Introduction to circle packing download

This is a preview of subscription content, access via your institution. Rent this article via DeepDyve. Andreev, E. Sbornik 81, No. Sbornik 83 c : — [Russian]. Ford, Lester R. Koebe, P. Leipzig Math. Google Scholar. Morgan, John W. Differential Geometry 26 : — Prehistory: I started developing CirclePack using the C language in the early 's, with continual improvements in capability, graphics, and features as the mathematics and its applications evolved.

I have always treated the software as an experimental laboratory for discrete conformal geometry and discrete analytic function theory.

This worked fine under Linux, and thanks to Fedor Andreev, there was a Windows version. Initial release of software was in Clic k here for current version. Current Version: The current release is an all Java version Java 1. This is a much more capable program and it seems to work on all platforms. Maps between circle packings, which preserve tangency and orientation, act many ways as discrete analogues of analytic functions.

Moreover, work flowing from a 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. Contact me if you have questions about my research, or would like to discuss any other topics. Phone: Fax: Email: kstephe2 utk. 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!

Maps between circle packings, which preserve tangency and orientation, act in many ways as discrete analogues of analytic functions.

Moreover, work flowing from a conjecture of Thurston, proven by Burt Rodin and Dennis Sullivan, shows that classical analytic functions and more general classical conformal objects can be approximated usin g circle packings.