Parallelization of Mesh Contraction and Fairing using OpenCL

Abstract

We propose a parallel method for computing local Laplacian curvature flows for triangular meshes. Laplace operator is widely used in mesh processing for mesh fairing, noise removal or curvature estimation. If the Laplacian flow is used in global sense constraining a whole mesh with an iterative weighted linear system, it can be used even for mesh contraction. However, numerical solution of such a global linear system is computationally expensive. Therefore, we have developed a method to compute such an iterative linear system using only local neighbourhoods of each vertex in parallel. Parallel computation of local linear systems is performed on GPU using OpenCL. We have evaluated speedups of the parallelization using both local and global Laplacian flows. We show test cases, where the parallel local method can be used for mesh fairing. In contrary, we also investigate and outline a fail case, where the local Laplacian flow cannot be used. When the local Laplacian flow has problems with global convergence, we offer a global parallelization of the linear system solving as an alternative.