3D Math: Calculate Bank (Roll) angle from Look and Up orthogonal vectors

Posted by 742 on Stack Overflow See other posts from Stack Overflow or by 742
Published on 2010-06-17T19:44:38Z Indexed on 2010/06/18 6:43 UTC
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math

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3dgraphics

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euler-angles

I hope this is the proper location to ask this question which is the same as this one, but expressed as pure math instead of graphically (at least I hope I translated the problem to math correctly).

Considering:

two vectors that are orthogonal: Up (ux, uy, uz) and Look (lx, ly, lz)
a plane P which is perpendicular to Look (hence including Up)
Y1 which is the projection of Y (vertical axis) along Look onto P

Question: what is the value of the angle between Y1 and Up?

As mathematicians will agree, this is a very basic question, but I've been scratching my head for at least two weeks without being able to visualize how to project Y onto P... maybe now too old for finding solutions to school exercises.

I'm looking for the trigonometric solution, not a solution using a matrix. Thanks.

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