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One this volumetric data has been acquired, it can be stored in a number of different representations:

The voxel or octree approach is popular, because it is easy to implement and manipulate. However, this representation is not amenable to simulations which require deformation and collision.

The slab representation locally aligns a volumetric grid with the surface. But it can be difficult to initialize for arbitrary models and has a limited depth for manipulations.

I have chosen to work primarily with tetrahedral models, because they are appropriate for both interactive sculpting and physical simulations, such as the Finite Element Method.