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An arbitrary rigid transformation in $\mathbf{SE}(3)$ can be separated into two parts, namely, a translation and a rigid rotation.
Lie groups, Lie algebras, and their representations
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Minimizing a differentiable function over a differential manifold
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The iterated Kalman filter update as a Gauss-Newton method
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Homogeneous coordinates
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Practical parameterization of rotations using the exponential map
F Sebastian Grassia · 1998
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The de Casteljau algorithm on SE(3)
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New method for extracting the quaternion from a rotation matrix
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A framework for sparse, non-linear least squares problems on manifolds
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