
Re: applying a rotational transform to align with normal vector
Posted:
Oct 20, 2007 4:23 PM


On Oct 19, 6:16 pm, carlos.jame...@gmail.com 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.

