id	sid	tid	token	lemma	pos
hjic-1079	1	1	hungar	hungar	NOUN
hjic-1079	1	2	~	~	SYM
hjic-1079	1	3	journal	journal	NOUN
hjic-1079	1	4	of	of	ADP
hjic-1079	1	5	indus1rial	indus1rial	ADJ
hjic-1079	1	6	chemis1ry	chemis1ry	NOUN
hjic-1079	1	7	veszprem	veszprem	PROPN
hjic-1079	1	8	vol	vol	NOUN
hjic-1079	1	9	.	.	PROPN
hjic-1079	1	10	29	29	NUM
hjic-1079	1	11	.	.	PUNCT
hjic-1079	2	1	pp	pp	ADJ
hjic-1079	2	2	.	.	PUNCT
hjic-1079	3	1	105	105	NUM
hjic-1079	3	2	-	-	SYM
hjic-1079	3	3	111	111	NUM
hjic-1079	3	4	(	(	PUNCT
hjic-1079	3	5	2001	2001	NUM
hjic-1079	3	6	)	)	PUNCT
hjic-1079	3	7	b	b	X
hjic-1079	3	8	-	-	PUNCT
hjic-1079	3	9	splines	spline	NOUN
hjic-1079	3	10	contra	contra	PROPN
hjic-1079	3	11	beziersplines	bezierspline	NOUN
hjic-1079	3	12	n.herfmann	n.herfmann	PROPN
hjic-1079	3	13	(	(	PUNCT
hjic-1079	3	14	institute	institute	NOUN
hjic-1079	3	15	fiir	fiir	PROPN
hjic-1079	3	16	angewandte	angewandte	PROPN
hjic-1079	3	17	mathematik	mathematik	PROPN
hjic-1079	3	18	,	,	PUNCT
hjic-1079	3	19	universitat	universitat	PROPN
hjic-1079	3	20	hannover	hannover	PROPN
hjic-1079	3	21	,	,	PUNCT
hjic-1079	3	22	hannover	hannover	PROPN
hjic-1079	3	23	,	,	PUNCT
hjic-1079	3	24	germany	germany	PROPN
hjic-1079	3	25	)	)	PUNCT
hjic-1079	3	26	received	receive	VERB
hjic-1079	3	27	:	:	PUNCT
hjic-1079	3	28	april	april	PROPN
hjic-1079	3	29	9	9	NUM
hjic-1079	3	30	,	,	PUNCT
hjic-1079	3	31	2001	2001	NUM
hjic-1079	4	1	p.	p.	NOUN
hjic-1079	4	2	e.	e.	PROPN
hjic-1079	4	3	bezier	bezier	PROPN
hjic-1079	4	4	,	,	PUNCT
hjic-1079	4	5	a	a	DET
hjic-1079	4	6	mechanical	mechanical	ADJ
hjic-1079	4	7	and	and	CCONJ
hjic-1079	4	8	electrical	electrical	ADJ
hjic-1079	4	9	engineer	engineer	NOUN
hjic-1079	4	10	,	,	PUNCT
hjic-1079	4	11	developed	develop	VERB
hjic-1079	4	12	his	his	PRON
hjic-1079	4	13	idea	idea	NOUN
hjic-1079	4	14	of	of	ADP
hjic-1079	4	15	interpolating	interpolate	VERB
hjic-1079	4	16	given	give	VERB
hjic-1079	4	17	data	datum	NOUN
hjic-1079	4	18	during	during	ADP
hjic-1079	4	19	his	his	PRON
hjic-1079	4	20	work	work	NOUN
hjic-1079	4	21	at	at	ADP
hjic-1079	4	22	renault	renault	PROPN
hjic-1079	4	23	.	.	PUNCT
hjic-1079	5	1	instead	instead	ADV
hjic-1079	5	2	of	of	ADP
hjic-1079	5	3	using	use	VERB
hjic-1079	5	4	ordinary	ordinary	ADJ
hjic-1079	5	5	polynomials	polynomial	NOUN
hjic-1079	5	6	he	he	PRON
hjic-1079	5	7	introduced	introduce	VERB
hjic-1079	5	8	bernstein	bernstein	PROPN
hjic-1079	5	9	polynomials	polynomial	NOUN
hjic-1079	5	10	in	in	ADP
hjic-1079	5	11	his	his	PRON
hjic-1079	5	12	algorithm	algorithm	NOUN
hjic-1079	5	13	.	.	PUNCT
hjic-1079	6	1	with	with	ADP
hjic-1079	6	2	the	the	DET
hjic-1079	6	3	help	help	NOUN
hjic-1079	6	4	of	of	ADP
hjic-1079	6	5	the	the	DET
hjic-1079	6	6	bernstein	bernstein	PROPN
hjic-1079	6	7	operator	operator	NOUN
hjic-1079	6	8	and	and	CCONJ
hjic-1079	6	9	a	a	DET
hjic-1079	6	10	piecewise	piecewise	NOUN
hjic-1079	6	11	forgoing	forgo	VERB
hjic-1079	6	12	he	he	PRON
hjic-1079	6	13	invented	invent	VERB
hjic-1079	6	14	a	a	DET
hjic-1079	6	15	method	method	NOUN
hjic-1079	6	16	to	to	PART
hjic-1079	6	17	interpolate	interpolate	VERB
hjic-1079	6	18	given	give	VERB
hjic-1079	6	19	data	datum	NOUN
hjic-1079	6	20	with	with	ADP
hjic-1079	6	21	a	a	DET
hjic-1079	6	22	smooth	smooth	ADJ
hjic-1079	6	23	spline	spline	NOUN
hjic-1079	6	24	curve	curve	NOUN
hjic-1079	6	25	.	.	PUNCT
hjic-1079	7	1	i.	i.	PROPN
hjic-1079	7	2	j.	j.	PROPN
hjic-1079	7	3	schoenberg	schoenberg	PROPN
hjic-1079	7	4	is	be	AUX
hjic-1079	7	5	often	often	ADV
hjic-1079	7	6	entitled	entitle	VERB
hjic-1079	7	7	as	as	ADP
hjic-1079	7	8	the	the	DET
hjic-1079	7	9	father	father	NOUN
hjic-1079	7	10	of	of	ADP
hjic-1079	7	11	b	b	NOUN
hjic-1079	7	12	-	-	PUNCT
hjic-1079	7	13	splines	spline	NOUN
hjic-1079	7	14	,	,	PUNCT
hjic-1079	7	15	although	although	SCONJ
hjic-1079	7	16	laplace	laplace	NOUN
hjic-1079	7	17	probably	probably	ADV
hjic-1079	7	18	worked	work	VERB
hjic-1079	7	19	with	with	ADP
hjic-1079	7	20	some	some	DET
hjic-1079	7	21	kind	kind	NOUN
hjic-1079	7	22	of	of	ADP
hjic-1079	7	23	b­	b­	NOUN
hjic-1079	7	24	splines	spline	NOUN
hjic-1079	7	25	in	in	ADP
hjic-1079	7	26	1820	1820	NUM
hjic-1079	7	27	.	.	PUNCT
hjic-1079	8	1	they	they	PRON
hjic-1079	8	2	are	be	AUX
hjic-1079	8	3	introduced	introduce	VERB
hjic-1079	8	4	as	as	ADP
hjic-1079	8	5	basis	basis	NOUN
hjic-1079	8	6	for	for	ADP
hjic-1079	8	7	the	the	DET
hjic-1079	8	8	spline	spline	NOUN
hjic-1079	8	9	functions	function	NOUN
hjic-1079	8	10	,	,	PUNCT
hjic-1079	8	11	and	and	CCONJ
hjic-1079	8	12	this	this	PRON
hjic-1079	8	13	is	be	AUX
hjic-1079	8	14	the	the	DET
hjic-1079	8	15	reason	reason	NOUN
hjic-1079	8	16	for	for	ADP
hjic-1079	8	17	their	their	PRON
hjic-1079	8	18	name	name	NOUN
hjic-1079	8	19	.	.	PUNCT
hjic-1079	9	1	we	we	PRON
hjic-1079	9	2	present	present	VERB
hjic-1079	9	3	the	the	DET
hjic-1079	9	4	basic	basic	ADJ
hjic-1079	9	5	properties	property	NOUN
hjic-1079	9	6	of	of	ADP
hjic-1079	9	7	bezierand	bezierand	NOUN
hjic-1079	9	8	b	b	NOUN
hjic-1079	9	9	-	-	PUNCT
hjic-1079	9	10	splines	spline	NOUN
hjic-1079	9	11	including	include	VERB
hjic-1079	9	12	their	their	PRON
hjic-1079	9	13	shape	shape	NOUN
hjic-1079	9	14	preserving	preserve	VERB
hjic-1079	9	15	behaviour	behaviour	NOUN
hjic-1079	9	16	.	.	PUNCT
hjic-1079	10	1	in	in	ADP
hjic-1079	10	2	many	many	ADJ
hjic-1079	10	3	examples	example	NOUN
hjic-1079	10	4	we	we	PRON
hjic-1079	10	5	illustrate	illustrate	VERB
hjic-1079	10	6	the	the	DET
hjic-1079	10	7	main	main	ADJ
hjic-1079	10	8	differences	difference	NOUN
hjic-1079	10	9	in	in	ADP
hjic-1079	10	10	their	their	PRON
hjic-1079	10	11	interpolating	interpolate	VERB
hjic-1079	10	12	properties	property	NOUN
hjic-1079	10	13	.	.	PUNCT
hjic-1079	11	1	keywords	keyword	NOUN
hjic-1079	11	2	:	:	PUNCT
hjic-1079	11	3	interpolation	interpolation	NOUN
hjic-1079	11	4	,	,	PUNCT
hjic-1079	11	5	algorithms	algorithm	NOUN
hjic-1079	11	6	of	of	ADP
hjic-1079	11	7	de	de	X
hjic-1079	11	8	boor	boor	NOUN
hjic-1079	11	9	and	and	CCONJ
hjic-1079	11	10	de	de	ADP
hjic-1079	11	11	casteljau	casteljau	PROPN
hjic-1079	11	12	,	,	PUNCT
hjic-1079	11	13	comonotone	comonotone	NOUN
hjic-1079	11	14	behaviour	behaviour	NOUN
hjic-1079	11	15	history	history	NOUN
hjic-1079	11	16	(	(	PUNCT
hjic-1079	11	17	a	a	NOUN
hjic-1079	11	18	)	)	PUNCT
hjic-1079	11	19	b	b	NOUN
hjic-1079	11	20	-	-	PUNCT
hjic-1079	11	21	splines	splines	PUNCT
hjic-1079	11	22	1820	1820	NUM
hjic-1079	11	23	p.s	p.s	PROPN
hjic-1079	11	24	.	.	PROPN
hjic-1079	11	25	laplace	laplace	PROPN
hjic-1079	11	26	worked	work	VERB
hjic-1079	11	27	with	with	ADP
hjic-1079	11	28	some	some	DET
hjic-1079	11	29	kind	kind	NOUN
hjic-1079	11	30	of	of	ADP
hjic-1079	11	31	b­	b­	NOUN
hjic-1079	11	32	splines	spline	NOUN
hjic-1079	11	33	1850	1850	NUM
hjic-1079	11	34	n.i	n.i	PROPN
hjic-1079	11	35	.	.	PROPN
hjic-1079	11	36	lobatschewski	lobatschewski	PROPN
hjic-1079	11	37	gave	give	VERB
hjic-1079	12	1	a	a	DET
hjic-1079	12	2	short	short	ADJ
hjic-1079	12	3	explanation	explanation	NOUN
hjic-1079	12	4	1946	1946	NUM
hjic-1079	12	5	i.j	i.j	PROPN
hjic-1079	12	6	.	.	PROPN
hjic-1079	12	7	schoenberg	schoenberg	PROPN
hjic-1079	12	8	started	start	VERB
hjic-1079	12	9	with	with	ADP
hjic-1079	12	10	the	the	DET
hjic-1079	12	11	investigation	investigation	NOUN
hjic-1079	12	12	of	of	ADP
hjic-1079	12	13	"	"	PUNCT
hjic-1079	12	14	basic	basic	ADJ
hjic-1079	12	15	spline	spline	NOUN
hjic-1079	12	16	curves	curve	NOUN
hjic-1079	12	17	"	"	PUNCT
hjic-1079	12	18	1967	1967	NUM
hjic-1079	12	19	i.j	i.j	PROPN
hjic-1079	12	20	.	.	PROPN
hjic-1079	12	21	schoenberg	schoenberg	PROPN
hjic-1079	12	22	introduced	introduce	VERB
hjic-1079	12	23	the	the	DET
hjic-1079	12	24	name	name	NOUN
hjic-1079	12	25	"	"	PUNCT
hjic-1079	12	26	b	b	X
hjic-1079	12	27	-	-	PUNCT
hjic-1079	12	28	splines	spline	NOUN
hjic-1079	12	29	"	"	PUNCT
hjic-1079	12	30	1972	1972	NUM
hjic-1079	12	31	m.cox	m.cox	NOUN
hjic-1079	12	32	,	,	PUNCT
hjic-1079	12	33	c.de	c.de	PROPN
hjic-1079	12	34	boor	boor	NOUN
hjic-1079	12	35	,	,	PUNCT
hjic-1079	12	36	l.mansfield	l.mansfield	PROPN
hjic-1079	12	37	invented	invent	VERB
hjic-1079	12	38	the	the	DET
hjic-1079	12	39	"	"	PUNCT
hjic-1079	12	40	recurrel}ce	recurrel}ce	NUM
hjic-1079	12	41	relation	relation	NOUN
hjic-1079	12	42	"	"	PUNCT
hjic-1079	12	43	(	(	PUNCT
hjic-1079	12	44	b	b	X
hjic-1079	12	45	)	)	PUNCT
hjic-1079	12	46	beziersplines	bezierspline	NOUN
hjic-1079	12	47	1959	1959	NUM
hjic-1079	13	1	p.	p.	NOUN
hjic-1079	13	2	de	de	PROPN
hjic-1079	13	3	casteljau	casteljau	PROPN
hjic-1079	13	4	worked	work	VERB
hjic-1079	13	5	the	the	DET
hjic-1079	13	6	first	first	ADJ
hjic-1079	13	7	time	time	NOUN
hjic-1079	13	8	with	with	ADP
hjic-1079	13	9	these	these	DET
hjic-1079	13	10	splines	spline	NOUN
hjic-1079	13	11	1962	1962	NUM
hjic-1079	13	12	p.	p.	NOUN
hjic-1079	13	13	bezier	bezier	PROPN
hjic-1079	13	14	developed	develop	VERB
hjic-1079	13	15	the	the	DET
hjic-1079	13	16	same	same	ADJ
hjic-1079	13	17	idea	idea	NOUN
hjic-1079	13	18	a	a	DET
hjic-1079	13	19	second	second	ADJ
hjic-1079	13	20	time	time	NOUN
hjic-1079	13	21	1970	1970	NUM
hjic-1079	13	22	r.	r.	PROPN
hjic-1079	13	23	forrest	forrest	PROPN
hjic-1079	13	24	found	find	VERB
hjic-1079	13	25	the	the	DET
hjic-1079	13	26	connection	connection	NOUN
hjic-1079	13	27	to	to	ADP
hjic-1079	13	28	bernstein	bernstein	PROPN
hjic-1079	13	29	polynomials	polynomials	PROPN
hjic-1079	13	30	b·splines	b·spline	NOUN
hjic-1079	13	31	:	:	PUNCT
hjic-1079	13	32	alternative	alternative	ADJ
hjic-1079	13	33	defmitions	defmition	NOUN
hjic-1079	13	34	we	we	PRON
hjic-1079	13	35	start	start	VERB
hjic-1079	13	36	proposing	propose	VERB
hjic-1079	13	37	four	four	NUM
hjic-1079	13	38	different	different	ADJ
hjic-1079	13	39	kinds	kind	NOUN
hjic-1079	13	40	of	of	ADP
hjic-1079	13	41	definitions	definition	NOUN
hjic-1079	13	42	for	for	ADP
hjic-1079	13	43	b	b	NOUN
hjic-1079	13	44	-	-	PUNCT
hjic-1079	13	45	splines	spline	NOUN
hjic-1079	13	46	.	.	PUNCT
hjic-1079	14	1	(	(	PUNCT
hjic-1079	14	2	a	a	X
hjic-1079	14	3	)	)	PUNCT
hjic-1079	14	4	recursive	recursive	ADJ
hjic-1079	14	5	definition	definition	NOUN
hjic-1079	14	6	given	give	VERB
hjic-1079	14	7	a	a	DET
hjic-1079	14	8	knot	knot	ADJ
hjic-1079	14	9	sequence	sequence	NOUN
hjic-1079	14	10	of	of	ADP
hjic-1079	14	11	real	real	ADJ
hjic-1079	14	12	numbers	number	NOUN
hjic-1079	14	13	in	in	ADP
hjic-1079	14	14	r.	r.	PROPN
hjic-1079	14	15	:	:	PUNCT
hjic-1079	14	16	t	t	PROPN
hjic-1079	14	17	=	=	SYM
hjic-1079	14	18	(	(	PUNCT
hjic-1079	14	19	xo	xo	PROPN
hjic-1079	14	20	'	'	PUNCT
hjic-1079	14	21	xi	xi	PROPN
hjic-1079	14	22	'	'	PUNCT
hjic-1079	14	23	xz	xz	PROPN
hjic-1079	14	24	,	,	PUNCT
hjic-1079	14	25	•••	•••	ADV
hjic-1079	14	26	,	,	PUNCT
hjic-1079	14	27	xn	xn	PROPN
hjic-1079	14	28	,	,	PUNCT
hjic-1079	14	29	xn+l	xn+l	PROPN
hjic-1079	14	30	,	,	PUNCT
hjic-1079	14	31	•••	•••	ADV
hjic-1079	14	32	,	,	PUNCT
hjic-1079	14	33	xn+l+l	xn+l+l	PROPN
hjic-1079	14	34	)	)	PUNCT
hjic-1079	14	35	then	then	ADV
hjic-1079	14	36	we	we	PRON
hjic-1079	14	37	define	define	VERB
hjic-1079	14	38	z	z	NOUN
hjic-1079	14	39	=	=	NOUN
hjic-1079	14	40	o	o	NOUN
hjic-1079	14	41	:	:	PUNCT
hjic-1079	14	42	{	{	PUNCT
hjic-1079	14	43	1	1	NUM
hjic-1079	14	44	if	if	SCONJ
hjic-1079	14	45	n0	n0	NUM
hjic-1079	14	46	.(x	.(x	PUNCT
hjic-1079	14	47	)	)	PUNCT
hjic-1079	15	1	=	=	PUNCT
hjic-1079	15	2	,	,	PUNCT
hjic-1079	15	3	i	i	PRON
hjic-1079	15	4	0	0	NUM
hjic-1079	15	5	xi	xi	ADP
hjic-1079	15	6	:	:	PUNCT
hjic-1079	15	7	:	:	PUNCT
hjic-1079	15	8	;	;	PUNCT
hjic-1079	15	9	;	;	PUNCT
hjic-1079	15	10	x	x	X
hjic-1079	15	11	:	:	PUNCT
hjic-1079	15	12	s;;xi+l	s;;xi+l	NOUN
hjic-1079	15	13	,	,	PUNCT
hjic-1079	15	14	i:::::o	i:::::o	PROPN
hjic-1079	15	15	,	,	PUNCT
hjic-1079	15	16	...	...	PUNCT
hjic-1079	15	17	,	,	PUNCT
hjic-1079	15	18	n	n	X
hjic-1079	15	19	otherwise	otherwise	ADV
hjic-1079	15	20	l	l	X
hjic-1079	15	21	>	>	PUNCT
hjic-1079	15	22	0	0	NUM
hjic-1079	15	23	:	:	PUNCT
hjic-1079	15	24	i	i	PROPN
hjic-1079	15	25	=	=	NOUN
hjic-1079	15	26	o	o	PROPN
hjic-1079	15	27	,	,	PUNCT
hjic-1079	15	28	...	...	PUNCT
hjic-1079	15	29	,	,	PUNCT
hjic-1079	15	30	n	n	X
hjic-1079	15	31	(	(	PUNCT
hjic-1079	15	32	b	b	NOUN
hjic-1079	15	33	)	)	PUNCT
hjic-1079	15	34	definition	definition	NOUN
hjic-1079	15	35	by	by	ADP
hjic-1079	15	36	divided	divide	VERB
hjic-1079	15	37	differences	difference	NOUN
hjic-1079	15	38	we	we	PRON
hjic-1079	15	39	use	use	VERB
hjic-1079	15	40	the	the	DET
hjic-1079	15	41	well	well	ADV
hjic-1079	15	42	-	-	PUNCT
hjic-1079	15	43	known	know	VERB
hjic-1079	15	44	divided	divide	VERB
hjic-1079	15	45	differences	difference	NOUN
hjic-1079	15	46	to	to	PART
hjic-1079	15	47	define	define	VERB
hjic-1079	15	48	with	with	ADP
hjic-1079	15	49	{	{	PUNCT
hjic-1079	15	50	{	{	PUNCT
hjic-1079	15	51	rx)1	rx)1	NOUN
hjic-1079	15	52	if	if	SCONJ
hjic-1079	15	53	t	t	PROPN
hjic-1079	15	54	~	~	PUNCT
hjic-1079	15	55	x	x	SYM
hjic-1079	15	56	(	(	PUNCT
hjic-1079	15	57	t	t	PROPN
hjic-1079	15	58	-	-	PUNCT
hjic-1079	15	59	x)~	x)~	PROPN
hjic-1079	15	60	:	:	PUNCT
hjic-1079	15	61	=	=	SYM
hjic-1079	15	62	0	0	NUM
hjic-1079	15	63	lu	lu	NOUN
hjic-1079	15	64	:	:	PUNCT
hjic-1079	15	65	~	~	PUNCT
hjic-1079	15	66	t	t	X
hjic-1079	15	67	<	<	X
hjic-1079	15	68	x	x	PROPN
hjic-1079	15	69	contact	contact	NOUN
hjic-1079	15	70	information	information	NOUN
hjic-1079	15	71	:	:	PUNCT
hjic-1079	15	72	e	e	X
hjic-1079	15	73	~	~	NOUN
hjic-1079	15	74	mail	mail	NOUN
hjic-1079	15	75	:	:	PUNCT
hjic-1079	16	1	herrmann@ifam.uni-hanoover.de	herrmann@ifam.uni-hanoover.de	ADP
hjic-1079	16	2	106	106	NUM
hjic-1079	16	3	i	i	PRON
hjic-1079	16	4	11-,---1	11-,---1	NUM
hjic-1079	16	5	!	!	PUNCT
hjic-1079	17	1	•	•	NOUN
hjic-1079	18	1	i	i	PRON
hjic-1079	18	2	0	0	PUNCT
hjic-1079	18	3	t	t	NOUN
hjic-1079	18	4	i	i	NOUN
hjic-1079	18	5	1	1	NUM
hjic-1079	18	6	~	~	PUNCT
hjic-1079	18	7	i	i	PRON
hjic-1079	18	8	i	i	PRON
hjic-1079	18	9	~	~	PUNCT
hjic-1079	18	10	0	0	NUM
hjic-1079	18	11	l	l	NOUN
hjic-1079	18	12	not(x	not(x	PROPN
hjic-1079	18	13	)	)	PUNCT
hjic-1079	18	14	2	2	NUM
hjic-1079	18	15	1	1	NUM
hjic-1079	18	16	..	..	PUNCT
hjic-1079	18	17	0.75	0.75	NUM
hjic-1079	18	18	0.5	0.5	NUM
hjic-1079	18	19	t	t	PROPN
hjic-1079	18	20	"	"	PUNCT
hjic-1079	18	21	'	'	PUNCT
hjic-1079	18	22	~	~	PUNCT
hjic-1079	18	23	0.25	0.25	NUM
hjic-1079	18	24	l	l	NOUN
hjic-1079	18	25	..	..	PUNCT
hjic-1079	18	26	0	0	NUM
hjic-1079	19	1	l	l	NOUN
hjic-1079	19	2	0.75	0.75	NUM
hjic-1079	19	3	l	l	NOUN
hjic-1079	19	4	0.25	0.25	NUM
hjic-1079	19	5	~­	~­	NOUN
hjic-1079	19	6	~	~	PUNCT
hjic-1079	19	7	0	0	PUNCT
hjic-1079	19	8	n2s{x	n2s{x	NOUN
hjic-1079	19	9	)	)	PUNCT
hjic-1079	19	10	(	(	PUNCT
hjic-1079	19	11	l5	l5	PROPN
hjic-1079	19	12	1	1	NUM
hjic-1079	19	13	t5	t5	PROPN
hjic-1079	19	14	2	2	NUM
hjic-1079	19	15	2.5	2.5	NUM
hjic-1079	19	16	3	3	NUM
hjic-1079	19	17	.3.5	.3.5	SYM
hjic-1079	19	18	4	4	NUM
hjic-1079	19	19	4.5	4.5	NUM
