Matching paper/map data Oblique Mercator Projection
I have a paper map of the UK which states:
"Drawn on the Oblique Mercator projection using the WGS84 spheroid at a scale of 1:1,000,000. Vertex of the equator occurs at N56'22'04, E012'31'15".
I also have a copy of the map data for this map. Question is, how do I define a projection that will match the one on the paper map?
In ArcMap I've noticed that there are four Hotine Oblique Mercator projections in the 'New Projected Coordinate System' dialog but don't know how to put them to use to get to the same projection as the paper map, or if I even have enough information to define the parameters of the projection.
Mapping Center Answer:
You can use the Hotine Oblique Mercator which as you note has several different types:
You define the tilt of the projection using types 1 and 2 by specifying a point and an angle measuring east of north (the azimuth). You define the tilt of the projection using types 3 and 4 by specifying two points.
Further, for types 2 and 4, the coordinate origin of the projected coordinates is located where the central line of the projection crosses the equator. As an example, if you use an Oblique Mercator (natural origin) for West Virginia, while the center of the projection is -80.75, 38.5, the natural origin is approximately -112.8253, 0.0.
You can move the projection origin to the center of your data by using the Two-Point Center or Azimuth Center types. Using the Two-Point Center type, the coordinates listed for the "vertex of the equator" (approx. 12.5208333333E and 56.3677777777N after you convert the coordinates in degrees minutes seconds to decimal degrees) can be used to set the first point. Then you can use the same longitude but substitute 0.0 for the latitude for the second point.
Using the Azimuth Center type, set the center at the given point, but then use an azimuth of 90. That would run the central line through the UK, at least.
We were caught by fact that the latitude value is about halfway, given the inclusion of the Shetland Islands, into a north-south calculation of the extent of the UK. But even stranger, the longitude is not even in the country! It's somewhere off the southwestern coast of Sweden. And to top it off, a map at a scale of 1:1,000,000 would show only a very small portion of the country, unless it was printed on a really large page.
It still doesn't make sense to us—if either of the two projection types and parameters we outline above are used, there should be a scale factor as well.
Have you tried to contact the publisher? They may know more.
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