ADS: Random Sampling of Occupancy Functions using Adaptive Delaunay Scaffolding

Suzuran Takikawa
Leo Foord-Kelcey
Oliver Oxford
Nicholas Vining
Alla Sheffer

- University of British Columbia, Canada
- University of British Columbia, Canada
- University of British Columbia, Canada
- NVIDIA, Canada and University of British Columbia, Canada
- University of British Columbia, Canada

SIGGRAPH 2026 Conference Paper

Dense random sampling and surfacing of shapes encoded via implicit occupancy functions (OFs) are critical elements of many applications. Existing methods largely provide either one or the other of random sampling or mesh surfaces: ray shooting approaches deliver random samples with no connectivity, and grid-based methods deliver mesh surfaces but their sampling is highly biased. We propose a new method which delivers both pseudorandom OF surface samples and an isosurface mesh connecting them. Our method achieves these goals while requiring an order of magnitude fewer function evaluations than prior approaches. Key to our Adaptive Delaunay Sampling (ADS) approach is a progressively computed Delaunay tetrahedralization of points in 3D space, which we use as a sampling and surfacing scaffold. Starting from an initial coarse Delaunay scaffold, we repeatedly refine crossing edges, ones whose end vertices lie on opposite sides of the surface, augmenting the scaffold with points closer and closer to the surface. Each refinement step uses the Delaunay criterion to incorporate the newly added vertices into the scaffold, introducing new crossing edges. We use the intersections of fine crossing edges with the OF surface as the output samples, and use the marching tetrahedra method to surface these samples. We subsequently use normal estimation to densify the sampling near fine features and in areas of high surface curvature. We validate ADS by sampling 150 inputs at different resolutions, and provide extensive comparisons to existing alternatives. Our experiments demonstrate significant improvement in accuracy/function evaluation count trade-off, and showcase downstream applications. We extensively test our method on diverse crown shapes and compare against baselines, demonstrating its effectiveness.

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Random (a) and uniformly random (b) ray-casting provide provably random sampling of occupancy surfaces but generate no connectivity information. Grid based isosurfacing methods such as Marching Cubes (c) or Occupancy dual contouring (d) output fully connected but grid-biased samplings. ADS generates pseudo-random samples and an isosurface connecting them (e). Inset spectral images highlight these differences: grid-based methods exhibit structured artifacts, while ADS and uniform sampling are largely artifact-free.

Additional visual comparisons of our ADS method to uniform ray casting, marching cubes (MC), and occupancy dual contouring (ODC). We achieve higher accuracy and higher sample count with fewer occupancy function evaluations and less time. Contrary to uniform ray casting, we generate both samples and iso-surfaces. Contrary to grid-based methods, we produce random, unbiased samplings.

A gallery of our samplings and isosurface meshes using different sampling resolutions and input sources. Skateboard and motorcycle (3DShape2VecSet), spiral, Sapphos, happy Buddha (NESI), Lucy, dragon, vaselion (Myles w/ Winding Numbers).