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Lie algebra/group functions for 3D rotations.
Interesting reads:
- Sophus c++ library: https://github.com/strasdat/Sophus
- Ethan Eade course on Lie Groups for 2D and 3D transformations:
- details: http://ethaneade.com/lie.pdf
- summary: http://ethaneade.com/lie_groups.pdf
Functionsยง
- exp
- Compute the exponential map from Lie algebra so3 to Lie group SO3. Goes from so3 parameterization to SO3 element (rotation).
- hat
- Hat operator. Goes from so3 parameterization to so3 element (skew-symmetric matrix).
- hat_2
- Squared hat operator (
hat_2(w) == hat(w) * hat(w)). Result is a symmetric matrix. - log
- Compute the logarithm map from the Lie group SO3 to the Lie algebra so3. Inverse of the exponential map.
- vee
- Vee operator. Inverse of hat operator. Warning! does not check that the given matrix is skew-symmetric.