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Add support for 'Coordinate Frame rotation full matrix (geocen)' and … #4348

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Add support for 'Coordinate Frame rotation full matrix (geocen)' and … #4348

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2 changes: 1 addition & 1 deletion data/CMakeLists.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -45,7 +45,7 @@ set(ALL_SQL_IN "${CMAKE_CURRENT_BINARY_DIR}/all.sql.in")
set(PROJ_DB "${CMAKE_CURRENT_BINARY_DIR}/proj.db")
include(sql_filelist.cmake)

set(PROJ_DB_SQL_EXPECTED_MD5 "3d51445a31ba6980332fa8e2348f7b16")
set(PROJ_DB_SQL_EXPECTED_MD5 "3e0b3f2f65e9bb051e2f5fb6b40e1a42")

add_custom_command(
OUTPUT ${PROJ_DB}
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4 changes: 4 additions & 0 deletions data/sql/helmert_transformation.sql
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Expand Up @@ -2690,10 +2690,14 @@ INSERT INTO "helmert_transformation" VALUES('EPSG','10607','WGS 84 (G2139) to WG
INSERT INTO "usage" VALUES('EPSG','21197','helmert_transformation','EPSG','10607','EPSG','1262','EPSG','1027');
INSERT INTO "helmert_transformation" VALUES('EPSG','10608','WGS 84 (G2296) to ITRF2020 (1)','Scale difference in ppb where 1/billion = 1E-9 or nm/m. Accuracy of 1cm applies at epoch 2024.0. Due to subsequent drift between the reference frames it may reach 2cm at other epochs.','EPSG','1032','Coordinate Frame rotation (geocentric domain)','EPSG','10604','EPSG','9988',0.01,0.0,0.0,0.0,'EPSG','1025',0.0,0.0,0.0,'EPSG','1031',0.0,'EPSG','1028',NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,'NGA-Wld 2024.0',0);
INSERT INTO "usage" VALUES('EPSG','21198','helmert_transformation','EPSG','10608','EPSG','1262','EPSG','1026');
INSERT INTO "helmert_transformation" VALUES('EPSG','10646','Saba to BES2020 Saba (1)','For the reverse transformation from BES2020 Saba to Saba, method 1133 [used here] is reversible with the parameter values given here (see GN7-2); the BESTRANS software uses different parameter values with the forward formulas: see BESTRANS documentation.','EPSG','1133','Coordinate Frame rotation full matrix (geog2D)','EPSG','10636','EPSG','10639',0.05,1138.7432,-2064.4761,110.7016,'EPSG','9001',-214.615206,479.360036,-164.703951,'EPSG','9104',-402.32073,'EPSG','9202',NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,'NSGI-Bes Saba',0);
INSERT INTO "usage" VALUES('EPSG','21861','helmert_transformation','EPSG','10646','EPSG','4757','EPSG','1144');
INSERT INTO "helmert_transformation" VALUES('EPSG','10647','BES2020 Saba to ITRF2014 (1)','Time-dependent component of official transformation BESTRANS2020.','EPSG','1056','Time-dependent Coordinate Frame rotation (geocen)','EPSG','10637','EPSG','7789',0.05,0.0,0.0,0.0,'EPSG','9001',0.0,0.0,0.0,'EPSG','9104',0.0,'EPSG','9202',0.00726,0.00848,0.01353,'EPSG','1042',0.0,0.0,0.0,'EPSG','1043',0.0,'EPSG','1041',2020.0,'EPSG','1029',NULL,NULL,NULL,NULL,NULL,'NSGI-Bes Saba',0);
INSERT INTO "usage" VALUES('EPSG','21765','helmert_transformation','EPSG','10647','EPSG','4757','EPSG','1079');
INSERT INTO "helmert_transformation" VALUES('EPSG','10648','BES2020 Saba to WGS 84 (1)','','EPSG','9603','Geocentric translations (geog2D domain)','EPSG','10639','EPSG','4326',0.5,0.0,0.0,0.0,'EPSG','9001',NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,'NSGI-Bes Saba',0);
INSERT INTO "usage" VALUES('EPSG','21743','helmert_transformation','EPSG','10648','EPSG','4757','EPSG','1252');
INSERT INTO "helmert_transformation" VALUES('EPSG','10676','Saba to WGS 84 (1)','Parameter values taken from Saba to BES2020 Saba (1) (transformation code 10646) assuming that BES2020 Saba is coincident with WGS 84 within the accuracy of the transformation.','EPSG','1133','Coordinate Frame rotation full matrix (geog2D)','EPSG','10636','EPSG','4326',1.0,1138.7432,-2064.4761,110.7016,'EPSG','9001',-214.615206,479.360036,-164.703951,'EPSG','9104',-402.32073,'EPSG','9202',NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,'IOGP-Bes Saba',0);
INSERT INTO "usage" VALUES('EPSG','21783','helmert_transformation','EPSG','10676','EPSG','4757','EPSG','1252');
INSERT INTO "helmert_transformation" VALUES('EPSG','10682','RGM04 to RGM23 (1)','Approximation at the +/- 0.1m level. For more accurate official transformation see RGM04 to RGM23 (2) (code 10683).','EPSG','9603','Geocentric translations (geog2D domain)','EPSG','4470','EPSG','10671',0.1,-0.5377,0.3946,0.3608,'EPSG','9001',NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,'IGN-Myt 10cm',0);
INSERT INTO "usage" VALUES('EPSG','21834','helmert_transformation','EPSG','10682','EPSG','1159','EPSG','1189');
INSERT INTO "helmert_transformation" VALUES('EPSG','10684','RGM23 to WGS 84 (1)','Approximation at the +/- 1m level assuming that RGM23 is equivalent to WGS 84.','EPSG','9603','Geocentric translations (geog2D domain)','EPSG','10671','EPSG','4326',1.0,0.0,0.0,0.0,'EPSG','9001',NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,'IOGP-Myt',0);
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9 changes: 8 additions & 1 deletion scripts/build_db.py
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Expand Up @@ -585,7 +585,7 @@ def fill_compound_crs(proj_db_cursor):
raise

