Quality tetrahedral mesh smoothing via boundary-optimized Delaunay triangulation

Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the L1L1 error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method.

► We present an optimization-based approach to improve the angle quality of a tetrahedral mesh. ► Our method can simultaneously smooth both interior and boundary nodes of a tetrahedral mesh. ► Our method is guaranteed to retain the volume of a smooth closed mesh and can also preserve sharp features.