id	sid	tid	token	lemma	pos
ap-4038	1	1	acta	acta	PROPN
ap-4038	1	2	polytechnica	polytechnica	PROPN
ap-4038	1	3	doi:10.14311	doi:10.14311	PROPN
ap-4038	1	4	/	/	SYM
ap-4038	1	5	ap.2017.57.0105	ap.2017.57.0105	PROPN
ap-4038	1	6	acta	acta	PROPN
ap-4038	1	7	polytechnica	polytechnica	PROPN
ap-4038	1	8	57(2):105–115	57(2):105–115	PROPN
ap-4038	1	9	,	,	PUNCT
ap-4038	1	10	2017	2017	NUM
ap-4038	1	11	©	©	PROPN
ap-4038	1	12	czech	czech	PROPN
ap-4038	1	13	technical	technical	PROPN
ap-4038	1	14	university	university	PROPN
ap-4038	1	15	in	in	ADP
ap-4038	1	16	prague	prague	PROPN
ap-4038	1	17	,	,	PUNCT
ap-4038	1	18	2017	2017	NUM
ap-4038	1	19	available	available	ADJ
ap-4038	1	20	online	online	ADV
ap-4038	1	21	at	at	ADP
ap-4038	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4038	1	23	implementation	implementation	NOUN
ap-4038	1	24	of	of	ADP
ap-4038	1	25	a	a	DET
ap-4038	1	26	3d	3d	NUM
ap-4038	1	27	vof	vof	NOUN
ap-4038	1	28	tracking	track	VERB
ap-4038	1	29	algorithm	algorithm	NOUN
ap-4038	1	30	based	base	VERB
ap-4038	1	31	on	on	ADP
ap-4038	1	32	binary	binary	ADJ
ap-4038	1	33	space	space	NOUN
ap-4038	1	34	-	-	PUNCT
ap-4038	1	35	partitioning	partition	VERB
ap-4038	1	36	filip	filip	NOUN
ap-4038	1	37	kolařík∗	kolařík∗	PROPN
ap-4038	1	38	,	,	PUNCT
ap-4038	1	39	bořek	bořek	PROPN
ap-4038	1	40	patzák	patzák	VERB
ap-4038	1	41	ctu	ctu	NOUN
ap-4038	1	42	in	in	ADP
ap-4038	1	43	prague	prague	PROPN
ap-4038	1	44	,	,	PUNCT
ap-4038	1	45	faculty	faculty	NOUN
ap-4038	1	46	of	of	ADP
ap-4038	1	47	civil	civil	ADJ
ap-4038	1	48	engineering	engineering	NOUN
ap-4038	1	49	,	,	PUNCT
ap-4038	1	50	department	department	NOUN
ap-4038	1	51	of	of	ADP
ap-4038	1	52	mechanics	mechanic	NOUN
ap-4038	1	53	,	,	PUNCT
ap-4038	1	54	thákurova	thákurova	X
ap-4038	1	55	7	7	NUM
ap-4038	1	56	,	,	PUNCT
ap-4038	1	57	166	166	NUM
ap-4038	1	58	29	29	NUM
ap-4038	1	59	praha	praha	NOUN
ap-4038	1	60	6	6	NUM
ap-4038	1	61	;	;	PUNCT
ap-4038	1	62	czech	czech	PROPN
ap-4038	1	63	republic	republic	NOUN
ap-4038	1	64	∗	∗	NOUN
ap-4038	1	65	corresponding	correspond	VERB
ap-4038	1	66	author	author	NOUN
ap-4038	1	67	:	:	PUNCT
ap-4038	1	68	filip.kolarik@fsv.cvut.cz	filip.kolarik@fsv.cvut.cz	NUM
ap-4038	1	69	abstract	abstract	NOUN
ap-4038	1	70	.	.	PUNCT
ap-4038	2	1	the	the	DET
ap-4038	2	2	paper	paper	NOUN
ap-4038	2	3	focuses	focus	VERB
ap-4038	2	4	on	on	ADP
ap-4038	2	5	modeling	model	VERB
ap-4038	2	6	free	free	ADJ
ap-4038	2	7	surface	surface	NOUN
ap-4038	2	8	flow	flow	NOUN
ap-4038	2	9	.	.	PUNCT
ap-4038	3	1	the	the	DET
ap-4038	3	2	interface	interface	NOUN
ap-4038	3	3	is	be	AUX
ap-4038	3	4	modeled	model	VERB
ap-4038	3	5	using	use	VERB
ap-4038	3	6	the	the	DET
ap-4038	3	7	volume	volume	NOUN
ap-4038	3	8	-	-	PUNCT
ap-4038	3	9	of	of	ADP
ap-4038	3	10	-	-	PUNCT
ap-4038	3	11	fluid	fluid	NOUN
ap-4038	3	12	method	method	NOUN
ap-4038	3	13	,	,	PUNCT
ap-4038	3	14	where	where	SCONJ
ap-4038	3	15	the	the	DET
ap-4038	3	16	advection	advection	NOUN
ap-4038	3	17	of	of	ADP
ap-4038	3	18	volume	volume	NOUN
ap-4038	3	19	fractions	fraction	NOUN
ap-4038	3	20	is	be	AUX
ap-4038	3	21	treated	treat	VERB
ap-4038	3	22	by	by	ADP
ap-4038	3	23	a	a	DET
ap-4038	3	24	purely	purely	ADV
ap-4038	3	25	geometrical	geometrical	ADJ
ap-4038	3	26	method	method	NOUN
ap-4038	3	27	.	.	PUNCT
ap-4038	4	1	the	the	DET
ap-4038	4	2	novelty	novelty	NOUN
ap-4038	4	3	of	of	ADP
ap-4038	4	4	the	the	DET
ap-4038	4	5	work	work	NOUN
ap-4038	4	6	lies	lie	VERB
ap-4038	4	7	in	in	ADP
ap-4038	4	8	the	the	DET
ap-4038	4	9	way	way	NOUN
ap-4038	4	10	that	that	PRON
ap-4038	4	11	it	it	PRON
ap-4038	4	12	incorporates	incorporate	VERB
ap-4038	4	13	binary	binary	ADJ
ap-4038	4	14	space	space	NOUN
ap-4038	4	15	-	-	PUNCT
ap-4038	4	16	partitioning	partition	VERB
ap-4038	4	17	trees	tree	NOUN
ap-4038	4	18	for	for	ADP
ap-4038	4	19	computing	compute	VERB
ap-4038	4	20	the	the	DET
ap-4038	4	21	intersections	intersection	NOUN
ap-4038	4	22	of	of	ADP
ap-4038	4	23	polyhedra	polyhedra	PROPN
ap-4038	4	24	.	.	PUNCT
ap-4038	5	1	volume	volume	NOUN
ap-4038	5	2	-	-	PUNCT
ap-4038	5	3	conserving	conserve	VERB
ap-4038	5	4	properties	property	NOUN
ap-4038	5	5	and	and	CCONJ
ap-4038	5	6	shape	shape	NOUN
ap-4038	5	7	-	-	PUNCT
ap-4038	5	8	preserving	preserve	VERB
ap-4038	5	9	properties	property	NOUN
ap-4038	5	10	are	be	AUX
ap-4038	5	11	presented	present	VERB
ap-4038	5	12	on	on	ADP
ap-4038	5	13	two	two	NUM
ap-4038	5	14	benchmarks	benchmark	NOUN
ap-4038	5	15	and	and	CCONJ
ap-4038	5	16	on	on	ADP
ap-4038	5	17	a	a	DET
ap-4038	5	18	simulation	simulation	NOUN
ap-4038	5	19	of	of	ADP
ap-4038	5	20	the	the	DET
ap-4038	5	21	famous	famous	ADJ
ap-4038	5	22	broken	broken	ADJ
ap-4038	5	23	dam	dam	NOUN
ap-4038	5	24	problem	problem	NOUN
ap-4038	5	25	.	.	PUNCT
ap-4038	6	1	keywords	keyword	NOUN
ap-4038	6	2	:	:	PUNCT
ap-4038	6	3	free	free	ADJ
ap-4038	6	4	surface	surface	NOUN
ap-4038	6	5	;	;	PUNCT
ap-4038	6	6	two	two	NUM
ap-4038	6	7	-	-	PUNCT
ap-4038	6	8	fluid	fluid	NOUN
ap-4038	6	9	flow	flow	NOUN
ap-4038	6	10	;	;	PUNCT
ap-4038	6	11	vof	vof	NOUN
ap-4038	6	12	;	;	PUNCT
ap-4038	6	13	binary	binary	ADJ
ap-4038	6	14	space	space	NOUN
ap-4038	6	15	-	-	PUNCT
ap-4038	6	16	partitioning	partitioning	NOUN
ap-4038	6	17	.	.	PUNCT
ap-4038	7	1	1	1	X
ap-4038	7	2	.	.	X
ap-4038	7	3	introduction	introduction	NOUN
ap-4038	7	4	free	free	PROPN
ap-4038	7	5	surface	surface	PROPN
ap-4038	7	6	flows	flow	NOUN
ap-4038	7	7	appear	appear	VERB
ap-4038	7	8	in	in	ADP
ap-4038	7	9	a	a	DET
ap-4038	7	10	wide	wide	ADJ
ap-4038	7	11	range	range	NOUN
ap-4038	7	12	of	of	ADP
ap-4038	7	13	industrial	industrial	ADJ
ap-4038	7	14	applications	application	NOUN
ap-4038	7	15	including	include	VERB
ap-4038	7	16	molten	molten	ADJ
ap-4038	7	17	metal	metal	NOUN
ap-4038	7	18	production	production	NOUN
ap-4038	7	19	in	in	ADP
ap-4038	7	20	steel	steel	NOUN
ap-4038	7	21	processing	processing	NOUN
ap-4038	7	22	[	[	X
ap-4038	7	23	1	1	NUM
ap-4038	7	24	]	]	PUNCT
ap-4038	7	25	,	,	PUNCT
ap-4038	7	26	resin	resin	NOUN
ap-4038	7	27	-	-	PUNCT
ap-4038	7	28	infusion	infusion	NOUN
ap-4038	7	29	processes	process	NOUN
ap-4038	7	30	in	in	ADP
ap-4038	7	31	structural	structural	ADJ
ap-4038	7	32	manufacturing	manufacturing	NOUN
ap-4038	7	33	[	[	X
ap-4038	7	34	2	2	NUM
ap-4038	7	35	]	]	PUNCT
ap-4038	7	36	,	,	PUNCT
ap-4038	7	37	water	water	NOUN
ap-4038	7	38	waves	wave	NOUN
ap-4038	7	39	in	in	ADP
ap-4038	7	40	ship	ship	NOUN
ap-4038	7	41	hydrodynamics	hydrodynamic	NOUN
ap-4038	7	42	[	[	X
ap-4038	7	43	3	3	NUM
ap-4038	7	44	]	]	PUNCT
ap-4038	7	45	,	,	PUNCT
ap-4038	7	46	and	and	CCONJ
ap-4038	7	47	fresh	fresh	ADJ
ap-4038	7	48	concrete	concrete	ADJ
ap-4038	7	49	casting	casting	NOUN
ap-4038	7	50	in	in	ADP
ap-4038	7	51	civil	civil	ADJ
ap-4038	7	52	engineering	engineering	NOUN
ap-4038	7	53	[	[	X
ap-4038	7	54	4	4	NUM
ap-4038	7	55	]	]	PUNCT
ap-4038	7	56	.	.	PUNCT
ap-4038	8	1	the	the	DET
ap-4038	8	2	development	development	NOUN
ap-4038	8	3	of	of	ADP
ap-4038	8	4	numerical	numerical	ADJ
ap-4038	8	5	techniques	technique	NOUN
ap-4038	8	6	for	for	ADP
ap-4038	8	7	describing	describe	VERB
ap-4038	8	8	the	the	DET
ap-4038	8	9	evolution	evolution	NOUN
ap-4038	8	10	of	of	ADP
ap-4038	8	11	a	a	DET
ap-4038	8	12	free	free	ADJ
ap-4038	8	13	surface	surface	NOUN
ap-4038	8	14	can	can	AUX
ap-4038	8	15	be	be	AUX
ap-4038	8	16	tracked	track	VERB
ap-4038	8	17	back	back	ADV
ap-4038	8	18	to	to	ADP
ap-4038	8	19	the	the	DET
ap-4038	8	20	early	early	ADJ
ap-4038	8	21	1980s	1980s	NUM
ap-4038	8	22	.	.	PUNCT
ap-4038	9	1	a	a	DET
ap-4038	9	2	good	good	ADJ
ap-4038	9	3	review	review	NOUN
ap-4038	9	4	of	of	ADP
ap-4038	9	5	the	the	DET
ap-4038	9	6	early	early	ADJ
ap-4038	9	7	development	development	NOUN
ap-4038	9	8	of	of	ADP
ap-4038	9	9	this	this	DET
ap-4038	9	10	field	field	NOUN
ap-4038	9	11	can	can	AUX
ap-4038	9	12	be	be	AUX
ap-4038	9	13	found	find	VERB
ap-4038	9	14	in	in	ADP
ap-4038	9	15	[	[	X
ap-4038	9	16	5	5	NUM
ap-4038	9	17	]	]	PUNCT
ap-4038	9	18	.	.	PUNCT
ap-4038	10	1	since	since	SCONJ
ap-4038	10	2	that	that	DET
ap-4038	10	3	time	time	NOUN
ap-4038	10	4	,	,	PUNCT
ap-4038	10	5	a	a	DET
ap-4038	10	6	number	number	NOUN
ap-4038	10	7	of	of	ADP
ap-4038	10	8	different	different	ADJ
ap-4038	10	9	approaches	approach	NOUN
ap-4038	10	10	and	and	CCONJ
ap-4038	10	11	methods	method	NOUN
ap-4038	10	12	have	have	AUX
ap-4038	10	13	been	be	AUX
ap-4038	10	14	proposed	propose	VERB
ap-4038	10	15	.	.	PUNCT
ap-4038	11	1	the	the	DET
ap-4038	11	2	existing	exist	VERB
ap-4038	11	3	methods	method	NOUN
ap-4038	11	4	can	can	AUX
ap-4038	11	5	be	be	AUX
ap-4038	11	6	divided	divide	VERB
ap-4038	11	7	into	into	ADP
ap-4038	11	8	so	so	ADV
ap-4038	11	9	-	-	PUNCT
ap-4038	11	10	called	call	VERB
ap-4038	11	11	interface	interface	NOUN
ap-4038	11	12	-	-	PUNCT
ap-4038	11	13	tracking	tracking	NOUN
ap-4038	11	14	and	and	CCONJ
ap-4038	11	15	interface	interface	NOUN
ap-4038	11	16	-	-	PUNCT
ap-4038	11	17	capturing	capture	VERB
ap-4038	11	18	methods	method	NOUN
ap-4038	11	19	[	[	X
ap-4038	11	20	6	6	NUM
ap-4038	11	21	]	]	PUNCT
ap-4038	11	22	.	.	PUNCT
ap-4038	12	1	in	in	ADP
ap-4038	12	2	the	the	DET
ap-4038	12	3	interface	interface	NOUN
ap-4038	12	4	tracking	tracking	NOUN
ap-4038	12	5	techniques	technique	NOUN
ap-4038	12	6	,	,	PUNCT
ap-4038	12	7	the	the	DET
ap-4038	12	8	underlying	underlying	ADJ
ap-4038	12	9	discretization	discretization	NOUN
ap-4038	12	10	follows	follow	VERB
ap-4038	12	11	the	the	DET
ap-4038	12	12	interface	interface	NOUN
ap-4038	12	13	in	in	ADP
ap-4038	12	14	a	a	DET
ap-4038	12	15	lagrangian	lagrangian	ADJ
ap-4038	12	16	manner	manner	NOUN
ap-4038	12	17	(	(	PUNCT
ap-4038	12	18	lagrangian	lagrangian	ADJ
ap-4038	12	19	formulation	formulation	NOUN
ap-4038	12	20	is	be	AUX
ap-4038	12	21	typically	typically	ADV
ap-4038	12	22	employed	employ	VERB
ap-4038	12	23	)	)	PUNCT
ap-4038	12	24	.	.	PUNCT
ap-4038	13	1	because	because	SCONJ
ap-4038	13	2	of	of	ADP
ap-4038	13	3	the	the	DET
ap-4038	13	4	large	large	ADJ
ap-4038	13	5	mesh	mesh	NOUN
ap-4038	13	6	distortions	distortion	NOUN
ap-4038	13	7	during	during	ADP
ap-4038	13	8	the	the	DET
ap-4038	13	9	flow	flow	NOUN
ap-4038	13	10	,	,	PUNCT
ap-4038	13	11	the	the	DET
ap-4038	13	12	mesh	mesh	NOUN
ap-4038	13	13	needs	need	VERB
ap-4038	13	14	to	to	PART
ap-4038	13	15	be	be	AUX
ap-4038	13	16	updated	update	VERB
ap-4038	13	17	as	as	SCONJ
ap-4038	13	18	the	the	DET
ap-4038	13	19	interface	interface	NOUN
ap-4038	13	20	evolves	evolve	VERB
ap-4038	13	21	.	.	PUNCT
ap-4038	14	1	the	the	DET
ap-4038	14	2	need	need	NOUN
ap-4038	14	3	for	for	ADP
ap-4038	14	4	frequent	frequent	ADJ
ap-4038	14	5	re	re	NOUN
ap-4038	14	6	-	-	NOUN
ap-4038	14	7	meshing	meshing	NOUN
ap-4038	14	8	can	can	AUX
ap-4038	14	9	sometimes	sometimes	ADV
ap-4038	14	10	involve	involve	VERB
ap-4038	14	11	an	an	DET
ap-4038	14	12	excessive	excessive	ADJ
ap-4038	14	13	expense	expense	NOUN
ap-4038	14	14	,	,	PUNCT
ap-4038	14	15	especially	especially	ADV
ap-4038	14	16	in	in	ADP
ap-4038	14	17	the	the	DET
ap-4038	14	18	case	case	NOUN
ap-4038	14	19	of	of	ADP
ap-4038	14	20	complex	complex	ADJ
ap-4038	14	21	3d	3d	NUM
ap-4038	14	22	flows	flow	NOUN
ap-4038	14	23	.	.	PUNCT
ap-4038	15	1	this	this	DET
ap-4038	15	2	disadvantage	disadvantage	NOUN
ap-4038	15	3	is	be	AUX
ap-4038	15	4	balanced	balance	VERB
ap-4038	15	5	by	by	ADP
ap-4038	15	6	the	the	DET
ap-4038	15	7	natural	natural	ADJ
ap-4038	15	8	representation	representation	NOUN
ap-4038	15	9	of	of	ADP
ap-4038	15	10	the	the	DET
ap-4038	15	11	interface	interface	NOUN
ap-4038	15	12	.	.	PUNCT
ap-4038	16	1	interface	interface	NOUN
ap-4038	16	2	-	-	PUNCT
ap-4038	16	3	capturing	capture	VERB
ap-4038	16	4	methods	method	NOUN
ap-4038	16	5	are	be	AUX
ap-4038	16	6	usually	usually	ADV
ap-4038	16	7	formulated	formulate	VERB
ap-4038	16	8	in	in	ADP
ap-4038	16	9	an	an	DET
ap-4038	16	10	eulerian	eulerian	ADJ
ap-4038	16	11	context	context	NOUN
ap-4038	16	12	,	,	PUNCT
ap-4038	16	13	where	where	SCONJ
ap-4038	16	14	the	the	DET
ap-4038	16	15	computations	computation	NOUN
ap-4038	16	16	are	be	AUX
ap-4038	16	17	performed	perform	VERB
ap-4038	16	18	on	on	ADP
ap-4038	16	19	a	a	DET
ap-4038	16	20	fixed	fix	VERB
ap-4038	16	21	mesh	mesh	NOUN
ap-4038	16	22	.	.	PUNCT
ap-4038	17	1	the	the	DET
ap-4038	17	2	free	free	ADJ
ap-4038	17	3	surface	surface	NOUN
ap-4038	17	4	flow	flow	NOUN
ap-4038	17	5	is	be	AUX
ap-4038	17	6	then	then	ADV
ap-4038	17	7	realized	realize	VERB
ap-4038	17	8	as	as	ADP
ap-4038	17	9	the	the	DET
ap-4038	17	10	flow	flow	NOUN
ap-4038	17	11	of	of	ADP
ap-4038	17	12	two	two	NUM
ap-4038	17	13	immiscible	immiscible	ADJ
ap-4038	17	14	fluids	fluid	NOUN
ap-4038	17	15	,	,	PUNCT
ap-4038	17	16	where	where	SCONJ
ap-4038	17	17	one	one	PRON
ap-4038	17	18	is	be	AUX
ap-4038	17	19	the	the	DET
ap-4038	17	20	fluid	fluid	NOUN
ap-4038	17	21	of	of	ADP
ap-4038	17	22	interest	interest	NOUN
ap-4038	17	23	(	(	PUNCT
ap-4038	17	24	the	the	DET
ap-4038	17	25	reference	reference	NOUN
ap-4038	17	26	fluid	fluid	NOUN
ap-4038	17	27	)	)	PUNCT
ap-4038	17	28	and	and	CCONJ
ap-4038	17	29	the	the	DET
ap-4038	17	30	other	other	ADJ
ap-4038	17	31	represents	represent	VERB
ap-4038	17	32	the	the	DET
ap-4038	17	33	ambient	ambient	ADJ
ap-4038	17	34	air	air	NOUN
ap-4038	17	35	.	.	PUNCT
ap-4038	18	1	the	the	DET
ap-4038	18	2	interface	interface	NOUN
ap-4038	18	3	between	between	ADP
ap-4038	18	4	the	the	DET
ap-4038	18	5	fluids	fluid	NOUN
ap-4038	18	6	is	be	AUX
ap-4038	18	7	determined	determine	VERB
ap-4038	18	8	with	with	ADP
ap-4038	18	9	the	the	DET
ap-4038	18	10	help	help	NOUN
ap-4038	18	11	of	of	ADP
ap-4038	18	12	a	a	DET
ap-4038	18	13	suitably	suitably	ADV
ap-4038	18	14	chosen	choose	VERB
ap-4038	18	15	(	(	PUNCT
ap-4038	18	16	scalar	scalar	ADJ
ap-4038	18	17	)	)	PUNCT
ap-4038	18	18	interface	interface	NOUN
ap-4038	18	19	function	function	NOUN
ap-4038	18	20	,	,	PUNCT
ap-4038	18	21	defined	define	VERB
ap-4038	18	22	on	on	ADP
ap-4038	18	23	the	the	DET
ap-4038	18	24	underlying	underlying	ADJ
ap-4038	18	25	mesh	mesh	NOUN
ap-4038	18	26	.	.	PUNCT
ap-4038	19	1	a	a	DET
ap-4038	19	2	direct	direct	ADJ
ap-4038	19	3	consequence	consequence	NOUN
ap-4038	19	4	of	of	ADP
ap-4038	19	5	this	this	DET
ap-4038	19	6	assumption	assumption	NOUN
ap-4038	19	7	is	be	AUX
ap-4038	19	8	that	that	SCONJ
ap-4038	19	9	the	the	DET
ap-4038	19	10	interface	interface	NOUN
ap-4038	19	11	is	be	AUX
ap-4038	19	12	captured	capture	VERB
ap-4038	19	13	within	within	ADP
ap-4038	19	14	the	the	DET
ap-4038	19	15	resolution	resolution	NOUN
ap-4038	19	16	of	of	ADP
ap-4038	19	17	the	the	DET
ap-4038	19	18	underlying	underlying	ADJ
ap-4038	19	19	mesh	mesh	NOUN
ap-4038	19	20	.	.	PUNCT
ap-4038	20	1	fundamental	fundamental	ADJ
ap-4038	20	2	examples	example	NOUN
ap-4038	20	3	of	of	ADP
ap-4038	20	4	interface	interface	NOUN
ap-4038	20	5	-	-	PUNCT
ap-4038	20	6	capturing	capture	VERB
ap-4038	20	7	methods	method	NOUN
ap-4038	20	8	are	be	AUX
ap-4038	20	9	the	the	DET
ap-4038	20	10	level	level	NOUN
ap-4038	20	11	set	set	NOUN
ap-4038	20	12	method	method	NOUN
ap-4038	20	13	[	[	X
ap-4038	20	14	7–9	7–9	NOUN
ap-4038	20	15	]	]	X
ap-4038	20	16	,	,	PUNCT
ap-4038	20	17	the	the	DET
ap-4038	20	18	volume	volume	NOUN
ap-4038	20	19	-	-	PUNCT
ap-4038	20	20	of	of	ADP
ap-4038	20	21	-	-	PUNCT
ap-4038	20	22	fluid	fluid	NOUN
ap-4038	20	23	(	(	PUNCT
ap-4038	20	24	vof	vof	NOUN
ap-4038	20	25	)	)	PUNCT
ap-4038	20	26	method	method	NOUN
ap-4038	20	27	[	[	X
ap-4038	20	28	5	5	NUM
ap-4038	20	29	,	,	PUNCT
ap-4038	20	30	10	10	NUM
ap-4038	20	31	]	]	PUNCT
ap-4038	20	32	,	,	PUNCT
ap-4038	20	33	and	and	CCONJ
ap-4038	20	34	a	a	DET
ap-4038	20	35	combination	combination	NOUN
ap-4038	20	36	of	of	ADP
ap-4038	20	37	these	these	DET
ap-4038	20	38	methods	method	NOUN
ap-4038	20	39	clsvof	clsvof	VERB
ap-4038	20	40	[	[	X
ap-4038	20	41	11	11	NUM
ap-4038	20	42	]	]	PUNCT
ap-4038	20	43	.	.	PUNCT
ap-4038	21	1	in	in	ADP
ap-4038	21	2	level	level	NOUN
ap-4038	21	3	set	set	VERB
ap-4038	21	4	methods	method	NOUN
ap-4038	21	5	,	,	PUNCT
ap-4038	21	6	the	the	DET
ap-4038	21	7	interface	interface	NOUN
ap-4038	21	8	is	be	AUX
ap-4038	21	9	typically	typically	ADV
ap-4038	21	10	represented	represent	VERB
ap-4038	21	11	as	as	ADP
ap-4038	21	12	a	a	DET
ap-4038	21	13	zero	zero	NUM
ap-4038	21	14	contour	contour	NOUN
ap-4038	21	15	of	of	ADP
ap-4038	21	16	the	the	DET
ap-4038	21	17	interface	interface	NOUN
ap-4038	21	18	signed	sign	VERB
ap-4038	21	19	distance	distance	NOUN
ap-4038	21	20	function	function	NOUN
ap-4038	21	21	,	,	PUNCT
ap-4038	21	22	which	which	PRON
ap-4038	21	23	is	be	AUX
ap-4038	21	24	defined	define	VERB
ap-4038	21	25	over	over	ADP
ap-4038	21	26	the	the	DET
ap-4038	21	27	whole	whole	ADJ
ap-4038	21	28	computational	computational	ADJ
ap-4038	21	29	domain	domain	NOUN
ap-4038	21	30	.	.	PUNCT
ap-4038	22	1	the	the	DET
ap-4038	22	2	interface	interface	NOUN
ap-4038	22	3	is	be	AUX
ap-4038	22	4	then	then	ADV
ap-4038	22	5	tracked	track	VERB
ap-4038	22	6	by	by	ADP
ap-4038	22	7	solving	solve	VERB
ap-4038	22	8	the	the	DET
ap-4038	22	9	transport	transport	NOUN
ap-4038	22	10	equation	equation	NOUN
ap-4038	22	11	which	which	PRON
ap-4038	22	12	is	be	AUX
ap-4038	22	13	of	of	ADP
ap-4038	22	14	hyperbolic	hyperbolic	ADJ
ap-4038	22	15	type	type	NOUN
ap-4038	22	16	,	,	PUNCT
ap-4038	22	17	and	and	CCONJ
ap-4038	22	18	therefore	therefore	ADV
ap-4038	22	19	introduces	introduce	VERB
ap-4038	22	20	some	some	DET
ap-4038	22	21	computational	computational	ADJ
ap-4038	22	22	difficulties	difficulty	NOUN
ap-4038	22	23	.	.	PUNCT
ap-4038	23	1	in	in	ADP
ap-4038	23	2	volume	volume	NOUN
ap-4038	23	3	-	-	PUNCT
ap-4038	23	4	of	of	ADP
ap-4038	23	5	-	-	PUNCT
ap-4038	23	6	fluid	fluid	NOUN
ap-4038	23	7	,	,	PUNCT
ap-4038	23	8	the	the	DET
ap-4038	23	9	volume	volume	NOUN
ap-4038	23	10	fractions	fraction	NOUN
ap-4038	23	11	of	of	ADP
ap-4038	23	12	the	the	DET
ap-4038	23	13	representative	representative	ADJ
ap-4038	23	14	fluid	fluid	NOUN
ap-4038	23	15	are	be	AUX
ap-4038	23	16	tracked	track	VERB
ap-4038	23	17	.	.	PUNCT
ap-4038	24	1	many	many	ADJ
ap-4038	24	2	different	different	ADJ
ap-4038	24	3	numerical	numerical	ADJ
ap-4038	24	4	schemes	scheme	NOUN
ap-4038	24	5	have	have	AUX
ap-4038	24	6	been	be	AUX
ap-4038	24	7	developed	develop	VERB
ap-4038	24	8	in	in	ADP
ap-4038	24	9	this	this	DET
ap-4038	24	10	area	area	NOUN
ap-4038	24	11	.	.	PUNCT
ap-4038	25	1	most	most	ADJ
ap-4038	25	2	of	of	ADP
ap-4038	25	3	them	they	PRON
ap-4038	25	4	are	be	AUX
ap-4038	25	5	based	base	VERB
ap-4038	25	6	on	on	ADP
ap-4038	25	7	finite	finite	ADJ
ap-4038	25	8	difference	difference	NOUN
ap-4038	25	9	schemes	scheme	NOUN
ap-4038	25	10	[	[	X
ap-4038	25	11	8	8	NUM
ap-4038	25	12	]	]	PUNCT
ap-4038	25	13	,	,	PUNCT
ap-4038	25	14	or	or	CCONJ
ap-4038	25	15	employ	employ	AUX
ap-4038	25	16	stabilized	stabilize	VERB
ap-4038	25	17	finite	finite	ADJ
ap-4038	25	18	elements	element	NOUN
ap-4038	25	19	(	(	PUNCT
ap-4038	25	20	supg	supg	NOUN
ap-4038	25	21	)	)	PUNCT
ap-4038	25	22	,	,	PUNCT
ap-4038	25	23	see	see	VERB
ap-4038	25	24	[	[	X
ap-4038	25	25	12	12	NUM
ap-4038	25	26	,	,	PUNCT
ap-4038	25	27	13	13	NUM
ap-4038	25	28	]	]	PUNCT
ap-4038	25	29	.	.	PUNCT
ap-4038	26	1	the	the	DET
ap-4038	26	2	work	work	NOUN
ap-4038	26	3	presented	present	VERB
ap-4038	26	4	here	here	ADV
ap-4038	26	5	employs	employ	VERB
ap-4038	26	6	the	the	DET
ap-4038	26	7	volume	volume	NOUN
ap-4038	26	8	-	-	PUNCT
ap-4038	26	9	of	of	ADP
ap-4038	26	10	-	-	PUNCT
ap-4038	26	11	fluid	fluid	NOUN
ap-4038	26	12	method	method	NOUN
ap-4038	26	13	which	which	PRON
ap-4038	26	14	,	,	PUNCT
ap-4038	26	15	within	within	ADP
ap-4038	26	16	the	the	DET
ap-4038	26	17	interface	interface	NOUN
ap-4038	26	18	capturing	capture	VERB
ap-4038	26	19	methods	method	NOUN
ap-4038	26	20	,	,	PUNCT
ap-4038	26	21	belongs	belong	VERB
ap-4038	26	22	to	to	ADP
ap-4038	26	23	the	the	DET
ap-4038	26	24	family	family	NOUN
ap-4038	26	25	of	of	ADP
ap-4038	26	26	so	so	ADV
ap-4038	26	27	-	-	PUNCT
ap-4038	26	28	called	call	VERB
ap-4038	26	29	volume	volume	NOUN
ap-4038	26	30	tracking	tracking	NOUN
ap-4038	26	31	methods	method	NOUN
ap-4038	26	32	[	[	X
ap-4038	26	33	5	5	NUM
ap-4038	26	34	]	]	PUNCT
ap-4038	26	35	.	.	PUNCT
ap-4038	27	1	here	here	ADV
ap-4038	27	2	,	,	PUNCT
ap-4038	27	3	instead	instead	ADV
ap-4038	27	4	of	of	ADP
ap-4038	27	5	tracking	track	VERB
ap-4038	27	6	the	the	DET
ap-4038	27	7	interface	interface	NOUN
ap-4038	27	8	itself	itself	PRON
ap-4038	27	9	according	accord	VERB
ap-4038	27	10	to	to	ADP
ap-4038	27	11	the	the	DET
ap-4038	27	12	transport	transport	NOUN
ap-4038	27	13	equation	equation	NOUN
ap-4038	27	14	(	(	PUNCT
ap-4038	27	15	as	as	ADP
ap-4038	27	16	in	in	ADP
ap-4038	27	17	the	the	DET
ap-4038	27	18	level	level	NOUN
ap-4038	27	19	-	-	PUNCT
ap-4038	27	20	set	set	NOUN
ap-4038	27	21	method	method	NOUN
ap-4038	27	22	)	)	PUNCT
ap-4038	27	23	,	,	PUNCT
ap-4038	27	24	we	we	PRON
ap-4038	27	25	track	track	VERB
ap-4038	27	26	the	the	DET
ap-4038	27	27	material	material	NOUN
ap-4038	27	28	volume	volume	NOUN
ap-4038	27	29	fraction	fraction	NOUN
ap-4038	27	30	inside	inside	ADP
ap-4038	27	31	each	each	DET
ap-4038	27	32	cell	cell	NOUN
ap-4038	27	33	along	along	ADP
ap-4038	27	34	the	the	DET
ap-4038	27	35	streamlines	streamline	NOUN
ap-4038	27	36	.	.	PUNCT
ap-4038	28	1	the	the	DET
ap-4038	28	2	interface	interface	NOUN
ap-4038	28	3	is	be	AUX
ap-4038	28	4	then	then	ADV
ap-4038	28	5	reconstructed	reconstruct	VERB
ap-4038	28	6	by	by	ADP
ap-4038	28	7	projecting	project	VERB
ap-4038	28	8	these	these	DET
ap-4038	28	9	advected	advect	VERB
ap-4038	28	10	volumes	volume	NOUN
ap-4038	28	11	onto	onto	ADP
ap-4038	28	12	the	the	DET
ap-4038	28	13	original	original	ADJ
ap-4038	28	14	mesh	mesh	NOUN
ap-4038	28	15	.	.	PUNCT
ap-4038	29	1	the	the	DET
ap-4038	29	2	volume	volume	NOUN
ap-4038	29	3	fraction	fraction	NOUN
ap-4038	29	4	f	f	PROPN
ap-4038	29	5	coincides	coincide	VERB
ap-4038	29	6	with	with	ADP
ap-4038	29	7	the	the	DET
ap-4038	29	8	characteristic	characteristic	ADJ
ap-4038	29	9	function	function	NOUN
ap-4038	29	10	of	of	ADP
ap-4038	29	11	the	the	DET
ap-4038	29	12	domain	domain	NOUN
ap-4038	29	13	occupied	occupy	VERB
ap-4038	29	14	by	by	ADP
ap-4038	29	15	the	the	DET
ap-4038	29	16	reference	reference	NOUN
ap-4038	29	17	fluid	fluid	NOUN
ap-4038	29	18	,	,	PUNCT
ap-4038	29	19	and	and	CCONJ
ap-4038	29	20	can	can	AUX
ap-4038	29	21	therefore	therefore	ADV
ap-4038	29	22	be	be	AUX
ap-4038	29	23	advected	advect	VERB
ap-4038	29	24	in	in	ADP
ap-4038	29	25	the	the	DET
ap-4038	29	26	same	same	ADJ
ap-4038	29	27	fashion	fashion	NOUN
ap-4038	29	28	as	as	ADP
ap-4038	29	29	in	in	ADP
ap-4038	29	30	the	the	DET
ap-4038	29	31	level	level	NOUN
ap-4038	29	32	set	set	VERB
ap-4038	29	33	methods	method	NOUN
ap-4038	29	34	.	.	PUNCT
ap-4038	30	1	in	in	ADP
ap-4038	30	2	the	the	DET
ap-4038	30	3	case	case	NOUN
ap-4038	30	4	of	of	ADP
ap-4038	30	5	incompressible	incompressible	ADJ
ap-4038	30	6	fluid	fluid	NOUN
ap-4038	30	7	,	,	PUNCT
ap-4038	30	8	this	this	DET
ap-4038	30	9	approach	approach	NOUN
ap-4038	30	10	leads	lead	VERB
ap-4038	30	11	to	to	ADP
ap-4038	30	12	numerical	numerical	ADJ
ap-4038	30	13	schemes	scheme	NOUN
ap-4038	30	14	where	where	SCONJ
ap-4038	30	15	it	it	PRON
ap-4038	30	16	is	be	AUX
ap-4038	30	17	necessary	necessary	ADJ
ap-4038	30	18	to	to	PART
ap-4038	30	19	compute	compute	VERB
ap-4038	30	20	the	the	DET
ap-4038	30	21	fluxes	flux	NOUN
ap-4038	30	22	across	across	ADP
ap-4038	30	23	the	the	DET
ap-4038	30	24	element	element	NOUN
ap-4038	30	25	boundaries	boundary	NOUN
ap-4038	30	26	[	[	X
ap-4038	30	27	14	14	NUM
ap-4038	30	28	]	]	PUNCT
ap-4038	30	29	.	.	PUNCT
ap-4038	31	1	this	this	DET
ap-4038	31	2	approach	approach	NOUN
ap-4038	31	3	is	be	AUX
ap-4038	31	4	sometimes	sometimes	ADV
ap-4038	31	5	referred	refer	VERB
ap-4038	31	6	to	to	ADP
ap-4038	31	7	as	as	ADP
ap-4038	31	8	eulerian	eulerian	ADJ
ap-4038	31	9	[	[	X
ap-4038	31	10	15	15	NUM
ap-4038	31	11	]	]	PUNCT
ap-4038	31	12	.	.	PUNCT
ap-4038	32	1	a	a	DET
ap-4038	32	2	different	different	ADJ
ap-4038	32	3	treatment	treatment	NOUN
ap-4038	32	4	of	of	ADP
ap-4038	32	5	volume	volume	NOUN
ap-4038	32	6	fraction	fraction	NOUN
ap-4038	32	7	advection	advection	NOUN
ap-4038	32	8	has	have	AUX
ap-4038	32	9	been	be	AUX
ap-4038	32	10	proposed	propose	VERB
ap-4038	32	11	by	by	ADP
ap-4038	32	12	dukowicz	dukowicz	NOUN
ap-4038	32	13	and	and	CCONJ
ap-4038	32	14	baumgardner	baumgardner	VERB
ap-4038	32	15	in	in	ADP
ap-4038	32	16	[	[	X
ap-4038	32	17	16	16	NUM
ap-4038	32	18	]	]	PUNCT
ap-4038	32	19	.	.	PUNCT
ap-4038	33	1	their	their	PRON
ap-4038	33	2	method	method	NOUN
ap-4038	33	3	is	be	AUX
ap-4038	33	4	based	base	VERB
ap-4038	33	5	on	on	ADP
ap-4038	33	6	two	two	NUM
ap-4038	33	7	simple	simple	ADJ
ap-4038	33	8	facts	fact	NOUN
ap-4038	33	9	.	.	PUNCT
ap-4038	34	1	the	the	DET
ap-4038	34	2	first	first	ADJ
ap-4038	34	3	is	be	AUX
ap-4038	34	4	that	that	SCONJ
ap-4038	34	5	the	the	DET
ap-4038	34	6	volume	volume	NOUN
ap-4038	34	7	of	of	ADP
ap-4038	34	8	a	a	DET
ap-4038	34	9	reference	reference	NOUN
ap-4038	34	10	fluid	fluid	NOUN
ap-4038	34	11	inside	inside	ADP
ap-4038	34	12	a	a	DET
ap-4038	34	13	sub	sub	NOUN
ap-4038	34	14	-	-	NOUN
ap-4038	34	15	domain	domain	NOUN
ap-4038	34	16	is	be	AUX
ap-4038	34	17	equal	equal	ADJ
ap-4038	34	18	to	to	ADP
ap-4038	34	19	its	its	PRON
ap-4038	34	20	volume	volume	NOUN
ap-4038	34	21	fraction	fraction	NOUN
ap-4038	34	22	integrated	integrate	VERB
ap-4038	34	23	over	over	ADP
ap-4038	34	24	that	that	DET
ap-4038	34	25	sub	sub	NOUN
ap-4038	34	26	-	-	NOUN
ap-4038	34	27	domain	domain	NOUN
ap-4038	34	28	.	.	PUNCT
ap-4038	35	1	the	the	DET
ap-4038	35	2	second	second	ADJ
ap-4038	35	3	states	state	NOUN
ap-4038	35	4	that	that	SCONJ
ap-4038	35	5	a	a	DET
ap-4038	35	6	certain	certain	ADJ
ap-4038	35	7	volume	volume	NOUN
ap-4038	35	8	of	of	ADP
ap-4038	35	9	the	the	DET
ap-4038	35	10	reference	reference	NOUN
ap-4038	35	11	fluid	fluid	NOUN
ap-4038	35	12	can	can	AUX
ap-4038	35	13	not	not	PART
ap-4038	35	14	change	change	VERB
ap-4038	35	15	in	in	ADP
ap-4038	35	16	time	time	NOUN
ap-4038	35	17	(	(	PUNCT
ap-4038	35	18	mass	mass	NOUN
ap-4038	35	19	conservation	conservation	NOUN
ap-4038	35	20	)	)	PUNCT
ap-4038	35	21	.	.	PUNCT
ap-4038	36	1	by	by	ADP
ap-4038	36	2	requiring	require	VERB
ap-4038	36	3	that	that	SCONJ
ap-4038	36	4	an	an	DET
ap-4038	36	5	arbitrary	arbitrary	ADJ
ap-4038	36	6	volume	volume	NOUN
ap-4038	36	7	projected	project	VERB
ap-4038	36	8	along	along	ADP
ap-4038	36	9	the	the	DET
ap-4038	36	10	streamlines	streamline	NOUN
ap-4038	36	11	at	at	ADP
ap-4038	36	12	time	time	NOUN
ap-4038	36	13	tn+1	tn+1	PROPN
ap-4038	36	14	is	be	AUX
ap-4038	36	15	equal	equal	ADJ
ap-4038	36	16	to	to	ADP
ap-4038	36	17	the	the	DET
ap-4038	36	18	same	same	ADJ
ap-4038	36	19	volume	volume	NOUN
ap-4038	36	20	at	at	ADP
ap-4038	36	21	time	time	NOUN
ap-4038	36	22	tn	tn	PROPN
ap-4038	36	23	,	,	PUNCT
ap-4038	36	24	they	they	PRON
ap-4038	36	25	derived	derive	VERB
ap-4038	36	26	a	a	DET
ap-4038	36	27	simple	simple	ADJ
ap-4038	36	28	method	method	NOUN
ap-4038	36	29	that	that	PRON
ap-4038	36	30	can	can	AUX
ap-4038	36	31	be	be	AUX
ap-4038	36	32	based	base	VERB
ap-4038	36	33	purely	purely	ADV
ap-4038	36	34	on	on	ADP
ap-4038	36	35	geometrical	geometrical	ADJ
ap-4038	36	36	procedures	procedure	NOUN
ap-4038	36	37	,	,	PUNCT
ap-4038	36	38	i.e.	i.e.	X
ap-4038	36	39	intersections	intersection	NOUN
ap-4038	36	40	of	of	ADP
ap-4038	36	41	polygons	polygon	NOUN
ap-4038	36	42	and	and	CCONJ
ap-4038	36	43	polyhedrons	polyhedron	NOUN
ap-4038	36	44	.	.	PUNCT
ap-4038	37	1	our	our	PRON
ap-4038	37	2	approach	approach	NOUN
ap-4038	37	3	in	in	ADP
ap-4038	37	4	this	this	DET
ap-4038	37	5	work	work	NOUN
ap-4038	37	6	follows	follow	VERB
ap-4038	37	7	dukowicz	dukowicz	NOUN
ap-4038	37	8	and	and	CCONJ
ap-4038	37	9	baumgardner	baumgardner	NOUN
ap-4038	37	10	[	[	X
ap-4038	37	11	16	16	NUM
ap-4038	37	12	]	]	PUNCT
ap-4038	37	13	,	,	PUNCT
ap-4038	37	14	with	with	ADP
ap-4038	37	15	later	later	ADJ
ap-4038	37	16	developments	development	NOUN
ap-4038	37	17	by	by	ADP
ap-4038	37	18	shah105	shah105	PROPN
ap-4038	37	19	http://dx.doi.org/10.14311/ap.2017.57.0105	http://dx.doi.org/10.14311/ap.2017.57.0105	CCONJ
ap-4038	37	20	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4038	37	21	filip	filip	NOUN
ap-4038	37	22	kolařík	kolařík	NOUN
ap-4038	37	23	,	,	PUNCT
ap-4038	37	24	bořek	bořek	PROPN
ap-4038	37	25	patzák	patzák	VERB
ap-4038	37	26	acta	acta	PROPN
ap-4038	37	27	polytechnica	polytechnica	PROPN
ap-4038	37	28	bazi	bazi	NOUN
ap-4038	38	1	[	[	X
ap-4038	38	2	15	15	NUM
ap-4038	38	3	]	]	PUNCT
ap-4038	38	4	.	.	PUNCT
ap-4038	39	1	the	the	DET
ap-4038	39	2	novelty	novelty	NOUN
ap-4038	39	3	lies	lie	VERB
ap-4038	39	4	in	in	ADP
ap-4038	39	5	incorporating	incorporate	VERB
ap-4038	39	6	so	so	ADV
ap-4038	39	7	-	-	PUNCT
ap-4038	39	8	called	call	VERB
ap-4038	39	9	binary	binary	ADJ
ap-4038	39	10	space	space	NOUN
ap-4038	39	11	-	-	PUNCT
ap-4038	39	12	partitioning	partition	VERB
ap-4038	39	13	(	(	PUNCT
ap-4038	39	14	bsp	bsp	NOUN
ap-4038	39	15	)	)	PUNCT
ap-4038	39	16	trees	tree	NOUN
ap-4038	39	17	.	.	PUNCT
ap-4038	40	1	bsp	bsp	NOUN
ap-4038	40	2	trees	tree	NOUN
ap-4038	40	3	were	be	AUX
ap-4038	40	4	originally	originally	ADV
ap-4038	40	5	developed	develop	VERB
ap-4038	40	6	in	in	ADP
ap-4038	40	7	connection	connection	NOUN
ap-4038	40	8	with	with	ADP
ap-4038	40	9	3d	3d	PROPN
ap-4038	40	10	computer	computer	NOUN
ap-4038	40	11	graphics	graphic	NOUN
ap-4038	40	12	and	and	CCONJ
ap-4038	40	13	are	be	AUX
ap-4038	40	14	nowadays	nowadays	ADV
ap-4038	40	15	heavily	heavily	ADV
ap-4038	40	16	used	use	VERB
ap-4038	40	17	in	in	ADP
ap-4038	40	18	the	the	DET
ap-4038	40	19	gaming	gaming	NOUN
ap-4038	40	20	industry	industry	NOUN
ap-4038	40	21	.	.	PUNCT
ap-4038	41	1	an	an	DET
ap-4038	41	2	early	early	ADJ
ap-4038	41	3	mention	mention	NOUN
ap-4038	41	4	of	of	ADP
ap-4038	41	5	bsp	bsp	NOUN
ap-4038	41	6	trees	tree	NOUN
ap-4038	41	7	can	can	AUX
ap-4038	41	8	be	be	AUX
ap-4038	41	9	found	find	VERB
ap-4038	41	10	in	in	ADP
ap-4038	41	11	[	[	X
ap-4038	41	12	17	17	NUM
ap-4038	41	13	]	]	PUNCT
ap-4038	41	14	,	,	PUNCT
ap-4038	41	15	and	and	CCONJ
ap-4038	41	16	a	a	DET
ap-4038	41	17	modern	modern	ADJ
ap-4038	41	18	exposition	exposition	NOUN
ap-4038	41	19	,	,	PUNCT
ap-4038	41	20	together	together	ADV
ap-4038	41	21	with	with	ADP
ap-4038	41	22	implementation	implementation	NOUN
ap-4038	41	23	notes	note	NOUN
ap-4038	41	24	,	,	PUNCT
ap-4038	41	25	is	be	AUX
ap-4038	41	26	contained	contain	VERB
ap-4038	41	27	in	in	ADP
ap-4038	41	28	[	[	X
ap-4038	41	29	18	18	NUM
ap-4038	41	30	]	]	PUNCT
ap-4038	41	31	.	.	PUNCT
ap-4038	42	1	the	the	DET
ap-4038	42	2	main	main	ADJ
ap-4038	42	3	idea	idea	NOUN
ap-4038	42	4	behind	behind	ADP
ap-4038	42	5	bsp	bsp	NOUN
ap-4038	42	6	trees	tree	NOUN
ap-4038	42	7	lies	lie	VERB
ap-4038	42	8	in	in	ADP
ap-4038	42	9	subdividing	subdivide	VERB
ap-4038	42	10	space	space	NOUN
ap-4038	42	11	into	into	ADP
ap-4038	42	12	convex	convex	NOUN
ap-4038	42	13	sets	set	NOUN
ap-4038	42	14	by	by	ADP
ap-4038	42	15	hyper	hyper	NOUN
ap-4038	42	16	-	-	NOUN
ap-4038	42	17	planes	plane	NOUN
ap-4038	42	18	.	.	PUNCT
ap-4038	43	1	this	this	DET
ap-4038	43	2	subdivision	subdivision	NOUN
ap-4038	43	3	can	can	AUX
ap-4038	43	4	be	be	AUX
ap-4038	43	5	represented	represent	VERB
ap-4038	43	6	by	by	ADP
ap-4038	43	7	a	a	DET
ap-4038	43	8	binary	binary	ADJ
ap-4038	43	9	tree	tree	NOUN
ap-4038	43	10	structure	structure	NOUN
ap-4038	43	11	,	,	PUNCT
ap-4038	43	12	which	which	PRON
ap-4038	43	13	is	be	AUX
ap-4038	43	14	used	use	VERB
ap-4038	43	15	in	in	ADP
ap-4038	43	16	our	our	PRON
ap-4038	43	17	work	work	NOUN
ap-4038	43	18	for	for	ADP
ap-4038	43	19	efficient	efficient	ADJ
ap-4038	43	20	implementation	implementation	NOUN
ap-4038	43	21	of	of	ADP
ap-4038	43	22	polyhedra	polyhedra	NOUN
ap-4038	43	23	intersections	intersection	NOUN
ap-4038	43	24	.	.	PUNCT
ap-4038	44	1	the	the	DET
ap-4038	44	2	main	main	ADJ
ap-4038	44	3	advantages	advantage	NOUN
ap-4038	44	4	of	of	ADP
ap-4038	44	5	this	this	DET
ap-4038	44	6	formulation	formulation	NOUN