hjic-1079	19	20	0.5	0.5	NUM
hjic-1079	19	21	1	1	NUM
hjic-1079	19	22	1.5	1.5	NUM
hjic-1079	19	23	2	2	NUM
hjic-1079	19	24	2.5	2.5	NUM
hjic-1079	19	25	3	3	NUM
hjic-1079	19	26	3.5	3.5	NUM
hjic-1079	19	27	4	4	NUM
hjic-1079	19	28	4.5	4.5	NUM
hjic-1079	19	29	5	5	NUM
hjic-1079	19	30	fig.l	fig.l	PROPN
hjic-1079	19	31	in	in	ADP
hjic-1079	19	32	each	each	DET
hjic-1079	19	33	figure	figure	NOUN
hjic-1079	19	34	we	we	PRON
hjic-1079	19	35	see	see	VERB
hjic-1079	19	36	two	two	NUM
hjic-1079	19	37	b	b	NOUN
hjic-1079	19	38	-	-	PUNCT
hjic-1079	19	39	splines	spline	NOUN
hjic-1079	19	40	of	of	ADP
hjic-1079	19	41	order	order	NOUN
hjic-1079	19	42	0,1,2	0,1,2	NUM
hjic-1079	19	43	and	and	CCONJ
hjic-1079	19	44	3	3	NUM
hjic-1079	19	45	.	.	PUNCT
hjic-1079	20	1	(	(	PUNCT
hjic-1079	20	2	c	c	X
hjic-1079	20	3	)	)	PUNCT
hjic-1079	20	4	definition	definition	NOUN
hjic-1079	20	5	by	by	ADP
hjic-1079	20	6	the	the	DET
hjic-1079	20	7	+	+	ADJ
hjic-1079	20	8	-functions	-function	NOUN
hjic-1079	20	9	without	without	ADP
hjic-1079	20	10	the	the	DET
hjic-1079	20	11	help	help	NOUN
hjic-1079	20	12	of	of	ADP
hjic-1079	20	13	the	the	DET
hjic-1079	20	14	divided	divide	VERB
hjic-1079	20	15	differences	difference	NOUN
hjic-1079	20	16	we	we	PRON
hjic-1079	20	17	can	can	AUX
hjic-1079	20	18	use	use	VERB
hjic-1079	20	19	the	the	DET
hjic-1079	20	20	+	+	ADJ
hjic-1079	20	21	-functions	-function	NOUN
hjic-1079	20	22	alone	alone	ADJ
hjic-1079	20	23	to	to	PART
hjic-1079	20	24	define	define	VERB
hjic-1079	20	25	the	the	DET
hjic-1079	20	26	b	b	NOUN
hjic-1079	20	27	-	-	PUNCT
hjic-1079	20	28	splines	spline	NOUN
hjic-1079	20	29	:	:	PUNCT
hjic-1079	20	30	i+l+1	i+l+1	PROPN
hjic-1079	20	31	nzj	nzj	PROPN
hjic-1079	20	32	(	(	PUNCT
hjic-1079	20	33	x	x	NOUN
hjic-1079	20	34	)	)	PUNCT
hjic-1079	20	35	:	:	PUNCT
hjic-1079	21	1	=	=	SYM
hjic-1079	21	2	(	(	PUNCT
hjic-1079	21	3	xi+l+l	xi+l+l	PROPN
hjic-1079	21	4	-xi	-xi	PROPN
hjic-1079	21	5	)	)	PUNCT
hjic-1079	21	6	·	·	PUNCT
hjic-1079	22	1	l	l	NOUN
hjic-1079	22	2	k;i	k;i	PROPN
hjic-1079	22	3	(	(	PUNCT
hjic-1079	22	4	xt	xt	PROPN
hjic-1079	22	5	-x)~	-x)~	PROPN
hjic-1079	22	6	i+l+l	i+l+l	NOUN
hjic-1079	23	1	it	it	PRON
hjic-1079	23	2	(	(	PUNCT
hjic-1079	23	3	xt	xt	PROPN
hjic-1079	23	4	-xz	-xz	CCONJ
hjic-1079	23	5	)	)	PUNCT
hjic-1079	23	6	r	r	X
hjic-1079	23	7	=	=	SYM
hjic-1079	23	8	i	i	PROPN
hjic-1079	23	9	,	,	PUNCT
hjic-1079	23	10	r.=k	r.=k	NOUN
hjic-1079	23	11	,	,	PUNCT
hjic-1079	23	12	i	i	PRON
hjic-1079	23	13	=	=	NOUN
hjic-1079	23	14	o	o	NOUN
hjic-1079	23	15	,	,	PUNCT
hjic-1079	23	16	...	...	PUNCT
hjic-1079	23	17	,	,	PUNCT
hjic-1079	23	18	n	n	X
hjic-1079	23	19	(	(	PUNCT
hjic-1079	23	20	d	d	NOUN
hjic-1079	23	21	)	)	PUNCT
hjic-1079	23	22	definition	definition	NOUN
hjic-1079	23	23	by	by	ADP
hjic-1079	23	24	construction	construction	NOUN
hjic-1079	23	25	let	let	VERB
hjic-1079	23	26	[	[	X
hjic-1079	23	27	a	a	DET
hjic-1079	23	28	~	~	ADJ
hjic-1079	23	29	b}t	b}t	NOUN
hjic-1079	23	30	;	;	PUNCT
hjic-1079	23	31	r	r	NOUN
hjic-1079	23	32	~	~	PUNCT
hjic-1079	23	33	a:=	a:=	X
hjic-1079	23	34	{	{	PUNCT
hjic-1079	23	35	xot•••txn+t	xot•••txn+t	NOUN
hjic-1079	23	36	}	}	PUNCT
hjic-1079	23	37	,	,	PUNCT
hjic-1079	23	38	x	x	X
hjic-1079	23	39	;	;	PUNCT
hjic-1079	23	40	e	e	X
hjic-1079	23	41	r	r	PROPN
hjic-1079	23	42	,	,	PUNCT
hjic-1079	23	43	a	a	PRON
hjic-1079	23	44	=	=	NOUN
hjic-1079	23	45	x0	x0	NOUN
hjic-1079	23	46	<	<	X
hjic-1079	23	47	x1	x1	PROPN
hjic-1079	23	48	<	<	X
hjic-1079	23	49	·	·	PUNCT
hjic-1079	23	50	..	..	PUNCT
hjic-1079	24	1	<	<	X
hjic-1079	24	2	xn	xn	X
hjic-1079	24	3	<	<	X
hjic-1079	24	4	xn+1	xn+1	PROPN
hjic-1079	24	5	=	=	PROPN
hjic-1079	24	6	b.	b.	PROPN
hjic-1079	24	7	then	then	ADV
hjic-1079	24	8	we	we	PRON
hjic-1079	24	9	define	define	VERB
hjic-1079	24	10	:	:	PUNCT
hjic-1079	24	11	s1(a):={se	s1(a):={se	PROPN
hjic-1079	24	12	c1	c1	PROPN
hjic-1079	24	13	1{a	1{a	NUM
hjic-1079	24	14	,	,	PUNCT
hjic-1079	24	15	b}:sltx,.x	b}:sltx,.x	PROPN
hjic-1079	24	16	.•	.•	PROPN
hjic-1079	24	17	de	de	X
hjic-1079	24	18	ip1	ip1	PROPN
hjic-1079	24	19	~t	~t	PUNCT
hjic-1079	25	1	=	=	PUNCT
hjic-1079	25	2	o	o	NOUN
hjic-1079	25	3	,	,	PUNCT
hjic-1079	25	4	..	..	PUNCT
hjic-1079	25	5	....	....	PUNCT
hjic-1079	26	1	n	n	CCONJ
hjic-1079	26	2	}	}	PUNCT
hjic-1079	26	3	for	for	ADP
hjic-1079	26	4	this	this	DET
hjic-1079	26	5	vector	vector	NOUN
hjic-1079	26	6	space	space	NOUN
hjic-1079	26	7	we	we	PRON
hjic-1079	26	8	have	have	VERB
hjic-1079	26	9	a	a	DET
hjic-1079	26	10	basis	basis	NOUN
hjic-1079	26	11	built	build	VERB
hjic-1079	26	12	with	with	ADP
hjic-1079	26	13	the	the	DET
hjic-1079	26	14	+	+	NOUN
hjic-1079	26	15	­	­	ADJ
hjic-1079	26	16	functions	function	NOUN
hjic-1079	26	17	:	:	PUNCT
hjic-1079	26	18	s1(a	s1(a	ADP
hjic-1079	26	19	}	}	PUNCT
hjic-1079	26	20	=	=	PRON
hjic-1079	26	21	span	span	NOUN
hjic-1079	26	22	<	<	X
hjic-1079	26	23	1~.t,.x2	1~.t,.x2	PROPN
hjic-1079	26	24	,	,	PUNCT
hjic-1079	26	25	•••	•••	ADV
hjic-1079	26	26	,	,	PUNCT
hjic-1079	26	27	x1	x1	NUM
hjic-1079	26	28	,	,	PUNCT
hjic-1079	26	29	(	(	PUNCT
hjic-1079	26	30	x	x	X
hjic-1079	26	31	-	-	PUNCT
hjic-1079	26	32	x1i	x1i	PROPN
hjic-1079	26	33	+	+	PROPN
hjic-1079	26	34	~	~	PUNCT
hjic-1079	26	35	•••	•••	ADV
hjic-1079	26	36	,	,	PUNCT
hjic-1079	26	37	(	(	PUNCT
hjic-1079	26	38	x	x	NOUN
hjic-1079	26	39	-	-	NOUN
hjic-1079	26	40	x11	x11	NOUN
hjic-1079	26	41	)	)	PUNCT
hjic-1079	26	42	1	1	NUM
hjic-1079	27	1	+	+	CCONJ
hjic-1079	27	2	>	>	X
hjic-1079	27	3	and	and	CCONJ
hjic-1079	27	4	we	we	PRON
hjic-1079	27	5	can	can	AUX
hjic-1079	27	6	prove	prove	VERB
hjic-1079	27	7	the	the	DET
hjic-1079	27	8	following	follow	VERB
hjic-1079	27	9	theorem	theorem	NOUN
hjic-1079	27	10	:	:	PUNCT
hjic-1079	27	11	theorem	theorem	ADJ
hjic-1079	27	12	:	:	PUNCT
hjic-1079	27	13	let	let	VERB
hjic-1079	27	14	q	q	VERB
hjic-1079	27	15	..	..	PUNCT
hjic-1079	27	16	,	,	PUNCT
hjic-1079	27	17	.	.	PUNCT
hjic-1079	28	1	:	:	PUNCT
hjic-1079	28	2	=	=	X
hjic-1079	28	3	{	{	PUNCT
hjic-1079	28	4	.x	.x	NOUN
hjic-1079	28	5	...	...	PUNCT
hjic-1079	28	6	}	}	PUNCT
hjic-1079	28	7	~z,.a	~z,.a	PUNCT
hjic-1079	28	8	;	;	PUNCT
hjic-1079	28	9	,	,	PUNCT
hjic-1079	28	10	<	<	X
hjic-1079	28	11	xv+t•	xv+t•	X
hjic-1079	28	12	for	for	ADP
hjic-1079	28	13	each	each	DET
hjic-1079	28	14	i	i	NOUN
hjic-1079	28	15	e	e	PROPN
hjic-1079	28	16	z	z	NOUN
hjic-1079	28	17	there	there	PRON
hjic-1079	28	18	exists	exist	VERB
hjic-1079	28	19	a	a	DET
hjic-1079	28	20	unique	unique	ADJ
hjic-1079	28	21	~pline	~pline	ADJ
hjic-1079	28	22	function	function	NOUN
hjic-1079	28	23	s	s	PROPN
hjic-1079	28	24	e	e	NOUN
hjic-1079	28	25	s1	s1	NOUN
hjic-1079	28	26	(	(	PUNCT
hjic-1079	28	27	a	a	NOUN
hjic-1079	28	28	}	}	PUNCT
hjic-1079	28	29	with	with	ADP
hjic-1079	28	30	...	...	PUNCT
hjic-1079	28	31	s(x)=o	s(x)=o	VERB
hjic-1079	28	32	in(-«>jlx,)u(x1	in(-«>jlx,)u(x1	ADJ
hjic-1079	28	33	+	+	NOUN
hjic-1079	28	34	1•	1•	NUM
hjic-1079	28	35	1,oo	1,oo	NUM
hjic-1079	28	36	)	)	PUNCT
hjic-1079	28	37	and	and	CCONJ
hjic-1079	28	38	js(:c}dx	js(:c}dx	PROPN
hjic-1079	28	39	=	=	PROPN
hjic-1079	28	40	l.	l.	PROPN
hjic-1079	28	41	it	it	PRON
hjic-1079	28	42	is	be	AUX
hjic-1079	28	43	not	not	PART
hjic-1079	28	44	very	very	ADV
hjic-1079	28	45	surprising	surprising	ADJ
hjic-1079	28	46	that	that	SCONJ
hjic-1079	28	47	we	we	PRON
hjic-1079	28	48	can	can	AUX
hjic-1079	28	49	prove	prove	VERB
hjic-1079	28	50	it	it	PRON
hjic-1079	28	51	easily	easily	ADV
hjic-1079	28	52	that	that	SCONJ
hjic-1079	28	53	the	the	DET
hjic-1079	28	54	four	four	NUM
hjic-1079	28	55	definitions	definition	NOUN
hjic-1079	28	56	lead	lead	VERB
hjic-1079	28	57	exactly	exactly	ADV
hjic-1079	28	58	to	to	ADP
hjic-1079	28	59	the	the	DET
hjic-1079	28	60	same	same	ADJ
hjic-1079	28	61	functions	function	NOUN
hjic-1079	28	62	.	.	PUNCT
hjic-1079	29	1	theorem	theorem	VERB
hjic-1079	29	2	:	:	PUNCT
hjic-1079	29	3	all	all	DET
hjic-1079	29	4	definitions	definition	NOUN
hjic-1079	29	5	above	above	ADV
hjic-1079	29	6	are	be	AUX
hjic-1079	29	7	equivalent	equivalent	ADJ
hjic-1079	29	8	.	.	PUNCT
hjic-1079	30	1	dermition	dermition	NOUN
hjic-1079	30	2	:	:	PUNCT
hjic-1079	30	3	we	we	PRON
hjic-1079	30	4	will	will	AUX
hjic-1079	30	5	call	call	VERB
hjic-1079	30	6	the	the	DET
hjic-1079	30	7	functions	function	NOUN
hjic-1079	30	8	developed	develop	VERB
hjic-1079	30	9	in	in	ADP
hjic-1079	30	10	the	the	DET
hjic-1079	30	11	four	four	NUM
hjic-1079	30	12	definitions	definition	NOUN
hjic-1079	30	13	b	b	NOUN
hjic-1079	30	14	-	-	PUNCT
hjic-1079	30	15	splines	spline	NOUN
hjic-1079	30	16	.	.	PUNCT
hjic-1079	31	1	basic	basic	ADJ
hjic-1079	31	2	properties	property	NOUN
hjic-1079	31	3	we	we	PRON
hjic-1079	31	4	summarize	summarize	VERB
hjic-1079	31	5	some	some	PRON
hjic-1079	31	6	of	of	ADP
hjic-1079	31	7	the	the	DET
hjic-1079	31	8	important	important	ADJ
hjic-1079	31	9	properties	property	NOUN
hjic-1079	31	10	of	of	ADP
hjic-1079	31	11	b­	b­	NOUN
hjic-1079	31	12	splines	spline	NOUN
hjic-1079	31	13	in	in	ADP
hjic-1079	31	14	the	the	DET
hjic-1079	31	15	following	following	NOUN
hjic-1079	31	16	theorem	theorem	NOUN
hjic-1079	31	17	:	:	PUNCT
hjic-1079	31	18	theorem	theorem	ADJ
hjic-1079	31	19	:	:	PUNCT
hjic-1079	31	20	1	1	X
hjic-1079	31	21	.	.	X
hjic-1079	32	1	we	we	PRON
hjic-1079	32	2	have	have	VERB
hjic-1079	32	3	n1	n1	NOUN
hjic-1079	32	4	/	/	SYM
hjic-1079	32	5	x	x	NOUN
hjic-1079	32	6	)	)	PUNCT
hjic-1079	32	7	=	=	SYM
hjic-1079	32	8	0	0	PUNCT
hjic-1079	33	1	if	if	SCONJ
hjic-1079	33	2	x\l	x\l	PROPN
hjic-1079	33	3	(	(	PUNCT
hjic-1079	33	4	xi'xi+l+l	xi'xi+l+l	PROPN
hjic-1079	33	5	)	)	PUNCT
hjic-1079	33	6	,	,	PUNCT
hjic-1079	33	7	2	2	X
hjic-1079	33	8	.	.	X
hjic-1079	34	1	we	we	PRON
hjic-1079	34	2	have	have	VERB
hjic-1079	34	3	nz,;(x)e	nz,;(x)e	NUM
hjic-1079	34	4	el	el	PROPN
hjic-1079	34	5	-	-	PROPN
hjic-1079	34	6	l	l	NOUN
hjic-1079	34	7	if	if	SCONJ
hjic-1079	34	8	xe	xe	PROPN
hjic-1079	34	9	[	[	X
hjic-1079	34	10	xi'xi+l+d	xi'xi+l+d	X
hjic-1079	34	11	'	'	PUNCT
hjic-1079	34	12	3	3	NUM
hjic-1079	34	13	.	.	PUNCT
hjic-1079	34	14	wehave	wehave	PROPN
hjic-1079	34	15	nl	nl	PROPN
hjic-1079	34	16	,	,	PUNCT
hjic-1079	34	17	i(x)>o	i(x)>o	PROPN
hjic-1079	34	18	if	if	SCONJ
hjic-1079	34	19	xe	xe	PROPN
hjic-1079	34	20	(	(	PUNCT
hjic-1079	34	21	xi.xi+l+1	xi.xi+l+1	PROPN
hjic-1079	34	22	)	)	PUNCT
hjic-1079	34	23	,	,	PUNCT
hjic-1079	34	24	4	4	X
hjic-1079	34	25	.	.	X
hjic-1079	35	1	we	we	PRON
hjic-1079	35	2	have	have	VERB
hjic-1079	35	3	the	the	DET
hjic-1079	35	4	property	property	NOUN
hjic-1079	35	5	of	of	ADP
hjic-1079	35	6	partition	partition	NOUN
hjic-1079	35	7	of	of	ADP
hjic-1079	35	8	unity	unity	NOUN
hjic-1079	35	9	:	:	PUNCT
hjic-1079	35	10	n-1	n-1	X
hjic-1079	35	11	l	l	NOUN
hjic-1079	35	12	n1,;(x	n1,;(x	NOUN
hjic-1079	35	13	)	)	PUNCT
hjic-1079	35	14	=	=	SYM
hjic-1079	35	15	1	1	NUM
hjic-1079	35	16	if	if	SCONJ
hjic-1079	35	17	xe	xe	PROPN
hjic-1079	35	18	[	[	X
hjic-1079	35	19	xi	xi	X
hjic-1079	35	20	,	,	PUNCT
hjic-1079	35	21	xi+l+d	xi+l+d	PROPN
hjic-1079	35	22	i=-l	i=-l	NUM
hjic-1079	35	23	remarks	remark	VERB
hjic-1079	35	24	:	:	PUNCT
hjic-1079	35	25	l.	l.	PROPN
hjic-1079	35	26	this	this	PRON
hjic-1079	35	27	means	mean	VERB
hjic-1079	35	28	that	that	SCONJ
hjic-1079	35	29	the	the	DET
hjic-1079	35	30	b	b	NOUN
hjic-1079	35	31	-	-	PUNCT
hjic-1079	35	32	splines	spline	NOUN
hjic-1079	35	33	have	have	VERB
hjic-1079	35	34	a	a	DET
hjic-1079	35	35	small	small	ADJ
hjic-1079	35	36	support	support	NOUN
hjic-1079	35	37	.	.	PUNCT
hjic-1079	36	1	only	only	ADV
hjic-1079	36	2	in	in	ADP
hjic-1079	36	3	an	an	DET
hjic-1079	36	4	interval	interval	NOUN
hjic-1079	36	5	with	with	ADP
hjic-1079	36	6	l	l	NOUN
hjic-1079	36	7	+	+	CCONJ
hjic-1079	36	8	2	2	NUM
hjic-1079	36	9	knots	knot	NOUN
hjic-1079	36	10	we	we	PRON
hjic-1079	36	11	have	have	VERB
hjic-1079	36	12	a	a	DET
hjic-1079	36	13	chance	chance	NOUN
hjic-1079	36	14	to	to	PART
hjic-1079	36	15	find	find	VERB
hjic-1079	36	16	values	value	NOUN
hjic-1079	36	17	unlike	unlike	ADP
hjic-1079	36	18	zero	zero	NUM
hjic-1079	36	19	.	.	PUNCT
hjic-1079	37	1	2	2	X
hjic-1079	37	2	.	.	X
hjic-1079	37	3	here	here	ADV
hjic-1079	37	4	we	we	PRON
hjic-1079	37	5	are	be	AUX
hjic-1079	37	6	told	tell	VERB
hjic-1079	37	7	,	,	PUNCT
hjic-1079	37	8	that	that	SCONJ
hjic-1079	37	9	the	the	DET
hjic-1079	37	10	b	b	NOUN
hjic-1079	37	11	-	-	PUNCT
hjic-1079	37	12	splines	spline	NOUN
hjic-1079	37	13	have	have	VERB
hjic-1079	37	14	a	a	DET
hjic-1079	37	15	defect	defect	NOUN
hjic-1079	37	16	of	of	ADP
hjic-1079	37	17	1	1	NUM
hjic-1079	37	18	,	,	PUNCT
hjic-1079	37	19	therefore	therefore	ADV
hjic-1079	37	20	the	the	DET
hjic-1079	37	21	b	b	NOUN
hjic-1079	37	22	-	-	PUNCT
hjic-1079	37	23	splines	spline	NOUN
hjic-1079	37	24	of	of	ADP
hjic-1079	37	25	degree	degree	NOUN
hjic-1079	37	26	l	l	NOUN
hjic-1079	37	27	are	be	AUX
hjic-1079	37	28	l-1times	l-1time	NOUN
hjic-1079	37	29	continuously	continuously	ADV
hjic-1079	37	30	differentiable	differentiable	ADJ
hjic-1079	37	31	.	.	PUNCT
hjic-1079	38	1	3	3	X
hjic-1079	38	2	.	.	X
hjic-1079	39	1	the	the	DET
hjic-1079	39	2	b	b	NOUN
hjic-1079	39	3	-	-	PUNCT
hjic-1079	39	4	splines	spline	NOUN
hjic-1079	39	5	are	be	AUX
hjic-1079	39	6	positive	positive	ADJ
hjic-1079	39	7	functions	function	NOUN
hjic-1079	39	8	.	.	PUNCT
hjic-1079	40	1	4	4	X
hjic-1079	40	2	.	.	X
hjic-1079	40	3	we	we	PRON
hjic-1079	40	4	can	can	AUX
hjic-1079	40	5	conclude	conclude	VERB
hjic-1079	40	6	on	on	ADP
hjic-1079	40	7	the	the	DET
hjic-1079	40	8	bound	bind	VERB
hjic-1079	40	9	1	1	NUM
hjic-1079	40	10	for	for	ADP
hjic-1079	40	11	ali	ali	PROPN
hjic-1079	40	12	b	b	PROPN
hjic-1079	40	13	~	~	PROPN
hjic-1079	40	14	splines	spline	NOUN
hjic-1079	40	15	.	.	PUNCT
hjic-1079	41	1	seefig.j	seefig.j	NOUN
hjic-1079	41	2	.	.	PUNCT
hjic-1079	42	1	t	t	PROPN
hjic-1079	42	2	=	=	PUNCT
hjic-1079	42	3	(	(	PUNCT
hjic-1079	42	4	to	to	PART
hjic-1079	42	5	,	,	PUNCT
hjic-1079	42	6	tt	tt	PROPN
hjic-1079	42	7	,	,	PUNCT
hjic-1079	42	8	t2	t2	NOUN
hjic-1079	42	9	,	,	PUNCT
hjic-1079	42	10	t:1	t:1	PROPN
hjic-1079	42	11	,	,	PUNCT
hjic-1079	42	12	t4	t4	PROPN
hjic-1079	42	13	)	)	PUNCT
hjic-1079	42	14	=	=	PUNCT
hjic-1079	43	1	(	(	PUNCT
hjic-1079	43	2	0~	0~	NOUN
hjic-1079	43	3	1	1	NUM
hjic-1079	43	4	,	,	PUNCT
hjic-1079	43	5	2~	2~	X
hjic-1079	43	6	a	a	PRON
hjic-1079	43	7	,	,	PUNCT
hjic-1079	43	8	4	4	X
hjic-1079	43	9	)	)	PUNCT
hjic-1079	43	10	f(t	f(t	NOUN
hjic-1079	43	11	)	)	PUNCT
hjic-1079	43	12	1	1	NUM
hjic-1079	43	13	t0.75	t0.75	PROPN
hjic-1079	43	14	r	r	NOUN
hjic-1079	43	15	..	..	PUNCT
hjic-1079	43	16	0.5	0.5	NUM
hjic-1079	43	17	10.2	10.2	NUM
hjic-1079	43	18	!	!	PUNCT
hjic-1079	43	19	)	)	PUNCT
hjic-1079	44	1	[	[	X
hjic-1079	44	2	0	0	NUM
hjic-1079	44	3	0.5	0.5	NUM
hjic-1079	44	4	1	1	NUM
hjic-1079	44	5	1.5	1.5	NUM
hjic-1079	44	6	2	2	NUM
hjic-1079	44	7	2.5	2.5	NUM
hjic-1079	44	8	3	3	NUM
hjic-1079	44	9	3.5	3.5	NUM
hjic-1079	44	10	4	4	NUM
