Subject: Re: 4D matrix equation?

From: [email-masked] (Sam Sirlin)
Date: 20 Feb 92 01:13:43 GMT

In article <[email-masked]>, [email-masked] writes:
|> 	Could someone direct me to a matrix capable of rotating a 4D object on
|> its 4 axes?  Every time I sit down and try to derive such a beast I end up
|> blowing my cerebral cortex :).

Just think of a planar rotation, embedded in 4 space. Recall from 3d
rotations you have a 3x3 matrix with 1 axis invariant - 3 different
ways to do this (e.g. Euler angles). In four space, you have the same
planar rotation (sin etc among 2 axes), but now you'll have 2 ones on
the diagonal in the matrix. Think of choosing 2 axes to form the plane
to do the rotation. You now have 4 chose 2 or 6 ways of doing this.
Hence a general 4 space rotation has 6 degrees of freedom. 6d is just
as easy!
-- 
Sam Sirlin
Jet Propulsion Laboratory         [email-masked]