Optimal angle bounds for quadrilateral meshes

TL;DR

This paper demonstrates a linear-time method to mesh any simple planar n-gon with quadrilaterals having angles strictly between 60 and 120 degrees, ensuring quality and efficiency.

Contribution

It introduces a novel linear-time algorithm for quadrilateral meshing of planar polygons with strict angle bounds, improving mesh quality and computational speed.

Findings

Meshes with O(n) quadrilaterals are achievable in linear time.

All new angles in the mesh are bounded between 60 and 120 degrees.

The method guarantees mesh quality and efficiency for simple planar polygons.

Abstract

We show that any simple planar n-gon can be meshed in linear time by $O(n)$ quadrilaterals with all new angles bounded between $60$ and $120$ degrees.