ap-4038	44	7	include	include	VERB
ap-4038	44	8	natural	natural	ADJ
ap-4038	44	9	geometrical	geometrical	ADJ
ap-4038	44	10	interpretation	interpretation	NOUN
ap-4038	44	11	,	,	PUNCT
ap-4038	44	12	mass	mass	NOUN
ap-4038	44	13	conservation	conservation	NOUN
ap-4038	44	14	,	,	PUNCT
ap-4038	44	15	and	and	CCONJ
ap-4038	44	16	applicability	applicability	NOUN
ap-4038	44	17	to	to	AUX
ap-4038	44	18	structured	structured	ADJ
ap-4038	44	19	and	and	CCONJ
ap-4038	44	20	unstructured	unstructured	ADJ
ap-4038	44	21	meshes	mesh	NOUN
ap-4038	44	22	.	.	PUNCT
ap-4038	45	1	the	the	DET
ap-4038	45	2	paper	paper	NOUN
ap-4038	45	3	is	be	AUX
ap-4038	45	4	organized	organize	VERB
ap-4038	45	5	as	as	SCONJ
ap-4038	45	6	follows	follow	VERB
ap-4038	45	7	.	.	PUNCT
ap-4038	46	1	the	the	DET
ap-4038	46	2	first	first	ADJ
ap-4038	46	3	section	section	NOUN
ap-4038	46	4	provides	provide	VERB
ap-4038	46	5	an	an	DET
ap-4038	46	6	overview	overview	NOUN
ap-4038	46	7	of	of	ADP
ap-4038	46	8	the	the	DET
ap-4038	46	9	governing	govern	VERB
ap-4038	46	10	equations	equation	NOUN
ap-4038	46	11	of	of	ADP
ap-4038	46	12	incompressible	incompressible	ADJ
ap-4038	46	13	immiscible	immiscible	ADJ
ap-4038	46	14	flow	flow	NOUN
ap-4038	46	15	,	,	PUNCT
ap-4038	46	16	together	together	ADV
ap-4038	46	17	with	with	ADP
ap-4038	46	18	discretization	discretization	NOUN
ap-4038	46	19	using	use	VERB
ap-4038	46	20	the	the	DET
ap-4038	46	21	finite	finite	ADJ
ap-4038	46	22	element	element	NOUN
ap-4038	46	23	method	method	NOUN
ap-4038	46	24	.	.	PUNCT
ap-4038	47	1	then	then	ADV
ap-4038	47	2	the	the	DET
ap-4038	47	3	vof	vof	NOUN
ap-4038	47	4	-	-	PUNCT
ap-4038	47	5	based	base	VERB
ap-4038	47	6	interface	interface	NOUN
ap-4038	47	7	tracking	tracking	NOUN
ap-4038	47	8	method	method	NOUN
ap-4038	47	9	is	be	AUX
ap-4038	47	10	presented	present	VERB
ap-4038	47	11	in	in	ADP
ap-4038	47	12	detail	detail	NOUN
ap-4038	47	13	,	,	PUNCT
ap-4038	47	14	covering	cover	VERB
ap-4038	47	15	the	the	DET
ap-4038	47	16	interface	interface	NOUN
ap-4038	47	17	reconstruction	reconstruction	NOUN
ap-4038	47	18	based	base	VERB
ap-4038	47	19	on	on	ADP
ap-4038	47	20	volume	volume	NOUN
ap-4038	47	21	fraction	fraction	NOUN
ap-4038	47	22	distribution	distribution	NOUN
ap-4038	47	23	,	,	PUNCT
ap-4038	47	24	a	a	DET
ap-4038	47	25	mass	mass	NOUN
ap-4038	47	26	conserving	conserve	VERB
ap-4038	47	27	interface	interface	NOUN
ap-4038	47	28	update	update	NOUN
ap-4038	47	29	using	use	VERB
ap-4038	47	30	a	a	DET
ap-4038	47	31	three	three	NUM
ap-4038	47	32	step	step	NOUN
ap-4038	47	33	procedure	procedure	NOUN
ap-4038	47	34	,	,	PUNCT
ap-4038	47	35	and	and	CCONJ
ap-4038	47	36	description	description	NOUN
ap-4038	47	37	of	of	ADP
ap-4038	47	38	the	the	DET
ap-4038	47	39	bsp	bsp	NOUN
ap-4038	47	40	algorithm	algorithm	NOUN
ap-4038	47	41	for	for	ADP
ap-4038	47	42	truncating	truncate	VERB
ap-4038	47	43	advected	advect	VERB
ap-4038	47	44	volumes	volume	NOUN
ap-4038	47	45	of	of	ADP
ap-4038	47	46	the	the	DET
ap-4038	47	47	representative	representative	ADJ
ap-4038	47	48	fluid	fluid	NOUN
ap-4038	47	49	.	.	PUNCT
ap-4038	48	1	finally	finally	ADV
ap-4038	48	2	,	,	PUNCT
ap-4038	48	3	the	the	DET
ap-4038	48	4	interface	interface	NOUN
ap-4038	48	5	tracking	tracking	NOUN
ap-4038	48	6	technique	technique	NOUN
ap-4038	48	7	is	be	AUX
ap-4038	48	8	presented	present	VERB
ap-4038	48	9	on	on	ADP
ap-4038	48	10	the	the	DET
ap-4038	48	11	basis	basis	NOUN
ap-4038	48	12	of	of	ADP
ap-4038	48	13	several	several	ADJ
ap-4038	48	14	examples	example	NOUN
ap-4038	48	15	that	that	PRON
ap-4038	48	16	illustrates	illustrate	VERB
ap-4038	48	17	its	its	PRON
ap-4038	48	18	capabilities	capability	NOUN
ap-4038	48	19	and	and	CCONJ
ap-4038	48	20	its	its	PRON
ap-4038	48	21	performance	performance	NOUN
ap-4038	48	22	.	.	PUNCT
ap-4038	49	1	2	2	X
ap-4038	49	2	.	.	X
ap-4038	49	3	a	a	DET
ap-4038	49	4	description	description	NOUN
ap-4038	49	5	of	of	ADP
ap-4038	49	6	the	the	DET
ap-4038	49	7	fluid	fluid	NOUN
ap-4038	49	8	this	this	DET
ap-4038	49	9	section	section	NOUN
ap-4038	49	10	provides	provide	VERB
ap-4038	49	11	a	a	DET
ap-4038	49	12	description	description	NOUN
ap-4038	49	13	of	of	ADP
ap-4038	49	14	the	the	DET
ap-4038	49	15	governing	govern	VERB
ap-4038	49	16	equations	equation	NOUN
ap-4038	49	17	for	for	ADP
ap-4038	49	18	the	the	DET
ap-4038	49	19	flow	flow	NOUN
ap-4038	49	20	of	of	ADP
ap-4038	49	21	two	two	NUM
ap-4038	49	22	immiscible	immiscible	ADJ
ap-4038	49	23	fluids	fluid	NOUN
ap-4038	49	24	.	.	PUNCT
ap-4038	50	1	as	as	SCONJ
ap-4038	50	2	the	the	DET
ap-4038	50	3	problem	problem	NOUN
ap-4038	50	4	is	be	AUX
ap-4038	50	5	by	by	ADP
ap-4038	50	6	nature	nature	NOUN
ap-4038	50	7	fully	fully	ADV
ap-4038	50	8	transient	transient	ADJ
ap-4038	50	9	,	,	PUNCT
ap-4038	50	10	the	the	DET
ap-4038	50	11	navier	navier	NOUN
ap-4038	50	12	-	-	PUNCT
ap-4038	50	13	stokes	stokes	PROPN
ap-4038	50	14	equations	equation	NOUN
ap-4038	50	15	(	(	PUNCT
ap-4038	50	16	nse	nse	NOUN
ap-4038	50	17	)	)	PUNCT
ap-4038	50	18	govern	govern	VERB
ap-4038	50	19	the	the	DET
ap-4038	50	20	motion	motion	NOUN
ap-4038	50	21	of	of	ADP
ap-4038	50	22	both	both	DET
ap-4038	50	23	fluids	fluid	NOUN
ap-4038	50	24	.	.	PUNCT
ap-4038	51	1	let	let	VERB
ap-4038	51	2	us	we	PRON
ap-4038	51	3	denote	denote	VERB
ap-4038	51	4	ω	ω	PROPN
ap-4038	51	5	⊂	⊂	PROPN
ap-4038	51	6	r3	r3	PROPN
ap-4038	51	7	as	as	ADP
ap-4038	51	8	a	a	DET
ap-4038	51	9	three	three	NUM
ap-4038	51	10	dimensional	dimensional	ADJ
ap-4038	51	11	domain	domain	NOUN
ap-4038	51	12	which	which	PRON
ap-4038	51	13	is	be	AUX
ap-4038	51	14	completely	completely	ADV
ap-4038	51	15	filled	fill	VERB
ap-4038	51	16	with	with	ADP
ap-4038	51	17	the	the	DET
ap-4038	51	18	two	two	NUM
ap-4038	51	19	immiscible	immiscible	ADJ
ap-4038	51	20	fluids	fluid	NOUN
ap-4038	51	21	,	,	PUNCT
ap-4038	51	22	occupying	occupy	VERB
ap-4038	51	23	the	the	DET
ap-4038	51	24	corresponding	correspond	VERB
ap-4038	51	25	subsets	subset	NOUN
ap-4038	51	26	ω1(t	ω1(t	NUM
ap-4038	51	27	)	)	PUNCT
ap-4038	51	28	and	and	CCONJ
ap-4038	51	29	ω2(t	ω2(t	NUM
ap-4038	51	30	)	)	PUNCT
ap-4038	51	31	,	,	PUNCT
ap-4038	51	32	where	where	SCONJ
ap-4038	51	33	t	t	PROPN
ap-4038	51	34	stresses	stress	VERB
ap-4038	51	35	the	the	DET
ap-4038	51	36	time	time	NOUN
ap-4038	51	37	dependence	dependence	NOUN
ap-4038	51	38	of	of	ADP
ap-4038	51	39	the	the	DET
ap-4038	51	40	two	two	NUM
ap-4038	51	41	subsets	subset	NOUN
ap-4038	51	42	.	.	PUNCT
ap-4038	52	1	the	the	DET
ap-4038	52	2	boundary	boundary	NOUN
ap-4038	52	3	of	of	ADP
ap-4038	52	4	the	the	DET
ap-4038	52	5	whole	whole	ADJ
ap-4038	52	6	domain	domain	NOUN
ap-4038	52	7	,	,	PUNCT
ap-4038	52	8	denoted	denote	VERB
ap-4038	52	9	as	as	ADP
ap-4038	52	10	∂ω	∂ω	PROPN
ap-4038	52	11	,	,	PUNCT
ap-4038	52	12	can	can	AUX
ap-4038	52	13	be	be	AUX
ap-4038	52	14	decomposed	decompose	VERB
ap-4038	52	15	into	into	ADP
ap-4038	52	16	two	two	NUM
ap-4038	52	17	mutually	mutually	ADV
ap-4038	52	18	disjoint	disjoint	ADJ
ap-4038	52	19	parts	part	NOUN
ap-4038	52	20	,	,	PUNCT
ap-4038	52	21	γd	γd	ADP
ap-4038	52	22	and	and	CCONJ
ap-4038	52	23	γn	γn	INTJ
ap-4038	52	24	,	,	PUNCT
ap-4038	52	25	on	on	ADP
ap-4038	52	26	which	which	PRON
ap-4038	52	27	the	the	DET
ap-4038	52	28	so	so	ADV
ap-4038	52	29	-	-	PUNCT
ap-4038	52	30	called	call	VERB
ap-4038	52	31	dirichlet	dirichlet	PROPN
ap-4038	52	32	and	and	CCONJ
ap-4038	52	33	neumann	neumann	PROPN
ap-4038	52	34	boundary	boundary	PROPN
ap-4038	52	35	conditions	condition	NOUN
ap-4038	52	36	are	be	AUX
ap-4038	52	37	prescribed	prescribe	VERB
ap-4038	52	38	,	,	PUNCT
ap-4038	52	39	respectively	respectively	ADV
ap-4038	52	40	.	.	PUNCT
ap-4038	53	1	the	the	DET
ap-4038	53	2	interface	interface	NOUN
ap-4038	53	3	between	between	ADP
ap-4038	53	4	the	the	DET
ap-4038	53	5	two	two	NUM
ap-4038	53	6	fluids	fluid	NOUN
ap-4038	53	7	is	be	AUX
ap-4038	53	8	denoted	denote	VERB
ap-4038	53	9	as	as	ADP
ap-4038	53	10	σ(t	σ(t	PROPN
ap-4038	53	11	)	)	PUNCT
ap-4038	53	12	.	.	PUNCT
ap-4038	54	1	then	then	ADV
ap-4038	54	2	,	,	PUNCT
ap-4038	54	3	for	for	ADP
ap-4038	54	4	each	each	DET
ap-4038	54	5	phase	phase	NOUN
ap-4038	54	6	j	j	PROPN
ap-4038	54	7	=	=	SYM
ap-4038	54	8	1	1	NUM
ap-4038	54	9	,	,	PUNCT
ap-4038	54	10	2	2	NUM
ap-4038	54	11	in	in	ADP
ap-4038	54	12	the	the	DET
ap-4038	54	13	domain	domain	NOUN
ap-4038	54	14	ω	ω	NOUN
ap-4038	54	15	and	and	CCONJ
ap-4038	54	16	on	on	ADP
ap-4038	54	17	its	its	PRON
ap-4038	54	18	boundary	boundary	ADJ
ap-4038	54	19	∂ω	∂ω	PROPN
ap-4038	54	20	,	,	PUNCT
ap-4038	54	21	and	and	CCONJ
ap-4038	54	22	for	for	ADP
ap-4038	54	23	each	each	DET
ap-4038	54	24	time	time	NOUN
ap-4038	54	25	t	t	PROPN
ap-4038	54	26	∈	∈	PROPN
ap-4038	55	1	[	[	X
ap-4038	55	2	0	0	NUM
ap-4038	55	3	,	,	PUNCT
ap-4038	55	4	t	t	X
ap-4038	55	5	]	]	PUNCT
ap-4038	55	6	,	,	PUNCT
ap-4038	55	7	the	the	DET
ap-4038	55	8	problem	problem	NOUN
ap-4038	55	9	can	can	AUX
ap-4038	55	10	be	be	AUX
ap-4038	55	11	formulated	formulate	VERB
ap-4038	55	12	as	as	SCONJ
ap-4038	55	13	follows	follow	VERB
ap-4038	55	14	,	,	PUNCT
ap-4038	55	15	see	see	VERB
ap-4038	55	16	[	[	X
ap-4038	55	17	19	19	NUM
ap-4038	55	18	]	]	X
ap-4038	55	19	ρj	ρj	NOUN
ap-4038	55	20	(	(	PUNCT
ap-4038	55	21	∂v	∂v	PROPN
ap-4038	55	22	∂t	∂t	PROPN
ap-4038	55	23	+	+	CCONJ
ap-4038	55	24	(	(	PUNCT
ap-4038	55	25	v	v	PROPN
ap-4038	55	26	·	·	SYM
ap-4038	55	27	∇)v	∇)v	PROPN
ap-4038	55	28	−	−	PROPN
ap-4038	55	29	b	b	PROPN
ap-4038	55	30	)	)	PUNCT
ap-4038	55	31	−∇	−∇	NOUN
ap-4038	55	32	·	·	PUNCT
ap-4038	55	33	σ	σ	NOUN
ap-4038	55	34	=	=	NOUN
ap-4038	55	35	0	0	NUM
ap-4038	55	36	in	in	ADP
ap-4038	55	37	ωj	ωj	ADP
ap-4038	55	38	,	,	PUNCT
ap-4038	55	39	∇	∇	X
ap-4038	55	40	·	·	PUNCT
ap-4038	55	41	v	v	X
ap-4038	55	42	=	=	SYM
ap-4038	55	43	0	0	NUM
ap-4038	55	44	in	in	ADP
ap-4038	55	45	ωj	ωj	ADP
ap-4038	55	46	,	,	PUNCT
ap-4038	55	47	v	v	NOUN
ap-4038	55	48	=	=	SYM
ap-4038	55	49	g	g	NOUN
ap-4038	55	50	on	on	ADP
ap-4038	55	51	γd	γd	ADP
ap-4038	55	52	,	,	PUNCT
ap-4038	55	53	σ	σ	NOUN
ap-4038	55	54	·	·	PUNCT
ap-4038	55	55	n	n	NOUN
ap-4038	55	56	=	=	SYM
ap-4038	55	57	h	h	NOUN
ap-4038	55	58	on	on	ADP
ap-4038	55	59	γn	γn	PRON
ap-4038	55	60	,	,	PUNCT
ap-4038	55	61	(	(	PUNCT
ap-4038	55	62	1	1	X
ap-4038	55	63	)	)	PUNCT
ap-4038	56	1	[	[	X
ap-4038	56	2	v]σ(t	v]σ(t	NOUN
ap-4038	56	3	)	)	PUNCT
ap-4038	56	4	=	=	SYM
ap-4038	56	5	0	0	NUM
ap-4038	57	1	on	on	ADP
ap-4038	57	2	σ	σ	PROPN
ap-4038	57	3	,	,	PUNCT
ap-4038	57	4	[	[	X
ap-4038	57	5	n	n	X
ap-4038	57	6	·	·	PUNCT
ap-4038	57	7	σ]σ(t	σ]σ(t	NOUN
ap-4038	57	8	)	)	PUNCT
ap-4038	57	9	=	=	SYM
ap-4038	57	10	0	0	NUM
ap-4038	58	1	on	on	ADP
ap-4038	58	2	σ	σ	PROPN
ap-4038	58	3	,	,	PUNCT
ap-4038	58	4	vt=0	vt=0	NOUN
ap-4038	58	5	=	=	SYM
ap-4038	58	6	v0	v0	NOUN
ap-4038	58	7	in	in	ADP
ap-4038	58	8	ωj	ωj	PROPN
ap-4038	58	9	.	.	PUNCT
ap-4038	59	1	in	in	ADP
ap-4038	59	2	the	the	DET
ap-4038	59	3	equations	equation	NOUN
ap-4038	59	4	presented	present	VERB
ap-4038	59	5	above	above	ADV
ap-4038	59	6	,	,	PUNCT
ap-4038	59	7	we	we	PRON
ap-4038	59	8	have	have	AUX
ap-4038	59	9	denoted	denote	VERB
ap-4038	59	10	as	as	ADP
ap-4038	59	11	n	n	ADP
ap-4038	59	12	the	the	DET
ap-4038	59	13	normal	normal	ADJ
ap-4038	59	14	vectors	vector	NOUN
ap-4038	59	15	to	to	ADP
ap-4038	59	16	both	both	CCONJ
ap-4038	59	17	∂ω	∂ω	PROPN
ap-4038	59	18	and	and	CCONJ
ap-4038	59	19	σ(t	σ(t	NOUN
ap-4038	59	20	)	)	PUNCT
ap-4038	59	21	,	,	PUNCT
ap-4038	59	22	since	since	SCONJ
ap-4038	59	23	it	it	PRON
ap-4038	59	24	will	will	AUX
ap-4038	59	25	be	be	AUX
ap-4038	59	26	clear	clear	ADJ
ap-4038	59	27	from	from	ADP
ap-4038	59	28	the	the	DET
ap-4038	59	29	context	context	NOUN
ap-4038	59	30	which	which	DET
ap-4038	59	31	normal	normal	ADJ
ap-4038	59	32	vector	vector	NOUN
ap-4038	59	33	we	we	PRON
ap-4038	59	34	have	have	VERB
ap-4038	59	35	in	in	ADP
ap-4038	59	36	mind	mind	NOUN
ap-4038	59	37	.	.	PUNCT
ap-4038	60	1	the	the	DET
ap-4038	60	2	unknowns	unknown	NOUN
ap-4038	60	3	are	be	AUX
ap-4038	60	4	velocity	velocity	NOUN
ap-4038	60	5	field	field	NOUN
ap-4038	60	6	v	v	NOUN
ap-4038	60	7	and	and	CCONJ
ap-4038	60	8	pressure	pressure	NOUN
ap-4038	60	9	field	field	NOUN
ap-4038	60	10	p.	p.	NOUN
ap-4038	60	11	density	density	NOUN
ap-4038	60	12	ρ	ρ	PROPN
ap-4038	60	13	,	,	PUNCT
ap-4038	60	14	body	body	NOUN
ap-4038	60	15	forces	force	NOUN
ap-4038	60	16	b	b	NOUN
ap-4038	60	17	and	and	CCONJ
ap-4038	60	18	functions	function	NOUN
ap-4038	60	19	g	g	NOUN
ap-4038	60	20	,	,	PUNCT
ap-4038	60	21	h	h	NOUN
ap-4038	60	22	and	and	CCONJ
ap-4038	60	23	v0	v0	PROPN
ap-4038	60	24	are	be	AUX
ap-4038	60	25	assumed	assume	VERB
ap-4038	60	26	to	to	PART
ap-4038	60	27	be	be	AUX
ap-4038	60	28	known	know	VERB
ap-4038	60	29	.	.	PUNCT
ap-4038	61	1	the	the	DET
ap-4038	61	2	square	square	ADJ
ap-4038	61	3	brackets	bracket	NOUN
ap-4038	61	4	[	[	X
ap-4038	61	5	·	·	PUNCT
ap-4038	61	6	]	]	X
ap-4038	61	7	σ(t	σ(t	NOUN
ap-4038	61	8	)	)	PUNCT
ap-4038	61	9	in	in	ADP
ap-4038	61	10	the	the	DET
ap-4038	61	11	interface	interface	NOUN
ap-4038	61	12	conditions	condition	NOUN
ap-4038	61	13	on	on	ADP
ap-4038	61	14	σ(t	σ(t	NOUN
ap-4038	61	15	)	)	PUNCT
ap-4038	61	16	denote	denote	VERB
ap-4038	61	17	a	a	DET
ap-4038	61	18	jump	jump	NOUN
ap-4038	61	19	in	in	ADP
ap-4038	61	20	the	the	DET
ap-4038	61	21	velocity	velocity	NOUN
ap-4038	61	22	and	and	CCONJ
ap-4038	61	23	the	the	DET
ap-4038	61	24	normal	normal	ADJ
ap-4038	61	25	stress	stress	NOUN
ap-4038	61	26	components	component	NOUN
ap-4038	61	27	.	.	PUNCT
ap-4038	62	1	in	in	ADP
ap-4038	62	2	the	the	DET
ap-4038	62	3	case	case	NOUN
ap-4038	62	4	of	of	ADP
ap-4038	62	5	a	a	DET
ap-4038	62	6	fluid	fluid	NOUN
ap-4038	62	7	with	with	ADP
ap-4038	62	8	surface	surface	NOUN
ap-4038	62	9	tension	tension	NOUN
ap-4038	62	10	,	,	PUNCT
ap-4038	62	11	the	the	DET
ap-4038	62	12	jump	jump	NOUN
ap-4038	62	13	in	in	ADP
ap-4038	62	14	the	the	DET
ap-4038	62	15	normal	normal	ADJ
ap-4038	62	16	stress	stress	NOUN
ap-4038	62	17	will	will	AUX
ap-4038	62	18	be	be	AUX
ap-4038	62	19	proportional	proportional	ADJ
ap-4038	62	20	to	to	ADP
ap-4038	62	21	the	the	DET
ap-4038	62	22	curvature	curvature	NOUN
ap-4038	62	23	of	of	ADP
ap-4038	62	24	the	the	DET
ap-4038	62	25	interface	interface	NOUN
ap-4038	62	26	σ(t	σ(t	PROPN
ap-4038	62	27	)	)	PUNCT
ap-4038	62	28	.	.	PUNCT
ap-4038	63	1	standard	standard	ADJ
ap-4038	63	2	decomposition	decomposition	NOUN
ap-4038	63	3	of	of	ADP
ap-4038	63	4	stress	stress	NOUN
ap-4038	63	5	tensor	tensor	NOUN
ap-4038	63	6	σ	σ	NOUN
ap-4038	63	7	into	into	ADP
ap-4038	63	8	deviatoric	deviatoric	ADJ
ap-4038	63	9	stress	stress	NOUN
ap-4038	63	10	τ	τ	PROPN
ap-4038	63	11	and	and	CCONJ
ap-4038	63	12	hydrostatic	hydrostatic	ADJ
ap-4038	63	13	pressure	pressure	NOUN
ap-4038	63	14	p	p	NOUN
ap-4038	63	15	is	be	AUX
ap-4038	63	16	used	use	VERB
ap-4038	63	17	σ	σ	X
ap-4038	63	18	=	=	SYM
ap-4038	63	19	τ	τ	PROPN
ap-4038	63	20	−	−	PROPN
ap-4038	63	21	pδ	pδ	PROPN
ap-4038	63	22	.	.	PUNCT
ap-4038	64	1	(	(	PUNCT
ap-4038	64	2	2	2	X
ap-4038	64	3	)	)	PUNCT
ap-4038	64	4	both	both	DET
ap-4038	64	5	fluids	fluid	NOUN
ap-4038	64	6	are	be	AUX
ap-4038	64	7	considered	consider	VERB
ap-4038	64	8	as	as	ADP
ap-4038	64	9	newtonian	newtonian	ADJ
ap-4038	64	10	fluids	fluid	NOUN
ap-4038	64	11	,	,	PUNCT
ap-4038	64	12	so	so	SCONJ
ap-4038	64	13	the	the	DET
ap-4038	64	14	constitutive	constitutive	ADJ
ap-4038	64	15	equations	equation	NOUN
ap-4038	64	16	read	read	VERB
ap-4038	64	17	τ	τ	PROPN
ap-4038	64	18	=	=	PUNCT
ap-4038	64	19	µd	µd	PROPN
ap-4038	64	20	,	,	PUNCT
ap-4038	64	21	(	(	PUNCT
ap-4038	64	22	3	3	X
ap-4038	64	23	)	)	PUNCT
ap-4038	64	24	where	where	SCONJ
ap-4038	64	25	d	d	PROPN
ap-4038	64	26	denotes	denote	VERB
ap-4038	64	27	the	the	DET
ap-4038	64	28	strain	strain	NOUN
ap-4038	64	29	rate	rate	NOUN
ap-4038	64	30	tensor	tensor	NOUN
ap-4038	64	31	,	,	PUNCT
ap-4038	64	32	which	which	PRON
ap-4038	64	33	is	be	AUX
ap-4038	64	34	defined	define	VERB
ap-4038	64	35	as	as	ADP
ap-4038	64	36	a	a	DET
ap-4038	64	37	symmetric	symmetric	ADJ
ap-4038	64	38	part	part	NOUN
ap-4038	64	39	of	of	ADP
ap-4038	64	40	the	the	DET
ap-4038	64	41	velocity	velocity	NOUN
ap-4038	64	42	gradient	gradient	NOUN
ap-4038	65	1	d	d	NOUN
ap-4038	65	2	=	=	SYM
ap-4038	65	3	1	1	NUM
ap-4038	65	4	2	2	NUM
ap-4038	65	5	(	(	PUNCT
ap-4038	65	6	∇v	∇v	ADV
ap-4038	65	7	+	+	CCONJ
ap-4038	65	8	(	(	PUNCT
ap-4038	65	9	∇v)t	∇v)t	X
ap-4038	65	10	)	)	PUNCT
ap-4038	65	11	(	(	PUNCT
ap-4038	65	12	4	4	NUM
ap-4038	65	13	)	)	PUNCT
ap-4038	65	14	and	and	CCONJ
ap-4038	65	15	µ	µ	X
ap-4038	65	16	is	be	AUX
ap-4038	65	17	the	the	DET
ap-4038	65	18	dynamic	dynamic	ADJ
ap-4038	65	19	viscosity	viscosity	NOUN
ap-4038	65	20	of	of	ADP
ap-4038	65	21	the	the	DET
ap-4038	65	22	fluid	fluid	NOUN
ap-4038	65	23	.	.	PUNCT
ap-4038	66	1	the	the	DET
ap-4038	66	2	numerical	numerical	ADJ
ap-4038	66	3	solution	solution	NOUN
ap-4038	66	4	of	of	ADP
ap-4038	66	5	(	(	PUNCT
ap-4038	66	6	1	1	NUM
ap-4038	66	7	)	)	PUNCT
ap-4038	66	8	is	be	AUX
ap-4038	66	9	based	base	VERB
ap-4038	66	10	on	on	ADP
ap-4038	66	11	stabilized	stabilize	VERB
ap-4038	66	12	finite	finite	ADJ
ap-4038	66	13	elements	element	NOUN
ap-4038	66	14	as	as	SCONJ
ap-4038	66	15	introduced	introduce	VERB
ap-4038	66	16	in	in	ADP
ap-4038	66	17	[	[	X
ap-4038	66	18	12	12	NUM
ap-4038	66	19	]	]	PUNCT
ap-4038	66	20	.	.	PUNCT
ap-4038	67	1	provided	provide	VERB
ap-4038	67	2	that	that	SCONJ
ap-4038	67	3	suitable	suitable	ADJ
ap-4038	67	4	finite	finite	ADJ
ap-4038	67	5	dimensional	dimensional	ADJ
ap-4038	67	6	sub	sub	NOUN
ap-4038	67	7	-	-	NOUN
ap-4038	67	8	spaces	space	NOUN
ap-4038	67	9	sh	sh	PROPN
ap-4038	67	10	⊂	⊂	PROPN
ap-4038	67	11	s	s	PROPN
ap-4038	67	12	,	,	PUNCT
ap-4038	67	13	vh	vh	PROPN
ap-4038	67	14	⊂	⊂	PROPN
ap-4038	67	15	v	v	PROPN
ap-4038	67	16	and	and	CCONJ
ap-4038	67	17	qh	qh	PROPN
ap-4038	67	18	⊂	⊂	PROPN
ap-4038	67	19	q	q	X
ap-4038	67	20	are	be	AUX
ap-4038	67	21	defined	define	VERB
ap-4038	67	22	,	,	PUNCT
ap-4038	67	23	the	the	DET
ap-4038	67	24	discretized	discretized	ADJ
ap-4038	67	25	problem	problem	NOUN
ap-4038	67	26	states	state	NOUN
ap-4038	67	27	:	:	PUNCT
ap-4038	67	28	find	find	VERB
ap-4038	67	29	vh	vh	PROPN
ap-4038	67	30	∈	∈	PROPN
ap-4038	67	31	sh	sh	PROPN
ap-4038	67	32	and	and	CCONJ
ap-4038	67	33	ph	ph	PROPN
ap-4038	67	34	∈	∈	PROPN
ap-4038	67	35	qh	qh	NOUN
ap-4038	68	1	such	such	ADJ
ap-4038	68	2	that	that	SCONJ
ap-4038	68	3	∀wh	∀wh	PROPN
ap-4038	68	4	∈	∈	PROPN
ap-4038	68	5	vh,∀qh	vh,∀qh	NOUN
ap-4038	68	6	∈	∈	PROPN
ap-4038	68	7	qh:∫	qh:∫	PROPN
ap-4038	68	8	ω	ω	PROPN
ap-4038	68	9	ρjw	ρjw	PROPN
ap-4038	68	10	h	h	NOUN
ap-4038	68	11	∂v	∂v	PROPN
ap-4038	68	12	h	h	PROPN
ap-4038	69	1	∂t	∂t	PROPN
ap-4038	69	2	dx+	dx+	PROPN
ap-4038	69	3	∫	∫	PROPN
ap-4038	69	4	ω	ω	NUM
ap-4038	69	5	ρjw	ρjw	PROPN
ap-4038	69	6	h	h	NOUN
ap-4038	69	7	·	·	PUNCT
ap-4038	69	8	(	(	PUNCT
ap-4038	69	9	vh	vh	PROPN
ap-4038	69	10	·	·	PUNCT
ap-4038	70	1	∇)vh	∇)vh	NUM
ap-4038	70	2	dx	dx	PROPN
ap-4038	70	3	+	+	CCONJ
ap-4038	70	4	∫	∫	PROPN
ap-4038	70	5	ω	ω	PROPN
ap-4038	70	6	∇wh	∇wh	VERB
ap-4038	70	7	:	:	PUNCT
ap-4038	70	8	τ	τ	PROPN
ap-4038	70	9	(	(	PUNCT
ap-4038	70	10	d(vh	d(vh	PROPN
ap-4038	70	11	)	)	PUNCT
ap-4038	70	12	)	)	PUNCT
ap-4038	71	1	dx−	dx−	NUM
ap-4038	71	2	∫	∫	PROPN
ap-4038	71	3	ω	ω	PROPN
ap-4038	71	4	(	(	PUNCT
ap-4038	71	5	∇	∇	X
ap-4038	71	6	·	·	PUNCT
ap-4038	71	7	wh)ph	wh)ph	X
ap-4038	71	8	dx	dx	PROPN
ap-4038	72	1	−	−	PROPN
ap-4038	72	2	∫	∫	PROPN
ap-4038	72	3	ω	ω	NUM
ap-4038	72	4	wh	wh	PROPN
ap-4038	72	5	·	·	PUNCT
ap-4038	73	1	bdx−	bdx−	ADP
ap-4038	73	2	∫	∫	PROPN
ap-4038	73	3	γn	γn	PART
ap-4038	73	4	wh	wh	NOUN
ap-4038	73	5	·	·	PUNCT
ap-4038	73	6	hds+	hds+	PUNCT
ap-4038	74	1	∫	∫	PROPN
ap-4038	74	2	ω	ω	NUM
ap-4038	74	3	qh(∇	qh(∇	PROPN
ap-4038	74	4	·	·	SYM
ap-4038	74	5	vh	vh	PROPN
ap-4038	74	6	)	)	PUNCT
ap-4038	74	7	dx	dx	PROPN
ap-4038	75	1	+	+	CCONJ
ap-4038	75	2	∑	∑	PROPN
ap-4038	75	3	el	el	PROPN
ap-4038	75	4	∫	∫	PROPN
ap-4038	75	5	ωe	ωe	PROPN
ap-4038	75	6	τsup	τsup	ADJ
ap-4038	75	7	g(vh	g(vh	PROPN
ap-4038	75	8	·	·	PUNCT
ap-4038	75	9	∇)wh	∇)wh	X
ap-4038	75	10	·	·	SYM
ap-4038	75	11	r(vh	r(vh	PROPN
ap-4038	75	12	,	,	PUNCT
ap-4038	75	13	ph	ph	ADJ
ap-4038	75	14	)	)	PUNCT
ap-4038	75	15	dx	dx	PROPN
ap-4038	76	1	+	+	CCONJ
ap-4038	76	2	∑	∑	PROPN
ap-4038	76	3	el	el	PROPN
ap-4038	76	4	∫	∫	PROPN
ap-4038	76	5	ωe	ωe	ADV
ap-4038	76	6	τp	τp	PROPN
ap-4038	76	7	sp	sp	ADP
ap-4038	76	8	g	g	PROPN
ap-4038	76	9	1	1	NUM
ap-4038	76	10	ρ	ρ	PROPN
ap-4038	76	11	∇qh	∇qh	PROPN
ap-4038	76	12	·	·	PUNCT
ap-4038	76	13	r(vh	r(vh	PROPN
ap-4038	76	14	,	,	PUNCT
ap-4038	76	15	ph	ph	ADJ
ap-4038	76	16	)	)	PUNCT
ap-4038	76	17	dx	dx	PROPN
ap-4038	77	1	=	=	SYM
ap-4038	77	2	0	0	PROPN
ap-4038	77	3	,	,	PUNCT
ap-4038	77	4	(	(	PUNCT
ap-4038	77	5	5	5	NUM
ap-4038	77	6	)	)	PUNCT
ap-4038	77	7	where	where	SCONJ
ap-4038	77	8	r(vh	r(vh	PROPN
ap-4038	77	9	,	,	PUNCT
ap-4038	77	10	ph	ph	ADJ
ap-4038	77	11	)	)	PUNCT
ap-4038	77	12	denotes	denote	NOUN
ap-4038	77	13	the	the	DET
ap-4038	77	14	residuum	residuum	NOUN
ap-4038	77	15	of	of	ADP
ap-4038	77	16	the	the	DET
ap-4038	77	17	linear	linear	ADJ
ap-4038	77	18	momentum	momentum	NOUN
ap-4038	77	19	balance	balance	NOUN
ap-4038	77	20	part	part	NOUN
ap-4038	77	21	of	of	ADP
ap-4038	77	22	(	(	PUNCT
ap-4038	77	23	1	1	NUM
ap-4038	77	24	)	)	PUNCT
ap-4038	77	25	.	.	PUNCT
ap-4038	78	1	the	the	DET
ap-4038	78	2	need	need	NOUN
ap-4038	78	3	for	for	ADP
ap-4038	78	4	stabilization	stabilization	NOUN
ap-4038	78	5	follows	follow	VERB
ap-4038	78	6	from	from	ADP
ap-4038	78	7	the	the	DET
ap-4038	78	8	use	use	NOUN
ap-4038	78	9	of	of	ADP
ap-4038	78	10	linear	linear	ADJ
ap-4038	78	11	tetrahedrons	tetrahedron	NOUN
ap-4038	78	12	(	(	PUNCT
ap-4038	78	13	i.e.	i.e.	X
ap-4038	78	14	both	both	CCONJ
ap-4038	78	15	velocity	velocity	NOUN
ap-4038	78	16	and	and	CCONJ
ap-4038	78	17	pressure	pressure	NOUN
ap-4038	78	18	fields	field	NOUN
ap-4038	78	19	are	be	AUX
ap-4038	78	20	approximated	approximate	VERB
ap-4038	78	21	by	by	ADP
ap-4038	78	22	linear	linear	PROPN
ap-4038	78	23	functions	function	NOUN
ap-4038	78	24	)	)	PUNCT
ap-4038	78	25	in	in	ADP
ap-4038	78	26	order	order	NOUN
ap-4038	78	27	to	to	PART
ap-4038	78	28	circumvent	circumvent	VERB
ap-4038	78	29	issues	issue	NOUN
ap-4038	78	30	with	with	ADP
ap-4038	78	31	the	the	DET
ap-4038	78	32	lbb	lbb	PROPN
ap-4038	78	33	condition	condition	NOUN
ap-4038	78	34	,	,	PUNCT
ap-4038	78	35	see	see	VERB
ap-4038	78	36	[	[	X
ap-4038	78	37	20	20	NUM
ap-4038	78	38	]	]	PUNCT
ap-4038	78	39	for	for	ADP
ap-4038	78	40	details	detail	NOUN
ap-4038	78	41	.	.	PUNCT
ap-4038	79	1	note	note	VERB
ap-4038	79	2	that	that	SCONJ
ap-4038	79	3	the	the	DET
ap-4038	79	4	effective	effective	ADJ
ap-4038	79	5	density	density	NOUN
ap-4038	79	6	ρ	ρ	NOUN
ap-4038	79	7	and	and	CCONJ
ap-4038	79	8	also	also	ADV
ap-4038	79	9	other	other	ADJ
ap-4038	79	10	material	material	NOUN
ap-4038	79	11	parameters	parameter	NOUN
ap-4038	79	12	such	such	ADJ
ap-4038	79	13	as	as	ADP
ap-4038	79	14	viscosity	viscosity	NOUN
ap-4038	79	15	µ	µ	NOUN
ap-4038	79	16	,	,	PUNCT
ap-4038	79	17	have	have	VERB
ap-4038	79	18	to	to	PART
ap-4038	79	19	be	be	AUX
ap-4038	79	20	averaged	average	VERB
ap-4038	79	21	in	in	ADP
ap-4038	79	22	elements	element	NOUN
ap-4038	79	23	which	which	PRON
ap-4038	79	24	are	be	AUX
ap-4038	79	25	cut	cut	VERB
ap-4038	79	26	by	by	ADP
ap-4038	79	27	the	the	DET
ap-4038	79	28	interface	interface	NOUN
ap-4038	79	29	.	.	PUNCT
ap-4038	80	1	averaging	average	VERB
ap-4038	80	2	is	be	AUX
ap-4038	80	3	performed	perform	VERB
ap-4038	80	4	using	use	VERB
ap-4038	80	5	the	the	DET
ap-4038	80	6	original	original	ADJ
ap-4038	80	7	material	material	NOUN
ap-4038	80	8	parameters	parameter	NOUN
ap-4038	80	9	of	of	ADP
ap-4038	80	10	both	both	DET
ap-4038	80	11	fluids	fluid	NOUN
ap-4038	80	12	,	,	PUNCT
ap-4038	80	13	which	which	PRON
ap-4038	80	14	are	be	AUX
ap-4038	80	15	weighted	weight	VERB
ap-4038	80	16	by	by	ADP
ap-4038	80	17	the	the	DET
ap-4038	80	18	respective	respective	ADJ
ap-4038	80	19	volume	volume	NOUN
ap-4038	80	20	fractions	fraction	NOUN
ap-4038	80	21	of	of	ADP
ap-4038	80	22	the	the	DET
ap-4038	80	23	fluids	fluid	NOUN
ap-4038	80	24	in	in	ADP
ap-4038	80	25	the	the	DET
ap-4038	80	26	cut	cut	NOUN
ap-4038	80	27	element	element	NOUN
ap-4038	80	28	.	.	PUNCT
ap-4038	81	1	the	the	DET
ap-4038	81	2	averaging	averaging	NOUN
ap-4038	81	3	is	be	AUX
ap-4038	81	4	computed	compute	VERB
ap-4038	81	5	as	as	ADP
ap-4038	81	6	µ	µ	NOUN
ap-4038	81	7	=	=	SYM
ap-4038	81	8	fµ1	fµ1	NOUN
ap-4038	81	9	+	+	CCONJ
ap-4038	81	10	(	(	PUNCT
ap-4038	81	11	1−	1−	NUM
ap-4038	81	12	f)µ2	f)µ2	PROPN
ap-4038	81	13	,	,	PUNCT
ap-4038	81	14	(	(	PUNCT
ap-4038	81	15	6	6	X
ap-4038	81	16	)	)	PUNCT
ap-4038	81	17	ρ	ρ	PROPN
ap-4038	81	18	=	=	PUNCT
ap-4038	82	1	fρ1	fρ1	PROPN
ap-4038	83	1	+	+	CCONJ
ap-4038	83	2	(	(	PUNCT
ap-4038	83	3	1−	1−	NUM
ap-4038	83	4	f)ρ2	f)ρ2	NOUN
ap-4038	83	5	,	,	PUNCT
ap-4038	83	6	(	(	PUNCT
ap-4038	83	7	7	7	X
ap-4038	83	8	)	)	PUNCT
ap-4038	83	9	106	106	NUM
ap-4038	83	10	vol	vol	NOUN
ap-4038	83	11	.	.	PUNCT
ap-4038	84	1	57	57	NUM
ap-4038	84	2	no	no	NOUN
ap-4038	84	3	.	.	PUNCT
ap-4038	85	1	2/2017	2/2017	NUM
ap-4038	85	2	implementation	implementation	NOUN
ap-4038	85	3	of	of	ADP
ap-4038	85	4	a	a	DET
ap-4038	85	5	3d	3d	NUM
ap-4038	85	6	vof	vof	NOUN
ap-4038	85	7	tracking	track	VERB
ap-4038	85	8	algorithm	algorithm	NOUN
ap-4038	85	9	where	where	SCONJ
ap-4038	85	10	f	f	PROPN
ap-4038	85	11	stands	stand	VERB
ap-4038	85	12	for	for	ADP
ap-4038	85	13	the	the	DET
ap-4038	85	14	vof	vof	NOUN
ap-4038	85	15	value	value	NOUN
ap-4038	85	16	at	at	ADP
ap-4038	85	17	the	the	DET
ap-4038	85	18	cut	cut	NOUN
ap-4038	85	19	element	element	NOUN
ap-4038	85	20	.	.	PUNCT
ap-4038	86	1	additional	additional	ADJ
ap-4038	86	2	stabilization	stabilization	NOUN
ap-4038	86	3	terms	term	NOUN
ap-4038	86	4	are	be	AUX
ap-4038	86	5	defined	define	VERB
ap-4038	86	6	only	only	ADV
ap-4038	86	7	element	element	NOUN
ap-4038	86	8	-	-	ADJ
ap-4038	86	9	wise	wise	ADJ
ap-4038	86	10	,	,	PUNCT
ap-4038	86	11	and	and	CCONJ
ap-4038	86	12	are	be	AUX
ap-4038	86	13	added	add	VERB
ap-4038	86	14	as	as	ADP
ap-4038	86	15	the	the	DET
ap-4038	86	16	sum	sum	NOUN
ap-4038	86	17	over	over	ADP
ap-4038	86	18	all	all	DET
ap-4038	86	19	elements	element	NOUN
ap-4038	86	20	ωe	ωe	PRON
ap-4038	86	21	.	.	PUNCT
ap-4038	87	1	parameters	parameter	NOUN
ap-4038	87	2	τsup	τsup	VERB
ap-4038	87	3	g	g	PROPN
ap-4038	87	4	and	and	CCONJ
ap-4038	87	5	τp	τp	PROPN
ap-4038	87	6	sp	sp	ADP
ap-4038	87	7	g	g	PROPN
ap-4038	87	8	depend	depend	VERB
ap-4038	87	9	on	on	ADP
ap-4038	87	10	the	the	DET
ap-4038	87	11	velocity	velocity	NOUN
ap-4038	87	12	and	and	CCONJ
ap-4038	87	13	material	material	NOUN
ap-4038	87	14	parameters	parameter	NOUN
ap-4038	87	15	.	.	PUNCT
ap-4038	88	1	details	detail	NOUN
ap-4038	88	2	on	on	ADP
ap-4038	88	3	how	how	SCONJ
ap-4038	88	4	they	they	PRON
ap-4038	88	5	are	be	AUX
ap-4038	88	6	determined	determined	ADJ
ap-4038	88	7	can	can	AUX
ap-4038	88	8	be	be	AUX
ap-4038	88	9	found	find	VERB
ap-4038	88	10	in	in	ADP
ap-4038	88	11	[	[	X
ap-4038	88	12	12	12	NUM
ap-4038	88	13	,	,	PUNCT
ap-4038	88	14	13	13	NUM
ap-4038	88	15	]	]	PUNCT
ap-4038	88	16	.	.	PUNCT
ap-4038	89	1	3	3	X
ap-4038	89	2	.	.	X
ap-4038	89	3	evolution	evolution	NOUN
ap-4038	89	4	of	of	ADP
ap-4038	89	5	the	the	DET
ap-4038	89	6	interface	interface	NOUN
ap-4038	89	7	this	this	DET
ap-4038	89	8	section	section	NOUN
ap-4038	89	9	presents	present	VERB
ap-4038	89	10	in	in	ADP
ap-4038	89	11	detail	detail	NOUN
ap-4038	89	12	the	the	DET
ap-4038	89	13	computational	computational	ADJ
ap-4038	89	14	representation	representation	NOUN
ap-4038	89	15	of	of	ADP
ap-4038	89	16	the	the	DET
ap-4038	89	17	interface	interface	NOUN
ap-4038	89	18	between	between	ADP
ap-4038	89	19	the	the	DET
ap-4038	89	20	two	two	NUM
ap-4038	89	21	fluids	fluid	NOUN
ap-4038	89	22	,	,	PUNCT
ap-4038	89	23	based	base	VERB
ap-4038	89	24	on	on	ADP
ap-4038	89	25	the	the	DET
ap-4038	89	26	vof	vof	NOUN
ap-4038	89	27	technique	technique	NOUN
ap-4038	89	28	.	.	PUNCT
ap-4038	90	1	first	first	ADV
ap-4038	90	2	,	,	PUNCT
ap-4038	90	3	we	we	PRON
ap-4038	90	4	present	present	VERB
ap-4038	90	5	the	the	DET
ap-4038	90	6	algorithms	algorithm	NOUN
ap-4038	90	7	for	for	ADP
ap-4038	90	8	interface	interface	NOUN
ap-4038	90	9	reconstruction	reconstruction	NOUN
ap-4038	90	10	and	and	CCONJ
ap-4038	90	11	tracking	tracking	NOUN
ap-4038	90	12	.	.	PUNCT
ap-4038	91	1	then	then	ADV
ap-4038	91	2	there	there	PRON
ap-4038	91	3	is	be	VERB
ap-4038	91	4	a	a	DET
ap-4038	91	5	description	description	NOUN
ap-4038	91	6	of	of	ADP
ap-4038	91	7	the	the	DET
ap-4038	91	8	method	method	NOUN
ap-4038	91	9	for	for	ADP
ap-4038	91	10	truncating	truncate	VERB
ap-4038	91	11	the	the	DET
ap-4038	91	12	polyhedra	polyhedra	NOUN
ap-4038	91	13	,	,	PUNCT
ap-4038	91	14	based	base	VERB
ap-4038	91	15	on	on	ADP
ap-4038	91	16	bsp	bsp	NOUN
ap-4038	91	17	trees	tree	NOUN
ap-4038	91	18	.	.	PUNCT
ap-4038	92	1	it	it	PRON
ap-4038	92	2	should	should	AUX
ap-4038	92	3	be	be	AUX
ap-4038	92	4	noted	note	VERB
ap-4038	92	5	that	that	SCONJ
ap-4038	92	6	there	there	PRON
ap-4038	92	7	is	be	VERB
ap-4038	92	8	only	only	ADV
ap-4038	92	9	one	one	NUM
ap-4038	92	10	-	-	PUNCT
ap-4038	92	11	way	way	NOUN
ap-4038	92	12	coupling	coupling	NOUN
ap-4038	92	13	between	between	ADP
ap-4038	92	14	solving	solve	VERB
ap-4038	92	15	(	(	PUNCT
ap-4038	92	16	5	5	NUM
ap-4038	92	17	)	)	PUNCT
ap-4038	92	18	and	and	CCONJ
ap-4038	92	19	interface	interface	NOUN
ap-4038	92	20	evolution	evolution	NOUN
ap-4038	92	21	;	;	PUNCT
ap-4038	92	22	the	the	DET
ap-4038	92	23	interface	interface	NOUN
ap-4038	92	24	advection	advection	NOUN
ap-4038	92	25	is	be	AUX
ap-4038	92	26	computed	compute	VERB
ap-4038	92	27	with	with	ADP
ap-4038	92	28	the	the	DET
ap-4038	92	29	given	give	VERB
ap-4038	92	30	velocity	velocity	NOUN
ap-4038	92	31	field	field	NOUN
ap-4038	92	32	obtained	obtain	VERB
ap-4038	92	33	as	as	ADP
ap-4038	92	34	a	a	DET
ap-4038	92	35	solution	solution	NOUN
ap-4038	92	36	to	to	ADP
ap-4038	92	37	(	(	PUNCT
ap-4038	92	38	5	5	NUM
ap-4038	92	39	)	)	PUNCT
ap-4038	92	40	.	.	PUNCT
ap-4038	93	1	the	the	DET
ap-4038	93	2	position	position	NOUN
ap-4038	93	3	of	of	ADP
ap-4038	93	4	the	the	DET
ap-4038	93	5	interface	interface	NOUN
ap-4038	93	6	can	can	AUX
ap-4038	93	7	be	be	AUX
ap-4038	93	8	obtained	obtain	VERB
ap-4038	93	9	from	from	ADP
ap-4038	93	10	the	the	DET
ap-4038	93	11	vof	vof	NOUN
ap-4038	93	12	spatial	spatial	ADJ
ap-4038	93	13	distribution	distribution	NOUN
ap-4038	93	14	.	.	PUNCT
ap-4038	94	1	the	the	DET
ap-4038	94	2	interface	interface	NOUN
ap-4038	94	3	is	be	AUX
ap-4038	94	4	located	locate	VERB
ap-4038	94	5	either	either	CCONJ
ap-4038	94	6	between	between	ADP
ap-4038	94	7	two	two	NUM
ap-4038	94	8	elements	element	NOUN
ap-4038	94	9	,	,	PUNCT
ap-4038	94	10	when	when	SCONJ
ap-4038	94	11	one	one	PRON
ap-4038	94	12	is	be	AUX
ap-4038	94	13	completely	completely	ADV
ap-4038	94	14	filled	fill	VERB
ap-4038	94	15	with	with	ADP
ap-4038	94	16	the	the	DET
ap-4038	94	17	reference	reference	NOUN
ap-4038	94	18	fluid	fluid	NOUN
ap-4038	94	19	(	(	PUNCT
ap-4038	94	20	vof	vof	NOUN
ap-4038	94	21	=	=	NOUN
ap-4038	94	22	1	1	X
ap-4038	94	23	)	)	PUNCT
ap-4038	94	24	while	while	SCONJ
ap-4038	94	25	the	the	DET
ap-4038	94	26	other	other	ADJ
ap-4038	94	27	is	be	AUX
ap-4038	94	28	fully	fully	ADV
ap-4038	94	29	filled	fill	VERB
ap-4038	94	30	with	with	ADP
ap-4038	94	31	the	the	DET
ap-4038	94	32	second	second	ADJ
ap-4038	94	33	fluid	fluid	NOUN
ap-4038	94	34	(	(	PUNCT
ap-4038	94	35	vof	vof	NOUN
ap-4038	94	36	=	=	NOUN
ap-4038	94	37	0	0	NUM
ap-4038	94	38	)	)	PUNCT
ap-4038	94	39	,	,	PUNCT
ap-4038	94	40	or	or	CCONJ
ap-4038	94	41	it	it	PRON
ap-4038	94	42	passes	pass	VERB
ap-4038	94	43	through	through	ADP
ap-4038	94	44	the	the	DET
ap-4038	94	45	partially	partially	ADV
ap-4038	94	46	filled	fill	VERB
ap-4038	94	47	element	element	NOUN
ap-4038	94	48	.	.	PUNCT
ap-4038	95	1	on	on	ADP
ap-4038	95	2	every	every	DET
ap-4038	95	3	partially	partially	ADV
ap-4038	95	4	filled	fill	VERB
