Název:	Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form
Autoři:	Bizzarri, Michal Lávička, Miroslav Vršek, Jan
Citace zdrojového dokumentu:	BIZZARRI, M., LÁVIČKA, M., VRŠEK, J. Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form. Computer aided geometric design, 2017, roč. 56, č. August, s. 52-66. ISSN 0167-8396.
Datum vydání:	2017
Nakladatel:	Elsevier
Typ dokumentu:	preprint preprint
URI:	http://hdl.handle.net/11025/29225
ISSN:	0167-8396
Klíčová slova:	parametrizace odmocniny;hypereliptické křivky;Weierstrassova forma;topologický graf;racionální aproximace
Klíčová slova v dalším jazyce:	Square-root parameterization;hyperelliptic curves;Weierstrass form;topological graph;rational approximation
Abstrakt v dalším 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.
Práva:	Plný text není přístupný. © Elsevier
Vyskytuje se v kolekcích:	Články / Articles (NTIS) Preprinty / Preprints (KMA) OBD

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