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arXiv · 2603.26964

Neural Approximation of Generalized Voronoi Diagrams

Panagiotis Rigas·George Ioannakis·Ioannis Emiris
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Abstract

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.

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Panagiotis Rigas, George Ioannakis, Ioannis Emiris. 2026-03-27. Neural Approximation of Generalized Voronoi Diagrams. https://arxiv.org/abs/2603.26964

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