Towards Variational Anisotropic Mesh Generation.

@inproceedings{LevyGM2012,
 abstract = { This paper investigates a new theoretical approach to anisotropic surface meshing, and shows some experimental results. From an input polygonal mesh and a specified number of vertices, the method generates a curvature-adapted mesh. The method is currently limited to 5000 vertices, due to a prohibitive computational cost.
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 (quantization noise power). Optimizing this objective function requires to compute the intersection between the (higher dimensional) Voronoi cells and the surface (Restricted Voronoi Diagram).
The main limitation of the method is the d-factorial cost of computing a Voronoi diagram of dimension d. We propose some ideas to overcome this limitation in the conclusion. },
 author = { Levy, Bruno },
 booktitle = { Proc. 32nd Gocad Meeting, Nancy },
 title = { Towards Variational Anisotropic Mesh Generation. },
 year = { 2012 }
}