From 90ad86d9ef8fbd9c14693672c7d434ab7f7c0d00 Mon Sep 17 00:00:00 2001
From: Even Rouault <even.rouault@spatialys.com>
Date: Fri, 17 Jan 2025 15:16:30 +0100
Subject: [PATCH] Inverse +proj=cass: fix non-convergence on inputs where
 easting=false_easting or northing=false_northing

Fixes #4385

For a unknown reason, a test in pj_generic_inverse_2d() was skipping
adding the iterative correction terms when the input was such that
easting=false_easting or northing=false_northing, causing the function
to do nothing useful and fail after its maximum allowed number of
iterations was reached. The remove tests might or might not have been
needed... Only future will tell...
---
 src/generic_inverse.cpp | 38 ++++++++++++++++----------------------
 test/gie/builtins.gie   | 15 +++++++++++++++
 2 files changed, 31 insertions(+), 22 deletions(-)

diff --git a/src/generic_inverse.cpp b/src/generic_inverse.cpp
index fc7f078556..4c99372c98 100644
--- a/src/generic_inverse.cpp
+++ b/src/generic_inverse.cpp
@@ -87,29 +87,23 @@ PJ_LP pj_generic_inverse_2d(PJ_XY xy, PJ *P, PJ_LP lpInitial,
             }
         }
 
-        if (xy.x != 0) {
-            // Limit the amplitude of correction to avoid overshoots due to
-            // bad initial guess
-            const double delta_lam = std::max(
-                std::min(deltaX * deriv_lam_X + deltaY * deriv_lam_Y, 0.3),
-                -0.3);
-            lp.lam -= delta_lam;
-            if (lp.lam < -M_PI)
-                lp.lam = -M_PI;
-            else if (lp.lam > M_PI)
-                lp.lam = M_PI;
-        }
+        // Limit the amplitude of correction to avoid overshoots due to
+        // bad initial guess
+        const double delta_lam = std::max(
+            std::min(deltaX * deriv_lam_X + deltaY * deriv_lam_Y, 0.3), -0.3);
+        lp.lam -= delta_lam;
+        if (lp.lam < -M_PI)
+            lp.lam = -M_PI;
+        else if (lp.lam > M_PI)
+            lp.lam = M_PI;
 
-        if (xy.y != 0) {
-            const double delta_phi = std::max(
-                std::min(deltaX * deriv_phi_X + deltaY * deriv_phi_Y, 0.3),
-                -0.3);
-            lp.phi -= delta_phi;
-            if (lp.phi < -M_HALFPI)
-                lp.phi = -M_HALFPI;
-            else if (lp.phi > M_HALFPI)
-                lp.phi = M_HALFPI;
-        }
+        const double delta_phi = std::max(
+            std::min(deltaX * deriv_phi_X + deltaY * deriv_phi_Y, 0.3), -0.3);
+        lp.phi -= delta_phi;
+        if (lp.phi < -M_HALFPI)
+            lp.phi = -M_HALFPI;
+        else if (lp.phi > M_HALFPI)
+            lp.phi = M_HALFPI;
     }
     proj_context_errno_set(P->ctx,
                            PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie
index 2091af5502..9e16336afc 100644
--- a/test/gie/builtins.gie
+++ b/test/gie/builtins.gie
@@ -920,6 +920,21 @@ accept  179.99433652777776 -16.841456527777776
 expect  16015.28901692     13369.66005367
 roundtrip 1
 
+
+-------------------------------------------------------------------------------
+# Scenario of https://github.com/OSGeo/PROJ/issues/4385
+-------------------------------------------------------------------------------
+operation +proj=cass +lat_0=50.6177 +lon_0=-1.19725 +x_0=500000 +y_0=100000 +ellps=airy +units=m
+
+tolerance 0.1 mm
+direction inverse
+
+accept 300000 100000
+expect -4.022094267169   50.583438725252
+
+accept 500000 100000
+expect -1.19725 50.6177
+
 ===============================================================================
 # Central Conic
 # 	Sph