id	sid	tid	token	lemma	pos
ejpam-3648	1	1	european	european	PROPN
ejpam-3648	1	2	journal	journal	PROPN
ejpam-3648	1	3	of	of	ADP
ejpam-3648	1	4	pure	pure	ADJ
ejpam-3648	1	5	and	and	CCONJ
ejpam-3648	1	6	applied	apply	VERB
ejpam-3648	1	7	mathematics	mathematic	NOUN
ejpam-3648	1	8	vol	vol	NOUN
ejpam-3648	1	9	.	.	PROPN
ejpam-3648	2	1	13	13	NUM
ejpam-3648	2	2	,	,	PUNCT
ejpam-3648	2	3	no	no	INTJ
ejpam-3648	2	4	.	.	NOUN
ejpam-3648	2	5	2	2	NUM
ejpam-3648	2	6	,	,	PUNCT
ejpam-3648	2	7	2020	2020	NUM
ejpam-3648	2	8	,	,	PUNCT
ejpam-3648	2	9	216	216	NUM
ejpam-3648	2	10	-	-	SYM
ejpam-3648	2	11	226	226	NUM
ejpam-3648	2	12	issn	issn	PROPN
ejpam-3648	2	13	1307	1307	NUM
ejpam-3648	2	14	-	-	SYM
ejpam-3648	2	15	5543	5543	NUM
ejpam-3648	2	16	–	–	PUNCT
ejpam-3648	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3648	2	18	published	publish	VERB
ejpam-3648	2	19	by	by	ADP
ejpam-3648	2	20	new	new	PROPN
ejpam-3648	2	21	york	york	PROPN
ejpam-3648	2	22	business	business	PROPN
ejpam-3648	2	23	global	global	PROPN
ejpam-3648	2	24	on	on	ADP
ejpam-3648	2	25	the	the	DET
ejpam-3648	2	26	involute	involute	NOUN
ejpam-3648	2	27	of	of	ADP
ejpam-3648	2	28	the	the	DET
ejpam-3648	2	29	cubic	cubic	ADJ
ejpam-3648	2	30	bezier	bezier	NOUN
ejpam-3648	2	31	curve	curve	NOUN
ejpam-3648	2	32	by	by	ADP
ejpam-3648	2	33	using	use	VERB
ejpam-3648	2	34	matrix	matrix	NOUN
ejpam-3648	2	35	representation	representation	NOUN
ejpam-3648	2	36	in	in	ADP
ejpam-3648	2	37	e3	e3	PROPN
ejpam-3648	2	38	şeyda	şeyda	PROPN
ejpam-3648	2	39	kılıçoğlu1,∗	kılıçoğlu1,∗	PROPN
ejpam-3648	2	40	,	,	PUNCT
ejpam-3648	2	41	süleyman	süleyman	PROPN
ejpam-3648	2	42	şenyurt2	şenyurt2	PUNCT
ejpam-3648	2	43	1	1	NUM
ejpam-3648	2	44	faculty	faculty	NOUN
ejpam-3648	2	45	of	of	ADP
ejpam-3648	2	46	education	education	NOUN
ejpam-3648	2	47	,	,	PUNCT
ejpam-3648	2	48	department	department	NOUN
ejpam-3648	2	49	of	of	ADP
ejpam-3648	2	50	mathematics	mathematic	NOUN
ejpam-3648	2	51	,	,	PUNCT
ejpam-3648	2	52	başkent	başkent	ADJ
ejpam-3648	2	53	university	university	NOUN
ejpam-3648	2	54	,	,	PUNCT
ejpam-3648	2	55	ankara	ankara	PROPN
ejpam-3648	2	56	,	,	PUNCT
ejpam-3648	2	57	turkey	turkey	NOUN
ejpam-3648	2	58	2	2	NUM
ejpam-3648	2	59	faculty	faculty	NOUN
ejpam-3648	2	60	of	of	ADP
ejpam-3648	2	61	arts	art	NOUN
ejpam-3648	2	62	and	and	CCONJ
ejpam-3648	2	63	sciences	science	NOUN
ejpam-3648	2	64	,	,	PUNCT
ejpam-3648	2	65	department	department	NOUN
ejpam-3648	2	66	of	of	ADP
ejpam-3648	2	67	mathematics	mathematics	PROPN
ejpam-3648	2	68	,	,	PUNCT
ejpam-3648	2	69	ordu	ordu	PROPN
ejpam-3648	2	70	universty	universty	PROPN
ejpam-3648	2	71	,	,	PUNCT
ejpam-3648	2	72	ordu	ordu	PROPN
ejpam-3648	2	73	,	,	PUNCT
ejpam-3648	2	74	turkey	turkey	NOUN
ejpam-3648	2	75	abstract	abstract	NOUN
ejpam-3648	2	76	.	.	PUNCT
ejpam-3648	3	1	in	in	ADP
ejpam-3648	3	2	this	this	DET
ejpam-3648	3	3	study	study	NOUN
ejpam-3648	3	4	we	we	PRON
ejpam-3648	3	5	have	have	AUX
ejpam-3648	3	6	examined	examine	VERB
ejpam-3648	3	7	,	,	PUNCT
ejpam-3648	3	8	involute	involute	ADJ
ejpam-3648	3	9	of	of	ADP
ejpam-3648	3	10	the	the	DET
ejpam-3648	3	11	cubic	cubic	ADJ
ejpam-3648	3	12	bezier	bezier	NOUN
ejpam-3648	3	13	curve	curve	NOUN
ejpam-3648	3	14	based	base	VERB
ejpam-3648	3	15	on	on	ADP
ejpam-3648	3	16	the	the	DET
ejpam-3648	3	17	control	control	NOUN
ejpam-3648	3	18	points	point	VERB
ejpam-3648	3	19	with	with	ADP
ejpam-3648	3	20	matrix	matrix	NOUN
ejpam-3648	3	21	form	form	NOUN
ejpam-3648	3	22	in	in	ADP
ejpam-3648	3	23	e3	e3	NOUN
ejpam-3648	3	24	.	.	PUNCT
ejpam-3648	4	1	frenet	frenet	ADJ
ejpam-3648	4	2	vector	vector	NOUN
ejpam-3648	4	3	fields	field	NOUN
ejpam-3648	4	4	and	and	CCONJ
ejpam-3648	4	5	also	also	ADV
ejpam-3648	4	6	curvatures	curvature	NOUN
ejpam-3648	4	7	of	of	ADP
ejpam-3648	4	8	involute	involute	NOUN
ejpam-3648	4	9	of	of	ADP
ejpam-3648	4	10	the	the	DET
ejpam-3648	4	11	cubic	cubic	ADJ
ejpam-3648	4	12	bezier	bezier	NOUN
ejpam-3648	4	13	curve	curve	NOUN
ejpam-3648	4	14	are	be	AUX
ejpam-3648	4	15	examined	examine	VERB
ejpam-3648	4	16	based	base	VERB
ejpam-3648	4	17	on	on	ADP
ejpam-3648	4	18	the	the	DET
ejpam-3648	4	19	frenet	frenet	NOUN
ejpam-3648	4	20	apparatus	apparatus	NOUN
ejpam-3648	4	21	of	of	ADP
ejpam-3648	4	22	the	the	DET
ejpam-3648	4	23	first	first	ADJ
ejpam-3648	4	24	cubic	cubic	ADJ
ejpam-3648	4	25	bezier	bezier	NOUN
ejpam-3648	4	26	curve	curve	NOUN
ejpam-3648	4	27	in	in	ADP
ejpam-3648	4	28	e3	e3	NOUN
ejpam-3648	4	29	.	.	PUNCT
ejpam-3648	5	1	2020	2020	NUM
ejpam-3648	5	2	mathematics	mathematic	NOUN
ejpam-3648	5	3	subject	subject	NOUN
ejpam-3648	5	4	classifications	classification	NOUN
ejpam-3648	5	5	:	:	PUNCT
ejpam-3648	5	6	53a04,53a05	53a04,53a05	NUM
ejpam-3648	5	7	key	key	ADJ
ejpam-3648	5	8	words	word	NOUN
ejpam-3648	5	9	and	and	CCONJ
ejpam-3648	5	10	phrases	phrase	NOUN
ejpam-3648	5	11	:	:	PUNCT
ejpam-3648	5	12	bezier	bezier	NOUN
ejpam-3648	5	13	curves	curve	NOUN
ejpam-3648	5	14	,	,	PUNCT
ejpam-3648	5	15	frenet	frenet	NOUN
ejpam-3648	5	16	vector	vector	NOUN
ejpam-3648	5	17	fields	field	NOUN
ejpam-3648	5	18	,	,	PUNCT
ejpam-3648	5	19	cubic	cubic	ADJ
ejpam-3648	5	20	bezier	bezier	NOUN
ejpam-3648	5	21	curve	curve	NOUN
ejpam-3648	5	22	1	1	NUM
ejpam-3648	5	23	.	.	PUNCT
ejpam-3648	5	24	introduction	introduction	NOUN
ejpam-3648	5	25	and	and	CCONJ
ejpam-3648	5	26	preliminaries	preliminary	NOUN
ejpam-3648	5	27	in	in	ADP
ejpam-3648	5	28	1962	1962	NUM
ejpam-3648	5	29	bézier	bézier	SCONJ
ejpam-3648	5	30	curves	curve	NOUN
ejpam-3648	5	31	was	be	AUX
ejpam-3648	5	32	studied	study	VERB
ejpam-3648	5	33	by	by	ADP
ejpam-3648	5	34	the	the	DET
ejpam-3648	5	35	french	french	ADJ
ejpam-3648	5	36	engineer	engineer	NOUN
ejpam-3648	5	37	pierre	pierre	PROPN
ejpam-3648	5	38	bézier	bézier	ADP
ejpam-3648	5	39	,	,	PUNCT
ejpam-3648	5	40	who	who	PRON
ejpam-3648	5	41	used	use	VERB
ejpam-3648	5	42	them	they	PRON
ejpam-3648	5	43	to	to	PART
ejpam-3648	5	44	design	design	VERB
ejpam-3648	5	45	automobile	automobile	NOUN
ejpam-3648	5	46	bodies	body	NOUN
ejpam-3648	5	47	.	.	PUNCT
ejpam-3648	6	1	but	but	CCONJ
ejpam-3648	6	2	the	the	DET
ejpam-3648	6	3	study	study	NOUN
ejpam-3648	6	4	of	of	ADP
ejpam-3648	6	5	these	these	DET
ejpam-3648	6	6	curves	curve	NOUN
ejpam-3648	6	7	was	be	AUX
ejpam-3648	6	8	first	first	ADV
ejpam-3648	6	9	developed	develop	VERB
ejpam-3648	6	10	in	in	ADP
ejpam-3648	6	11	1959	1959	NUM
ejpam-3648	6	12	by	by	ADP
ejpam-3648	6	13	mathematician	mathematician	ADJ
ejpam-3648	6	14	paul	paul	PROPN
ejpam-3648	6	15	de	de	PROPN
ejpam-3648	6	16	casteljau	casteljau	PROPN
ejpam-3648	6	17	using	use	VERB
ejpam-3648	6	18	de	de	PROPN
ejpam-3648	6	19	casteljau	casteljau	PROPN
ejpam-3648	6	20	’s	’s	PART
ejpam-3648	6	21	algorithm	algorithm	NOUN
ejpam-3648	6	22	,	,	PUNCT
ejpam-3648	6	23	a	a	DET
ejpam-3648	6	24	numerically	numerically	ADV
ejpam-3648	6	25	stable	stable	ADJ
ejpam-3648	6	26	method	method	NOUN
ejpam-3648	6	27	to	to	PART
ejpam-3648	6	28	evaluate	evaluate	VERB
ejpam-3648	6	29	bézier	bézier	ADP
ejpam-3648	6	30	curves	curve	NOUN
ejpam-3648	6	31	.	.	PUNCT
ejpam-3648	7	1	a	a	DET
ejpam-3648	7	2	bézier	bézier	PROPN
ejpam-3648	7	3	curve	curve	NOUN
ejpam-3648	7	4	is	be	AUX
ejpam-3648	7	5	frequently	frequently	ADV
ejpam-3648	7	6	used	use	VERB
ejpam-3648	7	7	in	in	ADP
ejpam-3648	7	8	computer	computer	NOUN
ejpam-3648	7	9	graphics	graphic	NOUN
ejpam-3648	7	10	and	and	CCONJ
ejpam-3648	7	11	related	related	ADJ
ejpam-3648	7	12	fields	field	NOUN
ejpam-3648	7	13	,	,	PUNCT
ejpam-3648	7	14	in	in	ADP
ejpam-3648	7	15	vector	vector	NOUN
ejpam-3648	7	16	graphics	graphic	NOUN
ejpam-3648	7	17	,	,	PUNCT
ejpam-3648	7	18	used	use	VERB
ejpam-3648	7	19	in	in	ADP
ejpam-3648	7	20	animation	animation	NOUN
ejpam-3648	7	21	as	as	ADP
ejpam-3648	7	22	a	a	DET
ejpam-3648	7	23	tool	tool	NOUN
ejpam-3648	7	24	to	to	PART
ejpam-3648	7	25	control	control	VERB
ejpam-3648	7	26	motion	motion	NOUN
ejpam-3648	7	27	.	.	PUNCT
ejpam-3648	8	1	for	for	ADP
ejpam-3648	8	2	more	more	ADJ
ejpam-3648	8	3	datail	datail	NOUN
ejpam-3648	8	4	using	use	VERB
ejpam-3648	8	5	computer	computer	NOUN
ejpam-3648	8	6	graphics	graphic	NOUN
ejpam-3648	8	7	see	see	VERB
ejpam-3648	8	8	in	in	ADP
ejpam-3648	8	9	[	[	X
ejpam-3648	8	10	8	8	NUM
ejpam-3648	8	11	]	]	PUNCT
ejpam-3648	8	12	.	.	PUNCT
ejpam-3648	9	1	in	in	ADP
ejpam-3648	9	2	[	[	X
ejpam-3648	9	3	2	2	X
ejpam-3648	9	4	]	]	PUNCT
ejpam-3648	9	5	some	some	DET
ejpam-3648	9	6	properties	property	NOUN
ejpam-3648	9	7	of	of	ADP
ejpam-3648	9	8	bezier	bezier	NOUN
ejpam-3648	9	9	curves	curve	NOUN
ejpam-3648	9	10	are	be	AUX
ejpam-3648	9	11	examined	examine	VERB
ejpam-3648	9	12	.	.	PUNCT
ejpam-3648	10	1	to	to	PART
ejpam-3648	10	2	guarantee	guarantee	VERB
ejpam-3648	10	3	smoothness	smoothness	PROPN
ejpam-3648	10	4	,	,	PUNCT
ejpam-3648	10	5	the	the	DET
ejpam-3648	10	6	control	control	NOUN
ejpam-3648	10	7	point	point	NOUN
ejpam-3648	10	8	at	at	ADP
ejpam-3648	10	9	which	which	PRON
ejpam-3648	10	10	two	two	NUM
ejpam-3648	10	11	curves	curve	NOUN
ejpam-3648	10	12	meet	meet	NOUN
ejpam-3648	10	13	must	must	AUX
ejpam-3648	10	14	be	be	AUX
ejpam-3648	10	15	on	on	ADP
ejpam-3648	10	16	the	the	DET
ejpam-3648	10	17	line	line	NOUN
ejpam-3648	10	18	between	between	ADP
ejpam-3648	10	19	the	the	DET
ejpam-3648	10	20	two	two	NUM
ejpam-3648	10	21	control	control	NOUN
ejpam-3648	10	22	points	point	NOUN
ejpam-3648	10	23	on	on	ADP
ejpam-3648	10	24	either	either	DET
ejpam-3648	10	25	side	side	NOUN
ejpam-3648	10	26	.	.	PUNCT
ejpam-3648	11	1	in	in	ADP
ejpam-3648	11	2	animation	animation	NOUN
ejpam-3648	11	3	applications	application	NOUN
ejpam-3648	11	4	,	,	PUNCT
ejpam-3648	11	5	such	such	ADJ
ejpam-3648	11	6	as	as	ADP
ejpam-3648	11	7	adobe	adobe	PROPN
ejpam-3648	11	8	flash	flash	NOUN
ejpam-3648	11	9	and	and	CCONJ
ejpam-3648	11	10	synfig	synfig	NOUN
ejpam-3648	11	11	,	,	PUNCT
ejpam-3648	11	12	bézier	bézier	ADP
ejpam-3648	11	13	curves	curve	NOUN
ejpam-3648	11	14	are	be	AUX
ejpam-3648	11	15	used	use	VERB
ejpam-3648	11	16	to	to	PART
ejpam-3648	11	17	outline	outline	VERB
ejpam-3648	11	18	,	,	PUNCT
ejpam-3648	11	19	for	for	ADP
ejpam-3648	11	20	example	example	NOUN
ejpam-3648	11	21	,	,	PUNCT
ejpam-3648	11	22	movement	movement	NOUN
ejpam-3648	11	23	.	.	PUNCT
ejpam-3648	12	1	users	user	NOUN
ejpam-3648	12	2	outline	outline	VERB
ejpam-3648	12	3	the	the	DET
ejpam-3648	12	4	wanted	wanted	ADJ
ejpam-3648	12	5	path	path	NOUN
ejpam-3648	12	6	in	in	ADP
ejpam-3648	12	7	bézier	bézier	ADP
ejpam-3648	12	8	curves	curve	NOUN
ejpam-3648	12	9	,	,	PUNCT
ejpam-3648	12	10	and	and	CCONJ
ejpam-3648	12	11	the	the	DET
ejpam-3648	12	12	application	application	NOUN
ejpam-3648	12	13	creates	create	VERB
ejpam-3648	12	14	the	the	DET
ejpam-3648	12	15	needed	need	VERB
ejpam-3648	12	16	frames	frame	NOUN
ejpam-3648	12	17	for	for	ADP
ejpam-3648	12	18	the	the	DET
ejpam-3648	12	19	object	object	NOUN
ejpam-3648	12	20	to	to	PART
ejpam-3648	12	21	move	move	VERB
ejpam-3648	12	22	along	along	ADP
ejpam-3648	12	23	the	the	DET
ejpam-3648	12	24	path	path	NOUN
ejpam-3648	12	25	.	.	PUNCT
ejpam-3648	13	1	for	for	ADP
ejpam-3648	13	2	3d	3d	NUM
ejpam-3648	13	3	animation	animation	NOUN
ejpam-3648	13	4	bézier	bézier	SCONJ
ejpam-3648	13	5	curves	curve	NOUN
ejpam-3648	13	6	are	be	AUX
ejpam-3648	13	7	often	often	ADV
ejpam-3648	13	8	used	use	VERB
ejpam-3648	13	9	to	to	PART
ejpam-3648	13	10	define	define	VERB
ejpam-3648	13	11	3d	3d	NUM
ejpam-3648	13	12	paths	path	NOUN
ejpam-3648	13	13	as	as	ADV
ejpam-3648	13	14	well	well	ADV
ejpam-3648	13	15	as	as	ADP
ejpam-3648	13	16	2d	2d	NUM
ejpam-3648	13	17	curves	curve	NOUN
ejpam-3648	13	18	for	for	ADP
ejpam-3648	13	19	keyframe	keyframe	NOUN
ejpam-3648	13	20	interpolation	interpolation	NOUN
ejpam-3648	13	21	.	.	PUNCT
ejpam-3648	14	1	we	we	PRON
ejpam-3648	14	2	have	have	AUX
ejpam-3648	14	3	been	be	AUX
ejpam-3648	14	4	motivated	motivate	VERB
ejpam-3648	14	5	by	by	ADP
ejpam-3648	14	6	the	the	DET
ejpam-3648	14	7	following	follow	VERB
ejpam-3648	14	8	studies	study	NOUN
ejpam-3648	14	9	.	.	PUNCT
ejpam-3648	15	1	first	first	ADJ
ejpam-3648	15	2	bezier	bezier	NOUN
ejpam-3648	15	3	-	-	PUNCT
ejpam-3648	15	4	curves	curve	NOUN
ejpam-3648	15	5	with	with	ADP
ejpam-3648	15	6	curvature	curvature	NOUN
ejpam-3648	15	7	and	and	CCONJ
ejpam-3648	15	8	torsion	torsion	NOUN
ejpam-3648	15	9	continuity	continuity	NOUN
ejpam-3648	15	10	has	have	AUX
ejpam-3648	15	11	been	be	AUX
ejpam-3648	15	12	examined	examine	VERB
ejpam-3648	15	13	in	in	ADP
ejpam-3648	15	14	[	[	X
ejpam-3648	15	15	5	5	NUM
ejpam-3648	15	16	]	]	PUNCT
ejpam-3648	15	17	.	.	PUNCT
ejpam-3648	16	1	also	also	ADV
ejpam-3648	16	2	in	in	ADP
ejpam-3648	16	3	[	[	X
ejpam-3648	16	4	10	10	NUM
ejpam-3648	16	5	]	]	PUNCT
ejpam-3648	16	6	bezier	bezier	NOUN
ejpam-3648	16	7	curves	curve	NOUN
ejpam-3648	16	8	and	and	CCONJ
ejpam-3648	16	9	surfaces	surface	NOUN
ejpam-3648	16	10	has	have	AUX
ejpam-3648	16	11	been	be	AUX
ejpam-3648	16	12	given	give	VERB
ejpam-3648	16	13	.	.	PUNCT
ejpam-3648	17	1	in	in	ADP
ejpam-3648	17	2	[	[	X
ejpam-3648	17	3	3	3	NUM
ejpam-3648	17	4	]	]	PUNCT
ejpam-3648	17	5	planar	planar	ADJ
ejpam-3648	17	6	bezier	bezier	NOUN
ejpam-3648	17	7	curves	curve	NOUN
ejpam-3648	17	8	and	and	CCONJ
ejpam-3648	17	9	bishop	bishop	PROPN
ejpam-3648	17	10	frame	frame	NOUN
ejpam-3648	17	11	of	of	ADP
ejpam-3648	17	12	bezier	bezier	NOUN
ejpam-3648	17	13	curves	curve	NOUN
ejpam-3648	17	14	are	be	AUX
ejpam-3648	17	15	examined	examine	VERB
ejpam-3648	17	16	,	,	PUNCT
ejpam-3648	17	17	respectively	respectively	ADV
ejpam-3648	17	18	.	.	PUNCT
ejpam-3648	18	1	recently	recently	ADV
ejpam-3648	18	2	equivalence	equivalence	NOUN
ejpam-3648	18	3	conditions	condition	NOUN
ejpam-3648	18	4	of	of	ADP
ejpam-3648	18	5	control	control	NOUN
ejpam-3648	18	6	points	point	NOUN
ejpam-3648	18	7	and	and	CCONJ
ejpam-3648	18	8	application	application	NOUN
ejpam-3648	18	9	to	to	PART
ejpam-3648	18	10	planar	planar	ADJ
ejpam-3648	18	11	bezier	bezier	NOUN
ejpam-3648	18	12	curves	curve	NOUN
ejpam-3648	18	13	have	have	AUX
ejpam-3648	18	14	been	be	AUX
ejpam-3648	18	15	examined	examine	VERB
ejpam-3648	18	16	in	in	ADP
ejpam-3648	18	17	[	[	X
ejpam-3648	18	18	6	6	NUM
ejpam-3648	18	19	]	]	PUNCT
ejpam-3648	18	20	.	.	PUNCT
ejpam-3648	19	1	in	in	ADP
ejpam-3648	19	2	this	this	DET
ejpam-3648	19	3	study	study	NOUN
ejpam-3648	19	4	we	we	PRON
ejpam-3648	19	5	will	will	AUX
ejpam-3648	19	6	define	define	VERB
ejpam-3648	19	7	and	and	CCONJ
ejpam-3648	19	8	work	work	VERB
ejpam-3648	19	9	on	on	ADP
ejpam-3648	19	10	frenet	frenet	ADJ
ejpam-3648	19	11	apparatus	apparatus	NOUN
ejpam-3648	19	12	of	of	ADP
ejpam-3648	19	13	bézier	bézier	ADP
ejpam-3648	19	14	curves	curve	NOUN
ejpam-3648	19	15	in	in	ADP
ejpam-3648	19	16	e3	e3	NOUN
ejpam-3648	19	17	.	.	PUNCT
ejpam-3648	20	1	so	so	ADV
ejpam-3648	20	2	we	we	PRON
ejpam-3648	20	3	need	need	VERB
ejpam-3648	20	4	the	the	DET
ejpam-3648	20	5	derivates	derivate	NOUN
ejpam-3648	20	6	of	of	ADP
ejpam-3648	20	7	them	they	PRON
ejpam-3648	20	8	.	.	PUNCT
ejpam-3648	21	1	recently	recently	ADV
ejpam-3648	21	2	bezier	bezier	NOUN
ejpam-3648	21	3	-	-	PUNCT
ejpam-3648	21	4	like	like	ADJ
ejpam-3648	21	5	curves	curve	NOUN
ejpam-3648	21	6	has	have	AUX
ejpam-3648	21	7	been	be	AUX
ejpam-3648	21	8	defined	define	VERB
ejpam-3648	21	9	and	and	CCONJ
ejpam-3648	21	10	cubic	cubic	ADJ
ejpam-3648	21	11	bezier	bezier	NOUN
ejpam-3648	21	12	curves	curve	NOUN
ejpam-3648	21	13	transitions	transition	NOUN
ejpam-3648	21	14	have	have	AUX
ejpam-3648	21	15	been	be	AUX
ejpam-3648	21	16	studied	study	VERB
ejpam-3648	21	17	in	in	ADP
ejpam-3648	21	18	[	[	X
ejpam-3648	21	19	7	7	NUM
ejpam-3648	21	20	]	]	PUNCT
ejpam-3648	21	21	.	.	PUNCT
ejpam-3648	22	1	also	also	ADV
ejpam-3648	22	2	in	in	ADP
ejpam-3648	22	3	[	[	X
ejpam-3648	22	4	9	9	NUM
ejpam-3648	22	5	]	]	PUNCT
ejpam-3648	22	6	designing	design	VERB
ejpam-3648	22	7	the	the	DET
ejpam-3648	22	8	ruled	rule	VERB
ejpam-3648	22	9	surface	surface	NOUN
ejpam-3648	22	10	are	be	AUX
ejpam-3648	22	11	examined	examine	VERB
ejpam-3648	22	12	as	as	ADP
ejpam-3648	22	13	a	a	DET
ejpam-3648	22	14	new	new	ADJ
ejpam-3648	22	15	approach	approach	NOUN
ejpam-3648	22	16	.	.	PUNCT
ejpam-3648	23	1	∗corresponding	∗corresponde	VERB
ejpam-3648	23	2	author	author	NOUN
ejpam-3648	23	3	.	.	PUNCT
ejpam-3648	24	1	doi	doi	NOUN
ejpam-3648	24	2	:	:	PUNCT
ejpam-3648	24	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3648	https://doi.org/10.29020/nybg.ejpam.v13i2.3648	NOUN
ejpam-3648	24	4	email	email	NOUN
ejpam-3648	24	5	addresses	address	NOUN
ejpam-3648	24	6	:	:	PUNCT
ejpam-3648	25	1	seyda@baskent.edu.tr	seyda@baskent.edu.tr	PROPN
ejpam-3648	25	2	(	(	PUNCT
ejpam-3648	25	3	ş.	ş.	PROPN
ejpam-3648	25	4	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	25	5	)	)	PUNCT
ejpam-3648	25	6	,	,	PUNCT
ejpam-3648	25	7	senyurtsuleyman52@gmail.com	senyurtsuleyman52@gmail.com	PROPN
ejpam-3648	25	8	(	(	PUNCT
ejpam-3648	25	9	s.	s.	PROPN
ejpam-3648	25	10	şenyurt	şenyurt	PROPN
ejpam-3648	25	11	)	)	PUNCT
ejpam-3648	25	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3648	26	1	216	216	NUM
ejpam-3648	26	2	c	c	X
ejpam-3648	26	3	©	©	NOUN
ejpam-3648	26	4	2020	2020	NUM
ejpam-3648	26	5	ejpam	ejpam	VERB
ejpam-3648	26	6	all	all	DET
ejpam-3648	26	7	rights	right	NOUN
ejpam-3648	26	8	reserved	reserve	VERB
ejpam-3648	26	9	.	.	PUNCT
ejpam-3648	27	1	ş.	ş.	PROPN
ejpam-3648	27	2	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	27	3	,	,	PUNCT
ejpam-3648	27	4	s.	s.	PROPN
ejpam-3648	27	5	şenyurt	şenyurt	PROPN
ejpam-3648	27	6	/	/	SYM
ejpam-3648	27	7	eur	eur	PROPN
ejpam-3648	27	8	.	.	PUNCT
ejpam-3648	28	1	j.	j.	PROPN
ejpam-3648	28	2	pure	pure	PROPN
ejpam-3648	28	3	appl	appl	PROPN
ejpam-3648	28	4	.	.	PROPN
ejpam-3648	28	5	math	math	PROPN
ejpam-3648	28	6	,	,	PUNCT
ejpam-3648	28	7	13	13	NUM
ejpam-3648	28	8	(	(	PUNCT
ejpam-3648	28	9	2	2	NUM
ejpam-3648	28	10	)	)	PUNCT
ejpam-3648	28	11	(	(	PUNCT
ejpam-3648	28	12	2020	2020	NUM
ejpam-3648	28	13	)	)	PUNCT
ejpam-3648	28	14	,	,	PUNCT
ejpam-3648	28	15	216	216	NUM
ejpam-3648	28	16	-	-	SYM
ejpam-3648	28	17	226	226	NUM
ejpam-3648	28	18	217	217	NUM
ejpam-3648	28	19	theorem	theorem	NOUN
ejpam-3648	28	20	1	1	NUM
ejpam-3648	28	21	.	.	PUNCT
ejpam-3648	29	1	the	the	DET
ejpam-3648	29	2	set	set	NOUN
ejpam-3648	29	3	,	,	PUNCT
ejpam-3648	29	4	whose	whose	DET
ejpam-3648	29	5	elements	element	NOUN
ejpam-3648	29	6	are	be	AUX
ejpam-3648	29	7	frenet	frenet	ADJ
ejpam-3648	29	8	vector	vector	NOUN
ejpam-3648	29	9	fields	field	NOUN
ejpam-3648	29	10	and	and	CCONJ
ejpam-3648	29	11	the	the	DET
ejpam-3648	29	12	curvatures	curvature	NOUN
ejpam-3648	29	13	of	of	ADP
ejpam-3648	29	14	a	a	DET
ejpam-3648	29	15	curve	curve	NOUN
