Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration

This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates 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 computing 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 restricted Voronoi cells with a new algorithm that can be easily parallelized (Vor-paline: Voronoi Parallel Linear Enumeration). The method is demonstrated with several examples comprising CAD and scanned meshes.