OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams

TL;DR

OffsetCrust introduces an efficient framework for computing variable-radius offset surfaces using power diagrams, improving accuracy and applicability in geometry processing tasks like surface reconstruction.

Contribution

The paper presents a novel method for variable-radius offsetting that leverages power diagrams and includes a fine-tuning step to enhance accuracy over crust-based approaches.

Findings

Accurately reconstructs boundary surfaces from medial axis transforms.

Demonstrates efficiency and robustness through extensive experiments.

Improves offset surface computation beyond constant-radius methods.

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.