Neural Approximation of Generalized Voronoi Diagrams
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911549592961024 |
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| author | Rigas, Panagiotis Ioannakis, George Emiris, Ioannis |
| author_facet | Rigas, Panagiotis Ioannakis, George Emiris, Ioannis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26964 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural Approximation of Generalized Voronoi Diagrams Rigas, Panagiotis Ioannakis, George Emiris, Ioannis Computational Geometry Machine Learning 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. |
| title | Neural Approximation of Generalized Voronoi Diagrams |
| topic | Computational Geometry Machine Learning |
| url | https://arxiv.org/abs/2603.26964 |