Calculating Voxel-Polyhedron Intersections for Meshing Images

Finite element meshes constructed from 3D images are useful in materials science and medical applications when it is necessary to model the actual geometry of a sample, rather than an idealized approximation of it. Constructing the mesh involves computing the intersection of the mesh elements with the voxels (3D pixels) of the image. If done naively, this process is unstable, and small errors in the computed position of an intersection point can lead to large errors in the computed volume. We demonstrate the source of the instability and present a robust and efficient method of doing the computation, based on the r3d algorithm of Powell and Abel. The method was developed in the context of the OOF3D program at NIST, but the freely available code is completely independent of OOF3D.