About: A symbolic-numerical method for computing approximate parameterizations of canal surfaces

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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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 one-parameter family of spheres centered at the spine curve m(t) and with the radii described by the function r(t). It was proved in Peternell and Pottmann (1997) that any canal surface to a rational spine curve and a rational radius function possesses a rational parameterization. Then a symbolic method forgenerating rational parameterizations of canal surfaces was developed in Landsmann et al. (2001) [21]. Indeed, this method leads to the problem of decomposing a polynomial into a sum of two squares over reals, which is solved numerically in general. Hence, approximate techniques generating a parameterization within a certain region of interest are also worth studying. In this paper, we present a method for the computation of approximate rational parameterizations of canal surfaces. A main feature of our approach is a combination of symbolic and numerical techniques yielding approximate topology-based parameterizations of contour curves which are then applied to compute an approximate parameterization of the given canal surface. The algorithm is mainly suitable for implicit blend surfaces of the canal-surface-type. A canal surface is the envelope of a one-parameter family of spheres centered at the spine curve m(t) and with the radii described by the function r(t). It was proved in Peternell and Pottmann (1997) that any canal surface to a rational spine curve and a rational radius function possesses a rational parameterization. Then a symbolic method forgenerating rational parameterizations of canal surfaces was developed in Landsmann et al. (2001) [21]. Indeed, this method leads to the problem of decomposing a polynomial into a sum of two squares over reals, which is solved numerically in general. Hence, approximate techniques generating a parameterization within a certain region of interest are also worth studying. In this paper, we present a method for the computation of approximate rational parameterizations of canal surfaces. A main feature of our approach is a combination of symbolic and numerical techniques yielding approximate topology-based parameterizations of contour curves which are then applied to compute an approximate parameterization of the given canal surface. The algorithm is mainly suitable for implicit blend surfaces of the canal-surface-type. (en)
Title	A symbolic-numerical method for computing approximate parameterizations of canal surfaces A symbolic-numerical method for computing approximate parameterizations of canal surfaces (en)
skos:prefLabel	A symbolic-numerical method for computing approximate parameterizations of canal surfaces A symbolic-numerical method for computing approximate parameterizations of canal surfaces (en)
skos:notation	RIV/49777513:23520/12:43915055!RIV13-MSM-23520___
http://linked.open...avai/riv/aktivita	P S Z
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0090), S, Z(MSM4977751301)
http://linked.open...iv/cisloPeriodika	9
http://linked.open...vai/riv/dodaniDat	2013
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	120677
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/12:43915055
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Implicit blends; Critical points; Approximate parameterization; Rational parameterization; Canal surface (en)
http://linked.open.../riv/klicoveSlovo	Approximate parameterization Critical points Implicit blends Rational parameterization Canal surface
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[BB5FFCA4B3B9]
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	2012
http://linked.open...v/svazekPeriodika	44
http://linked.open...iv/tvurceVysledku	Bizzarri, Michal Lávička, Miroslav
http://linked.open...n/vavai/riv/zamer	Spojité a diskrétní matematické struktury a vývoj odpovídajících metod jejich zkoumání
issn	0010-4485
number of pages	12 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.cad.2012.04.001
http://localhost/t...ganizacniJednotka	23520

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