNCT
ejpam-6498	143	59	aϑ2	aϑ2	NOUN
ejpam-6498	143	60	−	−	ADP
ejpam-6498	143	61	ϑr2√	ϑr2√	ADJ
ejpam-6498	143	62	ϑ2	ϑ2	NOUN
ejpam-6498	143	63	+	+	CCONJ
ejpam-6498	143	64	1	1	NUM
ejpam-6498	143	65	,	,	PUNCT
ejpam-6498	143	66	2aϑ−	2aϑ−	NUM
ejpam-6498	143	67	r2√	r2√	ADJ
ejpam-6498	143	68	ϑ2	ϑ2	NOUN
ejpam-6498	143	69	+	+	CCONJ
ejpam-6498	143	70	1	1	NUM
ejpam-6498	143	71	)	)	PUNCT
ejpam-6498	143	72	,	,	PUNCT
ejpam-6498	143	73	b3	b3	PROPN
ejpam-6498	143	74	=	=	SYM
ejpam-6498	143	75	(	(	PUNCT
ejpam-6498	143	76	aϑ2	aϑ2	PROPN
ejpam-6498	143	77	,	,	PUNCT
ejpam-6498	143	78	2aϑ	2aϑ	ADJ
ejpam-6498	143	79	)	)	PUNCT
ejpam-6498	143	80	.	.	PUNCT
ejpam-6498	144	1	theorem	theorem	ADJ
ejpam-6498	144	2	4	4	NUM
ejpam-6498	144	3	.	.	PUNCT
ejpam-6498	145	1	if	if	SCONJ
ejpam-6498	145	2	r1	r1	PROPN
ejpam-6498	145	3	=	=	SYM
ejpam-6498	145	4	2aϑ	2aϑ	ADJ
ejpam-6498	145	5	3	3	NUM
ejpam-6498	145	6	and	and	CCONJ
ejpam-6498	145	7	r2	r2	NOUN
ejpam-6498	145	8	=	=	SYM
ejpam-6498	146	1	2aϑ	2aϑ	ADJ
ejpam-6498	146	2	√	√	NUM
ejpam-6498	146	3	ϑ2	ϑ2	NOUN
ejpam-6498	146	4	+	+	PROPN
ejpam-6498	146	5	1	1	NUM
ejpam-6498	146	6	3	3	NUM
ejpam-6498	146	7	,	,	PUNCT
ejpam-6498	146	8	then	then	ADV
ejpam-6498	146	9	the	the	DET
ejpam-6498	146	10	hausdorff	hausdorff	NOUN
ejpam-6498	146	11	distance	distance	NOUN
ejpam-6498	146	12	between	between	ADP
ejpam-6498	146	13	the	the	DET
ejpam-6498	146	14	parabolic	parabolic	ADJ
ejpam-6498	146	15	arc	arc	NOUN
ejpam-6498	146	16	and	and	CCONJ
ejpam-6498	146	17	its	its	PRON
ejpam-6498	146	18	cubic	cubic	ADJ
ejpam-6498	146	19	bézier	bézier	ADP
ejpam-6498	146	20	approximating	approximate	VERB
ejpam-6498	146	21	curve	curve	NOUN
ejpam-6498	146	22	is	be	AUX
ejpam-6498	146	23	d̃h(ôq	d̃h(ôq	ADJ
ejpam-6498	146	24	,	,	PUNCT
ejpam-6498	146	25	b(t	b(t	NOUN
ejpam-6498	146	26	)	)	PUNCT
ejpam-6498	146	27	)	)	PUNCT
ejpam-6498	147	1	=	=	PUNCT
ejpam-6498	147	2	0	0	X
ejpam-6498	147	3	.	.	PUNCT
ejpam-6498	148	1	proof	proof	NOUN
ejpam-6498	148	2	.	.	PUNCT
ejpam-6498	149	1	using	use	VERB
ejpam-6498	149	2	theorem	theorem	NOUN
ejpam-6498	149	3	3	3	NUM
ejpam-6498	149	4	,	,	PUNCT
ejpam-6498	149	5	the	the	DET
ejpam-6498	149	6	parametric	parametric	ADJ
ejpam-6498	149	7	equations	equation	NOUN
ejpam-6498	149	8	of	of	ADP
ejpam-6498	149	9	the	the	DET
ejpam-6498	149	10	cubic	cubic	ADJ
ejpam-6498	149	11	bézier	bézier	ADP
ejpam-6498	149	12	curve	curve	NOUN
ejpam-6498	149	13	approximation	approximation	NOUN
ejpam-6498	149	14	of	of	ADP
ejpam-6498	149	15	parabolic	parabolic	ADJ
ejpam-6498	149	16	arc	arc	NOUN
ejpam-6498	149	17	are	be	AUX
ejpam-6498	149	18	given	give	VERB
ejpam-6498	149	19	in	in	ADP
ejpam-6498	149	20	(	(	PUNCT
ejpam-6498	149	21	13	13	NUM
ejpam-6498	149	22	)	)	PUNCT
ejpam-6498	149	23	and	and	CCONJ
ejpam-6498	149	24	(	(	PUNCT
ejpam-6498	149	25	14	14	NUM
ejpam-6498	149	26	)	)	PUNCT
ejpam-6498	149	27	.	.	PUNCT
ejpam-6498	150	1	x̃(t	x̃(t	NOUN
ejpam-6498	150	2	)	)	PUNCT
ejpam-6498	151	1	=	=	PUNCT
ejpam-6498	152	1	3(1−	3(1−	NUM
ejpam-6498	152	2	t)t2	t)t2	PROPN
ejpam-6498	152	3	(	(	PUNCT
ejpam-6498	152	4	aϑ2	aϑ2	NOUN
ejpam-6498	152	5	−	−	ADP
ejpam-6498	152	6	ϑr2√	ϑr2√	ADJ
ejpam-6498	152	7	ϑ2	ϑ2	NOUN
ejpam-6498	152	8	+	+	CCONJ
ejpam-6498	152	9	1	1	NUM
ejpam-6498	152	10	)	)	PUNCT
ejpam-6498	152	11	+	+	NUM
ejpam-6498	152	12	t3(aϑ2	t3(aϑ2	NOUN
ejpam-6498	152	13	)	)	PUNCT
ejpam-6498	152	14	.	.	PUNCT
ejpam-6498	153	1	(	(	PUNCT
ejpam-6498	153	2	13	13	X
ejpam-6498	153	3	)	)	PUNCT
ejpam-6498	153	4	m.	m.	NOUN
ejpam-6498	153	5	hussain	hussain	PROPN
ejpam-6498	153	6	,	,	PUNCT
ejpam-6498	153	7	h.	h.	PROPN
ejpam-6498	153	8	a.	a.	PROPN
ejpam-6498	153	9	wajid	wajid	PROPN
ejpam-6498	153	10	,	,	PUNCT
ejpam-6498	153	11	s.	s.	PROPN
ejpam-6498	153	12	aqeel	aqeel	PROPN
ejpam-6498	153	13	/	/	SYM
ejpam-6498	153	14	eur	eur	PROPN
ejpam-6498	153	15	.	.	PUNCT
ejpam-6498	154	1	j.	j.	PROPN
ejpam-6498	154	2	pure	pure	PROPN
ejpam-6498	154	3	appl	appl	PROPN
ejpam-6498	154	4	.	.	PROPN
ejpam-6498	154	5	math	math	PROPN
ejpam-6498	154	6	,	,	PUNCT
ejpam-6498	154	7	18	18	NUM
ejpam-6498	154	8	(	(	PUNCT
ejpam-6498	154	9	4	4	NUM
ejpam-6498	154	10	)	)	PUNCT
ejpam-6498	154	11	(	(	PUNCT
ejpam-6498	154	12	2025	2025	NUM
ejpam-6498	154	13	)	)	PUNCT
ejpam-6498	154	14	,	,	PUNCT
ejpam-6498	154	15	6498	6498	NUM
ejpam-6498	154	16	7	7	NUM
ejpam-6498	154	17	of	of	ADP
ejpam-6498	154	18	12	12	NUM
ejpam-6498	154	19	ỹ(t	ỹ(t	NOUN
ejpam-6498	154	20	)	)	PUNCT
ejpam-6498	154	21	=	=	PUNCT
ejpam-6498	155	1	3(1−	3(1−	NUM
ejpam-6498	155	2	t)2tr1	t)2tr1	NOUN
ejpam-6498	155	3	+	+	CCONJ
ejpam-6498	155	4	3(1−	3(1−	NUM
ejpam-6498	155	5	t)t2	t)t2	PROPN
ejpam-6498	155	6	(	(	PUNCT
ejpam-6498	155	7	2aϑ−	2aϑ−	NUM
ejpam-6498	155	8	r2√	r2√	ADJ
ejpam-6498	155	9	ϑ2	ϑ2	NOUN
ejpam-6498	155	10	+	+	CCONJ
ejpam-6498	155	11	1	1	NUM
ejpam-6498	155	12	)	)	PUNCT
ejpam-6498	155	13	+	+	PUNCT
ejpam-6498	155	14	t3(2aϑ	t3(2aϑ	NOUN
ejpam-6498	155	15	)	)	PUNCT
ejpam-6498	155	16	.	.	PUNCT
ejpam-6498	156	1	(	(	PUNCT
ejpam-6498	156	2	14	14	NUM
ejpam-6498	156	3	)	)	PUNCT
ejpam-6498	156	4	error	error	NOUN
ejpam-6498	156	5	function	function	NOUN
ejpam-6498	156	6	,	,	PUNCT
ejpam-6498	156	7	w̃(t	w̃(t	PROPN
ejpam-6498	156	8	)	)	PUNCT
ejpam-6498	156	9	,	,	PUNCT
ejpam-6498	156	10	for	for	ADP
ejpam-6498	156	11	the	the	DET
ejpam-6498	156	12	proposed	propose	VERB
ejpam-6498	156	13	parabolic	parabolic	NOUN
ejpam-6498	156	14	arc	arc	NOUN
ejpam-6498	156	15	approximation	approximation	NOUN
ejpam-6498	156	16	method	method	NOUN
ejpam-6498	156	17	is	be	AUX
ejpam-6498	156	18	the	the	DET
ejpam-6498	156	19	following	follow	VERB
ejpam-6498	156	20	:	:	PUNCT
ejpam-6498	156	21	w̃(t	w̃(t	NOUN
ejpam-6498	156	22	)	)	PUNCT
ejpam-6498	156	23	=	=	PUNCT
ejpam-6498	156	24	ỹ2(t)−	ỹ2(t)−	PROPN
ejpam-6498	156	25	4ax̃(t	4ax̃(t	PROPN
ejpam-6498	156	26	)	)	PUNCT
ejpam-6498	156	27	.	.	PUNCT
ejpam-6498	157	1	(	(	PUNCT
ejpam-6498	157	2	15	15	X
ejpam-6498	157	3	)	)	PUNCT
ejpam-6498	157	4	using	use	VERB
ejpam-6498	157	5	(	(	PUNCT
ejpam-6498	157	6	13	13	NUM
ejpam-6498	157	7	)	)	PUNCT
ejpam-6498	157	8	,	,	PUNCT
ejpam-6498	157	9	(	(	PUNCT
ejpam-6498	157	10	14	14	NUM
ejpam-6498	157	11	)	)	PUNCT
ejpam-6498	157	12	and	and	CCONJ
ejpam-6498	157	13	(	(	PUNCT
ejpam-6498	157	14	15	15	NUM
ejpam-6498	157	15	)	)	PUNCT
ejpam-6498	157	16	,	,	PUNCT
ejpam-6498	157	17	following	follow	VERB
ejpam-6498	157	18	observations	observation	NOUN
ejpam-6498	157	19	are	be	AUX
ejpam-6498	157	20	made	make	VERB
ejpam-6498	157	21	:	:	PUNCT
ejpam-6498	157	22	(	(	PUNCT
ejpam-6498	157	23	i	i	NOUN
ejpam-6498	157	24	)	)	PUNCT
ejpam-6498	157	25	the	the	DET
ejpam-6498	157	26	error	error	NOUN
ejpam-6498	157	27	function	function	NOUN
ejpam-6498	157	28	w̃(t	w̃(t	PROPN
ejpam-6498	157	29	)	)	PUNCT
ejpam-6498	157	30	is	be	AUX
ejpam-6498	157	31	a	a	DET
ejpam-6498	157	32	polynomial	polynomial	NOUN
ejpam-6498	157	33	of	of	ADP
ejpam-6498	157	34	degree	degree	NOUN
ejpam-6498	157	35	at	at	ADP
ejpam-6498	157	36	most	most	ADJ
ejpam-6498	157	37	six	six	NUM
ejpam-6498	157	38	(	(	PUNCT
ejpam-6498	157	39	ii	ii	NOUN
ejpam-6498	157	40	)	)	PUNCT
ejpam-6498	157	41	w̃(0	w̃(0	PROPN
ejpam-6498	157	42	)	)	PUNCT
ejpam-6498	158	1	=	=	SYM
ejpam-6498	158	2	0	0	NUM
ejpam-6498	158	3	(	(	PUNCT
ejpam-6498	158	4	iii	iii	NOUN
ejpam-6498	158	5	)	)	PUNCT
ejpam-6498	158	6	w̃(1	w̃(1	NOUN
ejpam-6498	158	7	)	)	PUNCT
ejpam-6498	158	8	=	=	SYM
ejpam-6498	159	1	0	0	X
ejpam-6498	159	2	.	.	PUNCT
ejpam-6498	160	1	we	we	PRON
ejpam-6498	160	2	assume	assume	VERB
ejpam-6498	160	3	w̃(0.5	w̃(0.5	NUM
ejpam-6498	160	4	)	)	PUNCT
ejpam-6498	160	5	=	=	SYM
ejpam-6498	160	6	0	0	NUM
ejpam-6498	160	7	,	,	PUNCT
ejpam-6498	160	8	then	then	ADV
ejpam-6498	160	9	it	it	PRON
ejpam-6498	160	10	follows	follow	VERB
ejpam-6498	160	11	by	by	ADP
ejpam-6498	160	12	symmetry	symmetry	NOUN
ejpam-6498	160	13	of	of	ADP
ejpam-6498	160	14	error	error	NOUN
ejpam-6498	160	15	function	function	NOUN
ejpam-6498	160	16	that	that	PRON
ejpam-6498	160	17	dw̃(t	dw̃(t	NOUN
ejpam-6498	160	18	)	)	PUNCT
ejpam-6498	160	19	dt	dt	X
ejpam-6498	161	1	∣∣∣	∣∣∣	ADJ
ejpam-6498	161	2	t=0.5	t=0.5	NOUN
ejpam-6498	161	3	=	=	NOUN
ejpam-6498	161	4	0	0	NUM
ejpam-6498	161	5	.	.	PUNCT
ejpam-6498	162	1	the	the	DET
ejpam-6498	162	2	conditions	condition	NOUN
ejpam-6498	162	3	w̃(0.5	w̃(0.5	NUM
ejpam-6498	162	4	)	)	PUNCT
ejpam-6498	162	5	=	=	SYM
ejpam-6498	162	6	0	0	NUM
