## Coordinate Transformation (GM)

Purpose: To translate or rotate a structure with respect to the coordinate system or to generate new structures translated or rotated from the original.

Card:

```     __________________________________________________________
/2|  5|   10|   20|   30|    40|    50|    60|    70|    80|
/  |   |     |     |     |      |      |      |      |      |
|   |   |     |     |     |      |      |      |      |      |
|GM |I1 | I2  | F1  | F2  | F3   |  F4  |  F5  |  F6  |  F7  |
|   |   |     |     |     |      |      |      |      |      |
|   | I |  M  | ROX | ROY | ROZ  |  XS  |  XY  |  XZ  | ITS  |
|   | T |  R  |     |     |      |      |      |      |      |
|   | G |  P  |     |     |      |      |      |      |      |
|   | G |  T  |     |     |      |      |      |      |      |
|   |   |     |     |     |      |      |      |      |      |
|   |   |     |     |     |      |      |      |      |      |
|   |   |     |     |     |      |      |      |      |      |
|The numbers along the top refer to the last column in each field
|   |   |     |     |     |      |      |      |      |      |
```
Parameters:
Integers
```ITSI  (I1) - Tag number increment.
NRPT  (I2) - The number of new Structures to be generated
```
Decimal Numbers
```ROX   (F1) - Angle in degrees through which the structure is rotated about
the X-axis.  A positive angle causes a right-hand rotation.
ROY   (F2) - Angle of rotation about Y-axis.
ROZ   (F3) - Angle of rotation about
XS    (F4) - X, Y. Z components of vector by which
YS    (F5) - structure ir translated with respect to
ZS    (F6) - the coordinate system.
ITS   (F7) - This number is input as a decimal number but is rounded
to an integer before use.  Tag numbers are searched sequentially
until a segment having a tag of this segment through the end of
the sequence of segments is moved by the card.  If ITS is blank
(usual Case) or zero the entire structure is moved.
```
Notes:
• If NRPT is zero, the structure Is moved by the specified rotation and translation leaving nothing in the originallocation. If NRPT is greater than zero, the original structure remains fixed and NRPT new structures are formed, each shifted from the previous one by the requested transformation.
• The tag increment, ITGI, is used when new structures are generated (NRPTgreater than zero) to avoid duplication of tag numbers. Tag numbers of the segments in each new copy of the structure are incremented by ITGI from the tags on the previous copy or original. Tags of segments which are generated from segments having no tags (tag equal to zero) are not incremented. Generally, ITGI will be greater than or equal to the largest tag number used on the original structure to avoid duplication of tags. For example, if tag numbers 1 through 100 have been used before a (GM) card is read having NRPT equal to 2, then ITGI equal to 100 will cause the first copy of the structure to have tags from 101 to 200 and the second copy from 201 to 300. If NRPT is zero, the tags on the original structure will be incremented.
• The result of a transformation depends on the order in which the rotations and translation are applied. The order used is first rotation about X-axis, then rotation about the Y-axls, then rotation about the Z-axis and, finally, translation by (XS, YS, ZS). All operations refer to the fixed coordinate system axes. If a different order is desired, separate GM cards may be used.