signed angle between two 3d vectors with same origin within the same plane? recipe?

Posted by Advanced Customer on Stack Overflow See other posts from Stack Overflow or by Advanced Customer
Published on 2011-03-04T01:07:32Z Indexed on 2011/03/04 7:24 UTC
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math

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vector

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3d

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geometry

Was looking through the web for an answer but it seems like there is no clear recipe for it.

What I need is a signed angle of rotation between two vectors Va and Vb lying within the same 3D plane and having the same origin knowing that:

the plane contatining both vectors is an arbitrary and is not parallel to XY or any other of cardinal planes
Vn - is a plane normal
both vectors along with the normal have the same origin O = { 0, 0, 0 }
Va - is a reference for measuring the left handed rotation at Vn

The angle should be measured in such a way so if the plane would be XY plane the Va would stand for X axis unit vector of it.

I guess I should perform a kind of coordinate space transformation by using the Va as the X-axis and the cross product of Vb and Vn as the Y-axis and then just using some 2d method like with atan2() or something. Any ideas? Formulas?

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