Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
COMPUTER AIDED GEOMETRIC DESIGN
ISSN
0167-8396
e-ISSN
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Volume of the periodical
56
Issue of the periodical within the volume
August
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
15
Pages from-to
52-66
UT code for WoS article
000412620700005
EID of the result in the Scopus database
2-s2.0-85027554796