ejpam-3648	29	16	α	α	PROPN
ejpam-3648	29	17	(	(	PUNCT
ejpam-3648	29	18	t	t	PROPN
ejpam-3648	29	19	)	)	PUNCT
ejpam-3648	29	20	⊂	⊂	PROPN
ejpam-3648	29	21	ie3	ie3	NOUN
ejpam-3648	29	22	,	,	PUNCT
ejpam-3648	29	23	is	be	AUX
ejpam-3648	29	24	called	call	VERB
ejpam-3648	29	25	frenet	frenet	NOUN
ejpam-3648	29	26	apparatus	apparatus	NOUN
ejpam-3648	29	27	of	of	ADP
ejpam-3648	29	28	the	the	DET
ejpam-3648	29	29	curves	curve	NOUN
ejpam-3648	29	30	.	.	PUNCT
ejpam-3648	30	1	let	let	AUX
ejpam-3648	30	2	α(t	α(t	NUM
ejpam-3648	30	3	)	)	PUNCT
ejpam-3648	30	4	be	be	AUX
ejpam-3648	30	5	the	the	DET
ejpam-3648	30	6	curve	curve	NOUN
ejpam-3648	30	7	,	,	PUNCT
ejpam-3648	30	8	with	with	SCONJ
ejpam-3648	30	9	η	η	PROPN
ejpam-3648	30	10	=	=	PRON
ejpam-3648	30	11	‖α′	‖α′	PROPN
ejpam-3648	30	12	(	(	PUNCT
ejpam-3648	30	13	t)‖	t)‖	NOUN
ejpam-3648	30	14	6=	6=	SYM
ejpam-3648	30	15	1	1	NUM
ejpam-3648	30	16	and	and	CCONJ
ejpam-3648	30	17	frenet	frenet	NOUN
ejpam-3648	30	18	apparatus	apparatus	NOUN
ejpam-3648	30	19	are	be	AUX
ejpam-3648	30	20	{	{	PUNCT
ejpam-3648	30	21	t	t	PROPN
ejpam-3648	30	22	(	(	PUNCT
ejpam-3648	30	23	t	t	PROPN
ejpam-3648	30	24	)	)	PUNCT
ejpam-3648	30	25	,	,	PUNCT
ejpam-3648	30	26	n	n	PROPN
ejpam-3648	30	27	(	(	PUNCT
ejpam-3648	30	28	t	t	PROPN
ejpam-3648	30	29	)	)	PUNCT
ejpam-3648	30	30	,	,	PUNCT
ejpam-3648	30	31	b	b	X
ejpam-3648	30	32	(	(	PUNCT
ejpam-3648	30	33	t	t	PROPN
ejpam-3648	30	34	)	)	PUNCT
ejpam-3648	30	35	,	,	PUNCT
ejpam-3648	30	36	κ	κ	X
ejpam-3648	30	37	(	(	PUNCT
ejpam-3648	30	38	t	t	PROPN
ejpam-3648	30	39	)	)	PUNCT
ejpam-3648	30	40	,	,	PUNCT
ejpam-3648	30	41	τ	τ	PROPN
ejpam-3648	30	42	(	(	PUNCT
ejpam-3648	30	43	t	t	PROPN
ejpam-3648	30	44	)	)	PUNCT
ejpam-3648	30	45	}	}	PUNCT
ejpam-3648	30	46	.	.	PUNCT
ejpam-3648	31	1	frenet	frenet	ADJ
ejpam-3648	31	2	vector	vector	NOUN
ejpam-3648	31	3	fields	field	NOUN
ejpam-3648	31	4	are	be	AUX
ejpam-3648	31	5	given	give	VERB
ejpam-3648	31	6	for	for	ADP
ejpam-3648	31	7	a	a	DET
ejpam-3648	31	8	non	non	ADJ
ejpam-3648	31	9	arc	arc	NOUN
ejpam-3648	31	10	-	-	PUNCT
ejpam-3648	31	11	lengthed	lengthe	VERB
ejpam-3648	31	12	curve	curve	NOUN
ejpam-3648	31	13	t	t	PROPN
ejpam-3648	31	14	(	(	PUNCT
ejpam-3648	31	15	t	t	PROPN
ejpam-3648	31	16	)	)	PUNCT
ejpam-3648	31	17	=	=	PUNCT
ejpam-3648	32	1	α′	α′	NUM
ejpam-3648	32	2	(	(	PUNCT
ejpam-3648	32	3	t	t	NOUN
ejpam-3648	32	4	)	)	PUNCT
ejpam-3648	32	5	‖α′	‖α′	PROPN
ejpam-3648	32	6	(	(	PUNCT
ejpam-3648	32	7	t)‖	t)‖	NOUN
ejpam-3648	32	8	,	,	PUNCT
ejpam-3648	32	9	n	n	PROPN
ejpam-3648	32	10	(	(	PUNCT
ejpam-3648	32	11	t	t	NOUN
ejpam-3648	32	12	)	)	PUNCT
ejpam-3648	33	1	=	=	SYM
ejpam-3648	33	2	b	b	PROPN
ejpam-3648	33	3	(	(	PUNCT
ejpam-3648	33	4	t	t	PROPN
ejpam-3648	33	5	)	)	PUNCT
ejpam-3648	33	6	λt	λt	X
ejpam-3648	33	7	(	(	PUNCT
ejpam-3648	33	8	t	t	PROPN
ejpam-3648	33	9	)	)	PUNCT
ejpam-3648	33	10	,	,	PUNCT
ejpam-3648	33	11	b	b	X
ejpam-3648	33	12	(	(	PUNCT
ejpam-3648	33	13	t	t	PROPN
ejpam-3648	33	14	)	)	PUNCT
ejpam-3648	33	15	=	=	SYM
ejpam-3648	34	1	α′	α′	NUM
ejpam-3648	34	2	(	(	PUNCT
ejpam-3648	34	3	t	t	NOUN
ejpam-3648	34	4	)	)	PUNCT
ejpam-3648	34	5	λα′′	λα′′	PROPN
ejpam-3648	34	6	(	(	PUNCT
ejpam-3648	34	7	t	t	NOUN
ejpam-3648	34	8	)	)	PUNCT
ejpam-3648	34	9	‖α′	‖α′	PROPN
ejpam-3648	34	10	(	(	PUNCT
ejpam-3648	34	11	t	t	NOUN
ejpam-3648	34	12	)	)	PUNCT
ejpam-3648	34	13	λα′′	λα′′	X
ejpam-3648	34	14	(	(	PUNCT
ejpam-3648	34	15	t)‖	t)‖	NOUN
ejpam-3648	34	16	where	where	SCONJ
ejpam-3648	34	17	curvature	curvature	NOUN
ejpam-3648	34	18	functions	function	NOUN
ejpam-3648	34	19	are	be	AUX
ejpam-3648	34	20	defined	define	VERB
ejpam-3648	34	21	by	by	ADP
ejpam-3648	34	22	κ	κ	PROPN
ejpam-3648	34	23	(	(	PUNCT
ejpam-3648	34	24	t	t	NOUN
ejpam-3648	34	25	)	)	PUNCT
ejpam-3648	34	26	=	=	SYM
ejpam-3648	34	27	∥∥∥α′	∥∥∥α′	PROPN
ejpam-3648	34	28	(	(	PUNCT
ejpam-3648	34	29	t	t	NOUN
ejpam-3648	34	30	)	)	PUNCT
ejpam-3648	34	31	λα	λα	PROPN
ejpam-3648	35	1	′′	′′	PROPN
ejpam-3648	35	2	(	(	PUNCT
ejpam-3648	35	3	t	t	PROPN
ejpam-3648	35	4	)	)	PUNCT
ejpam-3648	35	5	∥∥∥	∥∥∥	PROPN
ejpam-3648	35	6	‖α′	‖α′	PUNCT
ejpam-3648	35	7	(	(	PUNCT
ejpam-3648	35	8	t)‖3	t)‖3	INTJ
ejpam-3648	35	9	,	,	PUNCT
ejpam-3648	35	10	τ	τ	PROPN
ejpam-3648	35	11	(	(	PUNCT
ejpam-3648	35	12	t	t	PROPN
ejpam-3648	35	13	)	)	PUNCT
ejpam-3648	35	14	=	=	SYM
ejpam-3648	35	15	〈	〈	PROPN
ejpam-3648	35	16	α′	α′	PROPN
ejpam-3648	35	17	(	(	PUNCT
ejpam-3648	35	18	t	t	NOUN
ejpam-3648	35	19	)	)	PUNCT
ejpam-3648	35	20	λα	λα	PROPN
ejpam-3648	36	1	′′	′′	PROPN
ejpam-3648	36	2	(	(	PUNCT
ejpam-3648	36	3	t	t	PROPN
ejpam-3648	36	4	)	)	PUNCT
ejpam-3648	36	5	,	,	PUNCT
ejpam-3648	36	6	α′′′(t	α′′′(t	PROPN
ejpam-3648	36	7	)	)	PUNCT
ejpam-3648	36	8	〉	〉	NOUN
ejpam-3648	36	9	‖α′	‖α′	PUNCT
ejpam-3648	36	10	(	(	PUNCT
ejpam-3648	36	11	t	t	NOUN
ejpam-3648	36	12	)	)	PUNCT
ejpam-3648	36	13	λα′′	λα′′	X
ejpam-3648	36	14	(	(	PUNCT
ejpam-3648	36	15	t)‖2	t)‖2	ADJ
ejpam-3648	36	16	.	.	PUNCT
ejpam-3648	37	1	also	also	ADV
ejpam-3648	37	2	frenet	frenet	ADJ
ejpam-3648	37	3	formulae	formulae	NOUN
ejpam-3648	37	4	are	be	AUX
ejpam-3648	37	5	well	well	ADV
ejpam-3648	37	6	known	know	VERB
ejpam-3648	37	7	as	as	PROPN
ejpam-3648	37	8	t	t	PROPN
ejpam-3648	37	9	′	′	NUM
ejpam-3648	38	1	n	n	CCONJ
ejpam-3648	38	2	′	′	NUM
ejpam-3648	38	3	b′	b′	NOUN
ejpam-3648	38	4			NOUN
ejpam-3648	38	5	=	=	PUNCT
ejpam-3648	38	6			NOUN
ejpam-3648	38	7	0	0	NUM
ejpam-3648	39	1	ηκ	ηκ	NOUN
ejpam-3648	39	2	0	0	NUM
ejpam-3648	40	1	−ηκ	−ηκ	PROPN
ejpam-3648	40	2	0	0	PUNCT
ejpam-3648	40	3	ητ	ητ	NOUN
ejpam-3648	40	4	0	0	NUM
ejpam-3648	40	5	−ητ	−ητ	PROPN
ejpam-3648	40	6	0	0	PUNCT
ejpam-3648	41	1			NOUN
ejpam-3648	41	2	t	t	PROPN
ejpam-3648	41	3	n	n	CCONJ
ejpam-3648	41	4	b	b	NOUN
ejpam-3648	41	5			NOUN
ejpam-3648	41	6	,	,	PUNCT
ejpam-3648	42	1	[	[	X
ejpam-3648	42	2	4	4	NUM
ejpam-3648	42	3	]	]	PUNCT
ejpam-3648	42	4	.	.	PUNCT
ejpam-3648	43	1	theorem	theorem	NOUN
ejpam-3648	43	2	2	2	NUM
ejpam-3648	43	3	.	.	PUNCT
ejpam-3648	44	1	the	the	DET
ejpam-3648	44	2	frenet	frenet	NOUN
ejpam-3648	44	3	-	-	PUNCT
ejpam-3648	44	4	serret	serret	NOUN
ejpam-3648	44	5	vectors	vector	NOUN
ejpam-3648	44	6	fields	field	NOUN
ejpam-3648	44	7	of	of	ADP
ejpam-3648	44	8	the	the	DET
ejpam-3648	44	9	involute	involute	ADJ
ejpam-3648	44	10	α∗	α∗	NOUN
ejpam-3648	44	11	=	=	PUNCT
ejpam-3648	44	12	α	α	PROPN
ejpam-3648	44	13	(	(	PUNCT
ejpam-3648	44	14	t)+λ	t)+λ	PROPN
ejpam-3648	44	15	(	(	PUNCT
ejpam-3648	44	16	t)t	t)t	X
ejpam-3648	44	17	(	(	PUNCT
ejpam-3648	44	18	t	t	NOUN
ejpam-3648	44	19	)	)	PUNCT
ejpam-3648	44	20	,	,	PUNCT
ejpam-3648	44	21	which	which	PRON
ejpam-3648	44	22	is	be	AUX
ejpam-3648	44	23	not	not	PART
ejpam-3648	44	24	an	an	DET
ejpam-3648	44	25	arclengthed	arclengthed	ADJ
ejpam-3648	44	26	curve	curve	NOUN
ejpam-3648	44	27	with	with	ADP
ejpam-3648	44	28	‖α′‖	‖α′‖	PROPN
ejpam-3648	44	29	=	=	SYM
ejpam-3648	44	30	η	η	PROPN
ejpam-3648	44	31	6=	6=	PROPN
ejpam-3648	44	32	1	1	NUM
ejpam-3648	44	33	,	,	PUNCT
ejpam-3648	44	34	based	base	VERB
ejpam-3648	44	35	on	on	ADP
ejpam-3648	44	36	the	the	DET
ejpam-3648	44	37	its	its	PRON
ejpam-3648	44	38	evolute	evolute	PROPN
ejpam-3648	44	39	curve	curve	NOUN
ejpam-3648	44	40	α	α	PROPN
ejpam-3648	44	41	are	be	AUX
ejpam-3648	44	42	t	t	NOUN
ejpam-3648	44	43	∗	∗	NOUN
ejpam-3648	44	44	=	=	SYM
ejpam-3648	44	45	n	n	CCONJ
ejpam-3648	44	46	,	,	PUNCT
ejpam-3648	44	47	n∗	n∗	X
ejpam-3648	44	48	=	=	SYM
ejpam-3648	44	49	−κt	−κt	PROPN
ejpam-3648	44	50	+	+	CCONJ
ejpam-3648	44	51	τb	τb	PROPN
ejpam-3648	44	52	(	(	PUNCT
ejpam-3648	44	53	κ2	κ2	NOUN
ejpam-3648	44	54	+	+	CCONJ
ejpam-3648	44	55	τ2	τ2	NOUN
ejpam-3648	44	56	)	)	PUNCT
ejpam-3648	44	57	1	1	NUM
ejpam-3648	44	58	2	2	NUM
ejpam-3648	44	59	,	,	PUNCT
ejpam-3648	44	60	b∗	b∗	ADV
ejpam-3648	44	61	=	=	PUNCT
ejpam-3648	44	62	τt	τt	PROPN
ejpam-3648	45	1	+	+	NUM
ejpam-3648	45	2	κb	κb	INTJ
ejpam-3648	45	3	(	(	PUNCT
ejpam-3648	45	4	κ2	κ2	NOUN
ejpam-3648	45	5	+	+	CCONJ
ejpam-3648	45	6	τ2	τ2	NOUN
ejpam-3648	45	7	)	)	PUNCT
ejpam-3648	45	8	1	1	NUM
ejpam-3648	45	9	2	2	NUM
ejpam-3648	45	10	.	.	PUNCT
ejpam-3648	46	1	the	the	DET
ejpam-3648	46	2	first	first	ADJ
ejpam-3648	46	3	and	and	CCONJ
ejpam-3648	46	4	the	the	DET
ejpam-3648	46	5	second	second	ADJ
ejpam-3648	46	6	curvatures	curvature	NOUN
ejpam-3648	46	7	of	of	ADP
ejpam-3648	46	8	involute	involute	ADJ
ejpam-3648	46	9	α∗	α∗	NOUN
ejpam-3648	46	10	,	,	PUNCT
ejpam-3648	46	11	are	be	AUX
ejpam-3648	46	12	κ∗	κ∗	NOUN
ejpam-3648	46	13	=	=	SYM
ejpam-3648	46	14	√	√	NUM
ejpam-3648	46	15	κ2	κ2	NOUN
ejpam-3648	46	16	+	+	CCONJ
ejpam-3648	46	17	τ2	τ2	NOUN
ejpam-3648	46	18	(	(	PUNCT
ejpam-3648	46	19	c−	c−	X
ejpam-3648	46	20	ηt)κ	ηt)κ	PROPN
ejpam-3648	46	21	,	,	PUNCT
ejpam-3648	46	22	τ∗	τ∗	NOUN
ejpam-3648	46	23	=	=	SYM
ejpam-3648	46	24	−τ2	−τ2	PROPN
ejpam-3648	46	25	(	(	PUNCT
ejpam-3648	46	26	κ	κ	PROPN
ejpam-3648	46	27	τ	τ	PROPN
ejpam-3648	46	28	)	)	PUNCT
ejpam-3648	47	1	′	′	NUM
ejpam-3648	47	2	(	(	PUNCT
ejpam-3648	47	3	c−	c−	X
ejpam-3648	47	4	ηt)κ	ηt)κ	PROPN
ejpam-3648	47	5	(	(	PUNCT
ejpam-3648	47	6	κ2	κ2	NOUN
ejpam-3648	47	7	+	+	CCONJ
ejpam-3648	47	8	τ2	τ2	NOUN
ejpam-3648	47	9	)	)	PUNCT
ejpam-3648	47	10	(	(	PUNCT
ejpam-3648	47	11	1	1	X
ejpam-3648	47	12	)	)	PUNCT
ejpam-3648	47	13	respectively	respectively	ADV
ejpam-3648	47	14	,	,	PUNCT
ejpam-3648	47	15	where	where	SCONJ
ejpam-3648	47	16	dt	dt	X
ejpam-3648	47	17	ds∗	ds∗	NOUN
ejpam-3648	47	18	=	=	SYM
ejpam-3648	47	19	1	1	NUM
ejpam-3648	47	20	c−	c−	NOUN
ejpam-3648	47	21	ηt	ηt	ADV
ejpam-3648	47	22	,	,	PUNCT
ejpam-3648	47	23	[	[	X
ejpam-3648	47	24	4	4	NUM
ejpam-3648	47	25	]	]	PUNCT
ejpam-3648	47	26	.	.	PUNCT
ejpam-3648	48	1	generaly	generaly	NOUN
ejpam-3648	49	1	béziers	bézier	NOUN
ejpam-3648	49	2	curve	curve	NOUN
ejpam-3648	49	3	can	can	AUX
ejpam-3648	49	4	be	be	AUX
ejpam-3648	49	5	defined	define	VERB
ejpam-3648	49	6	by	by	ADP
ejpam-3648	49	7	n	n	PROPN
ejpam-3648	49	8	+	+	CCONJ
ejpam-3648	49	9	1	1	NUM
ejpam-3648	49	10	control	control	NOUN
ejpam-3648	49	11	points	point	NOUN
ejpam-3648	49	12	p0	p0	NOUN
ejpam-3648	49	13	,	,	PUNCT
ejpam-3648	49	14	p1	p1	NOUN
ejpam-3648	49	15	,	,	PUNCT
ejpam-3648	49	16	...	...	PUNCT
ejpam-3648	49	17	,	,	PUNCT
ejpam-3648	49	18	pn	pn	X
ejpam-3648	49	19	with	with	ADP
ejpam-3648	49	20	the	the	DET
ejpam-3648	49	21	parametrization	parametrization	NOUN
ejpam-3648	49	22	b(t	b(t	NOUN
ejpam-3648	49	23	)	)	PUNCT
ejpam-3648	50	1	=	=	SYM
ejpam-3648	50	2	n∑	n∑	PROPN
ejpam-3648	50	3	i=0	i=0	PROPN
ejpam-3648	50	4	(	(	PUNCT
ejpam-3648	50	5	n	n	X
ejpam-3648	50	6	i	i	NOUN
ejpam-3648	50	7	)	)	PUNCT
ejpam-3648	50	8	ti	ti	PROPN
ejpam-3648	50	9	(	(	PUNCT
ejpam-3648	50	10	1−	1−	NUM
ejpam-3648	50	11	t)n−i	t)n−i	X
ejpam-3648	50	12	(	(	PUNCT
ejpam-3648	50	13	t	t	NOUN
ejpam-3648	50	14	)	)	PUNCT
ejpam-3648	51	1	[	[	X
ejpam-3648	51	2	pi	pi	X
ejpam-3648	51	3	]	]	PUNCT
ejpam-3648	51	4	.	.	PUNCT
ejpam-3648	52	1	(	(	PUNCT
ejpam-3648	52	2	2	2	X
ejpam-3648	52	3	)	)	PUNCT
ejpam-3648	52	4	in	in	ADP
ejpam-3648	52	5	this	this	DET
ejpam-3648	52	6	study	study	NOUN
ejpam-3648	52	7	we	we	PRON
ejpam-3648	52	8	will	will	AUX
ejpam-3648	52	9	define	define	VERB
ejpam-3648	52	10	and	and	CCONJ
ejpam-3648	52	11	work	work	VERB
ejpam-3648	52	12	on	on	ADP
ejpam-3648	52	13	cubic	cubic	ADJ
ejpam-3648	52	14	bézier	bézier	ADP
ejpam-3648	52	15	curves	curve	NOUN
ejpam-3648	52	16	which	which	PRON
ejpam-3648	52	17	are	be	AUX
ejpam-3648	52	18	defined	define	VERB
ejpam-3648	52	19	in	in	ADP
ejpam-3648	52	20	e3	e3	NOUN
ejpam-3648	52	21	.	.	PUNCT
ejpam-3648	53	1	for	for	ADP
ejpam-3648	53	2	more	more	ADJ
ejpam-3648	53	3	detail	detail	NOUN
ejpam-3648	53	4	see	see	VERB
ejpam-3648	53	5	[	[	X
ejpam-3648	53	6	1	1	X
ejpam-3648	53	7	]	]	PUNCT
ejpam-3648	53	8	.	.	PUNCT
ejpam-3648	54	1	definition	definition	NOUN
ejpam-3648	54	2	1	1	NUM
ejpam-3648	54	3	.	.	PUNCT
ejpam-3648	55	1	a	a	DET
ejpam-3648	55	2	cubic	cubic	ADJ
ejpam-3648	55	3	bézier	bézier	ADP
ejpam-3648	55	4	curve	curve	NOUN
ejpam-3648	55	5	is	be	AUX
ejpam-3648	55	6	a	a	DET
ejpam-3648	55	7	special	special	ADJ
ejpam-3648	55	8	bézier	bézier	DET
ejpam-3648	55	9	curve	curve	NOUN
ejpam-3648	55	10	has	have	VERB
ejpam-3648	55	11	only	only	ADV
ejpam-3648	55	12	four	four	NUM
ejpam-3648	55	13	points	point	NOUN
ejpam-3648	55	14	p0	p0	NOUN
ejpam-3648	55	15	,	,	PUNCT
ejpam-3648	55	16	p1	p1	NOUN
ejpam-3648	55	17	,	,	PUNCT
ejpam-3648	55	18	p2	p2	PROPN
ejpam-3648	55	19	and	and	CCONJ
ejpam-3648	55	20	p3	p3	PROPN
ejpam-3648	55	21	,	,	PUNCT
ejpam-3648	55	22	with	with	ADP
ejpam-3648	55	23	the	the	DET
ejpam-3648	55	24	parametrization	parametrization	NOUN
ejpam-3648	55	25	b(t	b(t	NOUN
ejpam-3648	55	26	)	)	PUNCT
ejpam-3648	56	1	=	=	SYM
ejpam-3648	56	2	3∑	3∑	NUM
ejpam-3648	56	3	i=0	i=0	PROPN
ejpam-3648	56	4	(	(	PUNCT
ejpam-3648	56	5	3	3	NUM
ejpam-3648	56	6	i	i	NOUN
ejpam-3648	56	7	)	)	PUNCT
ejpam-3648	56	8	ti	ti	PROPN
ejpam-3648	56	9	(	(	PUNCT
ejpam-3648	56	10	1−	1−	NUM
ejpam-3648	56	11	t)3−i	t)3−i	PROPN
ejpam-3648	56	12	(	(	PUNCT
ejpam-3648	56	13	t	t	NOUN
ejpam-3648	56	14	)	)	PUNCT
ejpam-3648	57	1	[	[	X
ejpam-3648	57	2	pi	pi	X
ejpam-3648	57	3	]	]	X
ejpam-3648	57	4	,	,	PUNCT
ejpam-3648	57	5	(	(	PUNCT
ejpam-3648	57	6	3	3	X
ejpam-3648	57	7	)	)	PUNCT
ejpam-3648	57	8	b	b	PROPN
ejpam-3648	57	9	(	(	PUNCT
ejpam-3648	57	10	t	t	PROPN
ejpam-3648	57	11	)	)	PUNCT
ejpam-3648	57	12	=	=	PUNCT
ejpam-3648	58	1	(	(	PUNCT
ejpam-3648	58	2	1−	1−	NUM
ejpam-3648	58	3	t)3	t)3	NOUN
ejpam-3648	58	4	p0	p0	NOUN
ejpam-3648	58	5	+	+	CCONJ
ejpam-3648	58	6	3	3	NUM
ejpam-3648	58	7	t	t	NOUN
ejpam-3648	58	8	(	(	PUNCT
ejpam-3648	58	9	1−	1−	NUM
ejpam-3648	58	10	t)2	t)2	PROPN
ejpam-3648	58	11	p1	p1	NOUN
ejpam-3648	58	12	+	+	CCONJ
ejpam-3648	58	13	3t2	3t2	NUM
ejpam-3648	58	14	(	(	PUNCT
ejpam-3648	58	15	1−	1−	NUM
ejpam-3648	58	16	t)p2	t)p2	ADP
ejpam-3648	58	17	+	+	NOUN
ejpam-3648	58	18	t3p3	t3p3	AUX
ejpam-3648	58	19	.	.	PUNCT
ejpam-3648	59	1	ş.	ş.	PROPN
ejpam-3648	59	2	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	59	3	,	,	PUNCT
ejpam-3648	59	4	s.	s.	PROPN
ejpam-3648	59	5	şenyurt	şenyurt	PROPN
ejpam-3648	59	6	/	/	SYM
ejpam-3648	59	7	eur	eur	PROPN
ejpam-3648	59	8	.	.	PUNCT
ejpam-3648	60	1	j.	j.	PROPN
ejpam-3648	60	2	pure	pure	PROPN
ejpam-3648	60	3	appl	appl	PROPN
ejpam-3648	60	4	.	.	PROPN
ejpam-3648	60	5	math	math	PROPN
ejpam-3648	60	6	,	,	PUNCT
ejpam-3648	60	7	13	13	NUM
ejpam-3648	60	8	(	(	PUNCT
ejpam-3648	60	9	2	2	NUM
ejpam-3648	60	10	)	)	PUNCT
ejpam-3648	60	11	(	(	PUNCT
ejpam-3648	60	12	2020	2020	NUM
ejpam-3648	60	13	)	)	PUNCT
ejpam-3648	60	14	,	,	PUNCT
ejpam-3648	60	15	216	216	NUM
ejpam-3648	60	16	-	-	SYM
ejpam-3648	60	17	226	226	NUM
ejpam-3648	60	18	218	218	NUM
ejpam-3648	60	19	the	the	DET
ejpam-3648	60	20	matrix	matrix	NOUN
ejpam-3648	60	21	form	form	NOUN
ejpam-3648	60	22	of	of	ADP
ejpam-3648	60	23	the	the	DET
ejpam-3648	60	24	cubic	cubic	ADJ
ejpam-3648	60	25	bezier	bezier	NOUN
ejpam-3648	60	26	curve	curve	NOUN
ejpam-3648	60	27	with	with	ADP
ejpam-3648	60	28	control	control	NOUN
ejpam-3648	60	29	points	point	NOUN
ejpam-3648	60	30	p0	p0	NOUN
ejpam-3648	60	31	,	,	PUNCT
ejpam-3648	60	32	p1	p1	NOUN
ejpam-3648	60	33	,	,	PUNCT
ejpam-3648	60	34	p2	p2	NOUN
ejpam-3648	60	35	,	,	PUNCT
ejpam-3648	60	36	p3	p3	PROPN
ejpam-3648	60	37	,	,	PUNCT
ejpam-3648	60	38	is	be	AUX
ejpam-3648	60	39	α	α	PRON
ejpam-3648	60	40	(	(	PUNCT
ejpam-3648	60	41	t	t	NOUN
ejpam-3648	60	42	)	)	PUNCT
ejpam-3648	60	43	=	=	PUNCT
ejpam-3648	61	1	[	[	PUNCT
ejpam-3648	61	2	t3	t3	PROPN
ejpam-3648	61	3	t2	t2	PROPN
ejpam-3648	61	4	t	t	PROPN
ejpam-3648	61	5	1	1	NUM
ejpam-3648	61	6	]	]	PUNCT
ejpam-3648	61	7			NOUN
ejpam-3648	61	8	−1	−1	NOUN
ejpam-3648	61	9	3	3	NUM
ejpam-3648	61	10	−3	−3	NOUN
ejpam-3648	61	11	1	1	NUM
ejpam-3648	61	12	3	3	NUM
ejpam-3648	61	13	−6	−6	NOUN
ejpam-3648	61	14	3	3	NUM
ejpam-3648	61	15	0	0	NUM
ejpam-3648	61	16	−3	−3	PROPN
ejpam-3648	61	17	3	3	NUM
ejpam-3648	61	18	0	0	NUM
ejpam-3648	61	19	0	0	NUM
ejpam-3648	61	20	1	1	NUM
ejpam-3648	61	21	0	0	NUM
ejpam-3648	61	22	0	0	NUM
ejpam-3648	61	23	0	0	NUM
ejpam-3648	61	24			NOUN
ejpam-3648	61	25			NOUN
ejpam-3648	61	26	p0	p0	NOUN
ejpam-3648	61	27	p1	p1	NOUN
ejpam-3648	61	28	p2	p2	PROPN
ejpam-3648	61	29	p3	p3	PROPN
ejpam-3648	61	30			PROPN
ejpam-3648	61	31	.	.	PUNCT
ejpam-3648	62	1	also	also	ADV
ejpam-3648	62	2	using	use	VERB
ejpam-3648	62	3	the	the	DET
ejpam-3648	62	4	derivatives	derivative	NOUN
ejpam-3648	62	5	of	of	ADP
ejpam-3648	62	6	a	a	DET
ejpam-3648	62	7	cubic	cubic	ADJ
ejpam-3648	62	8	bézier	bézier	ADP
ejpam-3648	62	9	curve	curve	VERB
ejpam-3648	62	10	frenet	frenet	NOUN
ejpam-3648	62	11	apparatus	apparatus	NOUN
ejpam-3648	62	12	{	{	PUNCT
ejpam-3648	62	13	t	t	PROPN
ejpam-3648	62	14	(	(	PUNCT
ejpam-3648	62	15	t	t	PROPN
ejpam-3648	62	16	)	)	PUNCT
ejpam-3648	62	17	,	,	PUNCT
ejpam-3648	62	18	n	n	PROPN
ejpam-3648	62	19	(	(	PUNCT
ejpam-3648	62	20	t	t	PROPN
ejpam-3648	62	21	)	)	PUNCT
ejpam-3648	62	22	,	,	PUNCT
ejpam-3648	62	23	b	b	X
ejpam-3648	62	24	(	(	PUNCT
ejpam-3648	62	25	t	t	PROPN
ejpam-3648	62	26	)	)	PUNCT
ejpam-3648	62	27	,	,	PUNCT
ejpam-3648	62	28	κ	κ	X
ejpam-3648	62	29	(	(	PUNCT
ejpam-3648	62	30	t	t	PROPN
ejpam-3648	62	31	)	)	PUNCT
ejpam-3648	62	32	,	,	PUNCT
ejpam-3648	62	33	τ	τ	PROPN
ejpam-3648	62	34	(	(	PUNCT
ejpam-3648	62	35	t	t	PROPN
ejpam-3648	62	36	)	)	PUNCT
ejpam-3648	62	37	}	}	PUNCT
ejpam-3648	62	38	have	have	AUX
ejpam-3648	62	39	already	already	ADV
ejpam-3648	62	40	been	be	AUX
ejpam-3648	62	41	given	give	VERB
ejpam-3648	62	42	in	in	ADP
ejpam-3648	62	43	[	[	X
ejpam-3648	62	44	1	1	NUM
ejpam-3648	62	45	]	]	PUNCT
ejpam-3648	62	46	as	as	ADP
ejpam-3648	62	47	in	in	ADP
ejpam-3648	62	48	the	the	DET
ejpam-3648	62	49	following	follow	VERB
ejpam-3648	62	50	theorems	theorem	NOUN
ejpam-3648	62	51	by	by	ADP
ejpam-3648	62	52	using	use	VERB
ejpam-3648	62	53	matrix	matrix	NOUN
ejpam-3648	62	54	representation	representation	NOUN
ejpam-3648	62	55	.	.	PUNCT
ejpam-3648	63	1	for	for	ADP
ejpam-3648	63	2	more	more	ADJ
ejpam-3648	63	3	detail	detail	NOUN
ejpam-3648	63	4	see	see	VERB
ejpam-3648	63	5	in	in	ADP
ejpam-3648	63	6	[	[	X
ejpam-3648	63	7	1	1	NUM
ejpam-3648	63	8	]	]	PUNCT
ejpam-3648	63	9	.	.	PUNCT
ejpam-3648	64	1	theorem	theorem	NOUN
ejpam-3648	64	2	3	3	NUM
ejpam-3648	64	3	.	.	PUNCT
ejpam-3648	65	1	the	the	DET
ejpam-3648	65	2	first	first	ADJ
ejpam-3648	65	3	derivative	derivative	NOUN
ejpam-3648	65	4	of	of	ADP
ejpam-3648	65	5	a	a	DET
ejpam-3648	65	6	cubic	cubic	ADJ
ejpam-3648	65	7	bézier	bézier	ADP
ejpam-3648	65	8	curve	curve	NOUN
ejpam-3648	65	9	by	by	ADP
ejpam-3648	65	10	using	use	VERB
ejpam-3648	65	11	matrix	matrix	NOUN
ejpam-3648	65	12	representation	representation	NOUN
ejpam-3648	65	13	is	be	AUX
ejpam-3648	65	14	α′(t	α′(t	NOUN
