# OGR Coordinate Reference Systems and Coordinate Transformation tutorial

## Introduction

The `OGRSpatialReference` and `OGRCoordinateTransformation` classes provide respectively services to represent coordinate reference systems (known as CRS or SRS, such as typically a projected CRS associating a map projection with a geodetic datums) and to transform between them. These services are loosely modeled on the OpenGIS Coordinate Transformations specification, and rely on the Well Known Text (WKT) format (in its various versions: OGC WKT 1, ESRI WKT, WKT2:2015 and WKT2:2018) for describing coordinate systems.

## References and applicable standards

- PROJ documentation: projection methods and coordinate operations

- ISO:19111 and WKT standards

- GeoTIFF Projections Transform List: understanding formulations of projections in WKT for GeoTIFF

- EPSG Geodesy web page is also a useful resource

## Defining a Geographic Coordinate Reference System

CRS are encapsulated in the `OGRSpatialReference` class. There are a number of ways of initializing an OGRSpatialReference object to a valid coordinate reference system. There are two primary kinds of CRS. The first is geographic (positions are measured in long/lat) and the second is projected (such as UTM - positions are measured in meters or feet).

A Geographic CRS contains information on the datum (which implies a spheroid described by a semi-major axis, and inverse flattening), prime meridian (normally Greenwich), and an angular units type which is normally degrees. The following code initializes a geographic CRS on supplying all this information along with a user visible name for the geographic CRS.

    OGRSpatialReference oSRS;

    oSRS.SetGeogCS( "My geographic CRS",
                    "World Geodetic System 1984",
                    "My WGS84 Spheroid",
                    SRS_WGS84_SEMIMAJOR, SRS_WGS84_INVFLATTENING,
                    "Greenwich", 0.0,
                    "degree", SRS_UA_DEGREE_CONV );

Note

The abbreviation CS in `OGRSpatialReference::SetGeogCS()` is not appropriate according to current geodesic terminology, and should be understood as CRS

Of these values, the names "My geographic CRS", "My WGS84 Spheroid", "Greenwich" and "degree" are not keys, but are used for display to the user. However, the datum name "World Geodetic System 1984" is used as a key to identify the datum, and should be set to a known value from the EPSG registry, so that appropriate datum transformations can be done during coordinate operations. The list of valid geodetic datum can be seen in the 3rd column of the geodetic_datum.sql file.

Note

In WKT 1, space characters in datum names are normally replaced by underscore. And WGS_1984 is used as an alias of "World Geodetic System 1984"

The OGRSpatialReference has built in support for a few well known CRS, which include "NAD27", "NAD83", "WGS72" and "WGS84" which can be defined in a single call to `OGRSpatialReference::SetWellKnownGeogCS()`.

    oSRS.SetWellKnownGeogCS( "WGS84" );

Note

The abbreviation CS in SetWellKnownGeogCS() is not appropriate according to current geodesic terminology, and should be understood as CRS

Furthermore, any geographic CRS in the EPSG database can be set by its GCS code number if the EPSG database is available.

    oSRS.SetWellKnownGeogCS( "EPSG:4326" );

For serialization, and transmission of projection definitions to other packages, the OpenGIS Well Known Text format for coordinate systems is used. An OGRSpatialReference can be initialized from WKT, or converted back into WKT. As of GDAL 3.0, the default format for WKT export is still OGC WKT 1.

    char *pszWKT = NULL;
    oSRS.SetWellKnownGeogCS( "WGS84" );
    oSRS.exportToWkt( &pszWKT );
    printf( "%s\n", pszWKT );
    CPLFree(pszWKT);

outputs:

    GEOGCS["WGS 84",DATUM["WGS_1984",SPHEROID["WGS 84",6378137,298.257223563,
    AUTHORITY["EPSG","7030"]],AUTHORITY["EPSG","6326"]],PRIMEM["Greenwich",0,
    AUTHORITY["EPSG","8901"]],UNIT["degree",0.0174532925199433,
    AUTHORITY["EPSG","9122"]],AXIS["Latitude",NORTH],AXIS["Longitude",EAST],
    AUTHORITY["EPSG","4326"]]

or in more readable form:

    GEOGCS["WGS 84",
        DATUM["WGS_1984",
            SPHEROID["WGS 84",6378137,298.257223563,
                AUTHORITY["EPSG","7030"]],
            AUTHORITY["EPSG","6326"]],
        PRIMEM["Greenwich",0,
            AUTHORITY["EPSG","8901"]],
        UNIT["degree",0.0174532925199433,
            AUTHORITY["EPSG","9122"]],
        AXIS["Latitude",NORTH],
        AXIS["Longitude",EAST],
        AUTHORITY["EPSG","4326"]]

