{"slug": "power-foam-unified-3dgs-representation-for-both-rasterization-and-ray-tracing", "title": "Power Foam – unified 3DGS representation for both rasterization and ray-tracing", "summary": "Researchers introduced Power Foam, a differentiable 3D representation that unifies rasterization and ray tracing by generalizing Voronoi foams to bounded power diagrams, achieving rasterization performance competitive with 3DGS-MCMC while preserving state-of-the-art ray tracing efficiency. The method decouples geometry from appearance using oriented surfaces and embedded textures, enabling real-time differentiable rendering.", "body_md": "We introduce a differentiable 3D representation that unifies the ray tracing\ncapabilities of foam-based ray tracing with the efficiency of modern rasterization\npipelines. While prior foam representations enable constant-time ray traversal\nthrough an explicit volumetric partition of space, their potentially unbounded cells\nhinder efficient tile-based rasterization. We address this limitation by generalizing\nVoronoi foams to bounded **power diagrams** with controllable cell extents,\nenabling spatially bounded primitives without requiring expensive Delaunay\ntriangulations during training.\nWe further introduce an oriented surface formulation that explicitly models\ninterfaces between interior and exterior regions, and decouple geometry from\nappearance by embedding differentiable texture directly on these surfaces. Together,\nthese contributions yield a representation that preserves state-of-the-art ray\ntracing efficiency while achieving rasterization performance competitive with current\ngeneration 3DGS, providing a practical path toward unified real-time differentiable\nrendering.\n\nOur recipe is to employ *Voronoi at every scale*: a bounded\n*power* diagram gives us 3D geometry made of cells\nwith controllable extent, a 2D Voronoi on each cell\nprovides texture and displacement, and a spherical Voronoi\non each texture site captures directional radiance.\n\nOur goal is to construct a representation that can be both rasterized\nand ray traced, but while foam structures are natively amenable to\nray tracing, efficient rasterization requires bounded primitives that\nan unbounded foam lacks. Without such bounds, testing a cell's\nintersection with image tiles demands an unwieldy projected convex\nhull in screen space and often spans large regions where the cell is\nfully occluded. The simplest remedy is to restrict each Voronoi foam\ncell to its intersection with a rasterization-friendly bounding\nprimitive such as a sphere — a structure already provided by\ncomputational geometry as the weighted α-complex, or more\nspecifically its dual, which we refer to as the\n*bounded power diagram*. As illustrated below, the Voronoi\ndiagram (left) builds cell faces from planes equidistant to the cell\nsites and the power diagram (center) builds them from per-cell radii;\nusing those radii as bounding spheres (right) then ensures that all\ncell boundaries have gradients with respect to every cell parameter.\n\nRay traversal additionally requires an adjacency graph between neighbouring cells: Radiant Foam obtained this from the Delaunay triangulation of its sites (left), and an unbounded power diagram would analogously require a regular triangulation (center). The bounded power diagram, in contrast, needs only its α-complex (right, blue), which drops edges between non-overlapping spheres and is therefore cheaper to build. We can simplify construction even further by replacing it with the Čech complex — the graph of all pairwise-overlapping spheres — which is a strict superset of the α-complex (right, blue + green). This approximation costs only a small amount of rendering speed while leaving the final output exactly correct.\n\nFinally, for our decoupled geometry and appearance framework, the dipole face acts as a proxy for macro-scale geometry, while detail sites \\( s_i \\) are optimized to capture high-frequency geometric and appearance details without increasing the primitive count. As illustrated below by zooming into a leaf-tip cell of the Garden scene, displacement values \\( d_i \\) associated with each detail site push the surface up or down locally along the axis of the dipole, and our soft Voronoi formulation distributes both these displacements and the directional radiance \\( c_i \\) of each detail site across the dipole plane (shown top-down, with displacement, and side, left to right).\n\nPower Foam is the only method that simultaneously matches the\nrasterization FPS of the corresponding state-of-the-art\nrasterizer (3DGS-MCMC) *and* the ray tracing FPS\nof the corresponding state-of-the-art ray tracer (Radiant Foam).\n\nOur method achieves rendering quality comparable to 3DGUT and better than Radiant Foam. Specifically, we match the rasterization speed of 3DGUT while delivering superior ray tracing performance, and we achieve parity with Radiant Foam in ray tracing efficiency. For each scene, we display the ray tracing and rasterization frame rates (reported in that order) as an overlay in the top-right corner of the rendering.\n\nWe demonstrate Power Foam's ability to render fisheye images with both ray tracing and rasterization. Our pop-free sorting and exact volume rendering enable artifact-free fisheye rasterization — a regime where conventional rasterization-based methods typically fail.\n\nOur representation retains the ray tracing capabilities of Radiant Foam and can hence be used to model complex light-transport phenomena.\n\n```\n@article{govindarajan2026powerfoam,\n  title   = {Power Foam: Unifying Real-Time Differentiable Ray Tracing and Rasterization},\n  author  = {Govindarajan, Shrisudhan and Rebain, Daniel and Verbin, Dor and\n             Yi, Kwang Moo and Prabhu, Anish and Tagliasacchi, Andrea},\n  journal = {arXiv},\n  year    = {2026},\n}\n```\n\n", "url": "https://wpnews.pro/news/power-foam-unified-3dgs-representation-for-both-rasterization-and-ray-tracing", "canonical_source": "https://powerfoam.github.io/", "published_at": "2026-08-11 09:33:52+00:00", "updated_at": "2026-08-11 09:40:32.957660+00:00", "lang": "en", "topics": ["computer-vision", "artificial-intelligence", "machine-learning"], "entities": ["Power Foam", "3DGS-MCMC", "Radiant Foam"], "alternates": {"html": "https://wpnews.pro/news/power-foam-unified-3dgs-representation-for-both-rasterization-and-ray-tracing", "markdown": "https://wpnews.pro/news/power-foam-unified-3dgs-representation-for-both-rasterization-and-ray-tracing.md", "text": "https://wpnews.pro/news/power-foam-unified-3dgs-representation-for-both-rasterization-and-ray-tracing.txt", "jsonld": "https://wpnews.pro/news/power-foam-unified-3dgs-representation-for-both-rasterization-and-ray-tracing.jsonld"}}