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Approximate parametrization of plane algebraic curves by linear systems of curves
Citation
Perez Diaz, Sonia and Sendra Pons, J. Rafael and Rueda Perez, Sonia and Sendra Pons, Juana (2010). Approximate parametrization of plane algebraic curves by linear systems of curves. "Computer Aided Geometric Design", v. 27 (n. 2); pp. 212-231. ISSN 0167-8396. https://doi.org/10.1016/j.cagd.2009.12.002.
Description
| Title: | Approximate parametrization of plane algebraic curves by linear systems of curves |
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| Author/s: |
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| Item Type: | Article |
| Título de Revista/Publicación: | Computer Aided Geometric Design |
| Date: | February 2010 |
| ISSN: | 0167-8396 |
| Volume: | 27 |
| Subjects: | |
| Freetext Keywords: | Approximate; Parametrization; Plane algebraic curves; Linear systems of curves |
| Faculty: | E.U.I.T. Telecomunicación (UPM) |
| Department: | Matemática Aplicada a la Ingeniería Técnica de Telecomunicación [hasta 2014] |
| Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
Abstract
t is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance ϵ>0 and an ϵ-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ϵ-rationality, and we provide an algorithm to parametrize approximately affine ϵ-rational plane curves by means of linear systems of (d−2)-degree curves. The algorithm outputs a rational parametrization of a rational curve of degree d which has the same points at infinity as C. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that and C are close in practice.
More information
| Item ID: | 9458 |
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| DC Identifier: | https://oa.upm.es/9458/ |
| OAI Identifier: | oai:oa.upm.es:9458 |
| DOI: | 10.1016/j.cagd.2009.12.002 |
| Official URL: | http://www.sciencedirect.com/science/journal/01678396 |
| Deposited by: | Memoria Investigacion |
| Deposited on: | 10 Nov 2011 10:18 |
| Last Modified: | 20 Apr 2016 17:52 |
