On the Representation of Dupin Cyclides in Lie Sphere Geometry with Applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F09%3A00502071" target="_blank" >RIV/49777513:23520/09:00502071 - 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

On the Representation of Dupin Cyclides in Lie Sphere Geometry with Applications

Popis výsledku v původním jazyce

Dupin cyclides are canal surfaces defined as envelopes of a family of oriented spheres which touch three given oriented spheres. With respect to their attractive geometric properties they are often used in Computer Aided Geometric Design and in many engineering applications. In this paper, we study these surfaces from the point of view of Lie sphere geometry. This representation enables to solve many complicated problems through simple and well known methods of linear algebra. As for applications, we present an algorithm for computing their rational parametrizations and demonstrate a construction of blends between two canal surfaces using methods of Lie geometry.

Název v anglickém jazyce

On the Representation of Dupin Cyclides in Lie Sphere Geometry with Applications

Popis výsledku anglicky

Dupin cyclides are canal surfaces defined as envelopes of a family of oriented spheres which touch three given oriented spheres. With respect to their attractive geometric properties they are often used in Computer Aided Geometric Design and in many engineering applications. In this paper, we study these surfaces from the point of view of Lie sphere geometry. This representation enables to solve many complicated problems through simple and well known methods of linear algebra. As for applications, we present an algorithm for computing their rational parametrizations and demonstrate a construction of blends between two canal surfaces using methods of Lie geometry.

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)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název periodika

Journal for Geometry and Graphics

ISSN

1433-8157

e-ISSN

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Svazek periodika

13

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

18

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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