hjic-1079	44	11	lt0.7~	lt0.7~	NOUN
hjic-1079	44	12	[	[	PUNCT
hjic-1079	44	13	o.i	o.i	PROPN
hjic-1079	44	14	:>	:>	PROPN
hjic-1079	44	15	;	;	PUNCT
hjic-1079	44	16	fig.2a	fig.2a	NUM
hjic-1079	44	17	4	4	NUM
hjic-1079	44	18	intervals	interval	NOUN
hjic-1079	44	19	/"~\	/"~\	PUNCT
hjic-1079	44	20	/	/	SYM
hjic-1079	44	21	'	'	PUNCT
hjic-1079	44	22	\	\	NOUN
hjic-1079	44	23	0.25	0.25	NUM
hjic-1079	44	24	i/	i/	NOUN
hjic-1079	44	25	\	\	PROPN
hjic-1079	44	26	"	"	PUNCT
hjic-1079	44	27	"	"	PUNCT
hjic-1079	44	28	'	'	PUNCT
hjic-1079	44	29	;	;	PUNCT
hjic-1079	44	30	m,	m,	X
hjic-1079	44	31	....	....	SYM
hjic-1079	44	32	-/~"'----'-~	-/~"'----'-~	PROPN
hjic-1079	44	33	..	..	PROPN
hjic-1079	44	34	j	j	PROPN
hjic-1079	44	35	....	....	PUNCT
hjic-1079	44	36	-	-	PUNCT
hjic-1079	44	37	...	...	PUNCT
hjic-1079	44	38	-!.1	-!.1	PRON
hjic-1079	44	39	-"'.;;;.~.;.,	-"'.;;;.~.;.,	ADJ
hjic-1079	44	40	.	.	PUNCT
hjic-1079	44	41	,~---l--'-----'---	,~---l--'-----'---	PUNCT
hjic-1079	44	42	·	·	PUNCT
hjic-1079	45	1	t	t	NOUN
hjic-1079	45	2	0	0	NUM
hjic-1079	45	3	0.5	0.5	NUM
hjic-1079	45	4	1	1	NUM
hjic-1079	45	5	1.5	1.5	NUM
hjic-1079	45	6	2	2	NUM
hjic-1079	45	7	2.5	2.5	NUM
hjic-1079	45	8	3	3	NUM
hjic-1079	45	9	3.5	3.5	NUM
hjic-1079	45	10	4	4	NUM
hjic-1079	45	11	fig.2b	fig.2b	NOUN
hjic-1079	45	12	3	3	NUM
hjic-1079	45	13	intervals	interval	NOUN
hjic-1079	45	14	fig.2	fig.2	VERB
hjic-1079	45	15	support	support	NOUN
hjic-1079	45	16	-	-	PUNCT
hjic-1079	45	17	reduction	reduction	NOUN
hjic-1079	45	18	of	of	ADP
hjic-1079	45	19	a	a	DET
hjic-1079	45	20	b	b	NOUN
hjic-1079	45	21	-	-	NOUN
hjic-1079	45	22	spline	spline	NOUN
hjic-1079	45	23	of	of	ADP
hjic-1079	45	24	order	order	NOUN
hjic-1079	45	25	3	3	NUM
hjic-1079	45	26	from	from	ADP
hjic-1079	45	27	4	4	NUM
hjic-1079	45	28	intervals	interval	NOUN
hjic-1079	45	29	to	to	ADP
hjic-1079	45	30	2	2	NUM
hjic-1079	45	31	intervals	interval	NOUN
hjic-1079	45	32	,	,	PUNCT
hjic-1079	45	33	if	if	SCONJ
hjic-1079	45	34	1	1	NUM
hjic-1079	45	35	is	be	AUX
hjic-1079	45	36	a	a	DET
hjic-1079	45	37	knot	knot	NOUN
hjic-1079	45	38	of	of	ADP
hjic-1079	45	39	multiplicity	multiplicity	NOUN
hjic-1079	45	40	3	3	NUM
hjic-1079	45	41	.	.	PUNCT
hjic-1079	45	42	multiple	multiple	ADJ
hjic-1079	45	43	knots	knot	NOUN
hjic-1079	45	44	given	give	VERB
hjic-1079	45	45	a	a	DET
hjic-1079	45	46	knot	knot	ADJ
hjic-1079	45	47	sequence	sequence	NOUN
hjic-1079	45	48	xo	xo	NOUN
hjic-1079	45	49	'	'	PUNCT
hjic-1079	45	50	x1	x1	PROPN
hjic-1079	45	51	,	,	PUNCT
hjic-1079	45	52	xz	xz	PROPN
hjic-1079	45	53	'	'	PUNCT
hjic-1079	45	54	.•.	.•.	PUNCT
hjic-1079	46	1	'	'	NOUN
hjic-1079	46	2	xn	xn	NUM
hjic-1079	46	3	'	'	PUNCT
hjic-1079	46	4	xn+l	xn+l	NOUN
hjic-1079	46	5	'	'	PUNCT
hjic-1079	46	6	...	...	PUNCT
hjic-1079	46	7	,	,	PUNCT
hjic-1079	46	8	xn+l+l	xn+l+l	INTJ
hjic-1079	46	9	,	,	PUNCT
hjic-1079	46	10	we	we	PRON
hjic-1079	46	11	did	do	AUX
hjic-1079	46	12	not	not	PART
hjic-1079	46	13	demand	demand	VERB
hjic-1079	46	14	that	that	SCONJ
hjic-1079	46	15	ail	ail	NOUN
hjic-1079	46	16	points	point	NOUN
hjic-1079	46	17	should	should	AUX
hjic-1079	46	18	be	be	AUX
hjic-1079	46	19	different	different	ADJ
hjic-1079	46	20	.	.	PUNCT
hjic-1079	47	1	what	what	PRON
hjic-1079	47	2	happens	happen	VERB
hjic-1079	47	3	if	if	SCONJ
hjic-1079	47	4	some	some	DET
hjic-1079	47	5	neighbor	neighbor	NOUN
hjic-1079	47	6	points	point	NOUN
hjic-1079	47	7	fall	fall	VERB
hjic-1079	47	8	together	together	ADV
hjic-1079	47	9	?	?	PUNCT
hjic-1079	48	1	theorem	theorem	VERB
hjic-1079	48	2	:	:	PUNCT
hjic-1079	48	3	if	if	SCONJ
hjic-1079	48	4	xi	xi	PROPN
hjic-1079	48	5	=	=	PUNCT
hjic-1079	48	6	xi+	xi+	PROPN
hjic-1079	48	7	i	i	NOUN
hjic-1079	48	8	=	=	PUNCT
hjic-1079	48	9	·	·	PUNCT
hjic-1079	48	10	·	·	PUNCT
hjic-1079	48	11	·	·	PUNCT
hjic-1079	49	1	=	=	PUNCT
hjic-1079	49	2	xi+l+i	xi+l+i	X
hjic-1079	49	3	,	,	PUNCT
hjic-1079	49	4	then	then	ADV
hjic-1079	49	5	we	we	PRON
hjic-1079	49	6	have	have	VERB
hjic-1079	49	7	n	n	PROPN
hjic-1079	49	8	1,i	1,i	NUM
hjic-1079	49	9	(	(	PUNCT
hjic-1079	49	10	x	x	X
hjic-1079	49	11	;)	;)	SYM
hjic-1079	49	12	=	=	SYM
hjic-1079	49	13	0	0	NUM
hjic-1079	49	14	,	,	PUNCT
hjic-1079	49	15	i	i	PRON
hjic-1079	49	16	=	=	NOUN
hjic-1079	49	17	o	o	NOUN
hjic-1079	49	18	,	,	PUNCT
hjic-1079	49	19	...	...	PUNCT
hjic-1079	49	20	,	,	PUNCT
hjic-1079	49	21	n	n	CCONJ
hjic-1079	49	22	from	from	ADP
hjic-1079	49	23	this	this	PRON
hjic-1079	49	24	we	we	PRON
hjic-1079	49	25	conclude	conclude	VERB
hjic-1079	49	26	immediately	immediately	ADV
hjic-1079	49	27	that	that	SCONJ
hjic-1079	49	28	n1,i	n1,i	PROPN
hjic-1079	49	29	=	=	SYM
hjic-1079	49	30	0	0	PROPN
hjic-1079	49	31	,	,	PUNCT
hjic-1079	49	32	which	which	PRON
hjic-1079	49	33	is	be	AUX
hjic-1079	49	34	not	not	PART
hjic-1079	49	35	a	a	DET
hjic-1079	49	36	very	very	ADV
hjic-1079	49	37	interesting	interesting	ADJ
hjic-1079	49	38	result	result	NOUN
hjic-1079	49	39	.	.	PUNCT
hjic-1079	50	1	so	so	ADV
hjic-1079	50	2	we	we	PRON
hjic-1079	50	3	ask	ask	VERB
hjic-1079	50	4	for	for	ADP
hjic-1079	50	5	the	the	DET
hjic-1079	50	6	case	case	NOUN
hjic-1079	50	7	when	when	SCONJ
hjic-1079	50	8	less	less	ADJ
hjic-1079	50	9	than	than	ADP
hjic-1079	50	10	l	l	NOUN
hjic-1079	50	11	+	+	CCONJ
hjic-1079	50	12	2	2	NUM
hjic-1079	50	13	knots	knot	NOUN
hjic-1079	50	14	coincide	coincide	NOUN
hjic-1079	50	15	.	.	PUNCT
hjic-1079	51	1	theorem	theorem	VERB
hjic-1079	51	2	:	:	PUNCT
hjic-1079	51	3	if	if	SCONJ
hjic-1079	51	4	x	x	NOUN
hjic-1079	51	5	;	;	PUNCT
hjic-1079	51	6	is	be	AUX
hjic-1079	51	7	a	a	DET
hjic-1079	51	8	knot	knot	NOUN
hjic-1079	51	9	with	with	ADP
hjic-1079	51	10	multiplicity	multiplicity	NOUN
hjic-1079	51	11	m	m	X
hjic-1079	51	12	~	~	PUNCT
hjic-1079	51	13	l	l	NOUN
hjic-1079	51	14	,	,	PUNCT
hjic-1079	51	15	it	it	PRON
hjic-1079	51	16	follows	follow	VERB
hjic-1079	51	17	the	the	DET
hjic-1079	51	18	smoothness	smoothness	NOUN
hjic-1079	51	19	of	of	ADP
hjic-1079	51	20	a	a	DET
hjic-1079	51	21	b	b	NOUN
hjic-1079	51	22	-	-	PUNCT
hjic-1079	51	23	spline	spline	NOUN
hjic-1079	51	24	decreases	decrease	VERB
hjic-1079	51	25	therefore	therefore	ADV
hjic-1079	51	26	with	with	ADP
hjic-1079	51	27	multiple	multiple	ADJ
hjic-1079	51	28	knots	knot	NOUN
hjic-1079	51	29	.	.	PUNCT
hjic-1079	52	1	the	the	DET
hjic-1079	52	2	decrease	decrease	NOUN
hjic-1079	52	3	of	of	ADP
hjic-1079	52	4	the	the	DET
hjic-1079	52	5	smoothness	smoothness	NOUN
hjic-1079	52	6	comes	come	VERB
hjic-1079	52	7	together	together	ADV
hjic-1079	52	8	with	with	ADP
hjic-1079	52	9	a	a	DET
hjic-1079	52	10	decrease	decrease	NOUN
hjic-1079	52	11	of	of	ADP
hjic-1079	52	12	the	the	DET
hjic-1079	52	13	support	support	NOUN
hjic-1079	52	14	of	of	ADP
hjic-1079	52	15	the	the	DET
hjic-1079	52	16	b	b	NOUN
hjic-1079	52	17	-	-	PUNCT
hjic-1079	52	18	spline	spline	NOUN
hjic-1079	52	19	:	:	PUNCT
hjic-1079	52	20	theorem	theorem	VERB
hjic-1079	52	21	:	:	PUNCT
hjic-1079	52	22	if	if	SCONJ
hjic-1079	52	23	xi	xi	PROPN
hjic-1079	52	24	is	be	AUX
hjic-1079	52	25	a	a	DET
hjic-1079	52	26	knot	knot	NOUN
hjic-1079	52	27	of	of	ADP
hjic-1079	52	28	multiplicity	multiplicity	NOUN
hjic-1079	52	29	m	m	X
hjic-1079	52	30	~	~	PUNCT
hjic-1079	52	31	l	l	NOUN
hjic-1079	52	32	,	,	PUNCT
hjic-1079	52	33	then	then	ADV
hjic-1079	52	34	the	the	DET
hjic-1079	52	35	support	support	NOUN
hjic-1079	52	36	of	of	ADP
hjic-1079	52	37	nr.i(x	nr.i(x	NOUN
hjic-1079	52	38	)	)	PUNCT
hjic-1079	52	39	is	be	AUX
hjic-1079	52	40	reduced	reduce	VERB
hjic-1079	52	41	from	from	ADP
hjic-1079	52	42	l	l	NOUN
hjic-1079	52	43	+	+	PROPN
hjic-1079	52	44	!	!	NOUN
hjic-1079	52	45	intervals	interval	NOUN
hjic-1079	52	46	to	to	ADP
hjic-1079	52	47	l	l	NOUN
hjic-1079	52	48	+	+	CCONJ
hjic-1079	52	49	1-(m1	1-(m1	NUM
hjic-1079	52	50	)	)	PUNCT
hjic-1079	52	51	intervals	interval	NOUN
hjic-1079	52	52	.	.	PUNCT
hjic-1079	53	1	we	we	PRON
hjic-1079	53	2	show	show	VERB
hjic-1079	53	3	this	this	DET
hjic-1079	53	4	behaviour	behaviour	NOUN
hjic-1079	53	5	in	in	ADP
hjic-1079	53	6	fig.2	fig.2	PROPN
hjic-1079	53	7	.	.	PUNCT
hjic-1079	53	8	1	1	NUM
hjic-1079	53	9	0.75	0.75	NUM
hjic-1079	53	10	0.5	0.5	NUM
hjic-1079	53	11	0.25	0.25	NUM
hjic-1079	53	12	107	107	NUM
hjic-1079	53	13	0	0	NUM
hjic-1079	53	14	0.5	0.5	NUM
hjic-1079	53	15	1	1	NUM
hjic-1079	53	16	1.5	1.5	NUM
hjic-1079	53	17	2	2	NUM
hjic-1079	53	18	2.5	2.5	NUM
hjic-1079	53	19	3	3	NUM
hjic-1079	53	20	3.5	3.5	NUM
hjic-1079	53	21	4	4	NUM
hjic-1079	53	22	.	.	PUNCT
hjic-1079	54	1	fig.2c	fig.2c	ADJ
hjic-1079	54	2	2	2	NUM
hjic-1079	54	3	intervals	interval	NOUN
hjic-1079	54	4	fig.3	fig.3	PROPN
hjic-1079	54	5	example	example	NOUN
hjic-1079	54	6	of	of	ADP
hjic-1079	54	7	a	a	DET
hjic-1079	54	8	b	b	NOUN
hjic-1079	54	9	-	-	PUNCT
hjic-1079	54	10	spline	spline	NOUN
hjic-1079	54	11	curve	curve	NOUN
hjic-1079	54	12	with	with	ADP
hjic-1079	54	13	knot	knot	ADJ
hjic-1079	54	14	sequence	sequence	NOUN
hjic-1079	54	15	t=(o	t=(o	NOUN
hjic-1079	54	16	,	,	PUNCT
hjic-1079	54	17	o	o	NOUN
hjic-1079	54	18	,	,	PUNCT
hjic-1079	54	19	o	o	NOUN
hjic-1079	54	20	,	,	PUNCT
hjic-1079	54	21	o	o	NOUN
hjic-1079	54	22	,	,	PUNCT
hjic-1079	54	23	1,2,3,4,5,6,6,6,6	1,2,3,4,5,6,6,6,6	NUM
hjic-1079	54	24	)	)	PUNCT
hjic-1079	54	25	.	.	PUNCT
hjic-1079	55	1	b	b	X
hjic-1079	55	2	-	-	PUNCT
hjic-1079	55	3	spline	spline	NOUN
hjic-1079	55	4	curves	curve	NOUN
hjic-1079	55	5	of	of	ADP
hjic-1079	55	6	degree	degree	NOUN
hjic-1079	55	7	1	1	NUM
hjic-1079	56	1	now	now	ADV
hjic-1079	56	2	we	we	PRON
hjic-1079	56	3	come	come	VERB
hjic-1079	56	4	to	to	ADP
hjic-1079	56	5	curves	curve	NOUN
hjic-1079	56	6	built	build	VERB
hjic-1079	56	7	with	with	ADP
hjic-1079	56	8	b	b	NOUN
hjic-1079	56	9	-	-	PUNCT
hjic-1079	56	10	splinet	splinet	NOUN
hjic-1079	56	11	,	,	PUNCT
hjic-1079	56	12	at	at	ADP
hjic-1079	56	13	first	first	ADV
hjic-1079	56	14	the	the	DET
hjic-1079	56	15	definition	definition	NOUN
hjic-1079	56	16	:	:	PUNCT
hjic-1079	56	17	definition	definition	NOUN
hjic-1079	56	18	:	:	PUNCT
hjic-1079	56	19	given	give	VERB
hjic-1079	56	20	l	l	NOUN
hjic-1079	56	21	e	e	NOUN
hjic-1079	56	22	in	in	ADV
hjic-1079	56	23	and	and	CCONJ
hjic-1079	56	24	points	point	VERB
hjic-1079	56	25	2	2	NUM
hjic-1079	56	26	3	3	NUM
hjic-1079	56	27	d0	d0	NOUN
hjic-1079	56	28	,	,	PUNCT
hjic-1079	56	29	d1	d1	NOUN
hjic-1079	56	30	'	'	PUNCT
hjic-1079	56	31	...	...	PUNCT
hjic-1079	57	1	,	,	PUNCT
hjic-1079	57	2	d	d	PROPN
hjic-1079	57	3	11	11	NUM
hjic-1079	57	4	e	e	VERB
hjic-1079	57	5	ir	ir	PROPN
hjic-1079	57	6	or	or	CCONJ
hjic-1079	57	7	ir	ir	PROPN
hjic-1079	57	8	and	and	CCONJ
hjic-1079	57	9	a	a	DET
hjic-1079	57	10	knot	knot	NOUN
hjic-1079	57	11	sequence	sequence	NOUN
hjic-1079	57	12	then	then	ADV
hjic-1079	57	13	we	we	PRON
hjic-1079	57	14	call	call	VERB
hjic-1079	57	15	the	the	DET
hjic-1079	57	16	following	follow	VERB
hjic-1079	57	17	linear	linear	ADJ
hjic-1079	57	18	combination	combination	NOUN
hjic-1079	57	19	1l	1l	NUM
hjic-1079	57	20	b1(x	b1(x	NOUN
hjic-1079	57	21	)	)	PUNCT
hjic-1079	57	22	=	=	SYM
hjic-1079	57	23	ld;n1,;(x	ld;n1,;(x	NOUN
hjic-1079	57	24	)	)	PUNCT
hjic-1079	57	25	,	,	PUNCT
hjic-1079	57	26	i	i	PRON
hjic-1079	58	1	=	=	NOUN
hjic-1079	58	2	o	o	X
hjic-1079	58	3	a	a	DET
hjic-1079	58	4	b	b	PROPN
hjic-1079	58	5	~	~	PUNCT
hjic-1079	58	6	spline	spline	NOUN
hjic-1079	58	7	curve	curve	NOUN
hjic-1079	58	8	of	of	ADP
hjic-1079	58	9	degree	degree	NOUN
hjic-1079	58	10	l	l	NOUN
hjic-1079	58	11	for	for	ADP
hjic-1079	58	12	the	the	DET
hjic-1079	58	13	knot	knot	ADJ
hjic-1079	58	14	sequence	sequence	NOUN
hjic-1079	58	15	t.	t.	NOUN
hjic-1079	58	16	d0	d0	PROPN
hjic-1079	58	17	,	,	PUNCT
hjic-1079	58	18	d1p	d1p	PROPN
hjic-1079	58	19	..	..	PUNCT
hjic-1079	59	1	,	,	PUNCT
hjic-1079	59	2	d	d	NOUN
hjic-1079	59	3	11	11	NUM
hjic-1079	59	4	are	be	AUX
hjic-1079	59	5	the	the	DET
hjic-1079	59	6	de	de	X
hjic-1079	59	7	boor	boor	NOUN
hjic-1079	59	8	puints	puint	NOUN
hjic-1079	59	9	,	,	PUNCT
hjic-1079	59	10	they	they	PRON
hjic-1079	59	11	build	build	VERB
hjic-1079	59	12	the	the	DET
hjic-1079	59	13	de	de	X
hjic-1079	59	14	boor	boor	ADJ
hjic-1079	59	15	polygon	polygon	NOUN
hjic-1079	59	16	.	.	PUNCT
hjic-1079	60	1	one	one	NUM
hjic-1079	60	2	of	of	ADP
hjic-1079	60	3	the	the	DET
hjic-1079	60	4	most	most	ADV
hjic-1079	60	5	important	important	ADJ
hjic-1079	60	6	properties	property	NOUN
hjic-1079	60	7	for	for	ADP
hjic-1079	60	8	such	such	DET
hjic-1079	60	9	a	a	DET
hjic-1079	60	10	b­	b­	NOUN
hjic-1079	60	11	spline	spline	NOUN
hjic-1079	60	12	curve	curve	NOUN
hjic-1079	60	13	is	be	AUX
hjic-1079	60	14	its	its	PRON
hjic-1079	60	15	local	local	ADJ
hjic-1079	60	16	behaviour	behaviour	NOUN
hjic-1079	60	17	.	.	PUNCT
hjic-1079	61	1	if	if	SCONJ
hjic-1079	61	2	one	one	NUM
hjic-1079	61	3	of	of	ADP
hjic-1079	61	4	the	the	DET
hjic-1079	61	5	points	point	NOUN
hjic-1079	61	6	ji	ji	PROPN
hjic-1079	61	7	is	be	AUX
hjic-1079	61	8	changed	change	VERB
hjic-1079	61	9	,	,	PUNCT
hjic-1079	61	10	the	the	DET
hjic-1079	61	11	curve	curve	NOUN
hjic-1079	61	12	will	will	AUX
hjic-1079	61	13	be	be	AUX
hjic-1079	61	14	changed	change	VERB
hjic-1079	61	15	in	in	ADP
hjic-1079	61	16	a	a	DET
hjic-1079	61	17	small	small	ADJ
hjic-1079	61	18	vicinity	vicinity	NOUN
hjic-1079	61	19	of	of	ADP
hjic-1079	61	20	ji	ji	PROPN
hjic-1079	61	21	only	only	ADV
hjic-1079	61	22	.	.	PUNCT
hjic-1079	62	1	this	this	PRON
hjic-1079	62	2	is	be	AUX
hjic-1079	62	3	what	what	PRON
hjic-1079	62	4	designers	designer	NOUN
hjic-1079	62	5	whish	whish	VERB
hjic-1079	62	6	.	.	PUNCT
hjic-1079	63	1	so	so	ADV
hjic-1079	63	2	the	the	DET
hjic-1079	63	3	front	front	NOUN
hjic-1079	63	4	of	of	ADP
hjic-1079	63	5	a	a	DET
hjic-1079	63	6	car	car	NOUN
hjic-1079	63	7	can	can	AUX
hjic-1079	63	8	be	be	AUX
hjic-1079	63	9	changed	change	VERB
hjic-1079	63	10	whereas	whereas	SCONJ
hjic-1079	63	11	the	the	DET
hjic-1079	63	12	back	back	NOUN
hjic-1079	63	13	remains	remain	VERB
hjic-1079	63	14	unchanged	unchanged	ADJ
hjic-1079	63	15	.	.	PUNCT
hjic-1079	64	1	this	this	PRON
hjic-1079	64	2	is	be	AUX
hjic-1079	64	3	the	the	DET
hjic-1079	64	4	content	content	NOUN
hjic-1079	64	5	of	of	ADP
hjic-1079	64	6	the	the	DET
hjic-1079	64	7	following	following	NOUN
hjic-1079	64	8	theorem	theorem	NOUN
hjic-1079	64	9	:	:	PUNCT
hjic-1079	64	10	108	108	NUM
hjic-1079	64	11	theorem	theorem	VERB
hjic-1079	64	12	:	:	PUNCT
hjic-1079	64	13	given	give	VERB
hjic-1079	64	14	a	a	DET
hjic-1079	64	15	b	b	NUM
hjic-1079	64	16	-	-	PUNCT
hjic-1079	64	17	spline	spline	NOUN
hjic-1079	64	18	curve	curve	NOUN
hjic-1079	64	19	n	n	PROPN
hjic-1079	64	20	b1(x	b1(x	NOUN
hjic-1079	64	21	)	)	PUNCT
hjic-1079	64	22	=	=	SYM
hjic-1079	64	23	ld;n1,;(x	ld;n1,;(x	NOUN
hjic-1079	64	24	)	)	PUNCT
hjic-1079	64	25	,	,	PUNCT
hjic-1079	64	26	i	i	PRON
hjic-1079	64	27	=	=	NOUN
hjic-1079	64	28	o	o	X
hjic-1079	64	29	with	with	ADP
hjic-1079	64	30	knot	knot	ADJ
hjic-1079	64	31	sequence	sequence	NOUN
hjic-1079	64	32	t	t	PROPN
