Approximate parametrization of plane algebraic curves by linear systems of curves

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
Author/s:
  • Perez Diaz, Sonia
  • Sendra Pons, J. Rafael
  • Rueda Perez, Sonia
  • Sendra Pons, Juana
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

Full text

[img]
Preview
PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (713kB) | Preview

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
DC Identifier: http://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
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM