Adaptive Fairing of Surface Meshes by Geometric Diffusion

In triangulated surface meshes, there are often very noticeable size variances (the vertices are distributed unevenly). The presented noise of such surface meshes is therefore composite of vast frequencies. In this paper, we solve a diffusion partial differential equation numerically for noise removal of arbitrary triangular manifolds using an adaptive time discretization. The proposed approach is simple and is easy to incorporate into any uniform timestep diffusion implementation with significant improvements over evolution results with the uniform timesteps. As an additional alternative to the adaptive discretization in the time direction, we also provide an approach for the choice of an adaptive diffusion tensor in the diffusion equation.