def fill_helmert_transformation(proj_db_cursor):
proj_db_cursor.execute("SELECT coord_op_code, coord_op_name, coord_op_method_code, coord_op_method_name, source_crs_code, target_crs_code, coord_op_accuracy, coord_tfm_version, epsg_coordoperation.deprecated, epsg_coordoperation.remarks FROM epsg.epsg_coordoperation LEFT JOIN epsg.epsg_coordoperationmethod USING (coord_op_method_code) WHERE coord_op_type = 'transformation' AND coord_op_method_code IN (1031, 1032, 1033, 1034, 1035, 1037, 1038, 1039, 1053, 1054, 1055, 1056, 1057, 1058, 1061, 1062, 1063, 1065, 1066, 9603, 9606, 9607, 9636) ")
proj_db_cursor.execute("SELECT coord_op_code, coord_op_name, coord_op_method_code, coord_op_method_name, source_crs_code, target_crs_code, coord_op_accuracy, coord_tfm_version, epsg_coordoperation.deprecated, epsg_coordoperation.remarks FROM epsg.epsg_coordoperation LEFT JOIN epsg.epsg_coordoperationmethod USING (coord_op_method_code) WHERE coord_op_type = 'transformation' AND coord_op_method_code IN (1031, 1032, 1033, 1034, 1035, 1037, 1038, 1039, 1053, 1054, 1055, 1056, 1057, 1058, 1061, 1062, 1063, 1065, 1066, 1132, 1133, 9603, 9606, 9607, 9636) ")
for (code, name, method_code, method_name, source_crs_code, target_crs_code, coord_op_accuracy, coord_tfm_version, deprecated, remarks) in proj_db_cursor.fetchall():
expected_order = 1
max_n_params = 15
Expand Down Expand Up @@ -928,6 +928,13 @@ def fill_concatenated_operation(proj_db_cursor):
expected_order = 1
steps_code = []

