Meshless Voronoi on the GPU

Nicolas Ray 1 Dmitry Sokolov 1 Sylvain Lefebvre 2 Bruno Lévy 1
1 ALICE - Geometry and Lighting
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
2 MFX - Matter from Graphics
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [52 references]  Display  Hide  Download

https://hal.inria.fr/hal-01927559
Contributor : Dmitry Sokolov <>
Submitted on : Wednesday, November 21, 2018 - 1:35:51 PM
Last modification on : Monday, May 6, 2019 - 10:32:06 AM
Long-term archiving on : Friday, February 22, 2019 - 12:33:42 PM

File

voroGPU.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Nicolas Ray, Dmitry Sokolov, Sylvain Lefebvre, Bruno Lévy. Meshless Voronoi on the GPU. ACM Transactions on Graphics, Association for Computing Machinery, In press, 37, ⟨10.1145/3272127.3275092⟩. ⟨hal-01927559⟩

Share

Metrics

Record views

959

Files downloads

1101