Gap Processing for Adaptive Maximal Poisson-Disk Sampling

TL;DR

This paper introduces a geometric analysis and efficient algorithms for generating adaptive maximal Poisson-disk sets with varying radii, enhancing sampling and surface remeshing techniques.

Contribution

It provides a novel gap analysis framework and algorithms for adaptive Poisson-disk sampling on Euclidean spaces and manifolds, improving existing methods.

Findings

Effective gap detection and updating algorithms

Enhanced surface remeshing techniques

Improved adaptive sampling quality

Abstract

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.