Fix Oblique Mercator natural-origin offset to use the central-line azimuth

[sergei-malyshko-navvis]

Summary

Fixes the Oblique Mercator (+proj=omerc) natural-origin offset so that the projection centre maps to the false easting/northing when +gamma differs from +alpha — in particular for definitions with an explicit +gamma=0 and a non-zero azimuth (the ESRI "Local" / mine-grid convention).

Root cause

In ObliqueMercatorProjection.initialize(), the natural-origin (uc) offset is computed with cosrot = cos(Gamma) (the rectified bearing γ):

u_0 = no_uoff ? 0. :
    Math.abs(al * Math.atan(Math.sqrt(d * d - 1.) / cosrot) / bl);

Snyder's Hotine Oblique Mercator (and PROJ) define this offset from the central-line azimuth α:

u_c = (A / B) * atan( sqrt(D^2 - 1) / cos(alpha_c) )

project() computes the point's along-line coordinate from the natural azimuth (singam/cosgam), so the offset must be based on α, not γ. When γ = α the two coincide (the common case, and why this went unnoticed — e.g. the standard EPSG omerc grids store +gamma equal to +alpha). But when γ ≠ α — e.g. +gamma=0 with a non-zero azimuth — u_0 no longer cancels the centre's coordinate, and the centre is displaced along the central line.

Impact (before the fix)

For a grid like +proj=omerc +lat_0=-20 +lonc=140 +alpha=30 +gamma=0 +k=1 +x_0=200000 +y_0=300000 +ellps=GRS80, the centre (140, -20) should map to (200000, 300000). Before the fix it was off by ~2.5 km in the along-line direction (larger for larger azimuths). This is the ESRI PROJECTION["Local"] mine-grid convention (origin + scale + azimuth, no rectification), which is common for Australian survey grids.

Fix

Use cos(alpha) for the offset. This is a no-op when γ == α (verified by the full existing test suite) and matches PROJ output when γ ≠ α.

Test

Adds Proj4VariousTest#testObliqueMercatorExplicitGamma, covering +gamma=0 with a non-zero azimuth. It asserts the centre maps exactly to the false easting/northing and checks two further points; reference coordinates were computed with PROJ. With the fix the centre error is 0 and the points agree with PROJ to < 1e-4 m; before the fix the centre was ~2.5 km off.

Full core suite: 65 run, 0 failures, 0 errors, 2 skipped (pre-existing).

Related note (not addressed here)

The Gamma field defaults to 0.0 rather than NaN, so the gzi = Double.isNaN(Gamma) guard is always "provided" and the if (gzi == 0) Gamma = alpha; default (rectified bearing defaults to the azimuth when +gamma is omitted) never runs. That affects the rotation for the +gamma-omitted case and the unreachable two-point setup. I've kept this PR focused on the offset bug; happy to open a separate issue/PR for the Gamma default if useful.

[pomadchin]

Thanks for rising up a PR!

Also could I ask you to sign https://www.eclipse.org/legal/eca/? (ECA form link) that would help us to make the ECA bot happy.

[pomadchin]

Thanks, that's a great catch!

[pomadchin]

💥