ejpam-6498	162	7	and	and	CCONJ
ejpam-6498	162	8	dw̃(t	dw̃(t	NOUN
ejpam-6498	162	9	)	)	PUNCT
ejpam-6498	162	10	dt	dt	X
ejpam-6498	162	11	∣∣∣	∣∣∣	ADJ
ejpam-6498	162	12	t=0.5	t=0.5	NOUN
ejpam-6498	162	13	=	=	SYM
ejpam-6498	162	14	0	0	NUM
ejpam-6498	162	15	give	give	VERB
ejpam-6498	162	16	the	the	DET
ejpam-6498	162	17	following	follow	VERB
ejpam-6498	162	18	set	set	NOUN
ejpam-6498	162	19	of	of	ADP
ejpam-6498	162	20	simultaneous	simultaneous	ADJ
ejpam-6498	162	21	equations	equation	NOUN
ejpam-6498	162	22	in	in	ADP
ejpam-6498	162	23	r1	r1	PROPN
ejpam-6498	162	24	and	and	CCONJ
ejpam-6498	162	25	r2	r2	PROPN
ejpam-6498	162	26	:	:	PUNCT
ejpam-6498	162	27	9r21	9r21	NOUN
ejpam-6498	162	28	−	−	PROPN
ejpam-6498	162	29	64a2ϑ2	64a2ϑ2	NOUN
ejpam-6498	162	30	+	+	CCONJ
ejpam-6498	162	31	48aϑr1	48aϑr1	NOUN
ejpam-6498	162	32	+	+	NUM
ejpam-6498	162	33	9r22	9r22	NUM
ejpam-6498	162	34	(	(	PUNCT
ejpam-6498	162	35	ϑ2	ϑ2	NOUN
ejpam-6498	162	36	+	+	CCONJ
ejpam-6498	162	37	1	1	NUM
ejpam-6498	162	38	)	)	PUNCT
ejpam-6498	163	1	+	+	NUM
ejpam-6498	164	1	48aϑr2	48aϑr2	NUM
ejpam-6498	164	2	−	−	NOUN
ejpam-6498	164	3	18r1r2√	18r1r2√	NUM
ejpam-6498	164	4	ϑ2	ϑ2	NOUN
ejpam-6498	164	5	+	+	CCONJ
ejpam-6498	164	6	1	1	NUM
ejpam-6498	164	7	=	=	SYM
ejpam-6498	164	8	0	0	NUM
ejpam-6498	165	1	(	(	PUNCT
ejpam-6498	165	2	16	16	NUM
ejpam-6498	165	3	)	)	PUNCT
ejpam-6498	165	4	−	−	NOUN
ejpam-6498	165	5	9r21	9r21	NOUN
ejpam-6498	166	1	+	+	CCONJ
ejpam-6498	166	2	12aϑr1	12aϑr1	NOUN
ejpam-6498	166	3	+	+	CCONJ
ejpam-6498	166	4	9r22	9r22	NUM
ejpam-6498	166	5	(	(	PUNCT
ejpam-6498	166	6	ϑ2	ϑ2	NOUN
ejpam-6498	166	7	+	+	CCONJ
ejpam-6498	166	8	1	1	NUM
ejpam-6498	166	9	)	)	PUNCT
ejpam-6498	166	10	−	−	PROPN
ejpam-6498	166	11	12aϑr2√	12aϑr2√	NUM
ejpam-6498	166	12	ϑ2	ϑ2	PROPN
ejpam-6498	167	1	+	+	CCONJ
ejpam-6498	167	2	1	1	NUM
ejpam-6498	167	3	=	=	SYM
ejpam-6498	167	4	0	0	NUM
ejpam-6498	167	5	(	(	PUNCT
ejpam-6498	167	6	17	17	NUM
ejpam-6498	167	7	)	)	PUNCT
ejpam-6498	167	8	the	the	DET
ejpam-6498	167	9	solution	solution	NOUN
ejpam-6498	167	10	of	of	ADP
ejpam-6498	167	11	the	the	DET
ejpam-6498	167	12	above	above	ADJ
ejpam-6498	167	13	set	set	NOUN
ejpam-6498	167	14	of	of	ADP
ejpam-6498	167	15	simultaneous	simultaneous	ADJ
ejpam-6498	167	16	equations	equation	NOUN
ejpam-6498	167	17	is	be	AUX
ejpam-6498	167	18	given	give	VERB
ejpam-6498	167	19	in	in	ADP
ejpam-6498	167	20	(	(	PUNCT
ejpam-6498	167	21	18	18	NUM
ejpam-6498	167	22	):	):	PUNCT
ejpam-6498	167	23	r1	r1	NOUN
ejpam-6498	167	24	=	=	PUNCT
ejpam-6498	167	25	r2√	r2√	ADJ
ejpam-6498	167	26	ϑ2	ϑ2	NOUN
ejpam-6498	167	27	+	+	CCONJ
ejpam-6498	167	28	1	1	NUM
ejpam-6498	167	29	and	and	CCONJ
ejpam-6498	167	30	r2	r2	PROPN
ejpam-6498	167	31	=	=	SYM
ejpam-6498	167	32	2aϑ	2aϑ	ADJ
ejpam-6498	167	33	√	√	NUM
ejpam-6498	167	34	ϑ2	ϑ2	NOUN
ejpam-6498	167	35	+	+	CCONJ
ejpam-6498	167	36	1	1	NUM
ejpam-6498	167	37	3	3	NUM
ejpam-6498	167	38	.	.	PUNCT
ejpam-6498	168	1	(	(	PUNCT
ejpam-6498	168	2	18	18	NUM
ejpam-6498	168	3	)	)	PUNCT
ejpam-6498	168	4	the	the	DET
ejpam-6498	168	5	w̃(t	w̃(t	PROPN
ejpam-6498	168	6	)	)	PUNCT
ejpam-6498	168	7	has	have	VERB
ejpam-6498	168	8	three	three	NUM
ejpam-6498	168	9	zeros	zero	NOUN
ejpam-6498	168	10	,	,	PUNCT
ejpam-6498	168	11	t	t	NOUN
ejpam-6498	168	12	=	=	SYM
ejpam-6498	168	13	0	0	NUM
ejpam-6498	168	14	,	,	PUNCT
ejpam-6498	168	15	0.5	0.5	NUM
ejpam-6498	168	16	,	,	PUNCT
ejpam-6498	168	17	1	1	NUM
ejpam-6498	168	18	,	,	PUNCT
ejpam-6498	168	19	each	each	PRON
ejpam-6498	168	20	of	of	ADP
ejpam-6498	168	21	multiplicity	multiplicity	NOUN
ejpam-6498	168	22	two	two	NUM
ejpam-6498	168	23	.	.	PUNCT
ejpam-6498	169	1	therefore	therefore	ADV
ejpam-6498	169	2	w̃(t	w̃(t	PROPN
ejpam-6498	169	3	)	)	PUNCT
ejpam-6498	169	4	can	can	AUX
ejpam-6498	169	5	be	be	AUX
ejpam-6498	169	6	written	write	VERB
ejpam-6498	169	7	as	as	ADP
ejpam-6498	169	8	w̃(t	w̃(t	PROPN
ejpam-6498	169	9	)	)	PUNCT
ejpam-6498	169	10	=	=	SYM
ejpam-6498	169	11	kg(t	kg(t	NOUN
ejpam-6498	169	12	)	)	PUNCT
ejpam-6498	169	13	,	,	PUNCT
ejpam-6498	169	14	where	where	SCONJ
ejpam-6498	169	15	g(t	g(t	NOUN
ejpam-6498	169	16	)	)	PUNCT
ejpam-6498	170	1	=	=	PUNCT
ejpam-6498	170	2	t2(t−	t2(t−	NUM
ejpam-6498	171	1	1)2(t−	1)2(t−	NUM
ejpam-6498	171	2	0.5)2	0.5)2	NOUN
ejpam-6498	172	1	and	and	CCONJ
ejpam-6498	172	2	k	k	PROPN
ejpam-6498	172	3	is	be	AUX
ejpam-6498	172	4	the	the	DET
ejpam-6498	172	5	leading	leading	ADJ
ejpam-6498	172	6	coefficient	coefficient	NOUN
ejpam-6498	172	7	of	of	ADP
ejpam-6498	172	8	w̃(t	w̃(t	PROPN
ejpam-6498	172	9	)	)	PUNCT
ejpam-6498	172	10	.	.	PUNCT
ejpam-6498	173	1	using	use	VERB
ejpam-6498	173	2	(	(	PUNCT
ejpam-6498	173	3	13)-(18	13)-(18	NOUN
ejpam-6498	173	4	)	)	PUNCT
ejpam-6498	173	5	,	,	PUNCT
ejpam-6498	173	6	the	the	DET
ejpam-6498	173	7	leading	lead	VERB
ejpam-6498	173	8	coefficient	coefficient	NOUN
ejpam-6498	173	9	of	of	ADP
ejpam-6498	173	10	w̃(t	w̃(t	PROPN
ejpam-6498	173	11	)	)	PUNCT
ejpam-6498	173	12	is	be	AUX
ejpam-6498	173	13	calculated	calculate	VERB
ejpam-6498	173	14	and	and	CCONJ
ejpam-6498	173	15	it	it	PRON
ejpam-6498	173	16	turned	turn	VERB
ejpam-6498	173	17	out	out	ADP
ejpam-6498	173	18	k	k	PROPN
ejpam-6498	173	19	=	=	PUNCT
ejpam-6498	173	20	0	0	PROPN
ejpam-6498	173	21	.	.	PUNCT
ejpam-6498	174	1	hence	hence	ADV
ejpam-6498	174	2	w̃(t	w̃(t	PROPN
ejpam-6498	174	3	)	)	PUNCT
ejpam-6498	174	4	=	=	SYM
ejpam-6498	174	5	kg(t	kg(t	NOUN
ejpam-6498	174	6	)	)	PUNCT
ejpam-6498	175	1	=	=	SYM
ejpam-6498	175	2	0	0	X
ejpam-6498	175	3	.	.	PUNCT
ejpam-6498	176	1	the	the	DET
ejpam-6498	176	2	hausdorff	hausdorff	NOUN
ejpam-6498	176	3	distance	distance	NOUN
ejpam-6498	176	4	between	between	ADP
ejpam-6498	176	5	the	the	DET
ejpam-6498	176	6	parabolic	parabolic	ADJ
ejpam-6498	176	7	arc	arc	NOUN
ejpam-6498	176	8	and	and	CCONJ
ejpam-6498	176	9	its	its	PRON
ejpam-6498	176	10	cubic	cubic	ADJ
ejpam-6498	176	11	bézier	bézier	ADP
ejpam-6498	176	12	curve	curve	NOUN
ejpam-6498	176	13	approximation	approximation	NOUN
ejpam-6498	176	14	is	be	AUX
ejpam-6498	176	15	defined	define	VERB
ejpam-6498	176	16	as	as	ADP
ejpam-6498	176	17	:	:	PUNCT
ejpam-6498	176	18	d̃h(ôq	d̃h(ôq	NOUN
ejpam-6498	176	19	,	,	PUNCT
ejpam-6498	176	20	b(t	b(t	NOUN
ejpam-6498	176	21	)	)	PUNCT
ejpam-6498	176	22	)	)	PUNCT
ejpam-6498	177	1	=	=	SYM
ejpam-6498	177	2	max	max	PROPN
ejpam-6498	177	3	0≤t≤1	0≤t≤1	X
ejpam-6498	177	4	|w̃(t)|	|w̃(t)|	PROPN
ejpam-6498	177	5	.	.	PUNCT
ejpam-6498	178	1	as	as	ADP
ejpam-6498	178	2	w̃(t	w̃(t	PROPN
ejpam-6498	178	3	)	)	PUNCT
ejpam-6498	178	4	=	=	SYM
ejpam-6498	178	5	0	0	NUM
ejpam-6498	178	6	,	,	PUNCT
ejpam-6498	178	7	so	so	SCONJ
ejpam-6498	178	8	we	we	PRON
ejpam-6498	178	9	have	have	VERB
ejpam-6498	178	10	d̃h(ôq	d̃h(ôq	NOUN
ejpam-6498	178	11	,	,	PUNCT
ejpam-6498	178	12	b(t	b(t	NOUN
ejpam-6498	178	13	)	)	PUNCT
ejpam-6498	178	14	)	)	PUNCT
ejpam-6498	179	1	=	=	PUNCT
ejpam-6498	179	2	0	0	X
ejpam-6498	179	3	.	.	PUNCT
ejpam-6498	180	1	hence	hence	ADV
ejpam-6498	180	2	the	the	DET
ejpam-6498	180	3	proposed	propose	VERB
ejpam-6498	180	4	cubic	cubic	NOUN
ejpam-6498	180	5	bézier	bézier	ADP
ejpam-6498	180	6	curve	curve	NOUN
ejpam-6498	180	7	approximation	approximation	NOUN
ejpam-6498	180	8	method	method	NOUN
ejpam-6498	180	9	reconstructs	reconstruct	VERB
ejpam-6498	180	10	the	the	DET
ejpam-6498	180	11	given	give	VERB
ejpam-6498	180	12	parabolic	parabolic	ADJ
ejpam-6498	180	13	arc	arc	NOUN
ejpam-6498	180	14	.	.	PUNCT
ejpam-6498	181	1	3	3	X
ejpam-6498	181	2	.	.	X
ejpam-6498	181	3	numerical	numerical	PROPN
ejpam-6498	181	4	validation	validation	NOUN
ejpam-6498	181	5	we	we	PRON
ejpam-6498	181	6	validate	validate	VERB
ejpam-6498	181	7	the	the	DET
ejpam-6498	181	8	proposed	propose	VERB
ejpam-6498	181	9	cubic	cubic	NOUN
ejpam-6498	181	10	bézier	bézier	ADP
ejpam-6498	181	11	approximation	approximation	NOUN
ejpam-6498	181	12	method	method	NOUN
ejpam-6498	181	13	through	through	ADP
ejpam-6498	181	14	four	four	NUM
ejpam-6498	181	15	problems	problem	NOUN
ejpam-6498	181	16	,	,	PUNCT
ejpam-6498	181	17	comparing	compare	VERB
ejpam-6498	181	18	accuracy	accuracy	NOUN
ejpam-6498	181	19	(	(	PUNCT
ejpam-6498	181	20	absolute	absolute	ADJ
ejpam-6498	181	21	error	error	NOUN
ejpam-6498	181	22	)	)	PUNCT
ejpam-6498	181	23	,	,	PUNCT
ejpam-6498	181	24	computational	computational	ADJ
ejpam-6498	181	25	efficiency	efficiency	NOUN
ejpam-6498	181	26	,	,	PUNCT
