Visualization of three-dimensional maps

A three-dimensional map is a partition of a 3D manifold into topological polyhedra. We consider the problem of visualizing the topology of a three-dimensional map given only its combinatorial description. Our solution starts by automatically constructing a “nice” geometric realization of the map in R^m, for some m⩾4. The geometric realization is chosen by optimizing certain aesthetic criteria, measured by energy functions. We then project this model to R³, and display the resulting multi-celled solid object with a variety of specialized rendering techniques