Isotropic Remeshing by Dynamic Voronoi Tessellation on Voxelized Surface

Abstract

A novel algorithm for isotropic remeshing of a triangle mesh is presented in this paper. The algorithm is designed to work on a voxelized surface and integrates several novel ideas. One such is the notion of functional partitioning that aids in uniform distribution of seeds for initializing the process of dynamic Voronoi tessellation (DVT). The concept of DVT is also novel and found to be quite effective for iteratively transforming the input mesh into an isotropic mesh while keeping the tessellation aligned with the surface geometry. In each iteration, a Voronoi energy field is used to rearrange the seeds and to recreate the DVT. Over successive iterations, the DVT is found to keep on improving the mesh isotropy without compromising with the surface features. The Delaunay triangles corresponding to the final tessellation are further subdivided in high-curvature regions. The resultant mesh is finally projected back onto the original mesh in order to minimize the Hausdorff error. As our algorithm works in voxel space, it is readily implementable in GPU. Experimental results on various datasets demonstrate its efficiency and robustness.