Exploring hypersurfaces with offset-like convolutions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F12%3A43915714" target="_blank" >RIV/49777513:23520/12:43915714 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cagd.2012.07.002" target="_blank" >http://dx.doi.org/10.1016/j.cagd.2012.07.002</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2012.07.002" target="_blank" >10.1016/j.cagd.2012.07.002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Exploring hypersurfaces with offset-like convolutions

Popis výsledku v původním jazyce

Offsetting is one of the fundamental operations in Computer Aided Design. Due to their high applicability, studying offsets of hypersurfaces has become a popular research area and many interesting problems related to this topic have arisen. In addition,various generalizations of classical offsets have been introduced and then investigated. In this paper we study a generalization which is based on considering offsets to (not only parameterized) hypersurfaces as convolutions with hyperspheres. In other words, we study hypersurfaces sharing the same convolution properties with hyperspheres and thus yielding offset-like convolutions. We will present an algebraic analysis of these hypersurfaces and study their properties suitable for subsequent applications, e.g. in geometric modelling. Moreover, our approach allows to derive distinguished properties of the well-known PH/PN parameterizations as special subcases of the introduced QN parameterizations.

Název v anglickém jazyce

Exploring hypersurfaces with offset-like convolutions

Popis výsledku anglicky

Offsetting is one of the fundamental operations in Computer Aided Design. Due to their high applicability, studying offsets of hypersurfaces has become a popular research area and many interesting problems related to this topic have arisen. In addition,various generalizations of classical offsets have been introduced and then investigated. In this paper we study a generalization which is based on considering offsets to (not only parameterized) hypersurfaces as convolutions with hyperspheres. In other words, we study hypersurfaces sharing the same convolution properties with hyperspheres and thus yielding offset-like convolutions. We will present an algebraic analysis of these hypersurfaces and study their properties suitable for subsequent applications, e.g. in geometric modelling. Moreover, our approach allows to derive distinguished properties of the well-known PH/PN parameterizations as special subcases of the introduced QN parameterizations.

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

<a href="/cs/project/ED1.1.00%2F02.0090" target="_blank" >ED1.1.00/02.0090: NTIS - Nové technologie pro informační společnost</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

COMPUTER AIDED GEOMETRIC DESIGN

ISSN

0167-8396

e-ISSN

—

Svazek periodika

29

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

676-690

Kód UT WoS článku

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EID výsledku v databázi Scopus

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