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Journal for Geometry and Graphics 15 (2011), No. 1, 001--018
Copyright Heldermann Verlag 2011

Algorithm for the Parameterization of Rational Curves Revisited

Michal Bizzarri
NTIS - New Technologies for Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzen, Czech Republic

Miroslav Lávicka
Dept. of Mathematics, University of West Bohemia, Plzen, Czech Republic

A rational parameterization of an algebraic curve yields a rational correspondence between this curve and the affine or projective line. One of the parameterization methods is based on finding all singular points and d-3 simple points of an implicitly given curve of degree d. In this paper, we study some modifications of this well-known algorithm, which are then verified on several examples.

Keywords: Algebraic curve, singular points, genus, rational parameterization, quadratic transformation.

MSC: 51N35; 14H45, 68U05

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