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

(04/11/02)

PURPOSE

Rotates volume around an arbitrary center by three Eulerian angles. Uses tri-quadratic interpolation.

 ROT A [ROTate image/volume around arbitrary center] RT 90 [RoTate - image or volume, by 90, 180, or 270 degrees] RT SQ [Rotate and Shift - image, Quadratic interpolation ||] RT SF [Rotate and Shift - image, Fourier based spline 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 NX, in y from 1 to NY, and in z from 1 to NZ.]

NOTES

1. Tri-quadratic interpolation scheme is used.

2. 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.

3. 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
```

4. In the corners, old values are left.

5. Implemented by A. Leith.

SUBROUTINES

ROTAS3, ROTS3Q, BLDR

CALLER

UTIL3