hjic-1079	64	33	and	and	CCONJ
hjic-1079	64	34	x	x	X
hjic-1079	64	35	*	*	PUNCT
hjic-1079	64	36	e	e	X
hjic-1079	64	37	(	(	PUNCT
hjic-1079	64	38	xi	xi	PROPN
hjic-1079	64	39	,	,	PUNCT
hjic-1079	64	40	xi+l	xi+l	NOUN
hjic-1079	64	41	)	)	PUNCT
hjic-1079	64	42	.	.	PUNCT
hjic-1079	65	1	the	the	DET
hjic-1079	65	2	point	point	NOUN
hjic-1079	65	3	on	on	ADP
hjic-1079	65	4	the	the	DET
hjic-1079	65	5	curve	curve	NOUN
hjic-1079	65	6	belonging	belong	VERB
hjic-1079	65	7	to	to	ADP
hjic-1079	65	8	x	x	PROPN
hjic-1079	65	9	*	*	VERB
hjic-1079	65	10	is	be	AUX
hjic-1079	65	11	only	only	ADV
hjic-1079	65	12	influenced	influence	VERB
hjic-1079	65	13	by	by	ADP
hjic-1079	65	14	the	the	DET
hjic-1079	65	15	de	de	X
hjic-1079	65	16	boor	boor	NOUN
hjic-1079	65	17	points	point	NOUN
hjic-1079	65	18	di_1	di_1	PROPN
hjic-1079	65	19	,	,	PUNCT
hjic-1079	65	20	.	.	PUNCT
hjic-1079	66	1	••	••	NOUN
hjic-1079	66	2	,	,	PUNCT
hjic-1079	66	3	dr	dr	PROPN
hjic-1079	66	4	hereby	hereby	ADV
hjic-1079	66	5	ji	ji	PROPN
hjic-1079	66	6	acts	act	VERB
hjic-1079	66	7	in	in	ADP
hjic-1079	66	8	(	(	PUNCT
hjic-1079	66	9	xpxj+l+l	xpxj+l+l	PROPN
hjic-1079	66	10	)	)	PUNCT
hjic-1079	66	11	only	only	ADV
hjic-1079	66	12	.	.	PUNCT
hjic-1079	67	1	figure	figure	NOUN
hjic-1079	67	2	3	3	NUM
hjic-1079	67	3	gives	give	VERB
hjic-1079	67	4	an	an	DET
hjic-1079	67	5	example	example	NOUN
hjic-1079	67	6	of	of	ADP
hjic-1079	67	7	a	a	DET
hjic-1079	67	8	b	b	NOUN
hjic-1079	67	9	-	-	PUNCT
hjic-1079	67	10	spline	spline	NOUN
hjic-1079	67	11	curve	curve	NOUN
hjic-1079	67	12	.	.	PUNCT
hjic-1079	68	1	bezier	bezier	NOUN
hjic-1079	68	2	curves	curve	VERB
hjic-1079	68	3	the	the	DET
hjic-1079	68	4	main	main	ADJ
hjic-1079	68	5	tool	tool	NOUN
hjic-1079	68	6	in	in	ADP
hjic-1079	68	7	constructing	construct	VERB
hjic-1079	68	8	bezier	bezier	ADJ
hjic-1079	68	9	curves	curve	NOUN
hjic-1079	68	10	are	be	AUX
hjic-1079	68	11	the	the	DET
hjic-1079	68	12	berpstein	berpstein	NOUN
hjic-1079	68	13	polynomials	polynomial	NOUN
hjic-1079	68	14	.	.	PUNCT
hjic-1079	69	1	defmition	defmition	NOUN
hjic-1079	69	2	:	:	PUNCT
hjic-1079	70	1	b	b	X
hjic-1079	70	2	,	,	PUNCT
hjic-1079	70	3	"	"	PUNCT
hjic-1079	70	4	(	(	PUNCT
hjic-1079	70	5	x)=	x)=	X
hjic-1079	70	6	(;	(;	PUNCT
hjic-1079	70	7	}	}	PUNCT
hjic-1079	70	8	'	'	PUNCT
hjic-1079	70	9	(	(	PUNCT
hjic-1079	70	10	!	!	PUNCT
hjic-1079	70	11	-x)~1	-x)~1	NOUN
hjic-1079	70	12	,	,	PUNCT
hjic-1079	70	13	i	i	PRON
hjic-1079	70	14	=	=	NOUN
hjic-1079	70	15	0	0	NUM
hjic-1079	70	16	,	,	PUNCT
hjic-1079	70	17	...	...	PUNCT
hjic-1079	70	18	,	,	PUNCT
hjic-1079	70	19	n	n	CCONJ
hjic-1079	70	20	,	,	PUNCT
hjic-1079	70	21	x	x	X
hjic-1079	70	22	e	e	NOUN
hjic-1079	71	1	[	[	X
hjic-1079	71	2	0,1	0,1	NUM
hjic-1079	71	3	]	]	PUNCT
hjic-1079	71	4	we	we	PRON
hjic-1079	71	5	summarize	summarize	VERB
hjic-1079	71	6	some	some	DET
hjic-1079	71	7	important	important	ADJ
hjic-1079	71	8	properties	property	NOUN
hjic-1079	71	9	of	of	ADP
hjic-1079	71	10	the	the	DET
hjic-1079	71	11	bernstein	bernstein	PROPN
hjic-1079	71	12	polynomials	polynomial	NOUN
hjic-1079	71	13	in	in	ADP
hjic-1079	71	14	the	the	DET
hjic-1079	71	15	following	follow	VERB
hjic-1079	71	16	theorem	theorem	PROPN
hjic-1079	71	17	.	.	PUNCT
hjic-1079	71	18	theorem	theorem	VERB
hjic-1079	71	19	:	:	PUNCT
hjic-1079	72	1	bi11	bi11	PROPN
hjic-1079	72	2	(	(	PUNCT
hjic-1079	72	3	x	x	X
hjic-1079	72	4	)	)	PUNCT
hjic-1079	72	5	>	>	X
hjic-1079	72	6	0	0	PUNCT
hjic-1079	72	7	for	for	ADP
hjic-1079	72	8	xe	xe	PROPN
hjic-1079	72	9	(	(	PUNCT
hjic-1079	72	10	0,1	0,1	NOUN
hjic-1079	72	11	)	)	PUNCT
hjic-1079	72	12	a	a	DET
hjic-1079	72	13	ba	ba	PROPN
hjic-1079	72	14	{	{	PUNCT
hjic-1079	72	15	b;11	b;11	NOUN
hjic-1079	72	16	h=0	h=0	PROPN
hjic-1079	72	17	,	,	PUNCT
hjic-1079	72	18	...	...	PUNCT
hjic-1079	72	19	,	,	PUNCT
hjic-1079	72	20	n	n	PRON
hjic-1079	72	21	is	be	AUX
hjic-1079	72	22	a	a	DET
hjic-1079	72	23	basis	basis	NOUN
hjic-1079	72	24	for	for	ADP
hjic-1079	72	25	the	the	DET
hjic-1079	72	26	vector	vector	NOUN
hjic-1079	72	27	space	space	NOUN
hjic-1079	72	28	of	of	ADP
hjic-1079	72	29	all	all	DET
hjic-1079	72	30	polynomials	polynomial	NOUN
hjic-1079	72	31	of	of	ADP
hjic-1079	72	32	degree	degree	NOUN
hjic-1079	72	33	~	~	PUNCT
hjic-1079	72	34	n	n	X
hjic-1079	72	35	.	.	PUNCT
hjic-1079	73	1	if	if	SCONJ
hjic-1079	73	2	lb~	lb~	PROPN
hjic-1079	73	3	(	(	PUNCT
hjic-1079	73	4	x)=	x)=	PROPN
hjic-1079	73	5	1	1	NUM
hjic-1079	73	6	for	for	ADP
hjic-1079	73	7	xe	xe	PROPN
hjic-1079	73	8	(	(	PUNCT
hjic-1079	73	9	0,1	0,1	NUM
hjic-1079	73	10	)	)	PUNCT
hjic-1079	73	11	i	i	PROPN
hjic-1079	73	12	=	=	NOUN
hjic-1079	73	13	o	o	NOUN
hjic-1079	73	14	definition	definition	NOUN
hjic-1079	73	15	:	:	PUNCT
hjic-1079	73	16	a	a	DET
hjic-1079	73	17	bezier	bezier	NOUN
hjic-1079	73	18	curve	curve	NOUN
hjic-1079	73	19	is	be	AUX
hjic-1079	73	20	defined	define	VERB
hjic-1079	73	21	as	as	SCONJ
hjic-1079	73	22	follows	follow	VERB
hjic-1079	73	23	:	:	PUNCT
hjic-1079	73	24	if	if	SCONJ
hjic-1079	73	25	x	x	X
hjic-1079	73	26	11	11	NUM
hjic-1079	73	27	(	(	PUNCT
hjic-1079	73	28	x):=	x):=	PROPN
hjic-1079	74	1	l	l	NOUN
hjic-1079	74	2	:	:	PUNCT
hjic-1079	74	3	b.b~(x),xe	b.b~(x),xe	PROPN
hjic-1079	74	4	(	(	PUNCT
hjic-1079	74	5	oj	oj	PROPN
hjic-1079	74	6	)	)	PUNCT
hjic-1079	74	7	i	i	PROPN
hjic-1079	74	8	=	=	NOUN
hjic-1079	74	9	o	o	X
hjic-1079	74	10	the	the	DET
hjic-1079	74	11	points	point	NOUN
hjic-1079	74	12	b	b	NOUN
hjic-1079	74	13	;	;	PUNCT
hjic-1079	74	14	are	be	AUX
hjic-1079	74	15	called	call	VERB
hjic-1079	74	16	the	the	DET
hjic-1079	74	17	controlpoints	controlpoint	NOUN
hjic-1079	74	18	of	of	ADP
hjic-1079	74	19	the	the	DET
hjic-1079	74	20	bezier	bezier	PROPN
hjic-1079	74	21	cun·e	cun·e	PROPN
hjic-1079	74	22	.	.	PUNCT
hjic-1079	75	1	there	there	PRON
hjic-1079	75	2	are	be	VERB
hjic-1079	75	3	some	some	DET
hjic-1079	75	4	relations	relation	NOUN
hjic-1079	75	5	between	between	ADP
hjic-1079	75	6	b	b	NOUN
hjic-1079	75	7	-	-	PUNCT
hjic-1079	75	8	splines	spline	NOUN
hjic-1079	75	9	and	and	CCONJ
hjic-1079	75	10	beziersplines	bezierspline	NOUN
hjic-1079	75	11	.	.	PUNCT
hjic-1079	76	1	the	the	DET
hjic-1079	76	2	next	next	ADJ
hjic-1079	76	3	theorem	theorem	NOUN
hjic-1079	76	4	shows	show	VERB
hjic-1079	76	5	that	that	SCONJ
hjic-1079	76	6	each	each	DET
hjic-1079	76	7	spline	spline	NOUN
hjic-1079	76	8	curve	curve	NOUN
hjic-1079	76	9	can	can	AUX
hjic-1079	76	10	be	be	AUX
hjic-1079	76	11	expressed	express	VERB
hjic-1079	76	12	in	in	ADP
hjic-1079	76	13	terms	term	NOUN
hjic-1079	76	14	of	of	ADP
hjic-1079	76	15	b	b	NOUN
hjic-1079	76	16	-	-	PUNCT
hjic-1079	76	17	splines	spline	NOUN
hjic-1079	76	18	.	.	PUNCT
hjic-1079	77	1	theorem	theorem	VERB
hjic-1079	77	2	:	:	PUNCT
hjic-1079	77	3	lets	lets	AUX
hjic-1079	77	4	be	be	AUX
hjic-1079	77	5	a	a	DET
hjic-1079	77	6	spline	spline	NOUN
hjic-1079	77	7	function	function	NOUN
hjic-1079	77	8	of	of	ADP
hjic-1079	77	9	degree	degree	NOUN
hjic-1079	77	10	l	l	NOUN
hjic-1079	77	11	in	in	ADP
hjic-1079	77	12	[	[	PUNCT
hjic-1079	77	13	atb	atb	NOUN
hjic-1079	77	14	]	]	PUNCT
hjic-1079	77	15	.	.	PUNCT
hjic-1079	78	1	tltefl	tltefl	ADV
hjic-1079	78	2	we	we	PRON
hjic-1079	78	3	hal'e	hal'e	VERB
hjic-1079	78	4	a	a	DET
hjic-1079	78	5	unique	unique	ADJ
hjic-1079	78	6	representation	representation	NOUN
hjic-1079	78	7	it	it	PRON
hjic-1079	78	8	~.	~.	VERB
hjic-1079	79	1	3	3	NUM
hjic-1079	79	2	s(x	s(x	NOUN
hjic-1079	79	3	}	}	PUNCT
hjic-1079	79	4	=	=	SYM
hjic-1079	79	5	£	£	SYM
hjic-1079	79	6	..	..	PUNCT
hjic-1079	79	7	id;.nu	id;.nu	NOUN
hjic-1079	79	8	(	(	PUNCT
hjic-1079	79	9	x	x	NOUN
hjic-1079	79	10	)	)	PUNCT
hjic-1079	79	11	,	,	PUNCT
hjic-1079	79	12	d	d	NOUN
hjic-1079	79	13	;	;	PUNCT
hjic-1079	79	14	e	e	X
hjic-1079	79	15	r	r	NOUN
hjic-1079	79	16	,	,	PUNCT
hjic-1079	79	17	xe	xe	PROPN
hjic-1079	80	1	[	[	X
hjic-1079	80	2	a	a	X
hjic-1079	80	3	,	,	PUNCT
hjic-1079	80	4	b	b	NOUN
hjic-1079	80	5	]	]	PUNCT
hjic-1079	80	6	;	;	PUNCT
hjic-1079	80	7	..	..	PUNCT
hjic-1079	81	1	_	_	PUNCT
hjic-1079	81	2	,	,	PUNCT
hjic-1079	81	3	in	in	ADP
hjic-1079	81	4	a	a	DET
hjic-1079	81	5	very	very	ADV
hjic-1079	81	6	special	special	ADJ
hjic-1079	81	7	case	case	NOUN
hjic-1079	81	8	we	we	PRON
hjic-1079	81	9	have	have	VERB
hjic-1079	81	10	a	a	DET
hjic-1079	81	11	direct	direct	ADJ
hjic-1079	81	12	coincidence	coincidence	NOUN
hjic-1079	81	13	between	between	ADP
hjic-1079	81	14	b	b	NOUN
hjic-1079	81	15	-	-	PUNCT
hjic-1079	81	16	splines	spline	NOUN
hjic-1079	81	17	and	and	CCONJ
hjic-1079	81	18	beziersplines	bezierspline	NOUN
hjic-1079	81	19	.	.	PUNCT
hjic-1079	82	1	theorem	theorem	VERB
hjic-1079	82	2	:	:	PUNCT
hjic-1079	82	3	the	the	DET
hjic-1079	82	4	b	b	NOUN
hjic-1079	82	5	-	-	PUNCT
hjic-1079	82	6	splines	spline	NOUN
hjic-1079	82	7	nij	nij	NOUN
hjic-1079	82	8	(	(	PUNCT
hjic-1079	82	9	x	x	NOUN
hjic-1079	82	10	)	)	PUNCT
hjic-1079	82	11	of	of	ADP
hjic-1079	82	12	degree	degree	NOUN
hjic-1079	82	13	i	i	PRON
hjic-1079	82	14	are	be	AUX
hjic-1079	82	15	exactly	exactly	ADV
hjic-1079	82	16	the	the	DET
hjic-1079	82	17	bemsteitz	bemsteitz	NOUN
hjic-1079	82	18	polynomials	polynomial	VERB
hjic-1079	82	19	b:(x	b:(x	NOUN
hjic-1079	82	20	)	)	PUNCT
hjic-1079	82	21	.	.	PUNCT
hjic-1079	83	1	if	if	SCONJ
hjic-1079	83	2	the	the	DET
hjic-1079	83	3	knot	knot	NOUN
hjic-1079	83	4	sequence	sequence	NOUN
hjic-1079	83	5	t	t	NOUN
hjic-1079	83	6	contains	contain	VERB
hjic-1079	83	7	2	2	NUM
hjic-1079	83	8	(	(	PUNCT
hjic-1079	83	9	i+	i+	NUM
hjic-1079	83	10	1	1	NUM
hjic-1079	83	11	)	)	PUNCT
hjic-1079	83	12	elements	element	NOUN
hjic-1079	83	13	where	where	SCONJ
hjic-1079	83	14	both	both	DET
hjic-1079	83	15	0	0	PUNCT
hjic-1079	83	16	and	and	CCONJ
hjic-1079	83	17	/	/	SYM
hjic-1079	83	18	are	be	AUX
hjic-1079	83	19	of	of	ADP
hjic-1079	83	20	multiplicity	multiplicity	NOUN
hjic-1079	83	21	l+	l+	X
hjic-1079	83	22	i	i	PRON
hjic-1079	83	23	:	:	PUNCT
hjic-1079	83	24	t=(o	t=(o	PROPN
hjic-1079	83	25	,	,	PUNCT
hjic-1079	83	26	...	...	PUNCT
hjic-1079	83	27	•	•	NUM
hjic-1079	84	1	o.	o.	INTJ
hjic-1079	84	2	...	...	PUNCT
hjic-1079	85	1	_	_	PUNCT
hjic-1079	86	1	_	_	PUNCT
hjic-1079	86	2	,	,	PUNCT
hjic-1079	86	3	_	_	PUNCT
hjic-1079	86	4	..	..	PUNCT
hjic-1079	87	1	_	_	PUNCT
hjic-1079	87	2	dt	dt	ADJ
hjic-1079	87	3	-	-	PUNCT
hjic-1079	87	4	tlli.iim'l	tlli.iim'l	PROPN
hjic-1079	87	5	l	l	NOUN
hjic-1079	87	6	,	,	PUNCT
hjic-1079	87	7	...	...	PUNCT
hjic-1079	87	8	,	,	PUNCT
hjic-1079	87	9	l	l	NOUN
hjic-1079	87	10	)	)	PUNCT
hjic-1079	87	11	...............	...............	PUNCT
hjic-1079	88	1	tl+htws	tl+htws	PROPN
hjic-1079	88	2	the	the	DET
hjic-1079	88	3	algorithm	algorithm	NOUN
hjic-1079	88	4	of	of	ADP
hjic-1079	88	5	de	de	X
hjic-1079	88	6	boor	boor	NOUN
hjic-1079	88	7	and	and	CCONJ
hjic-1079	88	8	de	de	ADP
hjic-1079	88	9	casteljau	casteljau	VERB
hjic-1079	88	10	the	the	DET
hjic-1079	88	11	formula	formula	NOUN
hjic-1079	88	12	for	for	ADP
hjic-1079	88	13	a	a	DET
hjic-1079	88	14	b	b	NOUN
hjic-1079	88	15	-	-	PUNCT
hjic-1079	88	16	spline	spline	NOUN
hjic-1079	88	17	curve	curve	NOUN
hjic-1079	88	18	is	be	AUX
hjic-1079	88	19	not	not	PART
hjic-1079	88	20	easy	easy	ADJ
hjic-1079	88	21	to	to	PART
hjic-1079	88	22	handle	handle	VERB
hjic-1079	88	23	.	.	PUNCT
hjic-1079	89	1	for	for	ADP
hjic-1079	89	2	polynomials	polynomial	NOUN
hjic-1079	89	3	we	we	PRON
hjic-1079	89	4	have	have	VERB
hjic-1079	89	5	the	the	DET
hjic-1079	89	6	formula	formula	NOUN
hjic-1079	89	7	of	of	ADP
hjic-1079	89	8	horner	horner	NOUN
hjic-1079	89	9	for	for	ADP
hjic-1079	89	10	a	a	DET
hjic-1079	89	11	quick	quick	ADJ
hjic-1079	89	12	evaluation	evaluation	NOUN
hjic-1079	89	13	of	of	ADP
hjic-1079	89	14	single	single	ADJ
hjic-1079	89	15	values	value	NOUN
hjic-1079	89	16	.	.	PUNCT
hjic-1079	90	1	for	for	ADP
hjic-1079	90	2	b	b	NOUN
hjic-1079	90	3	-	-	PUNCT
hjic-1079	90	4	spline	spline	NOUN
hjic-1079	90	5	curves	curve	NOUN
hjic-1079	90	6	this	this	DET
hjic-1079	90	7	part	part	NOUN
hjic-1079	90	8	is	be	AUX
hjic-1079	90	9	played	play	VERB
hjic-1079	90	10	by	by	ADP
hjic-1079	90	11	the	the	DET
hjic-1079	90	12	algorithm	algorithm	NOUN
hjic-1079	90	13	of	of	ADP
hjic-1079	90	14	de	de	X
hjic-1079	90	15	boor	boor	NOUN
hjic-1079	90	16	.	.	PUNCT
hjic-1079	91	1	algorithm	algorithm	NOUN
hjic-1079	91	2	(	(	PUNCT
hjic-1079	91	3	de	de	X
hjic-1079	91	4	boor	boor	NOUN
hjic-1079	91	5	)	)	PUNCT
hjic-1079	91	6	forb	forb	NOUN
hjic-1079	91	7	-	-	PUNCT
hjic-1079	91	8	splines	spline	NOUN
hjic-1079	91	9	given	give	VERB
hjic-1079	91	10	n+1	n+1	NUM
hjic-1079	91	11	de	de	X
hjic-1079	91	12	boor	boor	NOUN
hjic-1079	91	13	points	point	NOUN
hjic-1079	91	14	d0	d0	NOUN
hjic-1079	91	15	,	,	PUNCT
hjic-1079	91	16	d1	d1	PROPN
hjic-1079	91	17	,	,	PUNCT
hjic-1079	91	18	•••	•••	ADV
hjic-1079	91	19	,	,	PUNCT
hjic-1079	91	20	dn	dn	ADP
hjic-1079	91	21	,	,	PUNCT
hjic-1079	91	22	n?:.l	n?:.l	PROPN
hjic-1079	91	23	,	,	PUNCT
hjic-1079	91	24	and	and	CCONJ
hjic-1079	91	25	a	a	DET
hjic-1079	91	26	knot	knot	NOUN
hjic-1079	91	27	sequence	sequence	NOUN
hjic-1079	91	28	find	find	VERB
hjic-1079	91	29	b(x	b(x	NOUN
hjic-1079	91	30	*	*	NUM
hjic-1079	91	31	):	):	PUNCT
hjic-1079	91	32	1	1	X
hjic-1079	91	33	.	.	X
hjic-1079	91	34	find	find	VERB
hjic-1079	91	35	r	r	NOUN
hjic-1079	91	36	with	with	ADP
hjic-1079	91	37	xr	xr	PROPN
hjic-1079	91	38	~	~	PUNCT
hjic-1079	91	39	x	x	X
hjic-1079	91	40	*	*	PUNCT
hjic-1079	91	41	<	<	X
hjic-1079	91	42	xr+l	xr+l	X
hjic-1079	91	43	*	*	PUNCT
hjic-1079	91	44	2	2	X
hjic-1079	91	45	.	.	X
hjic-1079	91	46	calculate	calculate	NOUN
hjic-1079	91	47	a~	a~	PROPN
hjic-1079	91	48	x	x	INTJ
hjic-1079	91	49	-xi	-xi	INTJ
hjic-1079	91	50	.	.	PUNCT
hjic-1079	92	1	1	1	NUM
hjic-1079	92	2	l	l	NOUN
hjic-1079	92	3	1	1	NUM
hjic-1079	92	4	,	,	PUNCT
hjic-1079	92	5	z	z	NOUN
hjic-1079	92	6	=	=	PUNCT
hjic-1079	92	7	r	r	NOUN
hjic-1079	92	8	+	+	NOUN
hjic-1079	92	9	,	,	PUNCT
hjic-1079	92	10	...	...	PUNCT
hjic-1079	92	11	,	,	PUNCT
hjic-1079	92	12	r	r	NOUN
hjic-1079	92	13	-z	-z	PROPN
hjic-1079	92	14	1	1	NUM
hjic-1079	92	15	zdi	zdi	PROPN
hjic-1079	92	16	=(	=(	NOUN
hjic-1079	92	17	1	1	NUM
hjic-1079	92	18	-	-	PUNCT
hjic-1079	92	19	a	a	DET
hjic-1079	92	20	t	t	NOUN
hjic-1079	92	21	)	)	PUNCT
hjic-1079	92	22	d;_1	d;_1	NOUN
hjic-1079	93	1	+	+	NOUN
hjic-1079	93	2	atdt	atdt	ADJ
hjic-1079	93	3	3	3	NUM
hjic-1079	93	4	.	.	PUNCT
hjic-1079	94	1	for	for	ADP
hjic-1079	94	2	j=2,3	j=2,3	PROPN
hjic-1079	94	3	,	,	PUNCT
hjic-1079	94	4	...	...	PUNCT
hjic-1079	94	5	,	,	PUNCT
hjic-1079	94	6	l	l	NOUN
hjic-1079	94	7	,	,	PUNCT
hjic-1079	94	8	i	i	PRON
hjic-1079	94	9	=	=	NOUN
hjic-1079	94	10	r	r	X
hjic-1079	94	11	-	-	PUNCT
hjic-1079	94	12	l+j	l+j	NUM
hjic-1079	94	13	,	,	PUNCT
hjic-1079	94	14	...	...	PUNCT
hjic-1079	94	15	,	,	PUNCT
hjic-1079	94	16	r	r	NOUN
hjic-1079	94	17	*	*	PUNCT
hjic-1079	94	18	a	a	NOUN
hjic-1079	94	19	!	!	PUNCT
hjic-1079	95	1	x	x	PUNCT
hjic-1079	95	2	-xi	-xi	PROPN
