Parametrization of approximate algebraic curves by lines
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49616DOI: 10.1016/j.tcs.2004.01.010
ISSN: 0304-3975
Publisher
Elsevier
Date
2004Funders
European Commission
Ministerio de Educación y Ciencia
Bibliographic citation
Pérez Díaz, S., Sendra, J. & Sendra, J.R. 2004, “Parametrization of approximate algebraic curves by lines”, Theoretical Computer Science, vol. 315, no. 2-3, pp. 627-650.
Keywords
Approximate algebraic curves
Rational parametrization
Hibrid symbolic-numeric methods
Project
info:eu-rep/grantAgreement/MEC//BMF2002-04402-C02-01
HU2001-0002
info:eu-repo/grantAgreement/EC/FP5-IST/IST-2001-35512/EU/INTERSECTION ALGORITHMS FOR GEOMETRY BASED IT-APPLICATIONS USING APPROXIMATE ALGEBRAIC METHODS/GAIA II
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.tcs.2004.01.010Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2004 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
It is well known that irreducible algebraic plane curves having a singularity of
maximum multiplicity are rational and can be parametrized by lines. In this paper,
given a tolerance > 0 and an –irreducible algebraic plane curve C of degree d
having an -singularity of multiplicity d−1, we provide an algorithm that computes
a proper parametrization of a rational curve that is exactly parametrizable by lines.
Furthermore, the error analysis shows that under certain initial conditions that
ensures that points are projectively well defined, the output curve lies within the
offset region of C at distance at most 2√
2
1/(2d)
exp(2).
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