Development of Curves on Polyhedra Via Conical Existence
Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011
We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without overlap. Our primary proof technique shows that such curves "live on a cone," and then develops the curves by cutting the cone along a "generator" and attening the cone in the plane. The conical existence results support a type of source unfold- ing of the surface of a polyhedron, described elsewhere.
© the author
O'Rourke, Joseph and Vîlcu, Costin, "Development of Curves on Polyhedra Via Conical Existence" (2011). Computer Science: Faculty Publications, Smith College, Northampton, MA.