Spherical Voronoi: Directional Appearance as a Differentiable Partition of the Sphere

Radiance field methods (e.g.~3D Gaussian Splatting) have emerged as a powerful paradigm for novel view synthesis, yet their appearance modeling often relies on Spherical Harmonics (SH), which impose fundamental limitations.SH struggle with high-frequency signals, exhibit Gibbs ringing artifacts, and critically fail to capture specular reflections -- a key component of realistic rendering. While alternatives like Spherical Gaussians offer improvements, they introduce significant optimization complexity.We propose Spherical Voronoi (SV) as a unified framework for appearance representation in 3D Gaussian Splatting.SV partitions the directional domain into learnable regions with smooth boundaries, providing an intuitive and stable parameterization for view-dependent effects. For diffuse appearance, SV achieves competitive results while maintaining simpler optimization compared to existing alternatives. For reflections -- where SH fundamentally fail -- we leverage SV as learnable reflection probes, taking reflected directions as input following principles from traditional graphics. This formulation achieves state-of-the-art results across both synthetic and real-world datasets, demonstrating that SV offers a principled, efficient, and general solution for appearance modeling in explicit 3D representations.