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.
An initial rough Voronoi surface is constructed from diverse inputs (implicit fields, point clouds, meshes, or multi-view images) using a boundary-reflection strategy. The surface is defined as Voronoi faces between oppositely labeled generators and refined via a differentiable Voronoi formulation.
Sphere-Intersection Training: To promote smooth surface geometry, we enforce controlled Voronoi degeneracy through sphere-intersection constraints. Each Voronoi surface vertex is associated with a trainable sphere, and each face defines symmetric target intersection points. We optimize sphere parameters and generator positions under a sphere-intersection loss that encourages higher-order equidistance among face-incident generators. This formulation couples neighboring face orientations and produces smooth, geometrically regular Voronoi surfaces while preserving intrinsic properties such as watertightness and convexity.
Volumetric Extension: The optimized surface is extended to a full volumetric Voronoi tessellation by introducing additional deep interior generators that do not interfere with the surface boundary. These interior generators are optimized under a centroidal Voronoi tessellation (CVT) objective to produce a uniform volumetric mesh with globally consistent surface–interior topology.
Volumetric mesh generation from implicit shape representations.
Mesh inputs are converted to point cloud reconstruction problems by densely sampling points on the target surface. Target mesh input reconstruction, compared to VoroMesh.
Reconstruction from noisy point clouds (clean to 2% noise), comparing VoroMesh and VoroLight performance. Use arrows to navigate through noise levels.
300-camera view inputs reconstruction, compared to TetSphere Splatting.
From an input front-view RGB image, we use Huanyuan3D to generate five additional RGB views (left, right, top, bottom, and back), as well as the corresponding normal fields of these total six views. VoroLight then reconstructs the 3D shape by optimizing the Voronoi surface to match six-view silhouette masks and normal fields via differentiable rasterization. After obtaining this refined geometry, the geometry is kept fixed, and a neural deferred shader (NDS) is trained on the RGB views to reproduce the input appearance on the Voronoi mesh.
VoroLight generates high-quality volumetric Voronoi meshes perfect for the creation of artistic 3D printed lamps. The convex cells allow light to pass through, creating beautiful patterns and effects. See the interactive lamp carousel at the top of this page for examples.
@article{lu2025vorolight,
title={VoroLight: Learning Voronoi Surface Meshes via Sphere Intersection},
author={Lu, Jiayin and Jiang, Ying and He, Yumeng and Yang, Yin and Jiang, Chenfanfu},
journal={arXiv preprint arXiv:2512.12984},
year={2025}
}Jiayin Lu is partially supported by the UCLA Institute for Digital Research and Education (IDRE) Postdoctoral Fellowship.