Adaptive Polygonal Mesh Simplification With Discrete Centroidal Voronoi Diagrams

In this paper, we propose an adaptive polygonal mesh coarsening algorithm. This approach is based on the clustering of the input mesh triangles, driven by a discretized variationnal definition of centroidal tesselations. It is able to simplify meshes with high complexity i.e. meshes with a large number of vertices and high genus. We demonstrate the ability our scheme to simplify meshes according to local features such as curvature measures. We also introduce an initial sampling strategy which speeds up the algorithm, an on-the-fly checking step to guarantee the validity of the clustering, and a postprocessing step to enhance the quality of the approximating mesh. Experimental results show the efficiency of our scheme both in terms of speed and visual quality.