2D Centroidal Voronoi Tessellations with Constraints

Jane Tournois 1 Pierre Alliez 1 Olivier Devillers 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We tackle the problem of constructing 2D centroidal Voronoi tessellations with constraints through an efficient and robust construction of bounded Voronoi diagrams, the pseudo-dual of the constrained Delaunay triangulation. We exploit the fact that the cells of the bounded Voronoi diagram can be obtained by clipping the ordinary ones against the constrained Delaunay edges. The clipping itself is efficiently computed by identifying for each constrained edge the (connected) set of triangles whose dual Voronoi vertex is hidden by the constraint. The resulting construction is amenable to Lloyd relaxation so as to obtain a centroidal tessellation with constraints.
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Submitted on : Wednesday, December 29, 2010 - 11:47:09 AM
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Jane Tournois, Pierre Alliez, Olivier Devillers. 2D Centroidal Voronoi Tessellations with Constraints. Numerical Mathematics: Theory, Methods and Applications, Global Science Press, 2010, 3 (2), pp.212--222. ⟨10.4208/nmtma.2010.32s.6⟩. ⟨inria-00523812v2⟩

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