Details:
Title | Parametrization of approximate algebraic surfaces by lines | Author(s) | Sonia Perez-Diaz, J. Rafael Sendra | Type | Article in Journal | Abstract | In 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)). | Keywords | algebraic surfaces, approximate parametrization, varepsilon-points | Length | 35 | Copyright | Elsevier B.V. |
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| URL |
doi:10.1016/j.cagd.2004.10.001 |
Language | English | Journal | Computer Aided Geometric Design | Volume | 22 | Number | 2 | Pages | 147 - 181 | Year | 2005 | Month | February | Translation |
No | Refereed |
No |
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