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OffsetCrust: Variable-Radius Offset Approximation With Power Diagrams
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DOI：10.1109/tvcg.2026.3701358.png)
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Abstract
En 中文
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 <i>constant-radius</i> offset surfaces, computing <i>variable-radius</i> offset surfaces remains a challenging problem. In this paper, we present <i>OffsetCrust</i>, a novel framework that efficiently addresses the variable-radius offsetting problem by computing a power diagram. Let <inline-formula><tex-math notation="LaTeX">${\mathcal {R}}$</tex-math></inline-formula> denote the radius function defined on the base surface <inline-formula><tex-math notation="LaTeX">$\mathcal {S}$</tex-math></inline-formula>. The power diagram is constructed from contributing sites, consisting of carefully sampled base points on <inline-formula><tex-math notation="LaTeX">$\mathcal {S}$</tex-math></inline-formula> and their corresponding off-surface points, displaced along <inline-formula><tex-math notation="LaTeX">${\mathcal {R}}$</tex-math></inline-formula>-dependent directions. In the constant-radius case only, these displacement directions align exactly with the surface normals of <inline-formula><tex-math notation="LaTeX">$\mathcal {S}$</tex-math></inline-formula>. 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.
Keywords:
Digital geometry processing
variable-radius offset
power diagram
medial axis transform
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6.5
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294
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