An algorithm for the Euclidean cell decomposition of a cusped strictly convex projective surface

TL;DR

This paper extends Weeks' algorithm to compute Euclidean cell decompositions from hyperbolic surfaces to strictly convex projective surfaces, broadening the applicability of geometric decomposition methods.

Contribution

It generalizes an existing algorithm for hyperbolic surfaces to the setting of strictly convex projective surfaces, enabling new computational approaches.

Findings

Weeks' algorithm successfully generalized to convex projective surfaces

The decomposition method applies to a broader class of geometric structures

Provides a computational tool for convex projective surface analysis

Abstract

Cooper and Long generalised Epstein and Penner's Euclidean cell decomposition of cusped hyperbolic manifolds of finite volume to non-compact strictly convex projective manifolds of finite volume. We show that Weeks' algorithm to compute this decomposition for a hyperbolic surface generalises to strictly convex projective surfaces.