Transform 3D vectors between coordinate systems

Posted by Nir Cig on Game Development See other posts from Game Development or by Nir Cig
Published on 2012-06-26T09:02:55Z Indexed on 2012/06/26 9:23 UTC
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Filed under:

3d

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math

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matrix

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vector

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transformation

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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