Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry
Computational Geometry
2026-03-31 v1
Abstract
Higher-order Voronoi diagrams and Delaunay mosaics in polygonal metrics have only recently been studied, yet no tools exist for visualizing them. We introduce a tool that fills this gap, providing dynamic interactive software for visualizing higher-order Voronoi diagrams and Delaunay mosaics along with clustering and tools for exploring overlap and outer regions in the Hilbert polygonal metric. We prove that order Voronoi cells are not always star-shaped and establish complexity bounds for our algorithm, which generates all order Voronoi diagrams at once. Our software unifies and extends previous tools for visualizing the Hilbert, Funk, and Thompson geometries.
Keywords
Cite
@article{arxiv.2603.27009,
title = {Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry},
author = {Hridhaan Banerjee and Soren Brown and June Cagan and Auguste H. Gezalyan and Megan Hunleth and Veena Kailad and Chaewoon Kyoung and Rowan Shigeno and Yasmine Tajeddin and Andrew Wagger and Kelin Zhu and David M. Moun},
journal= {arXiv preprint arXiv:2603.27009},
year = {2026}
}