| Title: | Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form |
| Authors: | Bizzarri, Michal Lávička, Miroslav Vršek, Jan |
| Citation: | 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. |
| Issue Date: | 2017 |
| Publisher: | Elsevier |
| Document type: | preprint preprint |
| URI: | http://hdl.handle.net/11025/29225 |
| ISSN: | 0167-8396 |
| Keywords: | parametrizace odmocniny;hypereliptické křivky;Weierstrassova forma;topologický graf;racionální aproximace |
| Keywords in different language: | Square-root parameterization;hyperelliptic curves;Weierstrass form;topological graph;rational approximation |
| Abstract in different language: | 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. |
| Rights: | Plný text není přístupný. © Elsevier |
| Appears in Collections: | Články / Articles (NTIS) Preprinty / Preprints (KMA) OBD |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| paper_v07.pdf | 1,55 MB | Adobe PDF | View/Open | |
| 1-s2.0-S0167839617300109-main.pdf | 1,08 MB | Adobe PDF | View/Open Request a copy |
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