Uniform Sampling of Surfaces by Casting Rays

TL;DR

This paper presents a general ray casting method for uniform surface sampling applicable to implicit and explicit shapes, improving efficiency and enabling advanced sampling techniques without mesh extraction.

Contribution

It introduces a novel, general scheme for uniform surface sampling via ray intersections, especially effective for implicit surfaces using sphere marching.

Findings

The method guarantees uniformity of sampling.

It is significantly more efficient than existing strategies.

Extensions include blue noise and stratified sampling, with applications to neural implicit surfaces.

Abstract

Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used implicit surfaces. This work studies a simple and general scheme for sampling points on a surface, which is derived from a connection to the intersections of random rays with the surface. Concretely, given a subroutine to cast a ray against a surface and find all intersections, we can use that subroutine to uniformly sample white noise points on the surface. This approach is particularly effective in the context of implicit signed distance functions, where sphere marching allows us to efficiently cast rays and sample points, without needing to extract an intermediate mesh. We analyze the basic method to show that it guarantees uniformity, and find experimentally that it is significantly more efficient than alternative strategies on a variety of representations. Furthermore, we show extensions to blue noise sampling and stratified sampling, and applications to deform neural implicit surfaces as well as moment estimation.