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# 14. Generic Quadric. Code: QUA

```      A QUA is a quadric surface defined by a 2nd degree equation F(x,y,z) = 0.
Each QUA is defined by 10 numbers:
A_xx, A_yy, A_zz, A_xy, A_xz, A_yz, A_x, A_y, A_z, A_0
corresponding to the equation:
A_xx x^2 + A_yy y^2 + A_zz z^2 + A_xy xy + A_xz xz + A_yz yz +
+ A_x x + A_y y + A_z x + A_0 = 0
A QUA definition extends over two cards in default fixed format,
and over 4 cards in high-accuracy body fixed format.

Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
QUA   27    0.0025      0.04    0.0064       0.0       0.0       0.0
0.055      0.64    0.0256    1.8881
* (an ellipsoid centred at x = 11 cm, y = 8 cm, z = -2 cm, with
* a semi-axis 20 cm long parallel to x, one 5 cm long parallel to y and
* one 12.5 cm long parallel to z)

The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
QUA   27                0.0025                  0.04                0.0064
0.0                   0.0                   0.0
0.055                  0.64                0.0256
1.8881

The same body, described in free format:
QUA  Elipsoid  0.0025 0.04 0.0064 0.0 0.0 0.0 0.055 0.64 0.0256 1.8881

NOTE
+---------------------------------------------------------------------+
| Whenever it is possible, the following bodies should be preferred:  |
|   PLA, QUA, RPP, SPH, XCC, XEC, XYP, XZP, YCC, YEC, YZP, ZCC, ZEC   |
| These should indeed make tracking faster, since for them extra      |
| coding ensures that unnecessary boundary intersection calculations  |
| are avoided when the length of the next step is smaller than the    |
| distance to any boundary of the current region.                     |
+---------------------------------------------------------------------+

```