hjic-1079	95	3	l	l	NOUN
hjic-1079	95	4	xi+t	xi+t	PROPN
hjic-1079	95	5	-	-	PUNCT
hjic-1079	95	6	u	u	NOUN
hjic-1079	95	7	-	-	NOUN
hjic-1079	95	8	n	n	CCONJ
hjic-1079	95	9	-xi	-xi	ADV
hjic-1079	95	10	j/	j/	VERB
hjic-1079	95	11	=	=	SYM
hjic-1079	95	12	(	(	PUNCT
hjic-1079	95	13	1	1	NUM
hjic-1079	95	14	-	-	PUNCT
hjic-1079	95	15	a	a	NOUN
hjic-1079	95	16	!	!	PUNCT
hjic-1079	95	17	)	)	PUNCT
hjic-1079	96	1	ji	ji	PROPN
hjic-1079	96	2	-	-	PUNCT
hjic-1079	96	3	li-1	li-1	PRON
hjic-1079	96	4	+	+	NOUN
hjic-1079	96	5	a	a	NOUN
hjic-1079	96	6	!	!	PUNCT
hjic-1079	97	1	j/-t	j/-t	PUNCT
hjic-1079	97	2	l	l	NOUN
hjic-1079	98	1	i	i	PRON
hjic-1079	98	2	i	i	VERB
hjic-1079	98	3	l	l	NOUN
hjic-1079	98	4	4	4	X
hjic-1079	98	5	.	.	PUNCT
hjic-1079	99	1	then	then	ADV
hjic-1079	99	2	we	we	PRON
hjic-1079	99	3	have	have	AUX
hjic-1079	99	4	b(x	b(x	VERB
hjic-1079	99	5	*	*	X
hjic-1079	99	6	)	)	PUNCT
hjic-1079	100	1	=	=	SYM
hjic-1079	100	2	j	j	PROPN
hjic-1079	100	3	;	;	PUNCT
hjic-1079	100	4	the	the	DET
hjic-1079	100	5	following	follow	VERB
hjic-1079	100	6	table	table	NOUN
hjic-1079	100	7	gives	give	VERB
hjic-1079	100	8	an	an	DET
hjic-1079	100	9	impression	impression	NOUN
hjic-1079	100	10	how	how	SCONJ
hjic-1079	100	11	this	this	DET
hjic-1079	100	12	algorithm	algorithm	NOUN
hjic-1079	100	13	works	work	VERB
hjic-1079	100	14	.	.	PUNCT
hjic-1079	101	1	on	on	ADP
hjic-1079	101	2	the	the	DET
hjic-1079	101	3	horizontal	horizontal	ADJ
hjic-1079	101	4	lines	line	NOUN
hjic-1079	101	5	we	we	PRON
hjic-1079	101	6	multiply	multiply	VERB
hjic-1079	101	7	by	by	ADP
hjic-1079	101	8	a/	a/	NOUN
hjic-1079	101	9	and	and	CCONJ
hjic-1079	101	10	on	on	ADP
hjic-1079	101	11	the	the	DET
hjic-1079	101	12	diagonal	diagonal	ADJ
hjic-1079	101	13	lines	line	NOUN
hjic-1079	101	14	by	by	ADP
hjic-1079	101	15	1	1	NUM
hjic-1079	101	16	-	-	PUNCT
hjic-1079	101	17	a/.	a/.	VERB
hjic-1079	101	18	the	the	DET
hjic-1079	101	19	sum	sum	NOUN
hjic-1079	101	20	of	of	ADP
hjic-1079	101	21	both	both	DET
hjic-1079	101	22	values	value	NOUN
hjic-1079	101	23	gives	give	VERB
hjic-1079	101	24	the	the	DET
hjic-1079	101	25	new	new	ADJ
hjic-1079	101	26	de	de	X
hjic-1079	101	27	boor	boor	ADJ
hjic-1079	101	28	point	point	NOUN
hjic-1079	101	29	on	on	ADP
hjic-1079	101	30	the	the	DET
hjic-1079	101	31	right	right	NOUN
hjic-1079	101	32	:	:	PUNCT
hjic-1079	101	33	dr-1	dr-1	NUM
hjic-1079	102	1	+	+	ADV
hjic-1079	102	2	1	1	NUM
hjic-1079	102	3	-1	-1	NOUN
hjic-1079	102	4	d	d	AUX
hjic-1079	102	5	r-1	r-1	VERB
hjic-1079	102	6	+	+	PROPN
hjic-1079	102	7	1	1	NUM
hjic-1079	102	8	dr-1	dr-1	NUM
hjic-1079	102	9	+	+	NOUN
hjic-1079	102	10	:	:	PUNCT
hjic-1079	102	11	!	!	PUNCT
hjic-1079	102	12	.	.	PUNCT
hjic-1079	103	1	-1	-1	PUNCT
hjic-1079	104	1	d	d	X
hjic-1079	104	2	r-1	r-1	VERB
hjic-1079	104	3	+	+	PROPN
hjic-1079	104	4	2	2	NUM
hjic-1079	104	5	-z	-z	NOUN
hjic-1079	104	6	d	d	NOUN
hjic-1079	104	7	r-1	r-1	VERB
hjic-1079	104	8	+	+	PROPN
hjic-1079	104	9	2	2	NUM
hjic-1079	104	10	dr-1	dr-1	NUM
hjic-1079	104	11	+	+	NOUN
hjic-1079	104	12	3	3	NUM
hjic-1079	104	13	-~	-~	PROPN
hjic-1079	104	14	d	d	X
hjic-1079	104	15	r-1	r-1	NOUN
hjic-1079	104	16	+	+	PROPN
hjic-1079	104	17	3	3	NUM
hjic-1079	104	18	-z	-z	NOUN
hjic-1079	104	19	d	d	X
hjic-1079	104	20	r-1	r-1	VERB
hjic-1079	104	21	+	+	PROPN
hjic-1079	104	22	3	3	NUM
hjic-1079	104	23	ji	ji	NOUN
hjic-1079	104	24	-	-	PROPN
hjic-1079	104	25	i	i	PRON
hjic-1079	104	26	r	r	PROPN
hjic-1079	104	27	-	-	PUNCT
hjic-1079	104	28	t	t	PROPN
hjic-1079	104	29	ii	ii	PROPN
hjic-1079	104	30	,	,	PUNCT
hjic-1079	104	31	jtr	jtr	PROPN
hjic-1079	105	1	-z	-z	X
hjic-1079	105	2	d	d	X
hjic-1079	105	3	r	r	NOUN
hjic-1079	105	4	{	{	PUNCT
hjic-1079	105	5	jl	jl	NOUN
hjic-1079	105	6	-	-	PUNCT
hjic-1079	105	7	lr	lr	NOUN
hjic-1079	105	8	tpr	tpr	NOUN
hjic-1079	105	9	=	=	AUX
hjic-1079	105	10	b(x	b(x	NOUN
hjic-1079	105	11	*	*	PUNCT
hjic-1079	105	12	)	)	PUNCT
hjic-1079	105	13	the	the	DET
hjic-1079	105	14	most	most	ADV
hjic-1079	105	15	important	important	ADJ
hjic-1079	105	16	advantage	advantage	NOUN
hjic-1079	105	17	of	of	ADP
hjic-1079	105	18	this	this	DET
hjic-1079	105	19	algorithm	algorithm	NOUN
hjic-1079	105	20	is	be	AUX
hjic-1079	105	21	how	how	SCONJ
hjic-1079	105	22	fast	fast	ADJ
hjic-1079	105	23	it	it	PRON
hjic-1079	105	24	works	work	VERB
hjic-1079	105	25	.	.	PUNCT
hjic-1079	106	1	it	it	PRON
hjic-1079	106	2	is	be	AUX
hjic-1079	106	3	possible	possible	ADJ
hjic-1079	106	4	to	to	PART
hjic-1079	106	5	evaluate	evaluate	VERB
hjic-1079	106	6	thousands	thousand	NOUN
hjic-1079	106	7	of	of	ADP
hjic-1079	106	8	points	point	NOUN
hjic-1079	106	9	in	in	ADP
hjic-1079	106	10	less	less	ADJ
hjic-1079	106	11	than	than	ADP
hjic-1079	106	12	a	a	DET
hjic-1079	106	13	second	second	NOUN
hjic-1079	106	14	.	.	PUNCT
hjic-1079	107	1	so	so	ADV
hjic-1079	107	2	this	this	DET
hjic-1079	107	3	algorithm	algorithm	NOUN
hjic-1079	107	4	makes	make	VERB
hjic-1079	107	5	it	it	PRON
hjic-1079	107	6	possible	possible	ADJ
hjic-1079	107	7	to	to	PART
hjic-1079	107	8	change	change	VERB
hjic-1079	107	9	a	a	DET
hjic-1079	107	10	curve	curve	NOUN
hjic-1079	107	11	and	and	CCONJ
hjic-1079	107	12	in	in	ADP
hjic-1079	107	13	the	the	DET
hjic-1079	107	14	same	same	ADJ
hjic-1079	107	15	way	way	NOUN
hjic-1079	107	16	a	a	DET
hjic-1079	107	17	surface	surface	NOUN
hjic-1079	107	18	nearly	nearly	ADV
hjic-1079	107	19	in	in	ADP
hjic-1079	107	20	real	real	ADJ
hjic-1079	107	21	time	time	NOUN
hjic-1079	107	22	.	.	PUNCT
hjic-1079	108	1	a	a	DET
hjic-1079	108	2	similar	similar	ADJ
hjic-1079	108	3	algorithm	algorithm	NOUN
hjic-1079	108	4	for	for	ADP
hjic-1079	108	5	the	the	DET
hjic-1079	108	6	bezier	bezi	ADJ
hjic-1079	108	7	splines	spline	NOUN
hjic-1079	108	8	was	be	AUX
hjic-1079	108	9	developed	develop	VERB
hjic-1079	108	10	by	by	ADP
hjic-1079	108	11	de	de	X
hjic-1079	108	12	casteljau	casteljau	PROPN
hjic-1079	108	13	.	.	PUNCT
hjic-1079	109	1	it	it	PRON
hjic-1079	109	2	is	be	AUX
hjic-1079	109	3	based	base	VERB
hjic-1079	109	4	on	on	ADP
hjic-1079	109	5	the	the	DET
hjic-1079	109	6	recurrence	recurrence	NOUN
hjic-1079	109	7	relation	relation	NOUN
hjic-1079	109	8	:	:	PUNCT
hjic-1079	109	9	b;(x	b;(x	X
hjic-1079	109	10	)	)	PUNCT
hjic-1079	110	1	=	=	SYM
hjic-1079	110	2	(	(	PUNCT
hjic-1079	110	3	1	1	NUM
hjic-1079	110	4	-	-	PUNCT
hjic-1079	110	5	x)b;-1(x)+b	x)b;-1(x)+b	NOUN
hjic-1079	110	6	1	1	NUM
hjic-1079	110	7	l!-l(x	l!-l(x	PROPN
hjic-1079	110	8	)	)	PUNCT
hjic-1079	110	9	fig.4	fig.4	SYM
hjic-1079	110	10	13	13	NUM
hjic-1079	110	11	given	give	VERB
hjic-1079	110	12	points	point	NOUN
hjic-1079	110	13	which	which	PRON
hjic-1079	110	14	build	build	VERB
hjic-1079	110	15	a	a	DET
hjic-1079	110	16	tunnel	tunnel	NOUN
hjic-1079	110	17	are	be	AUX
hjic-1079	110	18	interpolated	interpolate	VERB
hjic-1079	110	19	with	with	ADP
hjic-1079	110	20	b	b	NOUN
hjic-1079	110	21	-	-	PUNCT
hjic-1079	110	22	splines	spline	NOUN
hjic-1079	110	23	.	.	PUNCT
hjic-1079	111	1	algorithm	algorithm	NOUN
hjic-1079	111	2	(	(	PUNCT
hjic-1079	111	3	de	de	X
hjic-1079	111	4	casteljau	casteljau	PROPN
hjic-1079	111	5	)	)	PUNCT
hjic-1079	111	6	for	for	ADP
hjic-1079	111	7	beziersplines	bezierspline	NOUN
hjic-1079	111	8	given	give	VERB
hjic-1079	111	9	n	n	PROPN
hjic-1079	111	10	+	+	CCONJ
hjic-1079	111	11	1	1	NUM
hjic-1079	111	12	bezier	bezier	NOUN
hjic-1079	111	13	points	point	NOUN
hjic-1079	111	14	or	or	CCONJ
hjic-1079	111	15	control	control	NOUN
hjic-1079	111	16	points	point	NOUN
hjic-1079	111	17	e0	e0	PROPN
hjic-1079	111	18	,	,	PUNCT
hjic-1079	111	19	•••	•••	ADV
hjic-1079	111	20	,	,	PUNCT
hjic-1079	111	21	en	en	X
hjic-1079	111	22	.	.	PUNCT
hjic-1079	112	1	find	find	VERB
hjic-1079	112	2	x	x	SYM
hjic-1079	112	3	11	11	NUM
hjic-1079	112	4	(	(	PUNCT
hjic-1079	112	5	x	x	X
hjic-1079	112	6	*	*	NOUN
hjic-1079	112	7	):	):	PUNCT
hjic-1079	112	8	1	1	NUM
hjic-1079	112	9	.	.	NOUN
hjic-1079	112	10	2	2	NUM
hjic-1079	112	11	.	.	NOUN
hjic-1079	112	12	3	3	NUM
hjic-1079	112	13	.	.	NOUN
hjic-1079	112	14	4	4	NUM
hjic-1079	112	15	.	.	NUM
hjic-1079	112	16	·	·	PUNCT
hjic-1079	113	1	-o	-o	INTJ
hjic-1079	113	2	-o	-o	INTJ
hjic-1079	113	3	...	...	PUNCT
hjic-1079	113	4	-o	-o	INTJ
hjic-1079	113	5	....	....	PUNCT
hjic-1079	113	6	start	start	VERB
hjic-1079	113	7	wzth	wzth	NOUN
hjic-1079	113	8	b0	b0	NOUN
hjic-1079	113	9	:	:	PUNCT
hjic-1079	113	10	=	=	SYM
hjic-1079	113	11	b0	b0	NOUN
hjic-1079	113	12	,	,	PUNCT
hjic-1079	113	13	b1	b1	NOUN
hjic-1079	113	14	:	:	PUNCT
hjic-1079	113	15	=	=	PUNCT
hjic-1079	113	16	bl	bl	PROPN
hjic-1079	113	17	'	'	PUNCT
hjic-1079	113	18	...	...	PUNCT
hjic-1079	113	19	,	,	PUNCT
hjic-1079	113	20	b	b	X
hjic-1079	113	21	11	11	NUM
hjic-1079	113	22	:	:	PUNCT
hjic-1079	113	23	=	=	SYM
hjic-1079	113	24	bn	bn	PROPN
hjic-1079	113	25	....	....	SYM
hjic-1079	113	26	1	1	NUM
hjic-1079	113	27	-1	-1	PRON
hjic-1079	113	28	-1	-1	CCONJ
hjic-1079	113	29	calculate	calculate	NOUN
hjic-1079	113	30	b0	b0	NOUN
hjic-1079	113	31	,	,	PUNCT
hjic-1079	113	32	b1	b1	NOUN
hjic-1079	113	33	,	,	PUNCT
hjic-1079	113	34	...	...	PUNCT
hjic-1079	113	35	,	,	PUNCT
hjic-1079	113	36	h11	h11	NOUN
hjic-1079	113	37	_	_	NOUN
hjic-1079	113	38	1	1	NUM
hjic-1079	113	39	using	use	VERB
hjic-1079	113	40	the	the	DET
hjic-1079	113	41	recurrence	recurrence	NOUN
hjic-1079	113	42	relation	relation	NOUN
hjic-1079	113	43	above	above	ADV
hjic-1079	113	44	.	.	PUNCT
hjic-1079	114	1	continue	continue	VERB
hjic-1079	114	2	calculating	calculate	VERB
hjic-1079	114	3	b~	b~	PROPN
hjic-1079	114	4	,	,	PUNCT
hjic-1079	114	5	...	...	PUNCT
hjic-1079	114	6	,	,	PUNCT
hjic-1079	114	7	bli	bli	PROPN
hjic-1079	114	8	,	,	PUNCT
hjic-1079	114	9	i	i	NOUN
hjic-1079	114	10	=	=	NOUN
hjic-1079	114	11	2	2	NUM
hjic-1079	114	12	,	,	PUNCT
hjic-1079	114	13	...	...	PUNCT
hjic-1079	114	14	,	,	PUNCT
hjic-1079	114	15	n	n	PRON
hjic-1079	114	16	thenwehave	thenwehave	VERB
hjic-1079	114	17	x	x	SYM
hjic-1079	114	18	11	11	NUM
hjic-1079	114	19	(	(	PUNCT
hjic-1079	114	20	x*)=b;(x	x*)=b;(x	NOUN
hjic-1079	114	21	*	*	NUM
hjic-1079	114	22	)	)	PUNCT
hjic-1079	114	23	.	.	PUNCT
hjic-1079	115	1	this	this	DET
hjic-1079	115	2	calculation	calculation	NOUN
hjic-1079	115	3	cav	cav	NOUN
hjic-1079	115	4	be	be	AUX
hjic-1079	115	5	filled	fill	VERB
hjic-1079	115	6	in	in	ADP
hjic-1079	115	7	a	a	DET
hjic-1079	115	8	table	table	NOUN
hjic-1079	115	9	quite	quite	ADV
hjic-1079	115	10	similar	similar	ADJ
hjic-1079	115	11	to	to	ADP
hjic-1079	115	12	the	the	DET
hjic-1079	115	13	table	table	NOUN
hjic-1079	115	14	for	for	ADP
hjic-1079	115	15	the	the	DET
hjic-1079	115	16	de	de	X
hjic-1079	115	17	boor	boor	NOUN
hjic-1079	115	18	algorithm	algorithm	NOUN
hjic-1079	115	19	above	above	ADV
hjic-1079	115	20	.	.	PUNCT
hjic-1079	116	1	we	we	PRON
hjic-1079	116	2	have	have	VERB
hjic-1079	116	3	only	only	ADV
hjic-1079	116	4	to	to	PART
hjic-1079	116	5	replace	replace	VERB
hjic-1079	116	6	the	the	DET
hjic-1079	116	7	de	de	X
hjic-1079	116	8	boor	boor	NOUN
hjic-1079	116	9	points	point	NOUN
hjic-1079	116	10	a	a	PRON
hjic-1079	116	11	by	by	ADP
hjic-1079	116	12	the	the	DET
hjic-1079	116	13	bezier	bezier	PROPN
hjic-1079	116	14	points	point	NOUN
hjic-1079	116	15	b	b	NOUN
hjic-1079	116	16	and	and	CCONJ
hjic-1079	116	17	then	then	ADV
hjic-1079	116	18	to	to	PART
hjic-1079	116	19	multiply	multiply	VERB
hjic-1079	116	20	in	in	ADP
hjic-1079	116	21	the	the	DET
hjic-1079	116	22	horizontal	horizontal	ADJ
hjic-1079	116	23	line	line	NOUN
hjic-1079	116	24	with	with	ADP
hjic-1079	116	25	x	x	NOUN
hjic-1079	116	26	*	*	NOUN
hjic-1079	116	27	,	,	PUNCT
hjic-1079	116	28	in	in	ADP
hjic-1079	116	29	the	the	DET
hjic-1079	116	30	diagonal	diagonal	ADJ
hjic-1079	116	31	line	line	NOUN
hjic-1079	116	32	with	with	ADP
hjic-1079	116	33	1x	1x	NUM
hjic-1079	116	34	*	*	NUM
hjic-1079	116	35	,	,	PUNCT
hjic-1079	116	36	and	and	CCONJ
hjic-1079	116	37	afterwards	afterwards	ADV
hjic-1079	116	38	to	to	PART
hjic-1079	116	39	sum	sum	VERB
hjic-1079	116	40	up	up	ADP
hjic-1079	116	41	.	.	PUNCT
hjic-1079	117	1	interpolation	interpolation	NOUN
hjic-1079	117	2	using	use	VERB
hjic-1079	117	3	b	b	NOUN
hjic-1079	117	4	-	-	PUNCT
hjic-1079	117	5	splines	spline	NOUN
hjic-1079	117	6	now	now	ADV
hjic-1079	117	7	we	we	PRON
hjic-1079	117	8	will	will	AUX
hjic-1079	117	9	try	try	VERB
hjic-1079	117	10	to	to	PART
hjic-1079	117	11	compare	compare	VERB
hjic-1079	117	12	both	both	DET
hjic-1079	117	13	methods	method	NOUN
hjic-1079	117	14	in	in	ADP
hjic-1079	117	15	their	their	PRON
hjic-1079	117	16	behaviour	behaviour	NOUN
hjic-1079	117	17	regarding	regard	VERB
hjic-1079	117	18	interpolation	interpolation	NOUN
hjic-1079	117	19	problems	problem	NOUN
hjic-1079	117	20	.	.	PUNCT
hjic-1079	118	1	consider	consider	VERB
hjic-1079	118	2	the	the	DET
hjic-1079	118	3	points	point	NOUN
hjic-1079	118	4	po	po	NOUN
hjic-1079	118	5	,	,	PUNCT
hjic-1079	118	6	.f1	.f1	NOUN
hjic-1079	118	7	,	,	PUNCT
hjic-1079	118	8	...	...	PUNCT
hjic-1079	118	9	,	,	PUNCT
hjic-1079	118	10	pq	pq	NOUN
hjic-1079	118	11	-	-	PUNCT
hjic-1079	118	12	l	l	NOUN
hjic-1079	118	13	in	in	ADP
hjic-1079	118	14	ir2	ir2	PROPN
hjic-1079	118	15	or	or	CCONJ
hjic-1079	118	16	ir3	ir3	PROPN
hjic-1079	118	17	•	•	INTJ
hjic-1079	118	18	we	we	PRON
hjic-1079	118	19	want	want	VERB
hjic-1079	118	20	to	to	PART
hjic-1079	118	21	find	find	VERB
hjic-1079	118	22	an	an	DET
hjic-1079	118	23	interpolating	interpolate	VERB
hjic-1079	118	24	spline	spline	NOUN
hjic-1079	118	25	curve	curve	NOUN
hjic-1079	118	26	.	.	PUNCT
hjic-1079	119	1	for	for	ADP
hjic-1079	119	2	the	the	DET
hjic-1079	119	3	use	use	NOUN
hjic-1079	119	4	of	of	ADP
hjic-1079	119	5	b	b	NOUN
hjic-1079	119	6	-	-	PUNCT
hjic-1079	119	7	splines	spline	NOUN
hjic-1079	119	8	we	we	PRON
hjic-1079	119	9	could	could	AUX
hjic-1079	119	10	try	try	VERB
hjic-1079	119	11	to	to	PART
hjic-1079	119	12	take	take	VERB
hjic-1079	119	13	each	each	DET
hjic-1079	119	14	point	point	NOUN
hjic-1079	119	15	in	in	ADP
hjic-1079	119	16	the	the	DET
hjic-1079	119	17	knot	knot	ADJ
hjic-1079	119	18	sequence	sequence	NOUN
hjic-1079	119	19	(	(	PUNCT
hjic-1079	119	20	1	1	NUM
hjic-1079	119	21	+	+	NOUN
hjic-1079	119	22	1)-times	1)-times	NUM
hjic-1079	119	23	.	.	PUNCT
hjic-1079	120	1	then	then	ADV
hjic-1079	120	2	the	the	DET
hjic-1079	120	3	curve	curve	NOUN
hjic-1079	120	4	runs	run	VERB
hjic-1079	120	5	through	through	ADP
hjic-1079	120	6	each	each	PRON
hjic-1079	120	7	of	of	ADP
hjic-1079	120	8	the	the	DET
hjic-1079	120	9	points	point	NOUN
hjic-1079	120	10	,	,	PUNCT
hjic-1079	120	11	but	but	CCONJ
hjic-1079	120	12	it	it	PRON
hjic-1079	120	13	is	be	AUX
hjic-1079	120	14	really	really	ADV
hjic-1079	120	15	not	not	PART
hjic-1079	120	16	a	a	DET
hjic-1079	120	17	smoot!j	smoot!j	PROPN
hjic-1079	120	18	curve	curve	NOUN
hjic-1079	120	19	.	.	PUNCT
hjic-1079	121	1	in	in	ADP
hjic-1079	121	2	each	each	DET
hjic-1079	121	3	point	point	NOUN
hjic-1079	121	4	there	there	PRON
hjic-1079	121	5	is	be	VERB
