33 Matrices

**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

(2.2) **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. )