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Statements

Subject Item
n2:RIV%2F49777513%3A23520%2F13%3A43915848%21RIV14-MSM-23520___
rdf:type
n11:Vysledek skos:Concept
dcterms:description
A canal surface is the envelope of a 1-parameter set of spheres centered at the spine curve m(t) and with the radii described by the function r(t). Any canal surface given by rational m(t) and r(t) possesses a rational parameterization. However, an arbitrary rational canal surface does not have to fulfill the PN (Pythagorean normals) condition. Most (exact or approximate) parameterization methods are based on a construction of a rational unit normal vector field guaranteeing rational offsets. In this paper, we will study a condition which guarantees that a given canal surface has rational contour curves, which are later used for a straightforward computation of rational parameterizations of canal surfaces providing rational offsets. Using the contour curves in the parameterization algorithm brings another extra feature; the parameter lines do not unnecessarily wind around the canal surface. Our approach follows a construction of rational spatial MPH curves from the associated planar PH curves introduced in Kosinka and Lávička (2010) [28] and gives it to the relation with the contour curves of canal surfaces given by their medial axis transforms. We also present simple methods for computing approximate PN parameterizations of given canal surfaces and rational offset blends between two canal surfaces. A canal surface is the envelope of a 1-parameter set of spheres centered at the spine curve m(t) and with the radii described by the function r(t). Any canal surface given by rational m(t) and r(t) possesses a rational parameterization. However, an arbitrary rational canal surface does not have to fulfill the PN (Pythagorean normals) condition. Most (exact or approximate) parameterization methods are based on a construction of a rational unit normal vector field guaranteeing rational offsets. In this paper, we will study a condition which guarantees that a given canal surface has rational contour curves, which are later used for a straightforward computation of rational parameterizations of canal surfaces providing rational offsets. Using the contour curves in the parameterization algorithm brings another extra feature; the parameter lines do not unnecessarily wind around the canal surface. Our approach follows a construction of rational spatial MPH curves from the associated planar PH curves introduced in Kosinka and Lávička (2010) [28] and gives it to the relation with the contour curves of canal surfaces given by their medial axis transforms. We also present simple methods for computing approximate PN parameterizations of given canal surfaces and rational offset blends between two canal surfaces.
dcterms:title
Parameterizing rational offset canal surfaces via rational contour curves Parameterizing rational offset canal surfaces via rational contour curves
skos:prefLabel
Parameterizing rational offset canal surfaces via rational contour curves Parameterizing rational offset canal surfaces via rational contour curves
skos:notation
RIV/49777513:23520/13:43915848!RIV14-MSM-23520___
n11:predkladatel
n19:orjk%3A23520
n4:aktivita
n13:S n13:P
n4:aktivity
P(ED1.1.00/02.0090), S
n4:cisloPeriodika
2
n4:dodaniDat
n10:2014
n4:domaciTvurceVysledku
n5:1043161 n5:8941548
n4:druhVysledku
n15:J
n4:duvernostUdaju
n16:S
n4:entitaPredkladatele
n8:predkladatel
n4:idSjednocenehoVysledku
95324
n4:idVysledku
RIV/49777513:23520/13:43915848
n4:jazykVysledku
n9:eng
n4:klicovaSlova
Blends; Approximate parameterization; PN surfaces; PH and MPH curves; Contour curves; Rational offsets; Rational parameterizations; Canal surfaces
n4:klicoveSlovo
n6:Contour%20curves n6:Rational%20offsets n6:Approximate%20parameterization n6:PN%20surfaces n6:PH%20and%20MPH%20curves n6:Blends n6:Rational%20parameterizations n6:Canal%20surfaces
n4:kodStatuVydavatele
NL - Nizozemsko
n4:kontrolniKodProRIV
[1E832C04FC7A]
n4:nazevZdroje
COMPUTER-AIDED DESIGN
n4:obor
n20:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
2
n4:projekt
n17:ED1.1.00%2F02.0090
n4:rokUplatneniVysledku
n10:2013
n4:svazekPeriodika
45
n4:tvurceVysledku
Lávička, Miroslav Bizzarri, Michal
s:issn
0010-4485
s:numberOfPages
9
n18:doi
10.1016/j.cad.2012.10.017
n12:organizacniJednotka
23520