Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43932152" target="_blank" >RIV/49777513:23520/17:43932152 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cagd.2017.08.001" target="_blank" >http://dx.doi.org/10.1016/j.cagd.2017.08.001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2017.08.001" target="_blank" >10.1016/j.cagd.2017.08.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form

Popis výsledku v původním jazyce

In this paper we study situations when non-rational parameterizations of planar or space curves as results of certain geometric operations or constructions are obtained, in general. We focus especially on such cases in which one can identify a rational mapping which is a double cover of a rational curve. Hence, we deal with rational, elliptic or hyperelliptic curves that are birational to plane curves in the Weierstrass form and thus they are square-root parameterizable. We design a simple algorithm for computing an approximate (piecewise) rational parametrization using topological graphs of the Weierstrass curves. Predictable shapes reflecting a number of real roots of a univariate polynomial and a possibility to approximate easily the branches separately play a crucial role in the approximation algorithm. Our goal is not to give a comprehensive list of all such operations but to present at least selected interesting cases originated in geometric modelling and to show a unifying feature of the formulated method. We demonstrate our algorithm on a number of examples.

Název v anglickém jazyce

Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form

Popis výsledku anglicky

In this paper we study situations when non-rational parameterizations of planar or space curves as results of certain geometric operations or constructions are obtained, in general. We focus especially on such cases in which one can identify a rational mapping which is a double cover of a rational curve. Hence, we deal with rational, elliptic or hyperelliptic curves that are birational to plane curves in the Weierstrass form and thus they are square-root parameterizable. We design a simple algorithm for computing an approximate (piecewise) rational parametrization using topological graphs of the Weierstrass curves. Predictable shapes reflecting a number of real roots of a univariate polynomial and a possibility to approximate easily the branches separately play a crucial role in the approximation algorithm. Our goal is not to give a comprehensive list of all such operations but to present at least selected interesting cases originated in geometric modelling and to show a unifying feature of the formulated method. We demonstrate our algorithm on a number of examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

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

2017

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

56

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

52-66

Kód UT WoS článku

000412620700005

EID výsledku v databázi Scopus

2-s2.0-85027554796