Volumes with piecewise quadratic medial surface transforms: Computation of boundaries and trimmed offsets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F10%3A00503240" target="_blank" >RIV/49777513:23520/10:00503240 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Volumes with piecewise quadratic medial surface transforms: Computation of boundaries and trimmed offsets

Popis výsledku v původním jazyce

MOS surfaces (i.e., medial surface transforms obeying a sum of squares condition) are rational surfaces in R^{3,1} which possess rational envelopes of the associated two-parameter families of spheres. Moreover, all offsets of the envelopes admit rationalparameterizations as well. Recently, it has been proved that quadratic triangular Bézier patches in View the MathML source are MOS surfaces. Following this result, we describe an algorithm for computing an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in View the MathML source. The paper focuses mainly on the geometric aspects of the algorithm. Since these patches are capable of producing C1 smooth approximations of medial surface transforms of spatial domains,we use this algorithm to generate rational approximations of envelopes of general medial surface transforms. One of the main advantages of this approach to offsetting is the fact that the trimming procedure becomes considerably simpler.

Název v anglickém jazyce

Volumes with piecewise quadratic medial surface transforms: Computation of boundaries and trimmed offsets

Popis výsledku anglicky

MOS surfaces (i.e., medial surface transforms obeying a sum of squares condition) are rational surfaces in R^{3,1} which possess rational envelopes of the associated two-parameter families of spheres. Moreover, all offsets of the envelopes admit rationalparameterizations as well. Recently, it has been proved that quadratic triangular Bézier patches in View the MathML source are MOS surfaces. Following this result, we describe an algorithm for computing an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in View the MathML source. The paper focuses mainly on the geometric aspects of the algorithm. Since these patches are capable of producing C1 smooth approximations of medial surface transforms of spatial domains,we use this algorithm to generate rational approximations of envelopes of general medial surface transforms. One of the main advantages of this approach to offsetting is the fact that the trimming procedure becomes considerably simpler.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

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

2010

Kód důvěrnosti údajů

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

Název periodika

Computer-Aided Design

ISSN

0010-4485

e-ISSN

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Svazek periodika

42

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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