Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form
dc.contributor.author | Bizzarri, Michal | |
dc.contributor.author | Lávička, Miroslav | |
dc.contributor.author | Vršek, Jan | |
dc.date.accessioned | 2018-02-21T11:35:22Z | |
dc.date.available | 2018-02-21T11:35:22Z | |
dc.date.issued | 2017 | |
dc.description.abstract-translated | 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. | en |
dc.format | 15 s. | cs |
dc.format.mimetype | application/pdf | |
dc.identifier.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. | en |
dc.identifier.doi | 10.1016/j.cagd.2017.08.001 | |
dc.identifier.issn | 0167-8396 | |
dc.identifier.obd | 43918948 | |
dc.identifier.uri | http://hdl.handle.net/11025/29225 | |
dc.language.iso | en | en |
dc.project.ID | LO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost | cs |
dc.publisher | Elsevier | en |
dc.relation.ispartofseries | Computer aided geometric design | en |
dc.rights | Plný text není přístupný. | cs |
dc.rights | © Elsevier | en |
dc.rights.access | closedAccess | en |
dc.subject | parametrizace odmocniny | cs |
dc.subject | hypereliptické křivky | cs |
dc.subject | Weierstrassova forma | cs |
dc.subject | topologický graf | cs |
dc.subject | racionální aproximace | cs |
dc.subject.translated | Square-root parameterization | en |
dc.subject.translated | hyperelliptic curves | en |
dc.subject.translated | Weierstrass form | en |
dc.subject.translated | topological graph | en |
dc.subject.translated | rational approximation | en |
dc.title | Piecewise rational approximation of square-root parameterizable curves using the Weierstrass form | en |
dc.type | preprint | cs |
dc.type | preprint | en |
dc.type.status | Peer-reviewed | en |
dc.type.version | draft | en |