ap-4038	95	5	element	element	NOUN
ap-4038	95	6	,	,	PUNCT
ap-4038	95	7	we	we	PRON
ap-4038	95	8	adopted	adopt	VERB
ap-4038	95	9	a	a	DET
ap-4038	95	10	piece	piece	NOUN
ap-4038	95	11	-	-	PUNCT
ap-4038	95	12	wise	wise	ADJ
ap-4038	95	13	linear	linear	ADJ
ap-4038	95	14	approximation	approximation	NOUN
ap-4038	95	15	of	of	ADP
ap-4038	95	16	the	the	DET
ap-4038	95	17	interface	interface	NOUN
ap-4038	95	18	by	by	ADP
ap-4038	95	19	the	the	DET
ap-4038	95	20	line	line	NOUN
ap-4038	95	21	segment	segment	NOUN
ap-4038	95	22	in	in	ADP
ap-4038	95	23	2d	2d	NUM
ap-4038	95	24	and	and	CCONJ
ap-4038	95	25	the	the	DET
ap-4038	95	26	planar	planar	ADJ
ap-4038	95	27	segment	segment	NOUN
ap-4038	95	28	in	in	ADP
ap-4038	95	29	3d	3d	NUM
ap-4038	95	30	.	.	PUNCT
ap-4038	96	1	this	this	PRON
ap-4038	96	2	is	be	AUX
ap-4038	96	3	sometimes	sometimes	ADV
ap-4038	96	4	referred	refer	VERB
ap-4038	96	5	to	to	ADP
ap-4038	96	6	as	as	ADP
ap-4038	96	7	plic	plic	NOUN
ap-4038	96	8	-	-	PUNCT
ap-4038	96	9	vof	vof	NOUN
ap-4038	96	10	[	[	X
ap-4038	96	11	5	5	NUM
ap-4038	96	12	]	]	PUNCT
ap-4038	96	13	.	.	PUNCT
ap-4038	97	1	the	the	DET
ap-4038	97	2	interface	interface	NOUN
ap-4038	97	3	evolution	evolution	NOUN
ap-4038	97	4	algorithm	algorithm	PROPN
ap-4038	97	5	is	be	AUX
ap-4038	97	6	required	require	VERB
ap-4038	97	7	in	in	ADP
ap-4038	97	8	order	order	NOUN
ap-4038	97	9	to	to	PART
ap-4038	97	10	update	update	VERB
ap-4038	97	11	the	the	DET
ap-4038	97	12	interface	interface	NOUN
ap-4038	97	13	position	position	NOUN
ap-4038	97	14	with	with	ADP
ap-4038	97	15	the	the	DET
ap-4038	97	16	flow	flow	NOUN
ap-4038	97	17	.	.	PUNCT
ap-4038	98	1	the	the	DET
ap-4038	98	2	algorithm	algorithm	NOUN
ap-4038	98	3	presented	present	VERB
ap-4038	98	4	here	here	ADV
ap-4038	98	5	is	be	AUX
ap-4038	98	6	based	base	VERB
ap-4038	98	7	on	on	ADP
ap-4038	98	8	the	the	DET
ap-4038	98	9	paper	paper	NOUN
ap-4038	98	10	by	by	ADP
ap-4038	98	11	shahbazi	shahbazi	NOUN
ap-4038	98	12	et	et	PROPN
ap-4038	98	13	al	al	PROPN
ap-4038	98	14	.	.	PUNCT
ap-4038	99	1	(	(	PUNCT
ap-4038	99	2	see	see	VERB
ap-4038	99	3	[	[	X
ap-4038	99	4	15	15	NUM
ap-4038	99	5	]	]	NUM
ap-4038	99	6	)	)	PUNCT
ap-4038	99	7	,	,	PUNCT
ap-4038	99	8	and	and	CCONJ
ap-4038	99	9	consists	consist	VERB
ap-4038	99	10	of	of	ADP
ap-4038	99	11	three	three	NUM
ap-4038	99	12	parts	part	NOUN
ap-4038	99	13	(	(	PUNCT
ap-4038	99	14	see	see	VERB
ap-4038	99	15	also	also	ADV
ap-4038	99	16	figure	figure	VERB
ap-4038	99	17	1	1	NUM
ap-4038	99	18	):	):	PUNCT
ap-4038	99	19	(	(	PUNCT
ap-4038	99	20	1	1	NUM
ap-4038	99	21	.	.	PUNCT
ap-4038	99	22	)	)	PUNCT
ap-4038	100	1	the	the	DET
ap-4038	100	2	lagrangian	lagrangian	ADJ
ap-4038	100	3	part	part	NOUN
ap-4038	100	4	,	,	PUNCT
ap-4038	100	5	in	in	ADP
ap-4038	100	6	which	which	PRON
ap-4038	100	7	the	the	DET
ap-4038	100	8	original	original	ADJ
ap-4038	100	9	mesh	mesh	NOUN
ap-4038	100	10	is	be	AUX
ap-4038	100	11	projected	project	VERB
ap-4038	100	12	along	along	ADP
ap-4038	100	13	trajectories	trajectory	NOUN
ap-4038	100	14	.	.	PUNCT
ap-4038	101	1	this	this	PRON
ap-4038	101	2	is	be	AUX
ap-4038	101	3	achieved	achieve	VERB
ap-4038	101	4	by	by	ADP
ap-4038	101	5	advecting	advect	VERB
ap-4038	101	6	the	the	DET
ap-4038	101	7	nodal	nodal	NOUN
ap-4038	101	8	position	position	NOUN
ap-4038	101	9	with	with	ADP
ap-4038	101	10	the	the	DET
ap-4038	101	11	flow	flow	NOUN
ap-4038	101	12	.	.	PUNCT
ap-4038	102	1	the	the	DET
ap-4038	102	2	time	time	NOUN
ap-4038	102	3	integration	integration	NOUN
ap-4038	102	4	is	be	AUX
ap-4038	102	5	based	base	VERB
ap-4038	102	6	on	on	ADP
ap-4038	102	7	forward	forward	ADJ
ap-4038	102	8	trajectory	trajectory	NOUN
ap-4038	102	9	remapping	remappe	VERB
ap-4038	102	10	to	to	PART
ap-4038	102	11	evolve	evolve	VERB
ap-4038	102	12	positions	position	NOUN
ap-4038	102	13	and	and	CCONJ
ap-4038	102	14	volumes	volume	NOUN
ap-4038	102	15	in	in	ADP
ap-4038	102	16	time	time	NOUN
ap-4038	102	17	.	.	PUNCT
ap-4038	103	1	to	to	PART
ap-4038	103	2	determine	determine	VERB
ap-4038	103	3	the	the	DET
ap-4038	103	4	trajectories	trajectory	NOUN
ap-4038	103	5	,	,	PUNCT
ap-4038	103	6	the	the	DET
ap-4038	103	7	velocity	velocity	NOUN
ap-4038	103	8	field	field	NOUN
ap-4038	103	9	is	be	AUX
ap-4038	103	10	integrated	integrate	VERB
ap-4038	103	11	from	from	ADP
ap-4038	103	12	the	the	DET
ap-4038	103	13	original	original	ADJ
ap-4038	103	14	grid	grid	NOUN
ap-4038	103	15	to	to	ADP
ap-4038	103	16	the	the	DET
ap-4038	103	17	updated	update	VERB
ap-4038	103	18	grid	grid	NOUN
ap-4038	103	19	xl(tt+∆t	xl(tt+∆t	PUNCT
ap-4038	103	20	)	)	PUNCT
ap-4038	104	1	=	=	SYM
ap-4038	104	2	x(t	x(t	PROPN
ap-4038	104	3	)	)	PUNCT
ap-4038	105	1	+	+	NUM
ap-4038	105	2	∫	∫	PROPN
ap-4038	105	3	t+∆t	t+∆t	PROPN
ap-4038	105	4	t	t	PROPN
ap-4038	105	5	v	v	ADP
ap-4038	105	6	dt	dt	X
ap-4038	105	7	,	,	PUNCT
ap-4038	105	8	(	(	PUNCT
ap-4038	105	9	8)	8)	NUM
ap-4038	105	10	where	where	SCONJ
ap-4038	105	11	xl	xl	PROPN
ap-4038	105	12	is	be	AUX
ap-4038	105	13	the	the	DET
ap-4038	105	14	coordinate	coordinate	NOUN
ap-4038	105	15	of	of	ADP
ap-4038	105	16	the	the	DET
ap-4038	105	17	updated	update	VERB
ap-4038	105	18	(	(	PUNCT
ap-4038	105	19	lagrangian	lagrangian	ADJ
ap-4038	105	20	)	)	PUNCT
ap-4038	105	21	grid	grid	NOUN
ap-4038	105	22	and	and	CCONJ
ap-4038	105	23	the	the	DET
ap-4038	105	24	x	x	NOUN
ap-4038	105	25	is	be	AUX
ap-4038	105	26	the	the	DET
ap-4038	105	27	original	original	ADJ
ap-4038	105	28	coordinate	coordinate	NOUN
ap-4038	105	29	.	.	PUNCT
ap-4038	106	1	the	the	DET
ap-4038	106	2	discretized	discretized	ADJ
ap-4038	106	3	form	form	NOUN
ap-4038	106	4	of	of	ADP
ap-4038	106	5	equation	equation	NOUN
ap-4038	106	6	(	(	PUNCT
ap-4038	106	7	8)	8)	NUM
ap-4038	106	8	employing	employ	VERB
ap-4038	106	9	the	the	DET
ap-4038	106	10	midpoint	midpoint	NOUN
ap-4038	106	11	runge	runge	NOUN
ap-4038	106	12	-	-	PUNCT
ap-4038	106	13	kutta	kutta	NOUN
ap-4038	106	14	method	method	NOUN
ap-4038	106	15	is	be	AUX
ap-4038	106	16	k1	k1	NOUN
ap-4038	106	17	=	=	SYM
ap-4038	106	18	∆tv(t	∆tv(t	NOUN
ap-4038	106	19	,	,	PUNCT
ap-4038	106	20	x(t	x(t	PROPN
ap-4038	106	21	)	)	PUNCT
ap-4038	106	22	)	)	PUNCT
ap-4038	106	23	,	,	PUNCT
ap-4038	106	24	k2	k2	PROPN
ap-4038	106	25	=	=	SYM
ap-4038	106	26	∆tv(t+	∆tv(t+	PROPN
ap-4038	106	27	∆t	∆t	PROPN
ap-4038	106	28	,	,	PUNCT
ap-4038	106	29	x(t	x(t	PROPN
ap-4038	106	30	)	)	PUNCT
ap-4038	107	1	+	+	CCONJ
ap-4038	107	2	1	1	NUM
ap-4038	107	3	2k1	2k1	NUM
ap-4038	107	4	)	)	PUNCT
ap-4038	107	5	,	,	PUNCT
ap-4038	107	6	xt+∆t	xt+∆t	X
ap-4038	108	1	l	l	NOUN
ap-4038	108	2	=	=	SYM
ap-4038	108	3	x(t	x(t	PROPN
ap-4038	108	4	)	)	PUNCT
ap-4038	109	1	+	+	CCONJ
ap-4038	109	2	k2	k2	ADJ
ap-4038	109	3	.	.	PUNCT
ap-4038	109	4	time	time	NOUN
ap-4038	109	5	step	step	NOUN
ap-4038	109	6	∆t	∆t	PROPN
ap-4038	109	7	is	be	AUX
ap-4038	109	8	taken	take	VERB
ap-4038	109	9	to	to	PART
ap-4038	109	10	be	be	AUX
ap-4038	109	11	equal	equal	ADJ
ap-4038	109	12	to	to	ADP
ap-4038	109	13	the	the	DET
ap-4038	109	14	time	time	NOUN
ap-4038	109	15	step	step	NOUN
ap-4038	109	16	used	use	VERB
ap-4038	109	17	for	for	ADP
ap-4038	109	18	solving	solve	VERB
ap-4038	109	19	(	(	PUNCT
ap-4038	109	20	5	5	NUM
ap-4038	109	21	)	)	PUNCT
ap-4038	109	22	.	.	PUNCT
ap-4038	110	1	in	in	ADP
ap-4038	110	2	order	order	NOUN
ap-4038	110	3	to	to	PART
ap-4038	110	4	satisfy	satisfy	VERB
ap-4038	110	5	the	the	DET
ap-4038	110	6	cfl	cfl	NOUN
ap-4038	110	7	condition	condition	NOUN
ap-4038	110	8	,	,	PUNCT
ap-4038	110	9	we	we	PRON
ap-4038	110	10	used	use	VERB
ap-4038	110	11	adaptive	adaptive	ADJ
ap-4038	110	12	time	time	NOUN
ap-4038	110	13	stepping	step	VERB
ap-4038	110	14	where	where	SCONJ
ap-4038	110	15	the	the	DET
ap-4038	110	16	time	time	NOUN
ap-4038	110	17	step	step	NOUN
ap-4038	110	18	is	be	AUX
ap-4038	110	19	determined	determine	VERB
ap-4038	110	20	by	by	ADP
ap-4038	110	21	the	the	DET
ap-4038	110	22	element	element	NOUN
ap-4038	110	23	with	with	ADP
ap-4038	110	24	the	the	DET
ap-4038	110	25	most	most	ADV
ap-4038	110	26	unfavorable	unfavorable	ADJ
ap-4038	110	27	ratio	ratio	NOUN
ap-4038	110	28	h/||vh||	h/||vh||	NOUN
ap-4038	110	29	,	,	PUNCT
ap-4038	110	30	given	give	VERB
ap-4038	110	31	the	the	DET
ap-4038	110	32	velocity	velocity	NOUN
ap-4038	110	33	field	field	NOUN
ap-4038	110	34	previously	previously	ADV
ap-4038	110	35	obtained	obtain	VERB
ap-4038	110	36	by	by	ADP
ap-4038	110	37	solving	solve	VERB
ap-4038	110	38	(	(	PUNCT
ap-4038	110	39	5	5	NUM
ap-4038	110	40	)	)	PUNCT
ap-4038	110	41	.	.	PUNCT
ap-4038	111	1	(	(	PUNCT
ap-4038	111	2	2	2	NUM
ap-4038	111	3	.	.	PUNCT
ap-4038	111	4	)	)	PUNCT
ap-4038	112	1	the	the	DET
ap-4038	112	2	reconstruction	reconstruction	NOUN
ap-4038	112	3	part	part	NOUN
ap-4038	112	4	.	.	PUNCT
ap-4038	113	1	in	in	ADP
ap-4038	113	2	this	this	DET
ap-4038	113	3	step	step	NOUN
ap-4038	113	4	the	the	DET
ap-4038	113	5	fluid	fluid	ADJ
ap-4038	113	6	volumes	volume	NOUN
ap-4038	113	7	are	be	AUX
ap-4038	113	8	reconstructed	reconstruct	VERB
ap-4038	113	9	on	on	ADP
ap-4038	113	10	the	the	DET
ap-4038	113	11	updated	update	VERB
ap-4038	113	12	grid	grid	NOUN
ap-4038	113	13	,	,	PUNCT
ap-4038	113	14	assuming	assume	VERB
ap-4038	113	15	that	that	SCONJ
ap-4038	113	16	the	the	DET
ap-4038	113	17	vof	vof	NOUN
ap-4038	113	18	values	value	NOUN
ap-4038	113	19	remain	remain	VERB
ap-4038	113	20	constant	constant	ADJ
ap-4038	113	21	during	during	ADP
ap-4038	113	22	the	the	DET
ap-4038	113	23	lagrangian	lagrangian	ADJ
ap-4038	113	24	phase	phase	NOUN
ap-4038	113	25	.	.	PUNCT
ap-4038	114	1	the	the	DET
ap-4038	114	2	3d	3d	PROPN
ap-4038	114	3	polyhedron	polyhedron	NOUN
ap-4038	114	4	representation	representation	NOUN
ap-4038	114	5	of	of	ADP
ap-4038	114	6	the	the	DET
ap-4038	114	7	volume	volume	NOUN
ap-4038	114	8	occupied	occupy	VERB
ap-4038	114	9	by	by	ADP
ap-4038	114	10	the	the	DET
ap-4038	114	11	reference	reference	NOUN
ap-4038	114	12	fluid	fluid	NOUN
ap-4038	114	13	is	be	AUX
ap-4038	114	14	established	establish	VERB
ap-4038	114	15	on	on	ADP
ap-4038	114	16	the	the	DET
ap-4038	114	17	basis	basis	NOUN
ap-4038	114	18	of	of	ADP
ap-4038	114	19	the	the	DET
ap-4038	114	20	spatial	spatial	ADJ
ap-4038	114	21	vof	vof	NOUN
ap-4038	114	22	distribution	distribution	NOUN
ap-4038	114	23	in	in	ADP
ap-4038	114	24	each	each	DET
ap-4038	114	25	cell	cell	NOUN
ap-4038	114	26	and	and	CCONJ
ap-4038	114	27	its	its	PRON
ap-4038	114	28	neighborhood	neighborhood	NOUN
ap-4038	114	29	.	.	PUNCT
ap-4038	115	1	this	this	PRON
ap-4038	115	2	includes	include	VERB
ap-4038	115	3	the	the	DET
ap-4038	115	4	calculation	calculation	NOUN
ap-4038	115	5	of	of	ADP
ap-4038	115	6	the	the	DET
ap-4038	115	7	interface	interface	NOUN
ap-4038	115	8	segment	segment	NOUN
ap-4038	115	9	normal	normal	ADJ
ap-4038	115	10	,	,	PUNCT
ap-4038	115	11	the	the	DET
ap-4038	115	12	segment	segment	NOUN
ap-4038	115	13	constant	constant	ADJ
ap-4038	115	14	,	,	PUNCT
ap-4038	115	15	and	and	CCONJ
ap-4038	115	16	the	the	DET
ap-4038	115	17	material	material	NOUN
ap-4038	115	18	volume	volume	NOUN
ap-4038	115	19	truncation	truncation	NOUN
ap-4038	115	20	at	at	ADP
ap-4038	115	21	each	each	DET
ap-4038	115	22	lagrangian	lagrangian	ADJ
ap-4038	115	23	cell	cell	NOUN
ap-4038	115	24	,	,	PUNCT
ap-4038	115	25	as	as	SCONJ
ap-4038	115	26	described	describe	VERB
ap-4038	115	27	in	in	ADP
ap-4038	115	28	section	section	NOUN
ap-4038	115	29	3.1	3.1	NUM
ap-4038	115	30	.	.	PUNCT
ap-4038	116	1	(	(	PUNCT
ap-4038	116	2	3	3	NUM
ap-4038	116	3	.	.	PUNCT
ap-4038	116	4	)	)	PUNCT
ap-4038	117	1	the	the	DET
ap-4038	117	2	remapping	remappe	VERB
ap-4038	117	3	part	part	NOUN
ap-4038	117	4	.	.	PUNCT
ap-4038	118	1	this	this	PRON
ap-4038	118	2	involves	involve	VERB
ap-4038	118	3	assembling	assemble	VERB
ap-4038	118	4	the	the	DET
ap-4038	118	5	polyhedral	polyhedral	ADJ
ap-4038	118	6	representation	representation	NOUN
ap-4038	118	7	of	of	ADP
ap-4038	118	8	a	a	DET
ap-4038	118	9	reference	reference	NOUN
ap-4038	118	10	fluid	fluid	NOUN
ap-4038	118	11	material	material	NOUN
ap-4038	118	12	for	for	ADP
ap-4038	118	13	each	each	DET
ap-4038	118	14	cell	cell	NOUN
ap-4038	118	15	on	on	ADP
ap-4038	118	16	the	the	DET
ap-4038	118	17	updated	update	VERB
ap-4038	118	18	(	(	PUNCT
ap-4038	118	19	lagrangian	lagrangian	ADJ
ap-4038	118	20	)	)	PUNCT
ap-4038	118	21	grid	grid	NOUN
ap-4038	118	22	and	and	CCONJ
ap-4038	118	23	redepositing	redeposit	VERB
ap-4038	118	24	it	it	PRON
ap-4038	118	25	back	back	ADV
ap-4038	118	26	on	on	ADP
ap-4038	118	27	the	the	DET
ap-4038	118	28	target	target	NOUN
ap-4038	118	29	grid	grid	NOUN
ap-4038	118	30	(	(	PUNCT
ap-4038	118	31	i.e.	i.e.	X
ap-4038	118	32	on	on	ADP
ap-4038	118	33	the	the	DET
ap-4038	118	34	original	original	ADJ
ap-4038	118	35	grid	grid	NOUN
ap-4038	118	36	)	)	PUNCT
ap-4038	118	37	to	to	PART
ap-4038	118	38	obtain	obtain	VERB
ap-4038	118	39	updated	update	VERB
ap-4038	118	40	vof	vof	NOUN
ap-4038	118	41	values	value	NOUN
ap-4038	118	42	.	.	PUNCT
ap-4038	119	1	this	this	DET
ap-4038	119	2	phase	phase	NOUN
ap-4038	119	3	is	be	AUX
ap-4038	119	4	performed	perform	VERB
ap-4038	119	5	by	by	ADP
ap-4038	119	6	a	a	DET
ap-4038	119	7	series	series	NOUN
ap-4038	119	8	of	of	ADP
ap-4038	119	9	3d	3d	PROPN
ap-4038	119	10	polyhedron	polyhedron	NOUN
ap-4038	119	11	intersection	intersection	NOUN
ap-4038	119	12	procedures	procedure	NOUN
ap-4038	119	13	between	between	ADP
ap-4038	119	14	the	the	DET
ap-4038	119	15	polyhedron	polyhedron	NOUN
ap-4038	119	16	representing	represent	VERB
ap-4038	119	17	the	the	DET
ap-4038	119	18	reference	reference	NOUN
ap-4038	119	19	fluid	fluid	NOUN
ap-4038	119	20	on	on	ADP
ap-4038	119	21	the	the	DET
ap-4038	119	22	updated	update	VERB
ap-4038	119	23	grid	grid	NOUN
ap-4038	119	24	and	and	CCONJ
ap-4038	119	25	the	the	DET
ap-4038	119	26	polyhedra	polyhedra	NOUN
ap-4038	119	27	representing	represent	VERB
ap-4038	119	28	the	the	DET
ap-4038	119	29	original	original	ADJ
ap-4038	119	30	mesh	mesh	NOUN
ap-4038	119	31	cells	cell	NOUN
ap-4038	119	32	,	,	PUNCT
ap-4038	119	33	yielding	yield	VERB
ap-4038	119	34	the	the	DET
ap-4038	119	35	contributions	contribution	NOUN
ap-4038	119	36	to	to	ADP
ap-4038	119	37	the	the	DET
ap-4038	119	38	updated	update	VERB
ap-4038	119	39	reference	reference	NOUN
ap-4038	119	40	fluid	fluid	NOUN
ap-4038	119	41	volumes	volume	NOUN
ap-4038	119	42	in	in	ADP
ap-4038	119	43	particular	particular	ADJ
ap-4038	119	44	cells	cell	NOUN
ap-4038	119	45	.	.	PUNCT
ap-4038	120	1	the	the	DET
ap-4038	120	2	details	detail	NOUN
ap-4038	120	3	of	of	ADP
ap-4038	120	4	this	this	DET
ap-4038	120	5	algorithm	algorithm	NOUN
ap-4038	120	6	are	be	AUX
ap-4038	120	7	given	give	VERB
ap-4038	120	8	in	in	ADP
ap-4038	120	9	section	section	NOUN
ap-4038	120	10	3.2	3.2	NUM
ap-4038	120	11	.	.	PUNCT
ap-4038	121	1	3.1	3.1	NUM
ap-4038	121	2	.	.	PUNCT
ap-4038	121	3	interface	interface	NOUN
ap-4038	121	4	reconstruction	reconstruction	NOUN
ap-4038	121	5	as	as	SCONJ
ap-4038	121	6	was	be	AUX
ap-4038	121	7	mentioned	mention	VERB
ap-4038	121	8	above	above	ADV
ap-4038	121	9	,	,	PUNCT
ap-4038	121	10	the	the	DET
ap-4038	121	11	interface	interface	NOUN
ap-4038	121	12	at	at	ADP
ap-4038	121	13	each	each	DET
ap-4038	121	14	partially	partially	ADV
ap-4038	121	15	filled	fill	VERB
ap-4038	121	16	cell	cell	NOUN
ap-4038	121	17	(	(	PUNCT
ap-4038	121	18	so	so	ADV
ap-4038	121	19	-	-	PUNCT
ap-4038	121	20	called	call	VERB
ap-4038	121	21	interface	interface	NOUN
ap-4038	121	22	cell	cell	NOUN
ap-4038	121	23	)	)	PUNCT
ap-4038	121	24	is	be	AUX
ap-4038	121	25	represented	represent	VERB
ap-4038	121	26	as	as	ADP
ap-4038	121	27	a	a	DET
ap-4038	121	28	planar	planar	ADJ
ap-4038	121	29	segment	segment	NOUN
ap-4038	121	30	,	,	PUNCT
ap-4038	121	31	which	which	PRON
ap-4038	121	32	can	can	AUX
ap-4038	121	33	be	be	AUX
ap-4038	121	34	described	describe	VERB
ap-4038	121	35	as	as	ADP
ap-4038	121	36	n	n	PROPN
ap-4038	121	37	·	·	PUNCT
ap-4038	121	38	x−	x−	PROPN
ap-4038	121	39	c	c	PROPN
ap-4038	121	40	=	=	SYM
ap-4038	121	41	0	0	PROPN
ap-4038	121	42	,	,	PUNCT
ap-4038	121	43	(	(	PUNCT
ap-4038	121	44	9	9	X
ap-4038	121	45	)	)	PUNCT
ap-4038	121	46	where	where	SCONJ
ap-4038	121	47	n	n	PRON
ap-4038	121	48	is	be	AUX
ap-4038	121	49	the	the	DET
ap-4038	121	50	unit	unit	NOUN
ap-4038	121	51	normal	normal	ADJ
ap-4038	121	52	to	to	ADP
ap-4038	121	53	the	the	DET
ap-4038	121	54	planar	planar	ADJ
ap-4038	121	55	surface	surface	NOUN
ap-4038	121	56	representing	represent	VERB
ap-4038	121	57	the	the	DET
ap-4038	121	58	interface	interface	NOUN
ap-4038	121	59	,	,	PUNCT
ap-4038	121	60	x	x	X
ap-4038	121	61	is	be	AUX
ap-4038	121	62	a	a	DET
ap-4038	121	63	position	position	NOUN
ap-4038	121	64	vector	vector	NOUN
ap-4038	121	65	,	,	PUNCT
ap-4038	121	66	and	and	CCONJ
ap-4038	121	67	c	c	NOUN
ap-4038	121	68	is	be	AUX
ap-4038	121	69	the	the	DET
ap-4038	121	70	plane	plane	NOUN
ap-4038	121	71	constant	constant	ADJ
ap-4038	121	72	.	.	PUNCT
ap-4038	122	1	the	the	DET
ap-4038	122	2	interface	interface	NOUN
ap-4038	122	3	segment	segment	NOUN
ap-4038	122	4	normal	normal	ADJ
ap-4038	122	5	in	in	ADP
ap-4038	122	6	each	each	DET
ap-4038	122	7	cell	cell	NOUN
ap-4038	122	8	can	can	AUX
ap-4038	122	9	be	be	AUX
ap-4038	122	10	determined	determine	VERB
ap-4038	122	11	from	from	ADP
ap-4038	122	12	the	the	DET
ap-4038	122	13	spatial	spatial	ADJ
ap-4038	122	14	volume	volume	NOUN
ap-4038	122	15	fraction	fraction	NOUN
ap-4038	122	16	distribution	distribution	NOUN
ap-4038	122	17	in	in	ADP
ap-4038	122	18	the	the	DET
ap-4038	122	19	neighborhood	neighborhood	NOUN
ap-4038	122	20	of	of	ADP
ap-4038	122	21	the	the	DET
ap-4038	122	22	cell	cell	NOUN
ap-4038	122	23	.	.	PUNCT
ap-4038	123	1	the	the	DET
ap-4038	123	2	segment	segment	NOUN
ap-4038	123	3	constant	constant	ADJ
ap-4038	123	4	is	be	AUX
ap-4038	123	5	then	then	ADV
ap-4038	123	6	determined	determine	VERB
ap-4038	123	7	from	from	ADP
ap-4038	123	8	the	the	DET
ap-4038	123	9	volume	volume	NOUN
ap-4038	123	10	conservation	conservation	NOUN
ap-4038	123	11	requirement	requirement	NOUN
ap-4038	123	12	.	.	PUNCT
ap-4038	124	1	the	the	DET
ap-4038	124	2	method	method	NOUN
ap-4038	124	3	for	for	ADP
ap-4038	124	4	determining	determine	VERB
ap-4038	124	5	the	the	DET
ap-4038	124	6	normal	normal	ADJ
ap-4038	124	7	is	be	AUX
ap-4038	124	8	based	base	VERB
ap-4038	124	9	on	on	ADP
ap-4038	124	10	an	an	DET
ap-4038	124	11	extension	extension	NOUN
ap-4038	124	12	to	to	ADP
ap-4038	124	13	young	young	PROPN
ap-4038	124	14	’s	’s	PART
ap-4038	124	15	second	second	ADJ
ap-4038	124	16	method	method	NOUN
ap-4038	124	17	,	,	PUNCT
ap-4038	124	18	developed	develop	VERB
ap-4038	124	19	originally	originally	ADV
ap-4038	124	20	by	by	ADP
ap-4038	124	21	rider	rider	NOUN
ap-4038	124	22	and	and	CCONJ
ap-4038	124	23	kothe	kothe	NOUN
ap-4038	125	1	[	[	X
ap-4038	125	2	5	5	NUM
ap-4038	125	3	]	]	PUNCT
ap-4038	125	4	.	.	PUNCT
ap-4038	126	1	the	the	DET
ap-4038	126	2	idea	idea	NOUN
ap-4038	126	3	is	be	AUX
ap-4038	126	4	to	to	PART
ap-4038	126	5	form	form	VERB
ap-4038	126	6	a	a	DET
ap-4038	126	7	taylor	taylor	PROPN
ap-4038	126	8	series	series	PROPN
ap-4038	126	9	expansion	expansion	NOUN
ap-4038	126	10	of	of	ADP
ap-4038	126	11	volume	volume	NOUN
ap-4038	126	12	fraction	fraction	NOUN
ap-4038	126	13	ft	ft	X
ap-4038	126	14	s	s	NOUN
ap-4038	126	15	i	i	PRON
ap-4038	126	16	for	for	ADP
ap-4038	126	17	each	each	DET
ap-4038	126	18	interface	interface	NOUN
ap-4038	126	19	cell	cell	NOUN
ap-4038	126	20	i	i	PRON
ap-4038	126	21	with	with	ADP
ap-4038	126	22	vof	vof	NOUN
ap-4038	126	23	value	value	NOUN
ap-4038	126	24	fi	fi	NOUN
ap-4038	126	25	to	to	ADP
ap-4038	126	26	each	each	PRON
ap-4038	126	27	of	of	ADP
ap-4038	126	28	its	its	PRON
ap-4038	126	29	adjacent	adjacent	ADJ
ap-4038	126	30	cell	cell	NOUN
ap-4038	126	31	with	with	ADP
ap-4038	126	32	k	k	PROPN
ap-4038	126	33	with	with	ADP
ap-4038	126	34	vof	vof	NOUN
ap-4038	126	35	value	value	NOUN
ap-4038	126	36	fk	fk	INTJ
ap-4038	126	37	.	.	PUNCT
ap-4038	127	1	then	then	ADV
ap-4038	127	2	,	,	PUNCT
ap-4038	127	3	the	the	DET
ap-4038	127	4	sum	sum	NOUN
ap-4038	127	5	of	of	ADP
ap-4038	127	6	(	(	PUNCT
ap-4038	127	7	ft	ft	PROPN
ap-4038	127	8	s	s	NOUN
ap-4038	127	9	i	i	PRON
ap-4038	127	10	−	−	PROPN
ap-4038	127	11	fk)2	fk)2	VERB
ap-4038	127	12	over	over	ADP
ap-4038	127	13	all	all	DET
ap-4038	127	14	cells	cell	NOUN
ap-4038	127	15	neighboring	neighboring	NOUN
ap-4038	127	16	cell	cell	NOUN
ap-4038	127	17	i∑	i∑	NOUN
ap-4038	127	18	k	k	NOUN
ap-4038	127	19	(	(	PUNCT
ap-4038	127	20	ft	ft	NOUN
ap-4038	127	21	s	s	VERB
ap-4038	127	22	i	i	INTJ
ap-4038	127	23	(	(	PUNCT
ap-4038	127	24	xi	xi	PROPN
ap-4038	127	25	)	)	PUNCT
ap-4038	128	1	+	+	CCONJ
ap-4038	128	2	∇ft	∇ft	NOUN
ap-4038	128	3	s	s	VERB
ap-4038	128	4	i	i	NOUN
ap-4038	128	5	(	(	PUNCT
ap-4038	128	6	xi	xi	PROPN
ap-4038	128	7	)	)	PUNCT
ap-4038	128	8	·	·	PUNCT
ap-4038	129	1	(	(	PUNCT
ap-4038	129	2	xk	xk	INTJ
ap-4038	129	3	−	−	PROPN
ap-4038	129	4	xi)−	xi)−	PROPN
ap-4038	129	5	fk(xk	fk(xk	X
ap-4038	129	6	)	)	PUNCT
ap-4038	129	7	)	)	PUNCT
ap-4038	129	8	2	2	NUM
ap-4038	129	9	(	(	PUNCT
ap-4038	129	10	10	10	NUM
ap-4038	129	11	)	)	PUNCT
ap-4038	129	12	is	be	AUX
ap-4038	129	13	minimized	minimize	VERB
ap-4038	129	14	in	in	ADP
ap-4038	129	15	the	the	DET
ap-4038	129	16	least	least	ADJ
ap-4038	129	17	square	square	ADJ
ap-4038	129	18	sense	sense	NOUN
ap-4038	129	19	.	.	PUNCT
ap-4038	130	1	the	the	DET
ap-4038	130	2	minimization	minimization	NOUN
ap-4038	130	3	yields	yield	VERB
ap-4038	130	4	the	the	DET
ap-4038	130	5	volume	volume	NOUN
ap-4038	130	6	fraction	fraction	NOUN
ap-4038	130	7	gradient	gradient	NOUN
ap-4038	131	1	∇ft	∇ft	PRON
ap-4038	131	2	s	s	VERB
ap-4038	131	3	i	i	PRON
ap-4038	131	4	corresponding	correspond	VERB
ap-4038	131	5	to	to	ADP
ap-4038	131	6	the	the	DET
ap-4038	131	7	interface	interface	NOUN
ap-4038	131	8	segment	segment	NOUN
ap-4038	131	9	normal	normal	ADJ
ap-4038	131	10	ni	ni	PROPN
ap-4038	131	11	for	for	ADP
ap-4038	131	12	cell	cell	NOUN
ap-4038	131	13	i	i	PROPN
ap-4038	131	14	as	as	ADP
ap-4038	131	15	the	the	DET
ap-4038	131	16	solution	solution	NOUN
ap-4038	131	17	for	for	ADP
ap-4038	131	18	the	the	DET
ap-4038	131	19	resulting	result	VERB
ap-4038	131	20	system	system	NOUN
ap-4038	131	21	of	of	ADP
ap-4038	131	22	normal	normal	ADJ
ap-4038	131	23	equations	equation	NOUN
ap-4038	131	24	.	.	PUNCT
ap-4038	132	1	all	all	DET
ap-4038	132	2	coordinates	coordinate	NOUN
ap-4038	132	3	are	be	AUX
ap-4038	132	4	evaluated	evaluate	VERB
ap-4038	132	5	in	in	ADP
ap-4038	132	6	the	the	DET
ap-4038	132	7	mass	mass	ADJ
ap-4038	132	8	center	center	NOUN
ap-4038	132	9	of	of	ADP
ap-4038	132	10	the	the	DET
ap-4038	132	11	cells	cell	NOUN
ap-4038	132	12	.	.	PUNCT
ap-4038	133	1	this	this	DET
ap-4038	133	2	method	method	NOUN
ap-4038	133	3	guarantees	guarantee	VERB
ap-4038	133	4	exact	exact	ADJ
ap-4038	133	5	reconstruction	reconstruction	NOUN
ap-4038	133	6	of	of	ADP
ap-4038	133	7	the	the	DET
ap-4038	133	8	gradients	gradient	NOUN
ap-4038	133	9	for	for	ADP
ap-4038	133	10	a	a	DET
ap-4038	133	11	linear	linear	ADJ
ap-4038	133	12	function	function	NOUN
ap-4038	133	13	of	of	ADP
ap-4038	133	14	f	f	PROPN
ap-4038	133	15	.	.	PUNCT
ap-4038	134	1	however	however	ADV
ap-4038	134	2	,	,	PUNCT
ap-4038	134	3	even	even	ADV
ap-4038	134	4	for	for	ADP
ap-4038	134	5	the	the	DET
ap-4038	134	6	linear	linear	ADJ
ap-4038	134	7	interface	interface	NOUN
ap-4038	134	8	,	,	PUNCT
ap-4038	134	9	the	the	DET
ap-4038	134	10	distribution	distribution	NOUN
ap-4038	134	11	of	of	ADP
ap-4038	134	12	f	f	PROPN
ap-4038	134	13	through	through	ADP
ap-4038	134	14	tessellation	tessellation	NOUN
ap-4038	134	15	is	be	AUX
ap-4038	134	16	not	not	PART
ap-4038	134	17	linear	linear	ADJ
ap-4038	134	18	.	.	PUNCT
ap-4038	135	1	this	this	DET
ap-4038	135	2	method	method	NOUN
ap-4038	135	3	is	be	AUX
ap-4038	135	4	therefore	therefore	ADV
ap-4038	135	5	only	only	ADV
ap-4038	135	6	first	first	ADJ
ap-4038	135	7	order	order	NOUN
ap-4038	135	8	accurate	accurate	ADJ
ap-4038	135	9	.	.	PUNCT
ap-4038	136	1	in	in	ADP
ap-4038	136	2	[	[	X
ap-4038	136	3	15	15	NUM
ap-4038	136	4	]	]	X
ap-4038	136	5	,	,	PUNCT
ap-4038	136	6	a	a	DET
ap-4038	136	7	second	second	ADJ
ap-4038	136	8	order	order	NOUN
ap-4038	136	9	accurate	accurate	ADJ
ap-4038	136	10	107	107	NUM
ap-4038	136	11	filip	filip	NOUN
ap-4038	136	12	kolařík	kolařík	NOUN
ap-4038	136	13	,	,	PUNCT
ap-4038	136	14	bořek	bořek	PROPN
ap-4038	136	15	patzák	patzák	VERB
ap-4038	136	16	acta	acta	PROPN
ap-4038	136	17	polytechnica	polytechnica	PROPN
ap-4038	136	18	method	method	NOUN
ap-4038	136	19	is	be	AUX
ap-4038	136	20	proposed	propose	VERB
ap-4038	136	21	for	for	ADP
ap-4038	136	22	the	the	DET
ap-4038	136	23	2d	2d	NUM
ap-4038	136	24	case	case	NOUN
ap-4038	136	25	.	.	PUNCT
ap-4038	137	1	this	this	DET
ap-4038	137	2	method	method	NOUN
ap-4038	137	3	is	be	AUX
ap-4038	137	4	based	base	VERB
ap-4038	137	5	on	on	ADP
ap-4038	137	6	geometric	geometric	ADJ
ap-4038	137	7	minimization	minimization	NOUN
ap-4038	137	8	of	of	ADP
ap-4038	137	9	the	the	DET
ap-4038	137	10	differences	difference	NOUN
ap-4038	137	11	between	between	ADP
ap-4038	137	12	the	the	DET
ap-4038	137	13	real	real	ADJ
ap-4038	137	14	volume	volume	NOUN
ap-4038	137	15	fractions	fraction	NOUN
ap-4038	137	16	and	and	CCONJ
ap-4038	137	17	the	the	DET
ap-4038	137	18	fractions	fraction	NOUN
ap-4038	137	19	determined	determine	VERB
ap-4038	137	20	by	by	ADP
ap-4038	137	21	the	the	DET
ap-4038	137	22	given	give	VERB
ap-4038	137	23	line	line	NOUN
ap-4038	137	24	.	.	PUNCT
ap-4038	138	1	the	the	DET
ap-4038	138	2	value	value	NOUN
ap-4038	138	3	of	of	ADP
ap-4038	138	4	planar	planar	ADJ
ap-4038	138	5	segment	segment	NOUN
ap-4038	138	6	constant	constant	ADJ
ap-4038	138	7	c	c	NOUN
ap-4038	138	8	is	be	AUX
ap-4038	138	9	determined	determine	VERB
ap-4038	138	10	from	from	ADP
ap-4038	138	11	the	the	DET
ap-4038	138	12	volume	volume	NOUN
ap-4038	138	13	conservation	conservation	NOUN
ap-4038	138	14	requirement	requirement	NOUN
ap-4038	138	15	.	.	PUNCT
ap-4038	139	1	its	its	PRON
ap-4038	139	2	value	value	NOUN
ap-4038	139	3	is	be	AUX
ap-4038	139	4	constrained	constrain	VERB
ap-4038	139	5	such	such	ADJ
ap-4038	139	6	that	that	SCONJ
ap-4038	139	7	the	the	DET
ap-4038	139	8	resulting	result	VERB
ap-4038	139	9	planar	planar	ADJ
ap-4038	139	10	segment	segment	NOUN
ap-4038	139	11	(	(	PUNCT
ap-4038	139	12	with	with	ADP
ap-4038	139	13	the	the	DET
ap-4038	139	14	fixed	fix	VERB
ap-4038	139	15	normal	normal	ADJ
ap-4038	139	16	determined	determine	VERB
ap-4038	139	17	in	in	ADP
ap-4038	139	18	the	the	DET
ap-4038	139	19	previous	previous	ADJ
ap-4038	139	20	step	step	NOUN
ap-4038	139	21	)	)	PUNCT
ap-4038	139	22	passes	pass	VERB
ap-4038	139	23	through	through	ADP
ap-4038	139	24	the	the	DET
ap-4038	139	25	cell	cell	NOUN
ap-4038	139	26	with	with	ADP
ap-4038	139	27	a	a	DET
ap-4038	139	28	truncation	truncation	NOUN
ap-4038	139	29	volume	volume	NOUN
ap-4038	139	30	equal	equal	ADJ
ap-4038	139	31	to	to	ADP
ap-4038	139	32	the	the	DET
ap-4038	139	33	cell	cell	NOUN
ap-4038	139	34	material	material	NOUN
ap-4038	139	35	volume	volume	NOUN
ap-4038	139	36	v	v	NOUN
ap-4038	139	37	.	.	PUNCT
ap-4038	140	1	the	the	DET
ap-4038	140	2	planar	planar	ADJ
ap-4038	140	3	segment	segment	NOUN
ap-4038	140	4	constant	constant	ADJ
ap-4038	140	5	is	be	AUX
ap-4038	140	6	determined	determine	VERB
ap-4038	140	7	from	from	ADP
ap-4038	140	8	the	the	DET
ap-4038	140	9	following	follow	VERB
ap-4038	140	10	relation	relation	NOUN
ap-4038	140	11	f	f	PROPN
ap-4038	140	12	(	(	PUNCT
ap-4038	140	13	c	c	NOUN
ap-4038	140	14	)	)	PUNCT
ap-4038	140	15	=	=	NOUN
ap-4038	140	16	v	v	X
ap-4038	140	17	(	(	PUNCT
ap-4038	140	18	c)−	c)−	PROPN
ap-4038	140	19	v	v	NOUN
ap-4038	140	20	=	=	SYM
ap-4038	140	21	0	0	NUM
ap-4038	140	22	,	,	PUNCT
ap-4038	140	23	(	(	PUNCT
ap-4038	140	24	11	11	NUM
ap-4038	140	25	)	)	PUNCT
ap-4038	140	26	where	where	SCONJ
ap-4038	140	27	v	v	X
ap-4038	140	28	(	(	PUNCT
ap-4038	140	29	c	c	NOUN
ap-4038	140	30	)	)	PUNCT
ap-4038	140	31	is	be	AUX
ap-4038	140	32	the	the	DET
ap-4038	140	33	material	material	ADJ
ap-4038	140	34	volume	volume	NOUN
ap-4038	140	35	in	in	ADP
ap-4038	140	36	the	the	DET
ap-4038	140	37	cell	cell	NOUN
ap-4038	140	38	bounded	bound	VERB
ap-4038	140	39	by	by	ADP
ap-4038	140	40	the	the	DET
ap-4038	140	41	planar	planar	ADJ
ap-4038	140	42	interface	interface	NOUN
ap-4038	140	43	segment	segment	NOUN
ap-4038	140	44	with	with	ADP
ap-4038	140	45	constant	constant	ADJ
ap-4038	140	46	c	c	NOUN
ap-4038	140	47	and	and	CCONJ
ap-4038	140	48	the	the	DET
ap-4038	140	49	portion	portion	NOUN
ap-4038	140	50	of	of	ADP
ap-4038	140	51	the	the	DET
ap-4038	140	52	cell	cell	NOUN
ap-4038	140	53	boundary	boundary	ADJ
ap-4038	140	54	surfaces	surface	NOUN
ap-4038	140	55	within	within	ADP
ap-4038	140	56	the	the	DET
ap-4038	140	57	material	material	NOUN
ap-4038	140	58	.	.	PUNCT
ap-4038	141	1	the	the	DET
ap-4038	141	2	cell	cell	NOUN
ap-4038	141	3	material	material	NOUN
ap-4038	141	4	volume	volume	NOUN
ap-4038	141	5	v	v	NOUN
ap-4038	141	6	is	be	AUX
ap-4038	141	7	equal	equal	ADJ
ap-4038	141	8	to	to	ADP
ap-4038	141	9	the	the	DET
ap-4038	141	10	total	total	ADJ
ap-4038	141	11	cell	cell	NOUN
ap-4038	141	12	volume	volume	NOUN
ap-4038	141	13	multiplied	multiply	VERB
ap-4038	141	14	by	by	ADP
ap-4038	141	15	the	the	DET
ap-4038	141	16	volume	volume	NOUN
ap-4038	141	17	fraction	fraction	NOUN
ap-4038	141	18	.	.	PUNCT
ap-4038	142	1	brent	brent	PROPN
ap-4038	142	2	’s	’s	PART
ap-4038	142	3	method	method	NOUN
ap-4038	142	4	has	have	AUX
ap-4038	142	5	been	be	AUX
ap-4038	142	6	used	use	VERB
ap-4038	142	7	to	to	PART
ap-4038	142	8	find	find	VERB
ap-4038	142	9	zero	zero	NUM
ap-4038	142	10	of	of	ADP
ap-4038	142	11	the	the	DET
ap-4038	142	12	f	f	PROPN
ap-4038	142	13	(	(	PUNCT
ap-4038	142	14	c	c	NOUN
ap-4038	142	15	)	)	PUNCT
ap-4038	142	16	function	function	NOUN
ap-4038	142	17	(	(	PUNCT
ap-4038	142	18	and	and	CCONJ
ap-4038	142	19	to	to	PART
ap-4038	142	20	determine	determine	VERB
ap-4038	142	21	the	the	DET
ap-4038	142	22	volume	volume	NOUN
ap-4038	142	23	conserving	conserve	VERB
ap-4038	142	24	segment	segment	NOUN
ap-4038	142	25	constant	constant	ADJ
ap-4038	142	26	)	)	PUNCT
ap-4038	142	27	.	.	PUNCT
ap-4038	143	1	this	this	DET
ap-4038	143	2	method	method	NOUN
ap-4038	143	3	uses	use	VERB
ap-4038	143	4	inverse	inverse	NOUN
ap-4038	143	5	parabola	parabola	PROPN
ap-4038	143	6	interpolation	interpolation	NOUN
ap-4038	143	7	,	,	PUNCT
ap-4038	143	8	so	so	CCONJ
ap-4038	143	9	it	it	PRON
ap-4038	143	10	is	be	AUX
ap-4038	143	11	suitable	suitable	ADJ
ap-4038	143	12	for	for	ADP
ap-4038	143	13	finding	find	VERB
ap-4038	143	14	the	the	DET
ap-4038	143	15	root	root	NOUN
ap-4038	143	16	of	of	ADP
ap-4038	143	17	f	f	PROPN
ap-4038	143	18	(	(	PUNCT
ap-4038	143	19	c	c	NOUN
ap-4038	143	20	)	)	PUNCT
ap-4038	143	21	,	,	PUNCT
ap-4038	143	22	as	as	SCONJ
ap-4038	143	23	v	v	NOUN
ap-4038	143	24	often	often	ADV
ap-4038	143	25	varies	vary	VERB
ap-4038	143	26	quadratically	quadratically	ADV
ap-4038	143	27	with	with	ADP
ap-4038	143	28	c.	c.	PROPN
ap-4038	143	29	3.2	3.2	NUM
ap-4038	143	30	.	.	PUNCT
ap-4038	144	1	a	a	DET
ap-4038	144	2	bsp	bsp	NOUN
ap-4038	144	3	tree	tree	NOUN
ap-4038	144	4	based	base	VERB
ap-4038	144	5	approach	approach	NOUN
ap-4038	144	6	to	to	ADP
ap-4038	144	7	remapping	remappe	VERB
ap-4038	144	8	the	the	DET
ap-4038	144	9	tetrahedral	tetrahedral	ADJ
ap-4038	144	10	mesh	mesh	NOUN
ap-4038	144	11	the	the	DET
ap-4038	144	12	remapping	remappe	VERB
ap-4038	144	13	part	part	NOUN
ap-4038	144	14	of	of	ADP
ap-4038	144	15	the	the	DET
ap-4038	144	16	proposed	propose	VERB
ap-4038	144	17	algorithm	algorithm	NOUN
ap-4038	144	18	is	be	AUX
ap-4038	144	19	of	of	ADP
ap-4038	144	20	purely	purely	ADV
ap-4038	144	21	a	a	DET
ap-4038	144	22	geometric	geometric	ADJ
ap-4038	144	23	nature	nature	NOUN
ap-4038	144	24	.	.	PUNCT
ap-4038	145	1	it	it	PRON
ap-4038	145	2	involves	involve	VERB
ap-4038	145	3	establishing	establish	VERB
ap-4038	145	4	a	a	DET
ap-4038	145	5	representation	representation	NOUN
