Quadrilateral Splatting for Real-Time Radiance Field Rendering

Triangle Splatting (TS) has recently emerged as an effective explicit, non-volumetric surface representation for novel-view synthesis (NVS) and real-time rendering, but each triangular primitive is defined over a three-vertex surface domain, which can limit its flexibility for modeling fine-scale local geometry and spatial appearance variation. This limited geometric flexibility can result in less clearly resolved surface-normal structure in regions containing fine geometric detail. We propose Quadrilateral Splatting (QS), which represents scenes using independently optimized planar quadrilateral elements with a continuous bilinear appearance field. The quadrilateral domain provides additional flexibility for modeling local surface geometry, while the continuous bilinear appearance field represents spatial color variation within each primitive. QS jointly optimizes quadrilateral geometry, per-primitive opacity, and view-dependent appearance through differentiable polygon rasterization and alpha compositing, with planar-convex retraction maintaining valid quadrilateral geometry during optimization. Experiments on Mip-NeRF 360 and NeRF Synthetic show improved PSNR, SSIM, and LPIPS over TS and 2DGS on indoor scenes, with clearer fine-scale geometry in rendered normal maps and comparable outdoor quality while preserving real-time rendering. These results demonstrate the effectiveness of quadrilateral primitives with continuous bilinear appearance fields for real-time radiance field rendering.