Vertex-preserving Cutting of Elastic Objects

This paper proposes vertex-preserving cutting methods on finite element models for interactive soft tissue simulation. Unlike existing methods, we aim to shape variety of incisions using only initial vertices of tetrahedral meshes. Neither tetrahedral decomposition nor vertex creation is used. The number of vertices is preserved. This avoids increase of computation cost as well as allows fast update of physical status of finite element models. To preserve 3D shape and sharp feature of initial meshes through on-the-fly mesh modification, constraints are introduced to the topological update scheme. In our model, the size of stiffness matrix is constant. Our framework efficiently simulates several varieties of smooth incisions with sufficient quality for surgical simulation, and also achieves interactive performance in complex meshes with thousands of elements.