Approximation et intersection des surfaces procédurales utilisées en C.A.O.

Stéphane Chau 1, 2
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : The intersection problem is one of the major task in Computer Aided Geometric Design (CAGD). In order to deal with this topic, we choose a model of approximation for the parameterized surfaces that are given by evaluations (the so called procedural surfaces). Many authors use triangular meshes but in this thesis, we use more complex shape primitives. More precisely it is the polynomial parameterized surfaces of small degree. The quality of the resulted approximation is better than the usual mesh method especially for the computed intersection locus. But if we want to use this kind of representation, we have to intersect efficiently such two polynomial parameterized surfaces. So, as a preprocessing, a detection of suitable intersection configurations between patches is given. Then, several intersection methods for the polynomial parameterized surfaces are exposed in details. Finally, the elaborated algorithms are implemented in an algebraic geometric modeleur.
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Stéphane Chau. Approximation et intersection des surfaces procédurales utilisées en C.A.O.. Mathématiques [math]. Université Nice Sophia Antipolis, 2008. Français. ⟨tel-00560289⟩

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