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

CHANGELOG.md

@@ -7,6 +7,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
+### Fixed
+- Oblique Mercator: compute the natural-origin (uc) offset from the central-line azimuth (`+alpha`) instead of the rectified bearing (`+gamma`), so the projection centre maps to the false easting/northing when `+gamma` differs from `+alpha` (e.g. an explicit `+gamma=0` with a non-zero azimuth)
+
 ## [1.4.3] - 2026-06-02
 
 ### Added

core/src/main/java/org/locationtech/proj4j/proj/ObliqueMercatorProjection.java

@@ -158,8 +158,12 @@ else if (con > Math.PI)
 		sinrot = Math.sin(Gamma);
 		cosrot = Math.cos(Gamma);
 
+		// The natural-origin offset uses the azimuth of the central line (alpha), following Snyder's
+		// Hotine Oblique Mercator: u_c = (A / B) * atan(sqrt(D^2 - 1) / cos(alpha_c)). Using the
+		// rectified bearing (Gamma) here misplaces the projection centre whenever Gamma != alpha,
+		// e.g. for definitions with an explicit "+gamma=0" and a non-zero azimuth.
 		u_0 = no_uoff ? 0. :
-			Math.abs(al * Math.atan(Math.sqrt(d * d - 1.) / cosrot) / bl);
+			Math.abs(al * Math.atan(Math.sqrt(d * d - 1.) / Math.cos(alpha)) / bl);
 		if (projectionLatitude < 0.)
 			u_0 = - u_0;
 	}

core/src/test/java/org/locationtech/proj4j/Proj4VariousTest.java

@@ -91,6 +91,19 @@ public void testSTS() {
                 1e-5);
     }
 
+    @Test
+    public void testObliqueMercatorExplicitGamma() {
+        // Hotine Oblique Mercator with an explicit "+gamma=0" and a non-zero azimuth. The natural
+        // origin offset must place the projection centre (lonc, lat_0) exactly at the false
+        // easting/northing; a regression here shifted the centre by ~2.5 km. Reference coordinates
+        // computed with PROJ.
+        String omerc =
+                "+proj=omerc +lat_0=-20 +lonc=140 +alpha=30 +gamma=0 +k=1 +x_0=200000 +y_0=300000 +ellps=GRS80 +units=m";
+        checkTransform("+proj=latlong +ellps=GRS80", p("140 -20"), omerc, p("200000.00 300000.00"), 1e-2);
+        checkTransform("+proj=latlong +ellps=GRS80", p("140.5 -20.2"), omerc, p("256366.4343 306886.2489"), 1e-2);
+        checkTransform("+proj=latlong +ellps=GRS80", p("139.7 -19.8"), omerc, p("161721.1705 303433.2577"), 1e-2);
+    }
+
     // disabled - gamma param not implemented
 //    @Test
     public void XXX_testRSOBorneo() {