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The matrix construct allows one to specify a 3
3
real matrix. There are several modes available to
specify rotation matrices. An arbitrary 3
3 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
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with the constraint
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- SPHErical <vector>
- specifies input through
spherical polar angles
,
,
.
and
specify the rotation axis.
is the inclination versus the y-axis;
is
the azimuthal angle,
i.e., the angle between the x-axis 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