Comments on digital sanitation engineering: Rotating a point around a vector

I am the "anonymous" that said Wikipedia had Rodri...

2008-07-30T20:22:00.000-04:00

I am the "anonymous" that said Wikipedia had Rodrigues equation defined. You can see it at http://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula. I didn't bother going through the proof on that page but simply used the equation at the top of the page. Incidentally, I figured out the notation (u,v) in the third term to the right of the equal sign means dot-product.

I have to agre with the one that anonymous posted....

2008-07-20T10:00:00.000-04:00

I have to agre with the one that anonymous posted. If you visualize it, it makes sense. The first two use cosine to interpolate between X and where X would be if rotated 180 using U truncated (by the dot) as the center point. The last term shifts it on the perpendicular axis using sine. Beautiful! However, when I searched wikipedia for Rodrigues equation I got nothing like this.

Aha! I was delighted to find this "vector" solutio...

2008-04-02T16:48:00.000-04:00

Aha! I was delighted to find this "vector" solution posted here, but when I tried it gave the wrong answer. I Googled and found the correct form of this "Rodrigues" equation posted on Wikipedia:

X times (cos lambda) + U times (U dot X)(1 - cos lambda) + (U cross X) times (sin lambda)

Notice the additional first term. But thanks, stijn, for pointing me in the right direction to solve my geometry problem.

Or, in other words, the rotated vector is equal to...

2007-12-08T13:11:00.000-05:00

Or, in other words, the rotated vector is equal to

U times (U dot X)(1 - cos lambda) + (U cross X) times (sin lambda)

where U is the normalized form of (u,v,w) and X is (x,y,z). Thanks though :)