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Design géométrique de surfaces de topologie arbitraire

Abstract : This thesis is concerned with the definition of geometrically smooth surface interpolating a triangulated set of points in R^3. Such a triangulation, called a surface mesh in our context, is 2-manifold in the 3D space and can represent surfaces of arbitrary topological genus. It gives the topological information by means of a data structure containing the adjacency informations between the vertices, the edges and the faces. We have developped two methods for interpolating the vertices of the surface mesh. They are completely local and produce piecewise polynomial surfaces of degree 5 with G^1 continuity. A large number of free parameters are available and can be adjusted, either interactively or automatically, in order to smooth the surface. In the interactive case, a number of design handles are developed, based on the geometric interpretations of the free parameters. The desired form can be designed in real time thanks to the localness of the algorithms. In the case of automatic design, many algorithms have been developped to satisfy a number of shape features. A large number of simple heuristics and local optimizations are used to determine the shape parameters, that gives pleasing shapes and an optimal control over the surface.
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Submitted on : Tuesday, February 17, 2004 - 10:18:24 AM
Last modification on : Friday, March 25, 2022 - 11:09:12 AM
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  • HAL Id : tel-00004706, version 1



Riadh Taleb. Design géométrique de surfaces de topologie arbitraire. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2001. Français. ⟨tel-00004706⟩



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