Scalable GPU Construction of 3D Voronoi and Power Diagrams

TL;DR

This paper introduces a highly parallel GPU algorithm for efficiently constructing large-scale 3D Voronoi and power diagrams, overcoming previous scalability and heterogeneity limitations.

Contribution

It presents a novel GPU-based method that constructs convex cells through progressive clipping, enabling scalable and general construction of Voronoi and power diagrams.

Findings

Achieves performance comparable to state-of-the-art methods on small and moderate sizes.

Demonstrates robust scalability to large point sets and diverse distributions.

Generalizes naturally to power diagrams without extra assumptions.

Abstract

Voronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being extensively studied, the construction of 3D Voronoi diagrams for large-scale point sets remains computationally expensive, limiting their adoption in large-scale applications. Existing CPU-based approaches typically rely on computing its dual, the Delaunay tetrahedralization, but are prohibitively slow for large diagrams, while GPU-based methods either struggle to scale efficiently to large point sets or assume homogeneous point distributions. The weighted case, power diagrams, is even less explored in this context. Existing approaches are typically tailored to the application at hand, assuming homogeneous point distributions and small weight variations, making them unsuitable for general use in more complex heterogeneous data. In this paper, we present a highly parallelizable GPU algorithm for the fast construction of large-scale 3D Voronoi and power diagrams. Our approach constructs each convex cell from a weighted 3D point by progressively clipping an initial cell volume against bisecting planes induced by candidate neighboring points. To efficiently identify candidate neighbors under arbitrary spatial distributions, we introduce a culling criterion based on directional geometric bounds of the evolving cell, combined with a hierarchical best-first traversal of bounding volumes. We achieve performance on par with state-of-the-art Delaunay tetrahedralization methods on small and moderate problem sizes, while exhibiting robust scalability to large point sets and diverse spatial distributions. Moreover, our method naturally generalizes to power diagrams without additional assumptions. See https://research.zenseact.com/publications/paragram .