Analysis of Dynamic Voronoi Diagrams in the Hilbert Metric

2023/04/05 by Bumpus, Madeline, Dai, Xufeng Caesar, Gezalyan, Auguste H. +4
#Computational Geometry (cs.CG) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2304.02745

Abstract

The Hilbert metric is a projective metric defined on a convex body which generalizes the Cayley-Klein model of hyperbolic geometry to any convex set. In this paper we analyze Hilbert Voronoi diagrams in the Dynamic setting. In addition we introduce dynamic visualization software for Voronoi diagrams in the Hilbert metric on user specified convex polygons.

Related

• Voronoi Diagrams in the Hilbert Metric
• Dynamics of Hilbert nonexpansive maps
• Convex real projective structures and Hilbert metrics
• Dilation, smoothed distance, and minimization diagrams of convex functions
• Planar Voronoi Diagrams for Sums of Convex Functions, Smoothed Distance and Dilation