3D Gaussian Splatting (3DGS) achieves an appealing balance between rendering quality and efficiency, but relies on approximating 3D Gaussians as 2D projections--an assumption that degrades accuracy, especially under generic large field-of-view (FoV) cameras. Despite recent extensions, no prior work has simultaneously achieved both projective exactness and real-time efficiency for general cameras. We introduce 3DGEER, a geometrically exact and efficient Gaussian rendering framework. From first principles, we derive a closed-form expression for integrating Gaussian density along a ray, enabling precise forward rendering and differentiable optimization under arbitrary camera models. To retain efficiency, we propose the Particle Bounding Frustum (PBF), which provides tight ray-Gaussian association without BVH traversal, and the Bipolar Equiangular Projection (BEAP), which unifies FoV representations, accelerates association, and improves reconstruction quality. Experiments on both pinhole and fisheye datasets show that 3DGEER outperforms prior methods across all metrics, runs 5x faster than existing projective exact ray-based baselines, and generalizes to wider FoVs unseen during training--establishing a new state of the art in real-time radiance field rendering.

翻译：三维高斯泼溅（3DGS）在渲染质量与效率之间实现了理想的平衡，但其依赖于将三维高斯近似为二维投影的假设——这一假设会降低精度，尤其在通用大视场角相机下更为明显。尽管已有近期扩展研究，但此前尚无工作能同时为通用相机实现投影精确性与实时效率。本文提出3DGEER，一个几何精确且高效的高斯渲染框架。我们从基本原理出发，推导出沿光线积分高斯密度的闭式表达式，从而在任意相机模型下实现精确的前向渲染与可微分优化。为保持效率，我们提出了粒子边界视锥体（PBF），无需BVH遍历即可提供紧密的光线-高斯关联；以及双极等角投影（BEAP），它统一了视场角表示、加速了关联过程并提升了重建质量。在针孔相机与鱼眼相机数据集上的实验表明，3DGEER在所有指标上均优于现有方法，运行速度比现有基于投影精确光线的基线快5倍，并能泛化至训练时未见的更宽视场角——从而在实时辐射场渲染领域确立了新的技术标杆。