Metric-Driven Voronoi Diagrams: A Comprehensive Mathematical Framework

Document Type

Article

Publication Title

Computation

Abstract

Voronoi partitioning is a fundamental geometric concept with applications across computational geometry, robotics, optimization, and resource allocation. While Euclidean distance is the most commonly used metric, alternative distance functions can significantly influence the shape and properties of Voronoi cells. This paper presents a comprehensive mathematical analysis of various distance metrics used in Voronoi partitioning, including Euclidean, Manhattan, Minkowski, weighted, anisotropic, and geodesic metrics. We analyze their mathematical formulations, geometric properties, topological implications, and computational complexity. This work aims to provide a theoretical framework for selecting appropriate metrics for Voronoi-based modeling in diverse applications.

DOI

10.3390/computation13090212

Publication Date

9-1-2025

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