A Flexible and Interactive Approach for Cutting Deformable Objects

We present a hierarchical finite element method for interactively simulating cuts in linear elastic deformable bodies. Our method draws upon recent work on octree and multigrid schemes for the efficient numerical solution of partial differential equations. We propose a novel approach for incorporating topological changes in octree grids into multigrid schemes, including algorithms for updating the system equations on successive multigrid levels. A hexahedral grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is simulated by separating elements along the cell faces at this level. Since all elements have the same shape, only a scaling of a pre-computed matrix is required to construct the stiffness matrices of new elements. To build a multigrid hierarchy that reflects the induced discontinuities, elements at coarse-grid levels are duplicated to represent the resulting connectivity components. An extension of the splitting cubes algorithm is used to construct a surface that accurately aligns with the simulated cuts. A comparison to finite element simulations on tetrahedral grids in which cuts have been modeled explicitly shows very high accuracy of the proposed technique. By using our approach, interactive cuts at an effective object resolution of 256 can be achieved.