VoroLight: Learning Voronoi Surface Meshes via Sphere Intersection

Voronoi diagrams partition space into convex, watertight, and topologically consistent cells, properties that make them an attractive representation for geometric modeling, mesh generation, and simulation. 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, geometrically regular surface meshes. 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: a target mesh can be conformed to an implicit field, a point cloud or surface mesh, or a set of multi-view images, with 3D reconstruction from such data being one supported use case. 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 consistently produces smoother, more geometrically regular Voronoi surfaces than prior differentiable Voronoi methods, showing that higher-order degeneracy control is effective for regularizing Voronoi surface geometry.