Ordinary Facet Angles of a Stroked Path Tessellated by Uniform Tangent Angle Steps Are Bounded by Twice the Step Angle

Abstract

We explain geometrically why ordinary facet angles of a stroked path tessellated from uniform tangent angle steps are bounded by twice the step angle. This fact means---excluding a small number of extraordinary facet angles straddling offset cusps---our polar stroking method bounds the facet angle size to less than $2\theta$ where $\theta$ is the tangent step angle.

arXiv comment9 pages, supplemental paper for "Polar Stroking: New Theory and Methods for Stroking Paths" (SIGGRAPH 2020) arXiv:2007.00308