OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams
This work addresses the challenging problem of variable-radius offsetting in geometry processing, offering a practical solution for applications like coverage motion planning and brush modeling.
OffsetCrust introduces a power diagram-based framework for computing variable-radius offset surfaces, achieving accurate and efficient results. The method handles non-constant radius functions and mitigates misalignment issues common in crust-based approaches, with applications including reconstruction from medial axis transforms.
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.