Parametrization of approximate algebraic surfaces by lines

In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to e-irreducible algebraic surfaces of degree d having an e-singularity of multiplicity d - 1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance e > 0 and an e-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(e1/(2d)).

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