EPSG Helmert and Molodensky-Badekas methods in the Geographic 2D domain: use the push/pop v_3 operator to preserve the Z component

1 files changed, 133 insertions, 123 deletions

diff --git a/test/unit/test_operation.cpp b/test/unit/test_operation.cpp
index 6144663e..e855a818 100644
--- a/test/unit/test_operation.cpp
+++ b/test/unit/test_operation.cpp
@@ -561,11 +561,12 @@ TEST(operation, transformation_createGeocentricTranslations) {
     EXPECT_EQ(inv_transf_as_transf->getTOWGS84Parameters(), expected_inv);
 
     EXPECT_EQ(transf->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-              "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-              "+ellps=GRS80 +step +proj=helmert +x=1 +y=2 +z=3 +step +inv "
-              "+proj=cart +ellps=WGS84 +step +proj=unitconvert +xy_in=rad "
-              "+xy_out=deg +step +proj=axisswap +order=2,1");
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+              "+proj=cart +ellps=GRS80 +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+step +inv +proj=cart +ellps=WGS84 +step +proj=unitconvert "
+              "+xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1 +step "
+              "+proj=pop +v_3");
 }
 
 // ---------------------------------------------------------------------------
@@ -668,13 +669,13 @@ TEST(operation, transformation_createPositionVector) {
     EXPECT_EQ(transf->getTOWGS84Parameters(), expected);
 
     EXPECT_EQ(transf->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-              "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-              "+ellps=GRS80 +step +proj=helmert +x=1 +y=2 +z=3 +rx=4 +ry=5 "
-              "+rz=6 +s=7 +convention=position_vector +step +inv +proj=cart "
-              "+ellps=WGS84 +step "
-              "+proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap "
-              "+order=2,1");
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+              "+proj=cart +ellps=GRS80 +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
+              "+proj=cart +ellps=WGS84 +step +proj=unitconvert +xy_in=rad "
+              "+xy_out=deg +step +proj=axisswap +order=2,1 +step +proj=pop "
+              "+v_3");
 
     auto inv_transf = transf->inverse();
     ASSERT_EQ(inv_transf->coordinateOperationAccuracies().size(), 1);
@@ -691,12 +692,12 @@ TEST(operation, transformation_createPositionVector) {
 #else
     EXPECT_EQ(
         inv_transf->exportToPROJString(PROJStringFormatter::create().get()),
-        "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-        "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-        "+ellps=WGS84 +step +inv +proj=helmert +x=1 +y=2 +z=3 +rx=4 "
-        "+ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
-        "+proj=cart +ellps=GRS80 +step +proj=unitconvert +xy_in=rad "
-        "+xy_out=deg +step +proj=axisswap +order=2,1");
+        "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap +order=2,1 "
+        "+step +proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
+        "+ellps=WGS84 +step +inv +proj=helmert +x=1 +y=2 +z=3 +rx=4 +ry=5 "
+        "+rz=6 +s=7 +convention=position_vector +step +inv +proj=cart "
+        "+ellps=GRS80 +step +proj=unitconvert +xy_in=rad +xy_out=deg +step "
+        "+proj=axisswap +order=2,1 +step +proj=pop +v_3");
 
     // In WKT, use approximate formula
     auto wkt = inv_transf->exportToWKT(WKTFormatter::create().get());
@@ -737,13 +738,13 @@ TEST(operation, transformation_createCoordinateFrameRotation) {
     EXPECT_EQ(params, expected);
 
