About: Parameterizing rational offset canal surfaces via rational contour curves

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	Parameterizing rational offset canal surfaces via rational contour curves Parameterizing rational offset canal surfaces via rational contour curves (en)
skos:prefLabel	Parameterizing rational offset canal surfaces via rational contour curves Parameterizing rational offset canal surfaces via rational contour curves (en)
skos:notation	RIV/49777513:23520/13:43915848!RIV14-MSM-23520___
http://linked.open...avai/riv/aktivita	P S
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0090), S
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Lávička, Miroslav Bizzarri, Michal
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	95324
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/13:43915848
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Blends; Approximate parameterization; PN surfaces; PH and MPH curves; Contour curves; Rational offsets; Rational parameterizations; Canal surfaces (en)
http://linked.open.../riv/klicoveSlovo	Blends Contour curves PH and MPH curves Rational parameterizations PN surfaces Approximate parameterization Rational offsets Canal surfaces
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[1E832C04FC7A]
http://linked.open...i/riv/nazevZdroje	COMPUTER-AIDED DESIGN
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	NTIS - New Technologies for Information Society
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	45
http://linked.open...iv/tvurceVysledku	Bizzarri, Michal Lávička, Miroslav
issn	0010-4485
number of pages	9 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.cad.2012.10.017
http://localhost/t...ganizacniJednotka	23520

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