# FIXME: https://epsg.org/concatenated-operation_10675/BES2020-to-Saba-height-1.html ill defined in EPSG 11.023
# due to first step referencing BES2020 Saba geographic 2D (EPSG:10639), but source CRS of concatenated
# operation referencing BES2020 Saba geographic 3D (EPSG:10638)
if code == 10675:
print("FIXME! Skipping EPSG:10675 'BES2020 to Saba height (1)' for now")
continue

iterator = proj_db_cursor.execute("SELECT op_path_step, single_operation_code FROM epsg_coordoperationpath WHERE concat_operation_code = ? ORDER BY op_path_step", (code,))
for (order, single_operation_code) in iterator:
assert order == expected_order
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4 changes: 4 additions & 0 deletions src/iso19111/operation/coordinateoperationfactory.cpp
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Expand Up @@ -2381,8 +2381,12 @@ struct MyPROJStringExportableHorizVerticalHorizPROJBased final

methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOCENTRIC ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D ||
methodEPSGCode ==
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8 changes: 8 additions & 0 deletions src/iso19111/operation/parammappings.cpp
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Expand Up @@ -1003,7 +1003,9 @@ const struct MethodNameCode methodNameCodesList[] = {
METHOD_NAME_CODE(AFFINE_PARAMETRIC_TRANSFORMATION),
METHOD_NAME_CODE(SIMILARITY_TRANSFORMATION),
METHOD_NAME_CODE(COORDINATE_FRAME_GEOCENTRIC),
METHOD_NAME_CODE(COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC),
METHOD_NAME_CODE(COORDINATE_FRAME_GEOGRAPHIC_2D),
METHOD_NAME_CODE(COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D),
METHOD_NAME_CODE(COORDINATE_FRAME_GEOGRAPHIC_3D),
METHOD_NAME_CODE(POSITION_VECTOR_GEOCENTRIC),
METHOD_NAME_CODE(POSITION_VECTOR_GEOGRAPHIC_2D),
Expand Down Expand Up @@ -1534,9 +1536,15 @@ static const MethodMapping gOtherMethodMappings[] = {
{EPSG_NAME_METHOD_COORDINATE_FRAME_GEOCENTRIC,
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOCENTRIC, nullptr, nullptr, nullptr,
paramsHelmert7},
{EPSG_NAME_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC,
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC, nullptr, nullptr,
nullptr, paramsHelmert7},
{EPSG_NAME_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D,
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D, nullptr, nullptr, nullptr,
paramsHelmert7},
{EPSG_NAME_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D,
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D, nullptr,
nullptr, nullptr, paramsHelmert7},
{EPSG_NAME_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D,
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D, nullptr, nullptr, nullptr,
paramsHelmert7},
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20 changes: 16 additions & 4 deletions src/iso19111/operation/singleoperation.cpp
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Expand Up @@ -3473,6 +3473,7 @@ bool SingleOperation::exportToPROJStringGeneric(
bool sevenParamsTransform = false;
bool threeParamsTransform = false;
bool fifteenParamsTransform = false;
bool fullMatrix = false;
const auto &l_method = method();
const auto &methodName = l_method->nameStr();
const bool isMethodInverseOf = starts_with(methodName, INVERSE_OF);
Expand All @@ -3484,10 +3485,19 @@ bool SingleOperation::exportToPROJStringGeneric(
const bool isCoordinateFrame =
ci_find(methodName, "Coordinate Frame") != std::string::npos ||
ci_find(methodName, "CF") != std::string::npos;
if ((paramCount == 7 && isCoordinateFrame && !l_isTimeDependent) ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOCENTRIC ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D) {
if (methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D) {
positionVectorConvention = false;
sevenParamsTransform = true;
fullMatrix = true;
} else if ((paramCount == 7 && isCoordinateFrame && !l_isTimeDependent) ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOCENTRIC ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D) {
positionVectorConvention = false;
sevenParamsTransform = true;
} else if (
Expand Down Expand Up @@ -3558,6 +3568,8 @@ bool SingleOperation::exportToPROJStringGeneric(
}

