Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural approaches have shown promise in learning UDFs, they often suffer from numerical instability, high computational cost, and limited controllability. We present a lightweight, network-free method, Voronoi-Assisted Diffusion (VAD), for computing UDFs directly from unoriented point clouds. Our approach begins by assigning bi-directional normals to input points, guided by two Voronoi-based geometric criteria encoded in an energy function for optimal alignment. The aligned normals are then diffused to form an approximate UDF gradient field, which is subsequently integrated to recover the final UDF. Experiments demonstrate that VAD robustly handles watertight and open surfaces, as well as complex non-manifold and non-orientable geometries, while remaining computationally efficient and stable.

翻译：无符号距离场（UDFs）为具有任意拓扑结构的三维形状提供了灵活的表示方法，包括开放与封闭曲面、可定向与不可定向几何体以及非流形结构。尽管近期的神经网络方法在学习UDFs方面展现出潜力，但这些方法通常存在数值不稳定性、计算成本高和可控性有限等问题。本文提出一种轻量级、无需网络的Voronoi辅助扩散方法，用于直接从无定向点云计算UDFs。我们的方法首先通过两个基于Voronoi的几何准则（编码于能量函数中以实现最优对齐）为输入点分配双向法向量。随后通过对齐法向量进行扩散，形成近似的UDF梯度场，最终通过积分重建得到完整的UDF。实验表明，VAD方法能够稳健处理水密与开放曲面，以及复杂的非流形与不可定向几何结构，同时保持计算高效性和稳定性。