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Derivatives and Logarithms of 3D Transforms
Understanding derivatives and logarithms of transforms
The source code for the applet can be found here, which includes an implementation of closed-form log() and exp() for rigid body transforms. 3) There is an excellent PDF at the web site of Ethan Eade here which contains the closed form equations for the groups SO(3), SE(3), and SIM(3). 4) Compute the matrix exponential and logarithm by using the infinite series definitions above, and truncating after some number of terms.
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