ap-4038	145	6	of	of	ADP
ap-4038	145	7	the	the	DET
ap-4038	145	8	reference	reference	NOUN
ap-4038	145	9	fluid	fluid	NOUN
ap-4038	145	10	volume	volume	NOUN
ap-4038	145	11	in	in	ADP
ap-4038	145	12	each	each	DET
ap-4038	145	13	cell	cell	NOUN
ap-4038	145	14	(	(	PUNCT
ap-4038	145	15	in	in	ADP
ap-4038	145	16	the	the	DET
ap-4038	145	17	form	form	NOUN
ap-4038	145	18	of	of	ADP
ap-4038	145	19	polyhedra	polyhedra	NOUN
ap-4038	145	20	)	)	PUNCT
ap-4038	145	21	on	on	ADP
ap-4038	145	22	the	the	DET
ap-4038	145	23	updated	update	VERB
ap-4038	145	24	grid	grid	NOUN
ap-4038	145	25	,	,	PUNCT
ap-4038	145	26	projecting	project	VERB
ap-4038	145	27	it	it	PRON
ap-4038	145	28	onto	onto	ADP
ap-4038	145	29	the	the	DET
ap-4038	145	30	original	original	ADJ
ap-4038	145	31	grid	grid	NOUN
ap-4038	145	32	and	and	CCONJ
ap-4038	145	33	summing	sum	VERB
ap-4038	145	34	up	up	ADP
ap-4038	145	35	the	the	DET
ap-4038	145	36	contributions	contribution	NOUN
ap-4038	145	37	of	of	ADP
ap-4038	145	38	the	the	DET
ap-4038	145	39	truncated	truncated	ADJ
ap-4038	145	40	volumes	volume	NOUN
ap-4038	145	41	(	(	PUNCT
ap-4038	145	42	representing	represent	VERB
ap-4038	145	43	the	the	DET
ap-4038	145	44	contributing	contribute	VERB
ap-4038	145	45	volume	volume	NOUN
ap-4038	145	46	fractions	fraction	NOUN
ap-4038	145	47	)	)	PUNCT
ap-4038	145	48	in	in	ADP
ap-4038	145	49	each	each	DET
ap-4038	145	50	cell	cell	NOUN
ap-4038	145	51	.	.	PUNCT
ap-4038	146	1	the	the	DET
ap-4038	146	2	pseudo	pseudo	NOUN
ap-4038	146	3	-	-	NOUN
ap-4038	146	4	code	code	NOUN
ap-4038	146	5	is	be	AUX
ap-4038	146	6	presented	present	VERB
ap-4038	146	7	in	in	ADP
ap-4038	146	8	algorithm	algorithm	NOUN
ap-4038	146	9	1	1	NUM
ap-4038	146	10	the	the	DET
ap-4038	146	11	overall	overall	ADJ
ap-4038	146	12	procedure	procedure	NOUN
ap-4038	146	13	requires	require	VERB
ap-4038	146	14	two	two	NUM
ap-4038	146	15	basic	basic	ADJ
ap-4038	146	16	operations	operation	NOUN
ap-4038	146	17	.	.	PUNCT
ap-4038	147	1	the	the	DET
ap-4038	147	2	first	first	ADJ
ap-4038	147	3	operation	operation	NOUN
ap-4038	147	4	is	be	AUX
ap-4038	147	5	polyhedron	polyhedron	NOUN
ap-4038	147	6	formation	formation	NOUN
ap-4038	147	7	based	base	VERB
ap-4038	147	8	on	on	ADP
ap-4038	147	9	knowledge	knowledge	NOUN
ap-4038	147	10	of	of	ADP
ap-4038	147	11	the	the	DET
ap-4038	147	12	interface	interface	NOUN
ap-4038	147	13	segment	segment	NOUN
ap-4038	147	14	that	that	PRON
ap-4038	147	15	intersects	intersect	VERB
ap-4038	147	16	a	a	DET
ap-4038	147	17	given	give	VERB
ap-4038	147	18	cell	cell	NOUN
ap-4038	147	19	.	.	PUNCT
ap-4038	148	1	the	the	DET
ap-4038	148	2	second	second	ADJ
ap-4038	148	3	necessary	necessary	ADJ
ap-4038	148	4	operation	operation	NOUN
ap-4038	148	5	is	be	AUX
ap-4038	148	6	to	to	PART
ap-4038	148	7	compute	compute	VERB
ap-4038	148	8	the	the	DET
ap-4038	148	9	intersection	intersection	NOUN
ap-4038	148	10	between	between	ADP
ap-4038	148	11	two	two	NUM
ap-4038	148	12	(	(	PUNCT
ap-4038	148	13	convex	convex	NOUN
ap-4038	148	14	)	)	PUNCT
ap-4038	148	15	polyhedra	polyhedra	NOUN
ap-4038	148	16	and	and	CCONJ
ap-4038	148	17	to	to	PART
ap-4038	148	18	compute	compute	VERB
ap-4038	148	19	the	the	DET
ap-4038	148	20	volume	volume	NOUN
ap-4038	148	21	of	of	ADP
ap-4038	148	22	the	the	DET
ap-4038	148	23	intersection	intersection	NOUN
ap-4038	148	24	.	.	PUNCT
ap-4038	149	1	polyhedron	polyhedron	NOUN
ap-4038	149	2	formatting	formatting	NOUN
ap-4038	149	3	is	be	AUX
ap-4038	149	4	represented	represent	VERB
ap-4038	149	5	by	by	ADP
ap-4038	149	6	the	the	DET
ap-4038	149	7	truncatepoly	truncatepoly	ADJ
ap-4038	149	8	procedure	procedure	NOUN
ap-4038	149	9	in	in	ADP
ap-4038	149	10	algorithm	algorithm	NOUN
ap-4038	149	11	1	1	NUM
ap-4038	149	12	.	.	PUNCT
ap-4038	150	1	once	once	ADV
ap-4038	150	2	the	the	DET
ap-4038	150	3	tetrahedron	tetrahedron	NOUN
ap-4038	150	4	and	and	CCONJ
ap-4038	150	5	the	the	DET
ap-4038	150	6	corresponding	correspond	VERB
ap-4038	150	7	intersecting	intersecting	ADJ
ap-4038	150	8	plane	plane	NOUN
ap-4038	150	9	are	be	AUX
ap-4038	150	10	given	give	VERB
ap-4038	150	11	,	,	PUNCT
ap-4038	150	12	truncating	truncate	VERB
ap-4038	150	13	the	the	DET
ap-4038	150	14	polyhedron	polyhedron	NOUN
ap-4038	150	15	is	be	AUX
ap-4038	150	16	a	a	DET
ap-4038	150	17	trivial	trivial	ADJ
ap-4038	150	18	task	task	NOUN
ap-4038	150	19	,	,	PUNCT
ap-4038	150	20	at	at	ADP
ap-4038	150	21	least	least	ADJ
ap-4038	150	22	from	from	ADP
ap-4038	150	23	the	the	DET
ap-4038	150	24	theoretical	theoretical	ADJ
ap-4038	150	25	point	point	NOUN
ap-4038	150	26	of	of	ADP
ap-4038	150	27	view	view	NOUN
ap-4038	150	28	.	.	PUNCT
ap-4038	151	1	the	the	DET
ap-4038	151	2	only	only	ADJ
ap-4038	151	3	difficulty	difficulty	NOUN
ap-4038	151	4	lies	lie	VERB
ap-4038	151	5	in	in	ADP
ap-4038	151	6	the	the	DET
ap-4038	151	7	need	need	NOUN
ap-4038	151	8	to	to	PART
ap-4038	151	9	draw	draw	VERB
ap-4038	151	10	a	a	DET
ap-4038	151	11	correct	correct	ADJ
ap-4038	151	12	distinction	distinction	NOUN
ap-4038	151	13	for	for	ADP
ap-4038	151	14	each	each	DET
ap-4038	151	15	case	case	NOUN
ap-4038	151	16	of	of	ADP
ap-4038	151	17	tetrahedron	tetrahedron	NOUN
ap-4038	151	18	-	-	PUNCT
ap-4038	151	19	plane	plane	NOUN
ap-4038	151	20	intersection	intersection	NOUN
ap-4038	151	21	.	.	PUNCT
ap-4038	152	1	the	the	DET
ap-4038	152	2	truncatepoly	truncatepoly	ADJ
ap-4038	152	3	procedure	procedure	NOUN
ap-4038	152	4	consists	consist	VERB
ap-4038	152	5	of	of	ADP
ap-4038	152	6	a	a	DET
ap-4038	152	7	loop	loop	NOUN
ap-4038	152	8	over	over	ADP
ap-4038	152	9	the	the	DET
ap-4038	152	10	tetrahedron	tetrahedron	NOUN
ap-4038	152	11	faces	face	VERB
ap-4038	152	12	,	,	PUNCT
ap-4038	152	13	where	where	SCONJ
ap-4038	152	14	each	each	PRON
ap-4038	152	15	of	of	ADP
ap-4038	152	16	the	the	DET
ap-4038	152	17	faces	face	NOUN
ap-4038	152	18	is	be	AUX
ap-4038	152	19	cut	cut	VERB
ap-4038	152	20	by	by	ADP
ap-4038	152	21	the	the	DET
ap-4038	152	22	intersecting	intersecting	ADJ
ap-4038	152	23	plane	plane	NOUN
ap-4038	152	24	.	.	PUNCT
ap-4038	153	1	each	each	DET
ap-4038	153	2	such	such	ADJ
ap-4038	153	3	plane	plane	NOUN
ap-4038	153	4	-	-	PUNCT
ap-4038	153	5	face	face	NOUN
ap-4038	153	6	intersection	intersection	NOUN
ap-4038	153	7	results	result	NOUN
ap-4038	153	8	in	in	ADP
ap-4038	153	9	a	a	DET
ap-4038	153	10	sub	sub	NOUN
ap-4038	153	11	-	-	NOUN
ap-4038	153	12	face	face	NOUN
ap-4038	153	13	that	that	PRON
ap-4038	153	14	belongs	belong	VERB
ap-4038	153	15	to	to	ADP
ap-4038	153	16	the	the	DET
ap-4038	153	17	newly	newly	ADV
ap-4038	153	18	formed	form	VERB
ap-4038	153	19	polyhedron	polyhedron	NOUN
ap-4038	153	20	,	,	PUNCT
ap-4038	153	21	so	so	SCONJ
ap-4038	153	22	that	that	SCONJ
ap-4038	153	23	the	the	DET
ap-4038	153	24	new	new	ADJ
ap-4038	153	25	sub	sub	NOUN
ap-4038	153	26	-	-	ADJ
ap-4038	153	27	face	face	NOUN
ap-4038	153	28	lies	lie	NOUN
ap-4038	153	29	on	on	ADP
ap-4038	153	30	the	the	DET
ap-4038	153	31	side	side	NOUN
ap-4038	153	32	of	of	ADP
ap-4038	153	33	the	the	DET
ap-4038	153	34	interface	interface	NOUN
ap-4038	153	35	plane	plane	NOUN
ap-4038	153	36	filled	fill	VERB
ap-4038	153	37	with	with	ADP
ap-4038	153	38	the	the	DET
ap-4038	153	39	reference	reference	NOUN
ap-4038	153	40	fluid	fluid	NOUN
ap-4038	153	41	.	.	PUNCT
ap-4038	154	1	lastly	lastly	ADV
ap-4038	154	2	,	,	PUNCT
ap-4038	154	3	the	the	DET
ap-4038	154	4	closing	close	VERB
ap-4038	154	5	sub	sub	NOUN
ap-4038	154	6	-	-	NOUN
ap-4038	154	7	face	face	NOUN
ap-4038	154	8	of	of	ADP
ap-4038	154	9	the	the	DET
ap-4038	154	10	new	new	ADJ
ap-4038	154	11	polyhedron	polyhedron	NOUN
ap-4038	154	12	(	(	PUNCT
ap-4038	154	13	the	the	DET
ap-4038	154	14	sub	sub	ADJ
ap-4038	154	15	-	-	ADJ
ap-4038	154	16	face	face	ADJ
ap-4038	154	17	coincident	coincident	NOUN
ap-4038	154	18	with	with	ADP
ap-4038	154	19	the	the	DET
ap-4038	154	20	interface	interface	NOUN
ap-4038	154	21	plane	plane	NOUN
ap-4038	154	22	)	)	PUNCT
ap-4038	154	23	is	be	AUX
ap-4038	154	24	formed	form	VERB
ap-4038	154	25	as	as	ADP
ap-4038	154	26	a	a	DET
ap-4038	154	27	cross	cross	NOUN
ap-4038	154	28	-	-	NOUN
ap-4038	154	29	section	section	NOUN
ap-4038	154	30	originating	originating	NOUN
ap-4038	154	31	from	from	ADP
ap-4038	154	32	the	the	DET
ap-4038	154	33	union	union	NOUN
ap-4038	154	34	of	of	ADP
ap-4038	154	35	the	the	DET
ap-4038	154	36	intersecting	intersecting	ADJ
ap-4038	154	37	lines	line	NOUN
ap-4038	154	38	.	.	PUNCT
ap-4038	155	1	the	the	DET
ap-4038	155	2	formpoly	formpoly	ADJ
ap-4038	155	3	function	function	NOUN
ap-4038	155	4	algorithm	algorithm	NOUN
ap-4038	155	5	1	1	NUM
ap-4038	155	6	remmaping	remmaping	NOUN
ap-4038	155	7	algorithm	algorithm	NOUN
ap-4038	155	8	1	1	NUM
ap-4038	155	9	:	:	PUNCT
ap-4038	155	10	procedure	procedure	NOUN
ap-4038	155	11	dointerfaceremmaping	dointerfaceremmape	VERB
ap-4038	155	12	2	2	NUM
ap-4038	155	13	:	:	PUNCT
ap-4038	155	14	for	for	ADP
ap-4038	155	15	el	el	PROPN
ap-4038	155	16	:	:	PUNCT
ap-4038	155	17	=	=	SYM
ap-4038	155	18	1	1	NUM
ap-4038	155	19	to	to	PART
ap-4038	155	20	nel	nel	PROPN
ap-4038	155	21	do	do	VERB
ap-4038	155	22	3	3	NUM
ap-4038	155	23	:	:	PUNCT
ap-4038	155	24	if	if	SCONJ
ap-4038	155	25	el	el	PROPN
ap-4038	155	26	is	be	AUX
ap-4038	155	27	cut	cut	VERB
ap-4038	155	28	by	by	ADP
ap-4038	155	29	interface	interface	NOUN
ap-4038	155	30	then	then	ADV
ap-4038	155	31	4	4	NUM
ap-4038	155	32	:	:	PUNCT
ap-4038	155	33	n	n	PROPN
ap-4038	155	34	=	=	SYM
ap-4038	155	35	el.getplanenormal	el.getplanenormal	X
ap-4038	155	36	(	(	PUNCT
ap-4038	155	37	)	)	PUNCT
ap-4038	155	38	;	;	PUNCT
ap-4038	156	1	5	5	NUM
ap-4038	156	2	:	:	PUNCT
ap-4038	156	3	c	c	NOUN
ap-4038	156	4	=	=	SYM
ap-4038	156	5	el.getplaneconstant	el.getplaneconstant	X
ap-4038	156	6	(	(	PUNCT
ap-4038	156	7	)	)	PUNCT
ap-4038	156	8	;	;	PUNCT
ap-4038	156	9	6	6	NUM
ap-4038	156	10	:	:	PUNCT
ap-4038	156	11	p	p	X
ap-4038	156	12	=	=	PROPN
ap-4038	156	13	el.truncatepoly(n	el.truncatepoly(n	PROPN
ap-4038	156	14	,	,	PUNCT
ap-4038	156	15	c	c	NOUN
ap-4038	156	16	)	)	PUNCT
ap-4038	156	17	;	;	PUNCT
ap-4038	156	18	7	7	NUM
ap-4038	156	19	:	:	PUNCT
ap-4038	156	20	for	for	ADP
ap-4038	156	21	all	all	DET
ap-4038	156	22	neighbours	neighbour	NOUN
ap-4038	156	23	of	of	ADP
ap-4038	156	24	el	el	PROPN
ap-4038	156	25	do	do	VERB
ap-4038	156	26	8	8	NUM
ap-4038	156	27	:	:	PUNCT
ap-4038	156	28	q	q	X
ap-4038	156	29	=	=	SYM
ap-4038	156	30	neighbour.formpoly	neighbour.formpoly	NOUN
ap-4038	156	31	(	(	PUNCT
ap-4038	156	32	)	)	PUNCT
ap-4038	156	33	;	;	PUNCT
ap-4038	156	34	9	9	NUM
ap-4038	156	35	:	:	SYM
ap-4038	156	36	vol	vol	NOUN
ap-4038	156	37	=	=	SYM
ap-4038	156	38	intersectpoly(p	intersectpoly(p	PROPN
ap-4038	156	39	,	,	PUNCT
ap-4038	156	40	q	q	NOUN
ap-4038	156	41	)	)	PUNCT
ap-4038	156	42	;	;	PUNCT
ap-4038	156	43	10	10	NUM
ap-4038	156	44	:	:	PUNCT
ap-4038	156	45	neighbour.addvolume(vol	neighbour.addvolume(vol	NUM
ap-4038	156	46	)	)	PUNCT
ap-4038	156	47	;	;	PUNCT
ap-4038	156	48	11	11	NUM
ap-4038	156	49	:	:	PUNCT
ap-4038	156	50	end	end	VERB
ap-4038	156	51	for	for	ADP
ap-4038	156	52	12	12	NUM
ap-4038	156	53	:	:	PUNCT
ap-4038	156	54	end	end	VERB
ap-4038	156	55	if	if	SCONJ
ap-4038	156	56	13	13	NUM
ap-4038	156	57	:	:	PUNCT
ap-4038	156	58	end	end	VERB
ap-4038	156	59	for	for	ADP
ap-4038	156	60	14	14	NUM
ap-4038	156	61	:	:	PUNCT
ap-4038	156	62	end	end	NOUN
ap-4038	156	63	procedure	procedure	NOUN
ap-4038	156	64	forms	form	VERB
ap-4038	156	65	a	a	DET
ap-4038	156	66	polyhedron	polyhedron	NOUN
ap-4038	156	67	from	from	ADP
ap-4038	156	68	the	the	DET
ap-4038	156	69	plain	plain	ADJ
ap-4038	156	70	(	(	PUNCT
ap-4038	156	71	not	not	PART
ap-4038	156	72	intersected	intersect	VERB
ap-4038	156	73	)	)	PUNCT
ap-4038	156	74	element	element	NOUN
ap-4038	156	75	.	.	PUNCT
ap-4038	157	1	although	although	SCONJ
ap-4038	157	2	an	an	DET
ap-4038	157	3	problem	problem	NOUN
ap-4038	157	4	evaluation	evaluation	NOUN
ap-4038	157	5	of	of	ADP
ap-4038	157	6	the	the	DET
ap-4038	157	7	intersection	intersection	NOUN
ap-4038	157	8	of	of	ADP
ap-4038	157	9	two	two	NUM
ap-4038	157	10	arbitrary	arbitrary	ADJ
ap-4038	157	11	polyhedrons	polyhedron	NOUN
ap-4038	157	12	is	be	AUX
ap-4038	157	13	theoretically	theoretically	ADV
ap-4038	157	14	trivial	trivial	ADJ
ap-4038	157	15	,	,	PUNCT
ap-4038	157	16	implementing	implement	VERB
ap-4038	157	17	it	it	PRON
ap-4038	157	18	presents	present	VERB
ap-4038	157	19	an	an	DET
ap-4038	157	20	interesting	interesting	ADJ
ap-4038	157	21	problem	problem	NOUN
ap-4038	157	22	.	.	PUNCT
ap-4038	158	1	in	in	ADP
ap-4038	158	2	this	this	DET
ap-4038	158	3	work	work	NOUN
ap-4038	158	4	,	,	PUNCT
ap-4038	158	5	the	the	DET
ap-4038	158	6	intersections	intersection	NOUN
ap-4038	158	7	are	be	AUX
ap-4038	158	8	computed	compute	VERB
ap-4038	158	9	with	with	ADP
ap-4038	158	10	the	the	DET
ap-4038	158	11	help	help	NOUN
ap-4038	158	12	of	of	ADP
ap-4038	158	13	so	so	ADV
ap-4038	158	14	-	-	PUNCT
ap-4038	158	15	called	call	VERB
ap-4038	158	16	binary	binary	ADJ
ap-4038	158	17	space	space	NOUN
ap-4038	158	18	-	-	PUNCT
ap-4038	158	19	partitioning	partition	VERB
ap-4038	158	20	(	(	PUNCT
ap-4038	158	21	bsp	bsp	NOUN
ap-4038	158	22	)	)	PUNCT
ap-4038	158	23	trees	tree	NOUN
ap-4038	158	24	.	.	PUNCT
ap-4038	159	1	the	the	DET
ap-4038	159	2	original	original	ADJ
ap-4038	159	3	idea	idea	NOUN
ap-4038	159	4	of	of	ADP
ap-4038	159	5	space	space	NOUN
ap-4038	159	6	partitioning	partition	VERB
ap-4038	159	7	with	with	ADP
ap-4038	159	8	binary	binary	ADJ
ap-4038	159	9	trees	tree	NOUN
ap-4038	159	10	comes	come	VERB
ap-4038	159	11	from	from	ADP
ap-4038	159	12	a	a	DET
ap-4038	159	13	paper	paper	NOUN
ap-4038	159	14	by	by	ADP
ap-4038	159	15	fuchs	fuch	NOUN
ap-4038	159	16	,	,	PUNCT
ap-4038	159	17	kedem	kedem	PROPN
ap-4038	159	18	and	and	CCONJ
ap-4038	159	19	naylor	naylor	PROPN
ap-4038	160	1	[	[	X
ap-4038	160	2	17	17	NUM
ap-4038	160	3	]	]	PUNCT
ap-4038	160	4	in	in	ADP
ap-4038	160	5	1980	1980	NUM
ap-4038	160	6	.	.	PUNCT
ap-4038	161	1	binary	binary	ADJ
ap-4038	161	2	space	space	NOUN
ap-4038	161	3	-	-	PUNCT
ap-4038	161	4	partitioning	partitioning	NOUN
ap-4038	161	5	is	be	AUX
ap-4038	161	6	,	,	PUNCT
ap-4038	161	7	generally	generally	ADV
ap-4038	161	8	speaking	speak	VERB
ap-4038	161	9	,	,	PUNCT
ap-4038	161	10	a	a	DET
ap-4038	161	11	method	method	NOUN
ap-4038	161	12	for	for	ADP
ap-4038	161	13	recursively	recursively	ADV
ap-4038	161	14	subdividing	subdivide	VERB
ap-4038	161	15	a	a	DET
ap-4038	161	16	space	space	NOUN
ap-4038	161	17	into	into	ADP
ap-4038	161	18	convex	convex	NOUN
ap-4038	161	19	sets	set	NOUN
ap-4038	161	20	by	by	ADP
ap-4038	161	21	hyper	hyper	NOUN
ap-4038	161	22	-	-	NOUN
ap-4038	161	23	planes	plane	NOUN
ap-4038	161	24	.	.	PUNCT
ap-4038	162	1	this	this	DET
ap-4038	162	2	subdivision	subdivision	NOUN
ap-4038	162	3	of	of	ADP
ap-4038	162	4	the	the	DET
ap-4038	162	5	space	space	NOUN
ap-4038	162	6	enables	enable	VERB
ap-4038	162	7	polyhedra	polyhedra	NOUN
ap-4038	162	8	(	(	PUNCT
ap-4038	162	9	in	in	ADP
ap-4038	162	10	general	general	ADJ
ap-4038	162	11	not	not	PART
ap-4038	162	12	necessarily	necessarily	ADV
ap-4038	162	13	convex	convex	VERB
ap-4038	162	14	polyhedra	polyhedra	NOUN
ap-4038	162	15	)	)	PUNCT
ap-4038	162	16	to	to	PART
ap-4038	162	17	be	be	AUX
ap-4038	162	18	represented	represent	VERB
ap-4038	162	19	within	within	ADP
ap-4038	162	20	the	the	DET
ap-4038	162	21	space	space	NOUN
ap-4038	162	22	by	by	ADP
ap-4038	162	23	means	mean	NOUN
ap-4038	162	24	of	of	ADP
ap-4038	162	25	a	a	DET
ap-4038	162	26	tree	tree	NOUN
ap-4038	162	27	data	data	NOUN
ap-4038	162	28	structure	structure	NOUN
ap-4038	162	29	known	know	VERB
ap-4038	162	30	as	as	ADP
ap-4038	162	31	a	a	DET
ap-4038	162	32	bsp	bsp	NOUN
ap-4038	162	33	tree	tree	NOUN
ap-4038	162	34	,	,	PUNCT
ap-4038	162	35	see	see	VERB
ap-4038	162	36	[	[	X
ap-4038	162	37	18	18	NUM
ap-4038	162	38	]	]	PUNCT
ap-4038	162	39	.	.	PUNCT
ap-4038	163	1	the	the	DET
ap-4038	163	2	idea	idea	NOUN
ap-4038	163	3	is	be	AUX
ap-4038	163	4	that	that	SCONJ
ap-4038	163	5	a	a	DET
ap-4038	163	6	given	give	VERB
ap-4038	163	7	plane	plane	NOUN
ap-4038	163	8	n·x−c	n·x−c	NOUN
ap-4038	163	9	=	=	SYM
ap-4038	163	10	0	0	PROPN
ap-4038	163	11	partitions	partition	VERB
ap-4038	163	12	the	the	DET
ap-4038	163	13	space	space	NOUN
ap-4038	163	14	(	(	PUNCT
ap-4038	163	15	here	here	ADV
ap-4038	163	16	,	,	PUNCT
ap-4038	163	17	we	we	PRON
ap-4038	163	18	assume	assume	VERB
ap-4038	163	19	that	that	SCONJ
ap-4038	163	20	the	the	DET
ap-4038	163	21	space	space	NOUN
ap-4038	163	22	is	be	AUX
ap-4038	163	23	bounded	bound	VERB
ap-4038	163	24	)	)	PUNCT
ap-4038	163	25	into	into	ADP
ap-4038	163	26	two	two	NUM
ap-4038	163	27	sub	sub	NOUN
ap-4038	163	28	-	-	NOUN
ap-4038	163	29	spaces	space	NOUN
ap-4038	163	30	.	.	PUNCT
ap-4038	164	1	according	accord	VERB
ap-4038	164	2	to	to	ADP
ap-4038	164	3	the	the	DET
ap-4038	164	4	plane	plane	NOUN
ap-4038	164	5	normal	normal	ADJ
ap-4038	164	6	n	n	CCONJ
ap-4038	164	7	,	,	PUNCT
ap-4038	164	8	one	one	NUM
ap-4038	164	9	of	of	ADP
ap-4038	164	10	the	the	DET
ap-4038	164	11	sub	sub	NOUN
ap-4038	164	12	-	-	NOUN
ap-4038	164	13	spaces	space	NOUN
ap-4038	164	14	can	can	AUX
ap-4038	164	15	be	be	AUX
ap-4038	164	16	called	call	VERB
ap-4038	164	17	positive	positive	ADJ
ap-4038	164	18	(	(	PUNCT
ap-4038	164	19	the	the	DET
ap-4038	164	20	points	point	NOUN
ap-4038	164	21	in	in	ADP
ap-4038	164	22	that	that	DET
ap-4038	164	23	subspace	subspace	NOUN
ap-4038	164	24	lies	lie	VERB
ap-4038	164	25	on	on	ADP
ap-4038	164	26	the	the	DET
ap-4038	164	27	side	side	NOUN
ap-4038	164	28	to	to	ADP
ap-4038	164	29	which	which	PRON
ap-4038	164	30	n	n	NUM
ap-4038	164	31	points	point	NOUN
ap-4038	164	32	)	)	PUNCT
ap-4038	164	33	and	and	CCONJ
ap-4038	164	34	the	the	DET
ap-4038	164	35	other	other	ADJ
ap-4038	164	36	sub	sub	NOUN
ap-4038	164	37	-	-	NOUN
ap-4038	164	38	space	space	NOUN
ap-4038	164	39	can	can	AUX
ap-4038	164	40	be	be	AUX
ap-4038	164	41	called	call	VERB
ap-4038	164	42	negative	negative	ADJ
ap-4038	164	43	.	.	PUNCT
ap-4038	165	1	note	note	VERB
ap-4038	165	2	that	that	PRON
ap-4038	165	3	points	point	VERB
ap-4038	165	4	on	on	ADP
ap-4038	165	5	the	the	DET
ap-4038	165	6	positive	positive	ADJ
ap-4038	165	7	subspace	subspace	NOUN
ap-4038	165	8	satisfy	satisfy	VERB
ap-4038	165	9	the	the	DET
ap-4038	165	10	inequality	inequality	NOUN
ap-4038	165	11	n	n	PRON
ap-4038	165	12	·	·	PUNCT
ap-4038	165	13	x−	x−	PROPN
ap-4038	165	14	c	c	PROPN
ap-4038	165	15	>	>	X
ap-4038	165	16	0	0	NUM
ap-4038	165	17	,	,	PUNCT
ap-4038	165	18	and	and	CCONJ
ap-4038	165	19	vice	vice	ADV
ap-4038	165	20	versa	versa	ADV
ap-4038	165	21	.	.	PUNCT
ap-4038	166	1	both	both	CCONJ
ap-4038	166	2	the	the	DET
ap-4038	166	3	positive	positive	ADJ
ap-4038	166	4	subspaces	subspace	NOUN
ap-4038	166	5	and	and	CCONJ
ap-4038	166	6	the	the	DET
ap-4038	166	7	negative	negative	ADJ
ap-4038	166	8	sub	sub	NOUN
ap-4038	166	9	-	-	NOUN
ap-4038	166	10	spaces	space	NOUN
ap-4038	166	11	can	can	AUX
ap-4038	166	12	be	be	AUX
ap-4038	166	13	further	far	ADV
ap-4038	166	14	partitioned	partition	VERB
ap-4038	166	15	by	by	ADP
ap-4038	166	16	another	another	DET
ap-4038	166	17	plane	plane	NOUN
ap-4038	166	18	,	,	PUNCT
ap-4038	166	19	and	and	CCONJ
ap-4038	166	20	so	so	ADV
ap-4038	166	21	on	on	ADV
ap-4038	166	22	.	.	PUNCT
ap-4038	167	1	by	by	ADP
ap-4038	167	2	applying	apply	VERB
ap-4038	167	3	this	this	DET
ap-4038	167	4	recursive	recursive	ADJ
ap-4038	167	5	procedure	procedure	NOUN
ap-4038	167	6	,	,	PUNCT
ap-4038	167	7	one	one	PRON
ap-4038	167	8	obtains	obtain	VERB
ap-4038	167	9	the	the	DET
ap-4038	167	10	partitioning	partitioning	NOUN
ap-4038	167	11	of	of	ADP
ap-4038	167	12	the	the	DET
ap-4038	167	13	original	original	ADJ
ap-4038	167	14	space	space	NOUN
ap-4038	167	15	represented	represent	VERB
ap-4038	167	16	by	by	ADP
ap-4038	167	17	a	a	DET
ap-4038	167	18	binary	binary	ADJ
ap-4038	167	19	tree	tree	NOUN
ap-4038	167	20	.	.	PUNCT
ap-4038	168	1	tho	tho	INTJ
ap-4038	168	2	nodes	node	NOUN
ap-4038	168	3	of	of	ADP
ap-4038	168	4	the	the	DET
ap-4038	168	5	tree	tree	NOUN
ap-4038	168	6	represent	represent	VERB
ap-4038	168	7	the	the	DET
ap-4038	168	8	splitting	splitting	NOUN
ap-4038	168	9	planes	plane	NOUN
ap-4038	168	10	.	.	PUNCT
ap-4038	169	1	hence	hence	ADV
ap-4038	169	2	,	,	PUNCT
ap-4038	169	3	a	a	DET
ap-4038	169	4	left	left	ADJ
ap-4038	169	5	child	child	NOUN
ap-4038	169	6	of	of	ADP
ap-4038	169	7	the	the	DET
ap-4038	169	8	node	node	NOUN
ap-4038	169	9	corresponds	correspond	VERB
ap-4038	169	10	to	to	ADP
ap-4038	169	11	a	a	DET
ap-4038	169	12	positive	positive	ADJ
ap-4038	169	13	subspace	subspace	NOUN
ap-4038	169	14	created	create	VERB
ap-4038	169	15	by	by	ADP
ap-4038	169	16	the	the	DET
ap-4038	169	17	plane	plane	NOUN
ap-4038	169	18	that	that	PRON
ap-4038	169	19	the	the	DET
ap-4038	169	20	node	node	NOUN
ap-4038	169	21	represents	represent	VERB
ap-4038	169	22	;	;	PUNCT
ap-4038	169	23	a	a	DET
ap-4038	169	24	right	right	ADJ
ap-4038	169	25	child	child	NOUN
ap-4038	169	26	corresponds	correspond	VERB
ap-4038	169	27	to	to	ADP
ap-4038	169	28	the	the	DET
ap-4038	169	29	negative	negative	ADJ
ap-4038	169	30	subspace	subspace	NOUN
ap-4038	169	31	.	.	PUNCT
ap-4038	170	1	the	the	DET
ap-4038	170	2	leaf	leaf	NOUN
ap-4038	170	3	nodes	node	NOUN
ap-4038	170	4	then	then	ADV
ap-4038	170	5	represents	represent	VERB
ap-4038	170	6	convex	convex	ADJ
ap-4038	170	7	regions	region	NOUN
ap-4038	170	8	obtained	obtain	VERB
ap-4038	170	9	by	by	ADP
ap-4038	170	10	partitioning	partition	VERB
ap-4038	170	11	.	.	PUNCT
ap-4038	171	1	the	the	DET
ap-4038	171	2	idea	idea	NOUN
ap-4038	171	3	is	be	AUX
ap-4038	171	4	illustrated	illustrate	VERB
ap-4038	171	5	in	in	ADP
ap-4038	171	6	fig	fig	NOUN
ap-4038	171	7	.	.	PUNCT
ap-4038	172	1	2	2	NUM
ap-4038	172	2	,	,	PUNCT
ap-4038	172	3	which	which	PRON
ap-4038	172	4	is	be	AUX
ap-4038	172	5	for	for	ADP
ap-4038	172	6	clarity	clarity	NOUN
ap-4038	172	7	represented	represent	VERB
ap-4038	172	8	only	only	ADV
ap-4038	172	9	in	in	ADP
ap-4038	172	10	2d	2d	NOUN
ap-4038	172	11	.	.	PUNCT
ap-4038	173	1	splitting	splitting	NOUN
ap-4038	173	2	lines	line	NOUN
ap-4038	173	3	are	be	AUX
ap-4038	173	4	denoted	denote	VERB
ap-4038	173	5	as	as	ADP
ap-4038	173	6	pi	pi	NOUN
ap-4038	173	7	,	,	PUNCT
ap-4038	173	8	convex	convex	ADJ
ap-4038	173	9	regions	region	NOUN
ap-4038	173	10	are	be	AUX
ap-4038	173	11	denoted	denote	VERB
ap-4038	173	12	as	as	ADP
ap-4038	173	13	cj	cj	NOUN
ap-4038	173	14	.	.	PUNCT
ap-4038	174	1	the	the	DET
ap-4038	174	2	sign	sign	NOUN
ap-4038	174	3	over	over	ADP
ap-4038	174	4	each	each	DET
ap-4038	174	5	edge	edge	NOUN
ap-4038	174	6	of	of	ADP
ap-4038	174	7	the	the	DET
ap-4038	174	8	tree	tree	NOUN
ap-4038	174	9	indicates	indicate	VERB
ap-4038	174	10	the	the	DET
ap-4038	174	11	positive	positive	ADJ
ap-4038	174	12	and	and	CCONJ
ap-4038	174	13	negative	negative	ADJ
ap-4038	174	14	subspace	subspace	NOUN
ap-4038	174	15	.	.	PUNCT
ap-4038	175	1	the	the	DET
ap-4038	175	2	structure	structure	NOUN
ap-4038	175	3	of	of	ADP
ap-4038	175	4	the	the	DET
ap-4038	175	5	bsp	bsp	NOUN
ap-4038	175	6	tree	tree	NOUN
ap-4038	175	7	for	for	ADP
ap-4038	175	8	partitioning	partition	VERB
ap-4038	175	9	the	the	DET
ap-4038	175	10	space	space	NOUN
ap-4038	175	11	can	can	AUX
ap-4038	175	12	easily	easily	ADV
ap-4038	175	13	be	be	AUX
ap-4038	175	14	used	use	VERB
ap-4038	175	15	for	for	ADP
ap-4038	175	16	partitioning	partition	VERB
ap-4038	175	17	a	a	DET
ap-4038	175	18	polyhedron	polyhedron	NOUN
ap-4038	175	19	into	into	ADP
ap-4038	175	20	convex	convex	ADJ
ap-4038	175	21	sub	sub	NOUN
ap-4038	175	22	-	-	ADJ
ap-4038	175	23	polyhedra	polyhedra	ADJ
ap-4038	175	24	.	.	PUNCT
ap-4038	176	1	this	this	PRON
ap-4038	176	2	can	can	AUX
ap-4038	176	3	be	be	AUX
ap-4038	176	4	done	do	VERB
ap-4038	176	5	by	by	ADP
ap-4038	176	6	creating	create	VERB
ap-4038	176	7	the	the	DET
ap-4038	176	8	nodes	node	NOUN
ap-4038	176	9	of	of	ADP
ap-4038	176	10	the	the	DET
ap-4038	176	11	tree	tree	NOUN
ap-4038	176	12	in	in	ADP
ap-4038	176	13	such	such	DET
ap-4038	176	14	a	a	DET
ap-4038	176	15	way	way	NOUN
ap-4038	176	16	that	that	PRON
ap-4038	176	17	each	each	DET
ap-4038	176	18	node	node	NOUN
ap-4038	176	19	represents	represent	VERB
ap-4038	176	20	a	a	DET
ap-4038	176	21	suitable	suitable	ADJ
ap-4038	176	22	108	108	NUM
ap-4038	176	23	vol	vol	NOUN
ap-4038	176	24	.	.	PUNCT
ap-4038	177	1	57	57	NUM
ap-4038	178	1	no	no	NOUN
ap-4038	178	2	.	.	PUNCT
ap-4038	179	1	2/2017	2/2017	NUM
ap-4038	179	2	implementation	implementation	NOUN
ap-4038	179	3	of	of	ADP
ap-4038	179	4	a	a	DET
ap-4038	179	5	3d	3d	NUM
ap-4038	179	6	vof	vof	NOUN
ap-4038	179	7	tracking	tracking	NOUN
ap-4038	179	8	algorithm	algorithm	NOUN
ap-4038	179	9	f=0.8	f=0.8	VERB
ap-4038	179	10	(	(	PUNCT
ap-4038	179	11	a	a	X
ap-4038	179	12	)	)	PUNCT
ap-4038	179	13	lagrangian	lagrangian	ADJ
ap-4038	179	14	step	step	NOUN
ap-4038	179	15	f=0.8	f=0.8	VERB
ap-4038	179	16	(	(	PUNCT
ap-4038	179	17	c	c	NOUN
ap-4038	179	18	)	)	PUNCT
ap-4038	179	19	remapping	remappe	VERB
ap-4038	179	20	steps(b	steps(b	NOUN
ap-4038	179	21	)	)	PUNCT
ap-4038	179	22	reconstruction	reconstruction	NOUN
ap-4038	179	23	step	step	NOUN
ap-4038	179	24	f=0.8	f=0.8	NOUN
ap-4038	179	25	figure	figure	NOUN
ap-4038	179	26	1	1	NUM
ap-4038	179	27	.	.	PUNCT
ap-4038	179	28	illustration	illustration	NOUN
ap-4038	179	29	of	of	ADP
ap-4038	179	30	the	the	DET
ap-4038	179	31	three	three	NUM
ap-4038	179	32	phases	phase	NOUN
ap-4038	179	33	of	of	ADP
ap-4038	179	34	the	the	DET
ap-4038	179	35	interface	interface	NOUN
ap-4038	179	36	update	update	NOUN
ap-4038	179	37	algorithm	algorithm	NOUN
ap-4038	179	38	.	.	PUNCT
ap-4038	180	1	c2	c2	PROPN
ap-4038	180	2	c0	c0	PROPN
ap-4038	180	3	c3	c3	PROPN
ap-4038	180	4	c4	c4	PROPN
ap-4038	180	5	c1	c1	PROPN
ap-4038	180	6	p0	p0	PROPN
ap-4038	180	7	p1	p1	PROPN
ap-4038	180	8	p2	p2	PROPN
ap-4038	180	9	p3	p3	PROPN
ap-4038	180	10	+	+	PROPN
ap-4038	180	11	+	+	ADJ
ap-4038	180	12	+	+	ADJ
ap-4038	180	13	+	+	ADJ
ap-4038	180	14	+	+	ADJ
ap-4038	180	15	+	+	PUNCT
ap-4038	180	16	+	+	CCONJ
ap-4038	180	17	+	+	CCONJ
ap-4038	180	18	p0	p0	NOUN
ap-4038	180	19	p1	p1	NOUN
ap-4038	180	20	p2	p2	PROPN
ap-4038	180	21	c0	c0	PROPN
ap-4038	180	22	p3	p3	PROPN
ap-4038	180	23	c3	c3	PROPN
ap-4038	180	24	c4	c4	PROPN
ap-4038	180	25	c1	c1	PROPN
ap-4038	180	26	c2	c2	PROPN
ap-4038	180	27	figure	figure	NOUN
ap-4038	180	28	2	2	NUM
ap-4038	180	29	.	.	PUNCT
ap-4038	180	30	bsp	bsp	VERB
ap-4038	180	31	tree	tree	NOUN
ap-4038	180	32	2d	2d	NUM
ap-4038	180	33	illustration	illustration	NOUN
ap-4038	180	34	.	.	PUNCT
ap-4038	181	1	the	the	DET
ap-4038	181	2	nodes	node	NOUN
ap-4038	181	3	correspond	correspond	VERB
ap-4038	181	4	to	to	ADP
ap-4038	181	5	splitting	split	VERB
ap-4038	181	6	lines	line	NOUN
ap-4038	181	7	denoted	denote	VERB
ap-4038	181	8	as	as	ADP
ap-4038	181	9	p	p	PROPN
ap-4038	181	10	′s	′s	PROPN
ap-4038	181	11	.	.	PUNCT
ap-4038	182	1	the	the	DET
ap-4038	182	2	leaf	leaf	NOUN
ap-4038	182	3	nodes	node	NOUN
ap-4038	182	4	represent	represent	VERB
ap-4038	182	5	final	final	ADJ
ap-4038	182	6	convex	convex	ADJ
ap-4038	182	7	sub	sub	NOUN
ap-4038	182	8	-	-	NOUN
ap-4038	182	9	regions	region	NOUN
ap-4038	182	10	,	,	PUNCT
ap-4038	182	11	denoted	denote	VERB
ap-4038	182	12	as	as	ADP
ap-4038	182	13	c′s	c′s	ADJ
ap-4038	182	14	splitting	splitting	NOUN
ap-4038	182	15	plane	plane	NOUN
ap-4038	182	16	(	(	PUNCT
ap-4038	182	17	that	that	DET
ap-4038	182	18	splitting	splitting	NOUN
ap-4038	182	19	plane	plane	NOUN
ap-4038	182	20	may	may	AUX
ap-4038	182	21	or	or	CCONJ
ap-4038	182	22	may	may	AUX
ap-4038	182	23	not	not	PART
ap-4038	182	24	coincide	coincide	VERB
ap-4038	182	25	with	with	ADP
ap-4038	182	26	actual	actual	ADJ
ap-4038	182	27	face	face	NOUN
ap-4038	182	28	of	of	ADP
ap-4038	182	29	the	the	DET
ap-4038	182	30	polyhedron	polyhedron	NOUN
ap-4038	182	31	)	)	PUNCT
ap-4038	182	32	.	.	PUNCT
ap-4038	183	1	other	other	ADJ
ap-4038	183	2	faces	face	NOUN
ap-4038	183	3	are	be	AUX
ap-4038	183	4	split	split	VERB
ap-4038	183	5	at	at	ADP
ap-4038	183	6	that	that	DET
ap-4038	183	7	node	node	NOUN
ap-4038	183	8	by	by	ADP
ap-4038	183	9	using	use	VERB
ap-4038	183	10	the	the	DET
ap-4038	183	11	corresponding	corresponding	ADJ
ap-4038	183	12	splitting	splitting	NOUN
ap-4038	183	13	plane	plane	NOUN
ap-4038	183	14	.	.	PUNCT
ap-4038	184	1	all	all	DET
ap-4038	184	2	the	the	DET
ap-4038	184	3	faces	face	NOUN
ap-4038	184	4	that	that	PRON
ap-4038	184	5	are	be	AUX
ap-4038	184	6	on	on	ADP
ap-4038	184	7	the	the	DET
ap-4038	184	8	positive	positive	ADJ
ap-4038	184	9	side	side	NOUN
ap-4038	184	10	of	of	ADP
ap-4038	184	11	that	that	DET
ap-4038	184	12	plane	plane	NOUN
ap-4038	184	13	are	be	AUX
ap-4038	184	14	sent	send	VERB
ap-4038	184	15	to	to	ADP
ap-4038	184	16	the	the	DET
ap-4038	184	17	positive	positive	ADJ
ap-4038	184	18	child	child	NOUN
ap-4038	184	19	,	,	PUNCT
ap-4038	184	20	and	and	CCONJ
ap-4038	184	21	all	all	DET
ap-4038	184	22	the	the	DET
ap-4038	184	23	faces	face	NOUN
ap-4038	184	24	on	on	ADP
ap-4038	184	25	the	the	DET
ap-4038	184	26	negative	negative	ADJ
ap-4038	184	27	side	side	NOUN
ap-4038	184	28	are	be	AUX
ap-4038	184	29	sent	send	VERB
ap-4038	184	30	to	to	ADP
ap-4038	184	31	the	the	DET
ap-4038	184	32	negative	negative	ADJ
ap-4038	184	33	child	child	NOUN
ap-4038	184	34	of	of	ADP
ap-4038	184	35	the	the	DET
ap-4038	184	36	tree	tree	NOUN
ap-4038	184	37	.	.	PUNCT
ap-4038	185	1	the	the	DET
ap-4038	185	2	process	process	NOUN
ap-4038	185	3	is	be	AUX
ap-4038	185	4	then	then	ADV
ap-4038	185	5	repeated	repeat	VERB
ap-4038	185	6	,	,	PUNCT
ap-4038	185	7	so	so	CCONJ
ap-4038	185	8	the	the	DET
ap-4038	185	9	binary	binary	ADJ
ap-4038	185	10	tree	tree	NOUN
ap-4038	185	11	is	be	AUX
ap-4038	185	12	computed	compute	VERB
ap-4038	185	13	recursively	recursively	ADV
ap-4038	185	14	.	.	PUNCT
ap-4038	186	1	a	a	DET
ap-4038	186	2	face	face	NOUN
ap-4038	186	3	which	which	PRON
ap-4038	186	4	accidentally	accidentally	ADV
ap-4038	186	5	lies	lie	VERB
ap-4038	186	6	fully	fully	ADV
ap-4038	186	7	on	on	ADP
ap-4038	186	8	the	the	DET
ap-4038	186	9	splitting	splitting	NOUN
ap-4038	186	10	plane	plane	NOUN
ap-4038	186	11	is	be	AUX
ap-4038	186	12	also	also	ADV
ap-4038	186	13	stored	store	VERB
ap-4038	186	14	at	at	ADP
ap-4038	186	15	the	the	DET
ap-4038	186	16	corresponding	corresponding	ADJ
ap-4038	186	17	node	node	NOUN
ap-4038	186	18	,	,	PUNCT
ap-4038	186	19	and	and	CCONJ
ap-4038	186	20	it	it	PRON
ap-4038	186	21	is	be	AUX
ap-4038	186	22	denoted	denote	VERB
ap-4038	186	23	as	as	ADP
ap-4038	186	24	a	a	DET
ap-4038	186	25	coincident	coincident	ADJ
ap-4038	186	26	face	face	NOUN
ap-4038	186	27	.	.	PUNCT
ap-4038	187	1	the	the	DET
ap-4038	187	2	pseudo	pseudo	NOUN
ap-4038	187	3	-	-	NOUN
ap-4038	187	4	code	code	NOUN
ap-4038	187	5	for	for	ADP
ap-4038	187	6	constructing	construct	VERB
ap-4038	187	7	a	a	DET
ap-4038	187	8	bsp	bsp	NOUN
ap-4038	187	9	tree	tree	NOUN
ap-4038	187	10	,	,	PUNCT
ap-4038	187	11	motivated	motivate	VERB
ap-4038	187	12	by	by	ADP
ap-4038	187	13	[	[	X
ap-4038	187	14	18	18	NUM
ap-4038	187	15	]	]	PUNCT
ap-4038	187	16	,	,	PUNCT
ap-4038	187	17	is	be	AUX
ap-4038	187	18	shown	show	VERB
ap-4038	187	19	below	below	ADP
ap-4038	187	20	.	.	PUNCT
ap-4038	188	1	the	the	DET
ap-4038	188	2	key	key	ADJ
ap-4038	188	3	stage	stage	NOUN
ap-4038	188	4	of	of	ADP
ap-4038	188	5	bsp	bsp	NOUN
ap-4038	188	6	tree	tree	NOUN
ap-4038	188	7	construction	construction	NOUN
ap-4038	188	8	is	be	AUX
ap-4038	188	9	classification	classification	NOUN
ap-4038	188	10	of	of	ADP
ap-4038	188	11	the	the	DET
ap-4038	188	12	mutual	mutual	ADJ
ap-4038	188	13	position	position	NOUN
ap-4038	188	14	between	between	ADP
ap-4038	188	15	the	the	DET
ap-4038	188	16	splitting	splitting	NOUN
ap-4038	188	17	plane	plane	NOUN
ap-4038	188	18	and	and	CCONJ
ap-4038	188	19	the	the	DET
ap-4038	188	20	given	give	VERB
ap-4038	188	21	face	face	NOUN
ap-4038	188	22	,	,	PUNCT
ap-4038	188	23	represented	represent	VERB
ap-4038	188	24	by	by	ADP
ap-4038	188	25	the	the	DET
ap-4038	188	26	classifyface	classifyface	NOUN
