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“Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration”
Bruno Lévy and Nicolas Bonneel
International Meshing Roundtable conf. proc., 2012

Abstract: This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method gen- erates a curvature-adapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d or larger). In this high dimensional space, the mesh is optimized by com- puting a Centroidal Voronoi Tessellation (CVT), i.e. the minimizer of a C 2 objective function that depends on the coordinates at the vertices (quantiza- tion noise power). Optimizing this objective function requires to compute the intersection between the (higher dimensional) Voronoi cells and the surface (Restricted Voronoi Diagram). The method overcomes the d-factorial cost of computing a Voronoi diagram of dimension d by directly computing the re- stricted Voronoi cells with a new algorithm that can be easily parallelized (Vorpaline: Voronoi Parallel Linear Enumeration). The method is demonstrated with several examples comprising CAD and scanned meshes.

BibTex reference

@INPROCEEDINGS{levy:vorpaline_imr:12,
   AUTHOR     = "Bruno Lévy and Nicolas Bonneel",
   TITLE      = "Variational Anisotropic Surface Meshing with Voronoi Parallel Linear 
                   Enumeration",
   BOOKTITLE  = "International Meshing Roundtable conf. proc.",
   YEAR       = "2012",
}