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Maillages de volumes bornés par des surfaces lisses par morceaux

Laurent Rineau 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This thesis describes and analyses a new 3D meshes generation algorithm, for domains bounded by smooth or piecewise smooth surfaces, that is surfaces made of several smooth surface patches, joined by smooth curves. This algorithm is a greedy Delaunay refinement process that samples the interior and the boundary of the domain at once. The results are provably good meshes, with a control on the size of the elements through a user-defined sizing field. The analysis of the algorithm proves guarantees on the accuracy of the approximation of the domain boundary, unless an angle between two surface patches is less than 90~degrees. The removal of that restriction is the next research subject after the thesis. A noticeable feature of this algorithm is that the domain has to be known only through an oracle that can tell whether a given point lies inside the object, whether a given line segment intersects the boundary, and whether a triangle intersects the curves of the boundary. This makes the algorithm generic enough to be applied to a wide variety of objects, ranging from domains defined by implicit surfaces to domains defined by one of several regions in 3D images or by domain bounded by an already computed surface mesh.
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Laurent Rineau. Maillages de volumes bornés par des surfaces lisses par morceaux. Informatique [cs]. Université Paris-Diderot - Paris VII, 2007. Français. ⟨tel-00410864⟩

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