See: http://blogs.testbit.eu/timj/2005/06/20/13062005/ (page moved)
Today we’ve been having a visit of Ileana Streinu at our university, where she gave a very interesting talk about intersection-free polygon unfolding in 2D space and related topics. One idea struck me as particularly interesting. A bit oversimplified, it is the reduction of available degrees of freedom in polygon expansion until only one degree of freedom is left for the expansion algorithm to operate on. An older but somewhat shorter explanation can be found in this paper.