Edge-Unfolding Nearly Flat Convex Caps

07/04/2017

∙

by   Joseph O'Rourke, et al.

∙

0

∙

share

This paper proves a conjecture from [LO17]: A nearly flat, acutely triangulated convex cap C has an edge-unfolding to a non-overlapping polygon in the plane. "Nearly flat" means that every face normal forms a sufficiently small angle with the z-axis. Although the result is not surprising, the proof relies on some recently developed concepts, angle-monotone and radially monotone curves.