ejpam-3648	65	15	)	)	PUNCT
ejpam-3648	65	16	=	=	PUNCT
ejpam-3648	66	1	[	[	PUNCT
ejpam-3648	66	2	t2	t2	NOUN
ejpam-3648	66	3	t	t	PROPN
ejpam-3648	66	4	1	1	NUM
ejpam-3648	66	5	]	]	SYM
ejpam-3648	66	6			NOUN
ejpam-3648	66	7	1	1	NUM
ejpam-3648	66	8	−2	−2	NOUN
ejpam-3648	66	9	1	1	NUM
ejpam-3648	66	10	−2	−2	NOUN
ejpam-3648	66	11	2	2	NUM
ejpam-3648	66	12	0	0	NUM
ejpam-3648	66	13	1	1	NUM
ejpam-3648	66	14	0	0	NUM
ejpam-3648	66	15	0	0	NUM
ejpam-3648	66	16			ADJ
ejpam-3648	66	17	q0	q0	ADJ
ejpam-3648	66	18	q1	q1	NOUN
ejpam-3648	66	19	q2	q2	NOUN
ejpam-3648	66	20			NOUN
ejpam-3648	66	21	(	(	PUNCT
ejpam-3648	66	22	4	4	NUM
ejpam-3648	66	23	)	)	PUNCT
ejpam-3648	66	24	with	with	ADP
ejpam-3648	66	25	the	the	DET
ejpam-3648	66	26	control	control	NOUN
ejpam-3648	66	27	points	point	NOUN
ejpam-3648	66	28	q0	q0	PROPN
ejpam-3648	66	29	=	=	SYM
ejpam-3648	66	30	3	3	NUM
ejpam-3648	66	31	(	(	PUNCT
ejpam-3648	66	32	p1	p1	NOUN
ejpam-3648	66	33	−	−	PROPN
ejpam-3648	66	34	p0	p0	NOUN
ejpam-3648	66	35	)	)	PUNCT
ejpam-3648	66	36	=	=	SYM
ejpam-3648	66	37	(	(	PUNCT
ejpam-3648	66	38	x0	x0	PROPN
ejpam-3648	66	39	,	,	PUNCT
ejpam-3648	66	40	y0	y0	PROPN
ejpam-3648	66	41	,	,	PUNCT
ejpam-3648	66	42	z0	z0	PROPN
ejpam-3648	66	43	)	)	PUNCT
ejpam-3648	66	44	,	,	PUNCT
ejpam-3648	66	45	q1	q1	PROPN
ejpam-3648	66	46	=	=	SYM
ejpam-3648	66	47	3	3	NUM
ejpam-3648	66	48	(	(	PUNCT
ejpam-3648	66	49	p2	p2	PROPN
ejpam-3648	66	50	−	−	PROPN
ejpam-3648	66	51	p1	p1	NOUN
ejpam-3648	66	52	)	)	PUNCT
ejpam-3648	66	53	=	=	PUNCT
ejpam-3648	66	54	(	(	PUNCT
ejpam-3648	66	55	x1	x1	PROPN
ejpam-3648	66	56	,	,	PUNCT
ejpam-3648	66	57	y1	y1	NOUN
ejpam-3648	66	58	,	,	PUNCT
ejpam-3648	66	59	z1)q2	z1)q2	NOUN
ejpam-3648	66	60	=	=	SYM
ejpam-3648	66	61	3	3	NUM
ejpam-3648	66	62	(	(	PUNCT
ejpam-3648	66	63	p3	p3	NOUN
ejpam-3648	66	64	−	−	PROPN
ejpam-3648	66	65	p2	p2	PROPN
ejpam-3648	66	66	)	)	PUNCT
ejpam-3648	66	67	=	=	SYM
ejpam-3648	66	68	(	(	PUNCT
ejpam-3648	66	69	x2	x2	PROPN
ejpam-3648	66	70	,	,	PUNCT
ejpam-3648	66	71	y2	y2	PROPN
ejpam-3648	66	72	,	,	PUNCT
ejpam-3648	66	73	z2	z2	PROPN
ejpam-3648	66	74	)	)	PUNCT
ejpam-3648	66	75	.	.	PUNCT
ejpam-3648	67	1	theorem	theorem	ADJ
ejpam-3648	67	2	4	4	NUM
ejpam-3648	67	3	.	.	PUNCT
ejpam-3648	68	1	the	the	DET
ejpam-3648	68	2	second	second	ADJ
ejpam-3648	68	3	derivative	derivative	NOUN
ejpam-3648	68	4	of	of	ADP
ejpam-3648	68	5	a	a	DET
ejpam-3648	68	6	cubic	cubic	ADJ
ejpam-3648	68	7	bézier	bézier	ADP
ejpam-3648	68	8	curve	curve	NOUN
ejpam-3648	68	9	by	by	ADP
ejpam-3648	68	10	using	use	VERB
ejpam-3648	68	11	matrix	matrix	NOUN
ejpam-3648	68	12	representation	representation	NOUN
ejpam-3648	68	13	is	be	AUX
ejpam-3648	68	14	α′′(t	α′′(t	VERB
ejpam-3648	68	15	)	)	PUNCT
ejpam-3648	68	16	=	=	PUNCT
ejpam-3648	69	1	[	[	PUNCT
ejpam-3648	69	2	t	t	NOUN
ejpam-3648	69	3	1	1	NUM
ejpam-3648	69	4	]	]	PUNCT
ejpam-3648	69	5	[	[	PUNCT
ejpam-3648	69	6	−1	−1	NOUN
ejpam-3648	69	7	1	1	NUM
ejpam-3648	69	8	1	1	NUM
ejpam-3648	69	9	0	0	NUM
ejpam-3648	69	10	]	]	PUNCT
ejpam-3648	69	11	[	[	PUNCT
ejpam-3648	69	12	r0	r0	NOUN
ejpam-3648	69	13	r1	r1	PROPN
ejpam-3648	69	14	]	]	PUNCT
ejpam-3648	69	15	(	(	PUNCT
ejpam-3648	69	16	5	5	NUM
ejpam-3648	69	17	)	)	PUNCT
ejpam-3648	69	18	with	with	ADP
ejpam-3648	69	19	the	the	DET
ejpam-3648	69	20	control	control	NOUN
ejpam-3648	69	21	points	point	NOUN
ejpam-3648	69	22	r0	r0	NOUN
ejpam-3648	69	23	=	=	NOUN
ejpam-3648	69	24	6	6	NUM
ejpam-3648	69	25	(	(	PUNCT
ejpam-3648	69	26	p2	p2	PROPN
ejpam-3648	69	27	−	−	PROPN
ejpam-3648	69	28	2p1	2p1	NUM
ejpam-3648	69	29	+	+	CCONJ
ejpam-3648	69	30	p0	p0	NOUN
ejpam-3648	69	31	)	)	PUNCT
ejpam-3648	69	32	=	=	SYM
ejpam-3648	69	33	6	6	NUM
ejpam-3648	69	34	(	(	PUNCT
ejpam-3648	69	35	x1	x1	PROPN
ejpam-3648	69	36	−	−	NOUN
ejpam-3648	69	37	x0	x0	PROPN
ejpam-3648	69	38	,	,	PUNCT
ejpam-3648	69	39	y1	y1	INTJ
ejpam-3648	69	40	−	−	PROPN
ejpam-3648	69	41	y0	y0	NOUN
ejpam-3648	69	42	,	,	PUNCT
ejpam-3648	69	43	z1	z1	ADJ
ejpam-3648	69	44	−	−	PROPN
ejpam-3648	69	45	z0	z0	PROPN
ejpam-3648	69	46	)	)	PUNCT
ejpam-3648	69	47	,	,	PUNCT
ejpam-3648	69	48	r1	r1	NOUN
ejpam-3648	69	49	=	=	SYM
ejpam-3648	69	50	6	6	NUM
ejpam-3648	69	51	(	(	PUNCT
ejpam-3648	69	52	p3	p3	PROPN
ejpam-3648	69	53	−	−	PROPN
ejpam-3648	69	54	2p2	2p2	NUM
ejpam-3648	69	55	+	+	CCONJ
ejpam-3648	69	56	p1	p1	NOUN
ejpam-3648	69	57	)	)	PUNCT
ejpam-3648	69	58	=	=	SYM
ejpam-3648	69	59	6	6	NUM
ejpam-3648	69	60	(	(	PUNCT
ejpam-3648	69	61	x2	x2	NOUN
ejpam-3648	69	62	−	−	PROPN
ejpam-3648	69	63	x1	x1	PROPN
ejpam-3648	69	64	,	,	PUNCT
ejpam-3648	69	65	y2	y2	PROPN
ejpam-3648	69	66	−	−	PROPN
ejpam-3648	69	67	y1	y1	PROPN
ejpam-3648	69	68	,	,	PUNCT
ejpam-3648	69	69	z2	z2	PROPN
ejpam-3648	69	70	−	−	PROPN
ejpam-3648	69	71	z1	z1	PROPN
ejpam-3648	69	72	)	)	PUNCT
ejpam-3648	69	73	.	.	PUNCT
ejpam-3648	70	1	theorem	theorem	ADJ
ejpam-3648	70	2	5	5	NUM
ejpam-3648	70	3	.	.	PUNCT
ejpam-3648	71	1	the	the	DET
ejpam-3648	71	2	third	third	ADJ
ejpam-3648	71	3	derivative	derivative	NOUN
ejpam-3648	71	4	of	of	ADP
ejpam-3648	71	5	a	a	DET
ejpam-3648	71	6	cubic	cubic	ADJ
ejpam-3648	71	7	bézier	bézier	ADP
ejpam-3648	71	8	curve	curve	NOUN
ejpam-3648	71	9	by	by	ADP
ejpam-3648	71	10	using	use	VERB
ejpam-3648	71	11	matrix	matrix	NOUN
ejpam-3648	71	12	representation	representation	NOUN
ejpam-3648	71	13	is	be	AUX
ejpam-3648	71	14	α′′′(t	α′′′(t	VERB
ejpam-3648	71	15	)	)	PUNCT
ejpam-3648	71	16	=	=	PUNCT
ejpam-3648	72	1	[	[	X
ejpam-3648	72	2	r0r1	r0r1	X
ejpam-3648	72	3	]	]	X
ejpam-3648	72	4	(	(	PUNCT
ejpam-3648	72	5	6	6	NUM
ejpam-3648	72	6	)	)	PUNCT
ejpam-3648	72	7	with	with	ADP
ejpam-3648	72	8	the	the	DET
ejpam-3648	72	9	control	control	NOUN
ejpam-3648	72	10	points	point	NOUN
ejpam-3648	72	11	[	[	X
ejpam-3648	72	12	r0r1	r0r1	X
ejpam-3648	72	13	]	]	X
ejpam-3648	72	14	=	=	SYM
ejpam-3648	72	15	r1	r1	PROPN
ejpam-3648	72	16	−r0	−r0	NOUN
ejpam-3648	72	17	=	=	SYM
ejpam-3648	72	18	2	2	NUM
ejpam-3648	73	1	[	[	X
ejpam-3648	73	2	q1q2]−	q1q2]−	NOUN
ejpam-3648	73	3	2	2	NUM
ejpam-3648	73	4	[	[	X
ejpam-3648	73	5	q0q1	q0q1	X
ejpam-3648	73	6	]	]	X
ejpam-3648	73	7	=	=	SYM
ejpam-3648	73	8	6	6	NUM
ejpam-3648	73	9	(	(	PUNCT
ejpam-3648	73	10	p3	p3	NOUN
ejpam-3648	73	11	−	−	ADP
ejpam-3648	73	12	3p2	3p2	NUM
ejpam-3648	73	13	+	+	NUM
ejpam-3648	73	14	3p1	3p1	NUM
ejpam-3648	73	15	−	−	NOUN
ejpam-3648	73	16	p0	p0	NOUN
ejpam-3648	73	17	)	)	PUNCT
ejpam-3648	73	18	.	.	PUNCT
ejpam-3648	74	1	1.1	1.1	NUM
ejpam-3648	74	2	.	.	PUNCT
ejpam-3648	75	1	frenet	frenet	ADJ
ejpam-3648	75	2	apparatus	apparatus	NOUN
ejpam-3648	75	3	of	of	ADP
ejpam-3648	75	4	a	a	DET
ejpam-3648	75	5	cubic	cubic	ADJ
ejpam-3648	75	6	bezier	bezier	NOUN
ejpam-3648	75	7	curve	curve	NOUN
ejpam-3648	75	8	frenet	frenet	NOUN
ejpam-3648	75	9	apparatus	apparatus	NOUN
ejpam-3648	75	10	{	{	PUNCT
ejpam-3648	75	11	t	t	PROPN
ejpam-3648	75	12	(	(	PUNCT
ejpam-3648	75	13	t	t	PROPN
ejpam-3648	75	14	)	)	PUNCT
ejpam-3648	75	15	,	,	PUNCT
ejpam-3648	75	16	n	n	PROPN
ejpam-3648	75	17	(	(	PUNCT
ejpam-3648	75	18	t	t	PROPN
ejpam-3648	75	19	)	)	PUNCT
ejpam-3648	75	20	,	,	PUNCT
ejpam-3648	75	21	b	b	X
ejpam-3648	75	22	(	(	PUNCT
ejpam-3648	75	23	t	t	PROPN
ejpam-3648	75	24	)	)	PUNCT
ejpam-3648	75	25	,	,	PUNCT
ejpam-3648	75	26	κ	κ	X
ejpam-3648	75	27	(	(	PUNCT
ejpam-3648	75	28	t	t	PROPN
ejpam-3648	75	29	)	)	PUNCT
ejpam-3648	75	30	,	,	PUNCT
ejpam-3648	75	31	τ	τ	PROPN
ejpam-3648	75	32	(	(	PUNCT
ejpam-3648	75	33	t	t	PROPN
ejpam-3648	75	34	)	)	PUNCT
ejpam-3648	75	35	}	}	PUNCT
ejpam-3648	75	36	of	of	ADP
ejpam-3648	75	37	a	a	DET
ejpam-3648	75	38	cubic	cubic	ADJ
ejpam-3648	75	39	bézier	bézier	DET
ejpam-3648	75	40	curve	curve	NOUN
ejpam-3648	75	41	have	have	AUX
ejpam-3648	75	42	already	already	ADV
ejpam-3648	75	43	been	be	AUX
ejpam-3648	75	44	given	give	VERB
ejpam-3648	75	45	in	in	ADP
ejpam-3648	75	46	[	[	X
ejpam-3648	75	47	1	1	NUM
ejpam-3648	75	48	]	]	PUNCT
ejpam-3648	75	49	as	as	ADP
ejpam-3648	75	50	in	in	ADP
ejpam-3648	75	51	the	the	DET
ejpam-3648	75	52	following	follow	VERB
ejpam-3648	75	53	theorems	theorem	NOUN
ejpam-3648	75	54	by	by	ADP
ejpam-3648	75	55	using	use	VERB
ejpam-3648	75	56	the	the	DET
ejpam-3648	75	57	matrix	matrix	NOUN
ejpam-3648	75	58	representation	representation	NOUN
ejpam-3648	75	59	.	.	PUNCT
ejpam-3648	76	1	theorem	theorem	VERB
ejpam-3648	76	2	6	6	NUM
ejpam-3648	76	3	.	.	PUNCT
ejpam-3648	76	4	tangent	tangent	ADJ
ejpam-3648	76	5	vector	vector	NOUN
ejpam-3648	76	6	field	field	NOUN
ejpam-3648	76	7	of	of	ADP
ejpam-3648	76	8	a	a	DET
ejpam-3648	76	9	cubic	cubic	ADJ
ejpam-3648	76	10	bezier	bezier	NOUN
ejpam-3648	76	11	curve	curve	NOUN
ejpam-3648	76	12	by	by	ADP
ejpam-3648	76	13	using	use	VERB
ejpam-3648	76	14	the	the	DET
ejpam-3648	76	15	matrix	matrix	NOUN
ejpam-3648	76	16	representation	representation	NOUN
ejpam-3648	76	17	is	be	AUX
ejpam-3648	76	18	t	t	PROPN
ejpam-3648	76	19	(	(	PUNCT
ejpam-3648	76	20	t	t	PROPN
ejpam-3648	76	21	)	)	PUNCT
ejpam-3648	76	22	=	=	SYM
ejpam-3648	76	23	1	1	NUM
ejpam-3648	76	24	η	η	PROPN
ejpam-3648	76	25	[	[	X
ejpam-3648	76	26	t2	t2	PROPN
ejpam-3648	76	27	t	t	PROPN
ejpam-3648	76	28	1	1	NUM
ejpam-3648	76	29	]	]	SYM
ejpam-3648	76	30			NOUN
ejpam-3648	76	31	1	1	NUM
ejpam-3648	76	32	−2	−2	NOUN
ejpam-3648	76	33	1	1	NUM
ejpam-3648	76	34	−2	−2	NOUN
ejpam-3648	76	35	2	2	NUM
ejpam-3648	76	36	0	0	NUM
ejpam-3648	76	37	1	1	NUM
ejpam-3648	76	38	0	0	NUM
ejpam-3648	76	39	0	0	NUM
ejpam-3648	77	1			NOUN
ejpam-3648	77	2	x0	x0	NOUN
ejpam-3648	77	3	y0	y0	PROPN
ejpam-3648	77	4	z0	z0	NOUN
ejpam-3648	77	5	x1	x1	NUM
ejpam-3648	77	6	y1	y1	PROPN
ejpam-3648	77	7	z1	z1	VERB
ejpam-3648	77	8	x2	x2	PROPN
ejpam-3648	77	9	y2	y2	PROPN
ejpam-3648	77	10	z2	z2	PROPN
ejpam-3648	77	11			NOUN
ejpam-3648	77	12	where	where	SCONJ
ejpam-3648	77	13	η	η	PROPN
ejpam-3648	77	14	=	=	PROPN
ejpam-3648	77	15	‖α′‖	‖α′‖	PROPN
ejpam-3648	77	16	.	.	PUNCT
ejpam-3648	78	1	ş.	ş.	PROPN
ejpam-3648	78	2	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	78	3	,	,	PUNCT
ejpam-3648	78	4	s.	s.	PROPN
ejpam-3648	78	5	şenyurt	şenyurt	PROPN
ejpam-3648	78	6	/	/	SYM
ejpam-3648	78	7	eur	eur	PROPN
ejpam-3648	78	8	.	.	PUNCT
ejpam-3648	79	1	j.	j.	PROPN
ejpam-3648	79	2	pure	pure	PROPN
ejpam-3648	79	3	appl	appl	PROPN
ejpam-3648	79	4	.	.	PROPN
ejpam-3648	79	5	math	math	PROPN
ejpam-3648	79	6	,	,	PUNCT
ejpam-3648	79	7	13	13	NUM
ejpam-3648	79	8	(	(	PUNCT
ejpam-3648	79	9	2	2	NUM
ejpam-3648	79	10	)	)	PUNCT
ejpam-3648	79	11	(	(	PUNCT
ejpam-3648	79	12	2020	2020	NUM
ejpam-3648	79	13	)	)	PUNCT
ejpam-3648	79	14	,	,	PUNCT
ejpam-3648	79	15	216	216	NUM
ejpam-3648	79	16	-	-	SYM
ejpam-3648	79	17	226	226	NUM
ejpam-3648	79	18	219	219	NUM
ejpam-3648	79	19	theorem	theorem	NOUN
ejpam-3648	79	20	7	7	NUM
ejpam-3648	79	21	.	.	PUNCT
ejpam-3648	79	22	binormal	binormal	ADJ
ejpam-3648	79	23	vector	vector	NOUN
ejpam-3648	79	24	field	field	NOUN
ejpam-3648	79	25	of	of	ADP
ejpam-3648	79	26	a	a	DET
ejpam-3648	79	27	cubic	cubic	ADJ
ejpam-3648	79	28	bezier	bezier	NOUN
ejpam-3648	79	29	curve	curve	NOUN
ejpam-3648	79	30	by	by	ADP
ejpam-3648	79	31	using	use	VERB
ejpam-3648	79	32	the	the	DET
ejpam-3648	79	33	matrix	matrix	NOUN
ejpam-3648	79	34	representation	representation	NOUN
ejpam-3648	79	35	is	be	AUX
ejpam-3648	79	36	b	b	PROPN
ejpam-3648	79	37	(	(	PUNCT
ejpam-3648	79	38	t	t	PROPN
ejpam-3648	79	39	)	)	PUNCT
ejpam-3648	79	40	=	=	NOUN
ejpam-3648	79	41	6	6	NUM
ejpam-3648	79	42	m	m	NOUN
ejpam-3648	79	43	[	[	PUNCT
ejpam-3648	79	44	t2	t2	NOUN
ejpam-3648	79	45	t	t	PROPN
ejpam-3648	79	46	1	1	NUM
ejpam-3648	79	47	]	]	PUNCT
ejpam-3648	79	48			PROPN
ejpam-3648	79	49	b11	b11	NOUN
ejpam-3648	79	50	b12	b12	NOUN
ejpam-3648	79	51	b13	b13	PROPN
ejpam-3648	79	52	b21	b21	PROPN
ejpam-3648	79	53	b22	b22	PROPN
ejpam-3648	79	54	b23	b23	PROPN
ejpam-3648	79	55	b31	b31	PROPN
ejpam-3648	79	56	b32	b32	PROPN
ejpam-3648	79	57	b33	b33	NOUN
ejpam-3648	79	58			NOUN
ejpam-3648	79	59	where	where	SCONJ
ejpam-3648	79	60	‖α′λα′′‖	‖α′λα′′‖	ADJ
ejpam-3648	79	61	=	=	NOUN
ejpam-3648	79	62	m	m	PROPN
ejpam-3648	79	63	b11	b11	NOUN
ejpam-3648	79	64	=	=	SYM
ejpam-3648	79	65	y0(z1	y0(z1	NOUN
ejpam-3648	79	66	−	−	PROPN
ejpam-3648	79	67	z2	z2	PROPN
ejpam-3648	79	68	)	)	PUNCT
ejpam-3648	80	1	+	+	CCONJ
ejpam-3648	80	2	y1(z2	y1(z2	PRON
ejpam-3648	80	3	−	−	PROPN
ejpam-3648	80	4	z0	z0	PROPN
ejpam-3648	80	5	)	)	PUNCT
ejpam-3648	81	1	+	+	PUNCT
ejpam-3648	81	2	y2(z0	y2(z0	PRON
ejpam-3648	81	3	−	−	PROPN
ejpam-3648	81	4	z1	z1	ADJ
ejpam-3648	81	5	)	)	PUNCT
ejpam-3648	81	6	b12	b12	NOUN
ejpam-3648	81	7	=	=	SYM
ejpam-3648	81	8	−x0	−x0	NOUN
ejpam-3648	81	9	(	(	PUNCT
ejpam-3648	81	10	z1	z1	PROPN
ejpam-3648	81	11	−	−	PROPN
ejpam-3648	81	12	z2)−	z2)−	PROPN
ejpam-3648	81	13	x1	x1	PROPN
ejpam-3648	82	1	(	(	PUNCT
ejpam-3648	82	2	z2	z2	PROPN
ejpam-3648	82	3	−	−	PROPN
ejpam-3648	82	4	z0)−	z0)−	NOUN
ejpam-3648	83	1	x2	x2	PROPN
ejpam-3648	83	2	(	(	PUNCT
ejpam-3648	83	3	z0	z0	PROPN
ejpam-3648	83	4	−	−	PROPN
ejpam-3648	83	5	z1	z1	PROPN
ejpam-3648	83	6	)	)	PUNCT
ejpam-3648	83	7	b13	b13	NOUN
ejpam-3648	83	8	=	=	SYM
ejpam-3648	83	9	x0	x0	PROPN
ejpam-3648	83	10	(	(	PUNCT
ejpam-3648	83	11	y1	y1	INTJ
ejpam-3648	83	12	−	−	PROPN
ejpam-3648	83	13	y2	y2	PROPN
ejpam-3648	83	14	)	)	PUNCT
ejpam-3648	84	1	+	+	CCONJ
ejpam-3648	84	2	x1	x1	INTJ
ejpam-3648	84	3	(	(	PUNCT
ejpam-3648	84	4	y2	y2	PROPN
ejpam-3648	84	5	−	−	NOUN
ejpam-3648	84	6	y0	y0	NOUN
ejpam-3648	84	7	)	)	PUNCT
ejpam-3648	85	1	+	+	NUM
ejpam-3648	86	1	x2	x2	PROPN
ejpam-3648	86	2	(	(	PUNCT
ejpam-3648	86	3	y0	y0	PROPN
ejpam-3648	86	4	−	−	PROPN
ejpam-3648	86	5	y1	y1	PROPN
ejpam-3648	86	6	)	)	PUNCT
ejpam-3648	86	7	b21	b21	NOUN
ejpam-3648	86	8	=	=	SYM
ejpam-3648	86	9	2y1z0	2y1z0	NUM
ejpam-3648	86	10	+	+	CCONJ
ejpam-3648	86	11	y0z2	y0z2	NUM
ejpam-3648	86	12	−	−	PROPN
ejpam-3648	86	13	2y0z1	2y0z1	NUM
ejpam-3648	86	14	−	−	PROPN
ejpam-3648	86	15	y2z0	y2z0	SYM
ejpam-3648	86	16	b22	b22	PROPN
ejpam-3648	86	17	=	=	SYM
ejpam-3648	86	18	2x0z1	2x0z1	PROPN
ejpam-3648	87	1	−	−	PROPN
ejpam-3648	87	2	2x1z0	2x1z0	NUM
ejpam-3648	87	3	−	−	NOUN
ejpam-3648	88	1	x0z2	x0z2	ADP
ejpam-3648	89	1	+	+	CCONJ
ejpam-3648	89	2	x2z0	x2z0	X
ejpam-3648	89	3	b23	b23	PROPN
ejpam-3648	89	4	=	=	SYM
ejpam-3648	89	5	2x1y0	2x1y0	NUM
ejpam-3648	89	6	−	−	NOUN
ejpam-3648	89	7	2x0y1	2x0y1	NUM
ejpam-3648	89	8	+	+	CCONJ
ejpam-3648	89	9	x0y2	x0y2	X
ejpam-3648	89	10	−	−	PROPN
ejpam-3648	89	11	x2y0	x2y0	SYM
ejpam-3648	89	12	b31	b31	PROPN
ejpam-3648	89	13	=	=	SYM
ejpam-3648	89	14	y0z1	y0z1	PROPN
ejpam-3648	90	1	−	−	PROPN
ejpam-3648	90	2	y1z0	y1z0	NOUN
ejpam-3648	90	3	b32	b32	PROPN
ejpam-3648	90	4	=	=	SYM
ejpam-3648	90	5	x1z0	x1z0	PROPN
ejpam-3648	91	1	−	−	PROPN
ejpam-3648	91	2	x0z1	x0z1	PROPN
ejpam-3648	91	3	b33	b33	X
ejpam-3648	91	4	=	=	PUNCT
ejpam-3648	91	5	x0y1	x0y1	PROPN
ejpam-3648	92	1	−	−	PROPN
ejpam-3648	92	2	x1y0	x1y0	SYM
ejpam-3648	92	3	.	.	PROPN
ejpam-3648	92	4	theorem	theorem	VERB
ejpam-3648	92	5	8	8	NUM
ejpam-3648	92	6	.	.	PUNCT
ejpam-3648	92	7	normal	normal	ADJ
ejpam-3648	92	8	vecror	vecror	NOUN
ejpam-3648	92	9	field	field	NOUN
ejpam-3648	92	10	of	of	ADP
ejpam-3648	92	11	a	a	DET
ejpam-3648	92	12	cubic	cubic	ADJ
ejpam-3648	92	13	bezier	bezier	NOUN
ejpam-3648	92	14	curve	curve	NOUN
ejpam-3648	92	15	by	by	ADP
ejpam-3648	92	16	using	use	VERB
ejpam-3648	92	17	the	the	DET
ejpam-3648	92	18	matrix	matrix	NOUN
ejpam-3648	92	19	representation	representation	NOUN
ejpam-3648	92	20	is	be	AUX
ejpam-3648	92	21	n	n	PRON
ejpam-3648	92	22	(	(	PUNCT
ejpam-3648	92	23	t	t	PROPN
ejpam-3648	92	24	)	)	PUNCT
ejpam-3648	93	1	=	=	SYM
ejpam-3648	93	2	6	6	NUM
ejpam-3648	93	3	ηm	ηm	NOUN
ejpam-3648	93	4	[	[	PUNCT
ejpam-3648	93	5	t4	t4	PROPN
ejpam-3648	93	6	t3	t3	PROPN
ejpam-3648	93	7	t2	t2	PROPN
ejpam-3648	93	8	t1	t1	NOUN
ejpam-3648	93	9	1	1	NUM
ejpam-3648	93	10	]	]	PUNCT
ejpam-3648	93	11			ADJ
ejpam-3648	93	12	n11	n11	PROPN
ejpam-3648	93	13	n12	n12	PROPN
ejpam-3648	93	14	n13	n13	PROPN
ejpam-3648	93	15	n21	n21	PROPN
ejpam-3648	93	16	n22	n22	PROPN
ejpam-3648	93	17	n23	n23	PROPN
ejpam-3648	93	18	n31	n31	ADJ
ejpam-3648	93	19	n32	n32	NOUN
ejpam-3648	93	20	n33	n33	PROPN
ejpam-3648	93	21	n41	n41	PROPN
ejpam-3648	93	22	n41	n41	PROPN
ejpam-3648	93	23	n43	n43	PROPN
ejpam-3648	93	24	n51	n51	PROPN
ejpam-3648	93	25	n51	n51	PROPN
ejpam-3648	93	26	n53	n53	NOUN
ejpam-3648	93	27			NUM
ejpam-3648	93	28	where	where	SCONJ
ejpam-3648	93	29	n11	n11	PROPN
ejpam-3648	93	30	=	=	SYM
ejpam-3648	93	31	b12d13	b12d13	PROPN
ejpam-3648	93	32	−	−	PROPN
ejpam-3648	93	33	b13d12	b13d12	VERB
ejpam-3648	93	34	n21	n21	NOUN
ejpam-3648	93	35	=	=	PUNCT
ejpam-3648	93	36	b12d23	b12d23	NOUN
ejpam-3648	93	37	−	−	PROPN
ejpam-3648	93	38	b13d22	b13d22	NOUN
ejpam-3648	93	39	+	+	CCONJ
ejpam-3648	93	40	b22d13	b22d13	NOUN
ejpam-3648	93	41	−	−	PROPN
ejpam-3648	93	42	b23d12	b23d12	ADJ
ejpam-3648	93	43	n31	n31	NOUN
ejpam-3648	93	44	=	=	NOUN
ejpam-3648	93	45	b12d33	b12d33	VERB
ejpam-3648	93	46	−	−	PROPN
ejpam-3648	93	47	b13d32	b13d32	NOUN
ejpam-3648	93	48	+	+	CCONJ
ejpam-3648	93	49	b22d23	b22d23	NOUN
ejpam-3648	93	50	−	−	NOUN
ejpam-3648	93	51	b23d22	b23d22	NOUN
ejpam-3648	93	52	+	+	CCONJ
ejpam-3648	93	53	b32d13	b32d13	NOUN
ejpam-3648	93	54	−	−	NOUN
ejpam-3648	93	55	b33d12	b33d12	ADJ
ejpam-3648	93	56	n41	n41	NOUN
ejpam-3648	93	57	=	=	PUNCT
ejpam-3648	93	58	b22d33	b22d33	NOUN
ejpam-3648	93	59	−	−	NOUN
ejpam-3648	94	1	b23d32	b23d32	NOUN
ejpam-3648	94	2	+	+	CCONJ
ejpam-3648	94	3	b32d23	b32d23	NOUN
ejpam-3648	94	4	−	−	PROPN
ejpam-3648	94	5	b33d22	b33d22	NOUN
ejpam-3648	94	6	n51	n51	NOUN
ejpam-3648	94	7	=	=	SYM
ejpam-3648	94	8	b32d33	b32d33	NOUN
ejpam-3648	94	9	−	−	NOUN
ejpam-3648	94	10	b33d32	b33d32	ADJ
ejpam-3648	94	11	n12	n12	NOUN
ejpam-3648	94	12	=	=	PUNCT
ejpam-3648	94	13	b11d13	b11d13	PROPN
ejpam-3648	94	14	−	−	PROPN
ejpam-3648	94	15	b13d11	b13d11	PROPN
ejpam-3648	94	16	n22	n22	NOUN
ejpam-3648	94	17	=	=	PUNCT
ejpam-3648	94	18	−b11d23	−b11d23	NOUN
ejpam-3648	94	19	−	−	PROPN
ejpam-3648	94	20	b21d13	b21d13	PROPN
ejpam-3648	94	21	+	+	CCONJ
ejpam-3648	94	22	b13d21	b13d21	PROPN
ejpam-3648	94	23	+	+	CCONJ
ejpam-3648	94	24	b23d11	b23d11	NOUN
ejpam-3648	94	25	n32	n32	NOUN
ejpam-3648	94	26	=	=	PUNCT
ejpam-3648	94	27	b23d21	b23d21	NOUN
ejpam-3648	94	28	+	+	PROPN
ejpam-3648	94	29	b33d11	b33d11	PROPN
ejpam-3648	95	1	−	−	PROPN
ejpam-3648	95	2	b11d33	b11d33	PROPN
ejpam-3648	95	3	−	−	PROPN
ejpam-3648	95	4	b21d23	b21d23	NOUN
ejpam-3648	95	5	+	+	CCONJ
ejpam-3648	95	6	b13d31	b13d31	NOUN
ejpam-3648	95	7	−	−	PROPN
ejpam-3648	95	8	b31d13	b31d13	ADJ
ejpam-3648	95	9	n42	n42	NOUN
ejpam-3648	95	10	=	=	SYM
ejpam-3648	95	11	−b21d33	−b21d33	NOUN
ejpam-3648	96	1	−	−	PROPN
ejpam-3648	96	2	b31d23	b31d23	NOUN
ejpam-3648	96	3	+	+	CCONJ
ejpam-3648	96	4	b23d31	b23d31	ADJ
