Computations may be done in either hyperbolic, euclidean, or spherical geometry, though the routines for the latter are not yet complete, for the theory behind the package, one must consult the research literature.
One of the author's primary interests concerns the parallels between the developing theory of circle packings and the classical theory of analytic functions.
A circle packing is a configuration of circles with a specified pattern of tangencies.
See the examples below; the circles typically must assume a variety of different sizes in order to fit together in a prescribed tangency pattern. (It is easy to confuse this with the well-known topic of `sphere packing' -- how many ping-pong balls fit in a box car -- but there is almost no contact between these two topics!!)
Circle packings were introduced by William Thurston in his Notes.
Maps between circle packings which preserve tangency and orientation act in many ways as discrete analogues of analytic functions. Moreover, work flowing from a 1985 conjecture of Thurston, proven by Burt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated using circle packings.
Circle packings are computable, so they are introducing an experimental, and highly visual, component to research in conformal geometry and related areas. Circle packings are also useful in graph embedding and have interesting connections to random walks.