Cutting and FEM deformation

My first try at combining FEM deformation and cutting used linear elasticity and solved the equations using the conjugate gradient algorithm. This was done instead of the much more popular mass-spring system. A simple form of cutting (that produced a jagged cut surface in its first incarnation) was also implemented. These results were presented at Eurographics 2000.

A later version, presented at MICCAI 2001, also repositioned nodes within the mesh to smooth the cut surface. At this point I discovered how hard 3D meshing really is: when you take a naive approach to flattening the cut surface, you also flatten elements, which have to be removed again by heuristic methods. Two animations from the MICCAI presentation are also available. The first one shows a modest cut in a small object . The second one shows two cuts in larger cube, and clearly demonstrates the lack of realism in linear elasticity.