A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches

Popis výsledku v původním jazyce

In this paper, we describe an algorithm for generating an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in R^{3,1}, which is considered as a medial surface transform (MST) of a spatial domain. Recently, it has been proved that quadratic triangular Bézier patches in R^{3,1} belong to the class of MOS surfaces (i.e., surfaces providing rational envelopes of the associated two-parameter family of spheres). We give a detailed description of the symbolic and numerical steps of the envelope algorithm and study the error involved in the numerical part. The presented method is then demonstrated on several examples. Moreover, since quadratic MOS patches are capable of producing C1 approximations of MSTs, this algorithmoffers a good basis for consequent methods, e.g. computing rational approximations of envelopes associated to general (free-form) MSTs and inner offsets trimming.

Název v anglickém jazyce

A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches

Popis výsledku anglicky

In this paper, we describe an algorithm for generating an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in R^{3,1}, which is considered as a medial surface transform (MST) of a spatial domain. Recently, it has been proved that quadratic triangular Bézier patches in R^{3,1} belong to the class of MOS surfaces (i.e., surfaces providing rational envelopes of the associated two-parameter family of spheres). We give a detailed description of the symbolic and numerical steps of the envelope algorithm and study the error involved in the numerical part. The presented method is then demonstrated on several examples. Moreover, since quadratic MOS patches are capable of producing C1 approximations of MSTs, this algorithmoffers a good basis for consequent methods, e.g. computing rational approximations of envelopes associated to general (free-form) MSTs and inner offsets trimming.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

ACM Symposium on Solid and Physical Modeling: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling

ISBN

978-1-60558-711-0

ISSN

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e-ISSN

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Počet stran výsledku

12

Strana od-do

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Název nakladatele

ACM

Místo vydání

New York, NY, USA

Místo konání akce

San Francisco, California

Datum konání akce

8. 10. 2009

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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