Linear-Time Poisson-Disk Patterns

TL;DR

This paper introduces a linear-time algorithm for generating Poisson-disc patterns efficiently, utilizing a grid-based approach and modeling point arrivals as a Poisson process, enabling rapid pattern creation.

Contribution

The paper presents a novel O(N) time algorithm for Poisson-disc pattern generation using a grid and Poisson process modeling, improving efficiency over previous methods.

Findings

Achieves linear time complexity for pattern generation

Uses a grid to ensure no more than one point per region

Models point arrivals with a Poisson process

Abstract

We present an algorithm for generating Poisson-disc patterns taking O(N) time to generate $N$ points. The method is based on a grid of regions which can contain no more than one point in the final pattern, and uses an explicit model of point arrival times under a uniform Poisson process.