Starting with GDAL 3.0, the `OGRSpatialReference::exportToWkt()` method accepts options,

    char *pszWKT = nullptr;
    oSRS.SetWellKnownGeogCS( "WGS84" );
    const char* apszOptions[] = { "FORMAT=WKT2_2018", "MULTILINE=YES", nullptr };
    oSRS.exportToWkt( &pszWKT, apszOptions );
    printf( "%s\n", pszWKT );
    CPLFree(pszWKT);

    GEOGCRS["WGS 84",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        CS[ellipsoidal,2],
            AXIS["geodetic latitude (Lat)",north,
                ORDER[1],
                ANGLEUNIT["degree",0.0174532925199433]],
            AXIS["geodetic longitude (Lon)",east,
                ORDER[2],
                ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4326]]

This method with options is available in C as the `OSRExportToWktEx()` function.

The `OGRSpatialReference::importFromWkt()` method can be used to set an OGRSpatialReference from a WKT CRS definition.

## CRS and axis order

One "detail" that has been omitted in previous sections is the topic of the order of coordinate axis in a CRS. A Geographic CRS is, according to ISO:19111 modeling, made of two main components: a geodetic datum and a coordinate system. For 2D geographic CRS, the coordinate system axes are the longitude and the latitude, and the values along those axes are expressed generally in degree (ancient French-based CRS may use grad).

The order in which they are specified, that is latitude first, longitude second, or the reverse, is a constant matter of confusion and vary depending on conventions used by geodetic authorities, GIS user, file format and protocol specifications, etc. This is the source of various interoperability issues.

Before GDAL 3.0, the `OGRSpatialReference` class did not honour the axis order mandated by the authority defining a CRS and consequently stripped axis order information from the WKT string when the order was latitude first, longitude second. Coordinate transformations using the OGRCoordinateTransformation class also assumed that geographic coordinates passed or returned by the Transform() method of this class used the longitude, latitude order.

Starting with GDAL 3.0, the axis order mandated by the authority defining a CRS is by default honoured by the OGRCoordinateTransformation class, and always exported in WKT1. Consequently CRS created with the "EPSG:4326" or "WGS84" strings use the latitude first, longitude second axis order.

In order to help migration from code bases still using coordinates with the longitude, latitude order, it is possible to attach a metadata information to a OGRSpatialReference instance, to specify that for the purpose of coordinate transformations, the order of values effectively passed or returned, will be longitude, latitude. For that, the following must be called

    oSRS.SetAxisMappingStrategy(OAMS_TRADITIONAL_GIS_ORDER);

The argument passed to `OGRSpatialReference::SetAxisMappingStrategy()` is the data axis to CRS axis mapping strategy.

- `OAMS_TRADITIONAL_GIS_ORDER` means that for geographic CRS with lat/long order, the data will still be long/lat ordered. Similarly for a projected CRS with northing/easting order, the data will still be easting/northing ordered.

- `OAMS_AUTHORITY_COMPLIANT` means that the data axis will be identical to the CRS axis. This is the default value when instantiating OGRSpatialReference.

- `OAMS_CUSTOM` means that the data axes are customly defined with SetDataAxisToSRSAxisMapping().

What has been discussed in this section for the particular case of Geographic CRS also applies to Projected CRS. While most of them use Easting first, Northing second convention, some defined in the EPSG registry use the reverse convention.

Another way to keep using the Traditional GIS order for some specific well known CRS is to calling to `OGRSpatialReference::SetWellKnownGeogCS()` with "CRS27", "CRS83" or "CRS84" instead of "NAD27", "NAD83" and "WGS84" respectively.

    oSRS.SetWellKnownGeogCS( "CRS84" );

## Defining a Projected CRS

A projected CRS (such as UTM, Lambert Conformal Conic, etc.) requires and underlying geographic CRS as well as a definition for the projection transform used to translate between linear positions (in meters or feet) and angular long/lat positions. The following code defines a UTM zone 17 projected CRS with an underlying geographic CRS (datum) of WGS84.

    OGRSpatialReference oSRS;

    oSRS.SetProjCS( "UTM 17 (WGS84) in northern hemisphere." );
    oSRS.SetWellKnownGeogCS( "WGS84" );
    oSRS.SetUTM( 17, TRUE );

Calling `OGRSpatialReference::SetProjCS()` sets a user name for the projected CRS and establishes that the system is projected. The `OGRSpatialReference::SetWellKnownGeogCS()` associates a geographic coordinate system, and the `OGRSpatialReference::SetUTM()` call sets detailed projection transformation parameters. At this time the above order is important in order to create a valid definition, but in the future the object will automatically reorder the internal representation as needed to remain valid.