ap-4038	188	27	function	function	NOUN
ap-4038	188	28	.	.	PUNCT
ap-4038	189	1	the	the	DET
ap-4038	189	2	classification	classification	NOUN
ap-4038	189	3	is	be	AUX
ap-4038	189	4	performed	perform	VERB
ap-4038	189	5	with	with	ADP
ap-4038	189	6	the	the	DET
ap-4038	189	7	help	help	NOUN
ap-4038	189	8	of	of	ADP
ap-4038	189	9	standard	standard	ADJ
ap-4038	189	10	methods	method	NOUN
ap-4038	189	11	used	use	VERB
ap-4038	189	12	in	in	ADP
ap-4038	189	13	analytic	analytic	ADJ
ap-4038	189	14	geometry	geometry	NOUN
ap-4038	189	15	.	.	PUNCT
ap-4038	190	1	however	however	ADV
ap-4038	190	2	,	,	PUNCT
ap-4038	190	3	due	due	ADP
ap-4038	190	4	to	to	ADP
ap-4038	190	5	the	the	DET
ap-4038	190	6	round	round	VERB
ap-4038	190	7	-	-	PUNCT
ap-4038	190	8	off	off	ADP
ap-4038	190	9	errors	error	NOUN
ap-4038	190	10	,	,	PUNCT
ap-4038	190	11	it	it	PRON
ap-4038	190	12	is	be	AUX
ap-4038	190	13	necessary	necessary	ADJ
ap-4038	190	14	to	to	PART
ap-4038	190	15	set	set	VERB
ap-4038	190	16	up	up	ADP
ap-4038	190	17	appropriate	appropriate	ADJ
ap-4038	190	18	tolerance	tolerance	NOUN
ap-4038	190	19	ε	ε	PROPN
ap-4038	190	20	under	under	ADP
ap-4038	190	21	which	which	PRON
ap-4038	190	22	we	we	PRON
ap-4038	190	23	consider	consider	VERB
ap-4038	190	24	the	the	DET
ap-4038	190	25	face	face	NOUN
ap-4038	190	26	and	and	CCONJ
ap-4038	190	27	the	the	DET
ap-4038	190	28	splitting	splitting	NOUN
ap-4038	190	29	plane	plane	NOUN
ap-4038	190	30	as	as	ADP
ap-4038	190	31	coincident	coincident	NOUN
ap-4038	190	32	.	.	PUNCT
ap-4038	191	1	our	our	PRON
ap-4038	191	2	experience	experience	NOUN
ap-4038	191	3	is	be	AUX
ap-4038	191	4	that	that	SCONJ
ap-4038	191	5	ε	ε	PROPN
ap-4038	191	6	depends	depend	VERB
ap-4038	191	7	on	on	ADP
ap-4038	191	8	the	the	DET
ap-4038	191	9	problem	problem	NOUN
ap-4038	191	10	that	that	PRON
ap-4038	191	11	is	be	AUX
ap-4038	191	12	to	to	PART
ap-4038	191	13	be	be	AUX
ap-4038	191	14	solved	solve	VERB
ap-4038	191	15	(	(	PUNCT
ap-4038	191	16	i.e.	i.e.	X
ap-4038	191	17	element	element	ADJ
ap-4038	191	18	size	size	NOUN
ap-4038	191	19	and	and	CCONJ
ap-4038	191	20	time	time	NOUN
ap-4038	191	21	step	step	NOUN
ap-4038	191	22	)	)	PUNCT
ap-4038	191	23	and	and	CCONJ
ap-4038	191	24	a	a	DET
ap-4038	191	25	typical	typical	ADJ
ap-4038	191	26	value	value	NOUN
ap-4038	191	27	is	be	AUX
ap-4038	191	28	10−11	10−11	NUM
ap-4038	191	29	.	.	PUNCT
ap-4038	192	1	3.2.1	3.2.1	NUM
ap-4038	192	2	.	.	PUNCT
ap-4038	193	1	intersection	intersection	NOUN
ap-4038	193	2	of	of	ADP
ap-4038	193	3	polyhedra	polyhedra	NOUN
ap-4038	193	4	the	the	DET
ap-4038	193	5	intersection	intersection	NOUN
ap-4038	193	6	of	of	ADP
ap-4038	193	7	two	two	NUM
ap-4038	193	8	polyhedra	polyhedra	NOUN
ap-4038	193	9	is	be	AUX
ap-4038	193	10	theoretically	theoretically	ADV
ap-4038	193	11	a	a	DET
ap-4038	193	12	trivial	trivial	ADJ
ap-4038	193	13	task	task	NOUN
ap-4038	193	14	,	,	PUNCT
ap-4038	193	15	and	and	CCONJ
ap-4038	193	16	can	can	AUX
ap-4038	193	17	be	be	AUX
ap-4038	193	18	computed	compute	VERB
ap-4038	193	19	in	in	ADP
ap-4038	193	20	a	a	DET
ap-4038	193	21	straightforward	straightforward	ADJ
ap-4038	193	22	manner	manner	NOUN
ap-4038	193	23	.	.	PUNCT
ap-4038	194	1	however	however	ADV
ap-4038	194	2	,	,	PUNCT
ap-4038	194	3	implementation	implementation	NOUN
ap-4038	194	4	in	in	ADP
ap-4038	194	5	floating	float	VERB
ap-4038	194	6	point	point	NOUN
ap-4038	194	7	arithmetic	arithmetic	ADJ
ap-4038	194	8	requires	require	VERB
ap-4038	194	9	careful	careful	ADJ
ap-4038	194	10	treatment	treatment	NOUN
ap-4038	194	11	of	of	ADP
ap-4038	194	12	some	some	DET
ap-4038	194	13	special	special	ADJ
ap-4038	194	14	situations	situation	NOUN
ap-4038	194	15	.	.	PUNCT
ap-4038	195	1	we	we	PRON
ap-4038	195	2	will	will	AUX
ap-4038	195	3	go	go	VERB
ap-4038	195	4	into	into	ADP
ap-4038	195	5	this	this	DET
ap-4038	195	6	matter	matter	NOUN
ap-4038	195	7	below	below	ADV
ap-4038	195	8	.	.	PUNCT
ap-4038	196	1	let	let	VERB
ap-4038	196	2	us	we	PRON
ap-4038	196	3	say	say	VERB
ap-4038	196	4	that	that	SCONJ
ap-4038	196	5	we	we	PRON
ap-4038	196	6	want	want	VERB
ap-4038	196	7	to	to	PART
ap-4038	196	8	intersect	intersect	ADJ
ap-4038	196	9	polyhedron	polyhedron	NOUN
ap-4038	196	10	p	p	NOUN
ap-4038	196	11	with	with	ADP
ap-4038	196	12	polyhedron	polyhedron	NOUN
ap-4038	196	13	q.	q.	NOUN
ap-4038	196	14	the	the	DET
ap-4038	196	15	idea	idea	NOUN
ap-4038	196	16	is	be	AUX
ap-4038	196	17	to	to	PART
ap-4038	196	18	intersect	intersect	VERB
ap-4038	196	19	each	each	DET
ap-4038	196	20	face	face	NOUN
ap-4038	196	21	of	of	ADP
ap-4038	196	22	algorithm	algorithm	NOUN
ap-4038	196	23	2	2	NUM
ap-4038	196	24	bsp	bsp	NOUN
ap-4038	196	25	tree	tree	NOUN
ap-4038	196	26	construction	construction	NOUN
ap-4038	196	27	1	1	NUM
ap-4038	196	28	:	:	PUNCT
ap-4038	196	29	procedure	procedure	NOUN
ap-4038	196	30	constructbsptree(facelist	constructbsptree(facelist	PROPN
ap-4038	196	31	)	)	PUNCT
ap-4038	197	1	2	2	NUM
ap-4038	197	2	:	:	PUNCT
ap-4038	198	1	p	p	X
ap-4038	198	2	=	=	PUNCT
ap-4038	198	3	getplanefromface(facelist.first	getplanefromface(facelist.first	NOUN
ap-4038	198	4	(	(	PUNCT
ap-4038	198	5	)	)	PUNCT
ap-4038	198	6	)	)	PUNCT
ap-4038	199	1	3	3	NUM
ap-4038	199	2	:	:	PUNCT
ap-4038	199	3	for	for	ADP
ap-4038	199	4	all	all	DET
ap-4038	199	5	faces	face	NOUN
ap-4038	199	6	in	in	ADP
ap-4038	199	7	facelist	facelist	NOUN
ap-4038	199	8	do	do	VERB
ap-4038	199	9	4	4	NUM
ap-4038	199	10	:	:	PUNCT
ap-4038	199	11	type	type	NOUN
ap-4038	199	12	=	=	SYM
ap-4038	199	13	classifyface(p	classifyface(p	NOUN
ap-4038	199	14	,	,	PUNCT
ap-4038	199	15	face	face	NOUN
ap-4038	199	16	)	)	PUNCT
ap-4038	199	17	5	5	NUM
ap-4038	199	18	:	:	PUNCT
ap-4038	199	19	if	if	SCONJ
ap-4038	199	20	type	type	NOUN
ap-4038	199	21	=	=	NOUN
ap-4038	199	22	crosses	crosse	NOUN
ap-4038	199	23	then	then	ADV
ap-4038	199	24	6	6	NUM
ap-4038	199	25	:	:	PUNCT
ap-4038	199	26	(	(	PUNCT
ap-4038	199	27	posface	posface	NOUN
ap-4038	199	28	,	,	PUNCT
ap-4038	199	29	negface	negface	NOUN
ap-4038	199	30	)	)	PUNCT
ap-4038	199	31	=	=	SYM
ap-4038	199	32	splitface(p	splitface(p	NOUN
ap-4038	199	33	,	,	PUNCT
ap-4038	199	34	face	face	NOUN
ap-4038	199	35	)	)	PUNCT
ap-4038	199	36	;	;	PUNCT
ap-4038	199	37	7	7	NUM
ap-4038	199	38	:	:	PUNCT
ap-4038	199	39	addtoposlist(posface	addtoposlist(posface	PROPN
ap-4038	199	40	)	)	PUNCT
ap-4038	199	41	;	;	PUNCT
ap-4038	199	42	8	8	NUM
ap-4038	199	43	:	:	PUNCT
ap-4038	199	44	addtoneglist(negface	addtoneglist(negface	PROPN
ap-4038	199	45	)	)	PUNCT
ap-4038	199	46	;	;	PUNCT
ap-4038	199	47	9	9	NUM
ap-4038	199	48	:	:	PUNCT
ap-4038	199	49	else	else	ADV
ap-4038	199	50	if	if	SCONJ
ap-4038	199	51	type	type	NOUN
ap-4038	199	52	=	=	PUNCT
ap-4038	199	53	positive	positive	ADJ
ap-4038	199	54	then	then	ADV
ap-4038	199	55	10	10	NUM
ap-4038	199	56	:	:	PUNCT
ap-4038	199	57	addtoposlist(face	addtoposlist(face	PROPN
ap-4038	199	58	)	)	PUNCT
ap-4038	199	59	;	;	PUNCT
ap-4038	199	60	11	11	NUM
ap-4038	199	61	:	:	PUNCT
ap-4038	199	62	else	else	ADV
ap-4038	199	63	if	if	SCONJ
ap-4038	199	64	type	type	NOUN
ap-4038	199	65	=	=	PUNCT
ap-4038	199	66	negative	negative	ADJ
ap-4038	199	67	then	then	ADV
ap-4038	199	68	12	12	NUM
ap-4038	199	69	:	:	PUNCT
ap-4038	199	70	addtoneglist(face	addtoneglist(face	PROPN
ap-4038	199	71	)	)	PUNCT
ap-4038	199	72	;	;	PUNCT
ap-4038	199	73	13	13	NUM
ap-4038	199	74	:	:	PUNCT
ap-4038	199	75	else	else	ADV
ap-4038	199	76	if	if	SCONJ
ap-4038	199	77	type	type	NOUN
ap-4038	199	78	=	=	NOUN
ap-4038	199	79	coincident	coincident	NOUN
ap-4038	199	80	then	then	ADV
ap-4038	199	81	14	14	NUM
ap-4038	199	82	:	:	PUNCT
ap-4038	199	83	addtocoincident(face	addtocoincident(face	NOUN
ap-4038	199	84	)	)	PUNCT
ap-4038	199	85	;	;	PUNCT
ap-4038	199	86	15	15	NUM
ap-4038	199	87	:	:	PUNCT
ap-4038	199	88	end	end	VERB
ap-4038	199	89	if	if	SCONJ
ap-4038	199	90	16	16	NUM
ap-4038	199	91	:	:	PUNCT
ap-4038	199	92	end	end	VERB
ap-4038	199	93	for	for	ADP
ap-4038	199	94	17	17	NUM
ap-4038	199	95	:	:	PUNCT
ap-4038	199	96	constructtree(poslist	constructtree(poslist	PROPN
ap-4038	199	97	)	)	PUNCT
ap-4038	199	98	;	;	PUNCT
ap-4038	200	1	18	18	NUM
ap-4038	200	2	:	:	PUNCT
ap-4038	200	3	constructtree(neglist	constructtree(neglist	PROPN
ap-4038	200	4	)	)	PUNCT
ap-4038	200	5	;	;	PUNCT
ap-4038	200	6	19	19	NUM
ap-4038	200	7	:	:	PUNCT
ap-4038	200	8	end	end	NOUN
ap-4038	200	9	procedure	procedure	NOUN
ap-4038	200	10	algorithm	algorithm	NOUN
ap-4038	200	11	3	3	NUM
ap-4038	200	12	intersection	intersection	NOUN
ap-4038	200	13	of	of	ADP
ap-4038	200	14	polyhedra	polyhedra	NOUN
ap-4038	200	15	1	1	NUM
ap-4038	200	16	:	:	PUNCT
ap-4038	200	17	procedure	procedure	NOUN
ap-4038	200	18	intersectpoly(p	intersectpoly(p	PROPN
ap-4038	200	19	,	,	PUNCT
ap-4038	200	20	q	q	NOUN
ap-4038	200	21	)	)	PUNCT
ap-4038	200	22	2	2	NUM
ap-4038	200	23	:	:	PUNCT
ap-4038	200	24	q.constructbsptree(q.facelist	q.constructbsptree(q.facelist	PROPN
ap-4038	200	25	)	)	PUNCT
ap-4038	200	26	;	;	PUNCT
ap-4038	200	27	3	3	X
ap-4038	200	28	:	:	PUNCT
ap-4038	200	29	p.intersectwith(q	p.intersectwith(q	NOUN
ap-4038	200	30	)	)	PUNCT
ap-4038	200	31	;	;	PUNCT
ap-4038	200	32	4	4	NUM
ap-4038	200	33	:	:	PUNCT
ap-4038	200	34	p.constructbsptree(p.facelist	p.constructbsptree(p.facelist	NOUN
ap-4038	200	35	)	)	PUNCT
ap-4038	200	36	;	;	PUNCT
ap-4038	200	37	5	5	NUM
ap-4038	200	38	:	:	PUNCT
ap-4038	200	39	q.intersectwith(p	q.intersectwith(p	NOUN
ap-4038	200	40	)	)	PUNCT
ap-4038	200	41	;	;	PUNCT
ap-4038	200	42	6	6	NUM
ap-4038	200	43	:	:	PUNCT
ap-4038	200	44	end	end	NOUN
ap-4038	200	45	procedure	procedure	NOUN
ap-4038	200	46	p	p	NOUN
ap-4038	200	47	with	with	ADP
ap-4038	200	48	polyhedron	polyhedron	NOUN
ap-4038	200	49	q	q	NOUN
ap-4038	200	50	and	and	CCONJ
ap-4038	200	51	to	to	PART
ap-4038	200	52	keep	keep	VERB
ap-4038	200	53	all	all	DET
ap-4038	200	54	portions	portion	NOUN
ap-4038	200	55	of	of	ADP
ap-4038	200	56	the	the	DET
ap-4038	200	57	intersected	intersect	VERB
ap-4038	200	58	faces	face	NOUN
ap-4038	200	59	of	of	ADP
ap-4038	200	60	p	p	NOUN
ap-4038	200	61	that	that	PRON
ap-4038	200	62	lies	lie	VERB
ap-4038	200	63	inside	inside	ADP
ap-4038	200	64	q	q	NOUN
ap-4038	200	65	as	as	ADP
ap-4038	200	66	a	a	DET
ap-4038	200	67	part	part	NOUN
ap-4038	200	68	of	of	ADP
ap-4038	200	69	the	the	DET
ap-4038	200	70	intersection	intersection	NOUN
ap-4038	200	71	between	between	ADP
ap-4038	200	72	p	p	PROPN
ap-4038	200	73	and	and	CCONJ
ap-4038	200	74	q.	q.	PROPN
ap-4038	200	75	then	then	ADV
ap-4038	200	76	,	,	PUNCT
ap-4038	200	77	we	we	PRON
ap-4038	200	78	proceed	proceed	VERB
ap-4038	200	79	the	the	DET
ap-4038	200	80	other	other	ADJ
ap-4038	200	81	way	way	NOUN
ap-4038	200	82	around	around	ADV
ap-4038	200	83	,	,	PUNCT
ap-4038	200	84	i.e.	i.e.	X
ap-4038	200	85	we	we	PRON
ap-4038	200	86	intersect	intersect	VERB
ap-4038	200	87	all	all	DET
ap-4038	200	88	faces	face	NOUN
ap-4038	200	89	of	of	ADP
ap-4038	200	90	q	q	NOUN
ap-4038	200	91	with	with	ADP
ap-4038	200	92	polyhedron	polyhedron	NOUN
ap-4038	200	93	p	p	NOUN
ap-4038	200	94	and	and	CCONJ
ap-4038	200	95	keep	keep	VERB
ap-4038	200	96	all	all	DET
ap-4038	200	97	portions	portion	NOUN
ap-4038	200	98	of	of	ADP
ap-4038	200	99	the	the	DET
ap-4038	200	100	intersected	intersect	VERB
ap-4038	200	101	faces	face	NOUN
ap-4038	200	102	of	of	ADP
ap-4038	200	103	q	q	NOUN
ap-4038	200	104	lying	lie	VERB
ap-4038	200	105	inside	inside	ADP
ap-4038	200	106	p	p	NOUN
ap-4038	200	107	.	.	PUNCT
ap-4038	201	1	if	if	SCONJ
ap-4038	201	2	we	we	PRON
ap-4038	201	3	were	be	AUX
ap-4038	201	4	test	test	NOUN
ap-4038	201	5	for	for	ADP
ap-4038	201	6	intersection	intersection	NOUN
ap-4038	201	7	of	of	ADP
ap-4038	201	8	each	each	DET
ap-4038	201	9	face	face	NOUN
ap-4038	201	10	of	of	ADP
ap-4038	201	11	p	p	NOUN
ap-4038	201	12	with	with	ADP
ap-4038	201	13	each	each	DET
ap-4038	201	14	face	face	NOUN
ap-4038	201	15	of	of	ADP
ap-4038	201	16	q	q	NOUN
ap-4038	201	17	,	,	PUNCT
ap-4038	201	18	then	then	ADV
ap-4038	201	19	the	the	DET
ap-4038	201	20	resulting	result	VERB
ap-4038	201	21	algorithm	algorithm	NOUN
ap-4038	201	22	would	would	AUX
ap-4038	201	23	have	have	VERB
ap-4038	201	24	quadratic	quadratic	ADJ
ap-4038	201	25	complexity	complexity	NOUN
ap-4038	201	26	.	.	PUNCT
ap-4038	202	1	however	however	ADV
ap-4038	202	2	,	,	PUNCT
ap-4038	202	3	the	the	DET
ap-4038	202	4	use	use	NOUN
ap-4038	202	5	of	of	ADP
ap-4038	202	6	a	a	DET
ap-4038	202	7	bsp	bsp	NOUN
ap-4038	202	8	tree	tree	NOUN
ap-4038	202	9	reduces	reduce	VERB
ap-4038	202	10	the	the	DET
ap-4038	202	11	number	number	NOUN
ap-4038	202	12	of	of	ADP
ap-4038	202	13	comparisons	comparison	NOUN
ap-4038	202	14	,	,	PUNCT
ap-4038	202	15	because	because	SCONJ
ap-4038	202	16	a	a	DET
ap-4038	202	17	face	face	NOUN
ap-4038	202	18	on	on	ADP
ap-4038	202	19	one	one	NUM
ap-4038	202	20	side	side	NOUN
ap-4038	202	21	of	of	ADP
ap-4038	202	22	a	a	DET
ap-4038	202	23	splitting	splitting	NOUN
ap-4038	202	24	plane	plane	NOUN
ap-4038	202	25	does	do	AUX
ap-4038	202	26	not	not	PART
ap-4038	202	27	need	need	VERB
ap-4038	202	28	to	to	PART
ap-4038	202	29	be	be	AUX
ap-4038	202	30	tested	test	VERB
ap-4038	202	31	with	with	ADP
ap-4038	202	32	faces	face	NOUN
ap-4038	202	33	on	on	ADP
ap-4038	202	34	the	the	DET
ap-4038	202	35	other	other	ADJ
ap-4038	202	36	side	side	NOUN
ap-4038	202	37	of	of	ADP
ap-4038	202	38	the	the	DET
ap-4038	202	39	splitting	splitting	NOUN
ap-4038	202	40	plane	plane	NOUN
ap-4038	202	41	[	[	X
ap-4038	202	42	18	18	NUM
ap-4038	202	43	]	]	PUNCT
ap-4038	202	44	.	.	PUNCT
ap-4038	203	1	the	the	DET
ap-4038	203	2	main	main	ADJ
ap-4038	203	3	part	part	NOUN
ap-4038	203	4	of	of	ADP
ap-4038	203	5	algorithm	algorithm	NOUN
ap-4038	203	6	3	3	NUM
ap-4038	203	7	is	be	AUX
ap-4038	203	8	contained	contain	VERB
ap-4038	203	9	in	in	ADP
ap-4038	203	10	the	the	DET
ap-4038	203	11	intersectwith	intersectwith	ADJ
ap-4038	203	12	function	function	NOUN
ap-4038	203	13	.	.	PUNCT
ap-4038	204	1	basically	basically	ADV
ap-4038	204	2	,	,	PUNCT
ap-4038	204	3	this	this	PRON
ap-4038	204	4	function	function	VERB
ap-4038	204	5	109	109	NUM
ap-4038	204	6	filip	filip	NOUN
ap-4038	204	7	kolařík	kolařík	NOUN
ap-4038	204	8	,	,	PUNCT
ap-4038	204	9	bořek	bořek	PROPN
ap-4038	204	10	patzák	patzák	VERB
ap-4038	204	11	acta	acta	PROPN
ap-4038	204	12	polytechnica	polytechnica	PROPN
ap-4038	204	13	algorithm	algorithm	NOUN
ap-4038	204	14	4	4	NUM
ap-4038	204	15	intersection	intersection	NOUN
ap-4038	204	16	with	with	ADP
ap-4038	204	17	polyhedron	polyhedron	NOUN
ap-4038	204	18	1	1	NUM
ap-4038	204	19	:	:	PUNCT
ap-4038	204	20	procedure	procedure	NOUN
ap-4038	204	21	intersectwith(p	intersectwith(p	PROPN
ap-4038	204	22	)	)	PUNCT
ap-4038	204	23	2	2	NUM
ap-4038	204	24	:	:	PUNCT
ap-4038	204	25	for	for	ADP
ap-4038	204	26	all	all	DET
ap-4038	204	27	faces	face	NOUN
ap-4038	204	28	of	of	ADP
ap-4038	204	29	q	q	X
ap-4038	204	30	do	do	AUX
ap-4038	204	31	3	3	NUM
ap-4038	204	32	:	:	PUNCT
ap-4038	204	33	t	t	PROPN
ap-4038	204	34	=	=	SYM
ap-4038	204	35	p.givebsptree	p.givebsptree	NOUN
ap-4038	204	36	(	(	PUNCT
ap-4038	204	37	)	)	PUNCT
ap-4038	204	38	;	;	PUNCT
ap-4038	204	39	4	4	NUM
ap-4038	204	40	:	:	PUNCT
ap-4038	204	41	(	(	PUNCT
ap-4038	204	42	in	in	ADP
ap-4038	204	43	,	,	PUNCT
ap-4038	204	44	coin	coin	NOUN
ap-4038	204	45	)	)	PUNCT
ap-4038	204	46	=	=	SYM
ap-4038	204	47	getpartition(t	getpartition(t	NOUN
ap-4038	204	48	,	,	PUNCT
ap-4038	204	49	face	face	NOUN
ap-4038	204	50	)	)	PUNCT
ap-4038	204	51	;	;	PUNCT
ap-4038	204	52	5	5	NUM
ap-4038	204	53	:	:	PUNCT
ap-4038	204	54	end	end	VERB
ap-4038	204	55	for	for	ADP
ap-4038	204	56	6	6	NUM
ap-4038	204	57	:	:	PUNCT
ap-4038	204	58	end	end	NOUN
ap-4038	204	59	procedure	procedure	NOUN
ap-4038	204	60	takes	take	VERB
ap-4038	204	61	the	the	DET
ap-4038	204	62	faces	face	NOUN
ap-4038	204	63	of	of	ADP
ap-4038	204	64	one	one	NUM
ap-4038	204	65	polyhedron	polyhedron	NOUN
ap-4038	204	66	and	and	CCONJ
ap-4038	204	67	sends	send	VERB
ap-4038	204	68	them	they	PRON
ap-4038	204	69	in	in	ADP
ap-4038	204	70	a	a	DET
ap-4038	204	71	loop	loop	NOUN
ap-4038	204	72	for	for	ADP
ap-4038	204	73	further	further	ADJ
ap-4038	204	74	proceeding	proceeding	NOUN
ap-4038	204	75	into	into	ADP
ap-4038	204	76	the	the	DET
ap-4038	204	77	bsp	bsp	NOUN
ap-4038	204	78	tree	tree	NOUN
ap-4038	204	79	for	for	ADP
ap-4038	204	80	the	the	DET
ap-4038	204	81	other	other	ADJ
ap-4038	204	82	polyhedron	polyhedron	NOUN
ap-4038	204	83	,	,	PUNCT
ap-4038	204	84	see	see	VERB
ap-4038	204	85	algorithm	algorithm	NOUN
ap-4038	204	86	4	4	NUM
ap-4038	204	87	.	.	PUNCT
ap-4038	205	1	the	the	DET
ap-4038	205	2	intersection	intersection	NOUN
ap-4038	205	3	of	of	ADP
ap-4038	205	4	the	the	DET
ap-4038	205	5	two	two	NUM
ap-4038	205	6	polyhedra	polyhedra	NOUN
ap-4038	205	7	can	can	AUX
ap-4038	205	8	be	be	AUX
ap-4038	205	9	composed	compose	VERB
ap-4038	205	10	of	of	ADP
ap-4038	205	11	two	two	NUM
ap-4038	205	12	types	type	NOUN
ap-4038	205	13	of	of	ADP
ap-4038	205	14	faces	face	NOUN
ap-4038	205	15	/	/	SYM
ap-4038	205	16	sub	sub	NOUN
ap-4038	205	17	-	-	NOUN
ap-4038	205	18	faces	face	NOUN
ap-4038	205	19	.	.	PUNCT
ap-4038	206	1	to	to	ADP
ap-4038	206	2	the	the	DET
ap-4038	206	3	first	first	ADJ
ap-4038	206	4	type	type	NOUN
ap-4038	206	5	belong	belong	VERB
ap-4038	206	6	those	those	DET
ap-4038	206	7	faces	face	NOUN
ap-4038	206	8	of	of	ADP
ap-4038	206	9	polyhedron	polyhedron	NOUN
ap-4038	206	10	p	p	NOUN
ap-4038	206	11	,	,	PUNCT
ap-4038	206	12	which	which	PRON
ap-4038	206	13	lies	lie	VERB
ap-4038	206	14	inside	inside	ADV
ap-4038	206	15	of	of	ADP
ap-4038	206	16	polyhedron	polyhedron	NOUN
ap-4038	206	17	q	q	PUNCT
ap-4038	206	18	(	(	PUNCT
ap-4038	206	19	and	and	CCONJ
ap-4038	206	20	symmetrically	symmetrically	ADV
ap-4038	206	21	faces	face	NOUN
ap-4038	206	22	of	of	ADP
ap-4038	206	23	q	q	NOUN
ap-4038	206	24	lying	lie	VERB
ap-4038	206	25	inside	inside	ADV
ap-4038	206	26	of	of	ADP
ap-4038	206	27	p	p	NOUN
ap-4038	206	28	)	)	PUNCT
ap-4038	206	29	.	.	PUNCT
ap-4038	207	1	to	to	ADP
ap-4038	207	2	the	the	DET
ap-4038	207	3	second	second	ADJ
ap-4038	207	4	type	type	NOUN
ap-4038	207	5	belong	belong	VERB
ap-4038	207	6	faces	face	NOUN
ap-4038	207	7	of	of	ADP
ap-4038	207	8	p	p	NOUN
ap-4038	207	9	,	,	PUNCT
ap-4038	207	10	which	which	PRON
ap-4038	207	11	accidentally	accidentally	ADV
ap-4038	207	12	coincide	coincide	VERB
ap-4038	207	13	with	with	ADP
ap-4038	207	14	some	some	DET
ap-4038	207	15	faces	face	NOUN
ap-4038	207	16	of	of	ADP
ap-4038	207	17	q	q	PROPN
ap-4038	207	18	(	(	PUNCT
ap-4038	207	19	and	and	CCONJ
ap-4038	207	20	vice	vice	ADV
ap-4038	207	21	versa	versa	ADV
ap-4038	207	22	)	)	PUNCT
ap-4038	207	23	.	.	PUNCT
ap-4038	208	1	therefore	therefore	ADV
ap-4038	208	2	,	,	PUNCT
ap-4038	208	3	the	the	DET
ap-4038	208	4	output	output	NOUN
ap-4038	208	5	of	of	ADP
ap-4038	208	6	the	the	DET
ap-4038	208	7	intersectwith	intersectwith	ADJ
ap-4038	208	8	function	function	NOUN
ap-4038	208	9	is	be	AUX
ap-4038	208	10	composed	compose	VERB
ap-4038	208	11	of	of	ADP
ap-4038	208	12	the	the	DET
ap-4038	208	13	two	two	NUM
ap-4038	208	14	sets	set	NOUN
ap-4038	208	15	of	of	ADP
ap-4038	208	16	faces	face	NOUN
ap-4038	208	17	,	,	PUNCT
ap-4038	208	18	namely	namely	ADV
ap-4038	208	19	in	in	ADP
ap-4038	208	20	and	and	CCONJ
ap-4038	208	21	coin	coin	NOUN
ap-4038	208	22	.	.	PUNCT
ap-4038	209	1	in	in	ADP
ap-4038	209	2	contains	contain	VERB
ap-4038	209	3	sub	sub	NOUN
ap-4038	209	4	-	-	NOUN
ap-4038	209	5	faces	face	NOUN
ap-4038	209	6	and	and	CCONJ
ap-4038	209	7	faces	face	NOUN
ap-4038	209	8	of	of	ADP
ap-4038	209	9	q	q	NOUN
ap-4038	209	10	which	which	PRON
ap-4038	209	11	lies	lie	VERB
ap-4038	209	12	inside	inside	ADP
ap-4038	209	13	polyhedron	polyhedron	NOUN
ap-4038	209	14	p	p	NOUN
ap-4038	209	15	,	,	PUNCT
ap-4038	209	16	coin	coin	NOUN
ap-4038	209	17	contains	contain	VERB
ap-4038	209	18	sub	sub	NOUN
ap-4038	209	19	-	-	NOUN
ap-4038	209	20	faces	face	NOUN
ap-4038	209	21	and	and	CCONJ
ap-4038	209	22	faces	face	NOUN
ap-4038	209	23	of	of	ADP
ap-4038	209	24	q	q	X
ap-4038	209	25	which	which	DET
ap-4038	209	26	coincide	coincide	VERB
ap-4038	209	27	with	with	ADP
ap-4038	209	28	some	some	PRON
ap-4038	209	29	of	of	ADP
ap-4038	209	30	the	the	DET
ap-4038	209	31	faces	face	NOUN
ap-4038	209	32	of	of	ADP
ap-4038	209	33	p	p	NOUN
ap-4038	209	34	.	.	PUNCT
ap-4038	210	1	the	the	DET
ap-4038	210	2	intersection	intersection	NOUN
ap-4038	210	3	value	value	NOUN
ap-4038	210	4	is	be	AUX
ap-4038	210	5	computed	compute	VERB
ap-4038	210	6	from	from	ADP
ap-4038	210	7	these	these	DET
ap-4038	210	8	two	two	NUM
ap-4038	210	9	sets	set	NOUN
ap-4038	210	10	of	of	ADP
ap-4038	210	11	faces	face	NOUN
ap-4038	210	12	,	,	PUNCT
ap-4038	210	13	as	as	SCONJ
ap-4038	210	14	will	will	AUX
ap-4038	210	15	be	be	AUX
ap-4038	210	16	described	describe	VERB
ap-4038	210	17	below	below	ADV
ap-4038	210	18	.	.	PUNCT
ap-4038	211	1	the	the	DET
ap-4038	211	2	getpartition	getpartition	NOUN
ap-4038	211	3	function	function	NOUN
ap-4038	211	4	is	be	AUX
ap-4038	211	5	the	the	DET
ap-4038	211	6	core	core	ADJ
ap-4038	211	7	part	part	NOUN
ap-4038	211	8	of	of	ADP
ap-4038	211	9	the	the	DET
ap-4038	211	10	intersectwith	intersectwith	ADJ
ap-4038	211	11	procedure	procedure	NOUN
ap-4038	211	12	.	.	PUNCT
ap-4038	212	1	its	its	PRON
ap-4038	212	2	purpose	purpose	NOUN
ap-4038	212	3	is	be	AUX
ap-4038	212	4	to	to	PART
ap-4038	212	5	partition	partition	VERB
ap-4038	212	6	a	a	DET
ap-4038	212	7	given	give	VERB
ap-4038	212	8	face	face	NOUN
ap-4038	212	9	by	by	ADP
ap-4038	212	10	the	the	DET
ap-4038	212	11	bsp	bsp	NOUN
ap-4038	212	12	tree	tree	NOUN
ap-4038	212	13	into	into	ADP
ap-4038	212	14	sub	sub	NOUN
ap-4038	212	15	-	-	NOUN
ap-4038	212	16	faces	face	NOUN
ap-4038	212	17	which	which	PRON
ap-4038	212	18	belong	belong	VERB
ap-4038	212	19	to	to	ADP
ap-4038	212	20	a	a	DET
ap-4038	212	21	positive	positive	ADJ
ap-4038	212	22	sub	sub	NOUN
ap-4038	212	23	-	-	NOUN
ap-4038	212	24	space	space	NOUN
ap-4038	212	25	,	,	PUNCT
ap-4038	212	26	or	or	CCONJ
ap-4038	212	27	to	to	ADP
ap-4038	212	28	a	a	DET
ap-4038	212	29	negative	negative	ADJ
ap-4038	212	30	sub	sub	NOUN
ap-4038	212	31	-	-	NOUN
ap-4038	212	32	space	space	NOUN
ap-4038	212	33	,	,	PUNCT
ap-4038	212	34	or	or	CCONJ
ap-4038	212	35	which	which	PRON
ap-4038	212	36	are	be	AUX
ap-4038	212	37	coincident	coincident	ADJ
ap-4038	212	38	with	with	ADP
ap-4038	212	39	some	some	PRON
ap-4038	212	40	of	of	ADP
ap-4038	212	41	the	the	DET
ap-4038	212	42	splitting	splitting	NOUN
ap-4038	212	43	planes	plane	NOUN
ap-4038	212	44	.	.	PUNCT
ap-4038	213	1	the	the	DET
ap-4038	213	2	face	face	NOUN
ap-4038	213	3	is	be	AUX
ap-4038	213	4	processed	process	VERB
ap-4038	213	5	at	at	ADP
ap-4038	213	6	each	each	DET
ap-4038	213	7	node	node	NOUN
ap-4038	213	8	(	(	PUNCT
ap-4038	213	9	representing	represent	VERB
ap-4038	213	10	the	the	DET
ap-4038	213	11	splitting	splitting	NOUN
ap-4038	213	12	plane	plane	NOUN
ap-4038	213	13	)	)	PUNCT
ap-4038	213	14	.	.	PUNCT
ap-4038	214	1	according	accord	VERB
ap-4038	214	2	to	to	ADP
ap-4038	214	3	the	the	DET
ap-4038	214	4	result	result	NOUN
ap-4038	214	5	of	of	ADP
ap-4038	214	6	the	the	DET
ap-4038	214	7	classifyface	classifyface	NOUN
ap-4038	214	8	function	function	NOUN
ap-4038	214	9	,	,	PUNCT
ap-4038	214	10	the	the	DET
ap-4038	214	11	face	face	NOUN
ap-4038	214	12	is	be	AUX
ap-4038	214	13	sent	send	VERB
ap-4038	214	14	to	to	ADP
ap-4038	214	15	the	the	DET
ap-4038	214	16	positive	positive	ADJ
ap-4038	214	17	child	child	NOUN
ap-4038	214	18	or	or	CCONJ
ap-4038	214	19	to	to	ADP
ap-4038	214	20	the	the	DET
ap-4038	214	21	negative	negative	ADJ
ap-4038	214	22	child	child	NOUN
ap-4038	214	23	for	for	ADP
ap-4038	214	24	further	further	ADJ
ap-4038	214	25	processing	processing	NOUN
ap-4038	214	26	.	.	PUNCT
ap-4038	215	1	if	if	SCONJ
ap-4038	215	2	the	the	DET
ap-4038	215	3	face	face	NOUN
ap-4038	215	4	is	be	AUX
ap-4038	215	5	crossed	cross	VERB
ap-4038	215	6	by	by	ADP
ap-4038	215	7	the	the	DET
ap-4038	215	8	splitting	splitting	NOUN
ap-4038	215	9	plane	plane	NOUN
ap-4038	215	10	,	,	PUNCT
ap-4038	215	11	one	one	NUM
ap-4038	215	12	part	part	NOUN
ap-4038	215	13	of	of	ADP
ap-4038	215	14	the	the	DET
ap-4038	215	15	face	face	NOUN
ap-4038	215	16	lies	lie	VERB
ap-4038	215	17	on	on	ADP
ap-4038	215	18	the	the	DET
ap-4038	215	19	positive	positive	ADJ
ap-4038	215	20	side	side	NOUN
ap-4038	215	21	and	and	CCONJ
ap-4038	215	22	the	the	DET
ap-4038	215	23	other	other	ADJ
ap-4038	215	24	part	part	NOUN
ap-4038	215	25	of	of	ADP
ap-4038	215	26	the	the	DET
ap-4038	215	27	face	face	NOUN
ap-4038	215	28	lies	lie	VERB
ap-4038	215	29	on	on	ADP
ap-4038	215	30	the	the	DET
ap-4038	215	31	negative	negative	ADJ
ap-4038	215	32	side	side	NOUN
ap-4038	215	33	of	of	ADP
ap-4038	215	34	the	the	DET
ap-4038	215	35	splitting	splitting	NOUN
ap-4038	215	36	plane	plane	NOUN
ap-4038	215	37	.	.	PUNCT
ap-4038	216	1	therefore	therefore	ADV
ap-4038	216	2	the	the	DET
ap-4038	216	3	part	part	NOUN
ap-4038	216	4	of	of	ADP
ap-4038	216	5	the	the	DET
ap-4038	216	6	face	face	NOUN
ap-4038	216	7	on	on	ADP
ap-4038	216	8	the	the	DET
ap-4038	216	9	positive	positive	ADJ
ap-4038	216	10	side	side	NOUN
ap-4038	216	11	is	be	AUX
ap-4038	216	12	sent	send	VERB
ap-4038	216	13	to	to	ADP
ap-4038	216	14	the	the	DET
ap-4038	216	15	positive	positive	ADJ
ap-4038	216	16	child	child	NOUN
ap-4038	216	17	,	,	PUNCT
ap-4038	216	18	and	and	CCONJ
ap-4038	216	19	the	the	DET
ap-4038	216	20	other	other	ADJ
ap-4038	216	21	part	part	NOUN
ap-4038	216	22	is	be	AUX
ap-4038	216	23	sent	send	VERB
ap-4038	216	24	to	to	ADP
ap-4038	216	25	the	the	DET
ap-4038	216	26	negative	negative	ADJ
ap-4038	216	27	child	child	NOUN
ap-4038	216	28	.	.	PUNCT
ap-4038	217	1	the	the	DET
ap-4038	217	2	most	most	ADV
ap-4038	217	3	complicated	complicated	ADJ
ap-4038	217	4	case	case	NOUN
ap-4038	217	5	is	be	AUX
ap-4038	217	6	when	when	SCONJ
ap-4038	217	7	the	the	DET
ap-4038	217	8	face	face	NOUN
ap-4038	217	9	lies	lie	VERB
ap-4038	217	10	in	in	ADP
ap-4038	217	11	the	the	DET
ap-4038	217	12	splitting	splitting	NOUN
ap-4038	217	13	plane	plane	NOUN
ap-4038	217	14	,	,	PUNCT
ap-4038	217	15	i.e.	i.e.	X
ap-4038	217	16	when	when	SCONJ
ap-4038	217	17	the	the	DET
ap-4038	217	18	face	face	NOUN
ap-4038	217	19	and	and	CCONJ
ap-4038	217	20	the	the	DET
ap-4038	217	21	splitting	splitting	NOUN
ap-4038	217	22	plane	plane	NOUN
ap-4038	217	23	are	be	AUX
ap-4038	217	24	coincident	coincident	ADJ
ap-4038	217	25	.	.	PUNCT
ap-4038	218	1	in	in	ADP
ap-4038	218	2	this	this	DET
ap-4038	218	3	case	case	NOUN
ap-4038	218	4	,	,	PUNCT
ap-4038	218	5	the	the	DET
ap-4038	218	6	overlapping	overlap	VERB
ap-4038	218	7	portion	portion	NOUN
ap-4038	218	8	of	of	ADP
ap-4038	218	9	the	the	DET
ap-4038	218	10	processed	process	VERB
ap-4038	218	11	face	face	NOUN
ap-4038	218	12	and	and	CCONJ
ap-4038	218	13	the	the	DET
ap-4038	218	14	face	face	NOUN
ap-4038	218	15	which	which	PRON
ap-4038	218	16	served	serve	VERB
ap-4038	218	17	as	as	ADP
ap-4038	218	18	a	a	DET
ap-4038	218	19	basis	basis	NOUN
ap-4038	218	20	for	for	ADP
ap-4038	218	21	the	the	DET
ap-4038	218	22	splitting	splitting	NOUN
ap-4038	218	23	plane	plane	NOUN
ap-4038	218	24	has	have	VERB
ap-4038	218	25	to	to	PART
ap-4038	218	26	be	be	AUX
ap-4038	218	27	computed	compute	VERB
ap-4038	218	28	.	.	PUNCT
ap-4038	219	1	note	note	VERB
ap-4038	219	2	that	that	SCONJ
ap-4038	219	3	in	in	ADP
ap-4038	219	4	the	the	DET
ap-4038	219	5	case	case	NOUN
ap-4038	219	6	of	of	ADP
ap-4038	219	7	convex	convex	PROPN
ap-4038	219	8	polyhedra	polyhedra	NOUN
ap-4038	219	9	,	,	PUNCT
ap-4038	219	10	it	it	PRON
ap-4038	219	11	is	be	AUX
ap-4038	219	12	enough	enough	ADJ
ap-4038	219	13	to	to	PART
ap-4038	219	14	keep	keep	VERB
ap-4038	219	15	just	just	ADV
ap-4038	219	16	the	the	DET
ap-4038	219	17	overlapping	overlap	VERB
ap-4038	219	18	part	part	NOUN
ap-4038	219	19	of	of	ADP
ap-4038	219	20	the	the	DET
ap-4038	219	21	face	face	NOUN
ap-4038	219	22	;	;	PUNCT
ap-4038	219	23	the	the	DET
ap-4038	219	24	rest	rest	NOUN
ap-4038	219	25	is	be	AUX
ap-4038	219	26	of	of	ADP
ap-4038	219	27	no	no	DET
ap-4038	219	28	importance	importance	NOUN
ap-4038	219	29	.	.	PUNCT
ap-4038	220	1	in	in	ADP
ap-4038	220	2	the	the	DET
ap-4038	220	3	case	case	NOUN
ap-4038	220	4	of	of	ADP
ap-4038	220	5	general	general	ADJ
ap-4038	220	6	polyhedra	polyhedra	PROPN
ap-4038	220	7	,	,	PUNCT
ap-4038	220	8	the	the	DET
ap-4038	220	9	nonoverlapping	nonoverlapping	ADJ
ap-4038	220	10	portions	portion	NOUN
ap-4038	220	11	of	of	ADP
ap-4038	220	12	coincident	coincident	ADJ
ap-4038	220	13	faces	face	NOUN
ap-4038	220	14	would	would	AUX
ap-4038	220	15	have	have	VERB
ap-4038	220	16	to	to	PART
ap-4038	220	17	be	be	AUX
ap-4038	220	18	processed	process	VERB
ap-4038	220	19	by	by	ADP
ap-4038	220	20	the	the	DET
ap-4038	220	21	positive	positive	ADJ
ap-4038	220	22	or	or	CCONJ
ap-4038	220	23	negative	negative	ADJ
ap-4038	220	24	child	child	NOUN
ap-4038	220	25	of	of	ADP
ap-4038	220	26	the	the	DET
ap-4038	220	27	bsp	bsp	NOUN
ap-4038	220	28	tree	tree	NOUN
ap-4038	220	29	.	.	PUNCT
ap-4038	221	1	the	the	DET
ap-4038	221	2	modification	modification	NOUN
ap-4038	221	3	of	of	ADP
ap-4038	221	4	algorithm	algorithm	NOUN
ap-4038	221	5	proposed	propose	VERB
ap-4038	221	6	in	in	ADP
ap-4038	221	7	[	[	X
ap-4038	221	8	18	18	NUM
ap-4038	221	9	]	]	PUNCT
ap-4038	221	10	is	be	AUX
ap-4038	221	11	a	a	DET
ap-4038	221	12	contained	contain	VERB
ap-4038	221	13	in	in	ADP
ap-4038	221	14	pseudo	pseudo	NOUN
ap-4038	221	15	-	-	ADJ
ap-4038	221	16	code	code	NOUN
ap-4038	221	17	algorithm	algorithm	NOUN
ap-4038	221	18	5	5	NUM
ap-4038	221	19	.	.	PUNCT
ap-4038	222	1	in	in	ADP
ap-4038	222	2	general	general	ADJ
ap-4038	222	3	,	,	PUNCT
ap-4038	222	4	the	the	DET
ap-4038	222	5	result	result	NOUN
ap-4038	222	6	of	of	ADP
ap-4038	222	7	getpartition	getpartition	NOUN
ap-4038	222	8	procedure	procedure	NOUN
ap-4038	222	9	is	be	AUX
ap-4038	222	10	a	a	DET
ap-4038	222	11	representation	representation	NOUN
ap-4038	222	12	of	of	ADP
ap-4038	222	13	a	a	DET
ap-4038	222	14	face	face	NOUN
ap-4038	222	15	in	in	ADP
ap-4038	222	16	form	form	NOUN
ap-4038	222	17	of	of	ADP
ap-4038	222	18	a	a	DET
ap-4038	222	19	union	union	NOUN
ap-4038	222	20	of	of	ADP
ap-4038	222	21	the	the	DET
ap-4038	222	22	segments	segment	NOUN
ap-4038	222	23	(	(	PUNCT
ap-4038	222	24	sub	sub	ADJ
ap-4038	222	25	-	-	NOUN
ap-4038	222	26	faces	face	NOUN
ap-4038	222	27	)	)	PUNCT
ap-4038	222	28	which	which	PRON
ap-4038	222	29	are	be	AUX
ap-4038	222	30	contained	contain	VERB
ap-4038	222	31	in	in	ADP
ap-4038	222	32	positive	positive	ADJ
ap-4038	222	33	,	,	PUNCT
ap-4038	222	34	negative	negative	ADJ
ap-4038	222	35	or	or	CCONJ
ap-4038	222	36	coincident	coincident	ADJ
ap-4038	222	37	sub	sub	NOUN
ap-4038	222	38	-	-	NOUN
ap-4038	222	39	spaces	space	NOUN
ap-4038	222	40	according	accord	VERB
ap-4038	222	41	to	to	ADP
ap-4038	222	42	the	the	DET
ap-4038	222	43	bsp	bsp	NOUN
ap-4038	222	44	tree	tree	NOUN
ap-4038	222	45	.	.	PUNCT
ap-4038	223	1	however	however	ADV
ap-4038	223	2	,	,	PUNCT
ap-4038	223	3	all	all	PRON
ap-4038	223	4	we	we	PRON
ap-4038	223	5	need	need	VERB
ap-4038	223	6	here	here	ADV
ap-4038	223	7	is	be	AUX
ap-4038	223	8	to	to	PART
ap-4038	223	9	compute	compute	VERB
ap-4038	223	10	the	the	DET
ap-4038	223	11	volume	volume	NOUN
ap-4038	223	12	of	of	ADP
ap-4038	223	13	the	the	DET
ap-4038	223	14	polyhedra	polyhedra	NOUN
ap-4038	223	15	intersection	intersection	NOUN
ap-4038	223	16	.	.	PUNCT
ap-4038	224	1	therefore	therefore	ADV
ap-4038	224	2	,	,	PUNCT
ap-4038	224	3	only	only	ADV
ap-4038	224	4	the	the	DET
ap-4038	224	5	segments	segment	NOUN
ap-4038	224	6	in	in	ADP
ap-4038	224	7	the	the	DET
ap-4038	224	8	negative	negative	ADJ
ap-4038	224	9	and	and	CCONJ
ap-4038	224	10	coincident	coincident	ADJ
ap-4038	224	11	subalgorithm	subalgorithm	NOUN
ap-4038	224	12	5	5	NUM
ap-4038	224	13	partitioning	partitioning	NOUN
ap-4038	224	14	of	of	ADP
ap-4038	224	15	a	a	DET
ap-4038	224	16	face	face	NOUN
ap-4038	224	17	1	1	NUM
ap-4038	224	18	:	:	PUNCT
ap-4038	224	19	procedure	procedure	NOUN
