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From: hiebeler@csv.rpi.edu (David Hiebeler)
Newsgroups: comp.graphics,sci.math
Subject: N-dimensional rotation
Message-ID: <81@rpicsb8>
Date: Sat, 19-Sep-87 20:58:38 EDT
Article-I.D.: rpicsb8.81
Posted: Sat Sep 19 20:58:38 1987
Date-Received: Mon, 21-Sep-87 00:39:49 EDT
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Reply-To: hiebeler@csv.rpi.edu (David Hiebeler)
Organization: RPI CS Dept, Troy, New York
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Xref: mnetor comp.graphics:1186 sci.math:2053


   I have been playing around with using matrices to perform rotations on
objects defined using homogeneous-coordinates.  For example, using
  --                      --
  |  cos(O)  sin(O)  0  0  |
  | -sin(O)  cos(O)  0  0  |
  |    0       0     1  0  |
  |    0       0     0  1  |
  --                      --
  to multiply a row-vector  [ x y z 1 ] to rotate the point around the x-axis.
('O' is theta).

   What I am wondering is, how can I generalize this to N dimensions?  I can
understand the derivation of this matrix, and the ones for rotation about
y- and z-axis, but I don't know how to do this for N-D, with N >= 4.
   Can someone either show me a general derivation for N dimensions, or,
failing to do that, tell me the 4 matrices to rotate a point in 4-D about
each of the 4 orthogonal axes?  
  Any help whatsoever would be great and appreciated.

                             -D.H.
----
David Hiebeler       hiebeler@csv.rpi.edu
Troy, NY            "Illusions, Richard!  Every
                     bit of it illusions!"