ejpam-3648	96	5	+	+	CCONJ
ejpam-3648	96	6	b33d21	b33d21	ADJ
ejpam-3648	96	7	n52	n52	NOUN
ejpam-3648	96	8	=	=	NOUN
ejpam-3648	96	9	−b31d33	−b31d33	NOUN
ejpam-3648	96	10	+	+	CCONJ
ejpam-3648	96	11	b33d31	b33d31	PROPN
ejpam-3648	96	12	n13	n13	PROPN
ejpam-3648	96	13	=	=	SYM
ejpam-3648	96	14	b11d12	b11d12	VERB
ejpam-3648	96	15	−	−	PROPN
ejpam-3648	96	16	b12d11	b12d11	NOUN
ejpam-3648	96	17	n23	n23	NOUN
ejpam-3648	96	18	=	=	SYM
ejpam-3648	96	19	b11d22	b11d22	PROPN
ejpam-3648	96	20	−	−	PROPN
ejpam-3648	96	21	b12d21	b12d21	PROPN
ejpam-3648	96	22	+	+	CCONJ
ejpam-3648	96	23	b21d12	b21d12	PROPN
ejpam-3648	96	24	−	−	PROPN
ejpam-3648	96	25	b22d11	b22d11	NOUN
ejpam-3648	96	26	n33	n33	NOUN
ejpam-3648	96	27	=	=	SYM
ejpam-3648	96	28	b11d32	b11d32	PROPN
ejpam-3648	96	29	−	−	NOUN
ejpam-3648	96	30	b12d31	b12d31	NOUN
ejpam-3648	96	31	+	+	CCONJ
ejpam-3648	96	32	b21d22	b21d22	ADJ
ejpam-3648	96	33	−	−	PROPN
ejpam-3648	96	34	b22d21	b22d21	PROPN
ejpam-3648	96	35	+	+	CCONJ
ejpam-3648	96	36	b31d12	b31d12	PROPN
ejpam-3648	96	37	−	−	PROPN
ejpam-3648	96	38	b32d11	b32d11	PROPN
ejpam-3648	96	39	n43	n43	NOUN
ejpam-3648	96	40	=	=	PUNCT
ejpam-3648	96	41	b21d32	b21d32	NOUN
ejpam-3648	96	42	−	−	PROPN
ejpam-3648	96	43	b22d31	b22d31	NOUN
ejpam-3648	96	44	+	+	CCONJ
ejpam-3648	96	45	b31d22	b31d22	NOUN
ejpam-3648	96	46	−	−	PROPN
ejpam-3648	96	47	b32d21	b32d21	ADJ
ejpam-3648	96	48	n53	n53	NOUN
ejpam-3648	96	49	=	=	SYM
ejpam-3648	96	50	b31d32	b31d32	PROPN
ejpam-3648	96	51	−	−	PROPN
ejpam-3648	96	52	b32d31	b32d31	NOUN
ejpam-3648	96	53	.	.	PUNCT
ejpam-3648	97	1	theorem	theorem	VERB
ejpam-3648	97	2	9	9	NUM
ejpam-3648	97	3	.	.	PUNCT
ejpam-3648	97	4	first	first	ADJ
ejpam-3648	97	5	and	and	CCONJ
ejpam-3648	97	6	second	second	ADJ
ejpam-3648	97	7	curvatures	curvature	NOUN
ejpam-3648	97	8	of	of	ADP
ejpam-3648	97	9	a	a	DET
ejpam-3648	97	10	cubic	cubic	ADJ
ejpam-3648	97	11	bezier	bezier	NOUN
ejpam-3648	97	12	curve	curve	NOUN
ejpam-3648	97	13	by	by	ADP
ejpam-3648	97	14	using	use	VERB
ejpam-3648	97	15	the	the	DET
ejpam-3648	97	16	matrix	matrix	NOUN
ejpam-3648	97	17	ş.	ş.	PROPN
ejpam-3648	97	18	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	97	19	,	,	PUNCT
ejpam-3648	97	20	s.	s.	PROPN
ejpam-3648	97	21	şenyurt	şenyurt	PROPN
ejpam-3648	97	22	/	/	SYM
ejpam-3648	97	23	eur	eur	PROPN
ejpam-3648	97	24	.	.	PUNCT
ejpam-3648	98	1	j.	j.	PROPN
ejpam-3648	98	2	pure	pure	PROPN
ejpam-3648	98	3	appl	appl	PROPN
ejpam-3648	98	4	.	.	PROPN
ejpam-3648	98	5	math	math	PROPN
ejpam-3648	98	6	,	,	PUNCT
ejpam-3648	98	7	13	13	NUM
ejpam-3648	98	8	(	(	PUNCT
ejpam-3648	98	9	2	2	NUM
ejpam-3648	98	10	)	)	PUNCT
ejpam-3648	98	11	(	(	PUNCT
ejpam-3648	98	12	2020	2020	NUM
ejpam-3648	98	13	)	)	PUNCT
ejpam-3648	98	14	,	,	PUNCT
ejpam-3648	98	15	216	216	NUM
ejpam-3648	98	16	-	-	SYM
ejpam-3648	98	17	226	226	NUM
ejpam-3648	98	18	220	220	NUM
ejpam-3648	98	19	representation	representation	NOUN
ejpam-3648	98	20	are	be	AUX
ejpam-3648	98	21	κ	κ	PROPN
ejpam-3648	98	22	(	(	PUNCT
ejpam-3648	98	23	t	t	NOUN
ejpam-3648	98	24	)	)	PUNCT
ejpam-3648	98	25	=	=	SYM
ejpam-3648	98	26	6	6	NUM
ejpam-3648	98	27	η3	η3	NOUN
ejpam-3648	98	28	[	[	PUNCT
ejpam-3648	98	29	t4	t4	PROPN
ejpam-3648	98	30	t3	t3	PROPN
ejpam-3648	98	31	t2	t2	PROPN
ejpam-3648	98	32	t	t	PROPN
ejpam-3648	98	33	1	1	NUM
ejpam-3648	98	34	]	]	PUNCT
ejpam-3648	98	35			NOUN
ejpam-3648	98	36	b211	b211	PUNCT
ejpam-3648	99	1	+	+	PUNCT
ejpam-3648	99	2	b212	b212	PROPN
ejpam-3648	99	3	+	+	NUM
ejpam-3648	99	4	b213	b213	PROPN
ejpam-3648	99	5	2b11b21	2b11b21	PROPN
ejpam-3648	99	6	+	+	CCONJ
ejpam-3648	99	7	2b12b22	2b12b22	PROPN
ejpam-3648	99	8	+	+	CCONJ
ejpam-3648	99	9	2b13b23	2b13b23	NUM
ejpam-3648	99	10	2b11b31	2b11b31	NUM
ejpam-3648	100	1	+	+	CCONJ
ejpam-3648	101	1	2b12b32	2b12b32	NUM
ejpam-3648	101	2	+	+	CCONJ
ejpam-3648	101	3	2b13b33	2b13b33	ADJ
ejpam-3648	102	1	+	+	CCONJ
ejpam-3648	102	2	b221	b221	PROPN
ejpam-3648	102	3	+	+	CCONJ
ejpam-3648	103	1	b222	b222	NUM
ejpam-3648	103	2	+	+	NUM
ejpam-3648	103	3	b223	b223	PROPN
ejpam-3648	103	4	2b21b31	2b21b31	NOUN
ejpam-3648	103	5	+	+	CCONJ
ejpam-3648	103	6	2b22b32	2b22b32	NUM
ejpam-3648	103	7	+	+	CCONJ
ejpam-3648	103	8	2b23b33	2b23b33	PROPN
ejpam-3648	103	9	b231	b231	PROPN
ejpam-3648	103	10	+	+	CCONJ
ejpam-3648	103	11	b232	b232	PROPN
ejpam-3648	103	12	+	+	CCONJ
ejpam-3648	103	13	b233	b233	NUM
ejpam-3648	103	14	,	,	PUNCT
ejpam-3648	103	15			PRON
ejpam-3648	103	16	,	,	PUNCT
ejpam-3648	103	17	τ	τ	PROPN
ejpam-3648	103	18	(	(	PUNCT
ejpam-3648	103	19	t	t	PROPN
ejpam-3648	103	20	)	)	PUNCT
ejpam-3648	103	21	=	=	PUNCT
ejpam-3648	104	1	x0y1z2	x0y1z2	PROPN
ejpam-3648	104	2	−	−	PROPN
ejpam-3648	105	1	x0y2z1	x0y2z1	PROPN
ejpam-3648	105	2	−	−	PROPN
ejpam-3648	105	3	x1y0z2	x1y0z2	NOUN
ejpam-3648	105	4	+	+	CCONJ
ejpam-3648	105	5	x1y2z0	x1y2z0	X
ejpam-3648	106	1	+	+	CCONJ
ejpam-3648	106	2	x2y0z1	x2y0z1	PROPN
ejpam-3648	106	3	−	−	PROPN
ejpam-3648	106	4	x2y1z0	x2y1z0	PROPN
ejpam-3648	106	5	‖α′	‖α′	PROPN
ejpam-3648	106	6	(	(	PUNCT
ejpam-3648	106	7	t	t	PROPN
ejpam-3648	106	8	)	)	PUNCT
ejpam-3648	106	9	λα′′	λα′′	X
ejpam-3648	106	10	(	(	PUNCT
ejpam-3648	106	11	t)‖2	t)‖2	ADJ
ejpam-3648	106	12	.	.	PUNCT
ejpam-3648	107	1	2	2	X
ejpam-3648	107	2	.	.	X
ejpam-3648	107	3	involute	involute	NOUN
ejpam-3648	107	4	of	of	ADP
ejpam-3648	107	5	cubic	cubic	ADJ
ejpam-3648	107	6	bezier	bezier	NOUN
ejpam-3648	107	7	curve	curve	NOUN
ejpam-3648	107	8	definition	definition	NOUN
ejpam-3648	107	9	2	2	NUM
ejpam-3648	107	10	.	.	PUNCT
ejpam-3648	108	1	if	if	SCONJ
ejpam-3648	108	2	the	the	DET
ejpam-3648	108	3	curve	curve	NOUN
ejpam-3648	108	4	α∗	α∗	NOUN
ejpam-3648	108	5	which	which	PRON
ejpam-3648	108	6	lies	lie	VERB
ejpam-3648	108	7	on	on	ADP
ejpam-3648	108	8	the	the	DET
ejpam-3648	108	9	tangent	tangent	NOUN
ejpam-3648	108	10	surface	surface	NOUN
ejpam-3648	108	11	intersect	intersect	ADJ
ejpam-3648	108	12	the	the	DET
ejpam-3648	108	13	tangent	tangent	NOUN
ejpam-3648	108	14	lines	line	NOUN
ejpam-3648	108	15	orthogonally	orthogonally	ADV
ejpam-3648	108	16	is	be	AUX
ejpam-3648	108	17	called	call	VERB
ejpam-3648	108	18	an	an	DET
ejpam-3648	108	19	involute	involute	NOUN
ejpam-3648	108	20	of	of	ADP
ejpam-3648	108	21	α	α	NOUN
ejpam-3648	108	22	.	.	PUNCT
ejpam-3648	109	1	if	if	SCONJ
ejpam-3648	109	2	a	a	DET
ejpam-3648	109	3	curve	curve	NOUN
ejpam-3648	109	4	α∗	α∗	NOUN
ejpam-3648	109	5	is	be	AUX
ejpam-3648	109	6	an	an	DET
ejpam-3648	109	7	involute	involute	NOUN
ejpam-3648	109	8	of	of	ADP
ejpam-3648	109	9	α	α	NOUN
ejpam-3648	109	10	,	,	PUNCT
ejpam-3648	109	11	then	then	ADV
ejpam-3648	109	12	by	by	ADP
ejpam-3648	109	13	definition	definition	NOUN
ejpam-3648	109	14	α	α	PRON
ejpam-3648	109	15	which	which	PRON
ejpam-3648	109	16	is	be	AUX
ejpam-3648	109	17	not	not	PART
ejpam-3648	109	18	an	an	DET
ejpam-3648	109	19	arclengthed	arclengthe	VERB
ejpam-3648	109	20	curve.is	curve.is	PROPN
ejpam-3648	109	21	an	an	DET
ejpam-3648	109	22	evolute	evolute	NOUN
ejpam-3648	109	23	of	of	ADP
ejpam-3648	109	24	α∗.	α∗.	NOUN
ejpam-3648	109	25	hence	hence	ADV
ejpam-3648	109	26	given	give	VERB
ejpam-3648	109	27	α	α	PRON
ejpam-3648	109	28	,	,	PUNCT
ejpam-3648	109	29	its	its	PRON
ejpam-3648	109	30	evolutes	evolute	NOUN
ejpam-3648	109	31	are	be	AUX
ejpam-3648	109	32	the	the	DET
ejpam-3648	109	33	curves	curve	NOUN
ejpam-3648	109	34	whose	whose	DET
ejpam-3648	109	35	tangent	tangent	NOUN
ejpam-3648	109	36	lines	line	NOUN
ejpam-3648	109	37	intersect	intersect	VERB
ejpam-3648	109	38	α	α	PRON
ejpam-3648	109	39	orthogonally	orthogonally	ADV
ejpam-3648	109	40	.	.	PUNCT
ejpam-3648	110	1	let	let	VERB
ejpam-3648	110	2	the	the	DET
ejpam-3648	110	3	quantities	quantity	NOUN
ejpam-3648	110	4	{	{	PUNCT
ejpam-3648	110	5	t	t	NOUN
ejpam-3648	110	6	∗	∗	NOUN
ejpam-3648	110	7	,	,	PUNCT
ejpam-3648	110	8	n∗	n∗	PROPN
ejpam-3648	110	9	,	,	PUNCT
ejpam-3648	110	10	b∗	b∗	ADJ
ejpam-3648	110	11	,	,	PUNCT
ejpam-3648	110	12	κ∗	κ∗	PROPN
ejpam-3648	110	13	,	,	PUNCT
ejpam-3648	110	14	τ∗	τ∗	ADJ
ejpam-3648	110	15	}	}	PUNCT
ejpam-3648	110	16	be	be	VERB
ejpam-3648	110	17	collectively	collectively	ADV
ejpam-3648	110	18	frenet	frenet	ADJ
ejpam-3648	110	19	-	-	PUNCT
ejpam-3648	110	20	serret	serret	NOUN
ejpam-3648	110	21	apparatus	apparatus	NOUN
ejpam-3648	110	22	of	of	ADP
ejpam-3648	110	23	the	the	DET
ejpam-3648	110	24	curve	curve	NOUN
ejpam-3648	110	25	α∗	α∗	NOUN
ejpam-3648	110	26	which	which	PRON
ejpam-3648	110	27	is	be	AUX
ejpam-3648	110	28	not	not	PART
ejpam-3648	110	29	an	an	DET
ejpam-3648	110	30	arclengthed	arclengthed	ADJ
ejpam-3648	110	31	curve	curve	NOUN
ejpam-3648	110	32	with	with	ADP
ejpam-3648	110	33	‖α′‖	‖α′‖	PROPN
ejpam-3648	110	34	=	=	SYM
ejpam-3648	110	35	η	η	PROPN
ejpam-3648	110	36	6=	6=	PROPN
ejpam-3648	110	37	1	1	NUM
ejpam-3648	110	38	,	,	PUNCT
ejpam-3648	110	39	[	[	X
ejpam-3648	110	40	4	4	NUM
ejpam-3648	110	41	]	]	PUNCT
ejpam-3648	110	42	.	.	PUNCT
ejpam-3648	111	1	the	the	DET
ejpam-3648	111	2	equation	equation	NOUN
ejpam-3648	111	3	of	of	ADP
ejpam-3648	111	4	involute	involute	NOUN
ejpam-3648	111	5	of	of	ADP
ejpam-3648	111	6	the	the	DET
ejpam-3648	111	7	curve	curve	NOUN
ejpam-3648	111	8	α	α	PROPN
ejpam-3648	111	9	has	have	VERB
ejpam-3648	111	10	the	the	DET
ejpam-3648	111	11	following	follow	VERB
ejpam-3648	111	12	parametrization	parametrization	NOUN
ejpam-3648	111	13	;	;	PUNCT
ejpam-3648	111	14	α∗	α∗	NOUN
ejpam-3648	111	15	(	(	PUNCT
ejpam-3648	111	16	t	t	NOUN
ejpam-3648	111	17	)	)	PUNCT
ejpam-3648	111	18	=	=	SYM
ejpam-3648	111	19	α	α	PROPN
ejpam-3648	111	20	(	(	PUNCT
ejpam-3648	111	21	t	t	PROPN
ejpam-3648	111	22	)	)	PUNCT
ejpam-3648	112	1	+	+	NUM
ejpam-3648	112	2	λ	λ	X
ejpam-3648	112	3	(	(	PUNCT
ejpam-3648	112	4	t)t	t)t	X
ejpam-3648	112	5	(	(	PUNCT
ejpam-3648	112	6	t	t	NOUN
ejpam-3648	112	7	)	)	PUNCT
ejpam-3648	112	8	.	.	PUNCT
ejpam-3648	113	1	(	(	PUNCT
ejpam-3648	113	2	7	7	X
ejpam-3648	113	3	)	)	PUNCT
ejpam-3648	113	4	also	also	ADV
ejpam-3648	113	5	since	since	SCONJ
ejpam-3648	113	6	λ	λ	X
ejpam-3648	113	7	=	=	SYM
ejpam-3648	113	8	c−	c−	NOUN
ejpam-3648	113	9	ηt	ηt	ADP
ejpam-3648	113	10	it	it	PRON
ejpam-3648	113	11	can	can	AUX
ejpam-3648	113	12	be	be	AUX
ejpam-3648	113	13	written	write	VERB
ejpam-3648	113	14	as	as	ADP
ejpam-3648	113	15	in	in	ADP
ejpam-3648	113	16	the	the	DET
ejpam-3648	113	17	following	follow	VERB
ejpam-3648	113	18	parametrization	parametrization	NOUN
ejpam-3648	113	19	α∗	α∗	NOUN
ejpam-3648	113	20	(	(	PUNCT
ejpam-3648	113	21	t	t	NOUN
ejpam-3648	113	22	)	)	PUNCT
ejpam-3648	113	23	=	=	SYM
ejpam-3648	113	24	α	α	PROPN
ejpam-3648	113	25	(	(	PUNCT
ejpam-3648	113	26	t	t	PROPN
ejpam-3648	113	27	)	)	PUNCT
ejpam-3648	114	1	+	+	CCONJ
ejpam-3648	114	2	(	(	PUNCT
ejpam-3648	114	3	c−	c−	NOUN
ejpam-3648	114	4	ηt	ηt	ADP
ejpam-3648	114	5	)	)	PUNCT
ejpam-3648	114	6	η	η	PROPN
ejpam-3648	114	7	α′	α′	PROPN
ejpam-3648	114	8	(	(	PUNCT
ejpam-3648	114	9	t	t	PROPN
ejpam-3648	114	10	)	)	PUNCT
ejpam-3648	114	11	.	.	PUNCT
ejpam-3648	115	1	theorem	theorem	VERB
ejpam-3648	115	2	10	10	NUM
ejpam-3648	115	3	.	.	PUNCT
ejpam-3648	116	1	the	the	DET
ejpam-3648	116	2	involute	involute	NOUN
ejpam-3648	116	3	of	of	ADP
ejpam-3648	116	4	a	a	DET
ejpam-3648	116	5	cubic	cubic	ADJ
ejpam-3648	116	6	bezier	bezier	NOUN
ejpam-3648	116	7	curve	curve	NOUN
ejpam-3648	116	8	has	have	VERB
ejpam-3648	116	9	the	the	DET
ejpam-3648	116	10	matrix	matrix	NOUN
ejpam-3648	116	11	form	form	NOUN
ejpam-3648	116	12	based	base	VERB
ejpam-3648	116	13	on	on	ADP
ejpam-3648	116	14	the	the	DET
ejpam-3648	116	15	control	control	NOUN
ejpam-3648	116	16	points	point	VERB
ejpam-3648	116	17	p0	p0	NOUN
ejpam-3648	116	18	,	,	PUNCT
ejpam-3648	116	19	p1	p1	NOUN
ejpam-3648	116	20	,	,	PUNCT
ejpam-3648	116	21	p2	p2	PROPN
ejpam-3648	116	22	and	and	CCONJ
ejpam-3648	116	23	p3	p3	PROPN
ejpam-3648	116	24	of	of	ADP
ejpam-3648	116	25	any	any	DET
ejpam-3648	116	26	cubic	cubic	ADJ
ejpam-3648	116	27	bezier	bezier	NOUN
ejpam-3648	116	28	curve	curve	NOUN
ejpam-3648	116	29	α∗	α∗	NOUN
ejpam-3648	116	30	(	(	PUNCT
ejpam-3648	116	31	t	t	NOUN
ejpam-3648	116	32	)	)	PUNCT
ejpam-3648	116	33	=	=	NOUN
ejpam-3648	117	1	[	[	PUNCT
ejpam-3648	117	2	t3	t3	PROPN
ejpam-3648	117	3	t2	t2	PROPN
ejpam-3648	117	4	t	t	PROPN
ejpam-3648	117	5	1	1	NUM
ejpam-3648	117	6	]	]	PUNCT
ejpam-3648	117	7			NOUN
ejpam-3648	117	8	−1	−1	NOUN
ejpam-3648	117	9	3	3	NUM
ejpam-3648	117	10	−3	−3	NOUN
ejpam-3648	117	11	1	1	NUM
ejpam-3648	117	12	3−	3−	NUM
ejpam-3648	117	13	3µ	3µ	NUM
ejpam-3648	117	14	−6	−6	NOUN
ejpam-3648	117	15	+	+	CCONJ
ejpam-3648	117	16	9µ	9µ	NUM
ejpam-3648	117	17	3−	3−	NUM
ejpam-3648	117	18	9µ	9µ	NOUN
ejpam-3648	117	19	3µ	3µ	NUM
ejpam-3648	117	20	−3	−3	NOUN
ejpam-3648	118	1	+	+	NUM
ejpam-3648	119	1	6µ	6µ	NOUN
ejpam-3648	119	2	3−	3−	NUM
ejpam-3648	119	3	12µ	12µ	NOUN
ejpam-3648	119	4	6µ	6µ	VERB
ejpam-3648	119	5	0	0	NUM
ejpam-3648	119	6	1	1	NUM
ejpam-3648	120	1	+	+	NUM
ejpam-3648	120	2	3µ	3µ	NUM
ejpam-3648	120	3	−3	−3	NOUN
ejpam-3648	120	4	0	0	NUM
ejpam-3648	120	5	0	0	NUM
ejpam-3648	120	6			NOUN
ejpam-3648	120	7			NOUN
ejpam-3648	120	8	p0	p0	NOUN
ejpam-3648	120	9	p1	p1	NOUN
ejpam-3648	120	10	p2	p2	PROPN
ejpam-3648	120	11	p3	p3	PROPN
ejpam-3648	120	12			PROPN
ejpam-3648	120	13	with	with	ADP
ejpam-3648	120	14	µ	µ	NOUN
ejpam-3648	120	15	=	=	SYM
ejpam-3648	120	16	c−ηt	c−ηt	PROPN
ejpam-3648	120	17	η	η	PROPN
ejpam-3648	120	18	.	.	PUNCT
ejpam-3648	121	1	proof	proof	NOUN
ejpam-3648	121	2	.	.	PUNCT
ejpam-3648	122	1	lets	let	VERB
ejpam-3648	122	2	µ	µ	X
ejpam-3648	122	3	=	=	PUNCT
ejpam-3648	122	4	(	(	PUNCT
ejpam-3648	122	5	c−	c−	X
ejpam-3648	122	6	ηt	ηt	ADP
ejpam-3648	122	7	)	)	PUNCT
ejpam-3648	122	8	η	η	PROPN
ejpam-3648	122	9	,	,	PUNCT
ejpam-3648	122	10	since	since	SCONJ
ejpam-3648	122	11	α∗	α∗	NOUN
ejpam-3648	122	12	=	=	PUNCT
ejpam-3648	122	13	α	α	PROPN
ejpam-3648	122	14	(	(	PUNCT
ejpam-3648	122	15	t	t	PROPN
ejpam-3648	122	16	)	)	PUNCT
ejpam-3648	123	1	+	+	CCONJ
ejpam-3648	123	2	µα′	µα′	X
ejpam-3648	123	3	(	(	PUNCT
ejpam-3648	123	4	t	t	NOUN
ejpam-3648	123	5	)	)	PUNCT
ejpam-3648	123	6	α∗	α∗	NOUN
ejpam-3648	123	7	=	=	PUNCT
ejpam-3648	124	1	[	[	PUNCT
ejpam-3648	124	2	t3	t3	PROPN
ejpam-3648	124	3	t2	t2	PROPN
ejpam-3648	124	4	t	t	PROPN
ejpam-3648	124	5	1	1	NUM
ejpam-3648	124	6	]	]	PUNCT
ejpam-3648	124	7			NOUN
ejpam-3648	124	8	−1	−1	NOUN
ejpam-3648	124	9	3	3	NUM
ejpam-3648	124	10	−3	−3	NOUN
ejpam-3648	124	11	1	1	NUM
ejpam-3648	124	12	3	3	NUM
ejpam-3648	124	13	−6	−6	NOUN
ejpam-3648	124	14	3	3	NUM
ejpam-3648	124	15	0	0	NUM
ejpam-3648	124	16	−3	−3	PROPN
ejpam-3648	124	17	3	3	NUM
ejpam-3648	124	18	0	0	NUM
ejpam-3648	124	19	0	0	NUM
ejpam-3648	124	20	1	1	NUM
ejpam-3648	124	21	0	0	NUM
ejpam-3648	124	22	0	0	NUM
ejpam-3648	124	23	0	0	NUM
ejpam-3648	124	24			NOUN
ejpam-3648	124	25			NOUN
ejpam-3648	124	26	p0	p0	NOUN
ejpam-3648	124	27	p1	p1	NOUN
ejpam-3648	124	28	p2	p2	PROPN
ejpam-3648	124	29	p3	p3	PROPN
ejpam-3648	124	30	+µ	+µ	PROPN
ejpam-3648	125	1	[	[	PUNCT
ejpam-3648	125	2	t2	t2	NOUN
ejpam-3648	125	3	t	t	PROPN
ejpam-3648	125	4	1	1	NUM
ejpam-3648	125	5	]	]	SYM
ejpam-3648	125	6			NOUN
ejpam-3648	125	7	1	1	NUM
ejpam-3648	125	8	−2	−2	NOUN
ejpam-3648	125	9	1	1	NUM
ejpam-3648	125	10	−2	−2	NOUN
ejpam-3648	125	11	2	2	NUM
ejpam-3648	125	12	0	0	NUM
ejpam-3648	125	13	1	1	NUM
ejpam-3648	125	14	0	0	NUM
ejpam-3648	125	15	0	0	NUM
ejpam-3648	125	16			ADJ
ejpam-3648	125	17	q0	q0	ADJ
ejpam-3648	125	18	q1	q1	NOUN
ejpam-3648	125	19	q2	q2	NOUN
ejpam-3648	125	20			NOUN
ejpam-3648	125	21	ş.	ş.	PROPN
ejpam-3648	125	22	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	125	23	,	,	PUNCT
ejpam-3648	125	24	s.	s.	PROPN
ejpam-3648	125	25	şenyurt	şenyurt	PROPN
ejpam-3648	125	26	/	/	SYM
ejpam-3648	125	27	eur	eur	PROPN
ejpam-3648	125	28	.	.	PUNCT
ejpam-3648	126	1	j.	j.	PROPN
ejpam-3648	126	2	pure	pure	PROPN
ejpam-3648	126	3	appl	appl	PROPN
ejpam-3648	126	4	.	.	PROPN
ejpam-3648	126	5	math	math	PROPN
ejpam-3648	126	6	,	,	PUNCT
ejpam-3648	126	7	13	13	NUM
ejpam-3648	126	8	(	(	PUNCT
ejpam-3648	126	9	2	2	NUM
ejpam-3648	126	10	)	)	PUNCT
ejpam-3648	126	11	(	(	PUNCT
ejpam-3648	126	12	2020	2020	NUM
ejpam-3648	126	13	)	)	PUNCT
ejpam-3648	126	14	,	,	PUNCT
ejpam-3648	126	15	216	216	NUM
ejpam-3648	126	16	-	-	SYM
ejpam-3648	126	17	226	226	NUM
ejpam-3648	126	18	221	221	NUM
ejpam-3648	126	19	and	and	CCONJ
ejpam-3648	126	20	q0	q0	VERB
ejpam-3648	126	21	=	=	SYM
ejpam-3648	126	22	3	3	X
ejpam-3648	126	23	(	(	PUNCT
ejpam-3648	126	24	p1	p1	NOUN
ejpam-3648	126	25	−	−	PROPN
ejpam-3648	126	26	p0	p0	NOUN
ejpam-3648	126	27	)	)	PUNCT
ejpam-3648	126	28	,	,	PUNCT
ejpam-3648	126	29	q1	q1	PROPN
ejpam-3648	126	30	=	=	SYM
ejpam-3648	126	31	3	3	NUM
ejpam-3648	126	32	(	(	PUNCT
ejpam-3648	126	33	p2	p2	PROPN
ejpam-3648	126	34	−	−	PROPN
ejpam-3648	126	35	p1	p1	PROPN
ejpam-3648	126	36	)	)	PUNCT
ejpam-3648	126	37	,	,	PUNCT
ejpam-3648	126	38	q2	q2	NOUN
ejpam-3648	126	39	=	=	SYM
ejpam-3648	126	40	3	3	X
ejpam-3648	126	41	(	(	PUNCT
ejpam-3648	126	42	p3	p3	PROPN
ejpam-3648	126	43	−	−	PROPN
ejpam-3648	126	44	p2	p2	NOUN
ejpam-3648	126	45	)	)	PUNCT
ejpam-3648	126	46	it	it	PRON
ejpam-3648	126	47	can	can	AUX
ejpam-3648	126	48	be	be	AUX
ejpam-3648	126	49	written	write	VERB
ejpam-3648	126	50	in	in	ADP
ejpam-3648	126	51	matrix	matrix	NOUN
ejpam-3648	126	52	form	form	NOUN
ejpam-3648	126	53	as	as	ADP
ejpam-3648	126	54	in	in	ADP
ejpam-3648	126	55	α∗	α∗	NOUN
ejpam-3648	126	56	(	(	PUNCT
ejpam-3648	126	57	t	t	NOUN
ejpam-3648	126	58	)	)	PUNCT
ejpam-3648	126	59	=	=	NOUN
ejpam-3648	127	1	[	[	PUNCT
ejpam-3648	127	2	t3	t3	PROPN
ejpam-3648	127	3	t2	t2	PROPN
ejpam-3648	127	4	t	t	PROPN
ejpam-3648	127	5	1	1	NUM
ejpam-3648	127	6	]	]	PUNCT
ejpam-3648	127	7			NOUN
ejpam-3648	127	8	−1	−1	NOUN
ejpam-3648	127	9	3	3	NUM
ejpam-3648	127	10	−3	−3	NOUN
ejpam-3648	127	11	1	1	NUM
ejpam-3648	127	12	(	(	PUNCT
ejpam-3648	127	13	3−	3−	NUM
ejpam-3648	127	14	3µ	3µ	NUM
ejpam-3648	127	15	)	)	PUNCT
ejpam-3648	127	16	(	(	PUNCT
ejpam-3648	127	17	−6	−6	X
ejpam-3648	127	18	+	+	NUM
ejpam-3648	127	19	9µ	9µ	NUM
ejpam-3648	127	20	)	)	PUNCT
ejpam-3648	127	21	(	(	PUNCT
ejpam-3648	127	22	3−	3−	NUM
ejpam-3648	127	23	9µ	9µ	NUM
ejpam-3648	127	24	)	)	PUNCT
ejpam-3648	127	25	3µ	3µ	NUM
ejpam-3648	127	26	(	(	PUNCT
ejpam-3648	127	27	−3	−3	PROPN
ejpam-3648	127	28	+	+	NUM
ejpam-3648	127	29	6µ	6µ	NOUN
ejpam-3648	127	30	)	)	PUNCT
ejpam-3648	127	31	(	(	PUNCT
ejpam-3648	127	32	3−	3−	NUM
ejpam-3648	127	33	12µ	12µ	NOUN
ejpam-3648	127	34	)	)	PUNCT
ejpam-3648	127	35	6µ	6µ	NOUN
ejpam-3648	127	36	0	0	SYM
ejpam-3648	127	37	(	(	PUNCT
ejpam-3648	127	38	1	1	NUM
ejpam-3648	127	39	+	+	NUM
ejpam-3648	127	40	3µ	3µ	NUM
ejpam-3648	127	41	)	)	PUNCT
ejpam-3648	127	42	−3	−3	PROPN
ejpam-3648	127	43	0	0	NUM
