SpUDD: Superpower Contouring of Unsigned Distance Data

2026-04-21

AI Summary

This work addresses the challenge of reconstructing arbitrary types of surfaces—including open, non-orientable, or non-manifold geometries—from discrete unsigned distance data. The authors propose a novel power diagram–based approach that introduces the concept of a “super-power contour” as a surface proxy, enabling the generation of polygonal meshes that accurately approximate the underlying geometry without requiring signed distance values or gradient information. Theoretical analysis establishes that, under increasing sampling density, the super-power contour converges to the true surface in the limit. Experimental results demonstrate that the method significantly outperforms existing reconstruction techniques tailored for unsigned distance data, achieving high-fidelity geometric approximations even for highly complex surface topologies.

Technology Category

• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Unsigned distance functions offer a powerful and flexible implicit surface representation that, unlike their signed counterparts, allow for surfaces that are open, non-orientable, or non-manifold. We consider the problem of reconstructing arbitrary surfaces from a finite set of samples of unsigned distance data. Existing methods for mesh reconstruction from distance data rely on sign information, accurate gradients, a corresponding continuous distance function, or extensive data-dependent training. However, they fail when applied to input that is both discrete and unsigned. Inspired by this challenge, we study the power diagram generated by the distance samples and propose a novel theoretical concept, the superpower contour, which we prove converges to the true surface in the limit of sampling density. We use this superpower contour as an initial surface proxy and design an algorithm that leverages it to produce a polygonal mesh approximating the unknown true geometry. Our method vastly outperforms other conceivable strategies for the discrete unsigned distance reconstruction task, and sets the stage for future work on this mathematically rich problem.

Problem

• unsigned distance function
• surface reconstruction
• discrete data
• implicit surface
• mesh generation

Innovation

• unsigned distance function
• power diagram
• superpower contour
• surface reconstruction
• implicit surface