Presentations of circle packings on compact surfaces

Circle packings-as arrangements of circles with specific tangency patterns are geometrically very appealing. Current theory and computer software is unable to present (to visually represent) circle packings on certain (large) classes of surfaces. In particular, circle packings on compact, multiply connected surfaces are troublesome.

This thesis contains an expository overview of some of the key results in the theory of circle packing (namely, existence and uniqueness). Moreover, using the properties of circle packings and the properties of surface topology, an informative method for presenting circle packings is developed.

Fully automatized computer source code is provided which not only solves the presentation problem for the compact, multiply connected case, but which has also been generalized to supercede current methods in all other cases (except for spherical packings here not even a packing algorithm is known). The code was written in "C" and was tailor made for Kenneth Stephenson's CirclePack program.

Copious examples of general circle packings are provided; representative presentations of com- pact, multiply connected circle packings are given.