Splitting cubes: a fast and robust technique for virtual cutting

This paper presents the Splitting Cubes, a fast and robust technique to perform interactive virtual cutting on deformable objects. The technique relies on two ideas. The ¯rst one is to embed the deformable object in a regular grid, to apply the deformation function to the grid nodes and to interpolate the deformation inside each cell from its 8 nodes. The second idea is to produce a tessellation for the boundary of the object on the base of the intersections of such boundary with the edges of the grid. Please note that the boundary can be expressed in any way, for example it can be a triangle mesh, an implicit or a parametric surface. The only requirement is that the intersection between the boundary and the grid edges can be computed. This paper shows how the interpolation of the deformation inside the cells can be used to produce discontinuities in the deformation function, and the intersections of the cut surface can be used to visually show the cuts on the object. The Splitting Cubes is essentially a tessellation algorithm for growing, deformable surface and it can be applied to any method for animating deformable objects. In this paper the case of the mesh-free methods (MMs) is considered: in this context, we described a practical GPU friendly method, that we named the Extended Visibility criterion, to introduce discontinuities of the deformation.