# VoroLight: Learning Voronoi Surface Meshes via Sphere Intersection

arXiv: https://arxiv.org/abs/2512.12984 · HTML: https://mlsanity.com/paper/2512.12984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 22 of 22)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Wonder3D: Single Image to 3D using Cross-Domain Diffusion](https://mlsanity.com/paper/2310.15008/) (2023)
- [One-2-3-45: Any Single Image to 3D Mesh in 45 Seconds without Per-Shape Optimization](https://mlsanity.com/paper/2306.16928/) (2023)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generation](https://mlsanity.com/paper/2501.12202/) (2025)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [TextMesh: Generation of Realistic 3D Meshes From Text Prompts](https://mlsanity.com/paper/2304.12439/) (2023)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [Multi-View Mesh Reconstruction with Neural Deferred Shading](https://mlsanity.com/paper/2212.04386/) (2022)
- [TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes](https://mlsanity.com/paper/2405.20283/) (2024)
- [Differentiable Voronoi Diagrams for Simulation of Cell-Based Mechanical Systems](https://mlsanity.com/paper/2404.18629/) (2024)
- [VoroCrust: Voronoi Meshing Without Clipping](https://mlsanity.com/paper/1902.08767/) (2019)
- [An extension to VORO++ for multithreaded computation of Voronoi cells](https://mlsanity.com/paper/2209.11606/) (2022)

## Abstract (arXiv)

Voronoi diagrams naturally produce convex, watertight, and topologically consistent cells, making them an appealing representation for 3D shape reconstruction. However, standard differentiable Voronoi approaches typically optimize generator positions in stable configurations, which can lead to locally uneven surface geometry. We present VoroLight, a differentiable framework that promotes controlled Voronoi degeneracy for smooth surface reconstruction. Instead of optimizing generator positions alone, VoroLight associates each Voronoi surface vertex with a trainable sphere and introduces a sphere--intersection loss that encourages higher-order equidistance among face-incident generators. This formulation improves surface regularity while preserving intrinsic Voronoi properties such as watertightness and convexity. Because losses are defined directly on surface vertices, VoroLight supports multimodal shape supervision from implicit fields, point clouds, meshes, and multi--view images. By introducing additional interior generators optimized under a centroidal Voronoi tessellation objective, the framework naturally extends to volumetric Voronoi meshes with consistent surface--interior topology. Across diverse input modalities, VoroLight achieves competitive reconstruction fidelity while producing smoother and more geometrically regular Voronoi surfaces. Project page: https://jiayinlu19960224.github.io/vorolight/