Deformable Triangle Splatting: Flexible Primitives for Real-Time Radiance Field Rendering

Novel view synthesis has recently been revolutionized by 3D Gaussian Splatting (3DGS), which enables real-time rendering through explicit primitive rasterization. However, existing methods tie visual fidelity strictly to the number of primitives: quality downscaling is achieved only through pruning primitives. We propose the first inherently scalable primitive for radiance field rendering. Fourier Splatting employs scalable primitives with arbitrary closed shapes obtained by parameterizing planar surfels with Fourier encoded descriptors. This formulation allows a single trained model to be rendered at varying levels of detail simply by truncating Fourier coefficients at runtime. To facilitate stable optimization, we employ a straight-through estimator for gradient extension beyond the primitive boundary, and introduce HYDRA, a densification strategy that decomposes complex primitives into simpler constituents within the MCMC framework. Our method achieves state-of-the-art rendering quality among planar-primitive frameworks and comparable perceptual metrics compared to leading volumetric representations on standard benchmarks, providing a versatile solution for bandwidth-constrained high-fidelity rendering.

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.

Triangle-based neural rendering bridges neural scene representations and conventional graphics pipelines by optimizing explicit geometric primitives compatible with standard rasterization hardware. However, existing approaches are evaluated almost exclusively within custom research renderers, obscuring their practical deployability in production engines. To bridge this gap, we introduce \textbf{MeshSplatBench}, a unified benchmark that systematically investigates triangle-based neural rendering across the complete pipeline from native optimization to game-engine deployment. MeshSplatBench establishes a standardized evaluation protocol while preserving each method's native optimization semantics, reproducing published results within $0.8\%$ PSNR deviation. Furthermore, we introduce a hierarchical Unity deployment protocol spanning three rendering tiers: native CUDA renderers, method-specific dedicated engine shaders, and standard opaque mesh pipelines, isolating the exact fidelity losses caused by engine adaptation \textit{vs.} representation reduction. Finally, we conduct a topological audit of reconstructed surfaces, demonstrating that explicit connectivity and shared indexing alone are insufficient to guarantee production-ready assets due to prevalent non-manifold structures, fragmented components, and boundary artifacts. Overall, MeshSplatBench demonstrates that rasterizability is merely a primitive-level attribute, whereas graphics readiness requires jthe holistic alignment of representation, topology, and engine compatibility. Source code will be released.