Conversion d'un carreau de Bézier rationnel biquadratique en un carreau de cyclide de Dupin quartique

Dupin cyclides were introduced in 1822 by the French mathematician Pierre-Charles Dupin. They are algebraic surfaces of degree 3 or 4. The set of geometric properties of these surfaces has encouraged an increasing interest in using them for geometric modeling. A couple of algorithmes is already developed to convert a Dupin cyclide patch into a rational biquadratic Bézier patch. In this paper, we consider the inverse problem: we investigate the conditions of convertibility of a Bézier patch into a Dupin cyclide one, and we present a conversion algorithm to compute the parameters of a Dupin cyclide with the boundary of the patch that corresponds to the given Bézier patch. This conversion eliminates the lack of flexibility that handicaps the control and adjustment of the from of Dupin cyclides, lets them have the advantages of all the tools available for Bézier surfaces, and then gets them more closer to the world of surface modeling. MOTS-CLÉS : cyclide de Dupin, courbes et surfaces de Bézier Rationnelles de degré 2, conversion