Caution

For now, be careful of the order of steps defining an OGRSpatialReference!

The above definition would give a WKT version that looks something like the following. Note that the UTM 17 was expanded into the details transverse mercator definition of the UTM zone.

    PROJCS["UTM 17 (WGS84) in northern hemisphere.",
        GEOGCS["WGS 84",
            DATUM["WGS_1984",
                SPHEROID["WGS 84",6378137,298.257223563,
                    AUTHORITY["EPSG",7030]],
                TOWGS84[0,0,0,0,0,0,0],
                AUTHORITY["EPSG",6326]],
            PRIMEM["Greenwich",0,AUTHORITY["EPSG",8901]],
            UNIT["DMSH",0.0174532925199433,AUTHORITY["EPSG",9108]],
            AXIS["Lat",NORTH],
            AXIS["Long",EAST],
            AUTHORITY["EPSG",4326]],
        PROJECTION["Transverse_Mercator"],
        PARAMETER["latitude_of_origin",0],
        PARAMETER["central_meridian",-81],
        PARAMETER["scale_factor",0.9996],
        PARAMETER["false_easting",500000],
        PARAMETER["false_northing",0]]

There are methods for many projection methods including `OGRSpatialReference::SetTM()` (Transverse Mercator), `OGRSpatialReference::SetLCC()` (Lambert Conformal Conic), and `OGRSpatialReference::SetMercator()`.

## Querying Coordinate Reference System

Once an OGRSpatialReference has been established, various information about it can be queried. It can be established if it is a projected or geographic CRS using the `OGRSpatialReference::IsProjected()` and `OGRSpatialReference::IsGeographic()` methods. The `OGRSpatialReference::GetSemiMajor()`, `OGRSpatialReference::GetSemiMinor()` and `OGRSpatialReference::GetInvFlattening()` methods can be used to get information about the spheroid. The `OGRSpatialReference::GetAttrValue()` method can be used to get the PROJCS, GEOGCS, DATUM, SPHEROID, and PROJECTION names strings. The `OGRSpatialReference::GetProjParm()` method can be used to get the projection parameters. The `OGRSpatialReference::GetLinearUnits()` method can be used to fetch the linear units type, and translation to meters.

Note that the names of the projection method and parameters is the one of WKT 1.

The following code demonstrates use of `OGRSpatialReference::GetAttrValue()` to get the projection, and `OGRSpatialReference::GetProjParm()` to get projection parameters. The GetAttrValue() method searches for the first "value" node associated with the named entry in the WKT text representation. The #define'ed constants for projection parameters (such as SRS_PP_CENTRAL_MERIDIAN) should be used when fetching projection parameter with GetProjParm(). The code for the Set methods of the various projections in ogrspatialreference.cpp can be consulted to find which parameters apply to which projections.

    const char *pszProjection = poSRS->GetAttrValue("PROJECTION");

    if( pszProjection == NULL )
    {
        if( poSRS->IsGeographic() )
            sprintf( szProj4+strlen(szProj4), "+proj=longlat " );
        else
            sprintf( szProj4+strlen(szProj4), "unknown " );
    }
    else if( EQUAL(pszProjection,SRS_PT_CYLINDRICAL_EQUAL_AREA) )
    {
        sprintf( szProj4+strlen(szProj4),
        "+proj=cea +lon_0=%.9f +lat_ts=%.9f +x_0=%.3f +y_0=%.3f ",
                poSRS->GetProjParm(SRS_PP_CENTRAL_MERIDIAN,0.0),
                poSRS->GetProjParm(SRS_PP_STANDARD_PARALLEL_1,0.0),
                poSRS->GetProjParm(SRS_PP_FALSE_EASTING,0.0),
                poSRS->GetProjParm(SRS_PP_FALSE_NORTHING,0.0) );
    }
    ...

## Coordinate Transformation

The `OGRCoordinateTransformation` class is used for translating positions between different CRS. New transformation objects are created using `OGRCreateCoordinateTransformation()`, and then the `OGRCoordinateTransformation::Transform()` method can be used to convert points between CRS.