ejpam-6498	181	27	and	and	CCONJ
ejpam-6498	181	28	geometric	geometric	ADJ
ejpam-6498	181	29	utility	utility	NOUN
ejpam-6498	181	30	against	against	ADP
ejpam-6498	181	31	the	the	DET
ejpam-6498	181	32	existing	exist	VERB
ejpam-6498	181	33	methods	method	NOUN
ejpam-6498	181	34	presented	present	VERB
ejpam-6498	181	35	in	in	ADP
ejpam-6498	181	36	[	[	X
ejpam-6498	181	37	2	2	NUM
ejpam-6498	181	38	,	,	PUNCT
ejpam-6498	181	39	6	6	NUM
ejpam-6498	181	40	,	,	PUNCT
ejpam-6498	181	41	8	8	NUM
ejpam-6498	181	42	]	]	PUNCT
ejpam-6498	181	43	.	.	PUNCT
ejpam-6498	182	1	m.	m.	PROPN
ejpam-6498	182	2	hussain	hussain	PROPN
ejpam-6498	182	3	,	,	PUNCT
ejpam-6498	182	4	h.	h.	PROPN
ejpam-6498	182	5	a.	a.	PROPN
ejpam-6498	182	6	wajid	wajid	PROPN
ejpam-6498	182	7	,	,	PUNCT
ejpam-6498	182	8	s.	s.	PROPN
ejpam-6498	182	9	aqeel	aqeel	PROPN
ejpam-6498	182	10	/	/	SYM
ejpam-6498	182	11	eur	eur	PROPN
ejpam-6498	182	12	.	.	PUNCT
ejpam-6498	183	1	j.	j.	PROPN
ejpam-6498	183	2	pure	pure	PROPN
ejpam-6498	183	3	appl	appl	PROPN
ejpam-6498	183	4	.	.	PROPN
ejpam-6498	183	5	math	math	PROPN
ejpam-6498	183	6	,	,	PUNCT
ejpam-6498	183	7	18	18	NUM
ejpam-6498	183	8	(	(	PUNCT
ejpam-6498	183	9	4	4	NUM
ejpam-6498	183	10	)	)	PUNCT
ejpam-6498	183	11	(	(	PUNCT
ejpam-6498	183	12	2025	2025	NUM
ejpam-6498	183	13	)	)	PUNCT
ejpam-6498	183	14	,	,	PUNCT
ejpam-6498	183	15	6498	6498	NUM
ejpam-6498	183	16	8	8	NUM
ejpam-6498	183	17	of	of	ADP
ejpam-6498	183	18	12	12	NUM
ejpam-6498	183	19	figure	figure	NOUN
ejpam-6498	183	20	1	1	NUM
ejpam-6498	183	21	:	:	PUNCT
ejpam-6498	183	22	plot	plot	NOUN
ejpam-6498	183	23	of	of	ADP
ejpam-6498	183	24	the	the	DET
ejpam-6498	183	25	transformed	transform	VERB
ejpam-6498	183	26	horizontal	horizontal	ADJ
ejpam-6498	183	27	ellipse	ellipse	NOUN
ejpam-6498	183	28	.	.	PUNCT
ejpam-6498	184	1	red	red	ADJ
ejpam-6498	184	2	curve	curve	PROPN
ejpam-6498	184	3	:	:	PUNCT
ejpam-6498	184	4	approximated	approximate	VERB
ejpam-6498	184	5	curve	curve	NOUN
ejpam-6498	184	6	;	;	PUNCT
ejpam-6498	184	7	other	other	ADJ
ejpam-6498	184	8	colours	colour	NOUN
ejpam-6498	184	9	:	:	PUNCT
ejpam-6498	184	10	reflection	reflection	NOUN
ejpam-6498	184	11	curves	curve	NOUN
ejpam-6498	184	12	of	of	ADP
ejpam-6498	184	13	approximated	approximate	VERB
ejpam-6498	184	14	curve	curve	NOUN
ejpam-6498	184	15	.	.	PUNCT
ejpam-6498	185	1	problem-1	problem-1	PRON
ejpam-6498	185	2	let	let	VERB
ejpam-6498	185	3	the	the	DET
ejpam-6498	185	4	ellipse	ellipse	NOUN
ejpam-6498	185	5	for	for	ADP
ejpam-6498	185	6	approximation	approximation	NOUN
ejpam-6498	185	7	be	be	VERB
ejpam-6498	185	8	an	an	DET
ejpam-6498	185	9	oblique	oblique	ADJ
ejpam-6498	185	10	ellipse	ellipse	NOUN
ejpam-6498	185	11	29x2	29x2	NUM
ejpam-6498	185	12	−	−	PROPN
ejpam-6498	185	13	24xy	24xy	PROPN
ejpam-6498	186	1	+	+	CCONJ
ejpam-6498	186	2	36y2	36y2	NUM
ejpam-6498	186	3	+	+	CCONJ
ejpam-6498	186	4	118x	118x	PROPN
ejpam-6498	186	5	−	−	ADP
ejpam-6498	186	6	24y−	24y−	NUM
ejpam-6498	186	7	55	55	NUM
ejpam-6498	186	8	=	=	SYM
ejpam-6498	186	9	0	0	X
ejpam-6498	186	10	.	.	PUNCT
ejpam-6498	187	1	first	first	ADV
ejpam-6498	187	2	it	it	PRON
ejpam-6498	187	3	is	be	AUX
ejpam-6498	187	4	transformed	transform	VERB
ejpam-6498	187	5	into	into	ADP
ejpam-6498	187	6	horizontal	horizontal	ADJ
ejpam-6498	187	7	ellipse	ellipse	NOUN
ejpam-6498	187	8	x2	x2	NOUN
ejpam-6498	188	1	9	9	NUM
ejpam-6498	189	1	+	+	CCONJ
ejpam-6498	189	2	y	y	PROPN
ejpam-6498	189	3	2	2	NUM
ejpam-6498	189	4	4	4	NUM
ejpam-6498	189	5	=	=	SYM
ejpam-6498	189	6	1	1	NUM
ejpam-6498	189	7	through	through	ADP
ejpam-6498	189	8	rotation	rotation	NOUN
ejpam-6498	189	9	transformation	transformation	NOUN
ejpam-6498	189	10	with	with	ADP
ejpam-6498	189	11	angle	angle	NOUN
ejpam-6498	189	12	of	of	ADP
ejpam-6498	189	13	rotation	rotation	NOUN
ejpam-6498	189	14	tan−1	tan−1	PROPN
ejpam-6498	189	15	(	(	PUNCT
ejpam-6498	189	16	3	3	NUM
ejpam-6498	189	17	4	4	NUM
ejpam-6498	189	18	)	)	PUNCT
ejpam-6498	189	19	.	.	PUNCT
ejpam-6498	190	1	center	center	NOUN
ejpam-6498	190	2	of	of	ADP
ejpam-6498	190	3	the	the	DET
ejpam-6498	190	4	ellipse	ellipse	NOUN
ejpam-6498	190	5	is	be	AUX
ejpam-6498	190	6	o(0	o(0	ADJ
ejpam-6498	190	7	,	,	PUNCT
ejpam-6498	190	8	0	0	NUM
ejpam-6498	190	9	)	)	PUNCT
ejpam-6498	190	10	.	.	PUNCT
ejpam-6498	191	1	second	second	ADV
ejpam-6498	191	2	,	,	PUNCT
ejpam-6498	191	3	the	the	DET
ejpam-6498	191	4	transformed	transform	VERB
ejpam-6498	191	5	ellipse	ellipse	NOUN
ejpam-6498	191	6	is	be	AUX
ejpam-6498	191	7	approximated	approximate	VERB
ejpam-6498	191	8	in	in	ADP
ejpam-6498	191	9	first	first	ADJ
ejpam-6498	191	10	quadrant	quadrant	NOUN
ejpam-6498	191	11	by	by	ADP
ejpam-6498	191	12	the	the	DET
ejpam-6498	191	13	cubic	cubic	ADJ
ejpam-6498	191	14	bézier	bézier	ADP
ejpam-6498	191	15	curve	curve	NOUN
ejpam-6498	191	16	approximation	approximation	NOUN
ejpam-6498	191	17	method	method	NOUN
ejpam-6498	191	18	proposed	propose	VERB
ejpam-6498	191	19	in	in	ADP
ejpam-6498	191	20	section	section	NOUN
ejpam-6498	191	21	2	2	NUM
ejpam-6498	191	22	.	.	PUNCT
ejpam-6498	192	1	it	it	PRON
ejpam-6498	192	2	is	be	AUX
ejpam-6498	192	3	plotted	plot	VERB
ejpam-6498	192	4	in	in	ADP
ejpam-6498	192	5	figure	figure	NOUN
ejpam-6498	192	6	1	1	NUM
ejpam-6498	192	7	(	(	PUNCT
ejpam-6498	192	8	red	red	ADJ
ejpam-6498	192	9	curve	curve	NOUN
ejpam-6498	192	10	)	)	PUNCT
ejpam-6498	192	11	.	.	PUNCT
ejpam-6498	193	1	the	the	DET
ejpam-6498	193	2	complete	complete	ADJ
ejpam-6498	193	3	ellipse	ellipse	NOUN
ejpam-6498	193	4	is	be	AUX
ejpam-6498	193	5	obtained	obtain	VERB
ejpam-6498	193	6	in	in	ADP
ejpam-6498	193	7	figure	figure	NOUN
ejpam-6498	193	8	1	1	NUM
ejpam-6498	193	9	by	by	ADP
ejpam-6498	193	10	successive	successive	ADJ
ejpam-6498	193	11	reflection	reflection	NOUN
ejpam-6498	193	12	transformations	transformation	NOUN
ejpam-6498	193	13	.	.	PUNCT
ejpam-6498	194	1	the	the	DET
ejpam-6498	194	2	oblique	oblique	ADJ
ejpam-6498	194	3	ellipse	ellipse	NOUN
ejpam-6498	194	4	is	be	AUX
ejpam-6498	194	5	obtained	obtain	VERB
ejpam-6498	194	6	by	by	ADP
ejpam-6498	194	7	applying	apply	VERB
ejpam-6498	194	8	inverse	inverse	NOUN
ejpam-6498	194	9	transformation	transformation	NOUN
ejpam-6498	194	10	and	and	CCONJ
ejpam-6498	194	11	it	it	PRON
ejpam-6498	194	12	is	be	AUX
ejpam-6498	194	13	plotted	plot	VERB
ejpam-6498	194	14	in	in	ADP
ejpam-6498	194	15	figure	figure	NOUN
ejpam-6498	194	16	2	2	NUM
ejpam-6498	194	17	.	.	PUNCT
ejpam-6498	194	18	figure	figure	NOUN
ejpam-6498	194	19	2	2	NUM
ejpam-6498	194	20	:	:	PUNCT
ejpam-6498	194	21	plot	plot	NOUN
ejpam-6498	194	22	of	of	ADP
ejpam-6498	194	23	the	the	DET
ejpam-6498	194	24	oblique	oblique	ADJ
ejpam-6498	194	25	ellipse	ellipse	NOUN
ejpam-6498	194	26	(	(	PUNCT
ejpam-6498	194	27	obtained	obtain	VERB
ejpam-6498	194	28	after	after	ADP
ejpam-6498	194	29	inverse	inverse	NOUN
ejpam-6498	194	30	transformation	transformation	NOUN
ejpam-6498	194	31	of	of	ADP
ejpam-6498	194	32	the	the	DET
ejpam-6498	194	33	ellipse	ellipse	NOUN
ejpam-6498	194	34	in	in	ADP
ejpam-6498	194	35	figure	figure	NOUN
ejpam-6498	194	36	1	1	NUM
ejpam-6498	194	37	)	)	PUNCT
ejpam-6498	194	38	.	.	PUNCT
ejpam-6498	195	1	m.	m.	PROPN
ejpam-6498	195	2	hussain	hussain	PROPN
ejpam-6498	195	3	,	,	PUNCT
ejpam-6498	195	4	h.	h.	PROPN
ejpam-6498	195	5	a.	a.	PROPN
ejpam-6498	195	6	wajid	wajid	PROPN
ejpam-6498	195	7	,	,	PUNCT
ejpam-6498	195	8	s.	s.	PROPN
ejpam-6498	195	9	aqeel	aqeel	PROPN
ejpam-6498	195	10	/	/	SYM
ejpam-6498	195	11	eur	eur	PROPN
ejpam-6498	195	12	.	.	PUNCT
ejpam-6498	196	1	j.	j.	PROPN
ejpam-6498	196	2	pure	pure	PROPN
ejpam-6498	196	3	appl	appl	PROPN
ejpam-6498	196	4	.	.	PROPN
ejpam-6498	196	5	math	math	PROPN
ejpam-6498	196	6	,	,	PUNCT
ejpam-6498	196	7	18	18	NUM
ejpam-6498	196	8	(	(	PUNCT
ejpam-6498	196	9	4	4	NUM
ejpam-6498	196	10	)	)	PUNCT
ejpam-6498	196	11	(	(	PUNCT
ejpam-6498	196	12	2025	2025	NUM
ejpam-6498	196	13	)	)	PUNCT
ejpam-6498	196	14	,	,	PUNCT
ejpam-6498	196	15	6498	6498	NUM
ejpam-6498	196	16	9	9	NUM
ejpam-6498	196	17	of	of	ADP
ejpam-6498	196	18	12	12	NUM
ejpam-6498	196	19	problem-2	problem-2	PROPN
ejpam-6498	196	20	ellipsoid	ellipsoid	NOUN
ejpam-6498	196	21	in	in	ADP
ejpam-6498	196	22	figure	figure	NOUN
ejpam-6498	196	23	3	3	NUM
ejpam-6498	196	24	is	be	AUX
ejpam-6498	196	25	the	the	DET
ejpam-6498	196	26	surface	surface	NOUN
ejpam-6498	196	27	of	of	ADP
