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dc.contributor.authorBizzarri, Michal
dc.contributor.authorLávička, Miroslav
dc.contributor.authorVršek, Jan
dc.date.accessioned2018-02-21T11:35:22Z-
dc.date.available2018-02-21T11:35:22Z-
dc.date.issued2017
dc.identifier.citationBIZZARRI, 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.issn0167-8396
dc.identifier.urihttp://hdl.handle.net/11025/29225
dc.format15 s.
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.publisherElsevieren
dc.relation.ispartofseriesComputer aided geometric designen
dc.rightsPlný text není přístupný.cs
dc.rights© Elsevieren
dc.subjectparametrizace odmocninycs
dc.subjecthypereliptické křivkycs
dc.subjectWeierstrassova formacs
dc.subjecttopologický grafcs
dc.subjectracionální aproximacecs
dc.titlePiecewise rational approximation of square-root parameterizable curves using the Weierstrass formen
dc.typepreprintcs
dc.typepreprinten
dc.rights.accessclosedAccessen
dc.type.versiondraften
dc.description.abstract-translatedIn 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.subject.translatedSquare-root parameterizationen
dc.subject.translatedhyperelliptic curvesen
dc.subject.translatedWeierstrass formen
dc.subject.translatedtopological graphen
dc.subject.translatedrational approximationen
dc.identifier.doi10.1016/j.cagd.2017.08.001
dc.type.statusPeer-revieweden
dc.identifier.obd43918948
dc.project.IDLO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost
Appears in Collections:Články / Articles (NTIS)
Preprinty / Preprints (KMA)
OBD

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