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.
