A note on the rational parameterization of algebraic curves in Mathematica

Kód výsledku v IS VaVaI

RIV/49777513:23520/09:00501717 - isvavai.cz

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A note on the rational parameterization of algebraic curves in Mathematica

Popis výsledku v původním jazyce

The choice of an appropriate representation of geometric objects (explicit, parametric, or implicit one) is a fundamental issue for the development of efficient algorithms. Whereas for example Computer Graphics seem to use all the above mentioned representations, CAD focuses on a few of them -- mainly on the parametric one. Among all parameterizations, the most important ones are those that can be described with the help of polynomials or rational functions since these descriptions can be easily included into standard CAD systems and then used in technical applications. The main aim of the paper is to describe an efficient algorithm which can be used for finding rational parameterizations of special classes of algebraic curves. Some advantages and disadvantages of the presented method will be discussed.

Název v anglickém jazyce

A note on the rational parameterization of algebraic curves in Mathematica

Popis výsledku anglicky

The choice of an appropriate representation of geometric objects (explicit, parametric, or implicit one) is a fundamental issue for the development of efficient algorithms. Whereas for example Computer Graphics seem to use all the above mentioned representations, CAD focuses on a few of them -- mainly on the parametric one. Among all parameterizations, the most important ones are those that can be described with the help of polynomials or rational functions since these descriptions can be easily included into standard CAD systems and then used in technical applications. The main aim of the paper is to describe an efficient algorithm which can be used for finding rational parameterizations of special classes of algebraic curves. Some advantages and disadvantages of the presented method will be discussed.

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

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