We introduce a differentiable 3D representation that unifies the ray tracing capabilities of foam-based ray tracing with the efficiency of modern rasterization pipelines. While prior foam representations enable constant-time ray traversal through an explicit volumetric partition of space, their potentially unbounded cells hinder efficient tile-based rasterization. We address this limitation by generalizing Voronoi foams to bounded power diagrams with controllable cell extents, enabling spatially bounded primitives without requiring expensive Delaunay triangulations during training. We further introduce an oriented surface formulation that explicitly models interfaces between interior and exterior regions, and decouple geometry from appearance by embedding differentiable texture directly on these surfaces. Together, these contributions yield a representation that preserves state-of-the-art ray tracing efficiency while achieving rasterization performance competitive with current generation 3DGS, providing a practical path toward unified real-time differentiable rendering.

翻译：我们提出了一种可微的三维表示方法，该方法将基于泡沫（foam）的光线追踪能力与现代光栅化流水线的效率相统一。先前的泡沫表示通过显式的空间体积划分实现了常数时间的光线遍历，但其潜在的无限胞元阻碍了高效的基于图块（tile）的光栅化。我们通过将沃罗诺伊泡沫（Voronoi foams）推广到具有可控胞元范围的受限幂图（power diagram），从而在无需训练期间进行昂贵的德劳内三角剖分（Delaunay triangulation）的情况下，实现了空间受限的基元。此外，我们引入了一种定向表面公式，显式地对内部与外部区域之间的界面进行建模，并通过在这些表面上直接嵌入可微纹理，将几何形状与外观解耦。综合这些贡献，该表示在保持最先进光线追踪效率的同时，实现了与当前一代3DGS（三维高斯溅射）相竞争的光栅化性能，为统一的实时可微渲染提供了一条实用路径。