Parametrization of aproximate algebraic surfaces by lines
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49602DOI: 10.1016/j.cagd.2004.10.001
ISSN: 0167-8396
Publisher
Elsevier
Date
2005Funders
European Commission
Ministerio de Educación y Ciencia
Bibliographic citation
Pérez Díaz, S., Sendra, J. & Sendra, J.R. 2005, “Parametrization of approximate algebraic surfaces by lines”, Computer Aided Geometric Design, vol. 22, no. 2, pp. 147-181.
Keywords
Algebraic surfaces
Approximate parametrization
ϵ-points
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.cagd.2004.10.001Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2004 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to ²-irreducible algebraic
surfaces of degree d having an ²–singularity of multiplicity d−1, and therefore it
generalizes the existing approximate parametrization algorithms. In particular,
given a tolerance ² > 0 and an ²-irreducible algebraic surface V of degree d,
the algorithm computes a new algebraic surface V , that is rational, as well as a
rational parametrization of V . In addition, in the error analysis we show that
the output surface V and the input surface V are close. More precisely, we prove
that V lies in the offset region of V at distance, at most, O(²
1
2d ).
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