7 papers
On the Duality of Coverings in Hilbert Geometry
Sunil Arya, David M. Mount
We prove polarity duality for covering problems in Hilbert geometry. Let and be convex bodies in where and $\operatorname{i…
Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry
Hridhaan Banerjee, Soren Brown, June Cagan +9
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 thi…
Software for the Thompson and Funk Polygonal Geometry
Hridhaan Banerjee, Carmen Isabel Day, Auguste H. Gezalyan +6
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.…
French Onion Soup, Ipelets for Points and Polygons
Klint Faber, Auguste H. Gezalyan, Adam Martinson +6
There are many structures, both classical and modern, involving point-sets and polygons whose deeper understanding can be facilitated through interactive visualizations. The Ipe ex…
On The Heine-Borel Property and Minimum Enclosing Balls
Hridhaan Banerjee, Carmen Isabel Day, Megan Hunleth +6
In this paper, we contribute a proof that minimum radius balls over metric spaces with the Heine-Borel property are always LP type. Additionally, we prove that weak metric spaces,…
Ipelets for the Convex Polygonal Geometry
Nithin Parepally, Ainesh Chatterjee, Auguste Gezalyan +5
There are many structures, both classical and modern, involving convex polygonal geometries whose deeper understanding would be facilitated through interactive visualizations. The…
Delaunay Triangulations in the Hilbert Metric
Auguste Gezalyan, Soo Kim, Carlos Lopez +3
The Hilbert metric is a distance function defined for points lying within the interior of a convex body. It arises in the analysis and processing of convex bodies, machine learning…