Meshless Voronoi on the GPU - INRIA - Institut National de Recherche en Informatique et en Automatique Access content directly
Journal Articles ACM Transactions on Graphics Year : 2018

Meshless Voronoi on the GPU

Nicolas Ray
Dmitry Sokolov
Bruno Lévy


We propose a GPU algorithm that computes a 3D Voronoi diagram. Our algorithm is tailored for applications that solely make use of the geometry of the Voronoi cells, such as Lloyd's relaxation used in meshing, or some numerical schemes used in fluid simulations and astrophysics. Since these applications only require the geometry of the Voronoi cells, they do not need the combinatorial mesh data structure computed by the classical algorithms (Bowyer-Watson). Thus, by exploiting the specific spatial distribution of the point-sets used in this type of applications, our algorithm computes each cell independently, in parallel, based on its nearest neighbors. In addition, we show how to compute integrals over the Voronoi cells by decomposing them on the fly into tetrahedra, without needing to compute any global combinatorial information. The advantages of our algorithm is that it is fast, very simple to implement, has constant memory usage per thread and does not need any synchronization primitive. These specificities make it particularly efficient on the GPU: it gains one order of magnitude as compared to the fastest state-of-the-art multi-core CPU implementations. To ease the reproducibility of our results, the full documented source code is included in the supplemental material.
Fichier principal
Vignette du fichier
voroGPU.pdf (24.49 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01927559 , version 1 (21-11-2018)



Nicolas Ray, Dmitry Sokolov, Sylvain Lefebvre, Bruno Lévy. Meshless Voronoi on the GPU. ACM Transactions on Graphics, 2018, 37 (6), pp.1-12. ⟨10.1145/3272127.3275092⟩. ⟨hal-01927559⟩
2090 View
2169 Download



Gmail Mastodon Facebook X LinkedIn More