Multilevel mesh simplification

The goal of a multilevel simplification method is to produce different levels of refinement of a mesh, reducing the resolution (total number of faces), while preserving the original topology and a good approximation to the original geometry. A new approach to simplification based on the evolution of surfaces under p-Laplacian flow is presented. Such an evolution provides a natural geometric clustering process where the spatial effect of the p-Laplacian allows for identifying suitable regions that need to be simplified. The concrete scheme is a multiresolution framework composed, at each simplification level, of a spatial clustering diffusion flow to determine the potential candidates for deletion, followed by an incremental decimation process to update the mesh vertex locations in order to decrease the overall resolution. Numerical results show the effectiveness of our strategy in multilevel simplification of different models with different complexities, in particular for models characterized by sharp features and flat parts.