ejpam-3648	127	44	0	0	NUM
ejpam-3648	128	1			NOUN
ejpam-3648	128	2			NOUN
ejpam-3648	128	3	p0	p0	NOUN
ejpam-3648	128	4	p1	p1	NOUN
ejpam-3648	128	5	p2	p2	PROPN
ejpam-3648	128	6	p3	p3	PROPN
ejpam-3648	128	7			NOUN
ejpam-3648	128	8	we	we	PRON
ejpam-3648	128	9	have	have	VERB
ejpam-3648	128	10	its	its	PRON
ejpam-3648	128	11	matrix	matrix	NOUN
ejpam-3648	128	12	product	product	NOUN
ejpam-3648	128	13	form	form	NOUN
ejpam-3648	128	14	as	as	ADP
ejpam-3648	128	15	α∗	α∗	NOUN
ejpam-3648	128	16	(	(	PUNCT
ejpam-3648	128	17	t	t	NOUN
ejpam-3648	128	18	)	)	PUNCT
ejpam-3648	128	19	=	=	NOUN
ejpam-3648	129	1	[	[	PUNCT
ejpam-3648	129	2	t3	t3	PROPN
ejpam-3648	129	3	t2	t2	PROPN
ejpam-3648	129	4	t	t	PROPN
ejpam-3648	129	5	1	1	NUM
ejpam-3648	129	6	]	]	PUNCT
ejpam-3648	129	7			NOUN
ejpam-3648	129	8	3p1	3p1	NUM
ejpam-3648	129	9	−	−	PROPN
ejpam-3648	129	10	p0	p0	NOUN
ejpam-3648	129	11	−	−	NOUN
ejpam-3648	129	12	3p2	3p2	NUM
ejpam-3648	129	13	+	+	CCONJ
ejpam-3648	129	14	p3	p3	PROPN
ejpam-3648	129	15	p1	p1	NOUN
ejpam-3648	129	16	(	(	PUNCT
ejpam-3648	129	17	9µ−	9µ−	PROPN
ejpam-3648	129	18	6)−	6)−	NUM
ejpam-3648	129	19	p2	p2	PROPN
ejpam-3648	129	20	(	(	PUNCT
ejpam-3648	129	21	9µ−	9µ−	NOUN
ejpam-3648	129	22	3)−	3)−	NUM
ejpam-3648	129	23	p0	p0	NOUN
ejpam-3648	129	24	(	(	PUNCT
ejpam-3648	129	25	3µ−	3µ−	NUM
ejpam-3648	129	26	3	3	NUM
ejpam-3648	129	27	)	)	PUNCT
ejpam-3648	129	28	+	+	CCONJ
ejpam-3648	129	29	3µp3	3µp3	NUM
ejpam-3648	129	30	p0	p0	NOUN
ejpam-3648	129	31	(	(	PUNCT
ejpam-3648	129	32	6µ−	6µ−	NUM
ejpam-3648	129	33	3)−	3)−	PROPN
ejpam-3648	129	34	p1	p1	NOUN
ejpam-3648	129	35	(	(	PUNCT
ejpam-3648	129	36	12µ−	12µ−	NUM
ejpam-3648	129	37	3	3	NUM
ejpam-3648	129	38	)	)	PUNCT
ejpam-3648	129	39	+	+	CCONJ
ejpam-3648	129	40	6µp2	6µp2	NUM
ejpam-3648	129	41	p0	p0	NOUN
ejpam-3648	129	42	(	(	PUNCT
ejpam-3648	129	43	3µ+	3µ+	NUM
ejpam-3648	129	44	1)−	1)−	NUM
ejpam-3648	129	45	3p1	3p1	NUM
ejpam-3648	129	46			NOUN
ejpam-3648	129	47	.	.	PUNCT
ejpam-3648	130	1	(	(	PUNCT
ejpam-3648	130	2	8)	8)	NUM
ejpam-3648	130	3	theorem	theorem	NOUN
ejpam-3648	130	4	11	11	NUM
ejpam-3648	130	5	.	.	PUNCT
ejpam-3648	131	1	the	the	DET
ejpam-3648	131	2	control	control	NOUN
ejpam-3648	131	3	points	point	NOUN
ejpam-3648	131	4	of	of	ADP
ejpam-3648	131	5	the	the	DET
ejpam-3648	131	6	involute	involute	NOUN
ejpam-3648	131	7	of	of	ADP
ejpam-3648	131	8	any	any	DET
ejpam-3648	131	9	cubic	cubic	ADJ
ejpam-3648	131	10	bezier	bezier	NOUN
ejpam-3648	131	11	curve	curve	NOUN
ejpam-3648	131	12	with	with	ADP
ejpam-3648	131	13	constant	constant	ADJ
ejpam-3648	131	14	speed	speed	NOUN
ejpam-3648	131	15	,	,	PUNCT
ejpam-3648	131	16	based	base	VERB
ejpam-3648	131	17	on	on	ADP
ejpam-3648	131	18	the	the	DET
ejpam-3648	131	19	control	control	NOUN
ejpam-3648	131	20	points	point	NOUN
ejpam-3648	131	21	of	of	ADP
ejpam-3648	131	22	cubic	cubic	ADJ
ejpam-3648	131	23	bezier	bezier	NOUN
ejpam-3648	131	24	curve	curve	NOUN
ejpam-3648	131	25	,	,	PUNCT
ejpam-3648	131	26	as	as	ADP
ejpam-3648	131	27	in	in	ADP
ejpam-3648	131	28	the	the	DET
ejpam-3648	131	29	following	following	ADJ
ejpam-3648	131	30	way	way	NOUN
ejpam-3648	131	31	i0	i0	PROPN
ejpam-3648	131	32	=	=	SYM
ejpam-3648	131	33	3	3	NUM
ejpam-3648	131	34	c	c	PROPN
ejpam-3648	131	35	η	η	PROPN
ejpam-3648	131	36	p1	p1	PROPN
ejpam-3648	131	37	−	−	PROPN
ejpam-3648	131	38	p0	p0	NOUN
ejpam-3648	131	39	(	(	PUNCT
ejpam-3648	131	40	3	3	NUM
ejpam-3648	131	41	c	c	PROPN
ejpam-3648	131	42	η	η	X
ejpam-3648	131	43	−	−	PROPN
ejpam-3648	131	44	1	1	NUM
ejpam-3648	131	45	)	)	PUNCT
ejpam-3648	131	46	,	,	PUNCT
ejpam-3648	131	47	i1	i1	PROPN
ejpam-3648	131	48	=	=	PUNCT
ejpam-3648	131	49	3	3	NUM
ejpam-3648	131	50	c	c	PROPN
ejpam-3648	131	51	η	η	PROPN
ejpam-3648	131	52	p1	p1	PROPN
ejpam-3648	131	53	−	−	PROPN
ejpam-3648	132	1	p0	p0	NOUN
ejpam-3648	132	2	(	(	PUNCT
ejpam-3648	132	3	c	c	PROPN
ejpam-3648	132	4	η	η	PROPN
ejpam-3648	132	5	−	−	PROPN
ejpam-3648	132	6	1	1	NUM
ejpam-3648	132	7	)	)	PUNCT
ejpam-3648	132	8	−	−	PROPN
ejpam-3648	132	9	2	2	NUM
ejpam-3648	132	10	c	c	PROPN
ejpam-3648	132	11	η	η	PROPN
ejpam-3648	132	12	p2	p2	PROPN
ejpam-3648	132	13	,	,	PUNCT
ejpam-3648	132	14	i2	i2	NOUN
ejpam-3648	132	15	=	=	PUNCT
ejpam-3648	132	16	(	(	PUNCT
ejpam-3648	132	17	6	6	NUM
ejpam-3648	132	18	c	c	PROPN
ejpam-3648	132	19	η	η	X
ejpam-3648	132	20	+	+	ADP
ejpam-3648	132	21	2	2	X
ejpam-3648	132	22	)	)	PUNCT
ejpam-3648	132	23	p1	p1	NOUN
ejpam-3648	132	24	−	−	PROPN
ejpam-3648	132	25	p2	p2	PROPN
ejpam-3648	132	26	(	(	PUNCT
ejpam-3648	132	27	7	7	NUM
ejpam-3648	132	28	c	c	PROPN
ejpam-3648	132	29	η	η	X
ejpam-3648	132	30	+	+	PROPN
ejpam-3648	132	31	1	1	NUM
ejpam-3648	132	32	)	)	PUNCT
ejpam-3648	133	1	+	+	CCONJ
ejpam-3648	133	2	c	c	PROPN
ejpam-3648	133	3	η	η	PROPN
ejpam-3648	133	4	p3	p3	PROPN
ejpam-3648	133	5	,	,	PUNCT
ejpam-3648	133	6	i3	i3	NOUN
ejpam-3648	133	7	=	=	SYM
ejpam-3648	133	8	(	(	PUNCT
ejpam-3648	133	9	3	3	NUM
ejpam-3648	133	10	c	c	PROPN
ejpam-3648	133	11	η	η	PROPN
ejpam-3648	133	12	−	−	PROPN
ejpam-3648	133	13	2	2	NUM
ejpam-3648	133	14	)	)	PUNCT
ejpam-3648	133	15	p3	p3	PROPN
ejpam-3648	133	16	−	−	PROPN
ejpam-3648	133	17	p2	p2	PROPN
ejpam-3648	133	18	(	(	PUNCT
ejpam-3648	133	19	15	15	NUM
ejpam-3648	133	20	c	c	PROPN
ejpam-3648	133	21	η	η	PROPN
ejpam-3648	133	22	−	−	PROPN
ejpam-3648	133	23	3	3	NUM
ejpam-3648	133	24	)	)	PUNCT
ejpam-3648	134	1	+	+	CCONJ
ejpam-3648	134	2	12	12	NUM
ejpam-3648	134	3	c	c	PROPN
ejpam-3648	134	4	η	η	PROPN
ejpam-3648	134	5	p1	p1	PROPN
ejpam-3648	134	6	.	.	PUNCT
ejpam-3648	135	1	proof	proof	NOUN
ejpam-3648	135	2	.	.	PUNCT
ejpam-3648	136	1	let	let	VERB
ejpam-3648	136	2	i0	i0	PROPN
ejpam-3648	136	3	,	,	PUNCT
ejpam-3648	136	4	i1	i1	PROPN
ejpam-3648	136	5	,	,	PUNCT
ejpam-3648	136	6	i2	i2	PROPN
ejpam-3648	136	7	,	,	PUNCT
ejpam-3648	136	8	and	and	CCONJ
ejpam-3648	136	9	i3	i3	NOUN
ejpam-3648	136	10	be	be	VERB
ejpam-3648	136	11	control	control	NOUN
ejpam-3648	136	12	points	point	NOUN
ejpam-3648	136	13	of	of	ADP
ejpam-3648	136	14	involute	involute	ADJ
ejpam-3648	136	15	α∗	α∗	NOUN
ejpam-3648	136	16	,	,	PUNCT
ejpam-3648	136	17	so	so	SCONJ
ejpam-3648	136	18	we	we	PRON
ejpam-3648	136	19	can	can	AUX
ejpam-3648	136	20	write	write	VERB
ejpam-3648	136	21	α∗	α∗	NOUN
ejpam-3648	136	22	(	(	PUNCT
ejpam-3648	136	23	t	t	NOUN
ejpam-3648	136	24	)	)	PUNCT
ejpam-3648	136	25	=	=	NOUN
ejpam-3648	137	1	[	[	PUNCT
ejpam-3648	137	2	t3	t3	PROPN
ejpam-3648	137	3	t2	t2	PROPN
ejpam-3648	137	4	t	t	PROPN
ejpam-3648	137	5	1	1	NUM
ejpam-3648	137	6	]	]	PUNCT
ejpam-3648	137	7			NOUN
ejpam-3648	137	8	−1	−1	NOUN
ejpam-3648	137	9	3	3	NUM
ejpam-3648	137	10	−3	−3	NOUN
ejpam-3648	137	11	1	1	NUM
ejpam-3648	137	12	3	3	NUM
ejpam-3648	137	13	−6	−6	NOUN
ejpam-3648	137	14	3	3	NUM
ejpam-3648	137	15	0	0	NUM
ejpam-3648	137	16	−3	−3	PROPN
ejpam-3648	137	17	3	3	NUM
ejpam-3648	137	18	0	0	NUM
ejpam-3648	137	19	0	0	NUM
ejpam-3648	137	20	1	1	NUM
ejpam-3648	137	21	0	0	NUM
ejpam-3648	137	22	0	0	NUM
ejpam-3648	137	23	0	0	NUM
ejpam-3648	137	24			NOUN
ejpam-3648	137	25			NOUN
ejpam-3648	137	26	i0	i0	PROPN
ejpam-3648	137	27	i1	i1	PROPN
ejpam-3648	137	28	i2	i2	PROPN
ejpam-3648	137	29	i3	i3	PROPN
ejpam-3648	137	30			PROPN
ejpam-3648	137	31	.	.	PUNCT
ejpam-3648	138	1	(	(	PUNCT
ejpam-3648	138	2	9	9	NUM
ejpam-3648	138	3	)	)	PUNCT
ejpam-3648	138	4	from	from	ADP
ejpam-3648	138	5	the	the	DET
ejpam-3648	138	6	equality	equality	NOUN
ejpam-3648	138	7	of	of	ADP
ejpam-3648	138	8	the	the	DET
ejpam-3648	138	9	left	left	ADJ
ejpam-3648	138	10	sides	side	NOUN
ejpam-3648	138	11	of	of	ADP
ejpam-3648	138	12	8	8	NUM
ejpam-3648	138	13	and	and	CCONJ
ejpam-3648	138	14	9	9	NUM
ejpam-3648	138	15	,	,	PUNCT
ejpam-3648	138	16	we	we	PRON
ejpam-3648	138	17	have	have	VERB
ejpam-3648	138	18	−1	−1	NOUN
ejpam-3648	139	1	3	3	NUM
ejpam-3648	139	2	−3	−3	NOUN
ejpam-3648	139	3	1	1	NUM
ejpam-3648	139	4	3	3	NUM
ejpam-3648	139	5	−6	−6	NOUN
ejpam-3648	139	6	3	3	NUM
ejpam-3648	139	7	0	0	NUM
ejpam-3648	139	8	−3	−3	PROPN
ejpam-3648	139	9	3	3	NUM
ejpam-3648	139	10	0	0	NUM
ejpam-3648	139	11	0	0	NUM
ejpam-3648	139	12	1	1	NUM
ejpam-3648	139	13	0	0	NUM
ejpam-3648	139	14	0	0	NUM
ejpam-3648	139	15	0	0	NUM
ejpam-3648	139	16			NOUN
ejpam-3648	139	17			NOUN
ejpam-3648	139	18	i0	i0	PROPN
ejpam-3648	139	19	i1	i1	PROPN
ejpam-3648	139	20	i2	i2	PROPN
ejpam-3648	139	21	i3	i3	PROPN
ejpam-3648	139	22			NOUN
ejpam-3648	139	23	=	=	X
ejpam-3648	139	24			NOUN
ejpam-3648	139	25	2p0	2p0	NUM
ejpam-3648	139	26	−	−	NUM
ejpam-3648	139	27	6p1	6p1	NUM
ejpam-3648	139	28	+	+	CCONJ
ejpam-3648	139	29	6p2	6p2	NUM
ejpam-3648	139	30	−	−	NOUN
ejpam-3648	139	31	2p3	2p3	NUM
ejpam-3648	139	32	(	(	PUNCT
ejpam-3648	139	33	−3−	−3−	PROPN
ejpam-3648	139	34	3c	3c	NUM
ejpam-3648	139	35	η	η	PROPN
ejpam-3648	139	36	)	)	PUNCT
ejpam-3648	139	37	p0	p0	NOUN
ejpam-3648	139	38	+	+	CCONJ
ejpam-3648	139	39	(	(	PUNCT
ejpam-3648	139	40	6	6	NUM
ejpam-3648	139	41	+	+	NUM
ejpam-3648	139	42	9c	9c	NUM
ejpam-3648	139	43	η	η	X
ejpam-3648	139	44	)	)	PUNCT
ejpam-3648	139	45	p1	p1	PROPN
ejpam-3648	139	46	−	−	PROPN
ejpam-3648	139	47	(	(	PUNCT
ejpam-3648	139	48	3	3	NUM
ejpam-3648	139	49	+	+	NUM
ejpam-3648	139	50	9c	9c	NUM
ejpam-3648	139	51	η	η	NOUN
ejpam-3648	139	52	)	)	PUNCT
ejpam-3648	139	53	p2	p2	PROPN
ejpam-3648	139	54	+	+	CCONJ
ejpam-3648	139	55	3c	3c	NUM
ejpam-3648	139	56	η	η	PROPN
ejpam-3648	139	57	p3	p3	PROPN
ejpam-3648	139	58	6c	6c	PROPN
ejpam-3648	139	59	η	η	PROPN
ejpam-3648	139	60	p0	p0	PROPN
ejpam-3648	139	61	−	−	PROPN
ejpam-3648	139	62	6c	6c	PROPN
ejpam-3648	139	63	η	η	PROPN
ejpam-3648	139	64	p2	p2	PROPN
ejpam-3648	139	65	(	(	PUNCT
ejpam-3648	139	66	1−	1−	NUM
ejpam-3648	139	67	3c	3c	NUM
ejpam-3648	139	68	η	η	PROPN
ejpam-3648	139	69	)	)	PUNCT
ejpam-3648	139	70	p0	p0	NOUN
ejpam-3648	139	71	+	+	CCONJ
ejpam-3648	139	72	3c	3c	NUM
ejpam-3648	139	73	η	η	PROPN
ejpam-3648	139	74	p1	p1	PROPN
ejpam-3648	139	75			NOUN
ejpam-3648	139	76	=	=	PUNCT
ejpam-3648	139	77			ADJ
ejpam-3648	139	78	2	2	NUM
ejpam-3648	139	79	−6	−6	NOUN
ejpam-3648	139	80	6	6	NUM
ejpam-3648	139	81	−2	−2	NOUN
ejpam-3648	139	82	(	(	PUNCT
ejpam-3648	139	83	−3−	−3−	PROPN
ejpam-3648	139	84	3c	3c	NUM
ejpam-3648	139	85	η	η	PROPN
ejpam-3648	139	86	)	)	PUNCT
ejpam-3648	139	87	(	(	PUNCT
ejpam-3648	139	88	6	6	NUM
ejpam-3648	139	89	+	+	SYM
ejpam-3648	139	90	9c	9c	NUM
ejpam-3648	139	91	η	η	NOUN
ejpam-3648	139	92	)	)	PUNCT
ejpam-3648	139	93	−	−	PROPN
ejpam-3648	139	94	(	(	PUNCT
ejpam-3648	139	95	3	3	NUM
ejpam-3648	139	96	+	+	NUM
ejpam-3648	139	97	9c	9c	NUM
ejpam-3648	139	98	η	η	PROPN
ejpam-3648	139	99	)	)	PUNCT
ejpam-3648	139	100	+3c	+3c	PROPN
ejpam-3648	139	101	η	η	PROPN
ejpam-3648	139	102	6c	6c	PROPN
ejpam-3648	139	103	η	η	PROPN
ejpam-3648	139	104	0	0	PUNCT
ejpam-3648	139	105	−6c	−6c	PROPN
ejpam-3648	139	106	η	η	PROPN
ejpam-3648	139	107	0	0	PROPN
ejpam-3648	139	108	(	(	PUNCT
ejpam-3648	139	109	1−	1−	NUM
ejpam-3648	139	110	3c	3c	NUM
ejpam-3648	139	111	η	η	PROPN
ejpam-3648	139	112	)	)	PUNCT
ejpam-3648	139	113	3c	3c	NUM
ejpam-3648	139	114	η	η	PROPN
ejpam-3648	139	115	0	0	SYM
ejpam-3648	139	116	0	0	NUM
ejpam-3648	139	117			NOUN
ejpam-3648	139	118			NOUN
ejpam-3648	139	119	p0	p0	NOUN
ejpam-3648	139	120	p1	p1	NOUN
ejpam-3648	139	121	p2	p2	PROPN
ejpam-3648	139	122	p3	p3	PROPN
ejpam-3648	139	123			PROPN
ejpam-3648	139	124	ş.	ş.	PROPN
ejpam-3648	139	125	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	139	126	,	,	PUNCT
ejpam-3648	139	127	s.	s.	PROPN
ejpam-3648	139	128	şenyurt	şenyurt	PROPN
ejpam-3648	139	129	/	/	SYM
ejpam-3648	139	130	eur	eur	PROPN
ejpam-3648	139	131	.	.	PUNCT
ejpam-3648	140	1	j.	j.	PROPN
ejpam-3648	140	2	pure	pure	PROPN
ejpam-3648	140	3	appl	appl	PROPN
ejpam-3648	140	4	.	.	PROPN
ejpam-3648	140	5	math	math	PROPN
ejpam-3648	140	6	,	,	PUNCT
ejpam-3648	140	7	13	13	NUM
ejpam-3648	140	8	(	(	PUNCT
ejpam-3648	140	9	2	2	NUM
ejpam-3648	140	10	)	)	PUNCT
ejpam-3648	140	11	(	(	PUNCT
ejpam-3648	140	12	2020	2020	NUM
ejpam-3648	140	13	)	)	PUNCT
ejpam-3648	140	14	,	,	PUNCT
ejpam-3648	140	15	216	216	NUM
ejpam-3648	140	16	-	-	SYM
ejpam-3648	140	17	226	226	NUM
ejpam-3648	140	18	222	222	NUM
ejpam-3648	140	19	using	use	VERB
ejpam-3648	140	20	the	the	DET
ejpam-3648	140	21	inverse	inverse	NOUN
ejpam-3648	140	22	matrix	matrix	PROPN
ejpam-3648	140	23	i0	i0	PROPN
ejpam-3648	140	24	i1	i1	PROPN
ejpam-3648	140	25	i2	i2	PROPN
ejpam-3648	140	26	i3	i3	PROPN
ejpam-3648	140	27			NOUN
ejpam-3648	140	28	=	=	PUNCT
ejpam-3648	140	29			NOUN
ejpam-3648	140	30	−1	−1	NOUN
ejpam-3648	140	31	3	3	NUM
ejpam-3648	140	32	−3	−3	NOUN
ejpam-3648	140	33	1	1	NUM
ejpam-3648	140	34	3	3	NUM
ejpam-3648	140	35	−6	−6	NOUN
ejpam-3648	140	36	3	3	NUM
ejpam-3648	140	37	0	0	NUM
ejpam-3648	140	38	−3	−3	PROPN
ejpam-3648	141	1	3	3	NUM
ejpam-3648	141	2	0	0	NUM
ejpam-3648	141	3	0	0	NUM
ejpam-3648	141	4	1	1	NUM
ejpam-3648	141	5	0	0	NUM
ejpam-3648	141	6	0	0	NUM
ejpam-3648	141	7	0	0	NUM
ejpam-3648	141	8			NOUN
ejpam-3648	141	9	−1	−1	NOUN
ejpam-3648	141	10			NOUN
ejpam-3648	141	11	2	2	NUM
ejpam-3648	141	12	−6	−6	NOUN
ejpam-3648	141	13	6	6	NUM
ejpam-3648	141	14	−2	−2	NOUN
ejpam-3648	141	15	(	(	PUNCT
ejpam-3648	141	16	−3−	−3−	PROPN
ejpam-3648	141	17	3c	3c	NUM
ejpam-3648	141	18	η	η	PROPN
ejpam-3648	141	19	)	)	PUNCT
ejpam-3648	141	20	(	(	PUNCT
ejpam-3648	141	21	6	6	NUM
ejpam-3648	141	22	+	+	SYM
ejpam-3648	141	23	9c	9c	NUM
ejpam-3648	141	24	η	η	NOUN
ejpam-3648	141	25	)	)	PUNCT
ejpam-3648	141	26	−	−	PROPN
ejpam-3648	141	27	(	(	PUNCT
ejpam-3648	141	28	3	3	NUM
ejpam-3648	141	29	+	+	NUM
ejpam-3648	141	30	9c	9c	NUM
ejpam-3648	141	31	η	η	PROPN
ejpam-3648	141	32	)	)	PUNCT
ejpam-3648	141	33	+3c	+3c	PROPN
ejpam-3648	141	34	η	η	PROPN
ejpam-3648	141	35	6c	6c	PROPN
ejpam-3648	141	36	η	η	PROPN
ejpam-3648	141	37	0	0	PUNCT
ejpam-3648	141	38	−6c	−6c	PROPN
ejpam-3648	141	39	η	η	PROPN
ejpam-3648	141	40	0	0	PROPN
ejpam-3648	141	41	(	(	PUNCT
ejpam-3648	141	42	1−	1−	NUM
ejpam-3648	141	43	3c	3c	NUM
ejpam-3648	141	44	η	η	PROPN
ejpam-3648	141	45	)	)	PUNCT
ejpam-3648	141	46	3c	3c	NUM
ejpam-3648	141	47	η	η	PROPN
ejpam-3648	141	48	0	0	SYM
ejpam-3648	141	49	0	0	NUM
ejpam-3648	141	50			NOUN
ejpam-3648	141	51			NOUN
ejpam-3648	141	52	p0	p0	NOUN
ejpam-3648	141	53	p1	p1	NOUN
ejpam-3648	141	54	p2	p2	PROPN
ejpam-3648	141	55	p3	p3	PROPN
ejpam-3648	141	56			PROPN
ejpam-3648	141	57	.	.	PUNCT
ejpam-3648	142	1	(	(	PUNCT
ejpam-3648	142	2	10	10	NUM
ejpam-3648	142	3	)	)	PUNCT
ejpam-3648	142	4	theorem	theorem	NOUN
ejpam-3648	142	5	12	12	NUM
ejpam-3648	142	6	.	.	PUNCT
ejpam-3648	143	1	the	the	DET
ejpam-3648	143	2	control	control	NOUN
ejpam-3648	143	3	points	point	NOUN
ejpam-3648	143	4	of	of	ADP
ejpam-3648	143	5	the	the	DET
ejpam-3648	143	6	involute	involute	NOUN
ejpam-3648	143	7	of	of	ADP
ejpam-3648	143	8	any	any	DET
ejpam-3648	143	9	cubic	cubic	ADJ
ejpam-3648	143	10	bezier	bezier	NOUN
ejpam-3648	143	11	curve	curve	NOUN
ejpam-3648	143	12	,	,	PUNCT
ejpam-3648	143	13	under	under	ADP
ejpam-3648	143	14	the	the	DET
ejpam-3648	143	15	condition	condition	NOUN
ejpam-3648	143	16	c	c	PROPN
ejpam-3648	143	17	η	η	PROPN
ejpam-3648	143	18	−	−	PROPN
ejpam-3648	143	19	t	t	PROPN
ejpam-3648	143	20	=	=	SYM
ejpam-3648	143	21	µ	µ	X
ejpam-3648	143	22	=	=	SYM
ejpam-3648	143	23	constant	constant	ADJ
ejpam-3648	143	24	,	,	PUNCT
ejpam-3648	143	25	can	can	AUX
ejpam-3648	143	26	be	be	AUX
ejpam-3648	143	27	given	give	VERB
ejpam-3648	143	28	,	,	PUNCT
ejpam-3648	143	29	i0	i0	PROPN
ejpam-3648	143	30	=	=	PROPN
ejpam-3648	143	31	3µp1	3µp1	NUM
ejpam-3648	143	32	−	−	PROPN
ejpam-3648	143	33	(	(	PUNCT
ejpam-3648	143	34	3µ−	3µ−	NUM
ejpam-3648	143	35	1)p0	1)p0	NUM
ejpam-3648	143	36	,	,	PUNCT
ejpam-3648	143	37	i1	i1	PROPN
ejpam-3648	143	38	=	=	PUNCT
ejpam-3648	143	39	2µp2	2µp2	NUM
ejpam-3648	143	40	−	−	NOUN
ejpam-3648	143	41	µp0	µp0	NOUN
ejpam-3648	143	42	−	−	PROPN
ejpam-3648	143	43	p1	p1	NOUN
ejpam-3648	143	44	(	(	PUNCT
ejpam-3648	143	45	µ−	µ−	PROPN
ejpam-3648	143	46	1	1	NUM
ejpam-3648	143	47	)	)	PUNCT
ejpam-3648	143	48	,	,	PUNCT
ejpam-3648	143	49	i2	i2	PROPN
ejpam-3648	143	50	=	=	PUNCT
ejpam-3648	143	51	µp3	µp3	NOUN
ejpam-3648	143	52	−	−	X
ejpam-3648	143	53	2µp1	2µp1	PUNCT
ejpam-3648	143	54	+	+	CCONJ
ejpam-3648	143	55	p2	p2	X
ejpam-3648	143	56	(	(	PUNCT
ejpam-3648	143	57	µ+	µ+	X
ejpam-3648	143	58	1	1	NUM
ejpam-3648	143	59	)	)	PUNCT
ejpam-3648	143	60	,	,	PUNCT
ejpam-3648	143	61	i3	i3	NOUN
ejpam-3648	143	62	=	=	SYM
ejpam-3648	143	63	(	(	PUNCT
ejpam-3648	143	64	3µ+	3µ+	NUM
ejpam-3648	143	65	1)p3	1)p3	PROPN
ejpam-3648	143	66	−	−	PROPN
ejpam-3648	143	67	3µp2	3µp2	NUM
ejpam-3648	143	68	.	.	PUNCT
ejpam-3648	144	1	proof	proof	NOUN
ejpam-3648	144	2	.	.	PUNCT
ejpam-3648	145	1	if	if	SCONJ
ejpam-3648	145	2	c	c	PROPN
ejpam-3648	145	3	η	η	PROPN
ejpam-3648	145	4	−	−	PROPN
ejpam-3648	145	5	t	t	PROPN
ejpam-3648	145	6	=	=	SYM
ejpam-3648	145	7	µ	µ	X
ejpam-3648	145	8	is	be	AUX
ejpam-3648	145	9	constant	constant	ADJ
ejpam-3648	145	10	,	,	PUNCT
ejpam-3648	145	11	α∗	α∗	NOUN
ejpam-3648	145	12	(	(	PUNCT
ejpam-3648	145	13	t	t	NOUN
ejpam-3648	145	14	)	)	PUNCT
ejpam-3648	146	1	=	=	NOUN
ejpam-3648	147	1	[	[	PUNCT
ejpam-3648	147	2	t3	t3	PROPN
ejpam-3648	147	3	t2	t2	PROPN
ejpam-3648	147	4	t	t	PROPN
ejpam-3648	147	5	1	1	NUM
ejpam-3648	147	6	]	]	PUNCT
ejpam-3648	147	7			NOUN
ejpam-3648	147	8	−1	−1	NOUN
ejpam-3648	147	9	3	3	NUM
ejpam-3648	147	10	−3	−3	NOUN
ejpam-3648	147	11	1	1	NUM
ejpam-3648	147	12	3	3	NUM
ejpam-3648	147	13	−6	−6	NOUN
ejpam-3648	147	14	3	3	NUM
ejpam-3648	147	15	0	0	NUM
ejpam-3648	147	16	−3	−3	PROPN
ejpam-3648	147	17	3	3	NUM
ejpam-3648	147	18	0	0	NUM
ejpam-3648	147	19	0	0	NUM
ejpam-3648	147	20	1	1	NUM
ejpam-3648	147	21	0	0	NUM
ejpam-3648	147	22	0	0	NUM
ejpam-3648	147	23	0	0	NUM
ejpam-3648	147	24			NOUN
ejpam-3648	147	25			NOUN
ejpam-3648	147	26	p0	p0	NOUN
ejpam-3648	147	27	p1	p1	NOUN
ejpam-3648	147	28	p2	p2	PROPN
ejpam-3648	147	29	p3	p3	PROPN
ejpam-3648	147	30			PROPN
ejpam-3648	147	31	+	+	NOUN
ejpam-3648	147	32	µ	µ	X
ejpam-3648	147	33	[	[	PUNCT
ejpam-3648	147	34	t2	t2	NOUN
ejpam-3648	147	35	t	t	PROPN
ejpam-3648	147	36	1	1	NUM
ejpam-3648	147	37	]	]	SYM
ejpam-3648	147	38			NOUN
ejpam-3648	147	39	1	1	NUM
ejpam-3648	147	40	−2	−2	NOUN
ejpam-3648	147	41	1	1	NUM
ejpam-3648	147	42	−2	−2	NOUN
ejpam-3648	147	43	2	2	NUM
ejpam-3648	147	44	0	0	NUM
ejpam-3648	147	45	1	1	NUM
ejpam-3648	147	46	0	0	NUM
ejpam-3648	147	47	0	0	NUM
ejpam-3648	147	48			NOUN
ejpam-3648	147	49	3	3	NUM
ejpam-3648	147	50	(	(	PUNCT
ejpam-3648	147	51	p1	p1	NOUN
ejpam-3648	147	52	−	−	PROPN
ejpam-3648	147	53	p0	p0	NOUN
ejpam-3648	147	54	)	)	PUNCT
ejpam-3648	147	55	3	3	NUM
ejpam-3648	147	56	(	(	PUNCT
ejpam-3648	147	57	p2	p2	PROPN
ejpam-3648	147	58	−	−	PROPN
ejpam-3648	147	59	p1	p1	NOUN
ejpam-3648	147	60	)	)	PUNCT