     EXPECT_EQ(transf->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-              "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-              "+ellps=GRS80 +step +proj=helmert +x=1 +y=2 +z=3 +rx=-4 +ry=-5 "
-              "+rz=-6 +s=7 +convention=coordinate_frame +step +inv +proj=cart "
-              "+ellps=WGS84 +step "
-              "+proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap "
-              "+order=2,1");
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+              "+proj=cart +ellps=GRS80 +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=-4 +ry=-5 +rz=-6 +s=7 +convention=coordinate_frame +step "
+              "+inv +proj=cart +ellps=WGS84 +step +proj=unitconvert +xy_in=rad "
+              "+xy_out=deg +step +proj=axisswap +order=2,1 +step +proj=pop "
+              "+v_3");
 
     auto inv_transf = transf->inverse();
     ASSERT_EQ(inv_transf->coordinateOperationAccuracies().size(), 0);
@@ -760,12 +761,12 @@ TEST(operation, transformation_createCoordinateFrameRotation) {
 #else
     EXPECT_EQ(
         inv_transf->exportToPROJString(PROJStringFormatter::create().get()),
-        "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-        "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-        "+ellps=WGS84 +step +inv +proj=helmert +x=1 +y=2 +z=3 +rx=-4 "
-        "+ry=-5 +rz=-6 +s=7 +convention=coordinate_frame +step +inv "
-        "+proj=cart +ellps=GRS80 +step +proj=unitconvert +xy_in=rad "
-        "+xy_out=deg +step +proj=axisswap +order=2,1");
+        "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap +order=2,1 "
+        "+step +proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
+        "+ellps=WGS84 +step +inv +proj=helmert +x=1 +y=2 +z=3 +rx=-4 +ry=-5 "
+        "+rz=-6 +s=7 +convention=coordinate_frame +step +inv +proj=cart "
+        "+ellps=GRS80 +step +proj=unitconvert +xy_in=rad +xy_out=deg +step "
+        "+proj=axisswap +order=2,1 +step +proj=pop +v_3");
 
     // In WKT, use approximate formula
     auto wkt = inv_transf->exportToWKT(WKTFormatter::create().get());
@@ -4197,13 +4198,13 @@ TEST(operation, geogCRS_to_geogCRS_context_default) {
 
         EXPECT_EQ(
             list[0]->exportToPROJString(PROJStringFormatter::create().get()),
-            "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-            "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-            "+ellps=krass +step +proj=helmert +x=2.3287 +y=-147.0425 "
-            "+z=-92.0802 +rx=0.3092483 +ry=-0.32482185 +rz=-0.49729934 "
-            "+s=5.68906266 +convention=coordinate_frame +step +inv "
-            "+proj=cart +ellps=GRS80 +step +proj=unitconvert +xy_in=rad "
-            "+xy_out=deg +step +proj=axisswap +order=2,1");
+            "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+            "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+            "+proj=cart +ellps=krass +step +proj=helmert +x=2.3287 "
+            "+y=-147.0425 +z=-92.0802 +rx=0.3092483 +ry=-0.32482185 "
+            "+rz=-0.49729934 +s=5.68906266 +convention=coordinate_frame +step "
+            "+inv +proj=cart +ellps=GRS80 +step +proj=unitconvert +xy_in=rad "
+            "+xy_out=deg +step +proj=axisswap +order=2,1 +step +proj=pop +v_3");
     }
 
     // Reverse case
@@ -4218,13 +4219,13 @@ TEST(operation, geogCRS_to_geogCRS_context_default) {
 
         EXPECT_EQ(
             list[0]->exportToPROJString(PROJStringFormatter::create().get()),
-            "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-            "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-            "+ellps=GRS80 +step +inv +proj=helmert +x=2.3287 "
+            "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+            "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+            "+proj=cart +ellps=GRS80 +step +inv +proj=helmert +x=2.3287 "
             "+y=-147.0425 +z=-92.0802 +rx=0.3092483 +ry=-0.32482185 "
-            "+rz=-0.49729934 +s=5.68906266 +convention=coordinate_frame "
-            "+step +inv +proj=cart +ellps=krass +step +proj=unitconvert "
-            "+xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1");
+            "+rz=-0.49729934 +s=5.68906266 +convention=coordinate_frame +step "
+            "+inv +proj=cart +ellps=krass +step +proj=unitconvert +xy_in=rad "
+            "+xy_out=deg +step +proj=axisswap +order=2,1 +step +proj=pop +v_3");
     }
 }
 
