# proj: Oblique Mercator specifying two points on central line

I'm trying to use Oblique Mercator in QGIS 3.4, which uses `proj` to calculate coordinates conversion. I specify two points in the central line, rather than specifying the center and alpha.

Oblique Mercator: Usage explains

In the second case, the azimuth is given indirectly by specifying two points on the central line, using the options +lat_1, +lon_1, +lat_2, and +lon_2.

Here are the two locations I'm using:

• Tokyo: latitude: 35.652832, longitude: 139.839478
• New York: latitude: 40.730610, longitude: -73.935242

Calling `proj` command (Rel. 6.1.0) specifying the two locations for the central line of Oblique Mercator and converting the two points to x-y coordinates gives:

``````\$ echo -73.935242 40.730610 |proj +proj=omerc +lat_1=35.652832 +lon_1=139.839478 +lat_2=40.730610 +lon_2=-73.935242 +ellps=GRS80
5162164.32  14191389.18
\$ echo 139.839478 35.652832 |proj +proj=omerc +lat_1=35.652832 +lon_1=139.839478 +lat_2=40.730610 +lon_2=-73.935242 +ellps=GRS80
1450567.63  3987778.87
``````

In the output, I expect the "y" parts of the two coordinates are the same, because these two points are on the central line of projected coordinates. However, they are not (14191389.18 != 3987778.87).

Can somebody explain how omerc with two points in the central line works and provide correct parameter for `proj`?

• Possibly try two-point equidistant instead. it will align the two cities on a horizontal line or try adding +no_off to your omerc command. – mkennedy May 22 '19 at 17:38
• @mkennedy Unfortunately `+no_off` did not change the output and I want to know how "omerc with two points in the central line" works rather than calculating their equidistant by myself. – suztomo May 23 '19 at 14:10
• @mkennedy BTW, I feel it's a bug in proj. If you also think so and post it as an answer, I will be happy to accept that. – suztomo May 23 '19 at 22:28