Globally certified G¹ approximation of planar algebraic curves
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/57963DOI: 10.1016/j.cam.2023.115399
ISSN: 0377-0427
Publisher
Elsevier
Date
2023-06-28Embargo end date
2024-12-28Funders
Agencia Estatal de Investigación
Bibliographic citation
Wang, X.-Y., Shen, L.-Y., Yuan, C.-M. & Pérez Díaz, S. 2024, “Globally certified G¹ approximation of planar algebraic curves”, Journal of Computational and Applied Mathematics, vol. 436, art. no. 115399.
Keywords
Globally approximation
Topology analysis
Hausdorff distance
Bézier spline
Asymptote
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113192GB-I00/ES/VISUALIZACION MATEMATICA: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2023.115399Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2023 Elsevier
Access rights
info:eu-repo/semantics/embargoedAccess
Abstract
Topology analysis and geometric feature determination for curves and surfaces are basic problems in geometric modeling and computer aided design. When the curves and surfaces are given in implicit expressions, the problems become more difficult. This paper presents a complete algorithm framework for the problem of certified G¹
approximation of a planar algebraic curve under global error control. Compared to other work on topology and geometric analysis of algebraic curves, this method presents a new topology analysis as well as a geometric information computation. Moreover, this method uses generalized asymptotes as the approximation of the unbounded part, which makes it achieve global approximation with given precision.
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