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Experiments show state-of-the-art performance on small and moderate cases and robust scalability across large point sets and heterogeneous distributions, naturally extending to power diagrams.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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address?","Question",{"text":62,"@type":63},"It addresses the expensive construction of 3D Voronoi diagrams for large-scale point sets and the limited exploration of GPU methods for both Voronoi and weighted (power) cases under heterogeneous distributions.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How does the proposed GPU algorithm construct 3D cells?",{"text":67,"@type":63},"For each weighted 3D point, it constructs the convex cell by progressively clipping an initial cell volume with bisecting planes induced by candidate neighboring points.",{"name":69,"@type":60,"acceptedAnswer":70},"How are candidate neighbors identified efficiently?",{"text":71,"@type":63},"It uses a culling criterion based on directional geometric bounds of the evolving cell together with a hierarchical best-first traversal over bounding volumes to reduce unnecessary candidate 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Construction of 3D Voronoi and Power Diagrams  \nBERNARDO TAVEIRA∗ , Zenseact, Sweden and Chalmers University of Technology, Sweden CARL LINDSTRÖM∗ , Zenseact, Sweden and Chalmers University of Technology, Sweden MARYAM FATEMI, Zenseact, Sweden  \nLARS HAMMARSTRAND, Chalmers University of Technology, Sweden FREDRIK KAHL, Chalmers University of Technology, Sweden  \nLPIPS  \n0.325 0.300 0.275 0.250 0.225 0.200 0.175  \n0.150  \n300  \n200  \n100  \n0  \nTrain Time (min)  \nTraining Time (s)  \n2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0  \nNumber of Points (Millions)  \n20.0M  \n18.0M  \n16.0M  \n14.0M  \n12.0M  \n10.0M  \n8.0M  \n6.0M  \n4.0M  \nNumber ofPoints  \nVoronoi Volumetric Render  \nFig. 1. Scalability and perceptual quality. Our efficient construction of 3D Voronoi diagrams enables mesh-based neural rendering to scale to 20 million cells, and reveals a strong correlation between model capacity and perceptual quality. We apply our method to the Radiant Foam [Govindarajan et al. 2025] on the challenging “Garden” scene from the mip-NeRF 360 dataset [Barron et al. 2022]. (Left) The bottom plot shows that total training time (wall-clock, including all optimization steps) increases approximately linearly with the point-count limit. The top plot tracks the evolution of the LPIPS perceptual error across multiple training runs with different point budgets, demonstrating how higher point capacities allow for better visual convergence during training.(Right) A split view of the rendered image and a 2D slice of the Voronoi mesh, color-coded to reflect cell size, highlights the massive and highly varying cell density required to model this scene.  \nVoronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications in biology, physics simulation, and computer graphics. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being extensively studied, the construction of 3D Voronoi diagrams for largescale point sets remains computationally expensive, limiting their adoption in large-scale applications. Existing CPU-based approaches typically rely on  \n∗ Both authors contributed equally to the paper.  \nAuthors’ Contact Information: Bernardo Taveira, Zenseact, Sweden and Chalmers University of Technology, Sweden, [bernardo.taveira@chalmers.se](bernardo.taveira@chalmers.se); Carl Lindström, Zenseact, Sweden and Chalmers University of Technology, Sweden, carl.lindstrom@ [chalmers.se](chalmers.se); Maryam Fatemi, Zenseact, Sweden, [maryam.fatemi@zenseact.com](maryam.fatemi@zenseact.com); Lars Hammarstrand, Chalmers University of Technology, Sweden, lars.hammarstrand@ [chalmers.se](chalmers.se); Fredrik Kahl, Chalmers University of Technology, Sweden, fredrik.kahl@ [chalmers.se](chalmers.se).  \nThis work is licensed under a Creative Commons Attribution 4 .0 International License. SIGGRAPH Conference Papers ’26, Los Angeles, CA, USA  \n© 2026 Copyright held by the owner/author(s) .  \nACM ISBN 979-8-4007-2554-8/2026/07  \n[https://doi.org/10.1145/3799902.3811229](https://doi.org/10.1145/3799902.3811229)  \ncomputing 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.  \nIn 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 neighb","cbCais8JkZH45fL0","https://ap.wps.com/l/cbCais8JkZH45fL0","pdf",5922733,14,"English","# 1 Introduction\n## 2 Method Overview\n## 3 Neighbor Culling and Acceleration\n## 4 Experimental Results and Scalability\n## 5 Application to Neural Rendering","[{\"question\":\"What problem does the paper address?\",\"answer\":\"It addresses the expensive construction of 3D Voronoi diagrams for large-scale point sets and the limited exploration of GPU methods for both Voronoi and weighted (power) cases under heterogeneous distributions.\"},{\"question\":\"How does the proposed GPU algorithm construct 3D cells?\",\"answer\":\"For each weighted 3D point, it constructs the convex cell by progressively clipping an initial cell volume with bisecting planes induced by candidate neighboring points.\"},{\"question\":\"How are candidate neighbors identified efficiently?\",\"answer\":\"It uses a culling criterion based on directional geometric bounds of the evolving cell together with a hierarchical best-first traversal over bounding volumes to reduce unnecessary candidate checks.\"}]","Scalable GPU Construction of 3D Voronoi and Power Diagrams - Paper | PDF",35]