@@ -4358,11 +4359,12 @@ TEST(operation, geogCRS_to_geogCRS_context_inverse_needed) {
         ASSERT_EQ(list.size(), 3);
         EXPECT_EQ(
             list[0]->exportToPROJString(PROJStringFormatter::create().get()),
-            "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-            "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-            "+ellps=clrk80ign +step +proj=helmert +x=-168 +y=-60 +z=320 "
-            "+step +inv +proj=cart +ellps=GRS80 +step +proj=unitconvert "
-            "+xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1");
+            "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+            "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+            "+proj=cart +ellps=clrk80ign +step +proj=helmert +x=-168 +y=-60 "
+            "+z=320 +step +inv +proj=cart +ellps=GRS80 +step +proj=unitconvert "
+            "+xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1 +step "
+            "+proj=pop +v_3");
         EXPECT_EQ(list[1]->exportToPROJString(
                       PROJStringFormatter::create(
                           PROJStringFormatter::Convention::PROJ_5,
@@ -5299,15 +5301,15 @@ TEST(operation, boundCRS_of_geogCRS_to_geogCRS) {
     auto op = CoordinateOperationFactory::create()->createOperation(
         boundCRS, GeographicCRS::EPSG_4326);
     ASSERT_TRUE(op != nullptr);
-    EXPECT_EQ(
-        op->exportToPROJString(PROJStringFormatter::create().get()),
-        "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-        "+proj=unitconvert +xy_in=grad +xy_out=rad +step +inv +proj=longlat "
-        "+ellps=clrk80ign +pm=paris +step +proj=cart +ellps=clrk80ign "
-        "+step +proj=helmert +x=1 +y=2 +z=3 +rx=4 +ry=5 +rz=6 +s=7 "
-        "+convention=position_vector +step "
-        "+inv +proj=cart +ellps=WGS84 +step +proj=unitconvert +xy_in=rad "
-        "+xy_out=deg +step +proj=axisswap +order=2,1");
+    EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=grad +xy_out=rad "
+              "+step +inv +proj=longlat +ellps=clrk80ign +pm=paris +step "
+              "+proj=cart +ellps=clrk80ign +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
+              "+proj=cart +ellps=WGS84 +step +proj=unitconvert +xy_in=rad "
+              "+xy_out=deg +step +proj=axisswap +order=2,1 +step +proj=pop "
+              "+v_3");
 }
 
 // ---------------------------------------------------------------------------
@@ -5321,12 +5323,13 @@ TEST(operation, boundCRS_of_geogCRS_to_geogCRS_with_area) {
         boundCRS, authFactory->createCoordinateReferenceSystem("4326"));
     ASSERT_TRUE(op != nullptr);
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-              "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-              "+ellps=clrk66 +step +proj=helmert +x=1 +y=2 +z=3 +rx=4 +ry=5 "
-              "+rz=6 +s=7 +convention=position_vector +step +inv +proj=cart "
-              "+ellps=WGS84 +step +proj=unitconvert +xy_in=rad +xy_out=deg "
-              "+step +proj=axisswap +order=2,1");
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+              "+proj=cart +ellps=clrk66 +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
+              "+proj=cart +ellps=WGS84 +step +proj=unitconvert +xy_in=rad "
+              "+xy_out=deg +step +proj=axisswap +order=2,1 +step +proj=pop "
+              "+v_3");
 }
 
 // ---------------------------------------------------------------------------
@@ -5362,11 +5365,11 @@ TEST(operation, createOperation_boundCRS_identified_by_datum) {
         NN_CHECK_ASSERT(src), NN_CHECK_ASSERT(dest));
     ASSERT_TRUE(op != nullptr);
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=unitconvert +xy_in=deg +xy_out=rad "
-              "+step +proj=cart +ellps=WGS84 "
-              "+step +proj=helmert +x=263 +y=-6 +z=-431 "
-              "+step +inv +proj=cart +ellps=clrk80ign "
-              "+step +proj=utm +zone=32 +ellps=clrk80ign");
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=unitconvert "
+              "+xy_in=deg +xy_out=rad +step +proj=cart +ellps=WGS84 +step "
+              "+proj=helmert +x=263 +y=-6 +z=-431 +step +inv +proj=cart "
+              "+ellps=clrk80ign +step +proj=pop +v_3 +step +proj=utm +zone=32 "
+              "+ellps=clrk80ign");
 
