Neural Approximation of Generalized Voronoi Diagrams
Provides a continuous, differentiable surrogate for Voronoi diagrams, enabling applications in geometry processing and spatial analysis where traditional methods are infeasible.
VoroFields introduces a neural-field framework to approximate generalized Voronoi diagrams for arbitrary distance functions, achieving accurate cell and boundary recovery without combinatorial construction.
We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of constructing the diagram combinatorially, VoroFields learns a continuous, differentiable surrogate whose maximizer structure induces the partition implicitly. The Voronoi cells correspond to maximizer regions of the field, with boundaries defined by equal responses between competing sites. A hierarchical decomposition reduces the combinatorial complexity by refining only near envelope transition strata. Experiments across site families and metrics demonstrate accurate recovery of cells and boundary geometry without shape-specific constructions.