Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram

Abstract

AbstractWe propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation‐based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd‐tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O(mlog n), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi‐Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state‐of‐art approaches.