A New Approach to Cutting Tetrahedral Meshes

Volumetric models provide a realistic representation of three dimensional objects above and beyond what traditional surface models offer. The finite element method along with a volumetric model of an object can be used to create an effective representation of a deformable object that responds properly to external forces and stimuli. In particular, cutting is an important feature in many application areas for deformable 3D models. Surgery simulation is one obvious application area in which cutting a deformable 3D model takes on critical importance. In order to properly model the effects of a cut on soft tissue, it is important to model the effects of the cut accurately in real time. To that end, this paper presents an algorithm which satisfies the unique requirements of cutting such a model, specifically it must be efficient enough to run interactively, it must not create an excessive number of new tetrahedra which would complicate the finite element method, and it must accurately cut the mesh.