GPU Voronoi Diagrams for Random Moving Seeds

TL;DR

This paper introduces a GPU-based algorithm for efficiently computing dynamic Voronoi diagrams with moving seeds, enabling real-time applications in particle simulations.

Contribution

The paper proposes the dynamic Jump Flooding Algorithm (dJFA), a faster variant of JFA for dynamic Voronoi diagrams with moving seeds, achieving significant speedup.

Findings

dJFA achieves up to 5.3x speedup over JFA

Maintains at least 88% similarity with standard methods

Enables real-time GPU computation of dynamic Voronoi diagrams

Abstract

The Voronoi Diagram is a geometrical structure that is widely used in scientific or technological applications where proximity is a relevant aspect to consider, and it also resembles natural phenomena such as cellular banks, rock formations or bee hives, among others. Typically, computing the Voronoi Diagram is done in a static context, that is, the location of the input seeds is defined once and does not change. In this work we study the dynamic case where seeds move, which leads to a dynamic Voronoi Diagram that changes over time. In particular, we consider uniform random moving seeds, for which we propose the \textit{dynamic Jump Flooding Algorithm} (dJFA), a variant of JFA that uses less iterations than the standard JFA. An experimental evaluation shows that dJFA achieves a speedup of up to $\sim 5.3 \times$ over JFA, while maintaining a similarity of at least $88\%$ and close to $100\%$ in many cases. These results contribute with a step towards the achievement of real-time GPU-based computation of dynamic Voronoi diagrams for any particle simulation.