     auto authFactory =
         AuthorityFactory::create(DatabaseContext::create(), std::string());
@@ -5436,12 +5439,13 @@ TEST(operation, boundCRS_of_projCRS_to_geogCRS) {
     ASSERT_TRUE(op != nullptr);
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
               "+proj=pipeline +step +inv +proj=utm +zone=31 +ellps=clrk80ign "
-              "+pm=paris "
-              "+step +proj=cart +ellps=clrk80ign +step +proj=helmert +x=1 +y=2 "
-              "+z=3 +rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step "
-              "+inv +proj=cart +ellps=WGS84 "
+              "+pm=paris +step +proj=longlat +ellps=clrk80ign +pm=paris +step "
+              "+proj=push +v_3 +step +inv +proj=longlat +ellps=clrk80ign "
+              "+pm=paris +step +proj=cart +ellps=clrk80ign +step +proj=helmert "
+              "+x=1 +y=2 +z=3 +rx=4 +ry=5 +rz=6 +s=7 "
+              "+convention=position_vector +step +inv +proj=cart +ellps=WGS84 "
               "+step +proj=unitconvert +xy_in=rad +xy_out=deg +step "
-              "+proj=axisswap +order=2,1");
+              "+proj=axisswap +order=2,1 +step +proj=pop +v_3");
 }
 
 // ---------------------------------------------------------------------------
@@ -5456,15 +5460,14 @@ TEST(operation, boundCRS_of_geogCRS_to_projCRS) {
     auto op =
         CoordinateOperationFactory::create()->createOperation(boundCRS, utm31);
     ASSERT_TRUE(op != nullptr);
-    EXPECT_EQ(
-        op->exportToPROJString(PROJStringFormatter::create().get()),
-        "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-        "+proj=unitconvert +xy_in=grad +xy_out=rad +step +inv +proj=longlat "
-        "+ellps=clrk80ign +pm=paris +step +proj=cart +ellps=clrk80ign "
-        "+step +proj=helmert +x=1 +y=2 +z=3 +rx=4 +ry=5 +rz=6 +s=7 "
-        "+convention=position_vector +step "
-        "+inv +proj=cart +ellps=WGS84 +step +proj=utm +zone=31 "
-        "+ellps=WGS84");
+    EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=grad +xy_out=rad "
+              "+step +inv +proj=longlat +ellps=clrk80ign +pm=paris +step "
+              "+proj=cart +ellps=clrk80ign +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
+              "+proj=cart +ellps=WGS84 +step +proj=pop +v_3 +step +proj=utm "
+              "+zone=31 +ellps=WGS84");
 }
 
 // ---------------------------------------------------------------------------
@@ -5476,13 +5479,14 @@ TEST(operation, geogCRS_to_boundCRS_of_geogCRS) {
         GeographicCRS::EPSG_4326, boundCRS);
     ASSERT_TRUE(op != nullptr);
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-              "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-              "+ellps=WGS84 +step +inv +proj=helmert +x=1 +y=2 +z=3 +rx=4 "
-              "+ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+              "+proj=cart +ellps=WGS84 +step +inv +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
               "+proj=cart +ellps=clrk80ign +step +proj=longlat "
               "+ellps=clrk80ign +pm=paris +step +proj=unitconvert +xy_in=rad "
-              "+xy_out=grad +step +proj=axisswap +order=2,1");
+              "+xy_out=grad +step +proj=axisswap +order=2,1 +step +proj=pop "
+              "+v_3");
 }
 