hjic-1079	121	6	perhaps	perhaps	ADV
hjic-1079	121	7	a	a	DET
hjic-1079	121	8	sharp	sharp	ADJ
hjic-1079	121	9	cusp	cusp	NOUN
hjic-1079	121	10	.	.	PUNCT
hjic-1079	122	1	this	this	PRON
hjic-1079	122	2	is	be	AUX
hjic-1079	122	3	therefore	therefore	ADV
hjic-1079	122	4	no	no	DET
hjic-1079	122	5	answer	answer	NOUN
hjic-1079	122	6	to	to	ADP
hjic-1079	122	7	the	the	DET
hjic-1079	122	8	problem	problem	NOUN
hjic-1079	122	9	.	.	PUNCT
hjic-1079	123	1	in	in	ADP
hjic-1079	123	2	order	order	NOUN
hjic-1079	123	3	to	to	PART
hjic-1079	123	4	combine	combine	VERB
hjic-1079	123	5	the	the	DET
hjic-1079	123	6	given	give	VERB
hjic-1079	123	7	points	point	NOUN
hjic-1079	123	8	with	with	ADP
hjic-1079	123	9	the	the	DET
hjic-1079	123	10	points	point	NOUN
hjic-1079	123	11	in	in	ADP
hjic-1079	123	12	the	the	DET
hjic-1079	123	13	knot	knot	ADJ
hjic-1079	123	14	sequence	sequence	NOUN
hjic-1079	123	15	we	we	PRON
hjic-1079	123	16	should	should	AUX
hjic-1079	123	17	note	note	VERB
hjic-1079	123	18	,	,	PUNCT
hjic-1079	123	19	that	that	SCONJ
hjic-1079	123	20	in	in	ADP
hjic-1079	123	21	the	the	DET
hjic-1079	123	22	interval	interval	NOUN
hjic-1079	123	23	[	[	X
hjic-1079	123	24	x0	x0	PROPN
hjic-1079	123	25	,	,	PUNCT
hjic-1079	123	26	xz	xz	PROPN
hjic-1079	123	27	]	]	X
hjic-1079	123	28	less	less	ADJ
hjic-1079	123	29	than	than	ADP
hjic-1079	123	30	l+	l+	PROPN
hjic-1079	123	31	1	1	NUM
hjic-1079	123	32	b	b	X
hjic-1079	123	33	-	-	PUNCT
hjic-1079	123	34	splines	spline	NOUN
hjic-1079	123	35	are	be	AUX
hjic-1079	123	36	:1	:1	PUNCT
hjic-1079	123	37	:	:	PUNCT
hjic-1079	123	38	0	0	NUM
hjic-1079	123	39	.	.	PUNCT
hjic-1079	124	1	so	so	ADV
hjic-1079	124	2	we	we	PRON
hjic-1079	124	3	try	try	VERB
hjic-1079	124	4	the	the	DET
hjic-1079	124	5	following	follow	VERB
hjic-1079	124	6	combination	combination	NOUN
hjic-1079	124	7	:	:	PUNCT
hjic-1079	124	8	this	this	PRON
hjic-1079	124	9	leads	lead	VERB
hjic-1079	124	10	to	to	ADP
hjic-1079	124	11	the	the	DET
hjic-1079	124	12	following	follow	VERB
hjic-1079	124	13	linear	linear	ADJ
hjic-1079	124	14	system	system	NOUN
hjic-1079	124	15	:	:	PUNCT
hjic-1079	124	16	it	it	PRON
hjic-1079	124	17	:	:	PUNCT
hjic-1079	124	18	lji	lji	ADV
hjic-1079	124	19	ni;(xl+l	ni;(xl+l	NOUN
hjic-1079	124	20	,	,	PUNCT
hjic-1079	124	21	)	)	PUNCT
hjic-1079	124	22	=	=	SYM
hjic-1079	124	23	p.t	p.t	PROPN
hjic-1079	124	24	,	,	PUNCT
hjic-1079	124	25	u	u	NOUN
hjic-1079	124	26	=	=	NOUN
hjic-1079	124	27	o	o	PROPN
hjic-1079	124	28	,	,	PUNCT
hjic-1079	124	29	l	l	NOUN
hjic-1079	124	30	,	,	PUNCT
hjic-1079	124	31	...	...	PUNCT
hjic-1079	124	32	,	,	PUNCT
hjic-1079	124	33	q-1	q-1	ADJ
hjic-1079	124	34	io::o	io::o	NOUN
hjic-1079	124	35	109	109	NUM
hjic-1079	124	36	this	this	PRON
hjic-1079	124	37	is	be	AUX
hjic-1079	124	38	a	a	DET
hjic-1079	124	39	system	system	NOUN
hjic-1079	124	40	of	of	ADP
hjic-1079	124	41	q	q	PROPN
hjic-1079	124	42	linear	linear	ADJ
hjic-1079	124	43	equations	equation	NOUN
hjic-1079	124	44	for	for	ADP
hjic-1079	124	45	the	the	DET
hjic-1079	124	46	n+1unknown	n+1unknown	ADJ
hjic-1079	124	47	d0	d0	NOUN
hjic-1079	124	48	,	,	PUNCT
hjic-1079	124	49	dp	dp	NOUN
hjic-1079	124	50	...	...	PUNCT
hjic-1079	124	51	,	,	PUNCT
hjic-1079	124	52	jn.for	jn.for	ADP
hjic-1079	124	53	q	q	NOUN
hjic-1079	124	54	=	=	PRON
hjic-1079	124	55	n-1	n-1	ADJ
hjic-1079	124	56	+	+	ADJ
hjic-1079	124	57	2	2	NUM
hjic-1079	124	58	thereare	thereare	NOUN
hjic-1079	124	59	n	n	NOUN
hjic-1079	124	60	+	+	CCONJ
hjic-1079	124	61	1(n	1(n	NUM
hjic-1079	124	62	-l	-l	PUNCT
hjic-1079	124	63	+	+	NOUN
hjic-1079	124	64	2	2	X
hjic-1079	124	65	)	)	PUNCT
hjic-1079	124	66	equations	equation	NOUN
hjic-1079	124	67	missing	miss	VERB
hjic-1079	124	68	.	.	PUNCT
hjic-1079	125	1	for	for	ADP
hjic-1079	125	2	cubic	cubic	ADJ
hjic-1079	125	3	splines	spline	NOUN
hjic-1079	125	4	(	(	PUNCT
hjic-1079	125	5	l=3	l=3	VERB
hjic-1079	125	6	)	)	PUNCT
hjic-1079	125	7	we	we	PRON
hjic-1079	125	8	have	have	VERB
hjic-1079	125	9	to	to	PART
hjic-1079	125	10	find	find	VERB
hjic-1079	125	11	2	2	NUM
hjic-1079	125	12	equations	equation	NOUN
hjic-1079	125	13	more	more	ADJ
hjic-1079	125	14	.	.	PUNCT
hjic-1079	126	1	a	a	DET
hjic-1079	126	2	typical	typical	ADJ
hjic-1079	126	3	choice	choice	NOUN
hjic-1079	126	4	is	be	AUX
hjic-1079	126	5	to	to	PART
hjic-1079	126	6	consider	consider	VERB
hjic-1079	126	7	spline	spline	NOUN
hjic-1079	126	8	functions	function	NOUN
hjic-1079	126	9	which	which	PRON
hjic-1079	126	10	are	be	AUX
hjic-1079	126	11	linear	linear	ADJ
hjic-1079	126	12	outside	outside	ADP
hjic-1079	126	13	the	the	DET
hjic-1079	126	14	interval	interval	NOUN
hjic-1079	127	1	[	[	X
hjic-1079	127	2	x0	x0	PROPN
hjic-1079	127	3	,	,	PUNCT
hjic-1079	127	4	x11	x11	PROPN
hjic-1079	127	5	]	]	PUNCT
hjic-1079	127	6	•	•	ADP
hjic-1079	127	7	they	they	PRON
hjic-1079	127	8	are	be	AUX
hjic-1079	127	9	called	call	VERB
hjic-1079	127	10	natural	natural	ADJ
hjic-1079	127	11	and	and	CCONJ
hjic-1079	127	12	the	the	DET
hjic-1079	127	13	following	follow	VERB
hjic-1079	127	14	two	two	NUM
hjic-1079	127	15	equations	equation	NOUN
hjic-1079	127	16	are	be	AUX
hjic-1079	127	17	based	base	VERB
hjic-1079	127	18	on	on	ADP
hjic-1079	127	19	the	the	DET
hjic-1079	127	20	fact	fact	NOUN
hjic-1079	127	21	that	that	SCONJ
hjic-1079	127	22	their	their	PRON
hjic-1079	127	23	second	second	ADJ
hjic-1079	127	24	derivative	derivative	NOUN
hjic-1079	127	25	is	be	AUX
hjic-1079	127	26	zero	zero	NUM
hjic-1079	127	27	:	:	PUNCT
hjic-1079	127	28	dn_zn~:n-2	dn_zn~:n-2	NOUN
hjic-1079	127	29	(	(	PUNCT
hjic-1079	127	30	xn+l	xn+l	NOUN
hjic-1079	127	31	)	)	PUNCT
hjic-1079	128	1	+	+	ADJ
hjic-1079	128	2	dn	dn	PROPN
hjic-1079	128	3	-	-	PUNCT
hjic-1079	128	4	ln~:n(xn+2	ln~:n(xn+2	NOUN
hjic-1079	128	5	)	)	PUNCT
hjic-1079	129	1	+	+	ADJ
hjic-1079	129	2	dnn~:n	dnn~:n	PROPN
hjic-1079	129	3	(	(	PUNCT
hjic-1079	129	4	xn+3	xn+3	NOUN
hjic-1079	129	5	)	)	PUNCT
hjic-1079	129	6	=	=	SYM
hjic-1079	129	7	0	0	NUM
hjic-1079	130	1	altogether	altogether	ADV
hjic-1079	130	2	we	we	PRON
hjic-1079	130	3	come	come	VERB
hjic-1079	130	4	to	to	ADP
hjic-1079	130	5	the	the	DET
hjic-1079	130	6	following	follow	VERB
hjic-1079	130	7	pentadiagonal	pentadiagonal	ADJ
hjic-1079	130	8	system	system	NOUN
hjic-1079	130	9	for	for	ADP
hjic-1079	130	10	natural	natural	ADJ
hjic-1079	130	11	cubic	cubic	ADJ
hjic-1079	130	12	splines	spline	NOUN
hjic-1079	130	13	:	:	PUNCT
hjic-1079	130	14	6	6	NUM
hjic-1079	130	15	12	12	NUM
hjic-1079	130	16	6	6	NUM
hjic-1079	130	17	jr	jr	PROPN
hjic-1079	130	18	~o	~o	PUNCT
hjic-1079	130	19	l	l	NOUN
hjic-1079	130	20	11	11	NUM
hjic-1079	130	21	-11	-11	SYM
hjic-1079	130	22	11	11	NUM
hjic-1079	130	23	0	0	NUM
hjic-1079	130	24	1	1	NUM
hjic-1079	130	25	4	4	NUM
hjic-1079	130	26	1	1	NUM
hjic-1079	130	27	0	0	NUM
hjic-1079	130	28	dl	dl	PROPN
hjic-1079	130	29	po	po	PROPN
hjic-1079	130	30	0	0	NUM
hjic-1079	130	31	j2	j2	PROPN
hjic-1079	130	32	~	~	PUNCT
hjic-1079	130	33	6	6	NUM
hjic-1079	130	34	~:t	~:t	NOUN
hjic-1079	130	35	0	0	NUM
hjic-1079	130	36	0	0	NUM
hjic-1079	130	37	1	1	NUM
hjic-1079	130	38	4	4	NUM
hjic-1079	130	39	h~	h~	PROPN
hjic-1079	130	40	j	j	PROPN
hjic-1079	130	41	pq-1	pq-1	PART
hjic-1079	130	42	6	6	NUM
hjic-1079	130	43	12	12	NUM
hjic-1079	130	44	0	0	NUM
hjic-1079	130	45	11	11	NUM
hjic-1079	130	46	-11	-11	PUNCT
hjic-1079	130	47	in	in	ADP
hjic-1079	130	48	fig.4	fig.4	PRON
hjic-1079	130	49	we	we	PRON
hjic-1079	130	50	have	have	AUX
hjic-1079	130	51	interpolated	interpolate	VERB
hjic-1079	130	52	13	13	NUM
hjic-1079	130	53	points	point	NOUN
hjic-1079	130	54	,	,	PUNCT
hjic-1079	130	55	which	which	PRON
hjic-1079	130	56	could	could	AUX
hjic-1079	130	57	be	be	AUX
hjic-1079	130	58	understood	understand	VERB
hjic-1079	130	59	to	to	PART
hjic-1079	130	60	build	build	VERB
hjic-1079	130	61	a	a	DET
hjic-1079	130	62	tunnel	tunnel	NOUN
hjic-1079	130	63	,	,	PUNCT
hjic-1079	130	64	using	use	VERB
hjic-1079	130	65	b	b	NOUN
hjic-1079	130	66	-	-	PUNCT
hjic-1079	130	67	splines	spline	NOUN
hjic-1079	130	68	.	.	PUNCT
hjic-1079	131	1	but	but	CCONJ
hjic-1079	131	2	the	the	DET
hjic-1079	131	3	oscilating	oscilate	VERB
hjic-1079	131	4	behaviour	behaviour	NOUN
hjic-1079	131	5	of	of	ADP
hjic-1079	131	6	the	the	DET
hjic-1079	131	7	curve	curve	NOUN
hjic-1079	131	8	is	be	AUX
hjic-1079	131	9	not	not	PART
hjic-1079	131	10	acceptable	acceptable	ADJ
hjic-1079	131	11	.	.	PUNCT
hjic-1079	132	1	interpolation	interpolation	NOUN
hjic-1079	132	2	using	use	VERB
hjic-1079	132	3	beziersplinescomonotone	beziersplinescomonotone	NOUN
hjic-1079	132	4	interpoation	interpoation	NOUN
hjic-1079	132	5	after	after	ADP
hjic-1079	132	6	the	the	DET
hjic-1079	132	7	bad	bad	ADJ
hjic-1079	132	8	result	result	NOUN
hjic-1079	132	9	with	with	ADP
hjic-1079	132	10	our	our	PRON
hjic-1079	132	11	tunnel	tunnel	NOUN
hjic-1079	132	12	example	example	NOUN
hjic-1079	132	13	using	use	VERB
hjic-1079	132	14	b	b	NOUN
hjic-1079	132	15	-	-	PUNCT
hjic-1079	132	16	splines	spline	NOUN
hjic-1079	132	17	we	we	PRON
hjic-1079	132	18	are	be	AUX
hjic-1079	132	19	interested	interested	ADJ
hjic-1079	132	20	to	to	PART
hjic-1079	132	21	develop	develop	VERB
hjic-1079	132	22	a	a	DET
hjic-1079	132	23	better	well	ADJ
hjic-1079	132	24	method	method	NOUN
hjic-1079	132	25	for	for	ADP
hjic-1079	132	26	interpolating	interpolate	VERB
hjic-1079	132	27	given	give	VERB
hjic-1079	132	28	data	datum	NOUN
hjic-1079	132	29	.	.	PUNCT
hjic-1079	133	1	one	one	NUM
hjic-1079	133	2	reason	reason	NOUN
hjic-1079	133	3	for	for	ADP
hjic-1079	133	4	the	the	DET
hjic-1079	133	5	misbehaved	misbehave	VERB
hjic-1079	133	6	shape	shape	NOUN
hjic-1079	133	7	can	can	AUX
hjic-1079	133	8	be	be	AUX
hjic-1079	133	9	seen	see	VERB
hjic-1079	133	10	in	in	ADP
hjic-1079	133	11	fig.4	fig.4	PROPN
hjic-1079	133	12	.	.	PUNCT
hjic-1079	134	1	from	from	ADP
hjic-1079	134	2	the	the	DET
hjic-1079	134	3	left	left	ADJ
hjic-1079	134	4	hand	hand	NOUN
hjic-1079	134	5	side	side	NOUN
hjic-1079	134	6	up	up	ADP
hjic-1079	134	7	to	to	ADP
hjic-1079	134	8	the	the	DET
hjic-1079	134	9	midpoint	midpoint	NOUN
hjic-1079	134	10	the	the	DET
hjic-1079	134	11	datas	data	NOUN
hjic-1079	134	12	are	be	AUX
hjic-1079	134	13	monotone	monotone	ADJ
hjic-1079	134	14	increasing	increase	VERB
hjic-1079	134	15	,	,	PUNCT
hjic-1079	134	16	whereas	whereas	SCONJ
hjic-1079	134	17	the	the	DET
hjic-1079	134	18	spline	spline	NOUN
hjic-1079	134	19	curve	curve	NOUN
hjic-1079	134	20	oscilates	oscilate	VERB
hjic-1079	134	21	through	through	ADP
hjic-1079	134	22	the	the	DET
hjic-1079	134	23	first	first	ADJ
hjic-1079	134	24	four	four	NUM
hjic-1079	134	25	points	point	NOUN
hjic-1079	134	26	.	.	PUNCT
hjic-1079	135	1	at	at	ADP
hjic-1079	135	2	first	first	ADV
hjic-1079	135	3	let	let	VERB
hjic-1079	135	4	us	we	PRON
hjic-1079	135	5	define	define	VERB
hjic-1079	135	6	what	what	PRON
hjic-1079	135	7	we	we	PRON
hjic-1079	135	8	want	want	VERB
hjic-1079	135	9	to	to	PART
hjic-1079	135	10	understand	understand	VERB
hjic-1079	135	11	by	by	ADP
hjic-1079	135	12	a	a	DET
hjic-1079	135	13	comonotone	comonotone	NOUN
hjic-1079	135	14	interpolating	interpolate	VERB
hjic-1079	135	15	procedure	procedure	NOUN
hjic-1079	135	16	:	:	PUNCT
hjic-1079	135	17	deimition	deimition	NOUN
hjic-1079	135	18	:	:	PUNCT
hjic-1079	135	19	consider	consider	VERB
hjic-1079	135	20	the	the	DET
hjic-1079	135	21	given	give	VERB
hjic-1079	135	22	data	datum	NOUN
hjic-1079	135	23	(	(	PUNCT
hjic-1079	135	24	x0,y0),(xpy1	x0,y0),(xpy1	NOUN
hjic-1079	135	25	)	)	PUNCT
hjic-1079	135	26	,	,	PUNCT
hjic-1079	135	27	...	...	PUNCT
hjic-1079	135	28	,	,	PUNCT
hjic-1079	135	29	(	(	PUNCT
hjic-1079	135	30	xn	xn	PROPN
hjic-1079	135	31	,	,	PUNCT
hjic-1079	135	32	yn	yn	PROPN
hjic-1079	135	33	)	)	PUNCT
hjic-1079	135	34	with	with	ADP
hjic-1079	135	35	x0	x0	PROPN
hjic-1079	135	36	<	<	X
hjic-1079	136	1	x1	x1	X
hjic-1079	136	2	<	<	X
hjic-1079	136	3	·	·	PUNCT
hjic-1079	136	4	·	·	PUNCT
hjic-1079	136	5	·	·	PUNCT
hjic-1079	136	6	<	<	X
hjic-1079	136	7	xn	xn	X
hjic-1079	136	8	.	.	PUNCT
hjic-1079	137	1	let	let	AUX
hjic-1079	137	2	se	se	PROPN
hjic-1079	137	3	c1[x0	c1[x0	ADV
hjic-1079	137	4	,	,	PUNCT
hjic-1079	137	5	xn	xn	PROPN
hjic-1079	137	6	]	]	X
hjic-1079	137	7	be	be	VERB
hjic-1079	137	8	a	a	DET
hjic-1079	137	9	function	function	NOUN
hjic-1079	137	10	which	which	PRON
hjic-1079	137	11	interpolates	interpolate	VERB
hjic-1079	137	12	these	these	DET
hjic-1079	137	13	data	datum	NOUN
hjic-1079	137	14	.	.	PUNCT
hjic-1079	138	1	then	then	ADV
hjic-1079	138	2	we	we	PRON
hjic-1079	138	3	will	will	AUX
hjic-1079	138	4	calls	call	VERB
hjic-1079	138	5	comonotone	comonotone	NOUN
hjic-1079	138	6	with	with	ADP
hjic-1079	138	7	the	the	DET
hjic-1079	138	8	data	datum	NOUN
hjic-1079	138	9	,	,	PUNCT
hjic-1079	138	10	iff	iff	VERB
hjic-1079	138	11	s'(x)·m1	s'(x)·m1	PROPN
hjic-1079	138	12	>	>	PUNCT
hjic-1079	138	13	0	0	PROPN
hjic-1079	138	14	if	if	SCONJ
hjic-1079	138	15	m	m	PROPN
hjic-1079	138	16	;	;	PUNCT
hjic-1079	138	17	¢0,xe	¢0,xe	PROPN
hjic-1079	138	18	(	(	PUNCT
hjic-1079	138	19	xi_1,xi	xi_1,xi	PROPN
hjic-1079	138	20	)	)	PUNCT
hjic-1079	138	21	s"'(x	s"'(x	NOUN
hjic-1079	138	22	}	}	PUNCT
hjic-1079	139	1	=	=	NOUN
hjic-1079	139	2	0	0	PUNCT
hjic-1079	139	3	if	if	SCONJ
hjic-1079	139	4	mi	mi	PROPN
hjic-1079	139	5	=	=	NOUN
hjic-1079	139	6	0	0	PROPN
hjic-1079	139	7	this	this	PRON
hjic-1079	139	8	is	be	AUX
hjic-1079	139	9	easy	easy	ADJ
hjic-1079	139	10	to	to	PART
hjic-1079	139	11	explain	explain	VERB
hjic-1079	139	12	.	.	PUNCT
hjic-1079	140	1	the	the	DET
hjic-1079	140	2	slope	slope	NOUN
hjic-1079	140	3	of	of	ADP
hjic-1079	140	4	the	the	DET
hjic-1079	140	5	spline	spline	NOUN
hjic-1079	140	6	functions	function	NOUN
hjic-1079	140	7	should	should	AUX
hjic-1079	140	8	always	always	ADV
hjic-1079	140	9	be	be	AUX
hjic-1079	140	10	the	the	DET
hjic-1079	140	11	same	same	ADJ
hjic-1079	140	12	sign	sign	NOUN
hjic-1079	140	13	as	as	ADP
hjic-1079	140	14	the	the	DET
hjic-1079	140	15	slope	slope	NOUN
hjic-1079	140	16	of	of	ADP
hjic-1079	140	17	the	the	DET
hjic-1079	140	18	straight	straight	ADJ
hjic-1079	140	19	line	line	NOUN
hjic-1079	140	20	between	between	ADP
hjic-1079	140	21	two	two	NUM
hjic-1079	140	22	neighb	neighb	NOUN
hjic-1079	140	23	<	<	X
hjic-1079	140	24	'	'	PUNCT
hjic-1079	140	25	ur	ur	INTJ
hjic-1079	140	26	points	point	NOUN
hjic-1079	140	27	.	.	PUNCT
hjic-1079	141	1	then	then	ADV
hjic-1079	141	2	swill	swill	NOUN
hjic-1079	141	3	be	be	AUX
hjic-1079	141	4	monotone	monotone	ADJ
hjic-1079	141	5	increasing	increase	VERB
hjic-1079	141	6	or	or	CCONJ
hjic-1079	141	7	decrea	decrea	NOUN
hjic-1079	141	8	~	~	NOUN
hjic-1079	141	9	ing	ing	NOUN
hjic-1079	141	10	in	in	ADP
hjic-1079	141	11	the	the	DET
hjic-1079	141	12	same	same	ADJ
hjic-1079	141	13	intervals	interval	NOUN
hjic-1079	141	14	where	where	SCONJ
hjic-1079	141	15	the	the	DET
hjic-1079	141	16	data	datum	NOUN