ejpam-3648	147	61	3	3	NUM
ejpam-3648	147	62	(	(	PUNCT
ejpam-3648	147	63	p3	p3	PROPN
ejpam-3648	147	64	−	−	PROPN
ejpam-3648	147	65	p2	p2	NOUN
ejpam-3648	147	66	)	)	PUNCT
ejpam-3648	147	67			NOUN
ejpam-3648	147	68	.	.	PUNCT
ejpam-3648	148	1	hence	hence	PROPN
ejpam-3648	148	2	−1	−1	NOUN
ejpam-3648	148	3	3	3	NUM
ejpam-3648	148	4	−3	−3	NOUN
ejpam-3648	148	5	1	1	NUM
ejpam-3648	148	6	3	3	NUM
ejpam-3648	148	7	−6	−6	NOUN
ejpam-3648	148	8	3	3	NUM
ejpam-3648	148	9	0	0	NUM
ejpam-3648	148	10	−3	−3	PROPN
ejpam-3648	148	11	3	3	NUM
ejpam-3648	148	12	0	0	NUM
ejpam-3648	148	13	0	0	NUM
ejpam-3648	148	14	1	1	NUM
ejpam-3648	148	15	0	0	NUM
ejpam-3648	148	16	0	0	NUM
ejpam-3648	148	17	0	0	NUM
ejpam-3648	148	18			NOUN
ejpam-3648	148	19			NOUN
ejpam-3648	148	20	i0	i0	PROPN
ejpam-3648	148	21	i1	i1	PROPN
ejpam-3648	148	22	i2	i2	PROPN
ejpam-3648	148	23	i3	i3	PROPN
ejpam-3648	148	24			PROPN
ejpam-3648	148	25	=	=	SYM
ejpam-3648	148	26			NOUN
ejpam-3648	148	27	−p0	−p0	PROPN
ejpam-3648	148	28	+	+	PROPN
ejpam-3648	148	29	3p1	3p1	NUM
ejpam-3648	148	30	−	−	ADP
ejpam-3648	148	31	3p2	3p2	NUM
ejpam-3648	148	32	+	+	CCONJ
ejpam-3648	148	33	p3	p3	PROPN
ejpam-3648	148	34	(	(	PUNCT
ejpam-3648	148	35	(	(	PUNCT
ejpam-3648	148	36	3−	3−	NUM
ejpam-3648	148	37	3µ)p0	3µ)p0	NUM
ejpam-3648	148	38	+	+	CCONJ
ejpam-3648	148	39	(	(	PUNCT
ejpam-3648	148	40	−6	−6	X
ejpam-3648	149	1	+	+	NUM
ejpam-3648	149	2	9µ)p1	9µ)p1	NUM
ejpam-3648	149	3	+	+	CCONJ
ejpam-3648	149	4	(	(	PUNCT
ejpam-3648	149	5	3−	3−	NUM
ejpam-3648	149	6	9µ)p2	9µ)p2	NUM
ejpam-3648	149	7	+	+	CCONJ
ejpam-3648	149	8	3µp3	3µp3	NUM
ejpam-3648	149	9	)	)	PUNCT
ejpam-3648	149	10	(	(	PUNCT
ejpam-3648	149	11	(	(	PUNCT
ejpam-3648	149	12	−3	−3	X
ejpam-3648	150	1	+	+	CCONJ
ejpam-3648	150	2	6µ)p0	6µ)p0	NUM
ejpam-3648	150	3	+	+	CCONJ
ejpam-3648	150	4	(	(	PUNCT
ejpam-3648	150	5	3−	3−	NUM
ejpam-3648	150	6	12µ)p1	12µ)p1	NUM
ejpam-3648	150	7	+	+	CCONJ
ejpam-3648	150	8	6µp2	6µp2	NUM
ejpam-3648	150	9	)	)	PUNCT
ejpam-3648	150	10	(	(	PUNCT
ejpam-3648	150	11	1−	1−	NUM
ejpam-3648	150	12	3µ)p0	3µ)p0	NUM
ejpam-3648	150	13	+	+	CCONJ
ejpam-3648	150	14	3µp1	3µp1	CCONJ
ejpam-3648	150	15			NOUN
ejpam-3648	150	16	=	=	SYM
ejpam-3648	150	17			NOUN
ejpam-3648	150	18	−1	−1	NOUN
ejpam-3648	150	19	3	3	NUM
ejpam-3648	150	20	−3	−3	NOUN
ejpam-3648	150	21	1	1	NUM
ejpam-3648	150	22	(	(	PUNCT
ejpam-3648	150	23	3−	3−	NUM
ejpam-3648	150	24	3µ	3µ	NUM
ejpam-3648	150	25	)	)	PUNCT
ejpam-3648	150	26	(	(	PUNCT
ejpam-3648	150	27	−6	−6	X
ejpam-3648	150	28	+	+	NUM
ejpam-3648	150	29	9µ	9µ	NUM
ejpam-3648	150	30	)	)	PUNCT
ejpam-3648	150	31	(	(	PUNCT
ejpam-3648	150	32	3−	3−	NUM
ejpam-3648	150	33	9µ	9µ	NUM
ejpam-3648	150	34	)	)	PUNCT
ejpam-3648	150	35	3µ	3µ	NUM
ejpam-3648	150	36	(	(	PUNCT
ejpam-3648	150	37	−3	−3	PROPN
ejpam-3648	150	38	+	+	NUM
ejpam-3648	150	39	6µ	6µ	NOUN
ejpam-3648	150	40	)	)	PUNCT
ejpam-3648	150	41	(	(	PUNCT
ejpam-3648	150	42	3−	3−	NUM
ejpam-3648	150	43	12µ	12µ	NOUN
ejpam-3648	150	44	)	)	PUNCT
ejpam-3648	150	45	6µ	6µ	NOUN
ejpam-3648	150	46	0	0	NUM
ejpam-3648	150	47	(	(	PUNCT
ejpam-3648	150	48	1−	1−	NUM
ejpam-3648	150	49	3µ	3µ	NUM
ejpam-3648	150	50	)	)	PUNCT
ejpam-3648	150	51	3µ	3µ	NUM
ejpam-3648	150	52	0	0	NUM
ejpam-3648	150	53	0	0	NUM
ejpam-3648	150	54			NOUN
ejpam-3648	150	55			NOUN
ejpam-3648	150	56	p0	p0	NOUN
ejpam-3648	150	57	p1	p1	NOUN
ejpam-3648	150	58	p2	p2	PROPN
ejpam-3648	150	59	p3	p3	PROPN
ejpam-3648	150	60			PROPN
ejpam-3648	150	61	using	use	VERB
ejpam-3648	150	62	the	the	DET
ejpam-3648	150	63	inverse	inverse	NOUN
ejpam-3648	150	64	matrix	matrix	NOUN
ejpam-3648	150	65	we	we	PRON
ejpam-3648	150	66	can	can	AUX
ejpam-3648	150	67	find	find	VERB
ejpam-3648	150	68	the	the	DET
ejpam-3648	150	69	control	control	NOUN
ejpam-3648	150	70	points	point	NOUN
ejpam-3648	150	71	of	of	ADP
ejpam-3648	150	72	the	the	DET
ejpam-3648	150	73	involute	involute	NOUN
ejpam-3648	150	74	of	of	ADP
ejpam-3648	150	75	any	any	DET
ejpam-3648	150	76	cubic	cubic	ADJ
ejpam-3648	150	77	bezier	bezier	NOUN
ejpam-3648	150	78	curve	curve	NOUN
ejpam-3648	150	79	with	with	ADP
ejpam-3648	150	80	constant	constant	ADJ
ejpam-3648	150	81	µ	µ	NOUN
ejpam-3648	150	82	,	,	PUNCT
ejpam-3648	150	83	based	base	VERB
ejpam-3648	150	84	on	on	ADP
ejpam-3648	150	85	the	the	DET
ejpam-3648	150	86	control	control	NOUN
ejpam-3648	150	87	points	point	NOUN
ejpam-3648	150	88	of	of	ADP
ejpam-3648	150	89	cubic	cubic	ADJ
ejpam-3648	150	90	bezier	bezier	NOUN
ejpam-3648	150	91	curve	curve	NOUN
ejpam-3648	150	92	,	,	PUNCT
ejpam-3648	150	93	as	as	ADP
ejpam-3648	150	94	in	in	ADP
ejpam-3648	150	95	the	the	DET
ejpam-3648	150	96	following	follow	VERB
ejpam-3648	150	97	way:	way:	PROPN
ejpam-3648	150	98	i0	i0	PROPN
ejpam-3648	150	99	i1	i1	PROPN
ejpam-3648	150	100	i2	i2	PROPN
ejpam-3648	150	101	i3	i3	PROPN
ejpam-3648	150	102			NOUN
ejpam-3648	150	103	=	=	PUNCT
ejpam-3648	150	104			NOUN
ejpam-3648	150	105	−1	−1	NOUN
ejpam-3648	150	106	3	3	NUM
ejpam-3648	150	107	−3	−3	NOUN
ejpam-3648	150	108	1	1	NUM
ejpam-3648	150	109	3	3	NUM
ejpam-3648	150	110	−6	−6	NOUN
ejpam-3648	150	111	3	3	NUM
ejpam-3648	150	112	0	0	NUM
ejpam-3648	150	113	−3	−3	PROPN
ejpam-3648	150	114	3	3	NUM
ejpam-3648	150	115	0	0	NUM
ejpam-3648	150	116	0	0	NUM
ejpam-3648	150	117	1	1	NUM
ejpam-3648	150	118	0	0	NUM
ejpam-3648	150	119	0	0	NUM
ejpam-3648	150	120	0	0	NUM
ejpam-3648	151	1			NOUN
ejpam-3648	151	2	−1	−1	NOUN
ejpam-3648	151	3			NOUN
ejpam-3648	151	4	−1	−1	NOUN
ejpam-3648	151	5	3	3	NUM
ejpam-3648	151	6	−3	−3	NOUN
ejpam-3648	151	7	1	1	NUM
ejpam-3648	151	8	(	(	PUNCT
ejpam-3648	151	9	3−	3−	NUM
ejpam-3648	151	10	3µ	3µ	NUM
ejpam-3648	151	11	)	)	PUNCT
ejpam-3648	151	12	(	(	PUNCT
ejpam-3648	151	13	−6	−6	X
ejpam-3648	151	14	+	+	NUM
ejpam-3648	151	15	9µ	9µ	NUM
ejpam-3648	151	16	)	)	PUNCT
ejpam-3648	151	17	(	(	PUNCT
ejpam-3648	151	18	3−	3−	NUM
ejpam-3648	151	19	9µ	9µ	NUM
ejpam-3648	151	20	)	)	PUNCT
ejpam-3648	151	21	3µ	3µ	NUM
ejpam-3648	151	22	(	(	PUNCT
ejpam-3648	151	23	−3	−3	PROPN
ejpam-3648	151	24	+	+	NUM
ejpam-3648	151	25	6µ	6µ	NOUN
ejpam-3648	151	26	)	)	PUNCT
ejpam-3648	151	27	(	(	PUNCT
ejpam-3648	151	28	3−	3−	NUM
ejpam-3648	151	29	12µ	12µ	NOUN
ejpam-3648	151	30	)	)	PUNCT
ejpam-3648	151	31	6µ	6µ	NOUN
ejpam-3648	151	32	0	0	NUM
ejpam-3648	151	33	(	(	PUNCT
ejpam-3648	151	34	1−	1−	NUM
ejpam-3648	151	35	3µ	3µ	NUM
ejpam-3648	151	36	)	)	PUNCT
ejpam-3648	151	37	3µ	3µ	NUM
ejpam-3648	151	38	0	0	NUM
ejpam-3648	151	39	0	0	NUM
ejpam-3648	151	40			NOUN
ejpam-3648	151	41			NOUN
ejpam-3648	151	42	p0	p0	NOUN
ejpam-3648	151	43	p1	p1	NOUN
ejpam-3648	151	44	p2	p2	PROPN
ejpam-3648	151	45	p3	p3	PROPN
ejpam-3648	151	46			PROPN
ejpam-3648	151	47	,	,	PUNCT
ejpam-3648	151	48	ş.	ş.	PROPN
ejpam-3648	151	49	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	151	50	,	,	PUNCT
ejpam-3648	151	51	s.	s.	PROPN
ejpam-3648	151	52	şenyurt	şenyurt	PROPN
ejpam-3648	151	53	/	/	SYM
ejpam-3648	151	54	eur	eur	PROPN
ejpam-3648	151	55	.	.	PUNCT
ejpam-3648	152	1	j.	j.	PROPN
ejpam-3648	152	2	pure	pure	PROPN
ejpam-3648	152	3	appl	appl	PROPN
ejpam-3648	152	4	.	.	PROPN
ejpam-3648	152	5	math	math	PROPN
ejpam-3648	152	6	,	,	PUNCT
ejpam-3648	152	7	13	13	NUM
ejpam-3648	152	8	(	(	PUNCT
ejpam-3648	152	9	2	2	NUM
ejpam-3648	152	10	)	)	PUNCT
ejpam-3648	152	11	(	(	PUNCT
ejpam-3648	152	12	2020	2020	NUM
ejpam-3648	152	13	)	)	PUNCT
ejpam-3648	152	14	,	,	PUNCT
ejpam-3648	152	15	216	216	NUM
ejpam-3648	152	16	-	-	SYM
ejpam-3648	152	17	226	226	NUM
ejpam-3648	152	18	223	223	NUM
ejpam-3648	152	19			NOUN
ejpam-3648	152	20	i0	i0	PROPN
ejpam-3648	152	21	i1	i1	PROPN
ejpam-3648	152	22	i2	i2	PROPN
ejpam-3648	152	23	i3	i3	PROPN
ejpam-3648	152	24			NOUN
ejpam-3648	152	25	=	=	PUNCT
ejpam-3648	152	26			NOUN
ejpam-3648	152	27	0	0	NUM
ejpam-3648	152	28	0	0	NUM
ejpam-3648	152	29	0	0	NUM
ejpam-3648	152	30	1	1	NUM
ejpam-3648	152	31	0	0	NUM
ejpam-3648	152	32	0	0	NUM
ejpam-3648	152	33	1	1	NUM
ejpam-3648	152	34	3	3	NUM
ejpam-3648	152	35	1	1	NUM
ejpam-3648	152	36	0	0	NUM
ejpam-3648	152	37	1	1	NUM
ejpam-3648	152	38	3	3	NUM
ejpam-3648	152	39	2	2	NUM
ejpam-3648	152	40	3	3	NUM
ejpam-3648	152	41	1	1	NUM
ejpam-3648	152	42	1	1	NUM
ejpam-3648	152	43	1	1	NUM
ejpam-3648	152	44	1	1	NUM
ejpam-3648	152	45	1	1	NUM
ejpam-3648	152	46			NOUN
ejpam-3648	152	47			NOUN
ejpam-3648	152	48	−1	−1	NOUN
ejpam-3648	152	49	3	3	NUM
ejpam-3648	152	50	−3	−3	NOUN
ejpam-3648	152	51	1	1	NUM
ejpam-3648	152	52	(	(	PUNCT
ejpam-3648	152	53	3−	3−	NUM
ejpam-3648	152	54	3µ	3µ	NUM
ejpam-3648	152	55	)	)	PUNCT
ejpam-3648	152	56	(	(	PUNCT
ejpam-3648	152	57	−6	−6	X
ejpam-3648	152	58	+	+	NUM
ejpam-3648	152	59	9µ	9µ	NUM
ejpam-3648	152	60	)	)	PUNCT
ejpam-3648	152	61	(	(	PUNCT
ejpam-3648	152	62	3−	3−	NUM
ejpam-3648	152	63	9µ	9µ	NUM
ejpam-3648	152	64	)	)	PUNCT
ejpam-3648	152	65	3µ	3µ	NUM
ejpam-3648	152	66	(	(	PUNCT
ejpam-3648	152	67	−3	−3	PROPN
ejpam-3648	152	68	+	+	NUM
ejpam-3648	152	69	6µ	6µ	NOUN
ejpam-3648	152	70	)	)	PUNCT
ejpam-3648	152	71	(	(	PUNCT
ejpam-3648	152	72	3−	3−	NUM
ejpam-3648	152	73	12µ	12µ	NOUN
ejpam-3648	152	74	)	)	PUNCT
ejpam-3648	152	75	6µ	6µ	NOUN
ejpam-3648	152	76	0	0	NUM
ejpam-3648	152	77	(	(	PUNCT
ejpam-3648	152	78	1−	1−	NUM
ejpam-3648	152	79	3µ	3µ	NUM
ejpam-3648	152	80	)	)	PUNCT
ejpam-3648	152	81	3µ	3µ	NUM
ejpam-3648	152	82	0	0	NUM
ejpam-3648	152	83	0	0	NUM
ejpam-3648	152	84			NOUN
ejpam-3648	152	85			NOUN
ejpam-3648	152	86	p0	p0	NOUN
ejpam-3648	152	87	p1	p1	NOUN
ejpam-3648	152	88	p2	p2	PROPN
ejpam-3648	152	89	p3	p3	PROPN
ejpam-3648	152	90			NOUN
ejpam-3648	152	91	.	.	PUNCT
ejpam-3648	153	1	(	(	PUNCT
ejpam-3648	153	2	11	11	NUM
ejpam-3648	153	3	)	)	PUNCT
ejpam-3648	153	4	2.1	2.1	NUM
ejpam-3648	153	5	.	.	PUNCT
ejpam-3648	154	1	frenet	frenet	ADJ
ejpam-3648	154	2	apparatus	apparatus	NOUN
ejpam-3648	154	3	of	of	ADP
ejpam-3648	154	4	the	the	DET
ejpam-3648	154	5	involute	involute	ADJ
ejpam-3648	154	6	curve	curve	NOUN
ejpam-3648	154	7	of	of	ADP
ejpam-3648	154	8	any	any	DET
ejpam-3648	154	9	cubic	cubic	ADJ
ejpam-3648	154	10	bezier	bezier	NOUN
ejpam-3648	154	11	curve	curve	NOUN
ejpam-3648	154	12	in	in	ADP
ejpam-3648	154	13	e3	e3	NOUN
ejpam-3648	154	14	theorem	theorem	ADJ
ejpam-3648	154	15	13	13	NUM
ejpam-3648	154	16	.	.	PUNCT
ejpam-3648	155	1	tangent	tangent	ADJ
ejpam-3648	155	2	vector	vector	NOUN
ejpam-3648	155	3	field	field	NOUN
ejpam-3648	155	4	of	of	ADP
ejpam-3648	155	5	involute	involute	ADJ
ejpam-3648	155	6	curve	curve	NOUN
ejpam-3648	155	7	of	of	ADP
ejpam-3648	155	8	any	any	DET
ejpam-3648	155	9	cubic	cubic	ADJ
ejpam-3648	155	10	bezier	bezier	NOUN
ejpam-3648	155	11	curve	curve	NOUN
ejpam-3648	155	12	is	be	AUX
ejpam-3648	155	13	t	t	NOUN
ejpam-3648	155	14	∗	∗	NOUN
ejpam-3648	155	15	=	=	SYM
ejpam-3648	155	16	6	6	NUM
ejpam-3648	155	17	mη	mη	NOUN
ejpam-3648	155	18	[	[	PUNCT
ejpam-3648	155	19	t4	t4	PROPN
ejpam-3648	155	20	t3	t3	PROPN
ejpam-3648	155	21	t2	t2	PROPN
ejpam-3648	155	22	t1	t1	NOUN
ejpam-3648	155	23	1	1	NUM
ejpam-3648	155	24	]	]	PUNCT
ejpam-3648	155	25			ADJ
ejpam-3648	155	26	n11	n11	PROPN
ejpam-3648	155	27	n12	n12	PROPN
ejpam-3648	155	28	n13	n13	PROPN
ejpam-3648	155	29	n21	n21	PROPN
ejpam-3648	155	30	n22	n22	PROPN
ejpam-3648	155	31	n23	n23	PROPN
ejpam-3648	155	32	n31	n31	ADJ
ejpam-3648	155	33	n32	n32	NOUN
ejpam-3648	155	34	n33	n33	PROPN
ejpam-3648	155	35	n41	n41	PROPN
ejpam-3648	155	36	n41	n41	PROPN
ejpam-3648	155	37	n43	n43	PROPN
ejpam-3648	155	38	n51	n51	PROPN
ejpam-3648	155	39	n51	n51	PROPN
ejpam-3648	155	40	n53	n53	NOUN
ejpam-3648	155	41			NOUN
ejpam-3648	155	42	.	.	PUNCT
ejpam-3648	156	1	proof	proof	NOUN
ejpam-3648	156	2	.	.	PUNCT
ejpam-3648	157	1	we	we	PRON
ejpam-3648	157	2	have	have	AUX
ejpam-3648	157	3	already	already	ADV
ejpam-3648	157	4	known	know	VERB
ejpam-3648	157	5	that	that	SCONJ
ejpam-3648	157	6	tangent	tangent	ADJ
ejpam-3648	157	7	vector	vector	NOUN
ejpam-3648	157	8	field	field	NOUN
ejpam-3648	157	9	of	of	ADP
ejpam-3648	157	10	involute	involute	ADJ
ejpam-3648	157	11	curve	curve	NOUN
ejpam-3648	157	12	t	t	PROPN
ejpam-3648	157	13	∗	∗	NOUN
ejpam-3648	157	14	is	be	AUX
ejpam-3648	157	15	lineer	lineer	NOUN
ejpam-3648	157	16	dependent	dependent	ADJ
ejpam-3648	157	17	n	n	CCONJ
ejpam-3648	157	18	,	,	PUNCT
ejpam-3648	157	19	that	that	PRON
ejpam-3648	157	20	is	be	AUX
ejpam-3648	157	21	why	why	SCONJ
ejpam-3648	157	22	t	t	NOUN
ejpam-3648	157	23	∗	∗	NOUN
ejpam-3648	157	24	=	=	SYM
ejpam-3648	157	25	n.	n.	NOUN
ejpam-3648	157	26	theorem	theorem	VERB
ejpam-3648	157	27	14	14	NUM
ejpam-3648	157	28	.	.	PUNCT
ejpam-3648	158	1	normal	normal	ADJ
ejpam-3648	158	2	vector	vector	NOUN
ejpam-3648	158	3	field	field	NOUN
ejpam-3648	158	4	of	of	ADP
ejpam-3648	158	5	involute	involute	ADJ
ejpam-3648	158	6	α∗of	α∗of	NUM
ejpam-3648	158	7	any	any	DET
ejpam-3648	158	8	cubic	cubic	ADJ
ejpam-3648	158	9	bezier	bezier	NOUN
ejpam-3648	158	10	curve	curve	NOUN
ejpam-3648	158	11	in	in	ADP
ejpam-3648	158	12	e3is	e3is	PRON
ejpam-3648	158	13	n∗	n∗	PROPN
ejpam-3648	158	14	=	=	PRON
ejpam-3648	159	1	[	[	PUNCT
ejpam-3648	159	2	t2	t2	NOUN
ejpam-3648	159	3	t	t	PROPN
ejpam-3648	159	4	1	1	NUM
ejpam-3648	159	5	]	]	PUNCT
ejpam-3648	159	6	η	η	PROPN
ejpam-3648	159	7	(	(	PUNCT
ejpam-3648	159	8	κ2+τ2	κ2+τ2	NOUN
ejpam-3648	159	9	)	)	PUNCT
ejpam-3648	159	10	1	1	NUM
ejpam-3648	159	11	2	2	NUM
ejpam-3648	159	12	κ	κ	PRON
ejpam-3648	159	13			NOUN
ejpam-3648	159	14	2x1	2x1	NUM
ejpam-3648	159	15	−	−	NOUN
ejpam-3648	160	1	x0	x0	PROPN
ejpam-3648	161	1	−	−	PROPN
ejpam-3648	162	1	x2	x2	INTJ
ejpam-3648	163	1	+	+	CCONJ
ejpam-3648	163	2	6ητ	6ητ	NOUN
ejpam-3648	163	3	mκ	mκ	PROPN
ejpam-3648	163	4	b11	b11	PROPN
ejpam-3648	164	1	2y1	2y1	NUM
ejpam-3648	165	1	−	−	PROPN
ejpam-3648	165	2	y0	y0	NOUN
ejpam-3648	165	3	−	−	NOUN
ejpam-3648	166	1	y2	y2	NOUN
ejpam-3648	166	2	+	+	CCONJ
ejpam-3648	166	3	6ητ	6ητ	NOUN
ejpam-3648	166	4	mκ	mκ	ADP
ejpam-3648	166	5	b12	b12	NOUN
ejpam-3648	166	6	2z1	2z1	NUM
ejpam-3648	167	1	−	−	PROPN
ejpam-3648	167	2	z0	z0	PROPN
ejpam-3648	167	3	−	−	PROPN
ejpam-3648	167	4	z2	z2	PROPN
ejpam-3648	167	5	+	+	CCONJ
ejpam-3648	167	6	6ητ	6ητ	NOUN
ejpam-3648	167	7	mκ	mκ	AUX
ejpam-3648	167	8	b13	b13	NOUN
ejpam-3648	167	9	2x0	2x0	NUM
ejpam-3648	167	10	−	−	NOUN
ejpam-3648	167	11	2x1	2x1	NUM
ejpam-3648	168	1	+	+	CCONJ
ejpam-3648	168	2	6ητ	6ητ	NOUN
ejpam-3648	168	3	mκ	mκ	PROPN
ejpam-3648	168	4	b21	b21	PROPN
ejpam-3648	168	5	2y0	2y0	NUM
ejpam-3648	168	6	−	−	NOUN
ejpam-3648	168	7	2y1	2y1	NUM
ejpam-3648	169	1	+	+	CCONJ
ejpam-3648	169	2	6ητ	6ητ	NOUN
ejpam-3648	169	3	mκ	mκ	PROPN
ejpam-3648	169	4	b22	b22	PROPN
ejpam-3648	169	5	2z0	2z0	NUM
ejpam-3648	169	6	−	−	NUM
ejpam-3648	170	1	2z1	2z1	NUM
ejpam-3648	171	1	+	+	CCONJ
ejpam-3648	171	2	6ητ	6ητ	NOUN
ejpam-3648	171	3	mκ	mκ	PROPN
ejpam-3648	171	4	b23	b23	PROPN
ejpam-3648	171	5	6ητ	6ητ	NOUN
ejpam-3648	171	6	mκ	mκ	ADP
ejpam-3648	171	7	b31	b31	PROPN
ejpam-3648	172	1	−	−	PROPN
ejpam-3648	172	2	x0	x0	PROPN
ejpam-3648	172	3	6ητ	6ητ	NOUN
ejpam-3648	172	4	mκ	mκ	ADP
ejpam-3648	172	5	b32	b32	PROPN
ejpam-3648	173	1	−	−	NUM
ejpam-3648	173	2	y0	y0	PROPN
ejpam-3648	173	3	6ητ	6ητ	NOUN
ejpam-3648	173	4	mκ	mκ	PROPN
ejpam-3648	173	5	b33	b33	NOUN
ejpam-3648	173	6	−	−	PROPN
ejpam-3648	173	7	z0	z0	PROPN
ejpam-3648	173	8			NOUN
ejpam-3648	173	9	.	.	PUNCT
ejpam-3648	174	1	proof	proof	NOUN
ejpam-3648	174	2	.	.	PUNCT
ejpam-3648	175	1	since	since	SCONJ
ejpam-3648	175	2	n∗	n∗	PROPN
ejpam-3648	175	3	=	=	PUNCT
ejpam-3648	175	4	−κt	−κt	PROPN
ejpam-3648	175	5	+	+	CCONJ
ejpam-3648	175	6	τb	τb	PROPN
ejpam-3648	175	7	(	(	PUNCT
ejpam-3648	175	8	κ2	κ2	NOUN
ejpam-3648	175	9	+	+	CCONJ
ejpam-3648	175	10	τ2	τ2	NOUN
ejpam-3648	175	11	)	)	PUNCT
ejpam-3648	175	12	1	1	NUM
ejpam-3648	175	13	2	2	NUM
ejpam-3648	175	14	,	,	PUNCT
ejpam-3648	175	15	we	we	PRON
ejpam-3648	175	16	have	have	VERB
ejpam-3648	175	17	n∗	n∗	PROPN
ejpam-3648	175	18	=	=	PUNCT
ejpam-3648	175	19	−κ	−κ	PROPN
ejpam-3648	175	20	η	η	PROPN
ejpam-3648	175	21	[	[	X
ejpam-3648	175	22	t2	t2	PROPN
ejpam-3648	175	23	t	t	PROPN
ejpam-3648	175	24	1	1	NUM
ejpam-3648	175	25	]	]	SYM
ejpam-3648	175	26			NOUN
ejpam-3648	175	27	1	1	NUM
ejpam-3648	175	28	−2	−2	NOUN
ejpam-3648	175	29	1	1	NUM
ejpam-3648	175	30	−2	−2	NOUN
ejpam-3648	175	31	2	2	NUM
ejpam-3648	175	32	0	0	NUM
ejpam-3648	175	33	1	1	NUM
ejpam-3648	175	34	0	0	NUM
ejpam-3648	175	35	0	0	NUM
ejpam-3648	176	1			NOUN
ejpam-3648	176	2	x0	x0	NOUN
ejpam-3648	176	3	y0	y0	PROPN
ejpam-3648	176	4	z0	z0	NOUN
ejpam-3648	176	5	x1	x1	NUM
ejpam-3648	176	6	y1	y1	PROPN
ejpam-3648	176	7	z1	z1	VERB
ejpam-3648	176	8	x2	x2	PROPN
ejpam-3648	176	9	y2	y2	PROPN
ejpam-3648	176	10	z2	z2	PROPN
ejpam-3648	176	11	+	+	PROPN
ejpam-3648	176	12	τ6	τ6	PROPN
ejpam-3648	176	13	m	m	VERB
ejpam-3648	176	14	[	[	PUNCT
ejpam-3648	176	15	t2	t2	NOUN
ejpam-3648	176	16	t	t	PROPN
ejpam-3648	176	17	1	1	NUM
ejpam-3648	176	18	]	]	PUNCT
ejpam-3648	176	19			PROPN
ejpam-3648	176	20	b11	b11	NOUN
ejpam-3648	176	21	b12	b12	NOUN
ejpam-3648	176	22	b13	b13	PROPN
ejpam-3648	176	23	b21	b21	PROPN
ejpam-3648	176	24	b22	b22	PROPN
ejpam-3648	176	25	b23	b23	PROPN
ejpam-3648	176	26	b31	b31	PROPN
ejpam-3648	176	27	b32	b32	PROPN
ejpam-3648	176	28	b33	b33	NOUN
ejpam-3648	176	29			NOUN
ejpam-3648	176	30	(	(	PUNCT
ejpam-3648	176	31	κ2	κ2	NOUN
ejpam-3648	176	32	+	+	CCONJ
ejpam-3648	176	33	τ2	τ2	NOUN
ejpam-3648	176	34	)	)	PUNCT
ejpam-3648	176	35	1	1	NUM
ejpam-3648	176	36	2	2	NUM
ejpam-3648	176	37	n∗	n∗	NOUN
ejpam-3648	176	38	=	=	SYM
ejpam-3648	176	39	[	[	PUNCT
ejpam-3648	176	40	t2	t2	NOUN
ejpam-3648	176	41	t	t	PROPN
ejpam-3648	176	42	1	1	NUM
ejpam-3648	176	43	]	]	PUNCT
ejpam-3648	176	44	(	(	PUNCT
ejpam-3648	176	45	κ2	κ2	NOUN
ejpam-3648	176	46	+	+	CCONJ
ejpam-3648	176	47	τ2	τ2	NOUN
ejpam-3648	176	48	)	)	PUNCT
ejpam-3648	176	49	1	1	NUM
ejpam-3648	176	50	2	2	NUM
ejpam-3648	176	51	−κ	−κ	ADP
ejpam-3648	176	52	η	η	PROPN
ejpam-3648	176	53			PROPN
ejpam-3648	176	54	1	1	NUM
ejpam-3648	176	55	−2	−2	NOUN
ejpam-3648	176	56	1	1	NUM
ejpam-3648	176	57	−2	−2	NOUN
ejpam-3648	176	58	2	2	NUM
ejpam-3648	176	59	0	0	NUM
ejpam-3648	176	60	1	1	NUM
ejpam-3648	176	61	0	0	NUM
ejpam-3648	176	62	0	0	NUM
ejpam-3648	177	1			NOUN
ejpam-3648	177	2	x0	x0	NOUN
ejpam-3648	177	3	y0	y0	PROPN
ejpam-3648	177	4	z0	z0	NOUN
ejpam-3648	177	5	x1	x1	NUM
ejpam-3648	177	6	y1	y1	PROPN
ejpam-3648	177	7	z1	z1	VERB
ejpam-3648	177	8	x2	x2	PROPN
ejpam-3648	177	9	y2	y2	PROPN
ejpam-3648	177	10	z2	z2	PROPN
ejpam-3648	177	11	+	+	PROPN
ejpam-3648	177	12	6τ	6τ	PROPN
ejpam-3648	177	13	m	m	NOUN
ejpam-3648	177	14			NOUN
ejpam-3648	177	15	b11	b11	NUM
ejpam-3648	177	16	b12	b12	NOUN
ejpam-3648	177	17	b13	b13	PROPN
ejpam-3648	177	18	b21	b21	PROPN
ejpam-3648	177	19	b22	b22	PROPN
ejpam-3648	177	20	b23	b23	PROPN
ejpam-3648	177	21	b31	b31	PROPN