ejpam-6498	196	28	revolution	revolution	NOUN
ejpam-6498	196	29	of	of	ADP
ejpam-6498	196	30	cubic	cubic	ADJ
ejpam-6498	196	31	bézier	bézier	DET
ejpam-6498	196	32	approximation	approximation	NOUN
ejpam-6498	196	33	of	of	ADP
ejpam-6498	196	34	the	the	DET
ejpam-6498	196	35	horizontal	horizontal	ADJ
ejpam-6498	196	36	ellipse	ellipse	NOUN
ejpam-6498	196	37	x2	x2	NOUN
ejpam-6498	196	38	9	9	NUM
ejpam-6498	197	1	+	+	CCONJ
ejpam-6498	197	2	y2	y2	PROPN
ejpam-6498	197	3	4	4	NUM
ejpam-6498	197	4	=	=	SYM
ejpam-6498	197	5	1	1	NUM
ejpam-6498	197	6	by	by	ADP
ejpam-6498	197	7	the	the	DET
ejpam-6498	197	8	approximation	approximation	NOUN
ejpam-6498	197	9	method	method	NOUN
ejpam-6498	197	10	in	in	ADP
ejpam-6498	197	11	section	section	NOUN
ejpam-6498	197	12	2	2	NUM
ejpam-6498	197	13	.	.	PUNCT
ejpam-6498	198	1	figure	figure	NOUN
ejpam-6498	198	2	3	3	NUM
ejpam-6498	198	3	:	:	PUNCT
ejpam-6498	198	4	ellipsoid	ellipsoid	NOUN
ejpam-6498	198	5	(	(	PUNCT
ejpam-6498	198	6	surface	surface	NOUN
ejpam-6498	198	7	of	of	ADP
ejpam-6498	198	8	revolution	revolution	NOUN
ejpam-6498	198	9	of	of	ADP
ejpam-6498	198	10	ellipse	ellipse	NOUN
ejpam-6498	198	11	approximated	approximate	VERB
ejpam-6498	198	12	in	in	ADP
ejpam-6498	198	13	problem-2	problem-2	NOUN
ejpam-6498	198	14	)	)	PUNCT
ejpam-6498	198	15	.	.	PUNCT
ejpam-6498	199	1	problem-3	problem-3	NUM
ejpam-6498	199	2	the	the	DET
ejpam-6498	199	3	oblique	oblique	ADJ
ejpam-6498	199	4	parabola	parabola	PROPN
ejpam-6498	199	5	x2−2xy+y2−2	x2−2xy+y2−2	PROPN
ejpam-6498	199	6	√	√	NUM
ejpam-6498	200	1	2x−2	2x−2	NUM
ejpam-6498	200	2	√	√	NUM
ejpam-6498	200	3	2y+2	2y+2	PROPN
ejpam-6498	200	4	=	=	SYM
ejpam-6498	200	5	0	0	NUM
ejpam-6498	200	6	is	be	AUX
ejpam-6498	200	7	transformed	transform	VERB
ejpam-6498	200	8	into	into	ADP
ejpam-6498	200	9	horizontal	horizontal	ADJ
ejpam-6498	200	10	parabola	parabola	PROPN
ejpam-6498	200	11	through	through	ADP
ejpam-6498	200	12	rotation	rotation	NOUN
ejpam-6498	200	13	transformation	transformation	NOUN
ejpam-6498	200	14	with	with	ADP
ejpam-6498	200	15	angle	angle	NOUN
ejpam-6498	201	1	θ	θ	X
ejpam-6498	201	2	=	=	PUNCT
ejpam-6498	201	3	π	π	PROPN
ejpam-6498	201	4	4	4	NUM
ejpam-6498	201	5	.	.	PUNCT
ejpam-6498	202	1	the	the	DET
ejpam-6498	202	2	transformed	transform	VERB
ejpam-6498	202	3	horizontal	horizontal	ADJ
ejpam-6498	202	4	parabola	parabola	PROPN
ejpam-6498	202	5	is	be	AUX
ejpam-6498	202	6	y	y	PROPN
ejpam-6498	202	7	2	2	NUM
ejpam-6498	202	8	=	=	SYM
ejpam-6498	202	9	2x	2x	NOUN
ejpam-6498	202	10	in	in	ADP
ejpam-6498	202	11	xy	xy	PROPN
ejpam-6498	202	12	-plane	-plane	PROPN
ejpam-6498	202	13	.	.	PUNCT
ejpam-6498	203	1	the	the	DET
ejpam-6498	203	2	approximation	approximation	NOUN
ejpam-6498	203	3	of	of	ADP
ejpam-6498	203	4	horizontal	horizontal	ADJ
ejpam-6498	203	5	parabola	parabola	NOUN
ejpam-6498	203	6	by	by	ADP
ejpam-6498	203	7	the	the	DET
ejpam-6498	203	8	cubic	cubic	ADJ
ejpam-6498	203	9	bézier	bézier	ADP
ejpam-6498	203	10	approximation	approximation	NOUN
ejpam-6498	203	11	method	method	NOUN
ejpam-6498	203	12	is	be	AUX
ejpam-6498	203	13	plotted	plot	VERB
ejpam-6498	203	14	in	in	ADP
ejpam-6498	203	15	figure	figure	NOUN
ejpam-6498	203	16	4	4	NUM
ejpam-6498	203	17	.	.	PUNCT
ejpam-6498	204	1	the	the	DET
ejpam-6498	204	2	oblique	oblique	ADJ
ejpam-6498	204	3	parabola	parabola	NOUN
ejpam-6498	204	4	is	be	AUX
ejpam-6498	204	5	obtained	obtain	VERB
ejpam-6498	204	6	by	by	ADP
ejpam-6498	204	7	applying	apply	VERB
ejpam-6498	204	8	inverse	inverse	NOUN
ejpam-6498	204	9	transformation	transformation	NOUN
ejpam-6498	204	10	and	and	CCONJ
ejpam-6498	204	11	it	it	PRON
ejpam-6498	204	12	is	be	AUX
ejpam-6498	204	13	plotted	plot	VERB
ejpam-6498	204	14	in	in	ADP
ejpam-6498	204	15	figure	figure	NOUN
ejpam-6498	204	16	5	5	NUM
ejpam-6498	204	17	.	.	PUNCT
ejpam-6498	205	1	figure	figure	VERB
ejpam-6498	205	2	4	4	NUM
ejpam-6498	205	3	:	:	PUNCT
ejpam-6498	205	4	plot	plot	NOUN
ejpam-6498	205	5	of	of	ADP
ejpam-6498	205	6	the	the	DET
ejpam-6498	205	7	transformed	transform	VERB
ejpam-6498	205	8	horizontal	horizontal	PROPN
ejpam-6498	205	9	parabola	parabola	PROPN
ejpam-6498	205	10	approximated	approximate	VERB
ejpam-6498	205	11	in	in	ADP
ejpam-6498	205	12	problem-3	problem-3	PROPN
ejpam-6498	205	13	.	.	PUNCT
ejpam-6498	206	1	m.	m.	PROPN
ejpam-6498	206	2	hussain	hussain	PROPN
ejpam-6498	206	3	,	,	PUNCT
ejpam-6498	206	4	h.	h.	PROPN
ejpam-6498	206	5	a.	a.	PROPN
ejpam-6498	206	6	wajid	wajid	PROPN
ejpam-6498	206	7	,	,	PUNCT
ejpam-6498	206	8	s.	s.	PROPN
ejpam-6498	206	9	aqeel	aqeel	PROPN
ejpam-6498	206	10	/	/	SYM
ejpam-6498	206	11	eur	eur	PROPN
ejpam-6498	206	12	.	.	PUNCT
ejpam-6498	207	1	j.	j.	PROPN
ejpam-6498	207	2	pure	pure	PROPN
ejpam-6498	207	3	appl	appl	PROPN
ejpam-6498	207	4	.	.	PROPN
ejpam-6498	207	5	math	math	PROPN
ejpam-6498	207	6	,	,	PUNCT
ejpam-6498	207	7	18	18	NUM
ejpam-6498	207	8	(	(	PUNCT
ejpam-6498	207	9	4	4	NUM
ejpam-6498	207	10	)	)	PUNCT
ejpam-6498	207	11	(	(	PUNCT
ejpam-6498	207	12	2025	2025	NUM
ejpam-6498	207	13	)	)	PUNCT
ejpam-6498	207	14	,	,	PUNCT
ejpam-6498	207	15	6498	6498	NUM
ejpam-6498	207	16	10	10	NUM
ejpam-6498	207	17	of	of	ADP
ejpam-6498	207	18	12	12	NUM
ejpam-6498	207	19	figure	figure	NOUN
ejpam-6498	207	20	5	5	NUM
ejpam-6498	207	21	:	:	PUNCT
ejpam-6498	207	22	plot	plot	NOUN
ejpam-6498	207	23	of	of	ADP
ejpam-6498	207	24	the	the	DET
ejpam-6498	207	25	oblique	oblique	ADJ
ejpam-6498	207	26	parabola	parabola	NOUN
ejpam-6498	207	27	obtained	obtain	VERB
ejpam-6498	207	28	after	after	ADP
ejpam-6498	207	29	applying	apply	VERB
ejpam-6498	207	30	inverse	inverse	NOUN
ejpam-6498	207	31	transformation	transformation	NOUN
ejpam-6498	207	32	to	to	PART
ejpam-6498	207	33	figure	figure	VERB
ejpam-6498	207	34	4	4	NUM
ejpam-6498	207	35	.	.	PUNCT
ejpam-6498	208	1	problem-4	problem-4	VERB
ejpam-6498	208	2	the	the	DET
ejpam-6498	208	3	horizontal	horizontal	ADJ
ejpam-6498	208	4	parabola	parabola	PROPN
ejpam-6498	208	5	x2	x2	PROPN
ejpam-6498	209	1	=	=	PUNCT
ejpam-6498	209	2	12y	12y	PROPN
ejpam-6498	209	3	,	,	PUNCT
ejpam-6498	209	4	whose	whose	DET
ejpam-6498	209	5	surface	surface	NOUN
ejpam-6498	209	6	of	of	ADP
ejpam-6498	209	7	revolution	revolution	NOUN
ejpam-6498	209	8	is	be	AUX
ejpam-6498	209	9	produced	produce	VERB
ejpam-6498	209	10	in	in	ADP
ejpam-6498	209	11	figure	figure	NOUN
ejpam-6498	209	12	6	6	NUM
ejpam-6498	209	13	using	use	VERB
ejpam-6498	209	14	the	the	DET
ejpam-6498	209	15	approximation	approximation	NOUN
ejpam-6498	209	16	method	method	NOUN
ejpam-6498	209	17	in	in	ADP
ejpam-6498	209	18	section	section	NOUN
ejpam-6498	209	19	2	2	NUM
ejpam-6498	209	20	.	.	PUNCT
ejpam-6498	210	1	the	the	DET
ejpam-6498	210	2	surface	surface	NOUN
ejpam-6498	210	3	is	be	AUX
ejpam-6498	210	4	paraboloid	paraboloid	ADJ
ejpam-6498	210	5	.	.	PUNCT
ejpam-6498	211	1	figure	figure	NOUN
ejpam-6498	211	2	6	6	NUM
ejpam-6498	211	3	:	:	PUNCT
ejpam-6498	211	4	paraboloid	paraboloid	ADJ
ejpam-6498	211	5	(	(	PUNCT
ejpam-6498	211	6	surface	surface	NOUN
ejpam-6498	211	7	of	of	ADP
ejpam-6498	211	8	revolution	revolution	NOUN
ejpam-6498	211	9	of	of	ADP
ejpam-6498	211	10	parabola	parabola	PROPN
ejpam-6498	211	11	approximated	approximate	VERB
ejpam-6498	211	12	in	in	ADP
ejpam-6498	211	13	problem-4	problem-4	NUM
ejpam-6498	211	14	)	)	PUNCT
ejpam-6498	211	15	.	.	PUNCT
ejpam-6498	212	1	key	key	ADJ
ejpam-6498	212	2	insights	insight	NOUN
ejpam-6498	212	3	achieved	achieve	VERB
ejpam-6498	212	4	from	from	ADP
ejpam-6498	212	5	the	the	DET
ejpam-6498	212	6	proposed	propose	VERB
ejpam-6498	212	7	method	method	NOUN
ejpam-6498	212	8	are	be	AUX
ejpam-6498	212	9	listed	list	VERB
ejpam-6498	212	10	below	below	ADP
ejpam-6498	212	11	:	:	PUNCT
ejpam-6498	212	12	(	(	PUNCT
ejpam-6498	212	13	i	i	NOUN
ejpam-6498	212	14	)	)	PUNCT
ejpam-6498	212	15	figures	figure	NOUN
ejpam-6498	212	16	1	1	NUM
ejpam-6498	212	17	and	and	CCONJ
ejpam-6498	212	18	2	2	NUM
ejpam-6498	212	19	:	:	PUNCT
ejpam-6498	212	20	invariance	invariance	NOUN
ejpam-6498	212	21	to	to	PART
ejpam-6498	212	22	rotation	rotation	NOUN
ejpam-6498	212	23	ensures	ensure	VERB
ejpam-6498	212	24	robustness	robustness	NOUN
ejpam-6498	212	25	for	for	ADP
ejpam-6498	212	26	industrial	industrial	ADJ
ejpam-6498	212	27	designs	design	NOUN
ejpam-6498	212	28	with	with	ADP
ejpam-6498	212	29	arbitrary	arbitrary	ADJ
ejpam-6498	212	30	conic	conic	ADJ