hjic-1079	141	17	are	be	AUX
hjic-1079	141	18	monotone	monotone	ADJ
hjic-1079	141	19	mcreasing	mcreasing	NOUN
hjic-1079	141	20	or	or	CCONJ
hjic-1079	141	21	decreasing	decrease	VERB
hjic-1079	141	22	.	.	PUNCT
hjic-1079	142	1	respectively	respectively	ADV
hjic-1079	142	2	.	.	PUNCT
hjic-1079	143	1	110	110	NUM
hjic-1079	143	2	!	!	PUNCT
hjic-1079	143	3	)	)	PUNCT
hjic-1079	144	1	''	''	PUNCT
hjic-1079	144	2	"	"	PUNCT
hjic-1079	144	3	"	"	PUNCT
hjic-1079	144	4	"	"	PUNCT
hjic-1079	144	5	-'"'"~"--	-'"'"~"--	NOUN
hjic-1079	144	6	·	·	PUNCT
hjic-1079	144	7	,	,	PUNCT
hjic-1079	144	8	..	..	PUNCT
hjic-1079	144	9	...	...	PUNCT
hjic-1079	145	1	·	·	PUNCT
hjic-1079	145	2	-··--,---	-··--,---	INTJ
hjic-1079	145	3	.	.	PUNCT
hjic-1079	145	4	,	,	PUNCT
hjic-1079	145	5	i\	i\	VERB
hjic-1079	145	6	4	4	NUM
hjic-1079	145	7	.	.	PUNCT
hjic-1079	145	8	,	,	PUNCT
hjic-1079	146	1	i	i	PRON
hjic-1079	146	2	~r	~r	PUNCT
hjic-1079	146	3	j	j	PROPN
hjic-1079	146	4	1	1	NUM
hjic-1079	146	5	~	~	PUNCT
hjic-1079	146	6	·	·	PUNCT
hjic-1079	146	7	~	~	PUNCT
hjic-1079	146	8	"	"	PUNCT
hjic-1079	146	9	.	.	PUNCT
hjic-1079	146	10	;	;	PUNCT
hjic-1079	146	11	(	(	PUNCT
hjic-1079	146	12	j	j	PROPN
hjic-1079	146	13	·	·	PUNCT
hjic-1079	146	14	u	u	NOUN
hjic-1079	146	15	·	·	PROPN
hjic-1079	146	16	4	4	NUM
hjic-1079	146	17	..	..	PUNCT
hjic-1079	146	18	:	:	PUNCT
hjic-1079	146	19	l	l	NOUN
hjic-1079	146	20	{	{	PUNCT
hjic-1079	146	21	i	i	PRON
hjic-1079	146	22	fig.5	fig.5	VERB
hjic-1079	146	23	the	the	DET
hjic-1079	146	24	same	same	ADJ
hjic-1079	146	25	13	13	NUM
hjic-1079	146	26	given	give	VERB
hjic-1079	146	27	points	point	NOUN
hjic-1079	146	28	as	as	ADP
hjic-1079	146	29	in	in	ADP
hjic-1079	146	30	fig	fig	NOUN
hjic-1079	146	31	a	a	PRON
hjic-1079	146	32	are	be	AUX
hjic-1079	146	33	now	now	ADV
hjic-1079	146	34	interpolated	interpolate	VERB
hjic-1079	146	35	with	with	ADP
hjic-1079	146	36	the	the	DET
hjic-1079	146	37	comonotone	comonotone	NOUN
hjic-1079	146	38	algorithm	algorithm	NOUN
hjic-1079	146	39	using	use	VERB
hjic-1079	146	40	bezier­	bezier­	NOUN
hjic-1079	146	41	splines	spline	NOUN
hjic-1079	146	42	.	.	PUNCT
hjic-1079	147	1	the	the	DET
hjic-1079	147	2	bernstein	bernstein	PROPN
hjic-1079	147	3	operator	operator	NOUN
hjic-1079	147	4	and	and	CCONJ
hjic-1079	147	5	its	its	PRON
hjic-1079	147	6	shape	shape	NOUN
hjic-1079	147	7	preserving	preserve	VERB
hjic-1079	147	8	behaviour	behaviour	NOUN
hjic-1079	147	9	i	i	PRON
hjic-1079	147	10	the	the	DET
hjic-1079	147	11	·	·	PUNCT
hjic-1079	147	12	main	main	ADJ
hjic-1079	147	13	point	point	NOUN
hjic-1079	147	14	in	in	ADP
hjic-1079	147	15	developing	develop	VERB
hjic-1079	147	16	our	our	PRON
hjic-1079	147	17	new	new	ADJ
hjic-1079	147	18	algorithm	algorithm	NOUN
hjic-1079	147	19	is	be	AUX
hjic-1079	147	20	to	to	PART
hjic-1079	147	21	use	use	VERB
hjic-1079	147	22	the	the	DET
hjic-1079	147	23	bernstein	bernstein	PROPN
hjic-1079	147	24	operator	operator	NOUN
hjic-1079	147	25	.	.	PUNCT
hjic-1079	148	1	it	it	PRON
hjic-1079	148	2	works	work	VERB
hjic-1079	148	3	with	with	ADP
hjic-1079	148	4	the	the	DET
hjic-1079	148	5	help	help	NOUN
hjic-1079	148	6	of	of	ADP
hjic-1079	148	7	the	the	DET
hjic-1079	148	8	bernstein	bernstein	PROPN
hjic-1079	148	9	polynomials	polynomials	PROPN
hjic-1079	148	10	.	.	PUNCT
hjic-1079	149	1	deimition	deimition	NOUN
hjic-1079	149	2	:	:	PUNCT
hjic-1079	149	3	let	let	VERB
hjic-1079	149	4	f	f	PRON
hjic-1079	149	5	be	be	AUX
hjic-1079	149	6	a	a	DET
hjic-1079	149	7	vector	vector	NOUN
hjic-1079	149	8	valued	value	VERB
hjic-1079	149	9	continuous	continuous	ADJ
hjic-1079	149	10	function	function	NOUN
hjic-1079	149	11	on	on	ADP
hjic-1079	149	12	the	the	DET
hjic-1079	149	13	interval	interval	NOUN
hjic-1079	149	14	[	[	X
hjic-1079	149	15	0,1	0,1	NUM
hjic-1079	149	16	]	]	PUNCT
hjic-1079	149	17	.	.	PUNCT
hjic-1079	150	1	then	then	ADV
hjic-1079	150	2	the	the	DET
hjic-1079	150	3	bernstein	bernstein	PROPN
hjic-1079	150	4	operator	operator	NOUN
hjic-1079	150	5	is	be	AUX
hjic-1079	150	6	defined	define	VERB
hjic-1079	150	7	as	as	ADP
hjic-1079	150	8	in	in	ADP
hjic-1079	150	9	the	the	DET
hjic-1079	150	10	following	follow	VERB
hjic-1079	150	11	theorem	theorem	NOUN
hjic-1079	150	12	we	we	PRON
hjic-1079	150	13	summarize	summarize	VERB
hjic-1079	150	14	some	some	PRON
hjic-1079	150	15	of	of	ADP
hjic-1079	150	16	the	the	DET
hjic-1079	150	17	most	most	ADV
hjic-1079	150	18	important	important	ADJ
hjic-1079	150	19	properties	property	NOUN
hjic-1079	150	20	regarding	regard	VERB
hjic-1079	150	21	the	the	DET
hjic-1079	150	22	shape	shape	NOUN
hjic-1079	150	23	preserving	preserve	VERB
hjic-1079	150	24	of	of	ADP
hjic-1079	150	25	the	the	DET
hjic-1079	150	26	bernstein	bernstein	PROPN
hjic-1079	150	27	operator	operator	PROPN
hjic-1079	150	28	:	:	PUNCT
hjic-1079	150	29	theorem	theorem	VERB
hjic-1079	150	30	:	:	PUNCT
hjic-1079	150	31	for	for	ADP
hjic-1079	150	32	the	the	DET
hjic-1079	150	33	bernstein	bernstein	PROPN
hjic-1079	150	34	operator	operator	NOUN
hjic-1079	150	35	we	we	PRON
hjic-1079	150	36	have	have	VERB
hjic-1079	150	37	:	:	PUNCT
hjic-1079	151	1	1	1	X
hjic-1079	151	2	.	.	X
hjic-1079	151	3	f	f	PROPN
hjic-1079	151	4	bounded	bound	VERB
hjic-1079	151	5	=	=	PRON
hjic-1079	151	6	=	=	NOUN
hjic-1079	151	7	>	>	X
hjic-1079	151	8	bnf	bnf	PROPN
hjic-1079	151	9	is	be	AUX
hjic-1079	151	10	bounded	bound	VERB
hjic-1079	151	11	(	(	PUNCT
hjic-1079	151	12	with	with	ADP
hjic-1079	151	13	the	the	DET
hjic-1079	151	14	same	same	ADJ
hjic-1079	151	15	bounds	bound	NOUN
hjic-1079	151	16	)	)	PUNCT
hjic-1079	151	17	2	2	NUM
hjic-1079	151	18	.	.	X
hjic-1079	151	19	f	f	PROPN
hjic-1079	151	20	;	;	PUNCT
hjic-1079	151	21	?	?	PUNCT
hjic-1079	151	22	:	:	PUNCT
hjic-1079	151	23	:	:	PUNCT
hjic-1079	151	24	0	0	NUM
hjic-1079	151	25	in	in	ADP
hjic-1079	151	26	[	[	X
hjic-1079	151	27	0,1	0,1	NUM
hjic-1079	151	28	]	]	PUNCT
hjic-1079	151	29	:	:	PUNCT
hjic-1079	151	30	:	:	PUNCT
hjic-1079	151	31	:	:	PUNCT
hjic-1079	151	32	:	:	PUNCT
hjic-1079	151	33	:	:	PUNCT
hjic-1079	151	34	?	?	PUNCT
hjic-1079	152	1	bnf	bnf	PROPN
hjic-1079	152	2	~	~	PUNCT
hjic-1079	152	3	0	0	PUNCT
hjic-1079	152	4	in	in	ADP
hjic-1079	152	5	[	[	X
hjic-1079	152	6	0,1	0,1	NUM
hjic-1079	152	7	]	]	SYM
hjic-1079	152	8	3	3	NUM
hjic-1079	152	9	.	.	PUNCT
hjic-1079	152	10	bn/(0	bn/(0	NOUN
hjic-1079	152	11	)	)	PUNCT
hjic-1079	153	1	=	=	SYM
hjic-1079	153	2	/(0	/(0	NOUN
hjic-1079	153	3	)	)	PUNCT
hjic-1079	153	4	,	,	PUNCT
hjic-1079	153	5	bnf	bnf	PROPN
hjic-1079	153	6	(	(	PUNCT
hjic-1079	153	7	!	!	PUNCT
hjic-1079	153	8	)	)	PUNCT
hjic-1079	154	1	=	=	PUNCT
hjic-1079	155	1	/(1	/(1	PUNCT
hjic-1079	155	2	)	)	PUNCT
hjic-1079	155	3	4	4	X
hjic-1079	155	4	.	.	PUNCT
hjic-1079	155	5	/monotone	/monotone	X
hjic-1079	156	1	=	=	PUNCT
hjic-1079	156	2	=	=	NOUN
hjic-1079	156	3	>	>	X
hjic-1079	156	4	bnf	bnf	PROPN
hjic-1079	156	5	monotone	monotone	NOUN
hjic-1079	156	6	5	5	NUM
hjic-1079	156	7	.	.	PUNCT
hjic-1079	157	1	f	f	PROPN
hjic-1079	157	2	convex	convex	PROPN
hjic-1079	157	3	=	=	PROPN
hjic-1079	157	4	=	=	NOUN
hjic-1079	157	5	>	>	X
hjic-1079	157	6	blff	blff	NOUN
hjic-1079	157	7	convex	convex	NOUN
hjic-1079	157	8	now	now	ADV
hjic-1079	157	9	we	we	PRON
hjic-1079	157	10	are	be	AUX
hjic-1079	157	11	able	able	ADJ
hjic-1079	157	12	to	to	PART
hjic-1079	157	13	explain	explain	VERB
hjic-1079	157	14	the	the	DET
hjic-1079	157	15	algorithm	algorithm	NOUN
hjic-1079	157	16	:	:	PUNCT
hjic-1079	157	17	comonotone	comonotone	NOUN
hjic-1079	157	18	algorithm	algorithm	NOUN
hjic-1079	157	19	:	:	PUNCT
hjic-1079	158	1	1	1	X
hjic-1079	158	2	.	.	X
hjic-1079	158	3	construct	construct	VERB
hjic-1079	158	4	the	the	DET
hjic-1079	158	5	subknots	subknot	NOUN
hjic-1079	158	6	t	t	PROPN
hjic-1079	158	7	0	0	NUM
hjic-1079	158	8	,	,	PUNCT
hjic-1079	158	9	t	t	PROPN
hjic-1079	158	10	1	1	NUM
hjic-1079	158	11	,	,	PUNCT
hjic-1079	158	12	••••	••••	NOUN
hjic-1079	158	13	t	t	PROPN
hjic-1079	158	14	'	'	PUNCT
hjic-1079	158	15	1.n	1.n	NUM
hjic-1079	159	1	+	+	CCONJ
hjic-1079	159	2	1	1	NUM
hjic-1079	159	3	x.	x.	NOUN
hjic-1079	159	4	-x	-x	NOUN
hjic-1079	159	5	.	.	PROPN
hjic-1079	159	6	1	1	NUM
hjic-1079	159	7	witlt	witlt	PROPN
hjic-1079	159	8	r.	r.	PROPN
hjic-1079	159	9	=	=	PUNCT
hjic-1079	159	10	'	'	PART
hjic-1079	159	11	~hv	~hv	PROPN
hjic-1079	159	12	t	t	PROPN
hjic-1079	159	13	3	3	NUM
hjic-1079	159	14	•	•	NUM
hjic-1079	159	15	2	2	NUM
hjic-1079	159	16	.	.	PUNCT
hjic-1079	159	17	calculate	calculate	VERB
hjic-1079	159	18	the	the	DET
hjic-1079	159	19	difference	difference	NOUN
hjic-1079	159	20	quotients	quotient	VERB
hjic-1079	159	21	:	:	PUNCT
hjic-1079	159	22	y;yi-1	y;yi-1	NUM
hjic-1079	159	23	.	.	PUNCT
hjic-1079	160	1	1	1	NUM
hjic-1079	160	2	n	n	DET
hjic-1079	160	3	nz	nz	NOUN
hjic-1079	160	4	;	;	PUNCT
hjic-1079	160	5	=	=	SYM
hjic-1079	160	6	,	,	PUNCT
hjic-1079	160	7	l	l	NOUN
hjic-1079	160	8	=	=	PUNCT
hjic-1079	160	9	,	,	PUNCT
hjic-1079	160	10	...	...	PUNCT
hjic-1079	160	11	,	,	PUNCT
hjic-1079	160	12	x	x	X
hjic-1079	160	13	;	;	PUNCT
hjic-1079	160	14	-xi-	-xi-	X
hjic-1079	160	15	!	!	NOUN
hjic-1079	160	16	3	3	NUM
hjic-1079	160	17	.	.	X
hjic-1079	160	18	determine	determine	VERB
hjic-1079	160	19	a	a	DET
hjic-1079	160	20	piecewise	piecewise	NOUN
hjic-1079	160	21	linear	linear	ADJ
hjic-1079	160	22	comonotone	comonotone	NOUN
hjic-1079	160	23	function	function	NOUN
hjic-1079	160	24	l	l	NOUN
hjic-1079	160	25	by	by	ADP
hjic-1079	160	26	l	l	PROPN
hjic-1079	160	27	(	(	PUNCT
hjic-1079	160	28	x	x	NOUN
hjic-1079	160	29	;	;	PUNCT
hjic-1079	160	30	)	)	PUNCT
hjic-1079	160	31	:	:	PUNCT
hjic-1079	161	1	=	=	PUNCT
hjic-1079	161	2	y	y	INTJ
hjic-1079	161	3	i	i	PRON
hjic-1079	161	4	,	,	PUNCT
hjic-1079	161	5	r	r	X
hjic-1079	161	6	(	(	PUNCT
hjic-1079	161	7	x	x	NOUN
hjic-1079	161	8	;	;	PUNCT
hjic-1079	161	9	)	)	PUNCT
hjic-1079	161	10	:	:	PUNCT
hjic-1079	162	1	=	=	SYM
hjic-1079	162	2	d	d	NOUN
hjic-1079	162	3	;	;	PUNCT
hjic-1079	162	4	with	with	ADP
hjic-1079	162	5	d0	d0	NOUN
hjic-1079	162	6	:	:	PUNCT
hjic-1079	162	7	=	=	SYM
hjic-1079	162	8	2m1	2m1	X
hjic-1079	162	9	-d1,dn	-d1,dn	NOUN
hjic-1079	162	10	:	:	PUNCT
hjic-1079	162	11	=	=	X
hjic-1079	162	12	2mn	2mn	X
hjic-1079	162	13	-dn	-dn	NOUN
hjic-1079	162	14	-	-	SYM
hjic-1079	162	15	j	j	NOUN
hjic-1079	162	16	andfor	andfor	ADP
hjic-1079	162	17	i	i	PROPN
hjic-1079	162	18	=	=	PROPN
hjic-1079	162	19	l	l	PROPN
hjic-1079	162	20	,	,	PUNCT
hjic-1079	162	21	...	...	PUNCT
hjic-1079	162	22	,	,	PUNCT
hjic-1079	162	23	n-1	n-1	NOUN
hjic-1079	162	24	0	0	PUNCT
hjic-1079	163	1	if	if	SCONJ
hjic-1079	163	2	mi	mi	PROPN
hjic-1079	163	3	·	·	PUNCT
hjic-1079	163	4	m;+i	m;+i	X
hjic-1079	164	1	=	=	SYM
hjic-1079	164	2	0	0	PROPN
hjic-1079	164	3	d	d	PROPN
hjic-1079	164	4	·	·	PROPN
hjic-1079	164	5	m	m	PROPN
hjic-1079	164	6	;	;	PUNCT
hjic-1079	164	7	3mi+i	3mi+i	NUM
hjic-1079	164	8	-mi	-mi	ADP
hjic-1079	164	9	if	if	SCONJ
hjic-1079	164	10	o	o	NOUN
hjic-1079	164	11	<	<	X
hjic-1079	164	12	lmtl	lmtl	NOUN
hjic-1079	164	13	~	~	SYM
hjic-1079	164	14	lm;+ji	lm;+ji	NOUN
hjic-1079	165	1	i	i	PRON
hjic-1079	165	2	.2	.2	NUM
hjic-1079	165	3	mi+i	mi+i	PROPN
hjic-1079	165	4	mi+l	mi+l	NUM
hjic-1079	165	5	3	3	NUM
hjic-1079	165	6	m	m	NOUN
hjic-1079	165	7	;	;	PUNCT
hjic-1079	165	8	mi+l	mi+l	PROPN
hjic-1079	165	9	if	if	SCONJ
hjic-1079	165	10	jm	jm	PROPN
hjic-1079	165	11	;	;	PUNCT
hjic-1079	165	12	i	i	PRON
hjic-1079	165	13	>	>	X
hjic-1079	165	14	lmi+ll	lmi+ll	PROPN
hjic-1079	165	15	m	m	PROPN
hjic-1079	165	16	;	;	PUNCT
hjic-1079	165	17	2	2	NUM
hjic-1079	165	18	4	4	NUM
hjic-1079	165	19	.	.	PUNCT
hjic-1079	165	20	calculate	calculate	NOUN
hjic-1079	165	21	l(t1	l(t1	PROPN
hjic-1079	165	22	)	)	PUNCT
hjic-1079	165	23	,	,	PUNCT
hjic-1079	165	24	l(t2i	l(t2i	PUNCT
hjic-1079	165	25	)	)	PUNCT
hjic-1079	165	26	,	,	PUNCT
hjic-1079	165	27	l(t2;+1	l(t2;+1	PROPN
hjic-1079	165	28	)	)	PUNCT
hjic-1079	165	29	,	,	PUNCT
hjic-1079	165	30	l(t2n	l(t2n	NOUN
hjic-1079	165	31	)	)	PUNCT
hjic-1079	165	32	5	5	NUM
hjic-1079	165	33	.	.	X
hjic-1079	165	34	apply	apply	VERB
hjic-1079	165	35	in	in	ADP
hjic-1079	165	36	each	each	DET
hjic-1079	165	37	subinterval	subinterval	NOUN
hjic-1079	165	38	the	the	DET
hjic-1079	165	39	bernstein	bernstein	PROPN
hjic-1079	165	40	operator	operator	NOUN
hjic-1079	165	41	.	.	PUNCT
hjic-1079	166	1	this	this	PRON
hjic-1079	166	2	leads	lead	VERB
hjic-1079	166	3	to	to	ADP
hjic-1079	166	4	the	the	DET
hjic-1079	166	5	desired	desire	VERB
hjic-1079	166	6	function	function	NOUN
hjic-1079	166	7	:	:	PUNCT
hjic-1079	166	8	remark	remark	VERB
hjic-1079	166	9	:	:	PUNCT
hjic-1079	166	10	the	the	DET
hjic-1079	166	11	formula	formula	NOUN
hjic-1079	166	12	in	in	ADP
hjic-1079	166	13	3	3	NUM
hjic-1079	166	14	.	.	PUNCT
hjic-1079	166	15	is	be	AUX
hjic-1079	166	16	the	the	DET
hjic-1079	166	17	heart	heart	NOUN
hjic-1079	166	18	of	of	ADP
hjic-1079	166	19	the	the	DET
hjic-1079	166	20	algorithm	algorithm	NOUN
hjic-1079	166	21	.	.	PUNCT
hjic-1079	167	1	the	the	DET
hjic-1079	167	2	derivative	derivative	ADJ
hjic-1079	167	3	di	di	NOUN
hjic-1079	167	4	at	at	ADP
hjic-1079	167	5	the	the	DET
hjic-1079	167	6	knots	knot	NOUN
hjic-1079	167	7	xi	xi	X
hjic-1079	167	8	is	be	AUX
hjic-1079	167	9	evaluated	evaluate	VERB
hjic-1079	167	10	in	in	ADP
hjic-1079	167	11	a	a	DET
hjic-1079	167	12	way	way	NOUN
hjic-1079	167	13	that	that	PRON
hjic-1079	167	14	the	the	DET
hjic-1079	167	15	resulting	result	VERB
hjic-1079	167	16	linear	linear	ADJ
hjic-1079	167	17	spline	spline	NOUN
hjic-1079	167	18	function	function	NOUN
hjic-1079	167	19	is	be	AUX
hjic-1079	167	20	comonotone	comonotone	NOUN
hjic-1079	167	21	with	with	ADP
hjic-1079	167	22	the	the	DET
hjic-1079	167	23	data	datum	NOUN
hjic-1079	167	24	.	.	PUNCT
hjic-1079	168	1	because	because	SCONJ
hjic-1079	168	2	of	of	ADP
hjic-1079	168	3	the	the	DET
hjic-1079	168	4	shape	shape	NOUN
hjic-1079	168	5	preserving	preserve	VERB
hjic-1079	168	6	behaviour	behaviour	NOUN
hjic-1079	168	7	of	of	ADP
hjic-1079	168	8	the	the	DET
hjic-1079	168	9	bernstein	bernstein	PROPN
hjic-1079	168	10	operator	operator	NOUN
hjic-1079	168	11	we	we	PRON
hjic-1079	168	12	get	get	VERB
hjic-1079	168	13	therefore	therefore	ADV
hjic-1079	168	14	the	the	DET
hjic-1079	168	15	desired	desire	VERB
hjic-1079	168	16	comonotone	comonotone	NOUN
hjic-1079	168	17	cubic	cubic	ADJ
hjic-1079	168	18	spline	spline	NOUN
hjic-1079	168	19	function	function	NOUN
hjic-1079	168	20	.	.	PUNCT
hjic-1079	169	1	in	in	ADP
hjic-1079	169	2	fig.5	fig.5	NOUN
hjic-1079	169	3	we	we	PRON
hjic-1079	169	4	show	show	VERB
hjic-1079	169	5	the	the	DET
hjic-1079	169	6	tunnel	tunnel	NOUN
hjic-1079	169	7	data	datum	NOUN
hjic-1079	169	8	from	from	ADP
hjic-1079	169	9	above	above	ADV
hjic-1079	169	10	,	,	PUNCT
hjic-1079	169	11	but	but	CCONJ
hjic-1079	169	12	now	now	ADV
hjic-1079	169	13	comonotone	comonotone	NOUN
hjic-1079	169	14	interpolated	interpolate	VERB
hjic-1079	169	15	.	.	PUNCT