ap-4038	224	20	getpartition(tree	getpartition(tree	NOUN
ap-4038	224	21	,	,	PUNCT
ap-4038	224	22	face	face	NOUN
ap-4038	224	23	)	)	PUNCT
ap-4038	224	24	2	2	NUM
ap-4038	224	25	:	:	PUNCT
ap-4038	224	26	p	p	X
ap-4038	224	27	=	=	PROPN
ap-4038	224	28	getplanefromface(tree.coinface	getplanefromface(tree.coinface	PROPN
ap-4038	224	29	(	(	PUNCT
ap-4038	224	30	)	)	PUNCT
ap-4038	224	31	)	)	PUNCT
ap-4038	225	1	3	3	NUM
ap-4038	225	2	:	:	PUNCT
ap-4038	225	3	type	type	NOUN
ap-4038	225	4	=	=	SYM
ap-4038	225	5	classifyface(p	classifyface(p	NOUN
ap-4038	225	6	,	,	PUNCT
ap-4038	225	7	face	face	NOUN
ap-4038	225	8	)	)	PUNCT
ap-4038	225	9	4	4	NUM
ap-4038	225	10	:	:	PUNCT
ap-4038	225	11	if	if	SCONJ
ap-4038	225	12	type	type	NOUN
ap-4038	225	13	=	=	NOUN
ap-4038	225	14	crosses	crosse	NOUN
ap-4038	225	15	then	then	ADV
ap-4038	225	16	5	5	NUM
ap-4038	225	17	:	:	PUNCT
ap-4038	225	18	(	(	PUNCT
ap-4038	225	19	posface	posface	NOUN
ap-4038	225	20	,	,	PUNCT
ap-4038	225	21	negface	negface	NOUN
ap-4038	225	22	)	)	PUNCT
ap-4038	225	23	=	=	SYM
ap-4038	225	24	splitface(p	splitface(p	NOUN
ap-4038	225	25	,	,	PUNCT
ap-4038	225	26	face	face	NOUN
ap-4038	225	27	)	)	PUNCT
ap-4038	225	28	;	;	PUNCT
ap-4038	225	29	6	6	NUM
ap-4038	225	30	:	:	PUNCT
ap-4038	225	31	sendtoposchild(posface	sendtoposchild(posface	NOUN
ap-4038	225	32	)	)	PUNCT
ap-4038	225	33	;	;	PUNCT
ap-4038	225	34	7	7	X
ap-4038	225	35	:	:	PUNCT
ap-4038	225	36	sendtonegchild(negface	sendtonegchild(negface	PROPN
ap-4038	225	37	)	)	PUNCT
ap-4038	225	38	;	;	PUNCT
ap-4038	225	39	8	8	NUM
ap-4038	225	40	:	:	PUNCT
ap-4038	225	41	else	else	ADV
ap-4038	225	42	if	if	SCONJ
ap-4038	225	43	type	type	NOUN
ap-4038	225	44	=	=	PUNCT
ap-4038	225	45	positive	positive	ADJ
ap-4038	225	46	then	then	ADV
ap-4038	225	47	9	9	NUM
ap-4038	225	48	:	:	PUNCT
ap-4038	225	49	sendtoposchild(face	sendtoposchild(face	NUM
ap-4038	225	50	)	)	PUNCT
ap-4038	225	51	;	;	PUNCT
ap-4038	225	52	10	10	NUM
ap-4038	225	53	:	:	PUNCT
ap-4038	225	54	else	else	ADV
ap-4038	225	55	if	if	SCONJ
ap-4038	225	56	type	type	NOUN
ap-4038	225	57	=	=	PUNCT
ap-4038	225	58	negative	negative	ADJ
ap-4038	225	59	then	then	ADV
ap-4038	225	60	11	11	NUM
ap-4038	225	61	:	:	PUNCT
ap-4038	225	62	sendtonegchild(face	sendtonegchild(face	PROPN
ap-4038	225	63	)	)	PUNCT
ap-4038	225	64	;	;	PUNCT
ap-4038	225	65	12	12	NUM
ap-4038	225	66	:	:	PUNCT
ap-4038	225	67	else	else	ADV
ap-4038	225	68	if	if	SCONJ
ap-4038	225	69	type	type	NOUN
ap-4038	225	70	=	=	PUNCT
ap-4038	225	71	coincident	coincident	NOUN
ap-4038	225	72	then	then	ADV
ap-4038	225	73	13	13	NUM
ap-4038	225	74	:	:	PUNCT
ap-4038	225	75	overlap	overlap	NOUN
ap-4038	225	76	=	=	SYM
ap-4038	225	77	intersect(coinface	intersect(coinface	PROPN
ap-4038	225	78	,	,	PUNCT
ap-4038	225	79	face	face	NOUN
ap-4038	225	80	)	)	PUNCT
ap-4038	225	81	;	;	PUNCT
ap-4038	225	82	14	14	NUM
ap-4038	225	83	:	:	PUNCT
ap-4038	225	84	storeintersection(overlap	storeintersection(overlap	PROPN
ap-4038	225	85	)	)	PUNCT
ap-4038	225	86	;	;	PUNCT
ap-4038	225	87	15	15	NUM
ap-4038	225	88	:	:	PUNCT
ap-4038	225	89	end	end	VERB
ap-4038	225	90	if	if	SCONJ
ap-4038	225	91	16	16	NUM
ap-4038	225	92	:	:	PUNCT
ap-4038	225	93	end	end	NOUN
ap-4038	225	94	procedure	procedure	NOUN
ap-4038	225	95	spaces	space	NOUN
ap-4038	225	96	of	of	ADP
ap-4038	225	97	the	the	DET
ap-4038	225	98	bsp	bsp	NOUN
ap-4038	225	99	tree	tree	NOUN
ap-4038	225	100	are	be	AUX
ap-4038	225	101	needed	need	VERB
ap-4038	225	102	.	.	PUNCT
ap-4038	226	1	they	they	PRON
ap-4038	226	2	are	be	AUX
ap-4038	226	3	denoted	denote	VERB
ap-4038	226	4	as	as	ADP
ap-4038	226	5	in	in	ADP
ap-4038	226	6	and	and	CCONJ
ap-4038	226	7	coin	coin	NOUN
ap-4038	226	8	,	,	PUNCT
ap-4038	226	9	see	see	VERB
ap-4038	226	10	algorithm	algorithm	NOUN
ap-4038	226	11	4	4	NUM
ap-4038	226	12	.	.	PUNCT
ap-4038	227	1	finally	finally	ADV
ap-4038	227	2	,	,	PUNCT
ap-4038	227	3	the	the	DET
ap-4038	227	4	volume	volume	NOUN
ap-4038	227	5	is	be	AUX
ap-4038	227	6	computed	compute	VERB
ap-4038	227	7	with	with	ADP
ap-4038	227	8	the	the	DET
ap-4038	227	9	help	help	NOUN
ap-4038	227	10	of	of	ADP
ap-4038	227	11	the	the	DET
ap-4038	227	12	stokes	stoke	NOUN
ap-4038	227	13	formula∫	formula∫	PROPN
ap-4038	227	14	vp	vp	X
ap-4038	227	15	∇	∇	X
ap-4038	227	16	·	·	PUNCT
ap-4038	227	17	f	f	X
ap-4038	227	18	dx	dx	PROPN
ap-4038	227	19	=	=	SYM
ap-4038	227	20	∫	∫	PROPN
ap-4038	227	21	sp	sp	ADP
ap-4038	227	22	f	f	PROPN
ap-4038	227	23	·	·	PUNCT
ap-4038	227	24	nds	nds	PROPN
ap-4038	227	25	,	,	PUNCT
ap-4038	227	26	(	(	PUNCT
ap-4038	227	27	12	12	NUM
ap-4038	227	28	)	)	PUNCT
ap-4038	227	29	which	which	PRON
ap-4038	227	30	transforms	transform	VERB
ap-4038	227	31	the	the	DET
ap-4038	227	32	volume	volume	NOUN
ap-4038	227	33	integral	integral	ADJ
ap-4038	227	34	of	of	ADP
ap-4038	227	35	divergence	divergence	NOUN
ap-4038	227	36	of	of	ADP
ap-4038	227	37	vector	vector	NOUN
ap-4038	227	38	field	field	NOUN
ap-4038	227	39	f	f	PROPN
ap-4038	227	40	to	to	ADP
ap-4038	227	41	a	a	DET
ap-4038	227	42	surface	surface	NOUN
ap-4038	227	43	integral	integral	ADJ
ap-4038	227	44	of	of	ADP
ap-4038	227	45	the	the	DET
ap-4038	227	46	normal	normal	ADJ
ap-4038	227	47	component	component	NOUN
ap-4038	227	48	of	of	ADP
ap-4038	227	49	that	that	DET
ap-4038	227	50	field	field	NOUN
ap-4038	227	51	.	.	PUNCT
ap-4038	228	1	vp	vp	PROPN
ap-4038	228	2	and	and	CCONJ
ap-4038	228	3	sp	sp	ADP
ap-4038	228	4	denote	denote	VERB
ap-4038	228	5	the	the	DET
ap-4038	228	6	volume	volume	NOUN
ap-4038	228	7	and	and	CCONJ
ap-4038	228	8	the	the	DET
ap-4038	228	9	surface	surface	NOUN
ap-4038	228	10	of	of	ADP
ap-4038	228	11	the	the	DET
ap-4038	228	12	polyhedron	polyhedron	NOUN
ap-4038	228	13	,	,	PUNCT
ap-4038	228	14	respectively	respectively	ADV
ap-4038	228	15	.	.	PUNCT
ap-4038	229	1	in	in	ADP
ap-4038	229	2	order	order	NOUN
ap-4038	229	3	to	to	PART
ap-4038	229	4	compute	compute	VERB
ap-4038	229	5	the	the	DET
ap-4038	229	6	volume	volume	NOUN
ap-4038	229	7	v	v	NUM
ap-4038	229	8	of	of	ADP
ap-4038	229	9	the	the	DET
ap-4038	229	10	polyhedron	polyhedron	NOUN
ap-4038	229	11	resulting	result	VERB
ap-4038	229	12	from	from	ADP
ap-4038	229	13	the	the	DET
ap-4038	229	14	intersection	intersection	NOUN
ap-4038	229	15	,	,	PUNCT
ap-4038	229	16	we	we	PRON
ap-4038	229	17	can	can	AUX
ap-4038	229	18	proceed	proceed	VERB
ap-4038	229	19	as	as	SCONJ
ap-4038	229	20	follows	follow	VERB
ap-4038	229	21	v	v	NOUN
ap-4038	229	22	=	=	SYM
ap-4038	229	23	∫	∫	PROPN
ap-4038	229	24	vp	vp	PROPN
ap-4038	229	25	1	1	NUM
ap-4038	229	26	dx	dx	PROPN
ap-4038	229	27	=	=	SYM
ap-4038	229	28	∫	∫	PROPN
ap-4038	229	29	vp	vp	PROPN
ap-4038	229	30	∇	∇	X
ap-4038	229	31	·	·	PUNCT
ap-4038	229	32	(	(	PUNCT
ap-4038	229	33	x	x	SYM
ap-4038	229	34	3	3	X
ap-4038	229	35	)	)	PUNCT
ap-4038	229	36	dx	dx	PROPN
ap-4038	230	1	=	=	SYM
ap-4038	230	2	1	1	NUM
ap-4038	230	3	3	3	NUM
ap-4038	230	4	∫	∫	NOUN
ap-4038	230	5	sp	sp	ADP
ap-4038	230	6	x	x	PROPN
ap-4038	230	7	·	·	PUNCT
ap-4038	230	8	nds	nds	PROPN
ap-4038	230	9	=	=	SYM
ap-4038	230	10	1	1	NUM
ap-4038	230	11	3	3	NUM
ap-4038	230	12	∑	∑	SYM
ap-4038	230	13	fi∈{in∪coin	fi∈{in∪coin	PROPN
ap-4038	230	14	}	}	PUNCT
ap-4038	230	15	∫	∫	PROPN
ap-4038	230	16	fi	fi	NOUN
ap-4038	230	17	x	x	X
ap-4038	230	18	·	·	PUNCT
ap-4038	230	19	ni	ni	NOUN
ap-4038	230	20	ds	ds	PROPN
ap-4038	230	21	=	=	NOUN
ap-4038	230	22	1	1	NUM
ap-4038	230	23	3	3	NUM
ap-4038	230	24	∑	∑	SYM
ap-4038	230	25	fi∈{in∪coin	fi∈{in∪coin	PROPN
ap-4038	230	26	}	}	PUNCT
ap-4038	230	27	∫	∫	PROPN
ap-4038	230	28	fi	fi	NOUN
ap-4038	230	29	ci	ci	NOUN
ap-4038	230	30	ds	ds	PROPN
ap-4038	230	31	=	=	NOUN
ap-4038	230	32	1	1	NUM
ap-4038	230	33	3	3	NUM
ap-4038	230	34	∑	∑	SYM
ap-4038	230	35	fi∈{in∪coin	fi∈{in∪coin	PROPN
ap-4038	230	36	}	}	PUNCT
ap-4038	230	37	ciai	ciai	VERB
ap-4038	230	38	,	,	PUNCT
ap-4038	230	39	(	(	PUNCT
ap-4038	230	40	13	13	NUM
ap-4038	230	41	)	)	PUNCT
ap-4038	230	42	where	where	SCONJ
ap-4038	230	43	ni	ni	PROPN
ap-4038	230	44	and	and	CCONJ
ap-4038	230	45	ci	ci	PROPN
ap-4038	230	46	are	be	AUX
ap-4038	230	47	used	use	VERB
ap-4038	230	48	to	to	PART
ap-4038	230	49	denote	denote	VERB
ap-4038	230	50	the	the	DET
ap-4038	230	51	normal	normal	ADJ
ap-4038	230	52	vector	vector	NOUN
ap-4038	230	53	and	and	CCONJ
ap-4038	230	54	the	the	DET
ap-4038	230	55	plane	plane	NOUN
ap-4038	230	56	constant	constant	ADJ
ap-4038	230	57	of	of	ADP
ap-4038	230	58	face	face	NOUN
ap-4038	230	59	fi	fi	NOUN
ap-4038	230	60	,	,	PUNCT
ap-4038	230	61	respectively	respectively	ADV
ap-4038	230	62	.	.	PUNCT
ap-4038	231	1	the	the	DET
ap-4038	231	2	area	area	NOUN
ap-4038	231	3	of	of	ADP
ap-4038	231	4	face	face	NOUN
ap-4038	231	5	fi	fi	NOUN
ap-4038	231	6	is	be	AUX
ap-4038	231	7	denoted	denote	VERB
ap-4038	231	8	as	as	ADP
ap-4038	231	9	ai	ai	NOUN
ap-4038	231	10	.	.	PUNCT
ap-4038	232	1	the	the	DET
ap-4038	232	2	volume	volume	NOUN
ap-4038	232	3	of	of	ADP
ap-4038	232	4	the	the	DET
ap-4038	232	5	intersection	intersection	NOUN
ap-4038	232	6	of	of	ADP
ap-4038	232	7	the	the	DET
ap-4038	232	8	two	two	NUM
ap-4038	232	9	polyhedra	polyhedra	NOUN
ap-4038	232	10	then	then	ADV
ap-4038	232	11	reduces	reduce	VERB
ap-4038	232	12	to	to	ADP
ap-4038	232	13	an	an	DET
ap-4038	232	14	evaluation	evaluation	NOUN
ap-4038	232	15	of	of	ADP
ap-4038	232	16	the	the	DET
ap-4038	232	17	areas	area	NOUN
ap-4038	232	18	and	and	CCONJ
ap-4038	232	19	the	the	DET
ap-4038	232	20	plane	plane	NOUN
ap-4038	232	21	constants	constant	NOUN
ap-4038	232	22	of	of	ADP
ap-4038	232	23	the	the	DET
ap-4038	232	24	faces	face	NOUN
ap-4038	232	25	contained	contain	VERB
ap-4038	232	26	in	in	ADP
ap-4038	232	27	the	the	DET
ap-4038	232	28	set	set	NOUN
ap-4038	232	29	{	{	PUNCT
ap-4038	232	30	in	in	ADP
ap-4038	232	31	∪coin	∪coin	PROPN
ap-4038	232	32	}	}	PUNCT
ap-4038	232	33	.	.	PUNCT
ap-4038	233	1	all	all	DET
ap-4038	233	2	the	the	DET
ap-4038	233	3	procedures	procedure	NOUN
ap-4038	233	4	were	be	AUX
ap-4038	233	5	implemented	implement	VERB
ap-4038	233	6	into	into	ADP
ap-4038	233	7	the	the	DET
ap-4038	233	8	oofem	oofem	PROPN
ap-4038	233	9	code	code	PROPN
ap-4038	234	1	[	[	X
ap-4038	234	2	21	21	NUM
ap-4038	234	3	,	,	PUNCT
ap-4038	234	4	22	22	NUM
ap-4038	234	5	]	]	PUNCT
ap-4038	234	6	.	.	PUNCT
ap-4038	235	1	all	all	DET
ap-4038	235	2	the	the	DET
ap-4038	235	3	results	result	NOUN
ap-4038	235	4	presented	present	VERB
ap-4038	235	5	in	in	ADP
ap-4038	235	6	the	the	DET
ap-4038	235	7	following	follow	VERB
ap-4038	235	8	section	section	NOUN
ap-4038	235	9	were	be	AUX
ap-4038	235	10	also	also	ADV
ap-4038	235	11	obtained	obtain	VERB
ap-4038	235	12	with	with	ADP
ap-4038	235	13	oofem	oofem	PROPN
ap-4038	235	14	.	.	PUNCT
ap-4038	236	1	4	4	NUM
ap-4038	236	2	.	.	X
ap-4038	236	3	numerical	numerical	ADJ
ap-4038	236	4	examples	example	NOUN
ap-4038	236	5	in	in	ADP
ap-4038	236	6	this	this	DET
ap-4038	236	7	section	section	NOUN
ap-4038	236	8	,	,	PUNCT
ap-4038	236	9	we	we	PRON
ap-4038	236	10	present	present	VERB
ap-4038	236	11	several	several	ADJ
ap-4038	236	12	numerical	numerical	ADJ
ap-4038	236	13	examples	example	NOUN
ap-4038	236	14	that	that	PRON
ap-4038	236	15	illustrate	illustrate	VERB
ap-4038	236	16	the	the	DET
ap-4038	236	17	capability	capability	NOUN
ap-4038	236	18	of	of	ADP
ap-4038	236	19	the	the	DET
ap-4038	236	20	proposed	propose	VERB
ap-4038	236	21	bsp	bsp	NOUN
ap-4038	236	22	tree	tree	NOUN
ap-4038	236	23	-	-	PUNCT
ap-4038	236	24	based	base	VERB
ap-4038	236	25	vof	vof	NOUN
ap-4038	236	26	method	method	NOUN
ap-4038	236	27	.	.	PUNCT
ap-4038	237	1	the	the	DET
ap-4038	237	2	first	first	ADJ
ap-4038	237	3	example	example	NOUN
ap-4038	237	4	focuses	focus	VERB
ap-4038	237	5	on	on	ADP
ap-4038	237	6	the	the	DET
ap-4038	237	7	shape	shape	NOUN
ap-4038	237	8	-	-	PUNCT
ap-4038	237	9	preserving	preserve	VERB
ap-4038	237	10	ability	ability	NOUN
ap-4038	237	11	of	of	ADP
ap-4038	237	12	the	the	DET
ap-4038	237	13	method	method	NOUN
ap-4038	237	14	,	,	PUNCT
ap-4038	237	15	and	and	CCONJ
ap-4038	237	16	also	also	ADV
ap-4038	237	17	on	on	ADP
ap-4038	237	18	conservation	conservation	NOUN
ap-4038	237	19	of	of	ADP
ap-4038	237	20	volume	volume	NOUN
ap-4038	237	21	.	.	PUNCT
ap-4038	238	1	the	the	DET
ap-4038	238	2	second	second	ADJ
ap-4038	238	3	example	example	NOUN
ap-4038	238	4	110	110	NUM
ap-4038	238	5	vol	vol	NOUN
ap-4038	238	6	.	.	PUNCT
ap-4038	238	7	57	57	NUM
ap-4038	238	8	no	no	NOUN
ap-4038	238	9	.	.	PUNCT
ap-4038	239	1	2/2017	2/2017	NUM
ap-4038	239	2	implementation	implementation	NOUN
ap-4038	239	3	of	of	ADP
ap-4038	239	4	a	a	DET
ap-4038	239	5	3d	3d	NUM
ap-4038	239	6	vof	vof	NOUN
ap-4038	239	7	tracking	track	VERB
ap-4038	239	8	algorithm	algorithm	NOUN
ap-4038	239	9	figure	figure	NOUN
ap-4038	239	10	3	3	NUM
ap-4038	239	11	.	.	PUNCT
ap-4038	239	12	cube	cube	NOUN
ap-4038	239	13	translation	translation	NOUN
ap-4038	239	14	—	—	PUNCT
ap-4038	239	15	initial	initial	ADJ
ap-4038	239	16	position	position	NOUN
ap-4038	239	17	,	,	PUNCT
ap-4038	239	18	t	t	PROPN
ap-4038	239	19	=	=	SYM
ap-4038	239	20	0	0	NUM
ap-4038	239	21	s.	s.	PROPN
ap-4038	239	22	figure	figure	VERB
ap-4038	239	23	4	4	NUM
ap-4038	239	24	.	.	PUNCT
ap-4038	239	25	cube	cube	NOUN
ap-4038	239	26	translation	translation	NOUN
ap-4038	239	27	—	—	PUNCT
ap-4038	239	28	middle	middle	ADJ
ap-4038	239	29	position	position	NOUN
ap-4038	239	30	,	,	PUNCT
ap-4038	239	31	t	t	PROPN
ap-4038	239	32	=	=	SYM
ap-4038	239	33	5	5	NUM
ap-4038	239	34	s.	s.	PROPN
ap-4038	239	35	models	model	VERB
ap-4038	239	36	the	the	DET
ap-4038	239	37	famous	famous	ADJ
ap-4038	239	38	experiment	experiment	NOUN
ap-4038	239	39	performed	perform	VERB
ap-4038	239	40	by	by	ADP
ap-4038	239	41	martin	martin	PROPN
ap-4038	239	42	and	and	CCONJ
ap-4038	239	43	moyce	moyce	NOUN
ap-4038	239	44	in	in	ADP
ap-4038	239	45	the	the	DET
ap-4038	239	46	early	early	ADJ
ap-4038	239	47	1950s	1950	NOUN
ap-4038	240	1	[	[	X
ap-4038	240	2	23	23	NUM
ap-4038	240	3	]	]	PUNCT
ap-4038	240	4	.	.	PUNCT
ap-4038	241	1	4.1	4.1	NUM
ap-4038	241	2	.	.	PUNCT
ap-4038	241	3	cube	cube	NOUN
ap-4038	241	4	propagation	propagation	NOUN
ap-4038	241	5	through	through	ADP
ap-4038	241	6	the	the	DET
ap-4038	241	7	unstructured	unstructured	ADJ
ap-4038	241	8	mesh	mesh	NOUN
ap-4038	241	9	the	the	DET
ap-4038	241	10	example	example	NOUN
ap-4038	241	11	presented	present	VERB
ap-4038	241	12	here	here	ADV
ap-4038	241	13	considers	consider	VERB
ap-4038	241	14	the	the	DET
ap-4038	241	15	propagation	propagation	NOUN
ap-4038	241	16	of	of	ADP
ap-4038	241	17	a	a	DET
ap-4038	241	18	cube	cube	NOUN
ap-4038	241	19	through	through	ADP
ap-4038	241	20	the	the	DET
ap-4038	241	21	unstructured	unstructured	ADJ
ap-4038	241	22	mesh	mesh	NOUN
ap-4038	241	23	in	in	ADP
ap-4038	241	24	the	the	DET
ap-4038	241	25	case	case	NOUN
ap-4038	241	26	of	of	ADP
ap-4038	241	27	two	two	NUM
ap-4038	241	28	basic	basic	ADJ
ap-4038	241	29	motions	motion	NOUN
ap-4038	241	30	of	of	ADP
ap-4038	241	31	a	a	DET
ap-4038	241	32	fluid	fluid	NOUN
ap-4038	241	33	:	:	PUNCT
ap-4038	241	34	translation	translation	NOUN
ap-4038	241	35	and	and	CCONJ
ap-4038	241	36	rotation	rotation	NOUN
ap-4038	241	37	.	.	PUNCT
ap-4038	242	1	in	in	ADP
ap-4038	242	2	both	both	DET
ap-4038	242	3	cases	case	NOUN
ap-4038	242	4	,	,	PUNCT
ap-4038	242	5	the	the	DET
ap-4038	242	6	velocity	velocity	NOUN
ap-4038	242	7	field	field	NOUN
ap-4038	242	8	is	be	AUX
ap-4038	242	9	prescribed	prescribe	VERB
ap-4038	242	10	in	in	ADP
ap-4038	242	11	the	the	DET
ap-4038	242	12	whole	whole	ADJ
ap-4038	242	13	domain	domain	NOUN
ap-4038	242	14	,	,	PUNCT
ap-4038	242	15	so	so	SCONJ
ap-4038	242	16	we	we	PRON
ap-4038	242	17	can	can	AUX
ap-4038	242	18	focus	focus	VERB
ap-4038	242	19	exclusively	exclusively	ADV
ap-4038	242	20	on	on	ADP
ap-4038	242	21	the	the	DET
ap-4038	242	22	vof	vof	NOUN
ap-4038	242	23	method	method	NOUN
ap-4038	242	24	itself	itself	PRON
ap-4038	242	25	.	.	PUNCT
ap-4038	243	1	the	the	DET
ap-4038	243	2	focus	focus	NOUN
ap-4038	243	3	here	here	ADV
ap-4038	243	4	is	be	AUX
ap-4038	243	5	on	on	ADP
ap-4038	243	6	the	the	DET
ap-4038	243	7	shapepreserving	shapepreserve	VERB
ap-4038	243	8	and	and	CCONJ
ap-4038	243	9	volume	volume	NOUN
ap-4038	243	10	conservation	conservation	NOUN
ap-4038	243	11	properties	property	NOUN
ap-4038	243	12	.	.	PUNCT
ap-4038	244	1	4.1.1	4.1.1	X
ap-4038	244	2	.	.	PUNCT
ap-4038	244	3	cube	cube	NOUN
ap-4038	244	4	translation	translation	NOUN
ap-4038	244	5	the	the	DET
ap-4038	244	6	computational	computational	ADJ
ap-4038	244	7	domain	domain	NOUN
ap-4038	244	8	is	be	AUX
ap-4038	244	9	a	a	DET
ap-4038	244	10	10	10	NUM
ap-4038	244	11	×	×	NOUN
ap-4038	244	12	10	10	NUM
ap-4038	244	13	×	×	NOUN
ap-4038	244	14	20	20	NUM
ap-4038	244	15	prismatic	prismatic	ADJ
ap-4038	244	16	block	block	NOUN
ap-4038	244	17	with	with	ADP
ap-4038	244	18	a	a	DET
ap-4038	244	19	5×	5×	ADJ
ap-4038	244	20	5×	5×	ADJ
ap-4038	244	21	5	5	NUM
ap-4038	244	22	cube	cube	NOUN
ap-4038	244	23	inside	inside	ADV
ap-4038	244	24	,	,	PUNCT
ap-4038	244	25	see	see	VERB
ap-4038	244	26	figure	figure	NOUN
ap-4038	244	27	3	3	NUM
ap-4038	244	28	.	.	PUNCT
ap-4038	245	1	the	the	DET
ap-4038	245	2	velocity	velocity	NOUN
ap-4038	245	3	field	field	NOUN
ap-4038	245	4	is	be	AUX
ap-4038	245	5	prescribed	prescribe	VERB
ap-4038	245	6	as	as	ADP
ap-4038	245	7	a	a	DET
ap-4038	245	8	uniform	uniform	ADJ
ap-4038	245	9	field	field	NOUN
ap-4038	245	10	,	,	PUNCT
ap-4038	245	11	i.e.	i.e.	X
ap-4038	245	12	(	(	PUNCT
ap-4038	245	13	1	1	NUM
ap-4038	245	14	,	,	PUNCT
ap-4038	245	15	0	0	NUM
ap-4038	245	16	,	,	PUNCT
ap-4038	245	17	0	0	NUM
ap-4038	245	18	)	)	PUNCT
ap-4038	245	19	,	,	PUNCT
ap-4038	245	20	along	along	ADP
ap-4038	245	21	the	the	DET
ap-4038	245	22	longest	long	ADJ
ap-4038	245	23	side	side	NOUN
ap-4038	245	24	of	of	ADP
ap-4038	245	25	the	the	DET
ap-4038	245	26	block	block	NOUN
ap-4038	245	27	in	in	ADP
ap-4038	245	28	the	the	DET
ap-4038	245	29	x	x	NOUN
ap-4038	245	30	-	-	NOUN
ap-4038	245	31	direction	direction	NOUN
ap-4038	245	32	.	.	PUNCT
ap-4038	246	1	for	for	ADP
ap-4038	246	2	the	the	DET
ap-4038	246	3	computation	computation	NOUN
ap-4038	246	4	presented	present	VERB
ap-4038	246	5	here	here	ADV
ap-4038	246	6	,	,	PUNCT
ap-4038	246	7	we	we	PRON
ap-4038	246	8	used	use	VERB
ap-4038	246	9	an	an	DET
ap-4038	246	10	unstructured	unstructured	ADJ
ap-4038	246	11	mesh	mesh	NOUN
ap-4038	246	12	with	with	ADP
ap-4038	246	13	27910	27910	NUM
ap-4038	246	14	nodes	node	NOUN
ap-4038	246	15	and	and	CCONJ
ap-4038	246	16	150909	150909	NUM
ap-4038	246	17	elements	element	NOUN
ap-4038	246	18	.	.	PUNCT
ap-4038	247	1	for	for	ADP
ap-4038	247	2	shape	shape	NOUN
ap-4038	247	3	preservation	preservation	NOUN
ap-4038	247	4	,	,	PUNCT
ap-4038	247	5	figures	figure	VERB
ap-4038	247	6	3–5	3–5	NUM
ap-4038	247	7	show	show	VERB
ap-4038	247	8	the	the	DET
ap-4038	247	9	initial	initial	ADJ
ap-4038	247	10	position	position	NOUN
ap-4038	247	11	,	,	PUNCT
ap-4038	247	12	the	the	DET
ap-4038	247	13	middle	middle	ADJ
ap-4038	247	14	position	position	NOUN
ap-4038	247	15	and	and	CCONJ
ap-4038	247	16	the	the	DET
ap-4038	247	17	final	final	ADJ
ap-4038	247	18	position	position	NOUN
ap-4038	247	19	of	of	ADP
ap-4038	247	20	the	the	DET
ap-4038	247	21	cube	cube	NOUN
ap-4038	247	22	;	;	PUNCT
ap-4038	247	23	it	it	PRON
ap-4038	247	24	can	can	AUX
ap-4038	247	25	be	be	AUX
ap-4038	247	26	seen	see	VERB
ap-4038	247	27	that	that	SCONJ
ap-4038	247	28	the	the	DET
ap-4038	247	29	shape	shape	NOUN
ap-4038	247	30	preservation	preservation	NOUN
ap-4038	247	31	is	be	AUX
ap-4038	247	32	very	very	ADV
ap-4038	247	33	decent	decent	ADJ
ap-4038	247	34	.	.	PUNCT
ap-4038	248	1	figures	figure	NOUN
ap-4038	248	2	6	6	NUM
ap-4038	248	3	display	display	NOUN
ap-4038	248	4	slices	slice	NOUN
ap-4038	248	5	through	through	ADP
ap-4038	248	6	the	the	DET
ap-4038	248	7	cube	cube	NOUN
ap-4038	248	8	by	by	ADP
ap-4038	248	9	planes	plane	NOUN
ap-4038	248	10	with	with	ADP
ap-4038	248	11	the	the	DET
ap-4038	248	12	normal	normal	ADJ
ap-4038	248	13	vectors	vector	NOUN
ap-4038	248	14	in	in	ADP
ap-4038	248	15	x	x	PROPN
ap-4038	248	16	,	,	PUNCT
ap-4038	248	17	y	y	PROPN
ap-4038	248	18	and	and	CCONJ
ap-4038	248	19	z	z	NOUN
ap-4038	248	20	direction	direction	NOUN
ap-4038	248	21	respectively	respectively	ADV
ap-4038	248	22	,	,	PUNCT
ap-4038	248	23	at	at	ADP
ap-4038	248	24	times	time	NOUN
ap-4038	248	25	t	t	PROPN
ap-4038	248	26	=	=	SYM
ap-4038	248	27	0	0	NUM
ap-4038	248	28	s	s	PART
ap-4038	248	29	(	(	PUNCT
ap-4038	248	30	initial	initial	ADJ
ap-4038	248	31	position	position	NOUN
ap-4038	248	32	)	)	PUNCT
ap-4038	248	33	,	,	PUNCT
ap-4038	248	34	t	t	PROPN
ap-4038	248	35	=	=	SYM
ap-4038	248	36	5	5	NUM
ap-4038	248	37	s	s	PART
ap-4038	248	38	(	(	PUNCT
ap-4038	248	39	middle	middle	ADJ
ap-4038	248	40	position	position	NOUN
ap-4038	248	41	)	)	PUNCT
ap-4038	248	42	and	and	CCONJ
ap-4038	248	43	t	t	X
ap-4038	248	44	=	=	PUNCT
ap-4038	248	45	10	10	NUM
ap-4038	248	46	s	s	NOUN
ap-4038	248	47	(	(	PUNCT
ap-4038	248	48	final	final	ADJ
ap-4038	248	49	position	position	NOUN
ap-4038	248	50	)	)	PUNCT
ap-4038	248	51	.	.	PUNCT
ap-4038	249	1	visually	visually	ADV
ap-4038	249	2	,	,	PUNCT
ap-4038	249	3	there	there	PRON
ap-4038	249	4	is	be	VERB
ap-4038	249	5	no	no	DET
ap-4038	249	6	significant	significant	ADJ
ap-4038	249	7	error	error	NOUN
ap-4038	249	8	in	in	ADP
ap-4038	249	9	the	the	DET
ap-4038	249	10	original	original	ADJ
ap-4038	249	11	shape	shape	NOUN
ap-4038	249	12	of	of	ADP
ap-4038	249	13	the	the	DET
ap-4038	249	14	cube	cube	NOUN
ap-4038	249	15	.	.	PUNCT
ap-4038	250	1	detailed	detailed	ADJ
ap-4038	250	2	information	information	NOUN
ap-4038	250	3	about	about	ADP
ap-4038	250	4	shape	shape	NOUN
ap-4038	250	5	preservation	preservation	NOUN
ap-4038	250	6	is	be	AUX
ap-4038	250	7	provided	provide	VERB
ap-4038	250	8	in	in	ADP
ap-4038	250	9	figure	figure	NOUN
ap-4038	250	10	5	5	NUM
ap-4038	250	11	.	.	PUNCT
ap-4038	250	12	cube	cube	NOUN
ap-4038	250	13	translation	translation	NOUN
ap-4038	250	14	—	—	PUNCT
ap-4038	250	15	end	end	NOUN
ap-4038	250	16	position	position	NOUN
ap-4038	250	17	,	,	PUNCT
ap-4038	250	18	t	t	PROPN
ap-4038	250	19	=	=	SYM
ap-4038	250	20	10	10	NUM
ap-4038	250	21	s.	s.	PROPN
ap-4038	250	22	figure	figure	VERB
ap-4038	250	23	6	6	NUM
ap-4038	250	24	.	.	PUNCT
ap-4038	250	25	cube	cube	NOUN
ap-4038	250	26	translation	translation	NOUN
ap-4038	250	27	.	.	PUNCT
ap-4038	251	1	slices	slice	NOUN
ap-4038	251	2	with	with	ADP
ap-4038	251	3	the	the	DET
ap-4038	251	4	normal	normal	ADJ
ap-4038	251	5	in	in	ADP
ap-4038	251	6	the	the	DET
ap-4038	251	7	x	x	PROPN
ap-4038	251	8	,	,	PUNCT
ap-4038	251	9	y	y	PROPN
ap-4038	251	10	,	,	PUNCT
ap-4038	251	11	z	z	NOUN
ap-4038	251	12	-	-	PUNCT
ap-4038	251	13	direction	direction	NOUN
ap-4038	251	14	(	(	PUNCT
ap-4038	251	15	columns	column	NOUN
ap-4038	251	16	)	)	PUNCT
ap-4038	251	17	and	and	CCONJ
ap-4038	251	18	times	time	NOUN
ap-4038	251	19	t	t	PROPN
ap-4038	251	20	=	=	SYM
ap-4038	251	21	0	0	NUM
ap-4038	251	22	,	,	PUNCT
ap-4038	251	23	5	5	NUM
ap-4038	251	24	,	,	PUNCT
ap-4038	251	25	10	10	NUM
ap-4038	251	26	s	s	NOUN
ap-4038	251	27	(	(	PUNCT
ap-4038	251	28	rows	row	NOUN
ap-4038	251	29	)	)	PUNCT
ap-4038	251	30	.	.	PUNCT
ap-4038	252	1	table	table	NOUN
ap-4038	252	2	1	1	NUM
ap-4038	252	3	,	,	PUNCT
ap-4038	252	4	which	which	PRON
ap-4038	252	5	presents	present	VERB
ap-4038	252	6	a	a	DET
ap-4038	252	7	quantitative	quantitative	ADJ
ap-4038	252	8	evaluation	evaluation	NOUN
ap-4038	252	9	of	of	ADP
ap-4038	252	10	the	the	DET
ap-4038	252	11	vof	vof	NOUN
ap-4038	252	12	values	value	NOUN
ap-4038	252	13	at	at	ADP
ap-4038	252	14	time	time	NOUN
ap-4038	252	15	t	t	PROPN
ap-4038	252	16	=	=	SYM
ap-4038	252	17	0	0	PROPN
ap-4038	252	18	s	s	PART
ap-4038	252	19	and	and	CCONJ
ap-4038	252	20	t	t	NOUN
ap-4038	252	21	=	=	PUNCT
ap-4038	252	22	10	10	NUM
ap-4038	252	23	s	s	NOUN
ap-4038	252	24	;	;	PUNCT
ap-4038	252	25	the	the	DET
ap-4038	252	26	first	first	ADJ
ap-4038	252	27	column	column	NOUN
ap-4038	252	28	shows	show	VERB
ap-4038	252	29	the	the	DET
ap-4038	252	30	relative	relative	ADJ
ap-4038	252	31	error	error	NOUN
ap-4038	252	32	of	of	ADP
ap-4038	252	33	the	the	DET
ap-4038	252	34	vof	vof	NOUN
ap-4038	252	35	values	value	NOUN
ap-4038	252	36	(	(	PUNCT
ap-4038	252	37	denoted	denote	VERB
ap-4038	252	38	as	as	ADP
ap-4038	252	39	h	h	NOUN
ap-4038	252	40	)	)	PUNCT
ap-4038	252	41	on	on	ADP
ap-4038	252	42	each	each	DET
ap-4038	252	43	side	side	NOUN
ap-4038	252	44	of	of	ADP
ap-4038	252	45	the	the	DET
ap-4038	252	46	cube	cube	NOUN
ap-4038	252	47	.	.	PUNCT
ap-4038	253	1	the	the	DET
ap-4038	253	2	mean	mean	ADJ
ap-4038	253	3	value	value	NOUN
ap-4038	253	4	of	of	ADP
ap-4038	253	5	vof	vof	NOUN
ap-4038	253	6	is	be	AUX
ap-4038	253	7	shown	show	VERB
ap-4038	253	8	in	in	ADP
ap-4038	253	9	the	the	DET
ap-4038	253	10	middle	middle	ADJ
ap-4038	253	11	column	column	NOUN
ap-4038	253	12	,	,	PUNCT
ap-4038	253	13	and	and	CCONJ
ap-4038	253	14	the	the	DET
ap-4038	253	15	standard	standard	ADJ
ap-4038	253	16	deviation	deviation	NOUN
ap-4038	253	17	is	be	AUX
ap-4038	253	18	in	in	ADP
ap-4038	253	19	the	the	DET
ap-4038	253	20	third	third	ADJ
ap-4038	253	21	column	column	NOUN
ap-4038	253	22	.	.	PUNCT
ap-4038	254	1	the	the	DET
ap-4038	254	2	theoretically	theoretically	ADV
ap-4038	254	3	exact	exact	ADJ
ap-4038	254	4	value	value	NOUN
ap-4038	254	5	hex	hex	PROPN
ap-4038	254	6	=	=	NOUN
ap-4038	254	7	0.5	0.5	NUM
ap-4038	254	8	.	.	PUNCT
ap-4038	255	1	it	it	PRON
ap-4038	255	2	can	can	AUX
ap-4038	255	3	be	be	AUX
ap-4038	255	4	seen	see	VERB
ap-4038	255	5	that	that	SCONJ
ap-4038	255	6	there	there	PRON
ap-4038	255	7	are	be	VERB
ap-4038	255	8	no	no	DET
ap-4038	255	9	significant	significant	ADJ
ap-4038	255	10	changes	change	NOUN
ap-4038	255	11	in	in	ADP
ap-4038	255	12	the	the	DET
ap-4038	255	13	mean	mean	ADJ
ap-4038	255	14	value	value	NOUN
ap-4038	255	15	,	,	PUNCT
ap-4038	255	16	and	and	CCONJ
ap-4038	255	17	the	the	DET
ap-4038	255	18	first	first	ADJ
ap-4038	255	19	column	column	NOUN
ap-4038	255	20	shows	show	VERB
ap-4038	255	21	an	an	DET
ap-4038	255	22	average	average	ADJ
ap-4038	255	23	error	error	NOUN
ap-4038	255	24	of	of	ADP
ap-4038	255	25	approximately	approximately	ADV
ap-4038	255	26	12	12	NUM
ap-4038	255	27	%	%	NOUN
ap-4038	255	28	.	.	PUNCT
ap-4038	256	1	there	there	PRON
ap-4038	256	2	is	be	VERB
ap-4038	256	3	a	a	DET
ap-4038	256	4	slight	slight	ADJ
ap-4038	256	5	increment	increment	NOUN
ap-4038	256	6	in	in	ADP
ap-4038	256	7	the	the	DET
ap-4038	256	8	standard	standard	ADJ
ap-4038	256	9	deviation	deviation	NOUN
ap-4038	256	10	,	,	PUNCT
ap-4038	256	11	which	which	PRON
ap-4038	256	12	indicates	indicate	VERB
ap-4038	256	13	non	non	ADJ
ap-4038	256	14	-	-	ADJ
ap-4038	256	15	uniform	uniform	ADJ
ap-4038	256	16	distribution	distribution	NOUN
ap-4038	256	17	of	of	ADP
ap-4038	256	18	vof	vof	NOUN
ap-4038	256	19	values	value	NOUN
ap-4038	256	20	across	across	ADP
ap-4038	256	21	the	the	DET
ap-4038	256	22	planes	plane	NOUN
ap-4038	256	23	of	of	ADP
ap-4038	256	24	the	the	DET
ap-4038	256	25	cubes	cube	NOUN
ap-4038	256	26	and	and	CCONJ
ap-4038	256	27	increasing	increase	VERB
ap-4038	256	28	fluctuations	fluctuation	NOUN
ap-4038	256	29	.	.	PUNCT
ap-4038	257	1	other	other	ADJ
ap-4038	257	2	tests	test	NOUN
ap-4038	257	3	,	,	PUNCT
ap-4038	257	4	which	which	PRON
ap-4038	257	5	are	be	AUX
ap-4038	257	6	not	not	PART
ap-4038	257	7	reported	report	VERB
ap-4038	257	8	here	here	ADV
ap-4038	257	9	,	,	PUNCT
ap-4038	257	10	show	show	VERB
ap-4038	257	11	that	that	SCONJ
ap-4038	257	12	these	these	DET
ap-4038	257	13	fluctuations	fluctuation	NOUN
ap-4038	257	14	are	be	AUX
ap-4038	257	15	reduced	reduce	VERB
ap-4038	257	16	when	when	SCONJ
ap-4038	257	17	finer	fine	ADJ
ap-4038	257	18	meshes	mesh	NOUN
ap-4038	257	19	are	be	AUX
ap-4038	257	20	used	use	VERB
ap-4038	257	21	.	.	PUNCT
ap-4038	258	1	the	the	DET
ap-4038	258	2	volume	volume	NOUN
ap-4038	258	3	conservation	conservation	NOUN
ap-4038	258	4	is	be	AUX
ap-4038	258	5	also	also	ADV
ap-4038	258	6	excellent	excellent	ADJ
ap-4038	258	7	.	.	PUNCT
ap-4038	259	1	the	the	DET
ap-4038	259	2	ratio	ratio	NOUN
ap-4038	259	3	between	between	ADP
ap-4038	259	4	the	the	DET
ap-4038	259	5	final	final	ADJ
ap-4038	259	6	and	and	CCONJ
ap-4038	259	7	initial	initial	ADJ
ap-4038	259	8	the	the	DET
ap-4038	259	9	volume	volume	NOUN
ap-4038	259	10	is	be	AUX
ap-4038	259	11	only	only	ADV
ap-4038	259	12	1.000076	1.000076	NUM
ap-4038	259	13	,	,	PUNCT
ap-4038	259	14	which	which	PRON
ap-4038	259	15	represents	represent	VERB
ap-4038	259	16	an	an	DET
ap-4038	259	17	increase	increase	NOUN
ap-4038	259	18	in	in	ADP
ap-4038	259	19	volume	volume	NOUN
ap-4038	259	20	of	of	ADP
ap-4038	259	21	less	less	ADJ
ap-4038	259	22	than	than	ADP
ap-4038	259	23	0.1‰.	0.1‰.	PROPN
ap-4038	259	24	111	111	NUM
ap-4038	259	25	filip	filip	NOUN
ap-4038	259	26	kolařík	kolařík	NOUN
ap-4038	259	27	,	,	PUNCT
ap-4038	259	28	bořek	bořek	PROPN
ap-4038	259	29	patzák	patzák	VERB
ap-4038	259	30	acta	acta	PROPN
ap-4038	259	31	polytechnica	polytechnica	PROPN
ap-4038	259	32	cube	cube	PROPN
ap-4038	259	33	side	side	NOUN
ap-4038	259	34	|e(h)−hex|/hex	|e(h)−hex|/hex	PROPN
ap-4038	259	35	e(h	e(h	PROPN
ap-4038	259	36	)	)	PUNCT
ap-4038	259	37	σ(h	σ(h	PROPN
ap-4038	259	38	)	)	PUNCT
ap-4038	259	39	time	time	NOUN
ap-4038	259	40	t0	t0	PROPN
ap-4038	259	41	t10	t10	PROPN
ap-4038	259	42	t0	t0	PROPN
ap-4038	259	43	t10	t10	PROPN
ap-4038	259	44	t0	t0	PROPN
ap-4038	259	45	t10	t10	VERB
ap-4038	259	46	nx	nx	PROPN
ap-4038	259	47	front	front	NOUN
ap-4038	259	48	0.122	0.122	NUM
ap-4038	259	49	0.005	0.005	NUM
ap-4038	259	50	0.439	0.439	NUM
ap-4038	259	51	0.503	0.503	NUM
ap-4038	259	52	0.121	0.121	NUM
ap-4038	259	53	0.143	0.143	NUM
ap-4038	259	54	back	back	ADV
ap-4038	259	55	0.127	0.127	NUM
ap-4038	259	56	0.186	0.186	NUM
ap-4038	259	57	0.437	0.437	NUM
ap-4038	259	58	0.407	0.407	NUM
ap-4038	259	59	0.121	0.121	NUM
ap-4038	259	60	0.125	0.125	NUM
ap-4038	259	61	ny	ny	NOUN
ap-4038	259	62	left	leave	VERB
ap-4038	259	63	0.144	0.144	NUM
ap-4038	259	64	0.108	0.108	NUM
ap-4038	259	65	0.428	0.428	NUM
ap-4038	259	66	0.446	0.446	NUM
ap-4038	259	67	0.118	0.118	NUM
ap-4038	259	68	0.141	0.141	NUM
ap-4038	259	69	right	right	NOUN
ap-4038	259	70	0.141	0.141	NUM
ap-4038	259	71	0.121	0.121	NUM
ap-4038	259	72	0.429	0.429	NUM
ap-4038	259	73	0.439	0.439	NUM
ap-4038	259	74	0.121	0.121	NUM
ap-4038	259	75	0.133	0.133	NUM
ap-4038	259	76	nz	nz	NOUN
ap-4038	259	77	top	top	VERB
ap-4038	259	78	0.123	0.123	NUM
ap-4038	259	79	0.113	0.113	NUM
ap-4038	259	80	0.439	0.439	NUM
ap-4038	259	81	0.443	0.443	NUM
ap-4038	259	82	0.129	0.129	NUM
ap-4038	259	83	0.146	0.146	NUM
ap-4038	259	84	bottom	bottom	NOUN
ap-4038	259	85	0.132	0.132	NUM
ap-4038	259	86	0.136	0.136	NUM
ap-4038	259	87	0.434	0.434	NUM
ap-4038	259	88	0.432	0.432	NUM
ap-4038	259	89	0.124	0.124	NUM
ap-4038	259	90	0.152	0.152	NUM
ap-4038	259	91	table	table	NOUN
ap-4038	259	92	1	1	NUM
ap-4038	259	93	.	.	PUNCT
ap-4038	259	94	cube	cube	NOUN
ap-4038	259	95	propagation	propagation	NOUN
ap-4038	259	96	—	—	PUNCT
ap-4038	259	97	shape	shape	NOUN
ap-4038	259	98	preservation	preservation	NOUN
ap-4038	259	99	evaluation	evaluation	NOUN
ap-4038	259	100	.	.	PUNCT
ap-4038	260	1	figure	figure	NOUN
ap-4038	260	2	7	7	NUM
ap-4038	260	3	.	.	PUNCT
ap-4038	260	4	cube	cube	NOUN
ap-4038	260	5	rotation	rotation	NOUN
ap-4038	260	6	.	.	PUNCT
ap-4038	261	1	from	from	ADP
ap-4038	261	2	left	left	ADJ
ap-4038	261	3	to	to	ADP
ap-4038	261	4	right	right	NOUN
ap-4038	261	5	and	and	CCONJ
ap-4038	261	6	from	from	ADP
ap-4038	261	7	top	top	NOUN
ap-4038	261	8	to	to	ADP
ap-4038	261	9	bottom	bottom	NOUN
ap-4038	261	10	there	there	PRON
ap-4038	261	11	are	be	VERB
ap-4038	261	12	rotation	rotation	NOUN
ap-4038	261	13	angles	angle	NOUN
ap-4038	261	14	α	α	NOUN
ap-4038	261	15	=	=	SYM
ap-4038	261	16	0	0	NUM
ap-4038	261	17	°	°	NUM
ap-4038	261	18	,	,	PUNCT
ap-4038	261	19	90	90	NUM
ap-4038	261	20	°	°	NOUN
ap-4038	261	21	,	,	PUNCT
ap-4038	261	22	180	180	NUM
ap-4038	261	23	°	°	NOUN
ap-4038	261	24	,	,	PUNCT
ap-4038	261	25	270	270	NUM
