Geodesic
Comparison of Implicitization Methods
Journal for geometry and graphics, Tome 9 (2005) no. 1, pp. 11-29 Cet article a éte moissonné depuis la source Heldermann Verlag

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This paper overviews several methods for implicitization of an algebraic variety (finding an implicit representation of a rational algebraic variety given by its parametric equations): the classical implicitization using Gr�bner bases, the implicitization using resultants, polynomial interpolation, or moving curves and surfaces, and the direct implicitization method. All these methods are used for finding the implicit equation of NURBS curves and surfaces, which are typical objects in geometric modeling. At the end, the computational costs for finding the implicit equation needed by implementations of these different methods are compared.
Classification : 68W30, 13P10, 14Q05, 14Q10
Mots-clés : Implicitization methods, NURBS curves and surfaces 
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     author = {B. Bastl and F. Jezek },
     title = {Comparison of {Implicitization} {Methods}},
     journal = {Journal for geometry and graphics},
     pages = {11--29},
     year = {2005},
     volume = {9},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2005_9_1_JGG_2005_9_1_a1/}
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B. Bastl; F. Jezek . Comparison of Implicitization Methods. Journal for geometry and graphics, Tome 9 (2005) no. 1, pp. 11-29. http://geodesic.mathdoc.fr/item/JGG_2005_9_1_JGG_2005_9_1_a1/