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arXiv · 2503.22961

Distortion Bounds of Subdivision Models for SO(3)

Zhaoqi Zhang·Chee Yap
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Abstract

In the subdivision approach to robot path planning, we need to subdivide the configuration space of a robot into nice cells to perform various computations. For a rigid spatial robot, this configuration space is $SE(3)=\mathbb{R}^3\times SO(3)$. The subdivision of $\mathbb{R}^3$ is standard but so far, there are no global subdivision schemes for $SO(3)$. We recently introduced a representation for $SO(3)$ suitable for subdivision. This paper investigates the distortion of the natural metric on $SO(3)$ caused by our representation. The proper framework for this study lies in the Riemannian geometry of $SO(3)$, enabling us to obtain sharp distortion bounds.

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Zhaoqi Zhang, Chee Yap. 2025-03-29. Distortion Bounds of Subdivision Models for SO(3). https://arxiv.org/abs/2503.22961

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