ap-4038	261	26	°	°	NOUN
ap-4038	261	27	,	,	PUNCT
ap-4038	261	28	360	360	NUM
ap-4038	261	29	°	°	NOUN
ap-4038	261	30	.	.	PUNCT
ap-4038	262	1	the	the	DET
ap-4038	262	2	bottom	bottom	ADJ
ap-4038	262	3	-	-	PUNCT
ap-4038	262	4	right	right	NOUN
ap-4038	262	5	figure	figure	NOUN
ap-4038	262	6	shows	show	VERB
ap-4038	262	7	the	the	DET
ap-4038	262	8	top	top	ADJ
ap-4038	262	9	view	view	NOUN
ap-4038	262	10	of	of	ADP
ap-4038	262	11	the	the	DET
ap-4038	262	12	fully	fully	ADV
ap-4038	262	13	unstructured	unstructured	ADJ
ap-4038	262	14	mesh	mesh	NOUN
ap-4038	262	15	.	.	PUNCT
ap-4038	263	1	4.1.2	4.1.2	NUM
ap-4038	263	2	.	.	PUNCT
ap-4038	263	3	cube	cube	NOUN
ap-4038	263	4	rotation	rotation	NOUN
ap-4038	263	5	the	the	DET
ap-4038	263	6	second	second	ADJ
ap-4038	263	7	example	example	NOUN
ap-4038	263	8	performed	perform	VERB
ap-4038	263	9	in	in	ADP
ap-4038	263	10	order	order	NOUN
ap-4038	263	11	to	to	PART
ap-4038	263	12	investigate	investigate	VERB
ap-4038	263	13	the	the	DET
ap-4038	263	14	shape	shape	NOUN
ap-4038	263	15	and	and	CCONJ
ap-4038	263	16	volume	volume	NOUN
ap-4038	263	17	preserving	preserve	VERB
ap-4038	263	18	capabilities	capability	NOUN
ap-4038	263	19	deals	deal	NOUN
ap-4038	263	20	with	with	ADP
ap-4038	263	21	rotation	rotation	NOUN
ap-4038	263	22	of	of	ADP
ap-4038	263	23	the	the	DET
ap-4038	263	24	cube	cube	NOUN
ap-4038	263	25	.	.	PUNCT
ap-4038	264	1	the	the	DET
ap-4038	264	2	geometry	geometry	NOUN
ap-4038	264	3	is	be	AUX
ap-4038	264	4	formed	form	VERB
ap-4038	264	5	as	as	ADP
ap-4038	264	6	a	a	DET
ap-4038	264	7	1×	1×	NUM
ap-4038	264	8	1×	1×	NUM
ap-4038	264	9	1	1	NUM
ap-4038	264	10	cube	cube	NOUN
ap-4038	264	11	inside	inside	ADP
ap-4038	264	12	a	a	DET
ap-4038	264	13	cylinder	cylinder	NOUN
ap-4038	264	14	with	with	ADP
ap-4038	264	15	radius	radius	NOUN
ap-4038	264	16	1	1	NUM
ap-4038	264	17	and	and	CCONJ
ap-4038	264	18	height	height	NOUN
ap-4038	264	19	1.5	1.5	NUM
ap-4038	264	20	.	.	PUNCT
ap-4038	265	1	the	the	DET
ap-4038	265	2	velocity	velocity	NOUN
ap-4038	265	3	changes	change	VERB
ap-4038	265	4	linearly	linearly	ADV
ap-4038	265	5	from	from	ADP
ap-4038	265	6	0	0	NUM
ap-4038	265	7	at	at	ADP
ap-4038	265	8	the	the	DET
ap-4038	265	9	axis	axis	NOUN
ap-4038	265	10	of	of	ADP
ap-4038	265	11	rotation	rotation	NOUN
ap-4038	265	12	to	to	ADP
ap-4038	265	13	1	1	NUM
ap-4038	265	14	at	at	ADP
ap-4038	265	15	the	the	DET
ap-4038	265	16	surface	surface	NOUN
ap-4038	265	17	of	of	ADP
ap-4038	265	18	the	the	DET
ap-4038	265	19	cylinder	cylinder	NOUN
ap-4038	265	20	.	.	PUNCT
ap-4038	266	1	the	the	DET
ap-4038	266	2	computational	computational	ADJ
ap-4038	266	3	mesh	mesh	NOUN
ap-4038	266	4	consists	consist	VERB
ap-4038	266	5	of	of	ADP
ap-4038	266	6	24448	24448	NUM
ap-4038	266	7	nodes	node	NOUN
ap-4038	266	8	and	and	CCONJ
ap-4038	266	9	132971	132971	NUM
ap-4038	266	10	elements	element	NOUN
ap-4038	266	11	,	,	PUNCT
ap-4038	266	12	and	and	CCONJ
ap-4038	266	13	it	it	PRON
ap-4038	266	14	is	be	AUX
ap-4038	266	15	fully	fully	ADV
ap-4038	266	16	unstructured	unstructure	VERB
ap-4038	266	17	.	.	PUNCT
ap-4038	267	1	the	the	DET
ap-4038	267	2	whole	whole	ADJ
ap-4038	267	3	setup	setup	NOUN
ap-4038	267	4	is	be	AUX
ap-4038	267	5	shown	show	VERB
ap-4038	267	6	in	in	ADP
ap-4038	267	7	figure	figure	NOUN
ap-4038	267	8	7	7	NUM
ap-4038	267	9	,	,	PUNCT
ap-4038	267	10	where	where	SCONJ
ap-4038	267	11	the	the	DET
ap-4038	267	12	cube	cube	NOUN
ap-4038	267	13	is	be	AUX
ap-4038	267	14	presented	present	VERB
ap-4038	267	15	in	in	ADP
ap-4038	267	16	its	its	PRON
ap-4038	267	17	initial	initial	ADJ
ap-4038	267	18	position	position	NOUN
ap-4038	267	19	and	and	CCONJ
ap-4038	267	20	then	then	ADV
ap-4038	267	21	after	after	ADP
ap-4038	267	22	90	90	NUM
ap-4038	267	23	°	°	NOUN
ap-4038	267	24	,	,	PUNCT
ap-4038	267	25	180	180	NUM
ap-4038	267	26	°	°	NOUN
ap-4038	267	27	,	,	PUNCT
ap-4038	267	28	270	270	NUM
ap-4038	267	29	°	°	NUM
ap-4038	267	30	and	and	CCONJ
ap-4038	267	31	360	360	NUM
ap-4038	267	32	°	°	NOUN
ap-4038	267	33	of	of	ADP
ap-4038	267	34	rotation	rotation	NOUN
ap-4038	267	35	.	.	PUNCT
ap-4038	268	1	the	the	DET
ap-4038	268	2	last	last	ADJ
ap-4038	268	3	figure	figure	NOUN
ap-4038	268	4	shows	show	VERB
ap-4038	268	5	the	the	DET
ap-4038	268	6	top	top	ADJ
ap-4038	268	7	view	view	NOUN
ap-4038	268	8	on	on	ADP
ap-4038	268	9	the	the	DET
ap-4038	268	10	unstructured	unstructured	ADJ
ap-4038	268	11	mesh	mesh	NOUN
ap-4038	268	12	.	.	PUNCT
ap-4038	269	1	the	the	DET
ap-4038	269	2	conservation	conservation	NOUN
ap-4038	269	3	of	of	ADP
ap-4038	269	4	volume	volume	NOUN
ap-4038	269	5	is	be	AUX
ap-4038	269	6	again	again	ADV
ap-4038	269	7	excellent	excellent	ADJ
ap-4038	269	8	.	.	PUNCT
ap-4038	270	1	the	the	DET
ap-4038	270	2	ratio	ratio	NOUN
ap-4038	270	3	between	between	ADP
ap-4038	270	4	the	the	DET
ap-4038	270	5	initial	initial	NOUN
ap-4038	270	6	and	and	CCONJ
ap-4038	270	7	the	the	DET
ap-4038	270	8	final	final	ADJ
ap-4038	270	9	position	position	NOUN
ap-4038	270	10	of	of	ADP
ap-4038	270	11	the	the	DET
ap-4038	270	12	cube	cube	NOUN
ap-4038	270	13	(	(	PUNCT
ap-4038	270	14	after	after	ADP
ap-4038	270	15	360	360	NUM
ap-4038	270	16	deg	deg	PROPN
ap-4038	270	17	rotation	rotation	NOUN
ap-4038	270	18	)	)	PUNCT
ap-4038	270	19	is	be	AUX
ap-4038	270	20	0.9998012	0.9998012	NUM
ap-4038	270	21	which	which	PRON
ap-4038	270	22	represents	represent	VERB
ap-4038	270	23	an	an	DET
ap-4038	270	24	error	error	NOUN
ap-4038	270	25	of	of	ADP
ap-4038	270	26	less	less	ADJ
ap-4038	270	27	than	than	ADP
ap-4038	270	28	0.2	0.2	NUM
ap-4038	270	29	‰	‰	NUM
ap-4038	270	30	error	error	NOUN
ap-4038	270	31	.	.	PUNCT
ap-4038	271	1	figure	figure	NOUN
ap-4038	271	2	8	8	NUM
ap-4038	271	3	shows	show	VERB
ap-4038	271	4	slices	slice	NOUN
ap-4038	271	5	through	through	ADP
ap-4038	271	6	the	the	DET
ap-4038	271	7	cube	cube	NOUN
ap-4038	271	8	by	by	ADP
ap-4038	271	9	planes	plane	NOUN
ap-4038	271	10	with	with	ADP
ap-4038	271	11	the	the	DET
ap-4038	271	12	normal	normal	ADJ
ap-4038	271	13	in	in	ADP
ap-4038	271	14	the	the	DET
ap-4038	271	15	x	x	PROPN
ap-4038	271	16	,	,	PUNCT
ap-4038	271	17	y	y	PROPN
ap-4038	271	18	and	and	CCONJ
ap-4038	271	19	z	z	PROPN
ap-4038	271	20	direction	direction	NOUN
ap-4038	271	21	,	,	PUNCT
ap-4038	271	22	again	again	ADV
ap-4038	271	23	for	for	ADP
ap-4038	271	24	the	the	DET
ap-4038	271	25	initial	initial	ADJ
ap-4038	271	26	position	position	NOUN
ap-4038	271	27	and	and	CCONJ
ap-4038	271	28	after	after	ADP
ap-4038	271	29	90	90	NUM
ap-4038	271	30	°	°	NOUN
ap-4038	271	31	,	,	PUNCT
ap-4038	271	32	180	180	NUM
ap-4038	271	33	°	°	NOUN
ap-4038	271	34	,	,	PUNCT
ap-4038	271	35	270	270	NUM
ap-4038	271	36	°	°	NUM
ap-4038	271	37	and	and	CCONJ
ap-4038	271	38	360	360	NUM
ap-4038	271	39	°	°	NUM
ap-4038	271	40	rotation	rotation	NOUN
ap-4038	271	41	,	,	PUNCT
ap-4038	271	42	showing	show	VERB
ap-4038	271	43	shape	shape	NOUN
ap-4038	271	44	preservation	preservation	NOUN
ap-4038	271	45	.	.	PUNCT
ap-4038	272	1	quantitative	quantitative	ADJ
ap-4038	272	2	results	result	NOUN
ap-4038	272	3	connected	connect	VERB
ap-4038	272	4	to	to	PART
ap-4038	272	5	shape	shape	VERB
ap-4038	272	6	preservation	preservation	NOUN
ap-4038	272	7	are	be	AUX
ap-4038	272	8	summarized	summarize	VERB
ap-4038	272	9	in	in	ADP
ap-4038	272	10	table	table	NOUN
ap-4038	272	11	2	2	NUM
ap-4038	272	12	.	.	PUNCT
ap-4038	272	13	similarly	similarly	ADV
ap-4038	272	14	as	as	ADP
ap-4038	272	15	in	in	ADP
ap-4038	272	16	the	the	DET
ap-4038	272	17	cube	cube	NOUN
ap-4038	272	18	translation	translation	NOUN
ap-4038	272	19	,	,	PUNCT
ap-4038	272	20	the	the	DET
ap-4038	272	21	first	first	ADJ
ap-4038	272	22	column	column	NOUN
ap-4038	272	23	shows	show	VERB
ap-4038	272	24	the	the	DET
ap-4038	272	25	relative	relative	ADJ
ap-4038	272	26	error	error	NOUN
ap-4038	272	27	in	in	ADP
ap-4038	272	28	the	the	DET
ap-4038	272	29	vof	vof	NOUN
ap-4038	272	30	values	value	NOUN
ap-4038	272	31	on	on	ADP
ap-4038	272	32	each	each	DET
ap-4038	272	33	side	side	NOUN
ap-4038	272	34	of	of	ADP
ap-4038	272	35	the	the	DET
ap-4038	272	36	cube	cube	NOUN
ap-4038	272	37	for	for	ADP
ap-4038	272	38	the	the	DET
ap-4038	272	39	initial	initial	ADJ
ap-4038	272	40	position	position	NOUN
ap-4038	272	41	and	and	CCONJ
ap-4038	272	42	after	after	ADP
ap-4038	272	43	360	360	NUM
ap-4038	272	44	°	°	NOUN
ap-4038	272	45	rotation	rotation	NOUN
ap-4038	272	46	.	.	PUNCT
ap-4038	273	1	the	the	DET
ap-4038	273	2	second	second	ADJ
ap-4038	273	3	column	column	NOUN
ap-4038	273	4	shows	show	VERB
ap-4038	273	5	the	the	DET
ap-4038	273	6	mean	mean	ADJ
ap-4038	273	7	vof	vof	NOUN
ap-4038	273	8	values	value	NOUN
ap-4038	273	9	,	,	PUNCT
ap-4038	273	10	and	and	CCONJ
ap-4038	273	11	the	the	DET
ap-4038	273	12	third	third	ADJ
ap-4038	273	13	column	column	NOUN
ap-4038	273	14	shows	show	VERB
ap-4038	273	15	the	the	DET
ap-4038	273	16	standard	standard	ADJ
ap-4038	273	17	deviation	deviation	NOUN
ap-4038	273	18	.	.	PUNCT
ap-4038	274	1	note	note	VERB
ap-4038	274	2	that	that	SCONJ
ap-4038	274	3	the	the	DET
ap-4038	274	4	trend	trend	NOUN
ap-4038	274	5	is	be	AUX
ap-4038	274	6	the	the	DET
ap-4038	274	7	same	same	ADJ
ap-4038	274	8	as	as	ADP
ap-4038	274	9	in	in	ADP
ap-4038	274	10	cube	cube	NOUN
ap-4038	274	11	translation	translation	NOUN
ap-4038	274	12	,	,	PUNCT
ap-4038	274	13	i.e.	i.e.	X
ap-4038	274	14	the	the	DET
ap-4038	274	15	vof	vof	NOUN
ap-4038	274	16	values	value	NOUN
ap-4038	274	17	do	do	AUX
ap-4038	274	18	not	not	PART
ap-4038	274	19	change	change	VERB
ap-4038	274	20	significantly	significantly	ADV
ap-4038	274	21	on	on	ADP
ap-4038	274	22	an	an	DET
ap-4038	274	23	average	average	NOUN
ap-4038	274	24	,	,	PUNCT
ap-4038	274	25	but	but	CCONJ
ap-4038	274	26	,	,	PUNCT
ap-4038	274	27	as	as	ADP
ap-4038	274	28	the	the	DET
ap-4038	274	29	cube	cube	NOUN
ap-4038	274	30	rotates	rotate	NOUN
ap-4038	274	31	,	,	PUNCT
ap-4038	274	32	the	the	DET
ap-4038	274	33	fluctuations	fluctuation	NOUN
ap-4038	274	34	around	around	ADP
ap-4038	274	35	the	the	DET
ap-4038	274	36	mean	mean	ADJ
ap-4038	274	37	value	value	NOUN
ap-4038	274	38	increase	increase	NOUN
ap-4038	274	39	slightly	slightly	ADV
ap-4038	274	40	.	.	PUNCT
ap-4038	275	1	4.2	4.2	NUM
ap-4038	275	2	.	.	PUNCT
ap-4038	276	1	the	the	DET
ap-4038	276	2	martin	martin	PROPN
ap-4038	276	3	and	and	CCONJ
ap-4038	276	4	moyce	moyce	PROPN
ap-4038	276	5	broken	break	VERB
ap-4038	276	6	dam	dam	NOUN
ap-4038	276	7	experiment	experiment	NOUN
ap-4038	276	8	the	the	DET
ap-4038	276	9	final	final	ADJ
ap-4038	276	10	example	example	NOUN
ap-4038	276	11	makes	make	VERB
ap-4038	276	12	use	use	NOUN
ap-4038	276	13	of	of	ADP
ap-4038	276	14	the	the	DET
ap-4038	276	15	famous	famous	ADJ
ap-4038	276	16	martin	martin	NOUN
ap-4038	276	17	and	and	CCONJ
ap-4038	276	18	moyce	moyce	PROPN
ap-4038	276	19	experiment	experiment	NOUN
ap-4038	276	20	with	with	ADP
ap-4038	276	21	the	the	DET
ap-4038	276	22	problem	problem	NOUN
ap-4038	276	23	of	of	ADP
ap-4038	276	24	a	a	DET
ap-4038	276	25	broken	broken	ADJ
ap-4038	276	26	dam	dam	NOUN
ap-4038	276	27	(	(	PUNCT
ap-4038	276	28	also	also	ADV
ap-4038	276	29	known	know	VERB
ap-4038	276	30	as	as	ADP
ap-4038	276	31	the	the	DET
ap-4038	276	32	water	water	NOUN
ap-4038	276	33	column	column	NOUN
ap-4038	276	34	collapse	collapse	NOUN
ap-4038	276	35	problem	problem	NOUN
ap-4038	276	36	)	)	PUNCT
ap-4038	276	37	,	,	PUNCT
ap-4038	276	38	see	see	VERB
ap-4038	276	39	[	[	X
ap-4038	276	40	23	23	NUM
ap-4038	276	41	]	]	PUNCT
ap-4038	276	42	.	.	PUNCT
ap-4038	277	1	the	the	DET
ap-4038	277	2	setup	setup	NOUN
ap-4038	277	3	of	of	ADP
ap-4038	277	4	the	the	DET
ap-4038	277	5	experiment	experiment	NOUN
ap-4038	277	6	is	be	AUX
ap-4038	277	7	illustrated	illustrate	VERB
ap-4038	277	8	in	in	ADP
ap-4038	277	9	figure	figure	NOUN
ap-4038	277	10	9	9	NUM
ap-4038	277	11	in	in	ADP
ap-4038	277	12	the	the	DET
ap-4038	277	13	top	top	ADV
ap-4038	277	14	-	-	PUNCT
ap-4038	277	15	left	left	ADJ
ap-4038	277	16	picture	picture	NOUN
ap-4038	277	17	.	.	PUNCT
ap-4038	278	1	a	a	DET
ap-4038	278	2	rectangular	rectangular	ADJ
ap-4038	278	3	column	column	NOUN
ap-4038	278	4	112	112	NUM
ap-4038	278	5	vol	vol	NOUN
ap-4038	278	6	.	.	PUNCT
ap-4038	278	7	57	57	NUM
ap-4038	278	8	no	no	NOUN
ap-4038	278	9	.	.	PUNCT
ap-4038	279	1	2/2017	2/2017	NUM
ap-4038	279	2	implementation	implementation	NOUN
ap-4038	279	3	of	of	ADP
ap-4038	279	4	a	a	DET
ap-4038	279	5	3d	3d	NUM
ap-4038	279	6	vof	vof	NOUN
ap-4038	279	7	tracking	track	VERB
ap-4038	279	8	algorithm	algorithm	NOUN
ap-4038	279	9	cube	cube	NOUN
ap-4038	279	10	side	side	NOUN
ap-4038	279	11	|e(h)−hex|/hex	|e(h)−hex|/hex	PROPN
ap-4038	279	12	e(h	e(h	PROPN
ap-4038	279	13	)	)	PUNCT
ap-4038	279	14	σ(h	σ(h	PROPN
ap-4038	279	15	)	)	PUNCT
ap-4038	279	16	angle	angle	NOUN
ap-4038	279	17	0	0	NUM
ap-4038	279	18	deg	deg	PROPN
ap-4038	279	19	360	360	NUM
ap-4038	279	20	deg	deg	NOUN
ap-4038	279	21	0	0	PROPN
ap-4038	280	1	deg	deg	PROPN
ap-4038	280	2	360	360	NUM
ap-4038	280	3	deg	deg	NOUN
ap-4038	280	4	0	0	PROPN
ap-4038	281	1	deg	deg	PROPN
ap-4038	282	1	360	360	NUM
ap-4038	282	2	deg	deg	NOUN
ap-4038	282	3	nx	nx	PROPN
ap-4038	282	4	top	top	NOUN
ap-4038	282	5	0.139	0.139	NUM
ap-4038	282	6	0.186	0.186	NUM
ap-4038	282	7	0.431	0.431	NUM
ap-4038	282	8	0.407	0.407	NUM
ap-4038	282	9	0.135	0.135	NUM
ap-4038	282	10	0.171	0.171	NUM
ap-4038	282	11	bottom	bottom	NOUN
ap-4038	282	12	0.135	0.135	NUM
ap-4038	282	13	0.199	0.199	NUM
ap-4038	282	14	0.433	0.433	NUM
ap-4038	282	15	0.400	0.400	NUM
ap-4038	282	16	0.136	0.136	NUM
ap-4038	282	17	0.175	0.175	NUM
ap-4038	282	18	ny	ny	NOUN
ap-4038	282	19	left	leave	VERB
ap-4038	282	20	0.059	0.059	NUM
ap-4038	282	21	0.077	0.077	NUM
ap-4038	282	22	0.471	0.471	NUM
ap-4038	282	23	0.461	0.461	NUM
ap-4038	282	24	0.100	0.100	NUM
ap-4038	282	25	0.158	0.158	NUM
ap-4038	283	1	right	right	ADJ
ap-4038	283	2	0.058	0.058	NUM
ap-4038	283	3	0.061	0.061	NUM
ap-4038	283	4	0.471	0.471	NUM
ap-4038	283	5	0.469	0.469	NUM
ap-4038	283	6	0.101	0.101	NUM
ap-4038	283	7	0.156	0.156	NUM
ap-4038	283	8	nz	nz	PROPN
ap-4038	283	9	front	front	NOUN
ap-4038	283	10	0.054	0.054	NUM
ap-4038	283	11	0.019	0.019	NUM
ap-4038	283	12	0.473	0.473	NUM
ap-4038	283	13	0.491	0.491	NUM
ap-4038	283	14	0.100	0.100	NUM
ap-4038	283	15	0.181	0.181	NUM
ap-4038	283	16	back	back	ADV
ap-4038	283	17	0.059	0.059	NUM
ap-4038	283	18	0.040	0.040	NUM
ap-4038	283	19	0.470	0.470	NUM
ap-4038	283	20	0.480	0.480	NUM
ap-4038	283	21	0.104	0.104	NUM
ap-4038	283	22	0.187	0.187	NUM
ap-4038	283	23	table	table	NOUN
ap-4038	283	24	2	2	NUM
ap-4038	283	25	.	.	PUNCT
ap-4038	283	26	cube	cube	NOUN
ap-4038	283	27	rotation	rotation	NOUN
ap-4038	283	28	—	—	PUNCT
ap-4038	283	29	shape	shape	NOUN
ap-4038	283	30	preservation	preservation	NOUN
ap-4038	283	31	evaluation	evaluation	NOUN
ap-4038	283	32	.	.	PUNCT
ap-4038	284	1	figure	figure	NOUN
ap-4038	284	2	8	8	NUM
ap-4038	284	3	.	.	PUNCT
ap-4038	284	4	cube	cube	NOUN
ap-4038	284	5	rotation	rotation	NOUN
ap-4038	284	6	.	.	PUNCT
ap-4038	285	1	slices	slice	NOUN
ap-4038	285	2	with	with	ADP
ap-4038	285	3	the	the	DET
ap-4038	285	4	normal	normal	ADJ
ap-4038	285	5	in	in	ADP
ap-4038	285	6	the	the	DET
ap-4038	285	7	x	x	PROPN
ap-4038	285	8	,	,	PUNCT
ap-4038	285	9	y	y	PROPN
ap-4038	285	10	,	,	PUNCT
ap-4038	285	11	z	z	NOUN
ap-4038	285	12	-	-	PUNCT
ap-4038	285	13	direction	direction	NOUN
ap-4038	285	14	(	(	PUNCT
ap-4038	285	15	column	column	NOUN
ap-4038	285	16	)	)	PUNCT
ap-4038	285	17	and	and	CCONJ
ap-4038	285	18	rotation	rotation	NOUN
ap-4038	285	19	angles	angle	VERB
ap-4038	285	20	α	α	NOUN
ap-4038	285	21	=	=	SYM
ap-4038	285	22	0	0	NUM
ap-4038	285	23	°	°	NUM
ap-4038	285	24	,	,	PUNCT
ap-4038	285	25	90	90	NUM
ap-4038	285	26	°	°	NOUN
ap-4038	285	27	,	,	PUNCT
ap-4038	285	28	180	180	NUM
ap-4038	285	29	°	°	NOUN
ap-4038	285	30	,	,	PUNCT
ap-4038	285	31	270	270	NUM
ap-4038	285	32	°	°	NOUN
ap-4038	285	33	,	,	PUNCT
ap-4038	285	34	360	360	NUM
ap-4038	285	35	°	°	NUM
ap-4038	285	36	.	.	PUNCT
ap-4038	286	1	(	(	PUNCT
ap-4038	286	2	row	row	NOUN
ap-4038	286	3	)	)	PUNCT
ap-4038	286	4	.	.	PUNCT
ap-4038	287	1	of	of	ADP
ap-4038	287	2	water	water	NOUN
ap-4038	287	3	is	be	AUX
ap-4038	287	4	initially	initially	ADV
ap-4038	287	5	in	in	ADP
ap-4038	287	6	a	a	DET
ap-4038	287	7	state	state	NOUN
ap-4038	287	8	of	of	ADP
ap-4038	287	9	hydrostatic	hydrostatic	ADJ
ap-4038	287	10	equilibrium	equilibrium	NOUN
ap-4038	287	11	.	.	PUNCT
ap-4038	288	1	after	after	ADP
ap-4038	288	2	time	time	NOUN
ap-4038	288	3	t0	t0	PROPN
ap-4038	288	4	,	,	PUNCT
ap-4038	288	5	the	the	DET
ap-4038	288	6	water	water	NOUN
ap-4038	288	7	column	column	NOUN
ap-4038	288	8	starts	start	VERB
ap-4038	288	9	to	to	PART
ap-4038	288	10	collapse	collapse	VERB
ap-4038	288	11	due	due	ADP
ap-4038	288	12	to	to	ADP
ap-4038	288	13	its	its	PRON
ap-4038	288	14	gravity	gravity	NOUN
ap-4038	288	15	by	by	ADP
ap-4038	288	16	forming	form	VERB
ap-4038	288	17	an	an	DET
ap-4038	288	18	advancing	advance	VERB
ap-4038	288	19	water	water	NOUN
ap-4038	288	20	wave	wave	NOUN
ap-4038	288	21	,	,	PUNCT
ap-4038	288	22	as	as	SCONJ
ap-4038	288	23	can	can	AUX
ap-4038	288	24	be	be	AUX
ap-4038	288	25	seen	see	VERB
ap-4038	288	26	in	in	ADP
ap-4038	288	27	the	the	DET
ap-4038	288	28	rest	rest	NOUN
ap-4038	288	29	of	of	ADP
ap-4038	288	30	the	the	DET
ap-4038	288	31	pictures	picture	NOUN
ap-4038	288	32	of	of	ADP
ap-4038	288	33	figure	figure	NOUN
ap-4038	288	34	9	9	NUM
ap-4038	288	35	.	.	PUNCT
ap-4038	289	1	the	the	DET
ap-4038	289	2	initial	initial	ADJ
ap-4038	289	3	configuration	configuration	NOUN
ap-4038	289	4	is	be	AUX
ap-4038	289	5	chosen	choose	VERB
ap-4038	289	6	as	as	ADP
ap-4038	289	7	a	a	DET
ap-4038	289	8	cubic	cubic	ADJ
ap-4038	289	9	water	water	NOUN
ap-4038	289	10	block	block	NOUN
ap-4038	289	11	with	with	ADP
ap-4038	289	12	edge	edge	NOUN
ap-4038	289	13	-	-	PUNCT
ap-4038	289	14	length	length	NOUN
ap-4038	289	15	a	a	DET
ap-4038	289	16	=	=	SYM
ap-4038	289	17	0.05175	0.05175	NUM
ap-4038	289	18	m	m	PROPN
ap-4038	289	19	,	,	PUNCT
ap-4038	289	20	and	and	CCONJ
ap-4038	289	21	the	the	DET
ap-4038	289	22	bounding	bounding	NOUN
ap-4038	289	23	box	box	NOUN
ap-4038	289	24	is	be	AUX
ap-4038	289	25	a	a	DET
ap-4038	289	26	prismatic	prismatic	ADJ
ap-4038	289	27	block	block	NOUN
ap-4038	289	28	with	with	ADP
ap-4038	289	29	dimensions	dimension	NOUN
ap-4038	289	30	of	of	ADP
ap-4038	289	31	0.2286	0.2286	NUM
ap-4038	289	32	×	×	NOUN
ap-4038	289	33	0.05715	0.05715	NUM
ap-4038	289	34	×	×	NOUN
ap-4038	289	35	0.085725	0.085725	NUM
ap-4038	289	36	m.	m.	NOUN
ap-4038	289	37	frictionless	frictionless	NOUN
ap-4038	289	38	boundary	boundary	PROPN
ap-4038	289	39	conditions	condition	NOUN
ap-4038	289	40	are	be	AUX
ap-4038	289	41	assumed	assume	VERB
ap-4038	289	42	on	on	ADP
ap-4038	289	43	the	the	DET
ap-4038	289	44	bottom	bottom	NOUN
ap-4038	289	45	and	and	CCONJ
ap-4038	289	46	on	on	ADP
ap-4038	289	47	the	the	DET
ap-4038	289	48	vertical	vertical	ADJ
ap-4038	289	49	walls	wall	NOUN
ap-4038	289	50	.	.	PUNCT
ap-4038	290	1	the	the	DET
ap-4038	290	2	density	density	NOUN
ap-4038	290	3	and	and	CCONJ
ap-4038	290	4	the	the	DET
ap-4038	290	5	viscosity	viscosity	NOUN
ap-4038	290	6	of	of	ADP
ap-4038	290	7	water	water	NOUN
ap-4038	290	8	are	be	AUX
ap-4038	290	9	taken	take	VERB
ap-4038	290	10	as	as	ADP
ap-4038	290	11	1000	1000	NUM
ap-4038	290	12	kg	kg	NOUN
ap-4038	290	13	/	/	SYM
ap-4038	290	14	m3	m3	PROPN
ap-4038	290	15	and	and	CCONJ
ap-4038	290	16	1	1	NUM
ap-4038	290	17	×	×	NOUN
ap-4038	290	18	10−3	10−3	NUM
ap-4038	290	19	pa	pa	PROPN
ap-4038	290	20	s.	s.	PROPN
ap-4038	290	21	ambient	ambient	PROPN
ap-4038	290	22	air	air	PROPN
ap-4038	290	23	with	with	ADP
ap-4038	290	24	density	density	NOUN
ap-4038	290	25	equal	equal	ADJ
ap-4038	290	26	to	to	ADP
ap-4038	290	27	1	1	NUM
ap-4038	290	28	kg	kg	NOUN
ap-4038	290	29	/	/	SYM
ap-4038	290	30	m3	m3	PROPN
ap-4038	290	31	and	and	CCONJ
ap-4038	290	32	viscosity	viscosity	NOUN
ap-4038	290	33	1	1	NUM
ap-4038	290	34	×	×	NOUN
ap-4038	290	35	10−5	10−5	NUM
ap-4038	290	36	pa	pa	PROPN
ap-4038	290	37	s	s	PROPN
ap-4038	290	38	is	be	AUX
ap-4038	290	39	assumed	assume	VERB
ap-4038	290	40	.	.	PUNCT
ap-4038	291	1	four	four	NUM
ap-4038	291	2	different	different	ADJ
ap-4038	291	3	discretizations	discretization	NOUN
ap-4038	291	4	with	with	ADP
ap-4038	291	5	2454	2454	NUM
ap-4038	291	6	,	,	PUNCT
ap-4038	291	7	12589	12589	NUM
ap-4038	291	8	,	,	PUNCT
ap-4038	291	9	19111	19111	NUM
ap-4038	291	10	and	and	CCONJ
ap-4038	291	11	29604	29604	NUM
ap-4038	291	12	nodes	node	NOUN
ap-4038	291	13	have	have	AUX
ap-4038	291	14	been	be	AUX
ap-4038	291	15	used	use	VERB
ap-4038	291	16	to	to	PART
ap-4038	291	17	verify	verify	VERB
ap-4038	291	18	the	the	DET
ap-4038	291	19	objectivity	objectivity	NOUN
ap-4038	291	20	of	of	ADP
ap-4038	291	21	the	the	DET
ap-4038	291	22	description	description	NOUN
ap-4038	291	23	with	with	ADP
ap-4038	291	24	respect	respect	NOUN
ap-4038	291	25	to	to	ADP
ap-4038	291	26	mesh	mesh	NOUN
ap-4038	291	27	size	size	NOUN
ap-4038	291	28	.	.	PUNCT
ap-4038	292	1	the	the	DET
ap-4038	292	2	position	position	NOUN
ap-4038	292	3	of	of	ADP
ap-4038	292	4	the	the	DET
ap-4038	292	5	water	water	NOUN
ap-4038	292	6	front	front	NOUN
ap-4038	292	7	and	and	CCONJ
ap-4038	292	8	the	the	DET
ap-4038	292	9	residual	residual	ADJ
ap-4038	292	10	water	water	NOUN
ap-4038	292	11	column	column	NOUN
ap-4038	292	12	height	height	NOUN
ap-4038	292	13	with	with	ADP
ap-4038	292	14	respect	respect	NOUN
ap-4038	292	15	to	to	ADP
ap-4038	292	16	time	time	NOUN
ap-4038	292	17	are	be	AUX
ap-4038	292	18	compared	compare	VERB
ap-4038	292	19	with	with	ADP
ap-4038	292	20	the	the	DET
ap-4038	292	21	experimental	experimental	ADJ
ap-4038	292	22	results	result	NOUN
ap-4038	292	23	in	in	ADP
ap-4038	292	24	figure	figure	NOUN
ap-4038	292	25	10	10	NUM
ap-4038	292	26	and	and	CCONJ
ap-4038	292	27	figure	figure	VERB
ap-4038	292	28	11	11	NUM
ap-4038	292	29	,	,	PUNCT
ap-4038	292	30	respectively	respectively	ADV
ap-4038	292	31	.	.	PUNCT
ap-4038	293	1	for	for	ADP
ap-4038	293	2	convenience	convenience	NOUN
ap-4038	293	3	,	,	PUNCT
ap-4038	293	4	the	the	DET
ap-4038	293	5	dimensionless	dimensionless	NOUN
ap-4038	293	6	lengths	length	NOUN
ap-4038	293	7	x∗	x∗	NOUN
ap-4038	293	8	=	=	SYM
ap-4038	294	1	x	x	X
ap-4038	294	2	/	/	SYM
ap-4038	294	3	a	a	PRON
ap-4038	294	4	,	,	PUNCT
ap-4038	294	5	z∗	z∗	NOUN
ap-4038	294	6	=	=	PUNCT
ap-4038	294	7	z	z	NOUN
ap-4038	294	8	/	/	SYM
ap-4038	294	9	a	a	PRON
ap-4038	294	10	and	and	CCONJ
ap-4038	294	11	time	time	NOUN
ap-4038	294	12	t∗	t∗	NOUN
ap-4038	294	13	=	=	SYM
ap-4038	294	14	t	t	NOUN
ap-4038	294	15	√	√	PROPN
ap-4038	294	16	g	g	NOUN
ap-4038	294	17	/	/	SYM
ap-4038	294	18	a	a	PRON
ap-4038	294	19	are	be	AUX
ap-4038	294	20	used	use	VERB
ap-4038	294	21	in	in	ADP
ap-4038	294	22	the	the	DET
ap-4038	294	23	figures	figure	NOUN
ap-4038	294	24	.	.	PUNCT
ap-4038	295	1	it	it	PRON
ap-4038	295	2	can	can	AUX
ap-4038	295	3	be	be	AUX
ap-4038	295	4	seen	see	VERB
ap-4038	295	5	from	from	ADP
ap-4038	295	6	figure	figure	NOUN
ap-4038	295	7	10	10	NUM
ap-4038	295	8	that	that	SCONJ
ap-4038	295	9	numerical	numerical	ADJ
ap-4038	295	10	results	result	NOUN
ap-4038	295	11	converge	converge	VERB
ap-4038	295	12	to	to	ADP
ap-4038	295	13	the	the	DET
ap-4038	295	14	experimental	experimental	ADJ
ap-4038	295	15	results	result	NOUN
ap-4038	295	16	with	with	ADP
ap-4038	295	17	increasing	increase	VERB
ap-4038	295	18	fineness	fineness	NOUN
ap-4038	295	19	of	of	ADP
ap-4038	295	20	the	the	DET
ap-4038	295	21	mesh	mesh	NOUN
ap-4038	295	22	.	.	PUNCT
ap-4038	296	1	in	in	ADP
ap-4038	296	2	case	case	NOUN
ap-4038	296	3	of	of	ADP
ap-4038	296	4	the	the	DET
ap-4038	296	5	residual	residual	ADJ
ap-4038	296	6	height	height	NOUN
ap-4038	296	7	of	of	ADP
ap-4038	296	8	the	the	DET
ap-4038	296	9	column	column	NOUN
ap-4038	296	10	in	in	ADP
ap-4038	296	11	figure	figure	NOUN
ap-4038	296	12	11	11	NUM
ap-4038	296	13	,	,	PUNCT
ap-4038	296	14	the	the	DET
ap-4038	296	15	results	result	NOUN
ap-4038	296	16	are	be	AUX
ap-4038	296	17	less	less	ADV
ap-4038	296	18	sensitive	sensitive	ADJ
ap-4038	296	19	to	to	ADP
ap-4038	296	20	the	the	DET
ap-4038	296	21	mesh	mesh	NOUN
ap-4038	296	22	and	and	CCONJ
ap-4038	296	23	all	all	DET
ap-4038	296	24	the	the	DET
ap-4038	296	25	meshes	mesh	NOUN
ap-4038	296	26	that	that	PRON
ap-4038	296	27	were	be	AUX
ap-4038	296	28	performed	perform	VERB
ap-4038	296	29	seem	seem	VERB
ap-4038	296	30	to	to	PART
ap-4038	296	31	provide	provide	VERB
ap-4038	296	32	reasonably	reasonably	ADV
ap-4038	296	33	accurate	accurate	ADJ
ap-4038	296	34	results	result	NOUN
ap-4038	296	35	.	.	PUNCT
ap-4038	297	1	5	5	X
ap-4038	297	2	.	.	X
ap-4038	297	3	conclusion	conclusion	NOUN
ap-4038	297	4	the	the	DET
ap-4038	297	5	research	research	NOUN
ap-4038	297	6	presented	present	VERB
ap-4038	297	7	here	here	ADV
ap-4038	297	8	has	have	AUX
ap-4038	297	9	dealt	deal	VERB
ap-4038	297	10	with	with	ADP
ap-4038	297	11	numerical	numerical	ADJ
ap-4038	297	12	simulations	simulation	NOUN
ap-4038	297	13	of	of	ADP
ap-4038	297	14	flow	flow	NOUN
ap-4038	297	15	with	with	ADP
ap-4038	297	16	a	a	DET
ap-4038	297	17	free	free	ADJ
ap-4038	297	18	surface	surface	NOUN
ap-4038	297	19	.	.	PUNCT
ap-4038	298	1	the	the	DET
ap-4038	298	2	free	free	ADJ
ap-4038	298	3	surface	surface	NOUN
ap-4038	298	4	is	be	AUX
ap-4038	298	5	handled	handle	VERB
ap-4038	298	6	using	use	VERB
ap-4038	298	7	the	the	DET
ap-4038	298	8	volume	volume	NOUN
ap-4038	298	9	-	-	PUNCT
ap-4038	298	10	of	of	ADP
ap-4038	298	11	-	-	PUNCT
ap-4038	298	12	fluid	fluid	NOUN
ap-4038	298	13	method	method	NOUN
ap-4038	298	14	,	,	PUNCT
ap-4038	298	15	and	and	CCONJ
ap-4038	298	16	the	the	DET
ap-4038	298	17	strategy	strategy	NOUN
ap-4038	298	18	employed	employ	VERB
ap-4038	298	19	for	for	ADP
ap-4038	298	20	advancing	advance	VERB
ap-4038	298	21	the	the	DET
ap-4038	298	22	interface	interface	NOUN
ap-4038	298	23	is	be	AUX
ap-4038	298	24	based	base	VERB
ap-4038	298	25	on	on	ADP
ap-4038	298	26	purely	purely	ADV
ap-4038	298	27	geometric	geometric	ADJ
ap-4038	298	28	algorithms	algorithm	NOUN
ap-4038	298	29	.	.	PUNCT
ap-4038	299	1	in	in	ADP
ap-4038	299	2	particular	particular	ADJ
ap-4038	299	3	,	,	PUNCT
ap-4038	299	4	we	we	PRON
ap-4038	299	5	have	have	AUX
ap-4038	299	6	proposed	propose	VERB
ap-4038	299	7	a	a	DET
ap-4038	299	8	new	new	ADJ
ap-4038	299	9	approach	approach	NOUN
ap-4038	299	10	for	for	ADP
ap-4038	299	11	interface	interface	NOUN
ap-4038	299	12	reconstruction	reconstruction	NOUN
ap-4038	299	13	and	and	CCONJ
ap-4038	299	14	for	for	ADP
ap-4038	299	15	remapping	remappe	VERB
ap-4038	299	16	phases	phase	NOUN
ap-4038	299	17	of	of	ADP
ap-4038	299	18	the	the	DET
ap-4038	299	19	advecting	advect	VERB
ap-4038	299	20	algorithms	algorithm	NOUN
ap-4038	299	21	,	,	PUNCT
ap-4038	299	22	which	which	PRON
ap-4038	299	23	is	be	AUX
ap-4038	299	24	based	base	VERB
ap-4038	299	25	on	on	ADP
ap-4038	299	26	binary	binary	ADJ
ap-4038	299	27	space	space	NOUN
ap-4038	299	28	-	-	PUNCT
ap-4038	299	29	partitioning	partitioning	NOUN
ap-4038	299	30	.	.	PUNCT
ap-4038	300	1	to	to	ADP
ap-4038	300	2	the	the	DET
ap-4038	300	3	best	good	ADJ
ap-4038	300	4	of	of	ADP
ap-4038	300	5	our	our	PRON
ap-4038	300	6	knowledge	knowledge	NOUN
ap-4038	300	7	,	,	PUNCT
ap-4038	300	8	this	this	DET
ap-4038	300	9	approach	approach	NOUN
ap-4038	300	10	has	have	AUX
ap-4038	300	11	not	not	PART
ap-4038	300	12	been	be	AUX
ap-4038	300	13	published	publish	VERB
ap-4038	300	14	before	before	ADV
ap-4038	300	15	.	.	PUNCT
ap-4038	301	1	the	the	DET
ap-4038	301	2	presented	present	VERB
ap-4038	301	3	examples	example	NOUN
ap-4038	301	4	show	show	VERB
ap-4038	301	5	very	very	ADV
ap-4038	301	6	good	good	ADJ
ap-4038	301	7	volumeconserving	volumeconserving	NOUN
ap-4038	301	8	properties	property	NOUN
ap-4038	301	9	.	.	PUNCT
ap-4038	302	1	the	the	DET
ap-4038	302	2	shape	shape	NOUN
ap-4038	302	3	preserving	preserve	VERB
ap-4038	302	4	properties	property	NOUN
ap-4038	302	5	are	be	AUX
ap-4038	302	6	also	also	ADV
ap-4038	302	7	satisfactory	satisfactory	ADJ
ap-4038	302	8	.	.	PUNCT
ap-4038	303	1	we	we	PRON
ap-4038	303	2	believe	believe	VERB
ap-4038	303	3	that	that	SCONJ
ap-4038	303	4	this	this	PRON
ap-4038	303	5	is	be	AUX
ap-4038	303	6	achieved	achieve	VERB
ap-4038	303	7	mainly	mainly	ADV
ap-4038	303	8	due	due	ADP
ap-4038	303	9	to	to	ADP
ap-4038	303	10	the	the	DET
ap-4038	303	11	geometrical	geometrical	ADJ
ap-4038	303	12	nature	nature	NOUN
ap-4038	303	13	of	of	ADP
ap-4038	303	14	the	the	DET
ap-4038	303	15	algorithm	algorithm	NOUN
ap-4038	303	16	,	,	PUNCT
ap-4038	303	17	which	which	PRON
ap-4038	303	18	is	be	AUX
ap-4038	303	19	implemented	implement	VERB
ap-4038	303	20	in	in	ADP
ap-4038	303	21	a	a	DET
ap-4038	303	22	very	very	ADV
ap-4038	303	23	effective	effective	ADJ
ap-4038	303	24	manner	manner	NOUN
ap-4038	303	25	with	with	ADP
ap-4038	303	26	the	the	DET
ap-4038	303	27	help	help	NOUN
ap-4038	303	28	of	of	ADP
ap-4038	303	29	the	the	DET
ap-4038	303	30	idea	idea	NOUN
ap-4038	303	31	of	of	ADP
ap-4038	303	32	binary	binary	ADJ
ap-4038	303	33	spacepartitioning	spacepartitioning	NOUN
ap-4038	303	34	.	.	PUNCT
ap-4038	304	1	although	although	SCONJ
ap-4038	304	2	this	this	DET
ap-4038	304	3	work	work	NOUN
ap-4038	304	4	is	be	AUX
ap-4038	304	5	considered	consider	VERB
ap-4038	304	6	as	as	ADP
ap-4038	304	7	a	a	DET
ap-4038	304	8	proof	proof	NOUN
ap-4038	304	9	of	of	ADP
ap-4038	304	10	concept	concept	NOUN
ap-4038	304	11	,	,	PUNCT
ap-4038	304	12	and	and	CCONJ
ap-4038	304	13	additional	additional	ADJ
ap-4038	304	14	efforts	effort	NOUN
ap-4038	304	15	will	will	AUX
ap-4038	304	16	be	be	AUX
ap-4038	304	17	needed	need	VERB
ap-4038	304	18	in	in	ADP
ap-4038	304	19	order	order	NOUN
ap-4038	304	20	to	to	PART
ap-4038	304	21	develop	develop	VERB
ap-4038	304	22	a	a	DET
ap-4038	304	23	more	more	ADV
ap-4038	304	24	complex	complex	ADJ
ap-4038	304	25	code	code	NOUN
ap-4038	304	26	,	,	PUNCT
ap-4038	304	27	the	the	DET
ap-4038	304	28	results	result	NOUN
ap-4038	304	29	presented	present	VERB
ap-4038	304	30	here	here	ADV
ap-4038	304	31	are	be	AUX
ap-4038	304	32	more	more	ADJ
ap-4038	304	33	than	than	ADP
ap-4038	304	34	promising	promise	VERB
ap-4038	304	35	.	.	PUNCT
ap-4038	305	1	in	in	ADP
ap-4038	305	2	particular	particular	ADJ
ap-4038	305	3	,	,	PUNCT
ap-4038	305	4	more	more	ADV
ap-4038	305	5	accurate	accurate	ADJ
ap-4038	305	6	time	time	NOUN
ap-4038	305	7	integration	integration	NOUN
ap-4038	305	8	in	in	ADP
ap-4038	305	9	the	the	DET
ap-4038	305	10	lagrangian	lagrangian	ADJ
ap-4038	305	11	phase	phase	NOUN
ap-4038	305	12	of	of	ADP
ap-4038	305	13	the	the	DET
ap-4038	305	14	interface	interface	NOUN
ap-4038	305	15	advecting	advect	VERB
ap-4038	305	16	algorithm	algorithm	NOUN
ap-4038	305	17	,	,	PUNCT
ap-4038	305	18	and	and	CCONJ
ap-4038	305	19	an	an	DET
ap-4038	305	20	analysis	analysis	NOUN
ap-4038	305	21	of	of	ADP
ap-4038	305	22	its	its	PRON
ap-4038	305	23	influence	influence	NOUN
ap-4038	305	24	on	on	ADP
ap-4038	305	25	the	the	DET
ap-4038	305	26	volume	volume	NOUN
ap-4038	305	27	conserving	conserve	VERB
ap-4038	305	28	properties	property	NOUN
ap-4038	305	29	,	,	PUNCT
ap-4038	305	30	would	would	AUX
ap-4038	305	31	be	be	AUX
ap-4038	305	32	beneficial	beneficial	ADJ
ap-4038	305	33	.	.	PUNCT
ap-4038	306	1	113	113	NUM
ap-4038	306	2	filip	filip	PROPN
ap-4038	306	3	kolařík	kolařík	NOUN
ap-4038	306	4	,	,	PUNCT
ap-4038	306	5	bořek	bořek	PROPN
ap-4038	306	6	patzák	patzák	VERB
ap-4038	306	7	acta	acta	PROPN
ap-4038	306	8	polytechnica	polytechnica	PROPN
ap-4038	306	9	figure	figure	NOUN
ap-4038	306	10	9	9	NUM
ap-4038	306	11	.	.	PUNCT
ap-4038	307	1	martin	martin	PROPN
ap-4038	307	2	and	and	CCONJ
ap-4038	307	3	moyce	moyce	PROPN
ap-4038	307	4	.	.	PUNCT
ap-4038	308	1	from	from	ADP
ap-4038	308	2	left	left	ADJ
ap-4038	308	3	to	to	ADP
ap-4038	308	4	right	right	NOUN
ap-4038	308	5	and	and	CCONJ
ap-4038	308	6	from	from	ADP
ap-4038	308	7	top	top	NOUN
ap-4038	308	8	to	to	ADP
ap-4038	308	9	bottom	bottom	NOUN
ap-4038	308	10	,	,	PUNCT
ap-4038	308	11	the	the	DET
