Software for the Thompson and Funk Polygonal Geometry

Hridhaan Banerjee; Carmen Isabel Day; Auguste H. Gezalyan; Olga Golovatskaia; Megan Hunleth; Sarah Hwang; Nithin Parepally; Lucy Wang; David M. Mount

arXiv · 2503.01988

Software for the Thompson and Funk Polygonal Geometry

Hridhaan Banerjee·Carmen Isabel Day·Auguste H. Gezalyan·Olga Golovatskaia·Megan Hunleth·Sarah Hwang·Nithin Parepally·Lucy Wang·David M. Mount

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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.

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Hridhaan Banerjee, Carmen Isabel Day, Auguste H. Gezalyan, Olga Golovatskaia, Megan Hunleth, Sarah Hwang, Nithin Parepally, Lucy Wang, David M. Mount. 2025-03-03. Software for the Thompson and Funk Polygonal Geometry. https://arxiv.org/abs/2503.01988

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