Geodesic
Algebraic Approach to a Geometric Characterization of Parametric Cubics
Journal for geometry and graphics, Tome 11 (2007) no. 2, pp. 173-178
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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.
Classification : 68U05, 51N35
Mots-clés : Bezier curves, classification of cubics, polynomial cubics, Weierstrass normal form 
@article{JGG_2007_11_2_JGG_2007_11_2_a2,
     author = {P. Koprowski},
     title = {Algebraic {Approach} to a {Geometric} {Characterization} of {Parametric} {Cubics}},
     journal = {Journal for geometry and graphics},
     pages = {173--178},
     year = {2007},
     volume = {11},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2007_11_2_JGG_2007_11_2_a2/}
}
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P. Koprowski. Algebraic Approach to a Geometric Characterization of Parametric Cubics. Journal for geometry and graphics, Tome 11 (2007) no. 2, pp. 173-178. http://geodesic.mathdoc.fr/item/JGG_2007_11_2_JGG_2007_11_2_a2/