
Journal for Geometry and Graphics 11 (2007), No. 2, 173178 Copyright Heldermann Verlag 2007 Algebraic Approach to a Geometric Characterization of Parametric Cubics Przemyslaw Koprowski Faculty of Mathematics, University of Silesia, ul. Bankowa 14, 40007 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 [ Fulltextpdf (169 KB)] for subscribers only. 