Discrete Mesh Optimization on Surface and Volume Meshes

State of the art algorithms in surface mesh smoothing rely on computing new vertex positions on approximated shapes and re-projecting the results back onto the real surface or having no internal surface representation at all, which leads inevitably to suboptimal results. Discrete Mesh Optimization (DMO) is a greedy approach to topology- consistent mesh quality improvement, which was initially designed to smooth triangle and quadrilateral meshes in two dimensions and tetrahedral meshes in three dimensions. We present a generalization of DMO which allows optimization on discretized surfaces, or more general d-dimensional manifolds. As the method is not bound to search directions, it is capable of finding the optimal vertex positions directly on a surface without any re-projection. Therefore, the proposed technique preserves the underlying surface or volume. We present examples for surface and volume meshes, showing the improvement-potential of considering boundary vertices in the smoothing process.