formatter->addStep("helmert");
if (fullMatrix)
formatter->addParam("exact");
formatter->addParam("x", x);
formatter->addParam("y", y);
formatter->addParam("z", z);
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8 changes: 8 additions & 0 deletions src/iso19111/operation/transformation.cpp
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Expand Up @@ -206,7 +206,11 @@ std::vector<double> Transformation::getTOWGS84Parameters(
if ((paramCount == 7 &&
ci_find(methodName, "Coordinate Frame") != std::string::npos) ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOCENTRIC ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D) {
sevenParamsTransform = true;
invertRotSigns = true;
Expand Down Expand Up @@ -1407,7 +1411,11 @@ createApproximateInverseIfPossible(const Transformation *op) {
if ((paramCount == 7 && isCoordinateFrame &&
!isTimeDependent(methodName)) ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOCENTRIC ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D ||
methodEPSGCode ==
EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D ||
methodEPSGCode == EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D) {
sevenParamsTransform = true;
} else if (
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8 changes: 8 additions & 0 deletions src/proj_constants.h
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Expand Up @@ -410,10 +410,18 @@
"Coordinate Frame rotation (geocentric domain)"
#define EPSG_CODE_METHOD_COORDINATE_FRAME_GEOCENTRIC 1032

#define EPSG_NAME_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC \
"Coordinate Frame rotation full matrix (geocen)"
#define EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOCENTRIC 1132

#define EPSG_NAME_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D \
"Coordinate Frame rotation (geog2D domain)"
#define EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_2D 9607

#define EPSG_NAME_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D \
"Coordinate Frame rotation full matrix (geog2D)"
#define EPSG_CODE_METHOD_COORDINATE_FRAME_FULL_MATRIX_GEOGRAPHIC_2D 1133

#define EPSG_NAME_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D \
"Coordinate Frame rotation (geog3D domain)"
#define EPSG_CODE_METHOD_COORDINATE_FRAME_GEOGRAPHIC_3D 1038
Expand Down
105 changes: 105 additions & 0 deletions test/unit/test_operation.cpp
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Expand Up @@ -6059,3 +6059,108 @@ TEST(operation, inverse_of_Geographic3DToGravityRelatedHeight) {
PROJStringFormatter::create().get()),
"+proj=pipeline +step +inv +proj=affine +zoff=10");
}

