Laplacian mesh optimization

We introduce a framework for triangle shape optimization and feature preserving smoothing of triangular meshes that is guided by the vertex Laplacians, specifically, the uniformly weighted Laplacian and the discrete mean curvature normal. Vertices are relocated so that they approximate prescribed Laplacians and positions in a weighted least-squares sense; the resulting linear system leads to an efficient, non-iterative solution. We provide different weighting schemes and demonstrate the effectiveness of the framework on a number of detailed and highly irregular meshes; our technique successfully improves the quality of the triangulation while remaining faithful to the original surface geometry, and it is also capable of smoothing the surface while preserving geometric features.