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I've got 6 points in 3D space: A,B,C,D,E,F, that represent 4 vectors. AB is perpendicular to AC and DE is perpendicular to DF.

I need to find a transformation matrix M, that transforms AB to DE and AC to DF. In other words: M⋅AB=DE, M⋅AC=DF

If no scaling was involved, this could be solved with a simple rotation matrix. But since the ratios |AB|/|DE|, |AC|/|DF| might be different, I'm not sure how to proceed.

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The result is given in the M matrix. Note that Trans_DEF and Rot_DEF are constructed in the same manner as ABC.

Equations

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