## Tetrahedral Mesh Generation for Deformable Bodies

Neil Molino (Stanford University)

Robert Bridson (Stanford University)

Ronald Fedkiw (Stanford University)

Submitted to SCA 2003

### Abstract

Motivated by the simulation of deformable bodies, we propose a new
tetrahedral mesh generation algorithm that produces both high quality
elements and a mesh that is well conditioned for subsequent large
deformations. We use a signed distance function defined on a grid in
order to represent the object geometry. After tiling space with a uniform
lattice based on crystallography, we identify a subset of these tetrahedra
that adequately fill the space occupied by the object. Then we use the
signed distance function or other user defined criteria to guide a red
green mesh subdivision algorithm that results in a candidate mesh with
the appropriate level of detail. After this, both the signed distance
function and topological considerations are used to prune the mesh as
close to the desired shape as possible while keeping the mesh flexible
for large deformations. Finally, we compress the mesh to tightly fit the
object boundary using either masses and springs, the finite element method
or an optimization approach to relax the positions of both the interior
and boundary nodes. The resulting mesh is well suited for simulation since
it is highly structured, has robust topological connectivity in the face
of large deformations, and is readily refined if deemed necessary during
subsequent simulation.

PDF (3.4MB)