 // ---------------------------------------------------------------------------
@@ -5505,12 +5509,14 @@ TEST(operation, boundCRS_to_boundCRS) {
     ASSERT_TRUE(op != nullptr);
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
               "+proj=pipeline +step +inv +proj=utm +zone=31 +ellps=clrk80ign "
-              "+pm=paris "
-              "+step +proj=cart +ellps=clrk80ign +step +proj=helmert +x=1 +y=2 "
-              "+z=3 +rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step "
-              "+inv +proj=helmert +x=8 +y=9 +z=10 +rx=11 +ry=12 +rz=13 +s=14 "
-              "+convention=position_vector +step +inv +proj=cart +ellps=GRS80 "
-              "+step +proj=utm +zone=32 +ellps=GRS80");
+              "+pm=paris +step +proj=longlat +ellps=clrk80ign +pm=paris +step "
+              "+proj=push +v_3 +step +inv +proj=longlat +ellps=clrk80ign "
+              "+pm=paris +step +proj=cart +ellps=clrk80ign +step +proj=helmert "
+              "+x=1 +y=2 +z=3 +rx=4 +ry=5 +rz=6 +s=7 "
+              "+convention=position_vector +step +inv +proj=helmert +x=8 +y=9 "
+              "+z=10 +rx=11 +ry=12 +rz=13 +s=14 +convention=position_vector "
+              "+step +inv +proj=cart +ellps=GRS80 +step +proj=pop +v_3 +step "
+              "+proj=utm +zone=32 +ellps=GRS80");
 }
 
 // ---------------------------------------------------------------------------
@@ -5523,13 +5529,13 @@ TEST(operation, boundCRS_to_boundCRS_noop_for_TOWGS84) {
     auto op = CoordinateOperationFactory::create()->createOperation(boundCRS1,
                                                                     boundCRS2);
     ASSERT_TRUE(op != nullptr);
-    EXPECT_EQ(
-        op->exportToPROJString(PROJStringFormatter::create().get()),
-        "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-        "+proj=unitconvert +xy_in=grad +xy_out=rad +step +inv +proj=longlat "
-        "+ellps=clrk80ign +pm=paris +step +proj=cart +ellps=clrk80ign "
-        "+step +inv +proj=cart +ellps=GRS80 +step +proj=unitconvert "
-        "+xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1");
+    EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=grad +xy_out=rad "
+              "+step +inv +proj=longlat +ellps=clrk80ign +pm=paris +step "
+              "+proj=cart +ellps=clrk80ign +step +inv +proj=cart +ellps=GRS80 "
+              "+step +proj=unitconvert +xy_in=rad +xy_out=deg +step "
+              "+proj=axisswap +order=2,1 +step +proj=pop +v_3");
 }
 
 // ---------------------------------------------------------------------------
@@ -5927,12 +5933,13 @@ TEST(operation, compoundCRS_with_boundGeogCRS_to_geogCRS) {
         compound, GeographicCRS::EPSG_4979);
     ASSERT_TRUE(op != nullptr);
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-              "+proj=unitconvert +xy_in=deg +xy_out=rad +step +proj=cart "
-              "+ellps=WGS84 +step +proj=helmert +x=1 +y=2 +z=3 +rx=4 +ry=5 "
-              "+rz=6 +s=7 +convention=position_vector +step +inv +proj=cart "
-              "+ellps=WGS84 +step +proj=unitconvert +xy_in=rad +xy_out=deg "
-              "+step +proj=axisswap +order=2,1");
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad +step "
+              "+proj=cart +ellps=WGS84 +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
+              "+proj=cart +ellps=WGS84 +step +proj=unitconvert +xy_in=rad "
+              "+xy_out=deg +step +proj=axisswap +order=2,1 +step +proj=pop "
+              "+v_3");
 }
 