ap-4038	308	12	times	time	NOUN
ap-4038	308	13	are	be	AUX
ap-4038	308	14	t	t	NOUN
ap-4038	308	15	=	=	SYM
ap-4038	308	16	0	0	NUM
ap-4038	308	17	,	,	PUNCT
ap-4038	308	18	0.025	0.025	NUM
ap-4038	308	19	,	,	PUNCT
ap-4038	308	20	0.05	0.05	NUM
ap-4038	308	21	,	,	PUNCT
ap-4038	308	22	0.075	0.075	NUM
ap-4038	308	23	,	,	PUNCT
ap-4038	308	24	0.1	0.1	NUM
ap-4038	308	25	and	and	CCONJ
ap-4038	308	26	0.125	0.125	NUM
ap-4038	308	27	s.	s.	PROPN
ap-4038	308	28	0.5	0.5	NUM
ap-4038	308	29	1	1	NUM
ap-4038	308	30	1.5	1.5	NUM
ap-4038	308	31	2	2	NUM
ap-4038	308	32	2.5	2.5	NUM
ap-4038	308	33	3	3	NUM
ap-4038	308	34	0	0	NUM
ap-4038	308	35	0.5	0.5	NUM
ap-4038	308	36	1	1	NUM
ap-4038	308	37	1.5	1.5	NUM
ap-4038	308	38	2	2	NUM
ap-4038	308	39	x	x	SYM
ap-4038	308	40	*	*	PUNCT
ap-4038	308	41	[	[	PUNCT
ap-4038	308	42	-	-	SYM
ap-4038	308	43	]	]	X
ap-4038	308	44	t	t	PROPN
ap-4038	308	45	*	*	PUNCT
ap-4038	308	46	[	[	X
ap-4038	308	47	-	-	X
ap-4038	308	48	]	]	X
ap-4038	308	49	29604	29604	NUM
ap-4038	308	50	nodes	node	NOUN
ap-4038	308	51	19111	19111	NUM
ap-4038	308	52	nodes	node	NOUN
ap-4038	308	53	12589	12589	NUM
ap-4038	308	54	nodes	node	NOUN
ap-4038	308	55	2454	2454	NUM
ap-4038	308	56	nodes	node	NOUN
ap-4038	308	57	martin	martin	PROPN
ap-4038	308	58	moyce	moyce	PROPN
ap-4038	308	59	figure	figure	NOUN
ap-4038	308	60	10	10	NUM
ap-4038	308	61	.	.	PUNCT
ap-4038	309	1	martin	martin	PROPN
ap-4038	309	2	and	and	CCONJ
ap-4038	309	3	moyce	moyce	PROPN
ap-4038	309	4	.	.	PUNCT
ap-4038	310	1	dependence	dependence	NOUN
ap-4038	310	2	of	of	ADP
ap-4038	310	3	the	the	DET
ap-4038	310	4	wave	wave	NOUN
ap-4038	310	5	front	front	NOUN
ap-4038	310	6	on	on	ADP
ap-4038	310	7	time	time	NOUN
ap-4038	310	8	for	for	ADP
ap-4038	310	9	different	different	ADJ
ap-4038	310	10	meshes	mesh	NOUN
ap-4038	310	11	and	and	CCONJ
ap-4038	310	12	experimental	experimental	ADJ
ap-4038	310	13	results	result	NOUN
ap-4038	310	14	.	.	PUNCT
ap-4038	311	1	0.4	0.4	NUM
ap-4038	311	2	0.5	0.5	NUM
ap-4038	311	3	0.6	0.6	NUM
ap-4038	311	4	0.7	0.7	NUM
ap-4038	311	5	0.8	0.8	NUM
ap-4038	311	6	0.9	0.9	NUM
ap-4038	311	7	1	1	NUM
ap-4038	311	8	1.1	1.1	NUM
ap-4038	311	9	1.2	1.2	NUM
ap-4038	311	10	0	0	NUM
ap-4038	311	11	0.5	0.5	NUM
ap-4038	311	12	1	1	NUM
ap-4038	311	13	1.5	1.5	NUM
ap-4038	311	14	2	2	NUM
ap-4038	311	15	x	x	SYM
ap-4038	311	16	*	*	PUNCT
ap-4038	311	17	[	[	PUNCT
ap-4038	311	18	-	-	SYM
ap-4038	311	19	]	]	X
ap-4038	311	20	t	t	PROPN
ap-4038	311	21	*	*	PUNCT
ap-4038	311	22	[	[	X
ap-4038	311	23	-	-	X
ap-4038	311	24	]	]	X
ap-4038	311	25	29604	29604	NUM
ap-4038	311	26	nodes	node	NOUN
ap-4038	311	27	19111	19111	NUM
ap-4038	311	28	nodes	node	NOUN
ap-4038	311	29	12589	12589	NUM
ap-4038	311	30	nodes	node	NOUN
ap-4038	311	31	2454	2454	NUM
ap-4038	311	32	nodes	node	NOUN
ap-4038	311	33	martin	martin	PROPN
ap-4038	311	34	moyce	moyce	PROPN
ap-4038	311	35	figure	figure	NOUN
ap-4038	311	36	11	11	NUM
ap-4038	311	37	.	.	PUNCT
ap-4038	312	1	martin	martin	PROPN
ap-4038	312	2	and	and	CCONJ
ap-4038	312	3	moyce	moyce	PROPN
ap-4038	312	4	.	.	PUNCT
ap-4038	313	1	dependence	dependence	NOUN
ap-4038	313	2	of	of	ADP
ap-4038	313	3	the	the	DET
ap-4038	313	4	residual	residual	ADJ
ap-4038	313	5	height	height	NOUN
ap-4038	313	6	of	of	ADP
ap-4038	313	7	the	the	DET
ap-4038	313	8	column	column	NOUN
ap-4038	313	9	on	on	ADP
ap-4038	313	10	time	time	NOUN
ap-4038	313	11	for	for	ADP
ap-4038	313	12	different	different	ADJ
ap-4038	313	13	meshes	mesh	NOUN
ap-4038	313	14	and	and	CCONJ
ap-4038	313	15	experimental	experimental	ADJ
ap-4038	313	16	results	result	NOUN
ap-4038	313	17	.	.	PUNCT
ap-4038	314	1	114	114	NUM
ap-4038	314	2	vol	vol	NOUN
ap-4038	314	3	.	.	PUNCT
ap-4038	314	4	57	57	NUM
ap-4038	314	5	no	no	NOUN
ap-4038	314	6	.	.	PUNCT
ap-4038	315	1	2/2017	2/2017	NUM
ap-4038	315	2	implementation	implementation	NOUN
ap-4038	315	3	of	of	ADP
ap-4038	315	4	a	a	DET
ap-4038	315	5	3d	3d	NUM
ap-4038	315	6	vof	vof	NOUN
ap-4038	315	7	tracking	track	VERB
ap-4038	315	8	algorithm	algorithm	NOUN
ap-4038	315	9	acknowledgements	acknowledgement	NOUN
ap-4038	315	10	the	the	DET
ap-4038	315	11	authors	author	NOUN
ap-4038	315	12	would	would	AUX
ap-4038	315	13	like	like	VERB
ap-4038	315	14	to	to	PART
ap-4038	315	15	acknowledge	acknowledge	VERB
ap-4038	315	16	the	the	DET
ap-4038	315	17	support	support	NOUN
ap-4038	315	18	provided	provide	VERB
ap-4038	315	19	by	by	ADP
ap-4038	315	20	the	the	DET
ap-4038	315	21	czech	czech	PROPN
ap-4038	315	22	science	science	NOUN
ap-4038	315	23	foundation	foundation	PROPN
ap-4038	315	24	under	under	ADP
ap-4038	315	25	project	project	NOUN
ap-4038	315	26	13	13	NUM
ap-4038	315	27	-	-	PUNCT
ap-4038	315	28	23584s	23584s	NUM
ap-4038	315	29	.	.	PUNCT
ap-4038	316	1	references	reference	NOUN
ap-4038	316	2	[	[	X
ap-4038	316	3	1	1	NUM
ap-4038	316	4	]	]	X
ap-4038	316	5	g.	g.	PROPN
ap-4038	316	6	trapaga	trapaga	PROPN
ap-4038	316	7	,	,	PUNCT
ap-4038	316	8	e.	e.	PROPN
ap-4038	316	9	f.	f.	PROPN
ap-4038	316	10	matthys	matthys	PROPN
ap-4038	316	11	,	,	PUNCT
ap-4038	316	12	j.	j.	PROPN
ap-4038	316	13	j.	j.	PROPN
ap-4038	316	14	valencia	valencia	PROPN
ap-4038	316	15	,	,	PUNCT
ap-4038	316	16	j.	j.	PROPN
ap-4038	316	17	szekely	szekely	ADV
ap-4038	316	18	.	.	PUNCT
ap-4038	317	1	fluid	fluid	ADJ
ap-4038	317	2	flow	flow	NOUN
ap-4038	317	3	,	,	PUNCT
ap-4038	317	4	heat	heat	NOUN
ap-4038	317	5	transfer	transfer	NOUN
ap-4038	317	6	,	,	PUNCT
ap-4038	317	7	and	and	CCONJ
ap-4038	317	8	solidification	solidification	NOUN
ap-4038	317	9	of	of	ADP
ap-4038	317	10	molten	molten	ADJ
ap-4038	317	11	metal	metal	NOUN
ap-4038	317	12	droplets	droplet	NOUN
ap-4038	317	13	impinging	impinge	VERB
ap-4038	317	14	on	on	ADP
ap-4038	317	15	substrates	substrate	NOUN
ap-4038	317	16	:	:	PUNCT
ap-4038	317	17	comparison	comparison	NOUN
ap-4038	317	18	of	of	ADP
ap-4038	317	19	numerical	numerical	ADJ
ap-4038	317	20	and	and	CCONJ
ap-4038	317	21	experimental	experimental	ADJ
ap-4038	317	22	results	result	NOUN
ap-4038	317	23	.	.	PUNCT
ap-4038	318	1	metallurgical	metallurgical	ADJ
ap-4038	318	2	and	and	CCONJ
ap-4038	318	3	materials	material	NOUN
ap-4038	318	4	transactions	transaction	NOUN
ap-4038	318	5	b	b	PROPN
ap-4038	318	6	23	23	NUM
ap-4038	318	7	,	,	PUNCT
ap-4038	318	8	1992	1992	NUM
ap-4038	318	9	.	.	PUNCT
ap-4038	319	1	doi:10.1007	doi:10.1007	PROPN
ap-4038	319	2	/	/	SYM
ap-4038	319	3	bf02656450	bf02656450	ADJ
ap-4038	319	4	.	.	PUNCT
ap-4038	320	1	[	[	X
ap-4038	320	2	2	2	X
ap-4038	320	3	]	]	PUNCT
ap-4038	320	4	w.	w.	PROPN
ap-4038	320	5	brouwer	brouwer	PROPN
ap-4038	320	6	,	,	PUNCT
ap-4038	320	7	e.	e.	PROPN
ap-4038	320	8	van	van	PROPN
ap-4038	320	9	herpt	herpt	PROPN
ap-4038	320	10	,	,	PUNCT
ap-4038	320	11	m.	m.	NOUN
ap-4038	320	12	labordus	labordus	NOUN
ap-4038	320	13	.	.	PUNCT
ap-4038	321	1	vacuum	vacuum	NOUN
ap-4038	321	2	injection	injection	NOUN
ap-4038	321	3	moulding	moulding	NOUN
ap-4038	321	4	for	for	ADP
ap-4038	321	5	large	large	ADJ
ap-4038	321	6	structural	structural	ADJ
ap-4038	321	7	applications	application	NOUN
ap-4038	321	8	.	.	PUNCT
ap-4038	322	1	composites	composite	NOUN
ap-4038	322	2	part	part	VERB
ap-4038	322	3	a	a	DET
ap-4038	322	4	:	:	PUNCT
ap-4038	322	5	applied	apply	VERB
ap-4038	322	6	science	science	NOUN
ap-4038	322	7	and	and	CCONJ
ap-4038	322	8	manufacturing	manufacturing	NOUN
ap-4038	322	9	34	34	NUM
ap-4038	322	10	,	,	PUNCT
ap-4038	322	11	2003	2003	NUM
ap-4038	322	12	.	.	PUNCT
ap-4038	323	1	doi:10.1016	doi:10.1016	PROPN
ap-4038	323	2	/	/	SYM
ap-4038	323	3	s1359	s1359	NOUN
ap-4038	323	4	-	-	PUNCT
ap-4038	323	5	835x(03)00060	835x(03)00060	NOUN
ap-4038	323	6	-	-	PUNCT
ap-4038	323	7	5	5	NUM
ap-4038	323	8	.	.	PUNCT
ap-4038	324	1	[	[	X
ap-4038	324	2	3	3	NUM
ap-4038	324	3	]	]	X
ap-4038	324	4	i.	i.	NOUN
ap-4038	324	5	akkerman	akkerman	PROPN
ap-4038	324	6	,	,	PUNCT
ap-4038	324	7	y.	y.	PROPN
ap-4038	324	8	bazilevs	bazilevs	PROPN
ap-4038	324	9	,	,	PUNCT
ap-4038	324	10	d.	d.	PROPN
ap-4038	324	11	j.	j.	PROPN
ap-4038	324	12	benson	benson	PROPN
ap-4038	324	13	,	,	PUNCT
ap-4038	324	14	et	et	PROPN
ap-4038	324	15	al	al	PROPN
ap-4038	324	16	.	.	PUNCT
ap-4038	324	17	free	free	ADJ
ap-4038	324	18	-	-	PUNCT
ap-4038	324	19	surface	surface	NOUN
ap-4038	324	20	flow	flow	NOUN
ap-4038	324	21	and	and	CCONJ
ap-4038	324	22	fluid	fluid	ADJ
ap-4038	324	23	-	-	PUNCT
ap-4038	324	24	object	object	NOUN
ap-4038	324	25	interaction	interaction	NOUN
ap-4038	324	26	modeling	modeling	NOUN
ap-4038	324	27	with	with	ADP
ap-4038	324	28	emphasis	emphasis	NOUN
ap-4038	324	29	on	on	ADP
ap-4038	324	30	ship	ship	NOUN
ap-4038	324	31	hydrodynamics	hydrodynamic	NOUN
ap-4038	324	32	.	.	PUNCT
ap-4038	325	1	journal	journal	PROPN
ap-4038	325	2	of	of	ADP
ap-4038	325	3	applied	apply	VERB
ap-4038	325	4	mechanics	mechanic	NOUN
ap-4038	325	5	79	79	NUM
ap-4038	325	6	,	,	PUNCT
ap-4038	325	7	2012	2012	NUM
ap-4038	325	8	.	.	PUNCT
ap-4038	326	1	doi:10.1115/1.4005072	doi:10.1115/1.4005072	NOUN
ap-4038	326	2	.	.	PUNCT
ap-4038	327	1	[	[	X
ap-4038	327	2	4	4	X
ap-4038	327	3	]	]	PUNCT
ap-4038	327	4	b.	b.	PROPN
ap-4038	327	5	patzák	patzák	PROPN
ap-4038	327	6	,	,	PUNCT
ap-4038	327	7	z.	z.	PROPN
ap-4038	327	8	bittnar	bittnar	PROPN
ap-4038	327	9	.	.	PUNCT
ap-4038	328	1	modeling	modeling	NOUN
ap-4038	328	2	of	of	ADP
ap-4038	328	3	fresh	fresh	ADJ
ap-4038	328	4	concrete	concrete	ADJ
ap-4038	328	5	flow	flow	NOUN
ap-4038	328	6	.	.	PUNCT
ap-4038	329	1	computers	computer	NOUN
ap-4038	329	2	&	&	CCONJ
ap-4038	329	3	structures	structure	NOUN
ap-4038	329	4	87(15–16):962–969	87(15–16):962–969	NUM
ap-4038	329	5	,	,	PUNCT
ap-4038	329	6	2009	2009	NUM
ap-4038	329	7	.	.	PUNCT
ap-4038	330	1	doi:10.1016	doi:10.1016	PROPN
ap-4038	330	2	/	/	SYM
ap-4038	330	3	j.compstruc.2008.04.015	j.compstruc.2008.04.015	PROPN
ap-4038	330	4	.	.	PUNCT
ap-4038	331	1	[	[	X
ap-4038	331	2	5	5	X
ap-4038	331	3	]	]	PUNCT
ap-4038	331	4	w.	w.	PROPN
ap-4038	331	5	j.	j.	PROPN
ap-4038	331	6	rider	rider	PROPN
ap-4038	331	7	,	,	PUNCT
ap-4038	331	8	d.	d.	PROPN
ap-4038	331	9	b.	b.	PROPN
ap-4038	331	10	kothe	kothe	PROPN
ap-4038	331	11	.	.	PUNCT
ap-4038	332	1	reconstructing	reconstruct	VERB
ap-4038	332	2	volume	volume	NOUN
ap-4038	332	3	tracking	tracking	NOUN
ap-4038	332	4	.	.	PUNCT
ap-4038	333	1	journal	journal	PROPN
ap-4038	333	2	of	of	ADP
ap-4038	333	3	computational	computational	ADJ
ap-4038	333	4	physics	physic	NOUN
ap-4038	333	5	141	141	NUM
ap-4038	333	6	,	,	PUNCT
ap-4038	333	7	1998	1998	NUM
ap-4038	333	8	.	.	PUNCT
ap-4038	334	1	doi:10.1006	doi:10.1006	PROPN
ap-4038	334	2	/	/	SYM
ap-4038	334	3	jcph.1998.5906	jcph.1998.5906	PROPN
ap-4038	334	4	.	.	PUNCT
ap-4038	335	1	[	[	X
ap-4038	335	2	6	6	NUM
ap-4038	335	3	]	]	PUNCT
ap-4038	335	4	e.	e.	PROPN
ap-4038	335	5	stein	stein	PROPN
ap-4038	335	6	,	,	PUNCT
ap-4038	335	7	r.	r.	PROPN
ap-4038	335	8	d.	d.	PROPN
ap-4038	335	9	borst	borst	PROPN
ap-4038	335	10	,	,	PUNCT
ap-4038	335	11	t.	t.	PROPN
ap-4038	335	12	j.	j.	PROPN
ap-4038	335	13	hughes	hughes	PROPN
ap-4038	335	14	.	.	PUNCT
ap-4038	336	1	encyclopedia	encyclopedia	NOUN
ap-4038	336	2	of	of	ADP
ap-4038	336	3	computational	computational	ADJ
ap-4038	336	4	mechanics	mechanic	NOUN
ap-4038	336	5	,	,	PUNCT
ap-4038	336	6	vol	vol	NOUN
ap-4038	336	7	.	.	PUNCT
ap-4038	337	1	volume	volume	NOUN
ap-4038	337	2	3	3	NUM
ap-4038	337	3	.	.	PUNCT
ap-4038	338	1	john	john	PROPN
ap-4038	338	2	wiley	wiley	PROPN
ap-4038	338	3	,	,	PUNCT
ap-4038	338	4	1st	1st	ADJ
ap-4038	338	5	edn	edn	PROPN
ap-4038	338	6	.	.	PUNCT
ap-4038	338	7	,	,	PUNCT
ap-4038	338	8	2004	2004	NUM
ap-4038	338	9	.	.	PUNCT
ap-4038	339	1	[	[	X
ap-4038	339	2	7	7	X
ap-4038	339	3	]	]	PUNCT
ap-4038	339	4	s.	s.	PROPN
ap-4038	339	5	osher	osher	PROPN
ap-4038	339	6	,	,	PUNCT
ap-4038	339	7	j.	j.	PROPN
ap-4038	339	8	a.	a.	PROPN
ap-4038	339	9	sethian	sethian	PROPN
ap-4038	339	10	.	.	PUNCT
ap-4038	340	1	fronts	front	NOUN
ap-4038	340	2	propagating	propagate	VERB
ap-4038	340	3	with	with	ADP
ap-4038	340	4	curvature	curvature	NOUN
ap-4038	340	5	-	-	PUNCT
ap-4038	340	6	dependent	dependent	ADJ
ap-4038	340	7	speed	speed	NOUN
ap-4038	340	8	:	:	PUNCT
ap-4038	340	9	algorithms	algorithm	NOUN
ap-4038	340	10	based	base	VERB
ap-4038	340	11	on	on	ADP
ap-4038	340	12	hamilton	hamilton	PROPN
ap-4038	340	13	-	-	PUNCT
ap-4038	340	14	jacobi	jacobi	PROPN
ap-4038	340	15	formulations	formulation	NOUN
ap-4038	340	16	.	.	PUNCT
ap-4038	341	1	journal	journal	PROPN
ap-4038	341	2	of	of	ADP
ap-4038	341	3	computational	computational	ADJ
ap-4038	341	4	physics	physic	NOUN
ap-4038	341	5	79	79	NUM
ap-4038	341	6	,	,	PUNCT
ap-4038	341	7	1988	1988	NUM
ap-4038	341	8	.	.	PUNCT
ap-4038	342	1	doi:10.1016/0021	doi:10.1016/0021	VERB
ap-4038	342	2	-	-	PUNCT
ap-4038	342	3	9991(88)90002	9991(88)90002	NUM
ap-4038	342	4	-	-	PUNCT
ap-4038	342	5	2	2	NUM
ap-4038	342	6	.	.	PUNCT
ap-4038	343	1	[	[	X
ap-4038	343	2	8	8	X
ap-4038	343	3	]	]	PUNCT
ap-4038	343	4	j.	j.	PROPN
ap-4038	343	5	a.	a.	PROPN
ap-4038	343	6	sethian	sethian	PROPN
ap-4038	343	7	.	.	PUNCT
ap-4038	343	8	level	level	NOUN
ap-4038	343	9	set	set	VERB
ap-4038	343	10	methods	method	NOUN
ap-4038	343	11	and	and	CCONJ
ap-4038	343	12	fast	fast	ADJ
ap-4038	343	13	marching	marching	NOUN
ap-4038	343	14	methods	method	NOUN
ap-4038	343	15	:	:	PUNCT
ap-4038	343	16	evolving	evolve	VERB
ap-4038	343	17	interfaces	interface	NOUN
ap-4038	343	18	in	in	ADP
ap-4038	343	19	computational	computational	ADJ
ap-4038	343	20	geometry	geometry	NOUN
ap-4038	343	21	,	,	PUNCT
ap-4038	343	22	fluid	fluid	ADJ
ap-4038	343	23	mechanics	mechanic	NOUN
ap-4038	343	24	,	,	PUNCT
ap-4038	343	25	computer	computer	NOUN
ap-4038	343	26	vision	vision	NOUN
ap-4038	343	27	,	,	PUNCT
ap-4038	343	28	and	and	CCONJ
ap-4038	343	29	materials	material	NOUN
ap-4038	343	30	science	science	NOUN
ap-4038	343	31	.	.	PUNCT
ap-4038	344	1	cambridge	cambridge	PROPN
ap-4038	344	2	monographs	monograph	NOUN
ap-4038	344	3	on	on	ADP
ap-4038	344	4	applied	applied	ADJ
ap-4038	344	5	and	and	CCONJ
ap-4038	344	6	computational	computational	ADJ
ap-4038	344	7	mathematics	mathematic	NOUN
ap-4038	344	8	.	.	PUNCT
ap-4038	345	1	cambridge	cambridge	PROPN
ap-4038	345	2	university	university	PROPN
ap-4038	345	3	press	press	NOUN
ap-4038	345	4	,	,	PUNCT
ap-4038	345	5	2nd	2nd	ADJ
ap-4038	345	6	edn	edn	PROPN
ap-4038	345	7	.	.	PUNCT
ap-4038	345	8	,	,	PUNCT
ap-4038	345	9	1999	1999	NUM
ap-4038	345	10	.	.	PUNCT
ap-4038	346	1	[	[	X
ap-4038	346	2	9	9	NUM
ap-4038	346	3	]	]	PUNCT
ap-4038	346	4	r.	r.	PROPN
ap-4038	346	5	f.	f.	PROPN
ap-4038	346	6	a.	a.	PROPN
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ap-4038	346	8	osher	osher	PROPN
ap-4038	346	9	.	.	PUNCT
ap-4038	347	1	level	level	NOUN
ap-4038	347	2	set	set	VERB
ap-4038	347	3	methods	method	NOUN
ap-4038	347	4	and	and	CCONJ
ap-4038	347	5	dynamic	dynamic	ADJ
ap-4038	347	6	implicit	implicit	ADJ
ap-4038	347	7	surfaces	surface	NOUN
ap-4038	347	8	.	.	PUNCT
ap-4038	348	1	applied	apply	VERB
ap-4038	348	2	mathematical	mathematical	ADJ
ap-4038	348	3	sciences	science	NOUN
ap-4038	348	4	153	153	NUM
ap-4038	348	5	.	.	PUNCT
ap-4038	348	6	springer	springer	NOUN
ap-4038	348	7	-	-	PUNCT
ap-4038	348	8	verlag	verlag	PROPN
ap-4038	348	9	new	new	PROPN
ap-4038	348	10	york	york	PROPN
ap-4038	348	11	,	,	PUNCT
ap-4038	348	12	1st	1st	ADJ
ap-4038	348	13	edn	edn	PROPN
ap-4038	348	14	.	.	PUNCT
ap-4038	348	15	,	,	PUNCT
ap-4038	348	16	2003	2003	NUM
ap-4038	348	17	.	.	PUNCT
ap-4038	349	1	[	[	X
ap-4038	349	2	10	10	NUM
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ap-4038	349	4	c.	c.	PROPN
ap-4038	349	5	hirt	hirt	PROPN
ap-4038	349	6	,	,	PUNCT
ap-4038	349	7	b.	b.	PROPN
ap-4038	349	8	nichols	nichols	PROPN
ap-4038	349	9	.	.	PUNCT
ap-4038	350	1	volume	volume	NOUN
ap-4038	350	2	of	of	ADP
ap-4038	350	3	fluid	fluid	NOUN
ap-4038	350	4	(	(	PUNCT
ap-4038	350	5	vof	vof	NOUN
ap-4038	350	6	)	)	PUNCT
ap-4038	350	7	method	method	NOUN
ap-4038	350	8	for	for	ADP
ap-4038	350	9	the	the	DET
ap-4038	350	10	dynamics	dynamic	NOUN
ap-4038	350	11	of	of	ADP
ap-4038	350	12	free	free	ADJ
ap-4038	350	13	boundaries	boundary	NOUN
ap-4038	350	14	.	.	PUNCT
ap-4038	351	1	journal	journal	NOUN
ap-4038	351	2	of	of	ADP
ap-4038	351	3	computational	computational	ADJ
ap-4038	351	4	physics	physic	NOUN
ap-4038	351	5	39	39	NUM
ap-4038	351	6	,	,	PUNCT
ap-4038	351	7	1981	1981	NUM
ap-4038	351	8	.	.	PUNCT
ap-4038	352	1	doi:10.1016/0021	doi:10.1016/0021	VERB
ap-4038	352	2	-	-	PUNCT
ap-4038	352	3	9991(81)90145	9991(81)90145	NUM
ap-4038	352	4	-	-	PUNCT
ap-4038	352	5	5	5	NUM
ap-4038	352	6	.	.	PUNCT
ap-4038	353	1	[	[	X
ap-4038	353	2	11	11	NUM
ap-4038	353	3	]	]	PUNCT
ap-4038	353	4	m.	m.	NOUN
ap-4038	353	5	sussman	sussman	PROPN
ap-4038	353	6	,	,	PUNCT
ap-4038	353	7	e.	e.	PROPN
ap-4038	353	8	g.	g.	PROPN
ap-4038	353	9	puckett	puckett	PROPN
ap-4038	353	10	.	.	PUNCT
ap-4038	354	1	a	a	DET
ap-4038	354	2	coupled	couple	VERB
ap-4038	354	3	level	level	NOUN
ap-4038	354	4	set	set	VERB
ap-4038	354	5	and	and	CCONJ
ap-4038	354	6	volume	volume	NOUN
ap-4038	354	7	-	-	PUNCT
ap-4038	354	8	of	of	ADP
ap-4038	354	9	-	-	PUNCT
ap-4038	354	10	fluid	fluid	NOUN
ap-4038	354	11	method	method	NOUN
ap-4038	354	12	for	for	ADP
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ap-4038	354	14	3d	3d	NOUN
ap-4038	354	15	and	and	CCONJ
ap-4038	354	16	axisymmetric	axisymmetric	ADJ
ap-4038	354	17	incompressible	incompressible	ADJ
ap-4038	354	18	two	two	NUM
ap-4038	354	19	-	-	PUNCT
ap-4038	354	20	phase	phase	NOUN
ap-4038	354	21	flows	flow	NOUN
ap-4038	354	22	.	.	PUNCT
ap-4038	355	1	journal	journal	NOUN
ap-4038	355	2	of	of	ADP
ap-4038	355	3	computational	computational	ADJ
ap-4038	355	4	physics	physic	NOUN
ap-4038	355	5	162	162	NUM
ap-4038	355	6	,	,	PUNCT
ap-4038	355	7	2000	2000	NUM
ap-4038	355	8	.	.	PUNCT
ap-4038	356	1	doi:10.1006	doi:10.1006	PROPN
ap-4038	356	2	/	/	SYM
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ap-4038	356	4	.	.	PUNCT
ap-4038	357	1	[	[	X
ap-4038	357	2	12	12	NUM
ap-4038	357	3	]	]	PUNCT
ap-4038	357	4	t.	t.	PROPN
ap-4038	357	5	e.	e.	PROPN
ap-4038	357	6	tezduyar	tezduyar	PROPN
ap-4038	357	7	.	.	PUNCT
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ap-4038	358	3	element	element	NOUN
ap-4038	358	4	formulations	formulation	NOUN
ap-4038	358	5	for	for	ADP
ap-4038	358	6	incompressible	incompressible	ADJ
ap-4038	358	7	flow	flow	NOUN
ap-4038	358	8	computations	computation	NOUN
ap-4038	358	9	.	.	PUNCT
ap-4038	359	1	advances	advance	NOUN
ap-4038	359	2	in	in	ADP
ap-4038	359	3	applied	apply	VERB
ap-4038	359	4	mechanics	mechanic	NOUN
ap-4038	359	5	28:1–44	28:1–44	NUM
ap-4038	359	6	,	,	PUNCT
ap-4038	359	7	1991	1991	NUM
ap-4038	359	8	.	.	PUNCT
ap-4038	360	1	[	[	X
ap-4038	360	2	13	13	NUM
ap-4038	360	3	]	]	PUNCT
ap-4038	360	4	t.	t.	PROPN
ap-4038	360	5	e.	e.	PROPN
ap-4038	360	6	tezduyar	tezduyar	PROPN
ap-4038	360	7	,	,	PUNCT
ap-4038	360	8	y.	y.	PROPN
ap-4038	360	9	osawa	osawa	PROPN
ap-4038	360	10	.	.	PUNCT
ap-4038	361	1	finite	finite	PROPN
ap-4038	361	2	element	element	PROPN
ap-4038	361	3	stabilization	stabilization	NOUN
ap-4038	361	4	parameters	parameter	NOUN
ap-4038	361	5	computed	compute	VERB
ap-4038	361	6	from	from	ADP
ap-4038	361	7	element	element	ADJ
ap-4038	361	8	matrices	matrix	NOUN
ap-4038	361	9	and	and	CCONJ
ap-4038	361	10	vectors	vector	NOUN
ap-4038	361	11	.	.	PUNCT
ap-4038	362	1	computer	computer	NOUN
ap-4038	362	2	methods	method	NOUN
ap-4038	362	3	in	in	ADP
ap-4038	362	4	applied	applied	ADJ
ap-4038	362	5	mechanics	mechanic	NOUN
ap-4038	362	6	and	and	CCONJ
ap-4038	362	7	engineering	engineering	NOUN
ap-4038	362	8	190:411–430	190:411–430	NUM
ap-4038	362	9	,	,	PUNCT
ap-4038	362	10	2000	2000	NUM
ap-4038	362	11	.	.	PUNCT
ap-4038	363	1	[	[	X
ap-4038	363	2	14	14	NUM
ap-4038	363	3	]	]	PUNCT
ap-4038	363	4	j.	j.	PROPN
ap-4038	363	5	e.	e.	PROPN
ap-4038	363	6	pilliod	pilliod	PROPN
ap-4038	363	7	,	,	PUNCT
ap-4038	363	8	e.	e.	PROPN
ap-4038	363	9	g.	g.	PROPN
ap-4038	363	10	puckett	puckett	PROPN
ap-4038	363	11	.	.	PUNCT
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ap-4038	364	2	-	-	PUNCT
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ap-4038	364	4	accurate	accurate	ADJ
ap-4038	364	5	volume	volume	NOUN
ap-4038	364	6	-	-	PUNCT
ap-4038	364	7	of	of	ADP
ap-4038	364	8	-	-	PUNCT
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ap-4038	364	10	algorithms	algorithm	NOUN
ap-4038	364	11	for	for	ADP
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ap-4038	364	13	material	material	NOUN
ap-4038	364	14	interfaces	interface	NOUN
ap-4038	364	15	.	.	PUNCT
ap-4038	365	1	journal	journal	NOUN
ap-4038	365	2	of	of	ADP
ap-4038	365	3	computational	computational	ADJ
ap-4038	365	4	physics	physic	NOUN
ap-4038	365	5	199	199	NUM
ap-4038	365	6	,	,	PUNCT
ap-4038	365	7	2004	2004	NUM
ap-4038	365	8	.	.	PUNCT
ap-4038	366	1	doi:10.1016	doi:10.1016	PROPN
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ap-4038	366	4	.	.	PUNCT
ap-4038	367	1	[	[	X
ap-4038	367	2	15	15	NUM
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ap-4038	367	5	shahbazi	shahbazi	PROPN
ap-4038	367	6	,	,	PUNCT
ap-4038	367	7	m.	m.	NOUN
ap-4038	367	8	paraschivoiu	paraschivoiu	PROPN
ap-4038	367	9	,	,	PUNCT
ap-4038	367	10	j.	j.	PROPN
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ap-4038	367	12	.	.	PUNCT
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ap-4038	368	2	order	order	NOUN
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ap-4038	368	4	volume	volume	NOUN
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ap-4038	368	7	on	on	ADP
ap-4038	368	8	remapping	remappe	VERB
ap-4038	368	9	for	for	ADP
ap-4038	368	10	triangular	triangular	NOUN
ap-4038	368	11	meshes	mesh	NOUN
ap-4038	368	12	.	.	PUNCT
ap-4038	369	1	journal	journal	PROPN
ap-4038	369	2	of	of	ADP
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ap-4038	369	6	,	,	PUNCT
ap-4038	369	7	2003	2003	NUM
ap-4038	369	8	.	.	PUNCT
ap-4038	370	1	[	[	X
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ap-4038	370	3	]	]	PUNCT
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ap-4038	370	5	k.	k.	PROPN
ap-4038	370	6	dukowicz	dukowicz	PROPN
ap-4038	370	7	,	,	PUNCT
ap-4038	370	8	j.	j.	PROPN
ap-4038	370	9	r.	r.	PROPN
ap-4038	370	10	baumgardner	baumgardner	PROPN
ap-4038	370	11	.	.	PUNCT
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ap-4038	371	2	remapping	remapping	NOUN
ap-4038	371	3	as	as	ADP
ap-4038	371	4	a	a	DET
ap-4038	371	5	transport	transport	NOUN
ap-4038	371	6	/	/	SYM
ap-4038	371	7	advection	advection	NOUN
ap-4038	371	8	algorithm	algorithm	NOUN
ap-4038	371	9	.	.	PUNCT
ap-4038	372	1	journal	journal	NOUN
ap-4038	372	2	of	of	ADP
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ap-4038	372	5	160	160	NUM
ap-4038	372	6	,	,	PUNCT
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ap-4038	372	8	.	.	PUNCT
ap-4038	373	1	doi:10.1006	doi:10.1006	PROPN
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ap-4038	373	4	.	.	PUNCT
ap-4038	374	1	[	[	X
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ap-4038	375	2	visible	visible	ADJ
ap-4038	375	3	surface	surface	NOUN
ap-4038	375	4	generation	generation	NOUN
ap-4038	375	5	by	by	ADP
ap-4038	375	6	a	a	DET
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ap-4038	375	8	tree	tree	NOUN
ap-4038	375	9	structures	structure	NOUN
ap-4038	375	10	.	.	PUNCT
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ap-4038	376	5	14	14	NUM
ap-4038	376	6	,	,	PUNCT
ap-4038	376	7	1980	1980	NUM
ap-4038	376	8	.	.	PUNCT
ap-4038	377	1	doi:10.1145/965105.807481	doi:10.1145/965105.807481	ADV
ap-4038	377	2	.	.	PUNCT
ap-4038	378	1	[	[	X
ap-4038	378	2	18	18	NUM
ap-4038	378	3	]	]	PUNCT
ap-4038	378	4	p.	p.	NOUN
ap-4038	378	5	schneider	schneider	PROPN
ap-4038	378	6	,	,	PUNCT
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ap-4038	378	8	h.	h.	PROPN
ap-4038	378	9	eberly	eberly	PROPN
ap-4038	378	10	.	.	PUNCT
ap-4038	379	1	geometric	geometric	ADJ
ap-4038	379	2	tools	tool	NOUN
ap-4038	379	3	for	for	ADP
ap-4038	379	4	computer	computer	NOUN
ap-4038	379	5	graphics	graphic	NOUN
ap-4038	379	6	.	.	PUNCT
ap-4038	380	1	the	the	DET
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ap-4038	380	6	computer	computer	NOUN
ap-4038	380	7	graphics	graphic	NOUN
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ap-4038	380	9	geometric	geometric	ADJ
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ap-4038	381	8	2003	2003	NUM
ap-4038	381	9	.	.	PUNCT
ap-4038	382	1	[	[	X
ap-4038	382	2	19	19	NUM
ap-4038	382	3	]	]	PUNCT
ap-4038	382	4	h.	h.	PROPN
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ap-4038	382	9	fries	fry	NOUN
ap-4038	382	10	.	.	PUNCT
ap-4038	383	1	the	the	DET
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ap-4038	383	3	finite	finite	ADJ
ap-4038	383	4	element	element	NOUN
ap-4038	383	5	method	method	NOUN
ap-4038	383	6	for	for	ADP
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ap-4038	383	8	-	-	PUNCT
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ap-4038	383	12	-	-	PUNCT
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ap-4038	383	14	flows	flow	NOUN
ap-4038	383	15	:	:	PUNCT
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ap-4038	383	19	.	.	PUNCT
ap-4038	384	1	journal	journal	NOUN
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ap-4038	384	5	230:3369–3390	230:3369–3390	NUM
ap-4038	384	6	,	,	PUNCT
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ap-4038	384	8	.	.	PUNCT
ap-4038	385	1	[	[	X
ap-4038	385	2	20	20	NUM
ap-4038	385	3	]	]	PUNCT
ap-4038	385	4	i.	i.	NOUN
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ap-4038	385	6	.	.	PUNCT
ap-4038	386	1	the	the	DET
ap-4038	386	2	finite	finite	PROPN
ap-4038	386	3	element	element	NOUN
ap-4038	386	4	method	method	NOUN
ap-4038	386	5	with	with	ADP
ap-4038	386	6	lagrangian	lagrangian	ADJ
ap-4038	386	7	multipliers	multiplier	NOUN
ap-4038	386	8	.	.	PUNCT
ap-4038	387	1	nummath	nummath	PROPN
ap-4038	387	2	20:179–192	20:179–192	PROPN
ap-4038	387	3	,	,	PUNCT
ap-4038	387	4	1973	1973	NUM
ap-4038	387	5	.	.	PUNCT
ap-4038	388	1	[	[	X
ap-4038	388	2	21	21	NUM
ap-4038	388	3	]	]	X
ap-4038	388	4	b.	b.	PROPN
ap-4038	388	5	patzák	patzák	PROPN
ap-4038	388	6	.	.	PUNCT
ap-4038	389	1	oofem	oofem	PROPN
ap-4038	389	2	home	home	PROPN
ap-4038	389	3	page	page	NOUN
ap-4038	389	4	,	,	PUNCT
ap-4038	389	5	2000	2000	NUM
ap-4038	389	6	.	.	PUNCT
ap-4038	390	1	http://www.oofem.org	http://www.oofem.org	PROPN
ap-4038	390	2	.	.	PUNCT
ap-4038	391	1	[	[	X
ap-4038	391	2	22	22	NUM
ap-4038	391	3	]	]	X
ap-4038	391	4	b.	b.	PROPN
ap-4038	391	5	patzák	patzák	PROPN
ap-4038	391	6	,	,	PUNCT
ap-4038	391	7	z.	z.	PROPN
ap-4038	391	8	bittnar	bittnar	PROPN
ap-4038	391	9	.	.	PUNCT
ap-4038	392	1	design	design	NOUN
ap-4038	392	2	of	of	ADP
ap-4038	392	3	object	object	NOUN
ap-4038	392	4	oriented	orient	VERB
ap-4038	392	5	finite	finite	PROPN
ap-4038	392	6	element	element	PROPN
ap-4038	392	7	code	code	PROPN
ap-4038	392	8	.	.	PUNCT
ap-4038	393	1	advances	advance	NOUN
ap-4038	393	2	in	in	ADP
ap-4038	393	3	engineering	engineering	NOUN
ap-4038	393	4	software	software	NOUN
ap-4038	393	5	32:759–767	32:759–767	NOUN
ap-4038	393	6	,	,	PUNCT
ap-4038	393	7	2001	2001	NUM
ap-4038	393	8	.	.	PUNCT
ap-4038	394	1	[	[	X
ap-4038	394	2	23	23	NUM
ap-4038	394	3	]	]	PUNCT
ap-4038	394	4	j.	j.	PROPN
ap-4038	394	5	c.	c.	PROPN
ap-4038	394	6	martin	martin	PROPN
ap-4038	394	7	,	,	PUNCT
ap-4038	394	8	w.	w.	PROPN
ap-4038	394	9	j.	j.	PROPN
ap-4038	394	10	moyce	moyce	PROPN
ap-4038	394	11	.	.	PUNCT
ap-4038	395	1	part	part	NOUN
ap-4038	395	2	iv	iv	X
ap-4038	395	3	.	.	PUNCT
ap-4038	396	1	an	an	DET
ap-4038	396	2	experimental	experimental	ADJ
ap-4038	396	3	study	study	NOUN
ap-4038	396	4	of	of	ADP
ap-4038	396	5	the	the	DET
ap-4038	396	6	collapse	collapse	NOUN
ap-4038	396	7	of	of	ADP
ap-4038	396	8	liquid	liquid	ADJ
ap-4038	396	9	columns	column	NOUN
ap-4038	396	10	on	on	ADP
ap-4038	396	11	a	a	DET
ap-4038	396	12	rigid	rigid	ADJ
ap-4038	396	13	horizontal	horizontal	ADJ
ap-4038	396	14	plane	plane	NOUN
ap-4038	396	15	.	.	PUNCT
ap-4038	397	1	philosophical	philosophical	ADJ
ap-4038	397	2	transactions	transaction	NOUN
ap-4038	397	3	mathematical	mathematical	ADJ
ap-4038	397	4	physical	physical	ADJ
ap-4038	397	5	and	and	CCONJ
ap-4038	397	6	engineering	engineering	NOUN
ap-4038	397	7	sciences	science	NOUN
ap-4038	397	8	244	244	NUM
ap-4038	397	9	,	,	PUNCT
ap-4038	397	10	1952	1952	NUM
ap-4038	397	11	.	.	PUNCT
ap-4038	398	1	doi:10.1098	doi:10.1098	PROPN
ap-4038	398	2	/	/	SYM
ap-4038	398	3	rsta.1952.0006	rsta.1952.0006	ADJ
ap-4038	398	4	.	.	NOUN
ap-4038	399	1	115	115	NUM
ap-4038	399	2	http://dx.doi.org/10.1007/bf02656450	http://dx.doi.org/10.1007/bf02656450	NUM
ap-4038	399	3	http://dx.doi.org/10.1016/s1359-835x(03)00060-5	http://dx.doi.org/10.1016/s1359-835x(03)00060-5	NOUN
ap-4038	399	4	http://dx.doi.org/10.1115/1.4005072	http://dx.doi.org/10.1115/1.4005072	NOUN
ap-4038	399	5	http://dx.doi.org/10.1016/j.compstruc.2008.04.015	http://dx.doi.org/10.1016/j.compstruc.2008.04.015	PROPN
ap-4038	399	6	http://dx.doi.org/10.1006/jcph.1998.5906	http://dx.doi.org/10.1006/jcph.1998.5906	X
ap-4038	399	7	http://dx.doi.org/10.1016/0021-9991(88)90002-2	http://dx.doi.org/10.1016/0021-9991(88)90002-2	X
ap-4038	399	8	http://dx.doi.org/10.1016/0021-9991(81)90145-5	http://dx.doi.org/10.1016/0021-9991(81)90145-5	PROPN
ap-4038	400	1	http://dx.doi.org/10.1006/jcph.2000.6537	http://dx.doi.org/10.1006/jcph.2000.6537	PROPN
ap-4038	400	2	http://dx.doi.org/10.1016/j.jcp.2003.12.023	http://dx.doi.org/10.1016/j.jcp.2003.12.023	PROPN
ap-4038	400	3	http://dx.doi.org/10.1006/jcph.2000.6465	http://dx.doi.org/10.1006/jcph.2000.6465	PROPN
ap-4038	400	4	http://dx.doi.org/10.1145/965105.807481	http://dx.doi.org/10.1145/965105.807481	PROPN
ap-4038	400	5	http://dx.doi.org/10.1098/rsta.1952.0006	http://dx.doi.org/10.1098/rsta.1952.0006	PROPN
ap-4038	400	6	acta	acta	PROPN
ap-4038	400	7	polytechnica	polytechnica	PROPN
ap-4038	400	8	57(2):105–115	57(2):105–115	PROPN
ap-4038	400	9	,	,	PUNCT
ap-4038	400	10	2017	2017	NUM
ap-4038	400	11	1	1	NUM
ap-4038	400	12	introduction	introduction	NOUN
ap-4038	400	13	2	2	NUM
ap-4038	400	14	a	a	DET
ap-4038	400	15	description	description	NOUN
ap-4038	400	16	of	of	ADP
ap-4038	400	17	the	the	DET
ap-4038	400	18	fluid	fluid	ADJ
ap-4038	400	19	3	3	NUM
ap-4038	400	20	evolution	evolution	NOUN
ap-4038	400	21	of	of	ADP
ap-4038	400	22	the	the	DET
ap-4038	400	23	interface	interface	NOUN
ap-4038	400	24	3.1	3.1	NUM
ap-4038	400	25	interface	interface	NOUN
ap-4038	400	26	reconstruction	reconstruction	NOUN
ap-4038	400	27	3.2	3.2	NUM
ap-4038	400	28	a	a	DET
ap-4038	400	29	bsp	bsp	NOUN
ap-4038	400	30	tree	tree	NOUN
ap-4038	400	31	based	base	VERB
ap-4038	400	32	approach	approach	NOUN
ap-4038	400	33	to	to	ADP
ap-4038	400	34	remapping	remappe	VERB
ap-4038	400	35	the	the	DET
ap-4038	400	36	tetrahedral	tetrahedral	ADJ
ap-4038	400	37	mesh	mesh	NOUN
ap-4038	400	38	3.2.1	3.2.1	NUM
ap-4038	400	39	intersection	intersection	NOUN
ap-4038	400	40	of	of	ADP
ap-4038	400	41	polyhedra	polyhedra	PROPN
ap-4038	400	42	4	4	NUM
ap-4038	400	43	numerical	numerical	ADJ
ap-4038	400	44	examples	example	NOUN
ap-4038	400	45	4.1	4.1	NUM
ap-4038	400	46	cube	cube	NOUN
ap-4038	400	47	propagation	propagation	NOUN
ap-4038	400	48	through	through	ADP
ap-4038	400	49	the	the	DET
ap-4038	400	50	unstructured	unstructured	ADJ
ap-4038	400	51	mesh	mesh	NOUN
ap-4038	400	52	4.1.1	4.1.1	NUM
ap-4038	400	53	cube	cube	NOUN
ap-4038	400	54	translation	translation	NOUN
ap-4038	400	55	4.1.2	4.1.2	NUM
ap-4038	400	56	cube	cube	PROPN
ap-4038	400	57	rotation	rotation	NOUN
ap-4038	400	58	4.2	4.2	NUM
ap-4038	400	59	the	the	DET
ap-4038	400	60	martin	martin	PROPN
ap-4038	400	61	and	and	CCONJ
ap-4038	400	62	moyce	moyce	PROPN
ap-4038	400	63	broken	broken	ADJ
ap-4038	400	64	dam	dam	NOUN
ap-4038	400	65	experiment	experiment	NOUN
ap-4038	400	66	5	5	NUM
ap-4038	400	67	conclusion	conclusion	NOUN
ap-4038	400	68	acknowledgements	acknowledgement	NOUN
ap-4038	400	69	references	reference	NOUN