How would I identify a set of coordinates (x, y, z) to be in which octant in a 3d space? Is it just based on the x-value? Depending on the x-value (1-8) used?

1,1,1

1,1,-1
1,-1,1
1,-1,1
-1,1,1
-1,1,-1
-1,-1,1
-1,-1,-1
are all in different octants
you need the sign of x y and z.
They are called octants because there are 8 of them.
Draw a picture.

Like here:

http://en.wikipedia.org/wiki/Octant_(solid_geometry)

To identify which octant a set of coordinates (x, y, z) belongs to in 3D space, you need to consider the signs of the x, y, and z values.

In an octant system, the space is divided into eight regions, numbered from 1 to 8. Each octant consists of points where x, y, and z are all positive, all negative, or a combination of positive and negative values.

Here's how you can identify the octant based on the signs of the coordinates:
1. If all three coordinates (x, y, z) are positive, the point is in the first octant (x > 0, y > 0, z > 0).
2. If x is negative, but y and z are positive (x < 0, y > 0, z > 0), the point belongs to the second octant.
3. If x and y are negative, but z is positive (x < 0, y < 0, z > 0), the point falls within the third octant.
4. If x is positive, but y and z are negative (x > 0, y < 0, z < 0), the point is in the fourth octant.
5. If all three coordinates are negative (x < 0, y < 0, z < 0), the point belongs to the fifth octant.
6. If x is negative, but y and z are positive (x < 0, y > 0, z < 0), the point falls within the sixth octant.
7. If x and y are positive, but z is negative (x > 0, y > 0, z < 0), the point is in the seventh octant.
8. If x is positive, but y and z are negative (x > 0, y < 0, z < 0), the point belongs to the eighth octant.

Rather than only relying on the x-value, you need to consider the signs of all three coordinates to determine the octant in a 3D space.