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TitleParametrization of approximate algebraic surfaces by lines
Author(s) Sonia Perez-Diaz, J. Rafael Sendra
TypeArticle in Journal
AbstractIn this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to \varepsilon-irreducible algebraic surfaces of degree d having an \varepsilon-singularity of multiplicity d−1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance \varepsilon>0 and an \varepsilon-irreducible algebraic surface V of degree d, the algorithm computes a new algebraic surface Click to view the \bar{V} source, that is rational, as well as a rational parametrization of Click to view the \bar{V} source. In addition, in the error analysis we show that the output surface Click to view the \bar{V} source and the input surface V are close. More precisely, we prove that Click to view the \bar{V} source lies in the offset region of V at distance, at most, O(\varepsilon 1/(2d)).
Keywordsalgebraic surfaces, approximate parametrization, varepsilon-points
CopyrightElsevier B.V.
URL doi:10.1016/j.cagd.2004.10.001
JournalComputer Aided Geometric Design
Pages147 - 181
Translation No
Refereed No