Software for the Thompson and Funk Polygonal Geometry
Computational Geometry
2025-03-05 v1 Metric Geometry
Abstract
Metric spaces defined within convex polygons, such as the Thompson, Funk, reverse Funk, and Hilbert metrics, are subjects of recent exploration and study in computational geometry. This paper contributes an educational piece of software for understanding these unique geometries while also providing a tool to support their research. We provide dynamic software for manipulating the Funk, reverse Funk, and Thompson balls in convex polygonal domains. Additionally, we provide a visualization program for traversing the Hilbert polygonal geometry.
Cite
@article{arxiv.2503.01988,
title = {Software for the Thompson and Funk Polygonal Geometry},
author = {Hridhaan Banerjee and Carmen Isabel Day and Auguste H. Gezalyan and Olga Golovatskaia and Megan Hunleth and Sarah Hwang and Nithin Parepally and Lucy Wang and David M. Mount},
journal= {arXiv preprint arXiv:2503.01988},
year = {2025}
}