ejpam-6498	212	31	orientations	orientation	NOUN
ejpam-6498	212	32	.	.	PUNCT
ejpam-6498	213	1	(	(	PUNCT
ejpam-6498	213	2	ii	ii	NOUN
ejpam-6498	213	3	)	)	PUNCT
ejpam-6498	213	4	figure	figure	NOUN
ejpam-6498	213	5	3	3	NUM
ejpam-6498	213	6	:	:	PUNCT
ejpam-6498	213	7	since	since	SCONJ
ejpam-6498	213	8	surface	surface	NOUN
ejpam-6498	213	9	error	error	NOUN
ejpam-6498	213	10	remains	remains	AUX
ejpam-6498	213	11	bounded	bound	VERB
ejpam-6498	213	12	by	by	ADP
ejpam-6498	213	13	the	the	DET
ejpam-6498	213	14	2d	2d	PROPN
ejpam-6498	213	15	approximation	approximation	NOUN
ejpam-6498	213	16	error	error	NOUN
ejpam-6498	213	17	1.2×	1.2×	PROPN
ejpam-6498	213	18	10−3	10−3	NUM
ejpam-6498	213	19	,	,	PUNCT
ejpam-6498	213	20	validating	validate	VERB
ejpam-6498	213	21	scalability	scalability	NOUN
ejpam-6498	213	22	to	to	ADP
ejpam-6498	213	23	3d	3d	NUM
ejpam-6498	213	24	modeling	modeling	NOUN
ejpam-6498	213	25	.	.	PUNCT
ejpam-6498	214	1	more	more	ADV
ejpam-6498	214	2	specifically	specifically	ADV
ejpam-6498	214	3	in	in	ADP
ejpam-6498	214	4	pressure	pressure	NOUN
ejpam-6498	214	5	vessel	vessel	NOUN
ejpam-6498	214	6	designs	design	NOUN
ejpam-6498	214	7	for	for	ADP
ejpam-6498	214	8	which	which	PRON
ejpam-6498	214	9	smoothness	smoothness	ADJ
ejpam-6498	214	10	impacts	impact	VERB
ejpam-6498	214	11	manufacturability	manufacturability	NOUN
ejpam-6498	214	12	.	.	PUNCT
ejpam-6498	215	1	m.	m.	NOUN
ejpam-6498	215	2	hussain	hussain	PROPN
ejpam-6498	215	3	,	,	PUNCT
ejpam-6498	215	4	h.	h.	PROPN
ejpam-6498	215	5	a.	a.	PROPN
ejpam-6498	215	6	wajid	wajid	PROPN
ejpam-6498	215	7	,	,	PUNCT
ejpam-6498	215	8	s.	s.	PROPN
ejpam-6498	215	9	aqeel	aqeel	PROPN
ejpam-6498	215	10	/	/	SYM
ejpam-6498	215	11	eur	eur	PROPN
ejpam-6498	215	12	.	.	PUNCT
ejpam-6498	216	1	j.	j.	PROPN
ejpam-6498	216	2	pure	pure	PROPN
ejpam-6498	216	3	appl	appl	PROPN
ejpam-6498	216	4	.	.	PROPN
ejpam-6498	216	5	math	math	PROPN
ejpam-6498	216	6	,	,	PUNCT
ejpam-6498	216	7	18	18	NUM
ejpam-6498	216	8	(	(	PUNCT
ejpam-6498	216	9	4	4	NUM
ejpam-6498	216	10	)	)	PUNCT
ejpam-6498	216	11	(	(	PUNCT
ejpam-6498	216	12	2025	2025	NUM
ejpam-6498	216	13	)	)	PUNCT
ejpam-6498	216	14	,	,	PUNCT
ejpam-6498	216	15	6498	6498	NUM
ejpam-6498	216	16	11	11	NUM
ejpam-6498	216	17	of	of	ADP
ejpam-6498	216	18	12	12	NUM
ejpam-6498	216	19	(	(	PUNCT
ejpam-6498	216	20	iii	iii	NOUN
ejpam-6498	216	21	)	)	PUNCT
ejpam-6498	216	22	figures	figure	NOUN
ejpam-6498	216	23	4	4	NUM
ejpam-6498	216	24	and	and	CCONJ
ejpam-6498	216	25	5	5	NUM
ejpam-6498	216	26	:	:	PUNCT
ejpam-6498	216	27	exact	exact	ADJ
ejpam-6498	216	28	reconstruction	reconstruction	NOUN
ejpam-6498	216	29	stems	stem	VERB
ejpam-6498	216	30	from	from	ADP
ejpam-6498	216	31	the	the	DET
ejpam-6498	216	32	geometric	geometric	ADJ
ejpam-6498	216	33	invariance	invariance	NOUN
ejpam-6498	216	34	(	(	PUNCT
ejpam-6498	216	35	theorem	theorem	NOUN
ejpam-6498	216	36	4	4	NUM
ejpam-6498	216	37	)	)	PUNCT
ejpam-6498	216	38	of	of	ADP
ejpam-6498	216	39	the	the	DET
ejpam-6498	216	40	proposed	propose	VERB
ejpam-6498	216	41	method	method	NOUN
ejpam-6498	216	42	eliminating	eliminate	VERB
ejpam-6498	216	43	approximation	approximation	NOUN
ejpam-6498	216	44	error	error	NOUN
ejpam-6498	216	45	for	for	ADP
ejpam-6498	216	46	parabolas	parabola	NOUN
ejpam-6498	216	47	.	.	PUNCT
ejpam-6498	217	1	(	(	PUNCT
ejpam-6498	217	2	iv	iv	X
ejpam-6498	217	3	)	)	PUNCT
ejpam-6498	217	4	figure	figure	NOUN
ejpam-6498	217	5	6	6	NUM
ejpam-6498	217	6	:	:	PUNCT
ejpam-6498	217	7	execution	execution	NOUN
ejpam-6498	217	8	time	time	NOUN
ejpam-6498	217	9	of	of	ADP
ejpam-6498	217	10	1.015	1.015	NUM
ejpam-6498	217	11	sec	sec	PROPN
ejpam-6498	217	12	(	(	PUNCT
ejpam-6498	217	13	table	table	NOUN
ejpam-6498	217	14	2	2	NUM
ejpam-6498	217	15	)	)	PUNCT
ejpam-6498	217	16	makes	make	VERB
ejpam-6498	217	17	it	it	PRON
ejpam-6498	217	18	viable	viable	ADJ
ejpam-6498	217	19	for	for	ADP
ejpam-6498	217	20	real	real	ADJ
ejpam-6498	217	21	-	-	PUNCT
ejpam-6498	217	22	time	time	NOUN
ejpam-6498	217	23	rendering	rendering	NOUN
ejpam-6498	217	24	.	.	PUNCT
ejpam-6498	218	1	furthermore	furthermore	ADV
ejpam-6498	218	2	,	,	PUNCT
ejpam-6498	218	3	table	table	NOUN
ejpam-6498	218	4	1	1	NUM
ejpam-6498	218	5	demonstrates	demonstrate	VERB
ejpam-6498	218	6	the	the	DET
ejpam-6498	218	7	superior	superior	ADJ
ejpam-6498	218	8	accuracy	accuracy	NOUN
ejpam-6498	218	9	of	of	ADP
ejpam-6498	218	10	the	the	DET
ejpam-6498	218	11	proposed	propose	VERB
ejpam-6498	218	12	method	method	NOUN
ejpam-6498	218	13	.	.	PUNCT
ejpam-6498	219	1	in	in	ADP
ejpam-6498	219	2	case	case	NOUN
ejpam-6498	219	3	of	of	ADP
ejpam-6498	219	4	elliptic	elliptic	ADJ
ejpam-6498	219	5	arcs	arc	NOUN
ejpam-6498	219	6	,	,	PUNCT
ejpam-6498	219	7	the	the	DET
ejpam-6498	219	8	method	method	NOUN
ejpam-6498	219	9	achieves	achieve	VERB
ejpam-6498	219	10	a	a	DET
ejpam-6498	219	11	maximum	maximum	ADJ
ejpam-6498	219	12	absolute	absolute	ADJ
ejpam-6498	219	13	error	error	NOUN
ejpam-6498	219	14	(	(	PUNCT
ejpam-6498	219	15	mae	mae	PROPN
ejpam-6498	219	16	)	)	PUNCT
ejpam-6498	219	17	of	of	ADP
ejpam-6498	219	18	1.2×	1.2×	NUM
ejpam-6498	219	19	10−3	10−3	NUM
ejpam-6498	219	20	which	which	PRON
ejpam-6498	219	21	is	be	AUX
ejpam-6498	219	22	better	well	ADJ
ejpam-6498	219	23	than	than	SCONJ
ejpam-6498	219	24	achieved	achieve	VERB
ejpam-6498	219	25	in	in	ADP
ejpam-6498	219	26	[	[	X
ejpam-6498	219	27	2	2	NUM
ejpam-6498	219	28	,	,	PUNCT
ejpam-6498	219	29	6	6	NUM
ejpam-6498	219	30	]	]	PUNCT
ejpam-6498	219	31	.	.	PUNCT
ejpam-6498	220	1	however	however	ADV
ejpam-6498	220	2	,	,	PUNCT
ejpam-6498	220	3	in	in	ADP
ejpam-6498	220	4	case	case	NOUN
ejpam-6498	220	5	of	of	ADP
ejpam-6498	220	6	parabolic	parabolic	ADJ
ejpam-6498	220	7	arcs	arc	NOUN
ejpam-6498	220	8	,	,	PUNCT
ejpam-6498	220	9	it	it	PRON
ejpam-6498	220	10	attains	attain	VERB
ejpam-6498	220	11	machine	machine	NOUN
ejpam-6498	220	12	-	-	PUNCT
ejpam-6498	220	13	precision	precision	NOUN
ejpam-6498	220	14	error	error	NOUN
ejpam-6498	220	15	3.55×	3.55×	PROPN
ejpam-6498	220	16	10−15	10−15	NUM
ejpam-6498	220	17	by	by	ADP
ejpam-6498	220	18	exact	exact	ADJ
ejpam-6498	220	19	reconstruction	reconstruction	NOUN
ejpam-6498	220	20	.	.	PUNCT
ejpam-6498	221	1	table	table	NOUN
ejpam-6498	221	2	1	1	NUM
ejpam-6498	221	3	:	:	PUNCT
ejpam-6498	221	4	accuracy	accuracy	NOUN
ejpam-6498	221	5	comparison	comparison	NOUN
ejpam-6498	221	6	of	of	ADP
ejpam-6498	221	7	proposed	propose	VERB
ejpam-6498	221	8	method	method	NOUN
ejpam-6498	221	9	(	(	PUNCT
ejpam-6498	221	10	maximum	maximum	ADJ
ejpam-6498	221	11	absolute	absolute	ADJ
ejpam-6498	221	12	error	error	NOUN
ejpam-6498	221	13	)	)	PUNCT
ejpam-6498	221	14	curve	curve	NOUN
ejpam-6498	221	15	type	type	NOUN
ejpam-6498	222	1	[	[	X
ejpam-6498	222	2	6	6	NUM
ejpam-6498	222	3	]	]	PUNCT
ejpam-6498	222	4	(	(	PUNCT
ejpam-6498	222	5	2014	2014	NUM
ejpam-6498	222	6	)	)	PUNCT
ejpam-6498	223	1	[	[	X
ejpam-6498	223	2	2	2	NUM
ejpam-6498	223	3	]	]	PUNCT
ejpam-6498	223	4	(	(	PUNCT
ejpam-6498	223	5	2017	2017	NUM
ejpam-6498	223	6	)	)	PUNCT
ejpam-6498	224	1	[	[	X
ejpam-6498	224	2	8	8	NUM
ejpam-6498	224	3	]	]	SYM
ejpam-6498	224	4	(	(	PUNCT
ejpam-6498	224	5	2017	2017	NUM
ejpam-6498	224	6	)	)	PUNCT
ejpam-6498	224	7	proposed	propose	VERB
ejpam-6498	224	8	method	method	NOUN
ejpam-6498	224	9	ellipse	ellipse	NOUN
ejpam-6498	224	10	(	(	PUNCT
ejpam-6498	224	11	problem-1	problem-1	X
ejpam-6498	224	12	)	)	PUNCT
ejpam-6498	224	13	2.41×	2.41×	NUM
ejpam-6498	224	14	10−3	10−3	NUM
ejpam-6498	224	15	4.40×	4.40×	NUM
ejpam-6498	224	16	10−3	10−3	NUM
ejpam-6498	224	17	—	—	PUNCT
ejpam-6498	224	18	1.2×	1.2×	NUM
ejpam-6498	224	19	10−3	10−3	NUM
ejpam-6498	224	20	parabola	parabola	NOUN
ejpam-6498	224	21	(	(	PUNCT
ejpam-6498	224	22	problem-3	problem-3	NUM
ejpam-6498	224	23	)	)	PUNCT
ejpam-6498	224	24	1.36×	1.36×	PROPN
ejpam-6498	224	25	10−3	10−3	NUM
ejpam-6498	224	26	2.87×	2.87×	NUM
ejpam-6498	224	27	10−1	10−1	PROPN
ejpam-6498	224	28	4.60×	4.60×	NUM
ejpam-6498	224	29	10−4	10−4	NUM
ejpam-6498	224	30	3.55×	3.55×	NUM
ejpam-6498	224	31	10−15	10−15	PROPN
ejpam-6498	224	32	table	table	NOUN
ejpam-6498	224	33	2	2	NUM
ejpam-6498	224	34	confirms	confirm	VERB
ejpam-6498	224	35	computational	computational	ADJ
ejpam-6498	224	36	efficiency	efficiency	NOUN
ejpam-6498	224	37	,	,	PUNCT
ejpam-6498	224	38	with	with	ADP
ejpam-6498	224	39	execution	execution	NOUN