ejpam-3648	177	22	b32	b32	PROPN
ejpam-3648	177	23	b33	b33	NOUN
ejpam-3648	177	24			NOUN
ejpam-3648	177	25	.	.	PUNCT
ejpam-3648	178	1	hence	hence	ADV
ejpam-3648	178	2	it	it	PRON
ejpam-3648	178	3	is	be	AUX
ejpam-3648	178	4	easy	easy	ADJ
ejpam-3648	178	5	to	to	PART
ejpam-3648	178	6	calculate	calculate	VERB
ejpam-3648	178	7	the	the	DET
ejpam-3648	178	8	following	following	ADJ
ejpam-3648	178	9	result	result	NOUN
ejpam-3648	178	10	n∗	n∗	PROPN
ejpam-3648	179	1	=	=	PRON
ejpam-3648	179	2	[	[	PUNCT
ejpam-3648	179	3	t2	t2	NOUN
ejpam-3648	179	4	t	t	PROPN
ejpam-3648	179	5	1	1	NUM
ejpam-3648	179	6	]	]	PUNCT
ejpam-3648	179	7	η	η	PROPN
ejpam-3648	179	8	(	(	PUNCT
ejpam-3648	179	9	κ2+τ2	κ2+τ2	NOUN
ejpam-3648	179	10	)	)	PUNCT
ejpam-3648	179	11	1	1	NUM
ejpam-3648	179	12	2	2	NUM
ejpam-3648	179	13	κ	κ	PRON
ejpam-3648	179	14			NOUN
ejpam-3648	179	15	2x1	2x1	NUM
ejpam-3648	179	16	−	−	NOUN
ejpam-3648	179	17	x0	x0	PROPN
ejpam-3648	179	18	−	−	PROPN
ejpam-3648	180	1	x2	x2	INTJ
ejpam-3648	181	1	+	+	CCONJ
ejpam-3648	181	2	6ητ	6ητ	NOUN
ejpam-3648	181	3	mκ	mκ	PROPN
ejpam-3648	181	4	b11	b11	PROPN
ejpam-3648	182	1	2y1	2y1	NUM
ejpam-3648	183	1	−	−	PROPN
ejpam-3648	183	2	y0	y0	NOUN
ejpam-3648	183	3	−	−	NOUN
ejpam-3648	184	1	y2	y2	NOUN
ejpam-3648	184	2	+	+	CCONJ
ejpam-3648	184	3	6ητ	6ητ	NOUN
ejpam-3648	184	4	mκ	mκ	ADP
ejpam-3648	184	5	b12	b12	NOUN
ejpam-3648	184	6	2z1	2z1	NUM
ejpam-3648	185	1	−	−	PROPN
ejpam-3648	185	2	z0	z0	PROPN
ejpam-3648	185	3	−	−	PROPN
ejpam-3648	185	4	z2	z2	PROPN
ejpam-3648	185	5	+	+	CCONJ
ejpam-3648	185	6	6ητ	6ητ	NOUN
ejpam-3648	185	7	mκ	mκ	AUX
ejpam-3648	185	8	b13	b13	NOUN
ejpam-3648	185	9	2x0	2x0	NUM
ejpam-3648	185	10	−	−	NOUN
ejpam-3648	185	11	2x1	2x1	NUM
ejpam-3648	186	1	+	+	CCONJ
ejpam-3648	186	2	6ητ	6ητ	NOUN
ejpam-3648	186	3	mκ	mκ	PROPN
ejpam-3648	186	4	b21	b21	PROPN
ejpam-3648	186	5	2y0	2y0	NUM
ejpam-3648	186	6	−	−	NOUN
ejpam-3648	186	7	2y1	2y1	NUM
ejpam-3648	187	1	+	+	CCONJ
ejpam-3648	187	2	6ητ	6ητ	NOUN
ejpam-3648	187	3	mκ	mκ	PROPN
ejpam-3648	187	4	b22	b22	PROPN
ejpam-3648	187	5	2z0	2z0	NUM
ejpam-3648	187	6	−	−	NUM
ejpam-3648	188	1	2z1	2z1	NUM
ejpam-3648	189	1	+	+	CCONJ
ejpam-3648	189	2	6ητ	6ητ	NOUN
ejpam-3648	189	3	mκ	mκ	PROPN
ejpam-3648	189	4	b23	b23	PROPN
ejpam-3648	189	5	6ητ	6ητ	NOUN
ejpam-3648	189	6	mκ	mκ	ADP
ejpam-3648	189	7	b31	b31	PROPN
ejpam-3648	190	1	−	−	PROPN
ejpam-3648	190	2	x0	x0	PROPN
ejpam-3648	190	3	6ητ	6ητ	NOUN
ejpam-3648	190	4	mκ	mκ	ADP
ejpam-3648	190	5	b32	b32	PROPN
ejpam-3648	191	1	−	−	NUM
ejpam-3648	191	2	y0	y0	PROPN
ejpam-3648	191	3	6ητ	6ητ	NOUN
ejpam-3648	191	4	mκ	mκ	PROPN
ejpam-3648	191	5	b33	b33	NOUN
ejpam-3648	191	6	−	−	PROPN
ejpam-3648	191	7	z0	z0	PROPN
ejpam-3648	191	8			NOUN
ejpam-3648	191	9	.	.	PUNCT
ejpam-3648	192	1	ş.	ş.	PROPN
ejpam-3648	192	2	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	192	3	,	,	PUNCT
ejpam-3648	192	4	s.	s.	PROPN
ejpam-3648	192	5	şenyurt	şenyurt	PROPN
ejpam-3648	192	6	/	/	SYM
ejpam-3648	192	7	eur	eur	PROPN
ejpam-3648	192	8	.	.	PUNCT
ejpam-3648	193	1	j.	j.	PROPN
ejpam-3648	193	2	pure	pure	PROPN
ejpam-3648	193	3	appl	appl	PROPN
ejpam-3648	193	4	.	.	PROPN
ejpam-3648	193	5	math	math	PROPN
ejpam-3648	193	6	,	,	PUNCT
ejpam-3648	193	7	13	13	NUM
ejpam-3648	193	8	(	(	PUNCT
ejpam-3648	193	9	2	2	NUM
ejpam-3648	193	10	)	)	PUNCT
ejpam-3648	193	11	(	(	PUNCT
ejpam-3648	193	12	2020	2020	NUM
ejpam-3648	193	13	)	)	PUNCT
ejpam-3648	193	14	,	,	PUNCT
ejpam-3648	193	15	216	216	NUM
ejpam-3648	193	16	-	-	SYM
ejpam-3648	193	17	226	226	NUM
ejpam-3648	193	18	224	224	NUM
ejpam-3648	193	19	theorem	theorem	VERB
ejpam-3648	193	20	15	15	NUM
ejpam-3648	193	21	.	.	PUNCT
ejpam-3648	194	1	binormal	binormal	ADJ
ejpam-3648	194	2	vector	vector	NOUN
ejpam-3648	194	3	field	field	NOUN
ejpam-3648	194	4	of	of	ADP
ejpam-3648	194	5	involute	involute	ADJ
ejpam-3648	194	6	α∗of	α∗of	NUM
ejpam-3648	194	7	any	any	DET
ejpam-3648	194	8	cubic	cubic	ADJ
ejpam-3648	194	9	bezier	bezier	NOUN
ejpam-3648	194	10	curve	curve	NOUN
ejpam-3648	194	11	in	in	ADP
ejpam-3648	194	12	e3is	e3is	NUM
ejpam-3648	194	13	b∗	b∗	ADJ
ejpam-3648	195	1	=	=	PUNCT
ejpam-3648	196	1	[	[	PUNCT
ejpam-3648	196	2	t2	t2	NOUN
ejpam-3648	196	3	t	t	PROPN
ejpam-3648	196	4	1	1	NUM
ejpam-3648	196	5	]	]	PUNCT
ejpam-3648	196	6	(	(	PUNCT
ejpam-3648	196	7	κ2+τ2	κ2+τ2	NOUN
ejpam-3648	196	8	)	)	PUNCT
ejpam-3648	196	9	1	1	NUM
ejpam-3648	196	10	2	2	NUM
ejpam-3648	196	11	τ	τ	X
ejpam-3648	196	12	η	η	PROPN
ejpam-3648	196	13			PROPN
ejpam-3648	196	14	x0	x0	PROPN
ejpam-3648	196	15	−	−	PROPN
ejpam-3648	197	1	2x1	2x1	NUM
ejpam-3648	198	1	+	+	NUM
ejpam-3648	198	2	x2	x2	PROPN
ejpam-3648	198	3	+	+	CCONJ
ejpam-3648	198	4	6ηκ	6ηκ	ADJ
ejpam-3648	198	5	mτ	mτ	NOUN
ejpam-3648	198	6	b11	b11	PROPN
ejpam-3648	198	7	y0	y0	PROPN
ejpam-3648	198	8	−	−	PROPN
ejpam-3648	198	9	2y1	2y1	NUM
ejpam-3648	199	1	+	+	CCONJ
ejpam-3648	200	1	y2	y2	PROPN
ejpam-3648	200	2	+	+	CCONJ
ejpam-3648	200	3	6ηκ	6ηκ	NOUN
ejpam-3648	200	4	mτ	mτ	NOUN
ejpam-3648	200	5	b12	b12	NOUN
ejpam-3648	200	6	z0	z0	PROPN
ejpam-3648	200	7	−	−	PROPN
ejpam-3648	200	8	2z1	2z1	PROPN
ejpam-3648	201	1	+	+	CCONJ
ejpam-3648	201	2	z2	z2	NOUN
ejpam-3648	201	3	+	+	CCONJ
ejpam-3648	201	4	6ηκ	6ηκ	NOUN
ejpam-3648	201	5	mτ	mτ	NOUN
ejpam-3648	201	6	b13	b13	NOUN
ejpam-3648	201	7	2x1	2x1	NUM
ejpam-3648	201	8	−	−	PROPN
ejpam-3648	201	9	2x0	2x0	NUM
ejpam-3648	201	10	+	+	NUM
ejpam-3648	201	11	6ηκ	6ηκ	NOUN
ejpam-3648	201	12	mτ	mτ	X
ejpam-3648	201	13	b21	b21	PROPN
ejpam-3648	201	14	2y1	2y1	NUM
ejpam-3648	201	15	−	−	PROPN
ejpam-3648	201	16	2y0	2y0	NUM
ejpam-3648	201	17	+	+	CCONJ
ejpam-3648	201	18	6ηκ	6ηκ	NOUN
ejpam-3648	201	19	mτ	mτ	X
ejpam-3648	201	20	b22	b22	PROPN
ejpam-3648	201	21	2z1	2z1	NUM
ejpam-3648	201	22	−	−	PROPN
ejpam-3648	201	23	2z0	2z0	NUM
ejpam-3648	202	1	+	+	NUM
ejpam-3648	202	2	6ηκ	6ηκ	NOUN
ejpam-3648	202	3	mτ	mτ	NOUN
ejpam-3648	202	4	b23	b23	PROPN
ejpam-3648	202	5	x0	x0	PROPN
ejpam-3648	203	1	+	+	CCONJ
ejpam-3648	203	2	6ηκ	6ηκ	NOUN
ejpam-3648	203	3	mτ	mτ	NOUN
ejpam-3648	203	4	b31	b31	PROPN
ejpam-3648	203	5	y0	y0	PROPN
ejpam-3648	203	6	+	+	CCONJ
ejpam-3648	203	7	6ηκ	6ηκ	NOUN
ejpam-3648	203	8	mτ	mτ	ADP
ejpam-3648	203	9	b32	b32	PROPN
ejpam-3648	203	10	z0	z0	PROPN
ejpam-3648	203	11	+	+	PROPN
ejpam-3648	203	12	6ηκ	6ηκ	ADJ
ejpam-3648	203	13	mτ	mτ	NOUN
ejpam-3648	203	14	b33	b33	NOUN
ejpam-3648	203	15			NOUN
ejpam-3648	203	16	.	.	PUNCT
ejpam-3648	204	1	proof	proof	NOUN
ejpam-3648	204	2	.	.	PUNCT
ejpam-3648	205	1	since	since	SCONJ
ejpam-3648	205	2	b∗	b∗	ADJ
ejpam-3648	205	3	=	=	SYM
ejpam-3648	205	4	τt+κb	τt+κb	SYM
ejpam-3648	205	5	(	(	PUNCT
ejpam-3648	205	6	κ2+τ2	κ2+τ2	NOUN
ejpam-3648	205	7	)	)	PUNCT
ejpam-3648	205	8	1	1	NUM
ejpam-3648	205	9	2	2	NUM
ejpam-3648	205	10	,	,	PUNCT
ejpam-3648	205	11	b∗	b∗	ADJ
ejpam-3648	205	12	=	=	SYM
ejpam-3648	205	13	τ	τ	PROPN
ejpam-3648	205	14	η	η	PROPN
ejpam-3648	205	15	[	[	X
ejpam-3648	205	16	t2	t2	PROPN
ejpam-3648	205	17	t	t	PROPN
ejpam-3648	205	18	1	1	NUM
ejpam-3648	205	19	]	]	SYM
ejpam-3648	205	20			NOUN
ejpam-3648	205	21	1	1	NUM
ejpam-3648	205	22	−2	−2	NOUN
ejpam-3648	205	23	1	1	NUM
ejpam-3648	205	24	−2	−2	NOUN
ejpam-3648	205	25	2	2	NUM
ejpam-3648	205	26	0	0	NUM
ejpam-3648	205	27	1	1	NUM
ejpam-3648	205	28	0	0	NUM
ejpam-3648	205	29	0	0	NUM
ejpam-3648	205	30			NOUN
ejpam-3648	205	31	x0	x0	NOUN
ejpam-3648	205	32	y0	y0	PROPN
ejpam-3648	205	33	z0	z0	NOUN
ejpam-3648	205	34	x1	x1	NUM
ejpam-3648	205	35	y1	y1	PROPN
ejpam-3648	205	36	z1	z1	VERB
ejpam-3648	205	37	x2	x2	PROPN
ejpam-3648	205	38	y2	y2	PROPN
ejpam-3648	205	39	z2	z2	PROPN
ejpam-3648	205	40	+	+	PROPN
ejpam-3648	205	41	6κ	6κ	NOUN
ejpam-3648	205	42	m	m	NOUN
ejpam-3648	205	43	[	[	PUNCT
ejpam-3648	205	44	t2	t2	NOUN
ejpam-3648	205	45	t	t	PROPN
ejpam-3648	205	46	1	1	NUM
ejpam-3648	205	47	]	]	PUNCT
ejpam-3648	205	48			PROPN
ejpam-3648	205	49	b11	b11	NOUN
ejpam-3648	205	50	b12	b12	NOUN
ejpam-3648	205	51	b13	b13	PROPN
ejpam-3648	205	52	b21	b21	PROPN
ejpam-3648	205	53	b22	b22	PROPN
ejpam-3648	205	54	b23	b23	PROPN
ejpam-3648	205	55	b31	b31	PROPN
ejpam-3648	205	56	b32	b32	PROPN
ejpam-3648	205	57	b33	b33	NOUN
ejpam-3648	205	58			NOUN
ejpam-3648	205	59	(	(	PUNCT
ejpam-3648	205	60	κ2	κ2	NOUN
ejpam-3648	205	61	+	+	CCONJ
ejpam-3648	205	62	τ2	τ2	NOUN
ejpam-3648	205	63	)	)	PUNCT
ejpam-3648	205	64	1	1	NUM
ejpam-3648	205	65	2	2	NUM
ejpam-3648	205	66	,	,	PUNCT
ejpam-3648	205	67	b∗	b∗	ADJ
ejpam-3648	205	68	=	=	PUNCT
ejpam-3648	205	69	[	[	PUNCT
ejpam-3648	205	70	t2	t2	NOUN
ejpam-3648	205	71	t	t	PROPN
ejpam-3648	205	72	1	1	NUM
ejpam-3648	205	73	]	]	PUNCT
ejpam-3648	205	74	τη	τη	ADP
ejpam-3648	205	75			NOUN
ejpam-3648	205	76	1	1	NUM
ejpam-3648	205	77	−2	−2	NOUN
ejpam-3648	205	78	1	1	NUM
ejpam-3648	205	79	−2	−2	NOUN
ejpam-3648	205	80	2	2	NUM
ejpam-3648	205	81	0	0	NUM
ejpam-3648	205	82	1	1	NUM
ejpam-3648	205	83	0	0	NUM
ejpam-3648	205	84	0	0	NUM
ejpam-3648	205	85			NOUN
ejpam-3648	205	86	x0	x0	NOUN
ejpam-3648	205	87	y0	y0	PROPN
ejpam-3648	205	88	z0	z0	NOUN
ejpam-3648	205	89	x1	x1	NUM
ejpam-3648	205	90	y1	y1	PROPN
ejpam-3648	205	91	z1	z1	VERB
ejpam-3648	205	92	x2	x2	PROPN
ejpam-3648	205	93	y2	y2	PROPN
ejpam-3648	205	94	z2	z2	PROPN
ejpam-3648	205	95	+	+	PROPN
ejpam-3648	205	96	6κ	6κ	NOUN
ejpam-3648	205	97	m	m	VERB
ejpam-3648	205	98			NOUN
ejpam-3648	205	99	b11	b11	NUM
ejpam-3648	205	100	b12	b12	NOUN
ejpam-3648	205	101	b13	b13	PROPN
ejpam-3648	205	102	b21	b21	PROPN
ejpam-3648	205	103	b22	b22	PROPN
ejpam-3648	205	104	b23	b23	PROPN
ejpam-3648	205	105	b31	b31	PROPN
ejpam-3648	205	106	b32	b32	PROPN
ejpam-3648	205	107	b33	b33	NOUN
ejpam-3648	205	108			NOUN
ejpam-3648	205	109	(	(	PUNCT
ejpam-3648	205	110	κ2	κ2	NOUN
ejpam-3648	205	111	+	+	CCONJ
ejpam-3648	205	112	τ2	τ2	NOUN
ejpam-3648	205	113	)	)	PUNCT
ejpam-3648	205	114	1	1	NUM
ejpam-3648	205	115	2	2	NUM
ejpam-3648	205	116	.	.	PUNCT
ejpam-3648	206	1	hence	hence	ADV
ejpam-3648	206	2	it	it	PRON
ejpam-3648	206	3	is	be	AUX
ejpam-3648	206	4	easy	easy	ADJ
ejpam-3648	206	5	to	to	PART
ejpam-3648	206	6	give	give	VERB
ejpam-3648	206	7	the	the	DET
ejpam-3648	206	8	proof	proof	NOUN
ejpam-3648	206	9	.	.	PUNCT
ejpam-3648	207	1	2.2	2.2	NUM
ejpam-3648	207	2	.	.	PUNCT
ejpam-3648	208	1	the	the	DET
ejpam-3648	208	2	first	first	ADJ
ejpam-3648	208	3	and	and	CCONJ
ejpam-3648	208	4	second	second	ADJ
ejpam-3648	208	5	curvature	curvature	NOUN
ejpam-3648	208	6	of	of	ADP
ejpam-3648	208	7	involute	involute	ADJ
ejpam-3648	208	8	α∗	α∗	NOUN
ejpam-3648	208	9	theorem	theorem	VERB
ejpam-3648	208	10	16	16	NUM
ejpam-3648	208	11	.	.	PUNCT
ejpam-3648	209	1	the	the	DET
ejpam-3648	209	2	first	first	ADJ
ejpam-3648	209	3	curvature	curvature	NOUN
ejpam-3648	209	4	of	of	ADP
ejpam-3648	209	5	involute	involute	ADJ
ejpam-3648	209	6	α∗of	α∗of	NUM
ejpam-3648	209	7	any	any	DET
ejpam-3648	209	8	cubic	cubic	ADJ
ejpam-3648	209	9	bezier	bezier	NOUN
ejpam-3648	209	10	curve	curve	NOUN
ejpam-3648	209	11	in	in	ADP
ejpam-3648	209	12	e3is	e3is	DET
ejpam-3648	209	13	κ∗	κ∗	PROPN
ejpam-3648	209	14	=	=	SYM
ejpam-3648	209	15	1	1	NUM
ejpam-3648	209	16	m2(c−	m2(c−	NOUN
ejpam-3648	209	17	ηt	ηt	ADP
ejpam-3648	209	18	)	)	PUNCT
ejpam-3648	209	19	√	√	NOUN
ejpam-3648	209	20	m4	m4	PROPN
ejpam-3648	209	21	+	+	CCONJ
ejpam-3648	209	22	η6	η6	PROPN
ejpam-3648	209	23	(	(	PUNCT
ejpam-3648	209	24	x0y1z2	x0y1z2	PROPN
ejpam-3648	209	25	−	−	PROPN
ejpam-3648	210	1	x0y2z1	x0y2z1	PROPN
ejpam-3648	211	1	−	−	PROPN
ejpam-3648	212	1	x1y0z2	x1y0z2	NOUN
ejpam-3648	212	2	+	+	CCONJ
ejpam-3648	212	3	x1y2z0	x1y2z0	X
ejpam-3648	213	1	+	+	PUNCT
ejpam-3648	213	2	x2y0z1	x2y0z1	NOUN
ejpam-3648	213	3	−	−	PROPN
ejpam-3648	214	1	x2y1z0)2	x2y1z0)2	PROPN
ejpam-3648	214	2	proof	proof	NOUN
ejpam-3648	214	3	.	.	PUNCT
ejpam-3648	215	1	since	since	SCONJ
ejpam-3648	215	2	κ∗	κ∗	PROPN
ejpam-3648	215	3	=	=	SYM
ejpam-3648	215	4	√	√	NUM
ejpam-3648	215	5	κ2	κ2	NOUN
ejpam-3648	215	6	+	+	CCONJ
ejpam-3648	215	7	τ2	τ2	NOUN
ejpam-3648	215	8	(	(	PUNCT
ejpam-3648	215	9	c−	c−	X
ejpam-3648	215	10	ηt)κ	ηt)κ	PROPN
ejpam-3648	215	11	,	,	PUNCT
ejpam-3648	215	12	and	and	CCONJ
ejpam-3648	215	13	κ	κ	X
ejpam-3648	215	14	=	=	VERB
ejpam-3648	215	15	m	m	VERB
ejpam-3648	215	16	η3	η3	NOUN
ejpam-3648	215	17	κ∗	κ∗	NOUN
ejpam-3648	215	18	=	=	SYM
ejpam-3648	215	19	√	√	PROPN
ejpam-3648	215	20	m2	m2	PROPN
ejpam-3648	215	21	η6	η6	PROPN
ejpam-3648	215	22	+	+	CCONJ
ejpam-3648	215	23	(	(	PUNCT
ejpam-3648	215	24	x0y1z2−x0y2z1−x1y0z2+x1y2z0+x2y0z1−x2y1z0)2	x0y1z2−x0y2z1−x1y0z2+x1y2z0+x2y0z1−x2y1z0)2	PROPN
ejpam-3648	215	25	m2	m2	PROPN
ejpam-3648	215	26	(	(	PUNCT
ejpam-3648	215	27	c−	c−	PROPN
ejpam-3648	215	28	ηt)m	ηt)m	PROPN
ejpam-3648	215	29	η3	η3	PROPN
ejpam-3648	215	30	(	(	PUNCT
ejpam-3648	215	31	c−	c−	X
ejpam-3648	215	32	ηt)κ	ηt)κ	PROPN
ejpam-3648	215	33	>	>	X
ejpam-3648	215	34	0	0	NUM
ejpam-3648	215	35	,	,	PUNCT
ejpam-3648	215	36	κ	κ	X
ejpam-3648	215	37	6=	6=	PROPN
ejpam-3648	215	38	0	0	NUM
ejpam-3648	215	39	.	.	PUNCT
ejpam-3648	216	1	it	it	PRON
ejpam-3648	216	2	is	be	AUX
ejpam-3648	216	3	trivial	trivial	ADJ
ejpam-3648	216	4	.	.	PUNCT
ejpam-3648	217	1	theorem	theorem	VERB
ejpam-3648	217	2	17	17	NUM
ejpam-3648	217	3	.	.	PUNCT
ejpam-3648	218	1	the	the	DET
ejpam-3648	218	2	second	second	ADJ
ejpam-3648	218	3	curvature	curvature	NOUN
ejpam-3648	218	4	of	of	ADP
ejpam-3648	218	5	involute	involute	ADJ
ejpam-3648	218	6	α∗of	α∗of	NUM
ejpam-3648	218	7	any	any	DET
ejpam-3648	218	8	cubic	cubic	ADJ
ejpam-3648	218	9	bezier	bezier	NOUN
ejpam-3648	218	10	curve	curve	NOUN
ejpam-3648	218	11	in	in	ADP
ejpam-3648	218	12	e3is	e3is	NUM
ejpam-3648	218	13	τ∗	τ∗	X
ejpam-3648	218	14	=	=	PUNCT
ejpam-3648	218	15	η3	η3	PROPN
ejpam-3648	218	16	m3	m3	PROPN
ejpam-3648	218	17	(	(	PUNCT
ejpam-3648	218	18	κ−	κ−	PROPN
ejpam-3648	218	19	κ′	κ′	PROPN
ejpam-3648	218	20	(	(	PUNCT
ejpam-3648	218	21	x0y1z2	x0y1z2	PROPN
ejpam-3648	218	22	−	−	PROPN
ejpam-3648	219	1	x0y2z1	x0y2z1	PROPN
ejpam-3648	219	2	−	−	PROPN
ejpam-3648	219	3	x1y0z2	x1y0z2	NOUN
ejpam-3648	219	4	+	+	CCONJ
ejpam-3648	219	5	x1y2z0	x1y2z0	X
ejpam-3648	220	1	+	+	CCONJ
ejpam-3648	220	2	x2y0z1	x2y0z1	NOUN
ejpam-3648	220	3	−	−	PROPN
ejpam-3648	220	4	x2y1z0	x2y1z0	PROPN
ejpam-3648	220	5	)	)	PUNCT
ejpam-3648	220	6	(	(	PUNCT
ejpam-3648	220	7	c−	c−	NOUN
ejpam-3648	220	8	ηt	ηt	ADV
ejpam-3648	220	9	)	)	PUNCT
ejpam-3648	220	10	(	(	PUNCT
ejpam-3648	220	11	κ2	κ2	NOUN
ejpam-3648	220	12	+	+	CCONJ
ejpam-3648	220	13	τ2	τ2	NOUN
ejpam-3648	220	14	)	)	PUNCT
ejpam-3648	220	15	)	)	PUNCT
ejpam-3648	220	16	.	.	PUNCT
ejpam-3648	221	1	proof	proof	NOUN
ejpam-3648	221	2	.	.	PUNCT
ejpam-3648	222	1	considering	consider	VERB
ejpam-3648	222	2	the	the	DET
ejpam-3648	222	3	τ∗	τ∗	NOUN
ejpam-3648	222	4	=	=	PUNCT
ejpam-3648	222	5	κτ	κτ	NOUN
ejpam-3648	223	1	′	′	INTJ
ejpam-3648	223	2	−	−	PUNCT
ejpam-3648	224	1	κ′τ	κ′τ	NOUN
ejpam-3648	224	2	(	(	PUNCT
ejpam-3648	224	3	c−	c−	X
ejpam-3648	224	4	ηt)κ	ηt)κ	PROPN
ejpam-3648	224	5	(	(	PUNCT
ejpam-3648	224	6	κ2	κ2	NOUN
ejpam-3648	224	7	+	+	CCONJ
ejpam-3648	224	8	τ2	τ2	ADJ
ejpam-3648	224	9	)	)	PUNCT
ejpam-3648	224	10	equation	equation	NOUN
ejpam-3648	224	11	,	,	PUNCT
ejpam-3648	224	12	we	we	PRON
ejpam-3648	224	13	have	have	VERB
ejpam-3648	224	14	τ∗	τ∗	NOUN
ejpam-3648	224	15	=	=	SYM
ejpam-3648	224	16	κ−	κ−	PROPN
ejpam-3648	224	17	κ′	κ′	NOUN
ejpam-3648	224	18	(	(	PUNCT
ejpam-3648	224	19	x0y1z2	x0y1z2	PROPN
ejpam-3648	224	20	−	−	PROPN
ejpam-3648	225	1	x0y2z1	x0y2z1	PROPN
ejpam-3648	226	1	−	−	PROPN
ejpam-3648	227	1	x1y0z2	x1y0z2	NOUN
ejpam-3648	227	2	+	+	CCONJ
ejpam-3648	227	3	x1y2z0	x1y2z0	X
ejpam-3648	228	1	+	+	CCONJ
ejpam-3648	228	2	x2y0z1	x2y0z1	NOUN
ejpam-3648	228	3	−	−	PROPN
ejpam-3648	228	4	x2y1z0	x2y1z0	PROPN
ejpam-3648	228	5	)	)	PUNCT
ejpam-3648	228	6	m2(c−	m2(c−	NOUN
ejpam-3648	228	7	ηt)m	ηt)m	PROPN
ejpam-3648	228	8	η3	η3	PROPN
ejpam-3648	228	9	(	(	PUNCT
ejpam-3648	228	10	κ2	κ2	NOUN
ejpam-3648	228	11	+	+	CCONJ
ejpam-3648	228	12	τ2	τ2	NOUN
ejpam-3648	228	13	)	)	PUNCT
ejpam-3648	228	14	.	.	PUNCT
ejpam-3648	229	1	references	reference	NOUN
ejpam-3648	229	2	225	225	NUM
ejpam-3648	229	3	example	example	NOUN
ejpam-3648	229	4	1	1	NUM
ejpam-3648	229	5	.	.	PUNCT
ejpam-3648	229	6	find	find	VERB
ejpam-3648	229	7	the	the	DET
ejpam-3648	229	8	involute	involute	NOUN
ejpam-3648	229	9	of	of	ADP
ejpam-3648	229	10	the	the	DET
ejpam-3648	229	11	cubic	cubic	ADJ
ejpam-3648	229	12	bezier	bezier	NOUN
ejpam-3648	229	13	curve	curve	NOUN
ejpam-3648	229	14	with	with	ADP
ejpam-3648	229	15	control	control	NOUN
ejpam-3648	229	16	points	point	NOUN
ejpam-3648	229	17	p0	p0	NOUN
ejpam-3648	229	18	=	=	SYM
ejpam-3648	229	19	(	(	PUNCT
ejpam-3648	229	20	1	1	NUM
ejpam-3648	229	21	,	,	PUNCT
ejpam-3648	229	22	2	2	NUM
ejpam-3648	229	23	,	,	PUNCT
ejpam-3648	229	24	3	3	NUM
ejpam-3648	229	25	)	)	PUNCT
ejpam-3648	229	26	,	,	PUNCT
ejpam-3648	229	27	p1	p1	NOUN
ejpam-3648	229	28	=	=	SYM
ejpam-3648	229	29	(	(	PUNCT
ejpam-3648	229	30	1	1	NUM
ejpam-3648	229	31	,	,	PUNCT
ejpam-3648	229	32	1	1	NUM
ejpam-3648	229	33	,	,	PUNCT
ejpam-3648	229	34	1	1	NUM
ejpam-3648	229	35	)	)	PUNCT
ejpam-3648	229	36	,	,	PUNCT
ejpam-3648	229	37	p2	p2	PROPN
ejpam-3648	229	38	=	=	SYM
ejpam-3648	229	39	(	(	PUNCT
ejpam-3648	229	40	2	2	NUM
ejpam-3648	229	41	,	,	PUNCT
ejpam-3648	229	42	1	1	NUM
ejpam-3648	229	43	,	,	PUNCT
ejpam-3648	229	44	3	3	NUM
ejpam-3648	229	45	)	)	PUNCT
ejpam-3648	229	46	,	,	PUNCT
ejpam-3648	229	47	and	and	CCONJ
ejpam-3648	229	48	p3	p3	PROPN
ejpam-3648	229	49	=	=	SYM
ejpam-3648	229	50	(	(	PUNCT
ejpam-3648	229	51	1,−1	1,−1	NUM
ejpam-3648	229	52	,	,	PUNCT
ejpam-3648	229	53	0	0	NUM
ejpam-3648	229	54	)	)	PUNCT
ejpam-3648	229	55	the	the	DET
ejpam-3648	229	56	cubic	cubic	ADJ
ejpam-3648	229	57	bezier	bezier	NOUN
ejpam-3648	229	58	curve	curve	NOUN
ejpam-3648	229	59	has	have	VERB
ejpam-3648	229	60	the	the	DET
ejpam-3648	229	61	followowing	followowing	NOUN
ejpam-3648	229	62	matrix	matrix	NOUN
ejpam-3648	229	63	representation	representation	NOUN
ejpam-3648	229	64	α	α	PROPN
ejpam-3648	229	65	(	(	PUNCT
ejpam-3648	229	66	t	t	NOUN
ejpam-3648	229	67	)	)	PUNCT
ejpam-3648	229	68	=	=	PUNCT
ejpam-3648	230	1	[	[	PUNCT
ejpam-3648	230	2	t3	t3	PROPN
ejpam-3648	230	3	t2	t2	PROPN
ejpam-3648	230	4	t	t	PROPN
ejpam-3648	230	5	1	1	NUM
ejpam-3648	230	6	]	]	PUNCT
ejpam-3648	230	7			NOUN
ejpam-3648	230	8	−1	−1	NOUN
ejpam-3648	230	9	3	3	NUM
ejpam-3648	230	10	−3	−3	NOUN
ejpam-3648	230	11	1	1	NUM
ejpam-3648	230	12	3	3	NUM
ejpam-3648	230	13	−6	−6	NOUN
ejpam-3648	230	14	3	3	NUM
ejpam-3648	230	15	0	0	NUM
ejpam-3648	230	16	−3	−3	PROPN
ejpam-3648	230	17	3	3	NUM
ejpam-3648	230	18	0	0	NUM
ejpam-3648	230	19	0	0	NUM
ejpam-3648	230	20	1	1	NUM
ejpam-3648	230	21	0	0	NUM
ejpam-3648	230	22	0	0	NUM
ejpam-3648	230	23	0	0	NUM
ejpam-3648	230	24			NOUN
