General, robust, and efficient polyhedron intersection in the Interface Reconstruction Library

Abstract

Intersecting a polyhedron with a half-space or another polyhedron is required in various fields, including computer graphics, computer-aided design, and many methods used in computational physics. Often, the polyhedra involved are complicated non-convex objects, and intersecting them constitutes a significant computational cost. To address this, we present a general, geometrically robust, and efficient polyhedron intersection algorithm based on the half-edge data structure and implemented in the open-source Interface Reconstruction Library. We then employ this algorithm in a novel graph-based approach to distribute the volume of a polyhedron over a computational mesh. To demonstrate their performance, the two methods are tested on randomly generated configurations. Compared to the open-source packages VOFTools and R3D, the polyhedron intersection algorithm shows superior speed over the range of convex and non-convex polyhedra tested. The volume distribution method also proves to be discretely conservative, even for meshes containing degenerate faces.