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

TL;DR

This paper provides a geometric explanation for why facet angles in a stroked path tessellated with uniform tangent steps are bounded by twice the step angle, ensuring controlled facet size in the tessellation process.

Contribution

It introduces a geometric reasoning that explains the bound on facet angles in a specific tessellation method, improving understanding of the method's geometric properties.

Findings

Facet angles are bounded by twice the tangent step angle.

The method controls facet size except near offset cusps.

Provides geometric insight into tessellation bounds.

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.