Automatic Visualization of 3D Complexes

A three-dimensional complex is a partition of a three-dimensional manifold into simple cells, faces, edges and vertices. We consider here the problem of automatically producing a ``nice'' geometric representation (in $\Re^{m}$, for $m\geq 3$) of an arbitrary 3D complex, given only its combinatorial description. The geometric realization is chosen by optimizing certain aesthetic criteria, measured by certain ``energy functions.''

1999