RT 3A - RoTate - volume, arbitrary center, quadratic interpolation

PURPOSE

Rotates volume around an arbitrary center 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 3AS	[RoTate - volume, arbitrary center, simple interpolation]
RT 3DS	[RoTate - volume, fast, simple interpolation]
RT 3L	[RoTate - volume around an arbitrary line]
RT 3	[RoTate - volume, slow]
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 3A

.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)].

.X, Y, & Z CENTER OF ROTATION: 12, 27, 32
[Enter x,y coordinates of center of rotation. Volume extends in x from 1 to NSAM, in y from 1 to NROW, and in z from 1 to NSLICE.]

NOTES

1. Program reads input 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. Implemented by A. Leith.

SUBROUTINES

ROTAS3, ROTS3Q, BLDR

CALLER

UTIL3