Appendix D. Frame and Surface Evolution
Quaternion Frame Evolution
Using Equation C.7, we can express all 3D coordinate frames in the form of quaternions. If we assume that the columns of Equation C.7 are the vectors 
, respectively, one can explicitly express each vector in terms of the matrices
Equation D.1.
Equation D.2.
Equation D.3.
with the result ...
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