RT 3AS - RoTate - volume, arbitrary center, simple interpolation

PURPOSE

Rotates a volume around an arbitrary center by the three Eulerian angles. Uses tri-linear interpolation

SEE ALSO

RT	[RoTate - image or volume, use average as background]
RT 3	[RoTate - volume, slow]
RT 3D	[RoTate - volume, fast, quadratic interpolation]
RT 3A	[RoTate - volume, arbitrary center, quadratic interpolation]
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 3AS

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

.OUTPUT FILE: ROT001
[Enter the 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). All rotations are done in space coordinate system.]

.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 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-linear interpolation scheme is used.

3. All the rotations are done clockwise.

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 Paul Penczek.

SUBROUTINES

ROTAS3, ROTS3, BLDR

CALLER

UTIL3