6533b82efe1ef96bd1293aff
RESEARCH PRODUCT
Conversion d'un carreau de Bézier rationnel biquadratique en un carreau de cyclide de Dupin quartique
Sebti FoufouLionel GarnierMarc Neveusubject
Bézier surfacePure mathematicsDupin cyclideAlgebraic surfaceBoundary (topology)Bézier curveAlgebraic geometryGeometric modelingPolynomial interpolationMathematicsdescription
Dupin cyclides were introduced in 1822 by the French mathematician C-P. 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 Bezier patch. In this paper, we consider the inverse problem: we investigate the conditions of convertibility of a Bezier 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 Bezier patch.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-07-01 | Techniques et sciences informatiques |