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 Rotation matrices  (Read 3071 times) 0 Members and 1 Guest are viewing this topic.
Porlus

Junior Devvie

 « Posted 2013-04-04 03:01:36 »

Hi all, I'm trying to get my head the algorithm for rotating around an arbitrary axis like that produced by glRotate. By the algorithm I mean the one under the "Description" header in this article: http://www.talisman.org/opengl-1.1/Reference/glRotate.html
More importantly I want to understand how it's derived. Does anyone happen to know any good learning resources or books which explain this well?

Thanks

Paul
kramin42
 « Reply #1 - Posted 2013-04-04 03:22:45 »

This Wikipedia page might help, although it doesn't really have the derivation:

http://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions

I believe the matrix under the "Rotation matrix from axis and angle" heading is the same as the glRotate one.

Also this page has a derivation (it is quite terse though and doesn't explain everything):

http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/

I don't know of any textbook in particular, but a linear algebra textbook might have the derivation.

"All science is either physics or stamp collecting." - Ernest Rutherford.
CodeGolf4k
M4nkala
Porlus

Junior Devvie

 « Reply #2 - Posted 2013-04-04 03:46:49 »

Cheers for the reply. Yeah, I've found a few definitions through google but it's harder to find an explanation of the underlying maths. It's got such a broad definition that it's quite hard to find a clear relevant explanation.
kramin42
 « Reply #3 - Posted 2013-04-04 04:18:12 »

Have you done much linear algebra before? Do you understand how Txz and Tz are found in that second link I posted? I might be able to explain things a bit more...

"All science is either physics or stamp collecting." - Ernest Rutherford.
CodeGolf4k
M4nkala
Roquen

JGO Kernel

Medals: 517

 « Reply #4 - Posted 2013-04-04 04:20:44 »

All you need to know is: parallel projection (aka dot product).  You parallel project a point into three orthogonal vectors...you've rotated.  Put those three steps into a matrix...done.
relminator
 « Reply #5 - Posted 2013-04-05 15:37:06 »

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