{
  "$type": "site.standard.document",
  "bskyPostRef": {
    "cid": "bafyreigdcfuhcmfnakpx44mnyggs33oatlvwa4gdnb4w6e3er7b4twgahu",
    "uri": "at://did:plc:4rgrdigiftglskeax4wvmsev/app.bsky.feed.post/3miehyc3oby62"
  },
  "coverImage": {
    "$type": "blob",
    "ref": {
      "$link": "bafkreiflo6xt7is6b2iafwghkjahlgggocme5jwjsbeuqqwcywuvjhmszm"
    },
    "mimeType": "image/png",
    "size": 24783
  },
  "path": "/abs/2603.26964v1",
  "publishedAt": "2026-03-31T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Panagiotis Rigas",
    "George Ioannakis",
    "Ioannis Emiris"
  ],
  "textContent": "**Authors:** Panagiotis Rigas, George Ioannakis, Ioannis Emiris\n\nWe 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"
}