ejpam-6498	224	40	times	time	NOUN
ejpam-6498	224	41	under	under	ADP
ejpam-6498	224	42	1.5	1.5	NUM
ejpam-6498	224	43	seconds	second	NOUN
ejpam-6498	224	44	for	for	ADP
ejpam-6498	224	45	all	all	DET
ejpam-6498	224	46	problems	problem	NOUN
ejpam-6498	224	47	which	which	PRON
ejpam-6498	224	48	are	be	AUX
ejpam-6498	224	49	faster	fast	ADV
ejpam-6498	224	50	compared	compare	VERB
ejpam-6498	224	51	with	with	ADP
ejpam-6498	224	52	optimization	optimization	NOUN
ejpam-6498	224	53	-	-	PUNCT
ejpam-6498	224	54	based	base	VERB
ejpam-6498	224	55	methods	method	NOUN
ejpam-6498	224	56	[	[	X
ejpam-6498	224	57	8	8	NUM
ejpam-6498	224	58	,	,	PUNCT
ejpam-6498	224	59	9	9	NUM
ejpam-6498	224	60	]	]	PUNCT
ejpam-6498	224	61	and	and	CCONJ
ejpam-6498	224	62	competitive	competitive	ADJ
ejpam-6498	224	63	with	with	ADP
ejpam-6498	224	64	rational	rational	ADJ
ejpam-6498	224	65	bézier	bézier	ADP
ejpam-6498	224	66	approaches	approach	NOUN
ejpam-6498	224	67	[	[	X
ejpam-6498	224	68	6	6	NUM
ejpam-6498	224	69	]	]	PUNCT
ejpam-6498	224	70	.	.	PUNCT
ejpam-6498	225	1	table	table	NOUN
ejpam-6498	225	2	2	2	NUM
ejpam-6498	225	3	:	:	PUNCT
ejpam-6498	225	4	computational	computational	ADJ
ejpam-6498	225	5	efficiency	efficiency	NOUN
ejpam-6498	225	6	of	of	ADP
ejpam-6498	225	7	the	the	DET
ejpam-6498	225	8	proposed	propose	VERB
ejpam-6498	225	9	method	method	NOUN
ejpam-6498	225	10	problem	problem	NOUN
ejpam-6498	225	11	curve	curve	NOUN
ejpam-6498	225	12	type	type	NOUN
ejpam-6498	225	13	execution	execution	NOUN
ejpam-6498	225	14	time	time	NOUN
ejpam-6498	225	15	(	(	PUNCT
ejpam-6498	225	16	seconds	second	NOUN
ejpam-6498	225	17	)	)	PUNCT
ejpam-6498	225	18	1	1	NUM
ejpam-6498	225	19	oblique	oblique	ADJ
ejpam-6498	225	20	ellipse	ellipse	NOUN
ejpam-6498	225	21	0.640	0.640	NUM
ejpam-6498	225	22	2	2	NUM
ejpam-6498	225	23	ellipsoid	ellipsoid	NOUN
ejpam-6498	225	24	1.485	1.485	NUM
ejpam-6498	225	25	3	3	NUM
ejpam-6498	225	26	oblique	oblique	ADJ
ejpam-6498	225	27	parabola	parabola	NOUN
ejpam-6498	225	28	0.390	0.390	NUM
ejpam-6498	225	29	4	4	NUM
ejpam-6498	225	30	paraboloid	paraboloid	ADJ
ejpam-6498	225	31	1.015	1.015	NUM
ejpam-6498	225	32	hence	hence	ADV
ejpam-6498	225	33	,	,	PUNCT
ejpam-6498	225	34	the	the	DET
ejpam-6498	225	35	results	result	NOUN
ejpam-6498	225	36	validate	validate	VERB
ejpam-6498	225	37	that	that	SCONJ
ejpam-6498	225	38	proposed	propose	VERB
ejpam-6498	225	39	method	method	NOUN
ejpam-6498	225	40	eliminates	eliminate	VERB
ejpam-6498	225	41	the	the	DET
ejpam-6498	225	42	trade	trade	NOUN
ejpam-6498	225	43	-	-	PUNCT
ejpam-6498	225	44	off	off	NOUN
ejpam-6498	225	45	between	between	ADP
ejpam-6498	225	46	accuracy	accuracy	NOUN
ejpam-6498	225	47	and	and	CCONJ
ejpam-6498	225	48	complexity	complexity	NOUN
ejpam-6498	225	49	by	by	ADP
ejpam-6498	225	50	avoiding	avoid	VERB
ejpam-6498	225	51	both	both	DET
ejpam-6498	225	52	weight	weight	NOUN
ejpam-6498	225	53	optimization	optimization	NOUN
ejpam-6498	225	54	(	(	PUNCT
ejpam-6498	225	55	unlike	unlike	ADP
ejpam-6498	225	56	[	[	X
ejpam-6498	225	57	6	6	NUM
ejpam-6498	225	58	,	,	PUNCT
ejpam-6498	225	59	7	7	NUM
ejpam-6498	225	60	]	]	PUNCT
ejpam-6498	225	61	)	)	PUNCT
ejpam-6498	225	62	and	and	CCONJ
ejpam-6498	225	63	highdegree	highdegree	PROPN
ejpam-6498	225	64	curves	curve	NOUN
ejpam-6498	225	65	(	(	PUNCT
ejpam-6498	225	66	unlike	unlike	ADP
ejpam-6498	225	67	[	[	X
ejpam-6498	225	68	1	1	NUM
ejpam-6498	225	69	,	,	PUNCT
ejpam-6498	225	70	10	10	NUM
ejpam-6498	225	71	]	]	PUNCT
ejpam-6498	225	72	)	)	PUNCT
ejpam-6498	225	73	,	,	PUNCT
ejpam-6498	225	74	making	make	VERB
ejpam-6498	225	75	it	it	PRON
ejpam-6498	225	76	practical	practical	ADJ
ejpam-6498	225	77	for	for	ADP
ejpam-6498	225	78	cad	cad	NOUN
ejpam-6498	225	79	applications	application	NOUN
ejpam-6498	225	80	where	where	SCONJ
ejpam-6498	225	81	cubic	cubic	ADJ
ejpam-6498	225	82	béziers	béziers	PROPN
ejpam-6498	225	83	are	be	AUX
ejpam-6498	225	84	the	the	DET
ejpam-6498	225	85	standard	standard	NOUN
ejpam-6498	225	86	.	.	PUNCT
ejpam-6498	226	1	4	4	X
ejpam-6498	226	2	.	.	X
ejpam-6498	226	3	conclusion	conclusion	NOUN
ejpam-6498	226	4	this	this	DET
ejpam-6498	226	5	study	study	NOUN
ejpam-6498	226	6	presents	present	VERB
ejpam-6498	226	7	a	a	DET
ejpam-6498	226	8	tangent	tangent	ADJ
ejpam-6498	226	9	-	-	PUNCT
ejpam-6498	226	10	continuous	continuous	ADJ
ejpam-6498	226	11	,	,	PUNCT
ejpam-6498	226	12	optimization	optimization	NOUN
ejpam-6498	226	13	-	-	PUNCT
ejpam-6498	226	14	free	free	ADJ
ejpam-6498	226	15	method	method	NOUN
ejpam-6498	226	16	for	for	ADP
ejpam-6498	226	17	approximating	approximate	VERB
ejpam-6498	226	18	conic	conic	ADJ
ejpam-6498	226	19	sections	section	NOUN
ejpam-6498	226	20	using	use	VERB
ejpam-6498	226	21	cubic	cubic	ADV
ejpam-6498	226	22	bézier	bézier	ADP
ejpam-6498	226	23	curves	curve	NOUN
ejpam-6498	226	24	,	,	PUNCT
ejpam-6498	226	25	achieving	achieve	VERB
ejpam-6498	226	26	desired	desire	VERB
ejpam-6498	226	27	accuracy	accuracy	NOUN
ejpam-6498	226	28	-	-	PUNCT
ejpam-6498	226	29	efficiency	efficiency	NOUN
ejpam-6498	226	30	.	.	PUNCT
ejpam-6498	227	1	the	the	DET
ejpam-6498	227	2	proposed	propose	VERB
ejpam-6498	227	3	method	method	NOUN
ejpam-6498	227	4	derives	derive	VERB
ejpam-6498	227	5	control	control	NOUN
ejpam-6498	227	6	points	point	NOUN
ejpam-6498	227	7	analytically	analytically	ADV
ejpam-6498	227	8	from	from	ADP
ejpam-6498	227	9	endpoint	endpoint	NOUN
ejpam-6498	227	10	/	/	SYM
ejpam-6498	227	11	tangent	tangent	NOUN
ejpam-6498	227	12	data	datum	NOUN
ejpam-6498	227	13	alone	alone	ADV
ejpam-6498	227	14	,	,	PUNCT
ejpam-6498	227	15	avoiding	avoid	VERB
ejpam-6498	227	16	rational	rational	ADJ
ejpam-6498	227	17	forms	form	NOUN
ejpam-6498	227	18	[	[	X
ejpam-6498	227	19	1	1	NUM
ejpam-6498	227	20	,	,	PUNCT
ejpam-6498	227	21	6	6	NUM
ejpam-6498	227	22	]	]	PUNCT
ejpam-6498	227	23	and	and	CCONJ
ejpam-6498	227	24	optimization	optimization	NOUN
ejpam-6498	227	25	[	[	X
ejpam-6498	227	26	7–9	7–9	X
ejpam-6498	227	27	]	]	X
ejpam-6498	227	28	.	.	PUNCT
ejpam-6498	228	1	it	it	PRON
ejpam-6498	228	2	achieves	achieve	VERB
ejpam-6498	228	3	reduced	reduce	VERB
ejpam-6498	228	4	maximum	maximum	ADJ
ejpam-6498	228	5	absolute	absolute	ADJ
ejpam-6498	228	6	error	error	NOUN
ejpam-6498	228	7	of	of	ADP
ejpam-6498	228	8	1.2	1.2	NUM
ejpam-6498	228	9	×	×	NOUN
ejpam-6498	228	10	10−3	10−3	NUM
ejpam-6498	228	11	compared	compare	VERB
ejpam-6498	228	12	with	with	ADP
ejpam-6498	228	13	[	[	X
ejpam-6498	228	14	2	2	NUM
ejpam-6498	228	15	,	,	PUNCT
ejpam-6498	228	16	6	6	NUM
ejpam-6498	228	17	]	]	PUNCT
ejpam-6498	228	18	for	for	ADP
ejpam-6498	228	19	elliptic	elliptic	ADJ
ejpam-6498	228	20	arcs	arc	NOUN
ejpam-6498	228	21	.	.	PUNCT
ejpam-6498	229	1	the	the	DET
ejpam-6498	229	2	proposed	propose	VERB
ejpam-6498	229	3	method	method	NOUN
ejpam-6498	229	4	computes	compute	VERB
ejpam-6498	229	5	exact	exact	ADJ
ejpam-6498	229	6	reconstruction	reconstruction	NOUN
ejpam-6498	229	7	of	of	ADP
ejpam-6498	229	8	parabolic	parabolic	ADJ
ejpam-6498	229	9	arcs	arc	NOUN
ejpam-6498	229	10	via	via	ADP
ejpam-6498	229	11	geometric	geometric	ADJ
ejpam-6498	229	12	invariance	invariance	NOUN
ejpam-6498	229	13	and	and	CCONJ
ejpam-6498	229	14	performs	perform	VERB
ejpam-6498	229	15	better	well	ADJ
ejpam-6498	229	16	than	than	ADP
ejpam-6498	229	17	the	the	DET
ejpam-6498	229	18	prior	prior	ADJ
ejpam-6498	229	19	methods	method	NOUN
ejpam-6498	229	20	[	[	X
ejpam-6498	229	21	2	2	NUM
ejpam-6498	229	22	,	,	PUNCT
ejpam-6498	229	23	6	6	NUM
ejpam-6498	229	24	,	,	PUNCT
ejpam-6498	229	25	8	8	NUM
ejpam-6498	229	26	]	]	PUNCT
ejpam-6498	229	27	achieving	achieve	VERB
ejpam-6498	229	28	maximum	maximum	ADJ
ejpam-6498	229	29	absolute	absolute	ADJ
ejpam-6498	229	30	error	error	NOUN
ejpam-6498	229	31	of	of	ADP
ejpam-6498	229	32	3.55×	3.55×	NUM
ejpam-6498	229	33	10−15	10−15	NOUN
ejpam-6498	229	34	.	.	PUNCT
ejpam-6498	230	1	the	the	DET
ejpam-6498	230	2	necessity	necessity	NOUN
ejpam-6498	230	3	of	of	ADP
ejpam-6498	230	4	optimization	optimization	NOUN
ejpam-6498	230	5	[	[	X
ejpam-6498	230	6	8	8	NUM
ejpam-6498	230	7	,	,	PUNCT
ejpam-6498	230	8	9	9	NUM
ejpam-6498	230	9	]	]	PUNCT
ejpam-6498	230	10	and	and	CCONJ
ejpam-6498	230	11	rational	rational	ADJ
ejpam-6498	230	12	arithmetic	arithmetic	ADJ
ejpam-6498	230	13	[	[	X
ejpam-6498	230	14	6	6	NUM
ejpam-6498	230	15	]	]	PUNCT
