VoroUDF: Meshing Unsigned Distance Fields with Voronoi Optimization

2026-02-02

AI Summary

This work proposes a Voronoi optimization–based mesh reconstruction method that directly recovers high-quality triangle meshes from unsigned distance fields (UDFs), overcoming common challenges such as topological inconsistencies and geometric distortions caused by non-manifold structures, sharp features, and open boundaries. By integrating L₁ tangent plane minimization with a feature-aware repulsion mechanism, the approach reconstructs complex surface topologies without requiring inside-outside classification or lookup tables. Notably, it is the first to combine Voronoi optimization with feature-aware repulsion, effectively eliminating topological noise and reducing reliance on prior assumptions inherent in conventional methods. The resulting meshes exhibit significantly improved topological consistency and geometric fidelity while remaining lightweight, making them well-suited for real-time and interactive applications.

Technology Category

Machine Learning: Learning with ManifoldsComputer Vision: 3D Computer VisionPlanning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsUser Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationWeb Mining and Content Analysis: Web data generation and simulation

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.

Problem

• Unsigned Distance Fields
• Mesh Reconstruction
• Non-manifold Geometry
• Sharp Features
• Open Boundaries

Innovation

• Voronoi optimization
• Unsigned Distance Field
• mesh reconstruction
• non-manifold geometry
• feature-aware repulsion