Recognizing implicitly given rational canal surfaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43926966" target="_blank" >RIV/49777513:23520/16:43926966 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0747717115000760" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0747717115000760</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jsc.2015.08.003" target="_blank" >10.1016/j.jsc.2015.08.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Recognizing implicitly given rational canal surfaces

Popis výsledku v původním jazyce

It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In this paper we will investigate in more detail the case of canal surfaces that are often used in geometric modelling, Computer-Aided Design and technical practice (e.g. as blending surfaces smoothly joining two parts with circular ends). It is known that if the squared medial axis transform is a rational curve then so is also the corresponding surface. However, starting from a polynomial it is not known how to decide if the corresponding algebraic surface is a rational canal surface or not. Our goal is to formulate a simple and efficient algorithm whose input is a polynomial with the coefficients from some subfield of RR and the output is the answer whether the surface is a rational canal surface. In the affirmative case we also compute a rational parameterization of the squared medial axis transform which can be then used for finding a rational parameterization of the corresponding implicitly given canal surface.

Název v anglickém jazyce

Recognizing implicitly given rational canal surfaces

Popis výsledku anglicky

It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In this paper we will investigate in more detail the case of canal surfaces that are often used in geometric modelling, Computer-Aided Design and technical practice (e.g. as blending surfaces smoothly joining two parts with circular ends). It is known that if the squared medial axis transform is a rational curve then so is also the corresponding surface. However, starting from a polynomial it is not known how to decide if the corresponding algebraic surface is a rational canal surface or not. Our goal is to formulate a simple and efficient algorithm whose input is a polynomial with the coefficients from some subfield of RR and the output is the answer whether the surface is a rational canal surface. In the affirmative case we also compute a rational parameterization of the squared medial axis transform which can be then used for finding a rational parameterization of the corresponding implicitly given canal surface.

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/LO1506" target="_blank" >LO1506: Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Journal of Symbolic Computation

ISSN

0747-7171

e-ISSN

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Svazek periodika

74

Číslo periodika v rámci svazku

May-June 2016

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

367-377

Kód UT WoS článku

000366794100018

EID výsledku v databázi Scopus

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