Abstract: Circle packings are configurations of circles with
specified pattern of tangencies. These objects are in the heart of
the emerging theory of discrete analytic function theory with
interesting geometric, combinatorial, complex analytic and
computational aspects as well as surprising applications such as
mapping of the human brain.

Our problem: Given a graph G which defines a triangulation of
a simply connected surface, it is possible to construct a corresponding
pattern of circles (packing), such that each vertex of G represents
a circle center and the edges denote circle tangency.

Computing the radii of the circle packing from the tangency pattern can be
a daunting task which may involve solving a very large system of
non-linear equations.
In this talk we present a very efficient numerical algorithm to compute
such radii using an iterative process which is based on key geometric results.

This talk is based on a work by Charles R. Collins and Kenneth Stephenson.