Journal for Geometry and Graphics 11 (2007), No. 2, 173--178
Copyright Heldermann Verlag 2007
Algebraic Approach to a Geometric Characterization of Parametric Cubics
Przemyslaw Koprowski
Faculty of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland
pkoprowski@member.ams.org
We reprove the result of Stone and DeRose, which gives the geometric classification of the affine type of an untrimmed Bézier curve, using classical algebraic geometry. We show how to derive the characterization of Stone and DeRose from three classical results: Bézout theorem, polynomial parametrization criterion and classification of the singularity type of an algebraic curve given in Weierstrass normal form.
Keywords: Bezier curves, classification of cubics, polynomial cubics, Weierstrass normal form.
MSC: 68U05; 51N35
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