Default mesh optimization in GRUMMP

In two dimensions, the meshes GRUMMP generates in the tri executable are already excellent. The meshopt2d executable actually operates by computing an appropriate length scale for the input mesh, then using Ruppert's scheme to refine the mesh until quality is high; the guarantees on cell size provided with size and grading control in [11] ensure that the output mesh is still of reasonable size. In both cases, post-processing by using a pass or two smoothing to maximize the minimum sine of angles in the mesh generally increases the minimum angle by a few degrees at low cost.

In three dimensions, GRUMMP again produces good meshes in the tetra executable. Because slivers are still generated, tetra post-processes its meshes by swapping to increase the minimum sine of the dihedral angles in the mesh, and performs one pass of smoothing with the same goal. meshopt3d differs from its 2D counterpart in that insertion is not part of its operation; instead, a user-definable sequence of swapping, smoothing, and bad tetrahedron repair steps are performed. The default optimization sequence follows the experimentally-inspired recommendations of Freitag and Ollivier-Gooch [3], which typically performs well for meshes that are approximately isotropic.

Carl Ollivier-Gooch 2017-07-20