Isosurface Stuffing: Fast Tetrahedral Meshing with Good Dihedral Angles

“The isosurface stuffing algorithm fills an isosurface with a uniformly
sized tetrahedral mesh whose dihedral angles are bounded
between 10.7◦ and 164.8◦, or (with a change in parameters) between
8.9◦ and 158.8◦. The algorithm is whip fast, numerically robust,
and easy to implement because, like Marching Cubes, it generates
tetrahedra from a small set of precomputed stencils. A variant
of the algorithm creates a mesh with internal grading: on the boundary,
where high resolution is generally desired, the elements are fine
and uniformly sized, and in the interior they may be coarser and
vary in size. This combination of features makes isosurface stuffing
a powerful tool for dynamic fluid simulation, large-deformation
mechanics, and applications that require interactive remeshing or
use objects defined by smooth implicit surfaces. It is the first algorithm
that rigorously guarantees the suitability of tetrahedra for
finite element methods in domains whose shapes are substantially
more challenging than boxes. Our angle bounds are guaranteed by
a computer-assisted proof. If the isosurface is a smooth 2-manifold
with bounded curvature, and the tetrahedra are sufficiently small,
then the boundary of the mesh is guaranteed to be a geometrically
and topologically accurate approximation of the isosurface.”

Isosurface Stuffing: Fast Tetrahedral Meshing with Good Dihedral Angles

Again, although this is a geometry paper at heart, it has obvious applications to fluids and finite element simulation, so it’s definitely relevant. And allow me to editorialize for a moment and say, wow, that’s fast.