Automatic visualization of two-dimensional cellular complexes

A two-dimensional cellular complex is a partition of a surface into a finite number of elements—faces (open disks), edges (open arcs), and vertices (points). The topology of a cellular complex is the abstract incidence and adjacency relations among its elements. Here we describe a program that, given only the topology of a cellular complex, computes a geometric realization of the same—that is, a specific partition of a specific surface in three-space—guided by various aesthetic and presentational criteria.