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The method builds each convex cell by progressively clipping an initial volume against bisecting planes induced by candidate neighboring points. A culling criterion using directional geometric bounds, together with hierarchical best-first traversal of bounding volumes, efficiently identifies candidates under arbitrary spatial distributions. Results show performance comparable to state-of-the-art Delaunay tetrahedralization methods on small and moderate sizes, with robust scalability to large, heterogeneous point sets, and natural generalization to power diagrams.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/scalable-gpu-construction-of-3d-voronoi-and-power-diagrams/665473/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/scalable-gpu-construction-of-3d-voronoi-and-power-diagrams/665473.png","ImageObject",300,407,{"name":92,"@type":93},"Fahsai","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does the paper address?","Question",{"text":112,"@type":113},"It addresses the computational expense and limited scalability of constructing 3D Voronoi diagrams for large point sets, especially compared with slower CPU-based dual approaches and limited GPU methods.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the proposed GPU algorithm construct Voronoi cells?",{"text":117,"@type":113},"It constructs each convex cell from a weighted 3D point by progressively clipping an initial cell volume against bisecting planes from candidate neighboring points.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the method handle candidate neighbor search under arbitrary point distributions?",{"text":121,"@type":113},"It uses a culling criterion based on directional geometric bounds of the evolving cell combined with a hierarchical best-first traversal of bounding volumes to efficiently select candidates.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},665473,1793304381,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","Scalable GPU Construction of 3D Voronoi and Power Diagrams  \nDownloaded from: [https://research.chalmers.se](https://research.chalmers.se), 2026-10-29 20:06 UTC  \nCitation for the original published paper (version of record):  \nTaveira, B., Lindström, C., Fatemi, M. et al (2026) . Scalable GPU Construction of 3D Voronoi and Power Diagrams. Proceedings SIGGRAPH 2026 Conference Papers.  \n[http://dx.doi.org/10.1145/3799902.3811229](http://dx.doi.org/10.1145/3799902.3811229)  \nN. B. When citing this work, cite the original published paper.  \nresearch.chalmers.se offers the possibility of retrieving research publications produced at Chalmers University of Technology. It covers all kind of research output: articles, dissertations, conference papers, reports etc. since 2004. research.chalmers.se is administrated and maintained by Chalmers Library  \n(article starts on next page)  \nScalable GPU Construction of 3D Voronoi and Power Diagrams  \nBERNARDO TAVEIRA∗ , Chalmers University of Technology, Sweden and Zenseact, Sweden CARL LINDSTRÖM∗ , Chalmers University of Technology, Sweden and Zenseact, 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  \n∗ Both authors contributed equally to the paper.  \nAuthors’ Contact Information: Bernardo Taveira, Chalmers University of Technology, Gothenburg, Sweden and Zenseact, Gothenburg, Sweden, bernardo.taveira@chalmers. se; Carl Lindström, Chalmers University of Technology, Gothenburg, Sweden and Zenseact, Gothenburg, Sweden, [carl.lindstrom@chalmers.se](carl.lindstrom@chalmers.se); Maryam Fatemi, Zenseact, Gothenburg, Sweden, [maryam.fatemi@zenseact.com](maryam.fatemi@zenseact.com); Lars Hammarstrand, Chalmers University of Technology, Gothenburg, Sweden, [lars.hammarstrand@chalmers.se](lars.hammarstrand@chalmers.se); Fredrik Kahl, Chalmers University of Technology, Gothenburg, 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 979-8-4007-2554-8/26/07  \n[https://doi.org/10.1145/3799902.3811229](https://doi.org","cbCaia5p9hxGUNdb","https://ap.wps.com/l/cbCaia5p9hxGUNdb","pdf",5939239,11,"English","# Introduction\n# Problem Motivation\n# Proposed GPU Algorithm\n## Cell Construction by Clipping\n## Candidate Neighbor Culling and Traversal\n# Experimental Results and Scalability\n# Power Diagram Generalization\n# Reproducibility and Code Release\n# Licensing and Publication Details","[{\"question\":\"What problem does the paper address?\",\"answer\":\"It addresses the computational expense and limited scalability of constructing 3D Voronoi diagrams for large point sets, especially compared with slower CPU-based dual approaches and limited GPU methods.\"},{\"question\":\"How does the proposed GPU algorithm construct Voronoi cells?\",\"answer\":\"It constructs each convex cell from a weighted 3D point by progressively clipping an initial cell volume against bisecting planes from candidate neighboring points.\"},{\"question\":\"How does the method handle candidate neighbor search under arbitrary point distributions?\",\"answer\":\"It uses a culling criterion based on directional geometric bounds of the evolving cell combined with a hierarchical best-first traversal of bounding volumes to efficiently select candidates.\"}]","Scalable GPU Construction of 3D Voronoi and Power Diagrams | PDF",28]