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.