Efficient barycentric point sampling on meshes

TL;DR

This paper introduces a fast, analytical method for unbiased random sampling of points on triangle meshes based on barycentric interpolation, verified through statistical tests and outperforming rejection sampling.

Contribution

It provides an efficient, easy-to-implement inversion algorithm for sampling on meshes with specified barycentric surface densities, improving over rejection sampling methods.

Findings

The algorithm is faster than rejection sampling on average.

It produces unbiased samples verified by statistical tests.

The method is simple to implement and applicable to various mesh densities.

Abstract

We present an easy-to-implement and efficient analytical inversion algorithm for the unbiased random sampling of a set of points on a triangle mesh whose surface density is specified by barycentric interpolation of non-negative per-vertex weights. The correctness of the inversion algorithm is verified via statistical tests, and we show that it is faster on average than rejection sampling.