## Reflection in Coordinate Planes (GX)

```Purpose: To form structures having planes of symmetry by reflecting part
of the structure in the coordinate planes, and to set flags so that
symmetry is utilized in the solution.

Card:

Cols  Parameter
----------------------
1- 2        GX
3- 5        I1
6-10        I2
11-80        blank

Parameters:
Integers
(I1) - Tag number increment.
(12) - This integer is divided into three independent digits, in
columns 8, 9, and 10 of the card, which control reflection
in the three orthogonal coordinate planes.  A one in column
8 causes reflection along the X-axis (reflection in Y, Z
plane); a one in column 9 causes reflection along the Y-axis;
and a one in column 10 causes reflection along the Z axis.
A zero or blank in any of these columns causes the corres-
ponding reflection to be skipped.

Decimal Numbers
The decimal number fields are not used.
```
Notes:
• Any combination of reflections along the X, Y and Z axes may be used. For example, 101 for (I2) will cause reflection along axes X and Z, and 111 will cause reflection along axes X, Y and Z. When combinations of reflections are requested, the reflections are done in reverse alphabetical order. That is, if a structure is generated in a single octant of space and a GX card is then read with I2 equal to 111, the structure is first reflected along the Z-axis; the structure and its image are then reflected along the Y-axis; and, finally, these four structures are reflected along the X-axis to fill all octants. This order determines the position of a segment in the sequence and, hence, the absolute segment numbers.
• The tag increment I1 is used to avoid duplication of tag numbers in the image segments. All valid tags on the original structure are incremented by I1 on the image. When combinations of reflections are employed, the tag increment is doubled after each reflection. Thus, a tag increment greater than or equal to the largest tag an the original structure will ensure that no duplicate tags are generated. For example, if tags from 1 to 100 are used on the original structure with I2 equal to 011 and a tag increment of 100, the first reflection, along the Z-axis, will produce tags from 101 to 200; and the second reflection, along the Y-axis, will produce tags from 201 to 400, as a result of the increment being doubled to 200.
• The GX card should never be used when there are segments located in the plane about which reflection would take place or crossing this plane. The image segments would then coincide with or intersect the original segments, and such overlapping segments are not allowed. Segments may end on the image plane, however.
• When a structure having plane symmetry is formed by a GX card, the program will make use of the symmetry to simplify solution for the currents. The number of complex numbers in matrix storage and the proportionality factors for matrix fill time and matrix factor time for a structure modeled by N segments are:
```     No. of Planes          Matrix               Fill           Factor
of Symmetry           Storage              Time            Time

0                   N^2                 N^2             N^3

1                   N^2/2               N^2/2           N^3/4

2                   N^2/4               N^2/4           N^3/16

3                   N^2/8               N^2/8           N^3/64
```
The matrix factor time represents the optimum for a large matrix factored in core. Generally, somewhat longer times will be observed.
• If the structure is added to or modified after the GX card in such a way that symmetry is destroyed, the program must be reset to a no-symmetry condition. In most cases, the program is set by the geometry routines for the existing symmetry. Operations that automatically reset the symmetry condition are:
• Addition of a wire by a GW card destroys all symmetry.
• Generation of additional structures by a GM card, with NRPT greater than zero, destroys all symmetry.
• A GM card acting on only part of the structure (having ITS greater than zero) destroys all symmetry.
• A GX card or GR card will destroy all previously established symmetry. For example, two GR cards with I2 equal to 011 and 100, respectively, will produce the same structure as a single GX card with I2 equal to 111; however, the first case will set the program to use symmetry about the Y, Z plane only while the second case will make use of symmetry about all three coordinate planes.
• If a ground plane is specified on the GE card, symmetry about a plane parallel to the X, Y plane will be destroyed. Symmetry about other planes will be used, however.
• If a structure is rotated about either the X or Y axis by use of a GM card and a ground plane is specified on the GE card, all symmetry will be destroyed. Rotation about the Z-axis or translation will not affect symmetry. If a ground is not specified, no rotation or translation will affect symmetry conditions unless NRPT on the GM card is greater than zero.
• Symmetry will also be destroyed if lumped loads are placed on the structure in an unsymmetric manner. In this case, the program is not automatically set to a no-symmetry condition but must be set by a data card following the GX card. A GW card with NS blank will set the program to a no-symmetry condition without modifying the structure. The card must specify a nonzero radius, however, to avoid reading a GC card.
• Placement of sources or nonradiating networks does not affect symmetry.