OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams

2025-07-14

AI Summary

This paper addresses the fundamental challenge of computing offset surfaces with variable radii in geometric processing. We propose a novel modeling framework based on power diagrams, formulating the offset surface as the Minkowski sum of the base surface and a rolling sphere. To mitigate inherent misalignment issues in conventional shell-based methods, we introduce dual-layer sampling (inside/outside the surface), radius-dependent displacement directions, and an adaptive base-point sampling strategy. Furthermore, we design a unified algorithm comprising off-surface point generation and lightweight fine-tuning, supporting both constant- and variable-radius offsets. Experiments demonstrate that our method significantly outperforms state-of-the-art approaches in both accuracy and efficiency. It has been successfully applied to practical tasks such as inverse reconstruction from medial axis transforms, markedly improving boundary surface recovery quality.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been made in computing constant-radius offset surfaces, computing variable-radius offset surfaces remains a challenging problem. In this paper, we present OffsetCrust, a novel framework that efficiently addresses the variable-radius offsetting problem by computing a power diagram. Let $R$ denote the radius function defined on the base surface $S$. The power diagram is constructed from contributing sites, consisting of carefully sampled base points on $S$ and their corresponding off-surface points, displaced along $R$-dependent directions. In the constant-radius case only, these displacement directions align exactly with the surface normals of $S$. Moreover, our method mitigates the misalignment issues commonly seen in crust-based approaches through a lightweight fine-tuning procedure. We validate the accuracy and efficiency of OffsetCrust through extensive experiments, and demonstrate its practical utility in applications such as reconstructing original boundary surfaces from medial axis transform (MAT) representations.

Problem

• Efficiently computes variable-radius offset surfaces
• Mitigates misalignment in crust-based offset approaches
• Reconstructs boundary surfaces from medial axis transforms

Innovation

• Uses power diagrams for variable-radius offsetting
• Samples base and off-surface points adaptively
• Lightweight fine-tuning reduces misalignment errors