ejpam-6498	230	16	has	have	AUX
ejpam-6498	230	17	been	be	AUX
ejpam-6498	230	18	avoided	avoid	VERB
ejpam-6498	230	19	.	.	PUNCT
ejpam-6498	231	1	the	the	DET
ejpam-6498	231	2	reduced	reduce	VERB
ejpam-6498	231	3	runtime	runtime	NOUN
ejpam-6498	231	4	is	be	AUX
ejpam-6498	231	5	30	30	NUM
ejpam-6498	231	6	-	-	SYM
ejpam-6498	231	7	50	50	NUM
ejpam-6498	231	8	%	%	NOUN
ejpam-6498	231	9	(	(	PUNCT
ejpam-6498	231	10	an	an	DET
ejpam-6498	231	11	execution	execution	NOUN
ejpam-6498	231	12	time	time	NOUN
ejpam-6498	231	13	under	under	ADP
ejpam-6498	231	14	1.5	1.5	NUM
ejpam-6498	231	15	seconds	second	NOUN
ejpam-6498	231	16	)	)	PUNCT
ejpam-6498	231	17	for	for	ADP
ejpam-6498	231	18	all	all	DET
ejpam-6498	231	19	tested	test	VERB
ejpam-6498	231	20	problems	problem	NOUN
ejpam-6498	231	21	.	.	PUNCT
ejpam-6498	232	1	it	it	PRON
ejpam-6498	232	2	m.	m.	NOUN
ejpam-6498	232	3	hussain	hussain	PROPN
ejpam-6498	232	4	,	,	PUNCT
ejpam-6498	232	5	h.	h.	PROPN
ejpam-6498	232	6	a.	a.	PROPN
ejpam-6498	232	7	wajid	wajid	PROPN
ejpam-6498	232	8	,	,	PUNCT
ejpam-6498	232	9	s.	s.	PROPN
ejpam-6498	232	10	aqeel	aqeel	PROPN
ejpam-6498	232	11	/	/	SYM
ejpam-6498	232	12	eur	eur	PROPN
ejpam-6498	232	13	.	.	PUNCT
ejpam-6498	233	1	j.	j.	PROPN
ejpam-6498	233	2	pure	pure	PROPN
ejpam-6498	233	3	appl	appl	PROPN
ejpam-6498	233	4	.	.	PROPN
ejpam-6498	233	5	math	math	PROPN
ejpam-6498	233	6	,	,	PUNCT
ejpam-6498	233	7	18	18	NUM
ejpam-6498	233	8	(	(	PUNCT
ejpam-6498	233	9	4	4	NUM
ejpam-6498	233	10	)	)	PUNCT
ejpam-6498	233	11	(	(	PUNCT
ejpam-6498	233	12	2025	2025	NUM
ejpam-6498	233	13	)	)	PUNCT
ejpam-6498	233	14	,	,	PUNCT
ejpam-6498	233	15	6498	6498	NUM
ejpam-6498	233	16	12	12	NUM
ejpam-6498	233	17	of	of	ADP
ejpam-6498	233	18	12	12	NUM
ejpam-6498	233	19	has	have	VERB
ejpam-6498	233	20	real	real	ADJ
ejpam-6498	233	21	-	-	PUNCT
ejpam-6498	233	22	world	world	NOUN
ejpam-6498	233	23	viability	viability	NOUN
ejpam-6498	233	24	benchmarking	benchmarke	VERB
ejpam-6498	233	25	against	against	ADP
ejpam-6498	233	26	cad	cad	NOUN
ejpam-6498	233	27	-	-	PUNCT
ejpam-6498	233	28	standard	standard	ADJ
ejpam-6498	233	29	transformations	transformation	NOUN
ejpam-6498	233	30	.	.	PUNCT
ejpam-6498	234	1	also	also	ADV
ejpam-6498	234	2	,	,	PUNCT
ejpam-6498	234	3	maintain	maintain	VERB
ejpam-6498	234	4	g1	g1	ADJ
ejpam-6498	234	5	continuity	continuity	NOUN
ejpam-6498	234	6	under	under	ADP
ejpam-6498	234	7	affine	affine	NOUN
ejpam-6498	234	8	transformations	transformation	NOUN
ejpam-6498	234	9	.	.	PUNCT
ejpam-6498	235	1	to	to	PART
ejpam-6498	235	2	conclude	conclude	VERB
ejpam-6498	235	3	,	,	PUNCT
ejpam-6498	235	4	this	this	DET
ejpam-6498	235	5	work	work	NOUN
ejpam-6498	235	6	bridges	bridge	VERB
ejpam-6498	235	7	a	a	DET
ejpam-6498	235	8	critical	critical	ADJ
ejpam-6498	235	9	gap	gap	NOUN
ejpam-6498	235	10	between	between	ADP
ejpam-6498	235	11	theory	theory	NOUN
ejpam-6498	235	12	and	and	CCONJ
ejpam-6498	235	13	practice	practice	NOUN
ejpam-6498	235	14	,	,	PUNCT
ejpam-6498	235	15	delivering	deliver	VERB
ejpam-6498	235	16	provably	provably	ADV
ejpam-6498	235	17	optimal	optimal	ADJ
ejpam-6498	235	18	approximations	approximation	NOUN
ejpam-6498	235	19	without	without	ADP
ejpam-6498	235	20	sacrificing	sacrifice	VERB
ejpam-6498	235	21	computational	computational	ADJ
ejpam-6498	235	22	tractability	tractability	NOUN
ejpam-6498	235	23	which	which	PRON
ejpam-6498	235	24	is	be	AUX
ejpam-6498	235	25	a	a	DET
ejpam-6498	235	26	necessity	necessity	NOUN
ejpam-6498	235	27	for	for	ADP
ejpam-6498	235	28	next	next	ADJ
ejpam-6498	235	29	-	-	PUNCT
ejpam-6498	235	30	generation	generation	NOUN
ejpam-6498	235	31	cad	cad	PROPN
ejpam-6498	235	32	/	/	SYM
ejpam-6498	235	33	cae	cae	NOUN
ejpam-6498	235	34	systems	system	NOUN
ejpam-6498	235	35	.	.	PUNCT
ejpam-6498	236	1	(	(	PUNCT
ejpam-6498	236	2	i	i	NOUN
ejpam-6498	236	3	)	)	PUNCT
ejpam-6498	236	4	conflict	conflict	NOUN
ejpam-6498	236	5	of	of	ADP
ejpam-6498	236	6	interest	interest	NOUN
ejpam-6498	236	7	:	:	PUNCT
ejpam-6498	236	8	the	the	DET
ejpam-6498	236	9	authors	author	NOUN
ejpam-6498	236	10	state	state	VERB
ejpam-6498	236	11	that	that	SCONJ
ejpam-6498	236	12	there	there	PRON
ejpam-6498	236	13	is	be	VERB
ejpam-6498	236	14	no	no	DET
ejpam-6498	236	15	conflict	conflict	NOUN
ejpam-6498	236	16	of	of	ADP
ejpam-6498	236	17	interest	interest	NOUN
ejpam-6498	236	18	.	.	PUNCT
ejpam-6498	237	1	(	(	PUNCT
ejpam-6498	237	2	ii	ii	NOUN
ejpam-6498	237	3	)	)	PUNCT
ejpam-6498	237	4	funding	funding	NOUN
ejpam-6498	237	5	:	:	PUNCT
ejpam-6498	237	6	no	no	DET
ejpam-6498	237	7	funding	funding	NOUN
ejpam-6498	237	8	is	be	AUX
ejpam-6498	237	9	utilized	utilize	VERB
ejpam-6498	237	10	for	for	ADP
ejpam-6498	237	11	this	this	DET
ejpam-6498	237	12	research	research	NOUN
ejpam-6498	237	13	work	work	NOUN
ejpam-6498	237	14	/	/	SYM
ejpam-6498	237	15	publication	publication	NOUN
ejpam-6498	237	16	references	reference	NOUN
ejpam-6498	237	17	[	[	X
ejpam-6498	237	18	1	1	NUM
ejpam-6498	237	19	]	]	PUNCT
ejpam-6498	237	20	m.	m.	NOUN
ejpam-6498	237	21	z.	z.	PROPN
ejpam-6498	237	22	hussain	hussain	PROPN
ejpam-6498	237	23	,	,	PUNCT
ejpam-6498	237	24	a.	a.	PROPN
ejpam-6498	237	25	shakeel	shakeel	PROPN
ejpam-6498	237	26	,	,	PUNCT
ejpam-6498	237	27	and	and	CCONJ
ejpam-6498	237	28	m.	m.	NOUN
ejpam-6498	237	29	hussain	hussain	PROPN
ejpam-6498	237	30	.	.	PUNCT
ejpam-6498	238	1	g²-approximation	g²-approximation	NOUN
ejpam-6498	238	2	of	of	ADP
ejpam-6498	238	3	parabolic	parabolic	ADJ
ejpam-6498	238	4	arcs	arc	NOUN
ejpam-6498	238	5	.	.	PUNCT
ejpam-6498	239	1	in	in	ADP
ejpam-6498	239	2	21st	21st	ADJ
ejpam-6498	239	3	international	international	ADJ
ejpam-6498	239	4	conference	conference	NOUN
ejpam-6498	239	5	on	on	ADP
ejpam-6498	239	6	information	information	NOUN
ejpam-6498	239	7	visualization	visualization	NOUN
ejpam-6498	239	8	(	(	PUNCT
ejpam-6498	239	9	iv	iv	NUM
ejpam-6498	239	10	)	)	PUNCT
ejpam-6498	239	11	,	,	PUNCT
ejpam-6498	239	12	pages	page	NOUN
ejpam-6498	239	13	394–399	394–399	NUM
ejpam-6498	239	14	,	,	PUNCT
ejpam-6498	239	15	london	london	PROPN
ejpam-6498	239	16	,	,	PUNCT
ejpam-6498	239	17	uk	uk	PROPN
ejpam-6498	239	18	,	,	PUNCT
ejpam-6498	239	19	2017	2017	NUM
ejpam-6498	239	20	.	.	PUNCT
ejpam-6498	240	1	[	[	X
ejpam-6498	240	2	2	2	NUM
ejpam-6498	240	3	]	]	PUNCT
ejpam-6498	240	4	m.	m.	NOUN
ejpam-6498	240	5	z.	z.	PROPN
ejpam-6498	240	6	hussain	hussain	PROPN
ejpam-6498	240	7	,	,	PUNCT
ejpam-6498	240	8	a.	a.	PROPN
ejpam-6498	240	9	shakeel	shakeel	PROPN
ejpam-6498	240	10	,	,	PUNCT
ejpam-6498	240	11	and	and	CCONJ
ejpam-6498	240	12	m.	m.	NOUN
ejpam-6498	240	13	hussain	hussain	PROPN
ejpam-6498	240	14	.	.	PUNCT
ejpam-6498	241	1	approximation	approximation	NOUN
ejpam-6498	241	2	of	of	ADP
ejpam-6498	241	3	planar	planar	ADJ
ejpam-6498	241	4	curves	curve	NOUN
ejpam-6498	241	5	.	.	PUNCT
ejpam-6498	242	1	turkish	turkish	ADJ
ejpam-6498	242	2	journal	journal	NOUN
ejpam-6498	242	3	of	of	ADP
ejpam-6498	242	4	electrical	electrical	ADJ
ejpam-6498	242	5	engineering	engineering	NOUN
ejpam-6498	242	6	&	&	CCONJ
ejpam-6498	242	7	computer	computer	PROPN
ejpam-6498	242	8	sciences	sciences	PROPN
ejpam-6498	242	9	,	,	PUNCT
ejpam-6498	242	10	27:723–737	27:723–737	NUM
ejpam-6498	242	11	,	,	PUNCT
ejpam-6498	242	12	2019	2019	NUM
ejpam-6498	242	13	.	.	PUNCT
ejpam-6498	243	1	[	[	X
ejpam-6498	243	2	3	3	X
ejpam-6498	243	3	]	]	X
ejpam-6498	243	4	g.	g.	PROPN
ejpam-6498	243	5	farin	farin	PROPN
ejpam-6498	243	6	.	.	PUNCT
ejpam-6498	244	1	curves	curve	NOUN
ejpam-6498	244	2	and	and	CCONJ
ejpam-6498	244	3	surfaces	surface	NOUN
ejpam-6498	244	4	for	for	ADP
ejpam-6498	244	5	cagd	cagd	NOUN
ejpam-6498	244	6	:	:	PUNCT
ejpam-6498	244	7	a	a	DET
ejpam-6498	244	8	practical	practical	ADJ
ejpam-6498	244	9	guide	guide	NOUN
ejpam-6498	244	10	.	.	PUNCT
ejpam-6498	245	1	morgan	morgan	PROPN
ejpam-6498	245	2	kaufmann	kaufmann	PROPN
ejpam-6498	245	3	,	,	PUNCT
ejpam-6498	245	4	san	san	PROPN
ejpam-6498	245	5	francisco	francisco	PROPN
ejpam-6498	245	6	,	,	PUNCT
ejpam-6498	245	7	ca	ca	PROPN
ejpam-6498	245	8	,	,	PUNCT
ejpam-6498	245	9	usa	usa	PROPN
ejpam-6498	245	10	,	,	PUNCT
ejpam-6498	245	11	5	5	NUM
ejpam-6498	245	12	edition	edition	NOUN
ejpam-6498	245	13	,	,	PUNCT
ejpam-6498	245	14	2002	2002	NUM
ejpam-6498	245	15	.	.	PUNCT
ejpam-6498	246	1	[	[	X
ejpam-6498	246	2	4	4	NUM
ejpam-6498	246	3	]	]	X
ejpam-6498	246	4	c.	c.	NOUN
