[MetaCRS] failed epsg wkt (geotools)

[Norm Olsen]

Hello All . . .

The Oblique Mercator situation is a difficult one.  This is true for a variety of reasons.

The Hotine Oblique Mercator and the Rectified Skew Orthomorphic are essentially the same.  There are two azimuths involved.  The azimuth parameter can be either the azimuth of the central geodesic at the projection origin or the projection center.  The projection origin is the location where the central geodesic intersects the equator (actually the equator of the aposphere, whatever that is).  The projection center is that location that is commonly specified by the parameters.  If you know one, you can compute the other.  Thus, most implementations accept one parameter.  EPSG requires both be specified.  Unfortunately most documentation only provides one of these values, and usually don't specify exactly which one is given.  My experience suggests that when the projection is named as Hotine Oblique Mercator, the azimuth value is given at the center.  When the projection name is Rectified Skew Orthomorphic, the azimuth is given at the projection origin.  Thus, there is a significant difference between most every implementation with regard to projection and parameter names.  This confusion is amplified in WKT as there is no real specification for WKT.

Another area of confusion here is the meaning of the false origin.  Typically, the false origin is applied to the projection origin (i.e. the aposphere thing).  In other variations, the projection code computes an internal false adjustment which produces a 0:0 coordinate at the projection center, and the parameterized false origin then applies to the projection center.

So, it is not uncommon for a package to have four variations of the "Oblique Mercator" projection.

Another area of confusion results from the fact that there is yet another version of the Oblique Mercator.  In CS-MAP we call this the Oblique Cylindrical, it is also known as the Rosenmund Projection.  This projection is a completely different algorithm than the Hotine or RSO, although the Hotine (or RSO) is often used to approximate the Rosenmund.  This projection is that which is used in Switzerland and Hungary.  The Hungarian variation accepts a parameter that the Swiss version doesn't, so often this appears as two separate projections.

There are yet other rarely used variations, such as the two point form of the Oblique Mercator, all adding to the confusion.

So, the confusion here is a well known fact that we have to deal with.  I like to call it "job security" :>) :>)

Norm Olsen