[PROJ] Transverse and oblique Mercator

[Pierre Abbat]

I've been working on a surveying CAD program, one of whose parts is converting 
between lat/long and the coordinate systems used in surveying. I did Lambert 
conformal conic first, since it's easier (and I live in North Carolina), then 
figured out transverse Mercator. (I also did spherical stereographic, which 
Bezitopo uses for internal purposes.) The test for projections, before I wrote 
transverse Mercator, required that, at all but a negligible fraction of points 
(i.e. a branch cut), the inverse projection of the projection of a point be 
within 1 mm of the point and the distance between two points 1 m apart in a 
random direction match the computed scale. When I added transverse Mercator, I 
had to reduce all but a negligible fraction, but I lowered it to no less than 
80%. It is accurate to within 100 µm over 71% of the earth, which is within 
45° of the central meridian. How does this compare to PROJ?

Lambert conic and transverse Mercator together cover all but one of the US 
state plane grids and all of UTM, but there are others. I'd like to understand 
the oblique Mercator well enough to write code for it and what the differences 
are (besides the obvious) between Alaska and Switzerland.

Pierre
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