Simulating drilling on tetrahedral meshes

Bone drilling is a fundamental task in several surgical procedures, including mastoidectomy, cochlear implantation, orbital surgery. It consists in eroding the part of the bone in contact with the tip of the surgical tool when a sufficient pressure is exerted. Since the bone is an almost rigid material, the bone drilling simulations usually employ voxel-based representations of the bone, so that it is easy to show material removal by playing with material density in the voxels. Unfortunately, there are cases in which drilling is only a part of the task, and parts of the same object are also cut away or, worse, the bone is slightly deformable and therefore voxel-based representations do not work well. We propose a novel method to simulate drilling on objects represented explicitly by means of a tetrahedral mesh. The key idea of our method is to create an alternative representation of the tetrahedron when it is partially eroded. Such representation consists of a set of smaller tetrahedra obtained by a hierarchical decomposition of the original one, and combined to represent the current status of the erosion.