Having said that, I should give basic instructions for use, since I think many people do find this projection mysterious or difficult.
These examples all use "Hotine Oblique Mercator (B)" in Manifold 9, equivalent to "Oblique Mercator (B, centered)" in Manifold 8. Other versions are equally usable, but this form is usually simplest.
Start with your AOI, in any standard north-up projection.
Pick a local centre for your custom projection. Set center longitude and center latitude accordingly.
Determine the most important data axis. Usually this means the maximum extent of the data. For example: if you have a short, wide rectangle, pick 90°. If you have a tall, narrow rectangle, pick 0°.
This axis is with respect to north. It is only important for scale, and doesn't usually matter very much, especially for a local projection.
It can be varied. E.g. use -90° or 270° instead of 90° (equivalent), or 180° instead of 0° (equivalent). Or use an oblique axis, if your data follows an oblique extent, and for some reason you need to privilege measurement on that oblique axis. But normally, don't worry about this very much.
This axis is specified as center line azimuth.
Now decide how you want the data to be displayed--its orientation on screen or page.
This parameter is the rectified grid angle.
If you specify the same angle as the center line azimuth, you get standard north-up orientation. If different, you get a rotated map. Then the relationship is as follows:
- "up" = center line azimuth - rectified grid angle
For example, if center line azimuth is 90° (east), and rectified grid angle is 0°, then "up" is 90 - 0°: east.
Similarly, if center line azimuth is 0° (north), and rectified grid angle is -90°, then "up" is 0 - (-90)°: again east. (You can also use 0 - 270° here, same result.)
The difference between the two examples is that, while final orientation is the same (east-up), the line of constant scale is different: in the first case west-east, in the second case north-south. Again, for local maps of small extent, that difference is usually small to negligible. Be more careful with maps having a large extent.
Normally use scale X and scale Y = 1, and false easting and false northing = 0, unless you know you need to do something else.