hjic-1079	170	1	the	the	DET
hjic-1079	170	2	result	result	NOUN
hjic-1079	170	3	looks	look	VERB
hjic-1079	170	4	much	much	ADV
hjic-1079	170	5	better	well	ADJ
hjic-1079	170	6	.	.	PUNCT
hjic-1079	171	1	conclusion	conclusion	NOUN
hjic-1079	171	2	in	in	ADP
hjic-1079	171	3	this	this	DET
hjic-1079	171	4	paper	paper	NOUN
hjic-1079	171	5	we	we	PRON
hjic-1079	171	6	compared	compare	VERB
hjic-1079	171	7	b	b	NOUN
hjic-1079	171	8	-	-	PUNCT
hjic-1079	171	9	splines	spline	NOUN
hjic-1079	171	10	and	and	CCONJ
hjic-1079	171	11	beziersplines	bezierspline	NOUN
hjic-1079	171	12	.	.	PUNCT
hjic-1079	172	1	after	after	ADP
hjic-1079	172	2	a	a	DET
hjic-1079	172	3	short	short	ADJ
hjic-1079	172	4	introduction	introduction	NOUN
hjic-1079	172	5	for	for	ADP
hjic-1079	172	6	both	both	DET
hjic-1079	172	7	spline	spline	NOUN
hjic-1079	172	8	cancidates	cancidate	NOUN
hjic-1079	172	9	we	we	PRON
hjic-1079	172	10	explained	explain	VERB
hjic-1079	172	11	some	some	PRON
hjic-1079	172	12	of	of	ADP
hjic-1079	172	13	the	the	DET
hjic-1079	172	14	most	most	ADV
hjic-1079	172	15	important	important	ADJ
hjic-1079	172	16	properties	property	NOUN
hjic-1079	172	17	.	.	PUNCT
hjic-1079	173	1	the	the	DET
hjic-1079	173	2	similar	similar	ADJ
hjic-1079	173	3	algorithms	algorithm	NOUN
hjic-1079	173	4	of	of	ADP
hjic-1079	173	5	de	de	X
hjic-1079	173	6	boor	boor	NOUN
hjic-1079	173	7	and	and	CCONJ
hjic-1079	173	8	de	de	ADP
hjic-1079	173	9	casteljau	casteljau	PROPN
hjic-1079	173	10	lead	lead	VERB
hjic-1079	173	11	to	to	ADP
hjic-1079	173	12	very	very	ADV
hjic-1079	173	13	fast	fast	ADJ
hjic-1079	173	14	evaluation	evaluation	NOUN
hjic-1079	173	15	processes	process	NOUN
hjic-1079	173	16	.	.	PUNCT
hjic-1079	174	1	several	several	ADJ
hjic-1079	174	2	figures	figure	NOUN
hjic-1079	174	3	show	show	VERB
hjic-1079	174	4	the	the	DET
hjic-1079	174	5	different	different	ADJ
hjic-1079	174	6	behaviour	behaviour	NOUN
hjic-1079	174	7	regarding	regard	VERB
hjic-1079	174	8	the	the	DET
hjic-1079	174	9	interpolation	interpolation	NOUN
hjic-1079	174	10	procedure	procedure	NOUN
hjic-1079	174	11	.	.	PUNCT
hjic-1079	175	1	in	in	ADP
hjic-1079	175	2	contrast	contrast	NOUN
hjic-1079	175	3	to	to	ADP
hjic-1079	175	4	the	the	DET
hjic-1079	175	5	disadvantage	disadvantage	NOUN
hjic-1079	175	6	of	of	ADP
hjic-1079	175	7	the	the	DET
hjic-1079	175	8	monotony	monotony	NOUN
hjic-1079	175	9	preserving	preserving	NOUN
hjic-1079	175	10	of	of	ADP
hjic-1079	175	11	the	the	DET
hjic-1079	175	12	b	b	NOUN
hjic-1079	175	13	-	-	PUNCT
hjic-1079	175	14	splines	spline	NOUN
hjic-1079	175	15	we	we	PRON
hjic-1079	175	16	propose	propose	VERB
hjic-1079	175	17	a	a	DET
hjic-1079	175	18	comonotone	comonotone	NOUN
hjic-1079	175	19	interpolation	interpolation	NOUN
hjic-1079	175	20	algorithm	algorithm	NOUN
hjic-1079	175	21	using	use	VERB
hjic-1079	175	22	bezier	bezier	ADJ
hjic-1079	175	23	splines	spline	NOUN
hjic-1079	175	24	.	.	PUNCT
hjic-1079	176	1	r	r	NOUN
hjic-1079	176	2	symbols	symbol	NOUN
hjic-1079	176	3	real	real	ADJ
hjic-1079	176	4	numbers	number	NOUN
hjic-1079	176	5	knots	knot	VERB
hjic-1079	176	6	inr	inr	PROPN
hjic-1079	176	7	t	t	PROPN
hjic-1079	176	8	=	=	PUNCT
hjic-1079	176	9	(	(	PUNCT
hjic-1079	176	10	x0	x0	PROPN
hjic-1079	176	11	~	~	PUNCT
hjic-1079	176	12	....	....	PUNCT
hjic-1079	176	13	xn+l+i	xn+l+i	NOUN
hjic-1079	176	14	)	)	PUNCT
hjic-1079	176	15	knot	knot	NOUN
hjic-1079	176	16	sequence	sequence	NOUN
hjic-1079	176	17	n	n	PROPN
hjic-1079	176	18	li	li	PROPN
hjic-1079	176	19	b	b	X
hjic-1079	176	20	-	-	PUNCT
hjic-1079	176	21	splines	spline	NOUN
hjic-1079	176	22	(	(	PUNCT
hjic-1079	176	23	tx)~	tx)~	PROPN
hjic-1079	176	24	+	+	NOUN
hjic-1079	176	25	-function	-function	VERB
hjic-1079	176	26	a	a	DET
hjic-1079	176	27	=(	=(	NOUN
hjic-1079	176	28	x0	x0	PROPN
hjic-1079	176	29	,	,	PUNCT
hjic-1079	176	30	•••	•••	ADV
hjic-1079	176	31	,	,	PUNCT
hjic-1079	176	32	xn+l	xn+l	PROPN
hjic-1079	176	33	)	)	PUNCT
hjic-1079	176	34	given	give	VERB
hjic-1079	176	35	knots	knot	NOUN
hjic-1079	176	36	c1	c1	PROPN
hjic-1079	176	37	1[a.b	1[a.b	NUM
hjic-1079	176	38	]	]	PUNCT
hjic-1079	176	39	(	(	PUNCT
hjic-1079	176	40	l-1)-times	l-1)-times	DET
hjic-1079	176	41	continuously	continuously	ADV
hjic-1079	176	42	differentiable	differentiable	ADJ
hjic-1079	176	43	functions	function	NOUN
hjic-1079	176	44	ip	ip	VERB
hjic-1079	176	45	1	1	NUM
hjic-1079	176	46	vector	vector	NOUN
hjic-1079	176	47	space	space	NOUN
hjic-1079	176	48	of	of	ADP
hjic-1079	176	49	polynomials	polynomial	NOUN
hjic-1079	176	50	of	of	ADP
hjic-1079	176	51	degree	degree	NOUN
hjic-1079	176	52	less	less	ADJ
hjic-1079	176	53	or	or	CCONJ
hjic-1079	176	54	equall	equall	NOUN
hjic-1079	176	55	s1(a	s1(a	ADP
hjic-1079	176	56	)	)	PUNCT
hjic-1079	176	57	q	q	NOUN
hjic-1079	176	58	"	"	PUNCT
hjic-1079	176	59	"	"	PUNCT
hjic-1079	176	60	b1(x	b1(x	NOUN
hjic-1079	176	61	)	)	PUNCT
hjic-1079	176	62	do	do	VERB
hjic-1079	176	63	,	,	PUNCT
hjic-1079	176	64	...	...	PUNCT
hjic-1079	176	65	,	,	PUNCT
hjic-1079	176	66	dn	dn	PROPN
hjic-1079	176	67	bt(x	bt(x	NUM
hjic-1079	176	68	)	)	PUNCT
hjic-1079	176	69	xn(x	xn(x	NUM
hjic-1079	176	70	)	)	PUNCT
hjic-1079	176	71	s(x	s(x	PROPN
hjic-1079	176	72	)	)	PUNCT
hjic-1079	176	73	a/	a/	PROPN
hjic-1079	176	74	po	po	PROPN
hjic-1079	176	75	,	,	PUNCT
hjic-1079	176	76	...	...	PUNCT
hjic-1079	176	77	,	,	PUNCT
hjic-1079	176	78	pq	pq	INTJ
hjic-1079	176	79	l(x	l(x	PROPN
hjic-1079	176	80	)	)	PUNCT
hjic-1079	176	81	vector	vector	NOUN
hjic-1079	176	82	space	space	NOUN
hjic-1079	176	83	of	of	ADP
hjic-1079	176	84	spline	spline	NOUN
hjic-1079	176	85	functions	function	NOUN
hjic-1079	176	86	infinite	infinite	ADJ
hjic-1079	176	87	knot	knot	NOUN
hjic-1079	176	88	sequence	sequence	NOUN
hjic-1079	176	89	b	b	NOUN
hjic-1079	176	90	-	-	PUNCT
hjic-1079	176	91	spline	spline	NOUN
hjic-1079	176	92	curve	curve	NOUN
hjic-1079	176	93	de	de	PROPN
hjic-1079	176	94	boor	boor	PROPN
hjic-1079	176	95	points	point	NOUN
hjic-1079	176	96	bernstein	bernstein	PROPN
hjic-1079	176	97	polynomials	polynomials	PROPN
hjic-1079	176	98	bezier	bezier	PROPN
hjic-1079	176	99	curve	curve	PROPN
hjic-1079	176	100	spline	spline	NOUN
hjic-1079	176	101	function	function	NOUN
hjic-1079	176	102	coefficients	coefficient	NOUN
hjic-1079	176	103	in	in	ADP
hjic-1079	176	104	the	the	DET
hjic-1079	176	105	de	de	X
hjic-1079	176	106	boor	boor	NOUN
hjic-1079	176	107	algorithm	algorithm	NOUN
hjic-1079	176	108	interpolation	interpolation	NOUN
hjic-1079	176	109	points	point	NOUN
hjic-1079	176	110	linear	linear	PROPN
hjic-1079	176	111	spline	spline	NOUN
hjic-1079	176	112	function	function	NOUN
hjic-1079	176	113	difference	difference	NOUN
hjic-1079	176	114	quotients	quotient	NOUN
hjic-1079	176	115	references	reference	NOUN
hjic-1079	176	116	1	1	NUM
hjic-1079	176	117	.	.	PUNCT
hjic-1079	176	118	costatini	costatini	PROPN
hjic-1079	176	119	,	,	PUNCT
hjic-1079	176	120	p.	p.	PROPN
hjic-1079	176	121	,	,	PUNCT
hjic-1079	176	122	morandi	morandi	PROPN
hjic-1079	176	123	,	,	PUNCT
hjic-1079	176	124	r.	r.	PROPN
hjic-1079	176	125	:	:	PUNCT
hjic-1079	176	126	monotone	monotone	ADJ
hjic-1079	176	127	and	and	CCONJ
hjic-1079	176	128	convex	convex	ADJ
hjic-1079	176	129	cubic	cubic	ADJ
hjic-1079	176	130	spline	spline	NOUN
hjic-1079	176	131	interpolation	interpolation	NOUN
hjic-1079	176	132	,	,	PUNCT
hjic-1079	176	133	calcolo	calcolo	PROPN
hjic-1079	176	134	,	,	PUNCT
hjic-1079	176	135	1984	1984	NUM
hjic-1079	176	136	,	,	PUNCT
hjic-1079	176	137	21,281	21,281	NUM
hjic-1079	176	138	-	-	SYM
hjic-1079	176	139	294	294	NUM
hjic-1079	176	140	111	111	NUM
hjic-1079	176	141	2	2	NUM
hjic-1079	176	142	.	.	PUNCT
hjic-1079	176	143	costatini	costatini	PROPN
hjic-1079	176	144	,	,	PUNCT
hjic-1079	176	145	p.	p.	NOUN
hjic-1079	176	146	,	,	PUNCT
hjic-1079	176	147	morat	morat	PROPN
hjic-1079	176	148	~	~	SYM
hjic-1079	176	149	di	di	PROPN
hjic-1079	176	150	,	,	PUNCT
hjic-1079	176	151	r.	r.	PROPN
hjic-1079	176	152	:	:	PUNCT
hjic-1079	176	153	an	an	DET
hjic-1079	176	154	algrithm	algrithm	NOUN
hjic-1079	176	155	for	for	ADP
hjic-1079	176	156	computing	compute	VERB
hjic-1079	176	157	shape	shape	NOUN
hjic-1079	176	158	-	-	PUNCT
hjic-1079	176	159	preserving	preserve	VERB
hjic-1079	176	160	cubic	cubic	ADJ
hjic-1079	176	161	spline	spline	NOUN
hjic-1079	176	162	interpolation	interpolation	NOUN
hjic-1079	176	163	to	to	ADP
hjic-1079	176	164	data	data	PROPN
hjic-1079	176	165	,	,	PUNCT
hjic-1079	176	166	calcolo	calcolo	PROPN
hjic-1079	176	167	,	,	PUNCT
hjic-1079	176	168	1984,21	1984,21	NUM
hjic-1079	176	169	,	,	PUNCT
hjic-1079	176	170	295	295	NUM
hjic-1079	176	171	-	-	SYM
hjic-1079	176	172	305	305	NUM
hjic-1079	176	173	3	3	NUM
hjic-1079	176	174	.	.	PUNCT
hjic-1079	177	1	deppe	deppe	NOUN
hjic-1079	177	2	,	,	PUNCT
hjic-1079	177	3	u.	u.	PROPN
hjic-1079	177	4	:	:	PUNCT
hjic-1079	177	5	anwendung	anwendung	PROPN
hjic-1079	177	6	der	der	PROPN
hjic-1079	177	7	bem	bem	PROPN
hjic-1079	177	8	auf	auf	PROPN
hjic-1079	177	9	eine	eine	PROPN
hjic-1079	177	10	integralgleichung	integralgleichung	PROPN
hjic-1079	177	11	1	1	NUM
hjic-1079	177	12	.	.	PUNCT
hjic-1079	178	1	art	art	NOUN
hjic-1079	178	2	zur	zur	PROPN
hjic-1079	178	3	bestimmung	bestimmung	PROPN
hjic-1079	178	4	der	der	PROPN
hjic-1079	178	5	porenradienverteilung	porenradienverteilung	PROPN
hjic-1079	178	6	eines	eine	VERB
hjic-1079	178	7	slp	slp	PROPN
hjic-1079	178	8	-	-	PUNCT
hjic-1079	178	9	katalysator­	katalysator­	NOUN
hjic-1079	178	10	pellets	pellet	NOUN
hjic-1079	178	11	diploma	diploma	NOUN
hjic-1079	178	12	thesis	thesis	NOUN
hjic-1079	178	13	,	,	PUNCT
hjic-1079	178	14	universitat	universitat	PROPN
hjic-1079	178	15	hannover	hannover	PROPN
hjic-1079	178	16	,	,	PUNCT
hjic-1079	178	17	1994	1994	NUM
hjic-1079	178	18	4	4	NUM
hjic-1079	178	19	.	.	PUNCT
hjic-1079	179	1	farin	farin	PROPN
hjic-1079	179	2	,	,	PUNCT
hjic-1079	179	3	g.	g.	NOUN
hjic-1079	179	4	:	:	PUNCT
hjic-1079	179	5	curves	curve	NOUN
hjic-1079	179	6	and	and	CCONJ
hjic-1079	179	7	surfaces	surface	NOUN
hjic-1079	179	8	for	for	ADP
hjic-1079	179	9	computer	computer	NOUN
hjic-1079	179	10	aided	aid	VERB
hjic-1079	179	11	geometric	geometric	ADJ
hjic-1079	179	12	design	design	NOUN
hjic-1079	179	13	,	,	PUNCT
hjic-1079	179	14	academic	academic	ADJ
hjic-1079	179	15	press	press	NOUN
hjic-1079	179	16	,	,	PUNCT
hjic-1079	179	17	boston	boston	PROPN
hjic-1079	179	18	et	et	PROPN
hjic-1079	179	19	al	al	PROPN
hjic-1079	179	20	.	.	PROPN
hjic-1079	179	21	,	,	PUNCT
hjic-1079	179	22	1990	1990	NUM
hjic-1079	179	23	5	5	NUM
hjic-1079	179	24	.	.	PUNCT
hjic-1079	180	1	gronewold	gronewold	NOUN
hjic-1079	180	2	,	,	PUNCT
hjic-1079	180	3	g.	g.	PROPN
hjic-1079	180	4	:	:	PUNCT
hjic-1079	180	5	co	co	ADJ
hjic-1079	180	6	-	-	ADJ
hjic-1079	180	7	monotone	monotone	ADJ
hjic-1079	180	8	splineinterpolation	splineinterpolation	NOUN
hjic-1079	180	9	in	in	ADP
hjic-1079	180	10	chemical	chemical	ADJ
hjic-1079	180	11	engineering	engineering	NOUN
hjic-1079	180	12	,	,	PUNCT
hjic-1079	180	13	hung	hung	PROPN
hjic-1079	180	14	.	.	PUNCT
hjic-1079	181	1	j.	j.	PROPN
hjic-1079	181	2	ind	ind	PROPN
hjic-1079	181	3	.	.	PUNCT
hjic-1079	182	1	chern	chern	PROPN
hjic-1079	182	2	.	.	PROPN
hjic-1079	182	3	,	,	PUNCT
hjic-1079	182	4	1997,25,59	1997,25,59	NUM
hjic-1079	182	5	-	-	SYM
hjic-1079	182	6	62	62	NUM
hjic-1079	182	7	6	6	NUM
hjic-1079	182	8	.	.	PUNCT
hjic-1079	183	1	herrmann	herrmann	PROPN
hjic-1079	183	2	,	,	PUNCT
hjic-1079	183	3	n.	n.	PROPN
hjic-1079	183	4	:	:	PUNCT
hjic-1079	183	5	hohere	hohere	PROPN
hjic-1079	183	6	mathematik	mathematik	PROPN
hjic-1079	183	7	fur	fur	NOUN
hjic-1079	183	8	ingenieure	ingenieure	NOUN
hjic-1079	183	9	i	i	PROPN
hjic-1079	183	10	,	,	PUNCT
hjic-1079	183	11	ii	ii	PROPN
hjic-1079	183	12	,	,	PUNCT
hjic-1079	183	13	oldenbourg	oldenbourg	PROPN
hjic-1079	183	14	verlag	verlag	PROPN
hjic-1079	183	15	,	,	PUNCT
hjic-1079	183	16	mtinchen	mtinchen	ADJ
hjic-1079	183	17	,	,	PUNCT
hjic-1079	183	18	1995	1995	NUM
hjic-1079	183	19	7	7	NUM
hjic-1079	183	20	.	.	PUNCT
hjic-1079	183	21	herrmann	herrmann	PROPN
hjic-1079	183	22	,	,	PUNCT
hjic-1079	183	23	n.	n.	NOUN
hjic-1079	183	24	:	:	PUNCT
hjic-1079	183	25	spline	spline	ADJ
hjic-1079	183	26	-	-	PUNCT
hjic-1079	183	27	funktionen	funktionen	NOUN
hjic-1079	183	28	und	und	ADJ
hjic-1079	183	29	ihre	ihre	NOUN
hjic-1079	183	30	anwendung	anwendung	NOUN
hjic-1079	183	31	,	,	PUNCT
hjic-1079	183	32	preprint	preprint	NOUN
hjic-1079	183	33	institut	institut	PROPN
hjic-1079	183	34	fiir	fiir	PROPN
hjic-1079	183	35	angewandte	angewandte	PROPN
hjic-1079	183	36	mathematik	mathematik	PROPN
hjic-1079	183	37	,	,	PUNCT
hjic-1079	183	38	uni	uni	PROPN
hjic-1079	183	39	.	.	PROPN
hjic-1079	183	40	hannover	hannover	PROPN
hjic-1079	183	41	,	,	PUNCT
hjic-1079	183	42	1996	1996	NUM
hjic-1079	183	43	8	8	NUM
hjic-1079	183	44	.	.	PUNCT
hjic-1079	184	1	herrmann	herrmann	PROPN
hjic-1079	184	2	,	,	PUNCT
hjic-1079	184	3	n.	n.	NOUN
hjic-1079	184	4	:	:	PUNCT
hjic-1079	184	5	surface	surface	NOUN
hjic-1079	184	6	fitting	fitting	ADJ
hjic-1079	184	7	in	in	ADP
hjic-1079	184	8	cagd	cagd	NOUN
hjic-1079	184	9	via	via	ADP
hjic-1079	184	10	finite	finite	ADJ
hjic-1079	184	11	elements	element	NOUN
hjic-1079	184	12	,	,	PUNCT
hjic-1079	184	13	hung	hung	PROPN
hjic-1079	184	14	.	.	PUNCT
hjic-1079	185	1	j.	j.	PROPN
hjic-1079	185	2	ind	ind	PROPN
hjic-1079	185	3	.	.	PUNCT
hjic-1079	186	1	chern	chern	PROPN
hjic-1079	186	2	.	.	PROPN
hjic-1079	186	3	,	,	PUNCT
hjic-1079	186	4	1997,25,63	1997,25,63	NUM
hjic-1079	186	5	-	-	SYM
hjic-1079	186	6	69	69	NUM
hjic-1079	186	7	9	9	NUM
hjic-1079	186	8	.	.	PUNCT
hjic-1079	187	1	i!oschek	i!oschek	PROPN
hjic-1079	187	2	,	,	PUNCT
hjic-1079	187	3	1	1	NUM
hjic-1079	187	4	.	.	NUM
hjic-1079	187	5	,	,	PUNCT
hjic-1079	187	6	lasser	lasser	PROPN
hjic-1079	187	7	,	,	PUNCT
hjic-1079	187	8	d.	d.	PROPN
hjic-1079	187	9	:	:	PUNCT
hjic-1079	187	10	grundlagen	grundlagen	PROPN
hjic-1079	187	11	der	der	PROPN
hjic-1079	187	12	geometrischen	geometrischen	PROPN
hjic-1079	187	13	datenverarbeitung	datenverarbeitung	PROPN
hjic-1079	187	14	,	,	PUNCT
hjic-1079	187	15	b.	b.	PROPN
hjic-1079	187	16	g.	g.	PROPN
hjic-1079	187	17	teubner	teubner	PROPN
hjic-1079	187	18	,	,	PUNCT
hjic-1079	187	19	stuttgart	stuttgart	PROPN
hjic-1079	187	20	,	,	PUNCT
hjic-1079	187	21	2	2	NUM
hjic-1079	187	22	.	.	PUNCT
hjic-1079	188	1	ed	ed	NOUN
hjic-1079	188	2	.	.	PROPN
hjic-1079	188	3	1992	1992	NUM
hjic-1079	188	4	page	page	NOUN
hjic-1079	188	5	109	109	NUM
hjic-1079	188	6	page	page	NOUN
hjic-1079	188	7	110	110	NUM
hjic-1079	188	8	page	page	NOUN
hjic-1079	188	9	111	111	NUM
hjic-1079	188	10	page	page	NOUN
hjic-1079	188	11	112	112	NUM
hjic-1079	188	12	page	page	NOUN
hjic-1079	188	13	113	113	NUM
hjic-1079	188	14	page	page	NOUN
hjic-1079	188	15	114	114	NUM
hjic-1079	188	16	page	page	NOUN
hjic-1079	188	17	115	115	NUM