Conversion automatique de maillages en surfaces splines

Abstract : Aiming at converting a triangular mesh into a CAGD/CAM spline surface, this thesis focuses on one of the most crucial problems of the conversion process, i.e. extracting a good quadrilateral control mesh of the surface. What we mean by good is that the edges of the control mesh should be orthogonal and aligned with the principal directions of curvature of the surface. These two properties make the control mesh optimum in an approximation point of view, and greatly help to reduce unwanted oscillations on the final spline surface built from it. To solve this problem, we propose a new automatic algorithm, called periodic global parameterization. The basic idea is to find a geometry-meaningful parameterization guided by a pair of orthogonal anisotropic direction fields. Then, the iso-value lines of this parameterization will be extracted to define an initial control mesh, that satisfies the two criteria of a good control mesh. With the initial control mesh, we explain how to construct a T-spline approximation of the initial triangulated surface. We show several examples of the triangular mesh to T-spline conversion. The results show that thanks to the anisotropic control meshes, the final spline surfaces generated have much less oscillations as compared to results of previous methods, that do not take into account of the anisotropy
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Wan Chiu Li. Conversion automatique de maillages en surfaces splines. Autre [cs.OH]. Institut National Polytechnique de Lorraine, 2006. Français. ⟨NNT : 2006INPL078N⟩. ⟨tel-01752772⟩

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