ejpam-3648	230	25			NOUN
ejpam-3648	230	26	p0	p0	NOUN
ejpam-3648	230	27	p1	p1	NOUN
ejpam-3648	230	28	p2	p2	PROPN
ejpam-3648	230	29	p3	p3	PROPN
ejpam-3648	230	30			NOUN
ejpam-3648	230	31	.	.	PUNCT
ejpam-3648	231	1	(	(	PUNCT
ejpam-3648	231	2	12	12	NUM
ejpam-3648	231	3	)	)	PUNCT
ejpam-3648	231	4	the	the	DET
ejpam-3648	231	5	involute	involute	ADJ
ejpam-3648	231	6	α∗	α∗	NOUN
ejpam-3648	231	7	of	of	ADP
ejpam-3648	231	8	the	the	DET
ejpam-3648	231	9	cubic	cubic	ADJ
ejpam-3648	231	10	bezier	bezier	PROPN
ejpam-3648	231	11	curve	curve	PROPN
ejpam-3648	231	12	α	α	PROPN
ejpam-3648	231	13	,	,	PUNCT
ejpam-3648	231	14	has	have	VERB
ejpam-3648	231	15	the	the	DET
ejpam-3648	231	16	followowing	followowing	NOUN
ejpam-3648	231	17	matrix	matrix	NOUN
ejpam-3648	231	18	representation	representation	NOUN
ejpam-3648	231	19	α∗	α∗	NOUN
ejpam-3648	231	20	(	(	PUNCT
ejpam-3648	231	21	t	t	NOUN
ejpam-3648	231	22	)	)	PUNCT
ejpam-3648	231	23	=	=	NOUN
ejpam-3648	232	1	[	[	PUNCT
ejpam-3648	232	2	t3	t3	PROPN
ejpam-3648	232	3	t2	t2	PROPN
ejpam-3648	232	4	t	t	PROPN
ejpam-3648	232	5	1	1	NUM
ejpam-3648	232	6	]	]	PUNCT
ejpam-3648	232	7			NOUN
ejpam-3648	232	8	−1	−1	NOUN
ejpam-3648	232	9	3	3	NUM
ejpam-3648	232	10	−3	−3	NOUN
ejpam-3648	232	11	1	1	NUM
ejpam-3648	232	12	3−	3−	NUM
ejpam-3648	232	13	3µ	3µ	NUM
ejpam-3648	232	14	−6	−6	NOUN
ejpam-3648	232	15	+	+	CCONJ
ejpam-3648	232	16	9µ	9µ	NUM
ejpam-3648	232	17	3−	3−	NUM
ejpam-3648	232	18	9µ	9µ	NOUN
ejpam-3648	232	19	3µ	3µ	NUM
ejpam-3648	232	20	−3	−3	NOUN
ejpam-3648	233	1	+	+	NUM
ejpam-3648	234	1	6µ	6µ	NOUN
ejpam-3648	234	2	3−	3−	NUM
ejpam-3648	234	3	12µ	12µ	NOUN
ejpam-3648	234	4	6µ	6µ	VERB
ejpam-3648	234	5	0	0	NUM
ejpam-3648	234	6	1	1	NUM
ejpam-3648	235	1	+	+	NUM
ejpam-3648	235	2	3µ	3µ	NUM
ejpam-3648	235	3	−3	−3	NOUN
ejpam-3648	235	4	0	0	NUM
ejpam-3648	235	5	0	0	NUM
ejpam-3648	235	6			NOUN
ejpam-3648	235	7			NOUN
ejpam-3648	235	8	p0	p0	NOUN
ejpam-3648	235	9	p1	p1	NOUN
ejpam-3648	235	10	p2	p2	PROPN
ejpam-3648	235	11	p3	p3	PROPN
ejpam-3648	235	12			NOUN
ejpam-3648	235	13	.	.	PUNCT
ejpam-3648	236	1	(	(	PUNCT
ejpam-3648	236	2	13	13	NUM
ejpam-3648	236	3	)	)	PUNCT
ejpam-3648	236	4	using	use	VERB
ejpam-3648	236	5	control	control	NOUN
ejpam-3648	236	6	points	point	NOUN
ejpam-3648	236	7	as	as	ADP
ejpam-3648	236	8	α∗	α∗	NOUN
ejpam-3648	236	9	(	(	PUNCT
ejpam-3648	236	10	t	t	NOUN
ejpam-3648	236	11	)	)	PUNCT
ejpam-3648	236	12	=	=	NOUN
ejpam-3648	237	1	[	[	PUNCT
ejpam-3648	237	2	t3	t3	PROPN
ejpam-3648	237	3	t2	t2	PROPN
ejpam-3648	237	4	t	t	PROPN
ejpam-3648	237	5	1	1	NUM
ejpam-3648	237	6	]	]	PUNCT
ejpam-3648	237	7			NOUN
ejpam-3648	237	8	−1	−1	NOUN
ejpam-3648	237	9	3	3	NUM
ejpam-3648	237	10	−3	−3	NOUN
ejpam-3648	237	11	1	1	NUM
ejpam-3648	237	12	3−	3−	NUM
ejpam-3648	237	13	3µ	3µ	NUM
ejpam-3648	237	14	−6	−6	NOUN
ejpam-3648	237	15	+	+	CCONJ
ejpam-3648	237	16	9µ	9µ	NUM
ejpam-3648	237	17	3−	3−	NUM
ejpam-3648	237	18	9µ	9µ	NOUN
ejpam-3648	237	19	3µ	3µ	NUM
ejpam-3648	237	20	−3	−3	NOUN
ejpam-3648	238	1	+	+	NUM
ejpam-3648	239	1	6µ	6µ	NOUN
ejpam-3648	239	2	3−	3−	NUM
ejpam-3648	239	3	12µ	12µ	NOUN
ejpam-3648	239	4	6µ	6µ	VERB
ejpam-3648	239	5	0	0	NUM
ejpam-3648	239	6	1	1	NUM
ejpam-3648	239	7	+	+	NUM
ejpam-3648	239	8	3µ	3µ	NUM
ejpam-3648	239	9	−3	−3	NOUN
ejpam-3648	239	10	0	0	NUM
ejpam-3648	239	11	0	0	NUM
ejpam-3648	239	12			NOUN
ejpam-3648	239	13			NOUN
ejpam-3648	240	1	1	1	NUM
ejpam-3648	240	2	2	2	NUM
ejpam-3648	240	3	3	3	NUM
ejpam-3648	240	4	1	1	NUM
ejpam-3648	240	5	1	1	NUM
ejpam-3648	240	6	1	1	NUM
ejpam-3648	240	7	2	2	NUM
ejpam-3648	240	8	1	1	NUM
ejpam-3648	240	9	3	3	NUM
ejpam-3648	240	10	1	1	NUM
ejpam-3648	240	11	−1	−1	NOUN
ejpam-3648	240	12	0	0	NUM
ejpam-3648	240	13			NOUN
ejpam-3648	240	14	we	we	PRON
ejpam-3648	240	15	have	have	VERB
ejpam-3648	240	16	α∗	α∗	NOUN
ejpam-3648	240	17	(	(	PUNCT
ejpam-3648	240	18	t	t	NOUN
ejpam-3648	240	19	)	)	PUNCT
ejpam-3648	240	20	=	=	PUNCT
ejpam-3648	241	1	(	(	PUNCT
ejpam-3648	241	2	3µ+	3µ+	NUM
ejpam-3648	241	3	6tµ−	6tµ−	NUM
ejpam-3648	241	4	9t2µ+	9t2µ+	NUM
ejpam-3648	241	5	3t2	3t2	NUM
ejpam-3648	242	1	−	−	ADP
ejpam-3648	242	2	3t3	3t3	NUM
ejpam-3648	242	3	−	−	NOUN
ejpam-3648	242	4	2	2	NUM
ejpam-3648	242	5	,	,	PUNCT
ejpam-3648	242	6	6µ−	6µ−	NUM
ejpam-3648	242	7	3t+	3t+	NUM
ejpam-3648	242	8	6tµ−	6tµ−	NUM
ejpam-3648	242	9	9t2µ+	9t2µ+	NUM
ejpam-3648	242	10	3t2	3t2	NUM
ejpam-3648	243	1	−	−	ADP
ejpam-3648	243	2	3t3	3t3	NOUN
ejpam-3648	243	3	,	,	PUNCT
ejpam-3648	243	4	24tµ−	24tµ−	NUM
ejpam-3648	243	5	19µ−	19µ−	NUM
ejpam-3648	243	6	6t−	6t−	NUM
ejpam-3648	243	7	27t2µ+	27t2µ+	NOUN
ejpam-3648	243	8	12t2	12t2	NUM
ejpam-3648	243	9	−	−	NOUN
ejpam-3648	243	10	9t3	9t3	NUM
ejpam-3648	243	11	)	)	PUNCT
ejpam-3648	243	12	.	.	PUNCT
ejpam-3648	244	1	also	also	ADV
ejpam-3648	244	2	under	under	ADP
ejpam-3648	244	3	the	the	DET
ejpam-3648	244	4	condition	condition	NOUN
ejpam-3648	244	5	constant	constant	ADJ
ejpam-3648	244	6	c	c	PROPN
ejpam-3648	244	7	=	=	SYM
ejpam-3648	244	8	η	η	PROPN
ejpam-3648	244	9	=	=	SYM
ejpam-3648	244	10	‖α′‖	‖α′‖	PROPN
ejpam-3648	244	11	and	and	CCONJ
ejpam-3648	244	12	µ	µ	X
ejpam-3648	244	13	=	=	PUNCT
ejpam-3648	244	14	(	(	PUNCT
ejpam-3648	244	15	1−	1−	NUM
ejpam-3648	244	16	t	t	NUM
ejpam-3648	244	17	)	)	PUNCT
ejpam-3648	244	18	,	,	PUNCT
ejpam-3648	244	19	we	we	PRON
ejpam-3648	244	20	can	can	AUX
ejpam-3648	244	21	find	find	VERB
ejpam-3648	244	22	the	the	DET
ejpam-3648	244	23	special	special	ADJ
ejpam-3648	244	24	involute	involute	NOUN
ejpam-3648	244	25	of	of	ADP
ejpam-3648	244	26	α	α	NOUN
ejpam-3648	244	27	as	as	ADP
ejpam-3648	244	28	in	in	ADP
ejpam-3648	244	29	the	the	DET
ejpam-3648	244	30	following	follow	VERB
ejpam-3648	244	31	way	way	NOUN
ejpam-3648	244	32	α∗	α∗	NOUN
ejpam-3648	244	33	(	(	PUNCT
ejpam-3648	244	34	t	t	NOUN
ejpam-3648	244	35	)	)	PUNCT
ejpam-3648	244	36	=	=	NOUN
ejpam-3648	245	1	[	[	PUNCT
ejpam-3648	245	2	t3	t3	PROPN
ejpam-3648	245	3	t2	t2	PROPN
ejpam-3648	245	4	t	t	PROPN
ejpam-3648	245	5	1	1	NUM
ejpam-3648	245	6	]	]	PUNCT
ejpam-3648	245	7			NOUN
ejpam-3648	245	8	−1	−1	NOUN
ejpam-3648	245	9	3	3	NUM
ejpam-3648	245	10	−3	−3	NOUN
ejpam-3648	245	11	1	1	NUM
ejpam-3648	245	12	3−	3−	NUM
ejpam-3648	245	13	3	3	NUM
ejpam-3648	245	14	(	(	PUNCT
ejpam-3648	245	15	1−	1−	NUM
ejpam-3648	245	16	t	t	NOUN
ejpam-3648	245	17	)	)	PUNCT
ejpam-3648	245	18	−6	−6	NOUN
ejpam-3648	246	1	+	+	NOUN
ejpam-3648	246	2	9	9	NUM
ejpam-3648	246	3	(	(	PUNCT
ejpam-3648	246	4	1−	1−	NUM
ejpam-3648	246	5	t	t	PROPN
ejpam-3648	246	6	)	)	PUNCT
ejpam-3648	246	7	3−	3−	NUM
ejpam-3648	246	8	9	9	NUM
ejpam-3648	246	9	(	(	PUNCT
ejpam-3648	246	10	1−	1−	NUM
ejpam-3648	246	11	t	t	PROPN
ejpam-3648	246	12	)	)	PUNCT
ejpam-3648	246	13	3	3	NUM
ejpam-3648	246	14	(	(	PUNCT
ejpam-3648	246	15	1−	1−	NUM
ejpam-3648	246	16	t	t	PROPN
ejpam-3648	246	17	)	)	PUNCT
ejpam-3648	246	18	−3	−3	PROPN
ejpam-3648	247	1	+	+	CCONJ
ejpam-3648	247	2	6	6	NUM
ejpam-3648	247	3	(	(	PUNCT
ejpam-3648	247	4	1−	1−	NUM
ejpam-3648	247	5	t	t	PROPN
ejpam-3648	247	6	)	)	PUNCT
ejpam-3648	247	7	3−	3−	NUM
ejpam-3648	247	8	12	12	NUM
ejpam-3648	247	9	(	(	PUNCT
ejpam-3648	247	10	1−	1−	NUM
ejpam-3648	247	11	t	t	NOUN
ejpam-3648	247	12	)	)	PUNCT
ejpam-3648	247	13	6	6	NUM
ejpam-3648	247	14	(	(	PUNCT
ejpam-3648	247	15	1−	1−	NUM
ejpam-3648	247	16	t	t	PROPN
ejpam-3648	247	17	)	)	PUNCT
ejpam-3648	247	18	0	0	NUM
ejpam-3648	247	19	1	1	NUM
ejpam-3648	248	1	+	+	NUM
ejpam-3648	248	2	3	3	NUM
ejpam-3648	248	3	(	(	PUNCT
ejpam-3648	248	4	1−	1−	NUM
ejpam-3648	248	5	t	t	NOUN
ejpam-3648	248	6	)	)	PUNCT
ejpam-3648	248	7	−3	−3	PROPN
ejpam-3648	248	8	0	0	NUM
ejpam-3648	248	9	0	0	NUM
ejpam-3648	248	10			NOUN
ejpam-3648	248	11			NOUN
ejpam-3648	248	12	1	1	NUM
ejpam-3648	248	13	2	2	NUM
ejpam-3648	248	14	3	3	NUM
ejpam-3648	248	15	1	1	NUM
ejpam-3648	248	16	1	1	NUM
ejpam-3648	248	17	1	1	NUM
ejpam-3648	248	18	2	2	NUM
ejpam-3648	248	19	1	1	NUM
ejpam-3648	248	20	3	3	NUM
ejpam-3648	248	21	1	1	NUM
ejpam-3648	248	22	−1	−1	NOUN
ejpam-3648	248	23	0	0	NUM
ejpam-3648	248	24			NOUN
ejpam-3648	248	25	α∗	α∗	NOUN
ejpam-3648	248	26	(	(	PUNCT
ejpam-3648	248	27	t	t	NOUN
ejpam-3648	248	28	)	)	PUNCT
ejpam-3648	248	29	=	=	NOUN
ejpam-3648	249	1	[	[	PUNCT
ejpam-3648	249	2	t3	t3	PROPN
ejpam-3648	249	3	t2	t2	PROPN
ejpam-3648	249	4	t	t	PROPN
ejpam-3648	249	5	1	1	NUM
ejpam-3648	249	6	]	]	PUNCT
ejpam-3648	249	7			NOUN
ejpam-3648	249	8	−1	−1	NOUN
ejpam-3648	249	9	3	3	NUM
ejpam-3648	249	10	−3	−3	NOUN
ejpam-3648	249	11	1	1	NUM
ejpam-3648	249	12	3	3	NUM
ejpam-3648	249	13	t	t	NOUN
ejpam-3648	249	14	3−	3−	NUM
ejpam-3648	249	15	9	9	NUM
ejpam-3648	249	16	t	t	NOUN
ejpam-3648	249	17	9t−	9t−	NUM
ejpam-3648	249	18	6	6	NUM
ejpam-3648	249	19	3−	3−	NUM
ejpam-3648	249	20	3	3	NUM
ejpam-3648	249	21	t	t	NOUN
ejpam-3648	249	22	3−	3−	NUM
ejpam-3648	249	23	6	6	NUM
ejpam-3648	249	24	t	t	NOUN
ejpam-3648	249	25	12t−	12t−	NOUN
ejpam-3648	249	26	9	9	NUM
ejpam-3648	249	27	6−	6−	NUM
ejpam-3648	249	28	6	6	NUM
ejpam-3648	249	29	t	t	NOUN
ejpam-3648	249	30	0	0	NUM
ejpam-3648	249	31	4−	4−	NUM
ejpam-3648	249	32	3	3	NUM
ejpam-3648	249	33	t	t	NOUN
ejpam-3648	249	34	−3	−3	NOUN
ejpam-3648	249	35	0	0	NUM
ejpam-3648	249	36	0	0	NUM
ejpam-3648	249	37			NOUN
ejpam-3648	249	38			NOUN
ejpam-3648	249	39	p0	p0	NOUN
ejpam-3648	249	40	p1	p1	NOUN
ejpam-3648	249	41	p2	p2	PROPN
ejpam-3648	249	42	p3	p3	PROPN
ejpam-3648	249	43			PROPN
ejpam-3648	249	44	.	.	PUNCT
ejpam-3648	250	1	references	reference	NOUN
ejpam-3648	250	2	[	[	X
ejpam-3648	250	3	1	1	NUM
ejpam-3648	250	4	]	]	PUNCT
ejpam-3648	250	5	ş	ş	PROPN
ejpam-3648	250	6	kılıçoğlu	kılıçoğlu	PROPN
ejpam-3648	250	7	and	and	CCONJ
ejpam-3648	250	8	s	s	PROPN
ejpam-3648	250	9	şenyurt	şenyurt	NOUN
ejpam-3648	250	10	.	.	PUNCT
ejpam-3648	251	1	on	on	ADP
ejpam-3648	251	2	the	the	DET
ejpam-3648	251	3	cubic	cubic	ADJ
ejpam-3648	251	4	bezier	bezier	NOUN
ejpam-3648	251	5	curves	curve	NOUN
ejpam-3648	251	6	in	in	ADP
ejpam-3648	251	7	e3	e3	NOUN
ejpam-3648	251	8	.	.	PUNCT
ejpam-3648	252	1	ordu	ordu	PROPN
ejpam-3648	252	2	university	university	PROPN
ejpam-3648	252	3	journal	journal	PROPN
ejpam-3648	252	4	of	of	ADP
ejpam-3648	252	5	science	science	NOUN
ejpam-3648	252	6	and	and	CCONJ
ejpam-3648	252	7	technology	technology	NOUN
ejpam-3648	252	8	.	.	PUNCT
ejpam-3648	252	9	,	,	PUNCT
ejpam-3648	252	10	9(2):83–97	9(2):83–97	NUM
ejpam-3648	252	11	,	,	PUNCT
ejpam-3648	252	12	2019	2019	NUM
ejpam-3648	252	13	.	.	PUNCT
ejpam-3648	253	1	[	[	X
ejpam-3648	253	2	2	2	X
ejpam-3648	253	3	]	]	X
ejpam-3648	253	4	g	g	PROPN
ejpam-3648	253	5	farin	farin	PROPN
ejpam-3648	253	6	.	.	PUNCT
ejpam-3648	254	1	curves	curve	NOUN
ejpam-3648	254	2	and	and	CCONJ
ejpam-3648	254	3	surfaces	surface	NOUN
ejpam-3648	254	4	for	for	ADP
ejpam-3648	254	5	computer	computer	NOUN
ejpam-3648	254	6	-	-	PUNCT
ejpam-3648	254	7	aided	aid	VERB
ejpam-3648	254	8	geometric	geometric	ADJ
ejpam-3648	254	9	design	design	NOUN
ejpam-3648	254	10	.	.	PUNCT
ejpam-3648	255	1	academic	academic	ADJ
ejpam-3648	255	2	press	press	NOUN
ejpam-3648	255	3	,	,	PUNCT
ejpam-3648	255	4	1996	1996	NUM
ejpam-3648	255	5	.	.	PUNCT
ejpam-3648	256	1	references	reference	NOUN
ejpam-3648	256	2	226	226	NUM
ejpam-3648	257	1	[	[	X
ejpam-3648	257	2	3	3	NUM
ejpam-3648	257	3	]	]	X
ejpam-3648	257	4	s	s	PART
ejpam-3648	257	5	çelik	çelik	PROPN
ejpam-3648	257	6	h	h	PROPN
ejpam-3648	257	7	kusak	kusak	PROPN
ejpam-3648	257	8	and	and	CCONJ
ejpam-3648	257	9	m	m	PROPN
ejpam-3648	257	10	i̇ncesu	i̇ncesu	NOUN
ejpam-3648	257	11	.	.	PUNCT
ejpam-3648	258	1	the	the	DET
ejpam-3648	258	2	bishop	bishop	PROPN
ejpam-3648	258	3	frame	frame	NOUN
ejpam-3648	258	4	of	of	ADP
ejpam-3648	258	5	bezier	bezier	NOUN
ejpam-3648	258	6	curves	curve	NOUN
ejpam-3648	258	7	.	.	PUNCT
ejpam-3648	259	1	life	life	NOUN
ejpam-3648	259	2	science	science	PROPN
ejpam-3648	259	3	journal	journal	PROPN
ejpam-3648	259	4	.	.	PUNCT
ejpam-3648	259	5	,	,	PUNCT
ejpam-3648	259	6	12(6	12(6	NUM
ejpam-3648	259	7	)	)	PUNCT
ejpam-3648	259	8	,	,	PUNCT
ejpam-3648	259	9	2015	2015	NUM
ejpam-3648	259	10	.	.	PUNCT
ejpam-3648	260	1	[	[	X
ejpam-3648	260	2	4	4	NUM
ejpam-3648	260	3	]	]	X
ejpam-3648	260	4	h	h	NOUN
ejpam-3648	260	5	hacısalihoğlu	hacısalihoğlu	PROPN
ejpam-3648	260	6	.	.	PUNCT
ejpam-3648	261	1	diferensiyel	diferensiyel	PROPN
ejpam-3648	261	2	geometri	geometri	PROPN
ejpam-3648	261	3	(	(	PUNCT
ejpam-3648	261	4	in	in	ADP
ejpam-3648	261	5	turkish	turkish	NOUN
ejpam-3648	261	6	)	)	PUNCT
ejpam-3648	261	7	.	.	PUNCT
ejpam-3648	262	1	university	university	NOUN
ejpam-3648	262	2	of	of	ADP
ejpam-3648	262	3	ínönü	ínönü	PROPN
ejpam-3648	262	4	press	press	NOUN
ejpam-3648	262	5	,	,	PUNCT
ejpam-3648	262	6	malatya	malatya	NOUN
ejpam-3648	262	7	,	,	PUNCT
ejpam-3648	262	8	1994	1994	NUM
ejpam-3648	262	9	.	.	PUNCT
ejpam-3648	263	1	[	[	X
ejpam-3648	263	2	5	5	NUM
ejpam-3648	263	3	]	]	PUNCT
ejpam-3648	263	4	h	h	PROPN
ejpam-3648	263	5	hagen	hagen	PROPN
ejpam-3648	263	6	.	.	PUNCT
ejpam-3648	264	1	bezier	bezier	NOUN
ejpam-3648	264	2	-	-	PUNCT
ejpam-3648	264	3	curves	curve	NOUN
ejpam-3648	264	4	with	with	ADP
ejpam-3648	264	5	curvature	curvature	NOUN
ejpam-3648	264	6	and	and	CCONJ
ejpam-3648	264	7	torsion	torsion	NOUN
ejpam-3648	264	8	continuity	continuity	NOUN
ejpam-3648	264	9	.	.	PUNCT
ejpam-3648	265	1	rocky	rocky	ADJ
ejpam-3648	265	2	mountain	mountain	PROPN
ejpam-3648	265	3	j.	j.	PROPN
ejpam-3648	265	4	math	math	PROPN
ejpam-3648	265	5	.	.	PUNCT
ejpam-3648	265	6	,	,	PUNCT
ejpam-3648	265	7	16(3):629–638	16(3):629–638	PROPN
ejpam-3648	265	8	,	,	PUNCT
ejpam-3648	265	9	1986	1986	NUM
ejpam-3648	265	10	.	.	PUNCT
ejpam-3648	266	1	[	[	X
ejpam-3648	266	2	6	6	NUM
ejpam-3648	266	3	]	]	X
ejpam-3648	266	4	m	m	NOUN
ejpam-3648	266	5	i̇ncesu	i̇ncesu	NOUN
ejpam-3648	266	6	and	and	CCONJ
ejpam-3648	266	7	o	o	NOUN
ejpam-3648	266	8	gürsoy	gürsoy	NOUN
ejpam-3648	266	9	.	.	PUNCT
ejpam-3648	267	1	ls(2)-equivalence	ls(2)-equivalence	NOUN
ejpam-3648	267	2	conditions	condition	NOUN
ejpam-3648	267	3	of	of	ADP
ejpam-3648	267	4	control	control	NOUN
ejpam-3648	267	5	points	point	NOUN
ejpam-3648	267	6	and	and	CCONJ
ejpam-3648	267	7	application	application	NOUN
ejpam-3648	267	8	to	to	PART
ejpam-3648	267	9	planar	planar	ADJ
ejpam-3648	267	10	bezier	bezier	ADJ
ejpam-3648	267	11	curves	curve	NOUN
ejpam-3648	267	12	.	.	PUNCT
ejpam-3648	268	1	new	new	ADJ
ejpam-3648	268	2	trends	trend	NOUN
ejpam-3648	268	3	in	in	ADP
ejpam-3648	268	4	mathematical	mathematical	ADJ
ejpam-3648	268	5	sciences	science	NOUN
ejpam-3648	268	6	.	.	PUNCT
ejpam-3648	268	7	,	,	PUNCT
ejpam-3648	268	8	3(5):70–84	3(5):70–84	NUM
ejpam-3648	268	9	,	,	PUNCT
ejpam-3648	268	10	2017	2017	NUM
ejpam-3648	268	11	.	.	PUNCT
ejpam-3648	269	1	[	[	X
ejpam-3648	269	2	7	7	X
ejpam-3648	269	3	]	]	X
ejpam-3648	269	4	a	a	DET
ejpam-3648	269	5	levent	levent	NOUN
ejpam-3648	269	6	and	and	CCONJ
ejpam-3648	269	7	b	b	NOUN
ejpam-3648	269	8	şahin	şahin	PROPN
ejpam-3648	269	9	.	.	PROPN
ejpam-3648	269	10	cubic	cubic	ADJ
ejpam-3648	269	11	bezier	bezier	NOUN
ejpam-3648	269	12	-	-	PUNCT
ejpam-3648	269	13	like	like	ADJ
ejpam-3648	269	14	transition	transition	NOUN
ejpam-3648	269	15	curves	curve	NOUN
ejpam-3648	269	16	with	with	ADP
ejpam-3648	269	17	new	new	ADJ
ejpam-3648	269	18	basis	basis	NOUN
ejpam-3648	269	19	function	function	NOUN
ejpam-3648	269	20	.	.	PUNCT
ejpam-3648	270	1	proceedings	proceeding	NOUN
ejpam-3648	270	2	of	of	ADP
ejpam-3648	270	3	the	the	DET
ejpam-3648	270	4	institute	institute	NOUN
ejpam-3648	270	5	of	of	ADP
ejpam-3648	270	6	mathematics	mathematics	PROPN
ejpam-3648	270	7	and	and	CCONJ
ejpam-3648	270	8	mechanics	mechanic	NOUN
ejpam-3648	270	9	,	,	PUNCT
ejpam-3648	270	10	national	national	PROPN
ejpam-3648	270	11	academy	academy	PROPN
ejpam-3648	270	12	of	of	ADP
ejpam-3648	270	13	sciences	sciences	PROPN
ejpam-3648	270	14	of	of	ADP
ejpam-3648	270	15	azerbaijan	azerbaijan	PROPN
ejpam-3648	270	16	.	.	PROPN
ejpam-3648	270	17	,	,	PUNCT
ejpam-3648	270	18	44(2):222–228	44(2):222–228	PROPN
ejpam-3648	270	19	,	,	PUNCT
ejpam-3648	270	20	2018	2018	NUM
ejpam-3648	270	21	.	.	PUNCT
ejpam-3648	271	1	[	[	X
ejpam-3648	271	2	8	8	NUM
ejpam-3648	271	3	]	]	X
ejpam-3648	271	4	d	d	X
ejpam-3648	271	5	marsh	marsh	PROPN
ejpam-3648	271	6	.	.	PUNCT
ejpam-3648	272	1	applied	apply	VERB
ejpam-3648	272	2	geometry	geometry	NOUN
ejpam-3648	272	3	for	for	ADP
ejpam-3648	272	4	computer	computer	NOUN
ejpam-3648	272	5	graphics	graphic	NOUN
ejpam-3648	272	6	and	and	CCONJ
ejpam-3648	272	7	cad	cad	PROPN
ejpam-3648	272	8	.	.	PROPN
ejpam-3648	272	9	springer	springer	NOUN
ejpam-3648	272	10	science	science	PROPN
ejpam-3648	272	11	and	and	CCONJ
ejpam-3648	272	12	business	business	NOUN
ejpam-3648	272	13	media	medium	NOUN
ejpam-3648	272	14	.	.	PUNCT
ejpam-3648	272	15	,	,	PUNCT
ejpam-3648	272	16	2006	2006	NUM
ejpam-3648	272	17	.	.	PUNCT
ejpam-3648	273	1	[	[	X
ejpam-3648	273	2	9	9	NUM
ejpam-3648	273	3	]	]	SYM
ejpam-3648	273	4	f	f	PROPN
ejpam-3648	273	5	tas	tas	PROPN
ejpam-3648	273	6	and	and	CCONJ
ejpam-3648	273	7	k	k	PROPN
ejpam-3648	273	8	i̇larslan	i̇larslan	NOUN
ejpam-3648	273	9	.	.	PUNCT
ejpam-3648	274	1	a	a	DET
ejpam-3648	274	2	new	new	ADJ
ejpam-3648	274	3	approach	approach	NOUN
ejpam-3648	274	4	to	to	PART
ejpam-3648	274	5	design	design	VERB
ejpam-3648	274	6	the	the	DET
ejpam-3648	274	7	ruled	rule	VERB
ejpam-3648	274	8	surface	surface	NOUN
ejpam-3648	274	9	.	.	PUNCT
ejpam-3648	275	1	international	international	ADJ
ejpam-3648	275	2	journal	journal	NOUN
ejpam-3648	275	3	of	of	ADP
ejpam-3648	275	4	geometric	geometric	ADJ
ejpam-3648	275	5	methods	method	NOUN
ejpam-3648	275	6	in	in	ADP
ejpam-3648	275	7	modern	modern	ADJ
ejpam-3648	275	8	physics	physic	NOUN
ejpam-3648	275	9	.	.	PUNCT
ejpam-3648	275	10	,	,	PUNCT
ejpam-3648	275	11	16(6):1950093	16(6):1950093	NUM
ejpam-3648	275	12	,	,	PUNCT
ejpam-3648	275	13	2019	2019	NUM
ejpam-3648	275	14	.	.	PUNCT
ejpam-3648	276	1	[	[	X
ejpam-3648	276	2	10	10	NUM
ejpam-3648	276	3	]	]	X
ejpam-3648	276	4	h	h	PROPN
ejpam-3648	276	5	zhang	zhang	PROPN
ejpam-3648	276	6	and	and	CCONJ
ejpam-3648	276	7	f	f	PROPN
ejpam-3648	276	8	jieqing	jieqing	NOUN
ejpam-3648	276	9	.	.	PUNCT
ejpam-3648	277	1	bézier	bézier	ADP
ejpam-3648	277	2	curves	curve	NOUN
ejpam-3648	277	3	and	and	CCONJ
ejpam-3648	277	4	surfaces	surface	NOUN
ejpam-3648	277	5	(	(	PUNCT
ejpam-3648	277	6	2	2	NUM
ejpam-3648	277	7	)	)	PUNCT
ejpam-3648	277	8	.	.	PUNCT
ejpam-3648	278	1	state	state	NOUN
ejpam-3648	278	2	key	key	ADJ
ejpam-3648	278	3	lab	lab	NOUN
ejpam-3648	278	4	of	of	ADP
ejpam-3648	278	5	cad&cg	cad&cg	NOUN
ejpam-3648	278	6	zhejiang	zhejiang	PROPN
ejpam-3648	278	7	university	university	PROPN
ejpam-3648	278	8	,	,	PUNCT
ejpam-3648	278	9	2006	2006	NUM
ejpam-3648	278	10	.	.	PUNCT