MS_ROTEULER - Rotate an elasticity matrix using Bunge's Euler angles.

Rotate one or more elasticity matrices using Bunge's Euler angles

Usage:

[ CC ] = MS_rotEuler( C, phi1, Phi, phi2 )

For three angles in degrees (phi1, theta, phi2) representing a
rotation in Bunge convention rotate the elasticity matrix C. All
variables can be arrays or scalars but (1) the angles must all be the
same length and (2) either C or all the angles must be scalars unless
they are the same length.

[ CC ] = MS_rotEuler( C, phi1, Phi, phi2, 'sense', 'active' )
[ CC ] = MS_rotEuler( C, phi1, Phi, phi2, 'sense', 'passive' )

As above, but allow user choice between 'active' (the default) or
'passive' rotations (the usual description for texture analysis).
See notes, below, for details.

Notes:
   In the context of this function the term 'Euler angle' is used in
   the sense common in texture analysis not computer graphics etc. where
   the three angles are rotations around a fixes axis system (see
   MS_rot3 for this case). In the (Bunge) convention used here the
   relationship between the orientation of a set of "crystal" axes is
   considered with respect to an external "sample" axis system. This
   is described by considering a moving reference frame which starts out
   parallel to the sample axes. This moving reference frame is first
   rotated anticlockwise about its z axis by phi1 degrees. A second
   anticlockwise rotation of Phi degrees is made about the frame's x axis
   (which, at this point, is no longer parallel to the sample x axis).
   Finally, a second anticlockwise rotation of phi2 degrees about the
   frame's z axis is made to bring the moving reference into line with
   the crystal axes. See Figure 5 of Bunge 1985 for a graphical example.

As described, the Euler angles are passive rotations showing how the
reference frame must be rotated. However, for most applications one
knows the elasticity matrix of the crystal on the crystal axis system
and wants to calculate the elasticity matrix represented on the global
"sample" reference frame. In this case the corresponding active
rotation must be applied to the crystal's elasticity matrix. By
default, the MS_rotEuler function applies the active rotation.
The optional arguments 'sense' and 'passive' can be used to reverse
the sense of rotation. This can be used if, for example, the
elasticity has been measured on an experimental frame which is offset
from the crystal frame more usually used.

References:
   Bunge, H. J. (1985) "Representation of Preferred Orientations" in H.-R.
   Wenk (ed.) "Preferred Orientation in Deformed Metals and Rocks:
    An Introduction to Modern Texture Analysis" Academic Press inc.
    Orlando.

See also: MS_ROT3 MS_ROTR