Review paper systematically compares multiple rotation representations of SO(3)
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Aizierjiang Aiersilan and other authors published a review paper that systematically organizes and compares multiple rotation representations of SO(3), including Euler angles, axis-angle vectors, quaternions, rotation matrices, exponential maps, and emerging continuous and probabilistic methods. The paper compares them across dimensions such as mathematical formulation, continuity, sensitivity to gimbal lock, computational efficiency, storage requirements, interpolation, and composition operations. The empirical results reported in the paper show that quaternions are advantageous due to their compactness and efficiency; 6D continuous representations and the matrix Fisher distribution have greater advantages in continuity and uncertainty modeling.
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- arXiv cs.RO3D Rotation Representations: Mathematical Foundations and Comparative Analysis
This paper systematically reviews multiple rotation representations of SO(3), including Euler angles, axis-angle vectors, quaternions, rotation matrices, exponential maps, and emerging continuous and probabilistic methods, and compares them across dimensions such as continuity, susceptibility to gimbal lock, computational efficiency, storage requirements, interpolation, and composition operations. Empirical results show that quaternions are advantageous due to their compactness and efficiency, while 6D continuous representations and matrix Fisher distributions offer greater advantages in continuity and uncertainty modeling.
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