ejpam-6498	246	5	apprich	apprich	PROPN
ejpam-6498	246	6	,	,	PUNCT
ejpam-6498	246	7	a.	a.	PROPN
ejpam-6498	246	8	dieterich	dieterich	PROPN
ejpam-6498	246	9	,	,	PUNCT
ejpam-6498	246	10	k.	k.	PROPN
ejpam-6498	246	11	hölling	hölling	PROPN
ejpam-6498	246	12	,	,	PUNCT
ejpam-6498	246	13	and	and	CCONJ
ejpam-6498	246	14	e.	e.	PROPN
ejpam-6498	246	15	nava	nava	PROPN
ejpam-6498	246	16	-	-	PUNCT
ejpam-6498	246	17	yazdani	yazdani	PROPN
ejpam-6498	246	18	.	.	PUNCT
ejpam-6498	247	1	cubic	cubic	PROPN
ejpam-6498	247	2	spline	spline	PROPN
ejpam-6498	247	3	approximation	approximation	NOUN
ejpam-6498	247	4	of	of	ADP
ejpam-6498	247	5	a	a	DET
ejpam-6498	247	6	circle	circle	NOUN
ejpam-6498	247	7	with	with	ADP
ejpam-6498	247	8	maximal	maximal	ADJ
ejpam-6498	247	9	smoothness	smoothness	NOUN
ejpam-6498	247	10	and	and	CCONJ
ejpam-6498	247	11	accuracy	accuracy	NOUN
ejpam-6498	247	12	.	.	PUNCT
ejpam-6498	248	1	computer	computer	NOUN
ejpam-6498	248	2	aided	aid	VERB
ejpam-6498	248	3	geometric	geometric	ADJ
ejpam-6498	248	4	design	design	NOUN
ejpam-6498	248	5	,	,	PUNCT
ejpam-6498	248	6	56:1–3	56:1–3	NUM
ejpam-6498	248	7	,	,	PUNCT
ejpam-6498	248	8	2017	2017	NUM
ejpam-6498	248	9	.	.	PUNCT
ejpam-6498	249	1	[	[	X
ejpam-6498	249	2	5	5	X
ejpam-6498	249	3	]	]	PUNCT
ejpam-6498	249	4	q.	q.	PROPN
ejpam-6498	249	5	hu	hu	PROPN
ejpam-6498	249	6	.	.	PUNCT
ejpam-6498	250	1	explicit	explicit	ADJ
ejpam-6498	250	2	g¹-approximation	g¹-approximation	NOUN
ejpam-6498	250	3	of	of	ADP
ejpam-6498	250	4	conic	conic	ADJ
ejpam-6498	250	5	sections	section	NOUN
ejpam-6498	250	6	using	use	VERB
ejpam-6498	250	7	bézier	bézier	ADP
ejpam-6498	250	8	curves	curve	NOUN
ejpam-6498	250	9	of	of	ADP
ejpam-6498	250	10	arbitrary	arbitrary	ADJ
ejpam-6498	250	11	degree	degree	NOUN
ejpam-6498	250	12	.	.	PUNCT
ejpam-6498	251	1	journal	journal	NOUN
ejpam-6498	251	2	of	of	ADP
ejpam-6498	251	3	computational	computational	ADJ
ejpam-6498	251	4	and	and	CCONJ
ejpam-6498	251	5	applied	applied	ADJ
ejpam-6498	251	6	mathematics	mathematic	NOUN
ejpam-6498	251	7	,	,	PUNCT
ejpam-6498	251	8	292:505–512	292:505–512	NUM
ejpam-6498	251	9	,	,	PUNCT
ejpam-6498	251	10	2016	2016	NUM
ejpam-6498	251	11	.	.	PUNCT
ejpam-6498	252	1	[	[	X
ejpam-6498	252	2	6	6	NUM
ejpam-6498	252	3	]	]	PUNCT
ejpam-6498	252	4	m.	m.	NOUN
ejpam-6498	252	5	floater	floater	NOUN
ejpam-6498	252	6	.	.	PUNCT
ejpam-6498	253	1	high	high	ADJ
ejpam-6498	253	2	-	-	PUNCT
ejpam-6498	253	3	order	order	NOUN
ejpam-6498	253	4	approximation	approximation	NOUN
ejpam-6498	253	5	of	of	ADP
ejpam-6498	253	6	conic	conic	ADJ
ejpam-6498	253	7	sections	section	NOUN
ejpam-6498	253	8	by	by	ADP
ejpam-6498	253	9	quadratic	quadratic	ADJ
ejpam-6498	253	10	splines	spline	NOUN
ejpam-6498	253	11	.	.	PUNCT
ejpam-6498	254	1	computer	computer	NOUN
ejpam-6498	254	2	aided	aid	VERB
ejpam-6498	254	3	geometric	geometric	ADJ
ejpam-6498	254	4	design	design	NOUN
ejpam-6498	254	5	,	,	PUNCT
ejpam-6498	254	6	12(6):617–637	12(6):617–637	PROPN
ejpam-6498	254	7	,	,	PUNCT
ejpam-6498	254	8	1995	1995	NUM
ejpam-6498	254	9	.	.	PUNCT
ejpam-6498	255	1	[	[	X
ejpam-6498	255	2	7	7	X
ejpam-6498	255	3	]	]	PUNCT
ejpam-6498	255	4	m.	m.	NOUN
ejpam-6498	255	5	floater	floater	NOUN
ejpam-6498	255	6	.	.	PUNCT
ejpam-6498	256	1	an	an	DET
ejpam-6498	256	2	hermite	hermite	ADJ
ejpam-6498	256	3	approximation	approximation	NOUN
ejpam-6498	256	4	for	for	ADP
ejpam-6498	256	5	conic	conic	ADJ
ejpam-6498	256	6	sections	section	NOUN
ejpam-6498	256	7	.	.	PUNCT
ejpam-6498	257	1	computer	computer	NOUN
ejpam-6498	257	2	aided	aid	VERB
ejpam-6498	257	3	geometric	geometric	ADJ
ejpam-6498	257	4	design	design	NOUN
ejpam-6498	257	5	,	,	PUNCT
ejpam-6498	257	6	14(2):135–151	14(2):135–151	PROPN
ejpam-6498	257	7	,	,	PUNCT
ejpam-6498	257	8	1997	1997	NUM
ejpam-6498	257	9	.	.	PUNCT
ejpam-6498	258	1	[	[	X
ejpam-6498	258	2	8	8	X
ejpam-6498	258	3	]	]	X
ejpam-6498	258	4	y.	y.	PROPN
ejpam-6498	258	5	j.	j.	PROPN
ejpam-6498	258	6	ahn	ahn	PROPN
ejpam-6498	258	7	.	.	PROPN
ejpam-6498	258	8	approximation	approximation	NOUN
ejpam-6498	258	9	of	of	ADP
ejpam-6498	258	10	conic	conic	ADJ
ejpam-6498	258	11	sections	section	NOUN
ejpam-6498	258	12	by	by	ADP
ejpam-6498	258	13	curvature	curvature	NOUN
ejpam-6498	258	14	continuous	continuous	ADJ
ejpam-6498	258	15	quartic	quartic	ADJ
ejpam-6498	258	16	bézier	bézier	ADP
ejpam-6498	258	17	curves	curve	NOUN
ejpam-6498	258	18	.	.	PUNCT
ejpam-6498	259	1	computers	computer	NOUN
ejpam-6498	259	2	&	&	CCONJ
ejpam-6498	259	3	mathematics	mathematics	PROPN
ejpam-6498	259	4	with	with	ADP
ejpam-6498	259	5	applications	application	NOUN
ejpam-6498	259	6	,	,	PUNCT
ejpam-6498	259	7	60(7):1986–1993	60(7):1986–1993	NUM
ejpam-6498	259	8	,	,	PUNCT
ejpam-6498	259	9	2010	2010	NUM
ejpam-6498	259	10	.	.	PUNCT
ejpam-6498	260	1	[	[	X
ejpam-6498	260	2	9	9	NUM
ejpam-6498	260	3	]	]	PUNCT
ejpam-6498	260	4	q.	q.	PROPN
ejpam-6498	260	5	hu	hu	PROPN
ejpam-6498	260	6	.	.	PUNCT
ejpam-6498	261	1	g¹-approximation	g¹-approximation	NOUN
ejpam-6498	261	2	of	of	ADP
ejpam-6498	261	3	conic	conic	ADJ
ejpam-6498	261	4	sections	section	NOUN
ejpam-6498	261	5	by	by	ADP
ejpam-6498	261	6	quartic	quartic	ADJ
ejpam-6498	261	7	bézier	bézier	ADP
ejpam-6498	261	8	curves	curve	NOUN
ejpam-6498	261	9	.	.	PUNCT
ejpam-6498	262	1	computers	computer	NOUN
ejpam-6498	262	2	&	&	CCONJ
ejpam-6498	262	3	mathematics	mathematics	PROPN
ejpam-6498	262	4	with	with	ADP
ejpam-6498	262	5	applications	application	NOUN
ejpam-6498	262	6	,	,	PUNCT
ejpam-6498	262	7	68(2):1882–1891	68(2):1882–1891	NUM
ejpam-6498	262	8	,	,	PUNCT
ejpam-6498	262	9	2014	2014	NUM
ejpam-6498	262	10	.	.	PUNCT
ejpam-6498	263	1	[	[	X
ejpam-6498	263	2	10	10	NUM
ejpam-6498	263	3	]	]	PUNCT
ejpam-6498	263	4	j.	j.	PROPN
ejpam-6498	263	5	sánchez	sánchez	PROPN
ejpam-6498	263	6	-	-	PUNCT
ejpam-6498	263	7	reyes	reyes	PROPN
ejpam-6498	263	8	.	.	PUNCT
ejpam-6498	264	1	conics	conic	NOUN
ejpam-6498	264	2	in	in	ADP
ejpam-6498	264	3	rational	rational	ADJ
ejpam-6498	264	4	cubic	cubic	NOUN
ejpam-6498	264	5	bézier	bézier	SCONJ
ejpam-6498	264	6	form	form	NOUN
ejpam-6498	264	7	made	make	VERB
ejpam-6498	264	8	simple	simple	ADJ
ejpam-6498	264	9	.	.	PUNCT
ejpam-6498	265	1	computer	computer	NOUN
ejpam-6498	265	2	aided	aid	VERB
ejpam-6498	265	3	geometric	geometric	ADJ
ejpam-6498	265	4	design	design	NOUN
ejpam-6498	265	5	,	,	PUNCT
ejpam-6498	265	6	108:102266	108:102266	NUM
ejpam-6498	265	7	,	,	PUNCT
ejpam-6498	265	8	2024	2024	NUM
ejpam-6498	265	9	.	.	PUNCT
ejpam-6498	266	1	[	[	X
ejpam-6498	266	2	11	11	NUM
ejpam-6498	266	3	]	]	X
ejpam-6498	266	4	e.	e.	PROPN
ejpam-6498	266	5	nawara	nawara	PROPN
ejpam-6498	266	6	.	.	PUNCT
ejpam-6498	267	1	the	the	DET
ejpam-6498	267	2	hesse	hesse	PROPN
ejpam-6498	267	3	pencil	pencil	NOUN
ejpam-6498	267	4	of	of	ADP
ejpam-6498	267	5	plane	plane	NOUN
ejpam-6498	267	6	curves	curve	NOUN
ejpam-6498	267	7	and	and	CCONJ
ejpam-6498	267	8	osculating	osculate	VERB
ejpam-6498	267	9	conics	conic	NOUN
ejpam-6498	267	10	.	.	PUNCT
ejpam-6498	268	1	journal	journal	NOUN
ejpam-6498	268	2	of	of	ADP
ejpam-6498	268	3	algebra	algebra	PROPN
ejpam-6498	268	4	,	,	PUNCT
ejpam-6498	268	5	686:536–549	686:536–549	NUM
ejpam-6498	268	6	,	,	PUNCT
ejpam-6498	268	7	2026	2026	NUM
ejpam-6498	268	8	.	.	PUNCT
ejpam-6498	269	1	[	[	X
ejpam-6498	269	2	12	12	NUM
ejpam-6498	269	3	]	]	X
ejpam-6498	269	4	jun	jun	PROPN
ejpam-6498	269	5	-	-	PUNCT
ejpam-6498	269	6	muk	muk	PROPN
ejpam-6498	269	7	hwang	hwang	PROPN
ejpam-6498	269	8	and	and	CCONJ
ejpam-6498	269	9	q.	q.	PROPN
ejpam-6498	269	10	li	li	PROPN
ejpam-6498	269	11	.	.	PROPN
ejpam-6498	269	12	characteristics	characteristic	NOUN
ejpam-6498	269	13	conic	conic	ADJ
ejpam-6498	269	14	connections	connection	NOUN
ejpam-6498	269	15	and	and	CCONJ
ejpam-6498	269	16	torsion	torsion	NOUN
ejpam-6498	269	17	-	-	PUNCT
ejpam-6498	269	18	free	free	ADJ
ejpam-6498	269	19	principal	principal	ADJ
ejpam-6498	269	20	connections	connection	NOUN
ejpam-6498	269	21	.	.	PUNCT
ejpam-6498	270	1	journal	journal	PROPN
ejpam-6498	270	2	de	de	PROPN
ejpam-6498	270	3	mathématiques	mathématiques	PROPN
ejpam-6498	270	4	pures	pure	NOUN
ejpam-6498	270	5	et	et	NOUN
ejpam-6498	270	6	appliquées	appliquée	NOUN
ejpam-6498	270	7	,	,	PUNCT
ejpam-6498	270	8	191:103626	191:103626	NUM
ejpam-6498	270	9	,	,	PUNCT
ejpam-6498	270	10	2024	2024	NUM
ejpam-6498	270	11	.	.	PUNCT