// ---------------------------------------------------------------------------

TEST(operation, CoordinateFrameRotationFullMatrixGeog2D) {

auto wkt =
"COORDINATEOPERATION[\"Saba to WGS 84 (1)\",\n"
" VERSION[\"IOGP-Bes Saba\"],\n"
" SOURCECRS[\n"
" GEOGCRS[\"Saba\",\n"
" DATUM[\"Saba\",\n"
" ELLIPSOID[\"International 1924\",6378388,297,\n"
" LENGTHUNIT[\"metre\",1]]],\n"
" PRIMEM[\"Greenwich\",0,\n"
" ANGLEUNIT[\"degree\",0.0174532925199433]],\n"
" CS[ellipsoidal,2],\n"
" AXIS[\"geodetic latitude (Lat)\",north,\n"
" ORDER[1],\n"
" ANGLEUNIT[\"degree\",0.0174532925199433]],\n"
" AXIS[\"geodetic longitude (Lon)\",east,\n"
" ORDER[2],\n"
" ANGLEUNIT[\"degree\",0.0174532925199433]],\n"
" ID[\"EPSG\",10636]]],\n"
" TARGETCRS[\n"
" GEOGCRS[\"WGS 84\",\n"
" ENSEMBLE[\"World Geodetic System 1984 ensemble\",\n"
" MEMBER[\"World Geodetic System 1984 (Transit)\"],\n"
" MEMBER[\"World Geodetic System 1984 (G730)\"],\n"
" MEMBER[\"World Geodetic System 1984 (G873)\"],\n"
" MEMBER[\"World Geodetic System 1984 (G1150)\"],\n"
" MEMBER[\"World Geodetic System 1984 (G1674)\"],\n"
" MEMBER[\"World Geodetic System 1984 (G1762)\"],\n"
" MEMBER[\"World Geodetic System 1984 (G2139)\"],\n"
" MEMBER[\"World Geodetic System 1984 (G2296)\"],\n"
" ELLIPSOID[\"WGS 84\",6378137,298.257223563,\n"
" LENGTHUNIT[\"metre\",1]],\n"
" ENSEMBLEACCURACY[2.0]],\n"
" PRIMEM[\"Greenwich\",0,\n"
" ANGLEUNIT[\"degree\",0.0174532925199433]],\n"
" CS[ellipsoidal,2],\n"
" AXIS[\"geodetic latitude (Lat)\",north,\n"
" ORDER[1],\n"
" ANGLEUNIT[\"degree\",0.0174532925199433]],\n"
" AXIS[\"geodetic longitude (Lon)\",east,\n"
" ORDER[2],\n"
" ANGLEUNIT[\"degree\",0.0174532925199433]],\n"
" ID[\"EPSG\",4326]]],\n"
" METHOD[\"Coordinate Frame rotation full matrix (geog2D)\",\n"
" ID[\"EPSG\",1133]],\n"
" PARAMETER[\"X-axis translation\",1138.7432,\n"
" LENGTHUNIT[\"metre\",1],\n"
" ID[\"EPSG\",8605]],\n"
" PARAMETER[\"Y-axis translation\",-2064.4761,\n"
" LENGTHUNIT[\"metre\",1],\n"
" ID[\"EPSG\",8606]],\n"
" PARAMETER[\"Z-axis translation\",110.7016,\n"
" LENGTHUNIT[\"metre\",1],\n"
" ID[\"EPSG\",8607]],\n"
" PARAMETER[\"X-axis rotation\",-214.615206,\n"
" ANGLEUNIT[\"arc-second\",4.84813681109536E-06],\n"
" ID[\"EPSG\",8608]],\n"
" PARAMETER[\"Y-axis rotation\",479.360036,\n"
" ANGLEUNIT[\"arc-second\",4.84813681109536E-06],\n"
" ID[\"EPSG\",8609]],\n"
" PARAMETER[\"Z-axis rotation\",-164.703951,\n"
" ANGLEUNIT[\"arc-second\",4.84813681109536E-06],\n"
" ID[\"EPSG\",8610]],\n"
" PARAMETER[\"Scale difference\",-402.32073,\n"
" SCALEUNIT[\"parts per million\",1E-06],\n"
" ID[\"EPSG\",8611]],\n"
" OPERATIONACCURACY[1.0]]";

auto obj = WKTParser().createFromWKT(wkt);
auto transf = nn_dynamic_pointer_cast<Transformation>(obj);
ASSERT_TRUE(transf != nullptr);
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=push +v_3 "
"+step +proj=cart +ellps=intl "
"+step +proj=helmert +exact "
"+x=1138.7432 +y=-2064.4761 +z=110.7016 "
"+rx=-214.615206 +ry=479.360036 +rz=-164.703951 +s=-402.32073 "
"+convention=coordinate_frame "
"+step +inv +proj=cart +ellps=WGS84 "
"+step +proj=pop +v_3 "
"+step +proj=unitconvert +xy_in=rad +xy_out=deg "
"+step +proj=axisswap +order=2,1");
EXPECT_EQ(transf->inverse()->exportToPROJString(
PROJStringFormatter::create().get()),
"+proj=pipeline "
"+step +proj=axisswap +order=2,1 "
"+step +proj=unitconvert +xy_in=deg +xy_out=rad "
"+step +proj=push +v_3 "
"+step +proj=cart +ellps=WGS84 "
"+step +inv +proj=helmert +exact "
"+x=1138.7432 +y=-2064.4761 +z=110.7016 "
"+rx=-214.615206 +ry=479.360036 +rz=-164.703951 +s=-402.32073 "
"+convention=coordinate_frame "
"+step +inv +proj=cart +ellps=intl "
"+step +proj=pop +v_3 "
"+step +proj=unitconvert +xy_in=rad +xy_out=deg "
"+step +proj=axisswap +order=2,1");
}
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