VoroUDF: Meshing Unsigned Distance Fields with Voronoi Optimization

TL;DR

VoroUDF presents a Voronoi-based framework for reconstructing surfaces from unsigned distance fields, enabling faithful recovery of non-manifold, open-boundary, and sharp-feature geometries without sign estimations. It jointly optimizes an $L_1$ tangent energy and a feature-aware repulsion over a Voronoi partition, then constructs the mesh as the dual of a geodesic Voronoi diagram and applies thinning to produce a lightweight, real-time-friendly surface. The approach achieves state-of-the-art performance across non-manifold, CAD, and garment datasets, demonstrating improved topological consistency and geometric fidelity. This work advances UDF-to-mesh reconstruction by providing a topology-preserving, adaptable alternative to grid-based methods, with practical impact for graphics, simulation, and design workflows.

Abstract

We present VoroUDF, an algorithm for reconstructing high-quality triangle meshes from Unsigned Distance Fields (UDFs). Our algorithm supports non-manifold geometry, sharp features, and open boundaries, without relying on error-prone inside/outside estimation, restrictive look-up tables nor topologically noisy optimization. Our Voronoi-based formulation combines a L_1 tangent minimization with feature-aware repulsion to robustly recover complex surface topology. It achieves significantly improved topological consistency and geometric fidelity compared to existing methods, while producing lightweight meshes suitable for downstream real-time and interactive applications.

Figures (20)

• Figure 1: Unlike marching-cube-based methods guillard2022meshudfzhou2022capudfren2023geoudfstella2024nsdudf that rely on pseudo-sign estimation, double-covering-based methods hou2023dcudfchen2025dcudf2 that produce double-layered meshes, and dual-contouring-based methods zhang2023dualmeshUDF that introduce erroneous connectivity, our method is the only approach capable of reconstructing non-manifold structures (highlighted in red).
• Figure 2: Illustration of why marching-cubes-based methods (top row), double-covering-based methods (middle row), and dual-contouring-based methods (bottom row) fail to preserve the non-manifoldness of the iso-surface.
• Figure 3: Dual-contouring-based method zhang2023dualmeshUDF uses voxel grids struggles to reconstruct UDF iso-surfaces with thin layers, often resulting in zig-zag connectivity and holes when using a relatively small number of vertices. In contrast, our method, based on a Voronoi partition, avoids these issues and produces clean, consistent connectivity.
• Figure 4: Illustration of why our formulation uses $L_1$ tangent energy with Voronoi partitions, rather than $L_2$ tangent energy with voxel grids.
• Figure 5: Our method successfully reconstructs non-manifold structures from UDFs, whereas the double-covering-based method hou2023dcudf returns a two-layered mesh around non-manifold regions.