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Topic: applying a rotational transform to align with normal vector
Replies: 8   Last Post: Oct 20, 2007 4:23 PM

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Posts: 38
Registered: 10/27/05
Re: applying a rotational transform to align with normal vector
Posted: Oct 20, 2007 4:23 PM
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On Oct 19, 6:16 pm, wrote:

> I realize there are multiple ways to do the rotations to get to the
> location I desire; however, I did not think that would be a problem to
> finding one particular method to get there, is it?
> No, there are no other conditions.

Here are two minor points that no one else has mentioned.
(1) You want an orthogonal matrix of determinant 1 which transforms
(1,0,0) to u. This means that the first column of the orthogonal
matrix will just be vector u normalized (scaled by 1/||u|| ). The
second column, say u2, could then be any unit vector orthogonal to u1,
the first column. The third column must then be u1 x u2.

(2) You might be interested in googling SLERP, (spherical linear
interpolation). Given vectors u and v of the same length, the SLERP
algorithm interpolates along a circular path.

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