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Diagrammes de Voronoï et surfaces évolutives

David Lopez 1 
1 PIXEL - Structurer des formes géométriques
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : In this paper, we propose to address the problem of tracking a deformable surface using a remeshing technique on restricted Voronoi diagrams. The latter offer a partition of a surface domain allowing, among other things, to optimize the distribution of a set of samples on this domain and to define a remarkable triangulation : the restricted Delaunay triangulation. This remeshing solution is only effective when certain conditions are met. Thus, the first work consisted in implementing a cell configuration analysis technique and an automatic correction method allowing to generate a new new approximation homeomorphic to the initial domain whatever the given sampling. A second work proposes to improve the proximity between the initial mesh and the result of the remeshing : the aim is to minimize the approximation error which is here expressed as local volume differences. These two tools are associated with a sampling strategy that allows to maintain a constant sampling density throughout the deformation and thus proposes a new method to track free surfaces in incompressible fluid simulation.
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Submitted on : Tuesday, January 18, 2022 - 12:39:11 AM
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Long-term archiving on: : Tuesday, April 19, 2022 - 6:21:13 PM

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David Lopez. Diagrammes de Voronoï et surfaces évolutives. Géométrie algorithmique [cs.CG]. Université de Lorraine, 2021. Français. ⟨NNT : 2021LORR0247⟩. ⟨tel-03530955⟩

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