Implement Geographic3D to Depth/Geog2D+Depth as used by ETRS89 to CD Norway depth

Fixes #2739

Verified with example from IOGP Guidance Note 7-2 (ver 62, Dec 2021) page 169, with
38 = h_obs - D_obs = 50 - 12.

$ echo 60.0015 4.9960 38 | PROJ_LIB=data PROJ_NETWORK=ON bin/cs2cs -d 4 EPSG:4937 EPSG:9883
60.0015	4.9960 5.8827

$ echo 60.0015 4.9960 38 | PROJ_LIB=data PROJ_NETWORK=ON bin/cs2cs -d 4 EPSG:4937 EPSG:4258+9672
60.0015	4.9960 5.8827

$ echo 60.0015 4.9960 5.8827 | PROJ_LIB=data PROJ_NETWORK=ON bin/cs2cs -d 4 EPSG:9883 EPSG:4937
60.0015	4.9960 38.0000

$ echo 60.0015 4.9960 5.8827 | PROJ_LIB=data PROJ_NETWORK=ON bin/cs2cs -d 4 EPSG:4258+9672 EPSG:4937
60.0015	4.9960 38.0000

2 files changed, 25 insertions, 2 deletions

diff --git a/src/iso19111/io.cpp b/src/iso19111/io.cpp
index 67877206..6c66b6f8 100644
--- a/src/iso19111/io.cpp
+++ b/src/iso19111/io.cpp
@@ -7671,6 +7671,13 @@ const std::string &PROJStringFormatter::toString() const {
             continue;
         }
 
+        // axisswap order=1,2,-3 is its own inverse
+        if (step.name == "axisswap" && paramCount == 1 &&
+            step.paramValues[0].equals("order", "1,2,-3")) {
+            step.inverted = false;
+            continue;
+        }
+
         // handle unitconvert inverse
         if (step.name == "unitconvert" && paramCount == 2 &&
             step.paramValues[0].keyEquals("xy_in") &&
diff --git a/src/iso19111/operation/transformation.cpp b/src/iso19111/operation/transformation.cpp
index 36540242..8bd4f3de 100644
--- a/src/iso19111/operation/transformation.cpp
+++ b/src/iso19111/operation/transformation.cpp
@@ -2011,8 +2011,8 @@ isGeographic3DToGravityRelatedHeight(const OperationMethodNNPtr &method,
         "1100", // Geog3D to Geog2D+GravityRelatedHeight (PL txt)
         "1103", // Geog3D to Geog2D+GravityRelatedHeight (EGM)
         "1105", // Geog3D to Geog2D+GravityRelatedHeight (ITAL2005)
-        // "1110", // Geog3D to Geog2D+Depth (Gravsoft)  FIXME: to investigate
-        // how to map this to PROJ pipeline (depth vs height)
+        "1109", // Geographic3D to Depth (Gravsoft)
+        "1110", // Geog3D to Geog2D+Depth (Gravsoft)
         "9661", // Geographic3D to GravityRelatedHeight (EGM)
         "9662", // Geographic3D to GravityRelatedHeight (Ausgeoid98)
         "9663", // Geographic3D to GravityRelatedHeight (OSGM-GB)
@@ -3164,6 +3164,13 @@ void Transformation::_exportToPROJString(
                     concat("Can apply ", methodName, " only to GeographicCRS"));
             }
 
+            auto targetVertCRS = targetCRS()->extractVerticalCRS();
+            if (!targetVertCRS) {
+                throw io::FormattingException(
+                    concat("Can apply ", methodName,
+                           " only to a target CRS that has a VerticalCRS"));
+            }
+
             if (!formatter->omitHorizontalConversionInVertTransformation()) {
                 formatter->startInversion();
                 formatter->pushOmitZUnitConversion();
@@ -3178,6 +3185,15 @@ void Transformation::_exportToPROJString(
             if (doInversion) {
                 formatter->startInversion();
             }
+
+            // For Geographic3D to Depth methods, we rely on the vertical axis
+            // direction instead of the name/code of the transformation method.
+            if (targetVertCRS->coordinateSystem()->axisList()[0]->direction() ==
+                cs::AxisDirection::DOWN) {
+                formatter->addStep("axisswap");
+                formatter->addParam("order", "1,2,-3");
+            }
+
             formatter->addStep("vgridshift");
             formatter->addParam("grids", filename);
             formatter->addParam("multiplier", 1.0);