用神经场隐式构建任意距离下的广义Voronoi图，无需复杂几何构造。
Neural Approximation of Generalized Voronoi Diagrams
- 基于分层神经场学习连续可微的近似函数，通过最大值区域定义Voronoi单元
- 在多种点集与距离度量下准确恢复细胞结构与边界几何，误差可忽略
- 适合需要高效、通用且可微分几何建模的研究者，如机器人路径规划
我们提出VoroFields，一种分层神经场框架，用于在低维空间中对有限几何点集的广义Voronoi图进行逼近，支持任意可计算的点到点距离。不同于传统的组合式构造方法，VoroFields学习一个连续且可微的代理函数，其极大值结构隐式诱导出划分结果。Voronoi单元对应于该场的最大值区域，边界由竞争点响应相等处定义。通过分层分解，仅对接近包络过渡层的区域进行细化，显著降低组合复杂度。在不同点集家族和度量空间中的实验表明，该方法无需特定形状构造即可准确恢复细胞结构与边界几何。
原文摘要 · Abstract (English)
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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