 // ---------------------------------------------------------------------------
@@ -5950,15 +5957,15 @@ TEST(operation, compoundCRS_with_boundGeogCRS_and_boundVerticalCRS_to_geogCRS) {
     // Not completely sure the order of horizontal and vertical operations
     // makes sense
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
-              "+proj=pipeline +step +proj=axisswap +order=2,1 +step "
-              "+proj=unitconvert +xy_in=grad +xy_out=rad +step +inv "
-              "+proj=longlat +ellps=clrk80ign +pm=paris +step +proj=cart "
-              "+ellps=clrk80ign +step +proj=helmert +x=1 +y=2 +z=3 +rx=4 +ry=5 "
-              "+rz=6 +s=7 +convention=position_vector +step +inv +proj=cart "
-              "+ellps=WGS84 +step +proj=vgridshift +grids=egm08_25.gtx "
-              "+multiplier=1 +step "
-              "+proj=unitconvert +xy_in=rad +xy_out=deg +step "
-              "+proj=axisswap +order=2,1");
+              "+proj=pipeline +step +proj=push +v_3 +step +proj=axisswap "
+              "+order=2,1 +step +proj=unitconvert +xy_in=grad +xy_out=rad "
+              "+step +inv +proj=longlat +ellps=clrk80ign +pm=paris +step "
+              "+proj=cart +ellps=clrk80ign +step +proj=helmert +x=1 +y=2 +z=3 "
+              "+rx=4 +ry=5 +rz=6 +s=7 +convention=position_vector +step +inv "
+              "+proj=cart +ellps=WGS84 +step +proj=pop +v_3 +step "
+              "+proj=vgridshift +grids=egm08_25.gtx +multiplier=1 +step "
+              "+proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap "
+              "+order=2,1");
 
     auto grids = op->gridsNeeded(DatabaseContext::create());
     EXPECT_EQ(grids.size(), 1);
@@ -5989,12 +5996,14 @@ TEST(operation, compoundCRS_with_boundProjCRS_and_boundVerticalCRS_to_geogCRS) {
     // makes sense
     EXPECT_EQ(op->exportToPROJString(PROJStringFormatter::create().get()),
               "+proj=pipeline +step +inv +proj=utm +zone=31 +ellps=clrk80ign "
+              "+pm=paris +step +proj=longlat +ellps=clrk80ign +pm=paris +step "
+              "+proj=push +v_3 +step +inv +proj=longlat +ellps=clrk80ign "
               "+pm=paris +step +proj=cart +ellps=clrk80ign +step +proj=helmert "
               "+x=1 +y=2 +z=3 +rx=4 +ry=5 +rz=6 +s=7 "
               "+convention=position_vector +step +inv +proj=cart +ellps=WGS84 "
-              "+step +proj=vgridshift +grids=egm08_25.gtx +multiplier=1 +step "
-              "+proj=unitconvert +xy_in=rad +xy_out=deg +step "
-              "+proj=axisswap +order=2,1");
+              "+step +proj=pop +v_3 +step +proj=vgridshift +grids=egm08_25.gtx "
+              "+multiplier=1 +step +proj=unitconvert +xy_in=rad +xy_out=deg "
+              "+step +proj=axisswap +order=2,1");
 
     auto opInverse = CoordinateOperationFactory::create()->createOperation(
         GeographicCRS::EPSG_4979, compound);
@@ -6200,10 +6209,11 @@ TEST(operation, IGNF_LAMB1_TO_EPSG_4326) {
     EXPECT_EQ(list[1]->exportToPROJString(PROJStringFormatter::create().get()),
               "+proj=pipeline +step +inv +proj=lcc +lat_1=49.5 +lat_0=49.5 "
               "+lon_0=0 +k_0=0.99987734 +x_0=600000 +y_0=200000 "
-              "+ellps=clrk80ign +pm=paris +step +proj=cart +ellps=clrk80ign "
-              "+step +proj=helmert +x=-168 +y=-60 +z=320 +step +inv +proj=cart "
-              "+ellps=WGS84 +step +proj=unitconvert +xy_in=rad +xy_out=deg "
-              "+step +proj=axisswap +order=2,1");
+              "+ellps=clrk80ign +pm=paris +step +proj=push +v_3 +step "
+              "+proj=cart +ellps=clrk80ign +step +proj=helmert +x=-168 +y=-60 "
+              "+z=320 +step +inv +proj=cart +ellps=WGS84 +step "
+              "+proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap "
+              "+order=2,1 +step +proj=pop +v_3");
 
     auto list2 = CoordinateOperationFactory::create()->createOperations(
         AuthorityFactory::create(DatabaseContext::create(), "EPSG")