RT 3D - RoTate - volume, fast, quadratic interpolation

PURPOSE

Rotates a volume by three Eulerian angles. Uses tri-quadratic interpolation.

SEE ALSO

RT	[RoTate - image or volume, use average as background]
RT 3	[RoTate - volume, slow]
RT 3A	[RoTate - volume, arbitrary center, quadratic interpolation]
RT 3DS	[RoTate - volume, fast, simple interpolation]
RT 3AS	[RoTate - volume, arbitrary center, simple interpolation]
RT 3L	[RoTate - volume around an arbitrary line]
RT 90	[RoTate - image or volume, by 90, 180, or 270 degrees]
RT B	[RoTate - image or volume, supply Background]
RT M	[RoTate - image or volume, use minimum as background]
RT SQ	[Rotate and Shift - image, Quadratic interpolation ||]

USAGE

.OPERATION: RT 3D

.INPUT FILE: PIC001
[Enter name of the file to be rotated.]

.OUTPUT FILE: ROT001
[Enter name of the file where the rotated volume is to be stored.]

.PHI, THETA, & PSI: 10.5, 13.7, 45.8
[Enter the rotation angles Phi (around Z), Theta (around Y), and Psi (around Z).]

NOTES

1. Program reads first volume into the memory - larger volumes may not fit. In this case use 'RT 3' instead. Unfortunately 'RT 3' gives slightly incorrect results and does not use the proper interpolation scheme and has sign of theta reversed.

2. Tri-quadratic interpolation scheme is used.

3. First rotation is done around Z-axis (clockwise), second rotation is done around Y-axis (clockwise) and the third rotation is done around Z-axis (clockwise). All rotations are done in space coordinate system.

4. Rotation matrix used:

    
             R = R(psi) * R(theta) * R(phi) 
              c  s  0        c  0 -s      c  s  0 
             -s  c  0    *   0  1  0   * -s  c  0 
              0  0  1        s  0  c      0  0  1 
   

5. In the corners, old values are left.

6. How to rotate volumes.
   If both X and Y axis rotations are needed, it may be simpler to use two rotations consecutively.
   Pick a slice (either X or Y) from the volume and do a test rotation in 2D using operation: 'RT'.
   Change the sign of the angle you determimed using 'RT' and apply the angles as shown here.
   For X rotation: 90, -angle, -90
   For Y rotation: 0, -angle, 0
   (This note provided by: Mike Marko) (Interpolation quality will be poorer)

7. Implemented by A. Leith.

SUBROUTINES

ROTAS3, ROTS3Q, BLDR

CALLER

UTIL3