Harmonic Field Based Volume Model Construction from Triangle Soup

Abstract

Surface triangle meshes and volume data are two commonly used representations of digital geometry. Converting from triangle meshes to volume data is challenging, since triangle meshes often contain defects such as small holes, internal structures, or self-intersections. In the extreme case, we may be simply presented with a set of arbitrarily connected triangles, a “triangle soup”. This paper presents a novel method to generate volume data represented as an octree from a general 3D triangle soup. Our motivation is the Faraday cage from electrostatics. We consider the input triangles as forming an approximately closed Faraday cage, and set its potential to zero. We then introduce a second conductor surrounding it, and give it a higher constant potential. Due to the electrostatic shielding effect, the resulting electric field approximately lies in that part of space outside the shape implicitly determined by the triangle soup. Unlike previous approaches, our method is insensitive to small holes and internal structures, and is observed to generate volumes with low topological complexity. While our approach is somewhat limited in accuracy by the requirement of filling holes, it is still useful, for example, as a preprocessing step for applications such as mesh repair and skeleton extraction.