Software for the Thompson and Funk Polygonal Geometry
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arXiv
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866912257611399168 |
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| author | Banerjee, Hridhaan Day, Carmen Isabel Gezalyan, Auguste H. Golovatskaia, Olga Hunleth, Megan Hwang, Sarah Parepally, Nithin Wang, Lucy Mount, David M. |
| author_facet | Banerjee, Hridhaan Day, Carmen Isabel Gezalyan, Auguste H. Golovatskaia, Olga Hunleth, Megan Hwang, Sarah Parepally, Nithin Wang, Lucy Mount, David M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Software for the Thompson and Funk Polygonal Geometry Banerjee, Hridhaan Day, Carmen Isabel Gezalyan, Auguste H. Golovatskaia, Olga Hunleth, Megan Hwang, Sarah Parepally, Nithin Wang, Lucy Mount, David M. Computational Geometry Metric Geometry 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. |
| title | Software for the Thompson and Funk Polygonal Geometry |
| topic | Computational Geometry Metric Geometry |
| url | https://arxiv.org/abs/2503.01988 |