Computational Geometry: Theory and Applications
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 flattening the cone in the plane. The conical existence results support a type of source unfolding of the surface of a polyhedron, described elsewhere.
Cones, Curve development, Polyhedra, Unfolding
© the authors
OʼRourke, Joseph and Vîlcu, Costin, "Development of Curves on Polyhedra Via Conical Existence" (2014). Computer Science: Faculty Publications, Smith College, Northampton, MA.