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The matrix construct allows one to specify a 33
real matrix. There are several modes available to
specify rotation matrices. An arbitrary 33 matrix can be
specified by using the MATRix construct. Note: all rotations are
counterclockwise.
 <matrix>:==

 AXIS <vector> <real>
 specifies input through
the axis vector and the rotation angle .
 EULEr <vector>
 specifies input through the
Eulerian angles ,,.
is the rotation around the z axis,
around the new x axis, and around
the new z axis.
 LATTman <vector>
 specifies input
through Lattman's angles
(, ,
).
 MATRix <vector> <vector> <vector>

specifies direct input of the matrix by three 3d vectors.
 QUATernions
 <real> <real>
<real> <real> specifies quaternions ,
, , , which are defined as
with the constraint
 SPHErical <vector>
 specifies input through
spherical polar angles , , .
and specify the rotation axis.
is the inclination versus the yaxis; is
the azimuthal angle,
i.e., the angle between the xaxis and the
projection of the axis into the x,z plane; and
is the rotation around the rotation axis.
In the following example, a rotation matrix is specified by
a rotation axis (2,3,4) and a rotation angle (40) around
the axis (counterclockwise rotation):
AXIS=( 2, 3, 4 ) 40.
In the next example, a matrix is specified by direct input:
MATRix=( 1. 3. 5. )
( 4. 2. 1. )
( 2. 1. 8. )
The last example shows how to specify a rotation matrix by
using the Eulerian angles ,,:
EULEr=( 30. 40. 120. )
Web Manager
Sat Mar 11 09:37:37 PST 1995