8.2.5.3} Roto-translation transformation

 This directive provides a coordinate transformation, predefined by a ROT--DEFIni
 card, for all bodies embedded between the two lines.

 $Start_transform [ROT-DEFIni name] (or [ROT-DEFIni number])
 ..............
 ..............
 ..............
 $End_transform


 Two nested (signed) transformations R2 and R1 can be used, acting on a
 body vector r as   r'=R2(R1(r)):

 $Start_transform R2
 ...
 $Start_transform R1
 ...
 $End_transform
 ...
 $End_transform

 
Example 1:
 ....
 * Cylindrical target is transformed with transformation "Rotdefi1"
 $Start_transform  Rotdefi1
 RCC targRepl   0.0 0.0 -5.0 0.0 0.0 10.0 5.0
 $End_transform
 ....
 * ROT-DEFI transformation: shift of (0,-2,-30) then rotation of -21 degrees
 * around the x axis
 ROT-DEFI         0.0                                    -2.0     -30.0Rotdefi1
 ROT-DEFI        100.                -21.                              Rotdefi1

 Example 2 (with lattice):
 ....
 * Cylindrical target
 RCC target     0.0 0.0 -5.0 0.0 0.0 10.0 5.0
 * Target replica is transformed with inverse transformation of the lattice
 $Start_transform  -Rotdefi1
 RCC targRepl   0.0 0.0 -5.0 0.0 0.0 10.0 5.0
 $End_transform
 ....
 * Regions
 TARGET       5 +target
 REPLICA      5 +targRepl
 ....
 * Lattice
 LATTICE      REPLICA                                                  Rotdefi1
 ....
 * ROT-DEFI transformations shift of (0,-2,-30) then rotation of -21 degrees
 * around the x axis
 ROT-DEFI         0.0                                    -2.0     -30.0Rotdefi1
 ROT-DEFI        100.                -21.                              Rotdefi1

 
Example 3:
 ROT-DEFIni  3. -90.  0.  0.  0.  0. XtoZ
 ........................................
 $Start_transform XtoZ
 $Start_translat 0. -30. +20.
 $Start_expansion 10.
 QUA  Elipsoid  0.0025 0.04 0.0064 0.0 0.0 0.0 0.055 0.64 0.0256 1.8881
 $End_expansion
 $End_translat
 $End_transform
 transforms an ellipsoid centred at (11, 8, -2), with semiaxes 20, 5 and
 12.5 cm long parallel to the coordinate axes, to a similar one with
 semiaxes 200, 50 and 125 cm, centred at (11, -22, 18) and rotated by 90
 degrees (axis z becomes axis x).

 
Example 4:
 Trivial example where the combined nested transformation is the
 identity. The first transformation (ft) is a rotation by 90 deg around
 the y axis, followed by a shift of 10 cm along the z axis. The second
 transformation is the inverse: a shift of -10 cm along the z axis and a
 rotation of -90 deg around the y axis.
 ROT-DEFI        200.                 90.                              ft
 ROT-DEFI         0.0                                               10.ft
 ROT-DEFI         0.0                                              -10.st
 ROT-DEFI        200.                -90.                              st
 $start_transform st
 $start_transform ft
 * Cylindrical target
 RCC target     0.0 0.0 0.0 0.0 0.0 10. 2.
 $end_transform
 $end_transform

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