# Directed Distance Fields for Constant-Time Ray Queries on Gaussian Splatting

arXiv: https://arxiv.org/abs/2606.00817 · HTML: https://mlsanity.com/paper/2606.00817/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 18 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [GaussianShader: 3D Gaussian Splatting with Shading Functions for Reflective Surfaces](https://mlsanity.com/paper/2311.17977/) (2023)
- [GS-IR: 3D Gaussian Splatting for Inverse Rendering](https://mlsanity.com/paper/2311.16473/) (2023)
- [Relightable 3D Gaussians: Realistic Point Cloud Relighting with BRDF Decomposition and Ray Tracing](https://mlsanity.com/paper/2311.16043/) (2023)
- [3D Gaussian Ray Tracing: Fast Tracing of Particle Scenes](https://mlsanity.com/paper/2407.07090/) (2024)
- [Representing 3D Shapes with Probabilistic Directed Distance Fields](https://mlsanity.com/paper/2112.05300/) (2021)
- [RaySplats: Ray Tracing based Gaussian Splatting](https://mlsanity.com/paper/2501.19196/) (2025)
- [Neural directional distance field object representation for uni-directional path-traced rendering](https://mlsanity.com/paper/2306.16142/) (2023)

## Abstract (arXiv)

3D Gaussian Splatting (3DGS) renders new views of a scene in real time. Like every rasterizer, it answers only primary rays, the rays from the camera through the image. It cannot trace the secondary rays that shadows, ambient occlusion, and global illumination need. We turn a trained 3DGS scene into a ray oracle by distilling a Directed Distance Function (DDF). The DDF is a small neural field. It takes a ray, given by an origin and a direction, and returns the distance to the first surface and whether the ray hits anything. Each query is one forward pass. The field is 52~MB, and its size does not depend on the number of Gaussians, so its cost and memory stay flat as the scene grows. We make three points. First, we study what supervision a DDF needs. Depth rendered from the Gaussians is too blurry to teach thin parts, while clean distance supervision recovers them. Second, we measure speed. The DDF is 26 to 72 times faster than sphere tracing an equivalent signed distance field, and unlike a bounding volume hierarchy built over the Gaussians, even on dedicated RT-core hardware, its query time and memory do not grow with the scene. Third, we show a pipeline that needs no mesh: images give a 3DGS scene, a neural surface gives clean distances, and the DDF learns from them. We use the DDF as a secondary-ray oracle for global illumination. It reproduces reference ray-traced shadows at 30.3~dB and ambient occlusion at 21.3~dB across 142 objects, and on real captured scenes. Our codes are available at https://github.com/smlab-niser/ddf-gs.