Fast cutting simulations with underlying lattices

We present a method for real-time simulations of the arbitrary cutting of a deformable object. Our method augments the surface mesh with underlying lattices for fast and robust numerical simulations. The algorithm contains two phases: cutting and reconstruction. During the cutting, the underlying lattice is split approximately according to the blade and the soft body simulation is conducted on the lattices. Simulating the cutting and deformation on lattices rather than on the surface mesh avoids degenerating elements caused by cutting, which may lead to numerical instability. In the next, inspired by the fracture modeling, the surface mesh is split in response to the change of material stress tolerance caused by the blade in the simulation domain. In the reconstruction phase, we propose an improved Delaunay triangulation algorithm to reconstruct the inner incision surface, to alleviate the problems such as poor mesh quality and redundant faces. Due to the regularity of the lattice mesh, as well as the avoidance of the subdivision, our approach is fast and stable. The application of our method in a virtual training system for the liver surgery demonstrates its practical effectiveness.