    OGRSpatialReference oSourceSRS, oTargetSRS;
    OGRCoordinateTransformation *poCT;
    double x, y;

    oSourceSRS.importFromEPSG( atoi(papszArgv[i+1]) );
    oTargetSRS.importFromEPSG( atoi(papszArgv[i+2]) );

    poCT = OGRCreateCoordinateTransformation( &oSourceSRS,
                                              &oTargetSRS );
    x = atof( papszArgv[i+3] );
    y = atof( papszArgv[i+4] );

    if( poCT == NULL || !poCT->Transform( 1, &x, &y ) )
        printf( "Transformation failed.\n" );
    else
    {
        printf( "(%f,%f) -> (%f,%f)\n",
                atof( papszArgv[i+3] ),
                atof( papszArgv[i+4] ),
                x, y );
    }

There are a couple of points at which transformations can fail. First, OGRCreateCoordinateTransformation() may fail, generally because the internals recognize that no transformation between the indicated systems can be established, and will return a NULL pointer.

The OGRCoordinateTransformation::Transform() method itself can also fail. This may be as a delayed result of one of the above problems, or as a result of an operation being numerically undefined for one or more of the passed in points. The Transform() function will return TRUE on success, or FALSE if any of the points fail to transform. The point array is left in an indeterminate state on error.

Though not shown above, the coordinate transformation service can take 3D points, and will adjust elevations for elevation differences in spheroids, and datums. Elevations given on a geographic or projected CRS are assumed to be ellipsoidal heights. When using a compound CRS made of a horizontal CRS (geographic or projected) and a vertical CRS, elevations will be related to a vertical datum (mean sea level, gravity based, etc.).

Starting with GDAL 3.0, a time value (generally as a value in decimal years) can also be specified for time-dependent coordinate operations.

The following example shows how to conveniently create a long/lat coordinate system using the same geographic CRS as a projected coordinate system, and using that to transform between projected coordinates and long/lat. The returned coordinates will be in longitude, latitude order due to the call to SetAxisMappingStrategy(OAMS_TRADITIONAL_GIS_ORDER)

    OGRSpatialReference    oUTM, *poLongLat;
    OGRCoordinateTransformation *poTransform;

    oUTM.SetProjCS("UTM 17 / WGS84");
    oUTM.SetWellKnownGeogCS( "WGS84" );
    oUTM.SetUTM( 17 );

    poLongLat = oUTM.CloneGeogCS();
    poLongLat->SetAxisMappingStrategy(OAMS_TRADITIONAL_GIS_ORDER);

    poTransform = OGRCreateCoordinateTransformation( &oUTM, poLongLat );
    if( poTransform == NULL )
    {
        ...
    }

    ...

    if( !poTransform->Transform( nPoints, x, y, z ) )
    ...

## Advanced Coordinate Transformation

OGRCreateCoordinateTransformation() under-the-hood may determine several candidate coordinate operations transforming from the source CRS to the target CRS. Those candidate coordinate operations each have their own area of use. When Transform() is invoked, it will determine the most appropriate coordinate operation based on the coordinates of the point to transform and area of use. For example, there are several dozens of possible coordinate operations for the NAD27 to WGS84 transformation.

If a bounding box of the area of interest into which coordinates to transform are located is known, it is possible to specify it to restrict the candidate coordinate operations to consider:

    OGRCoordinateTransformationOptions options;
    options.SetAreaOfInterest(-100,40,-99,41);
    poTransform = OGRCreateCoordinateTransformation( &oNAD27, &oWGS84, options );

For cases where a particular coordinate operation must be used, it is possible to specify it as as a PROJ string (single step operation or multiple step string starting with +proj=pipeline), a WKT2 string describing a CoordinateOperation, or a urn:ogc:def:coordinateOperation:EPSG::XXXX URN

    OGRCoordinateTransformationOptions options;

    // EPSG:8599, NAD27 to WGS 84 (46), 1.15 m, USA - Indiana
    options.SetCoordinateOperation(
        "+proj=pipeline +step +proj=axisswap +order=2,1 "
        "+step +proj=unitconvert +xy_in=deg +xy_out=rad "
        "+step +proj=hgridshift +grids=conus "
        "+step +proj=hgridshift +grids=inhpgn.gsb "
        "+step +proj=unitconvert +xy_in=rad +xy_out=deg +step "
        "+proj=axisswap +order=2,1", false );

    // or
    // options.SetCoordinateOperation(
    //      "urn:ogc:def:coordinateOperation:EPSG::8599", false);

    poTransform = OGRCreateCoordinateTransformation( &oNAD27, &oWGS84, options );

## Alternate Interfaces

A C interface to the coordinate system services is defined in ogr_srs_api.h, and Python bindings are available via the osr.py module. Methods are close analogs of the C++ methods but C and Python bindings are missing for some C++ methods.

### C bindings

    typedef void *OGRSpatialReferenceH;
    typedef void *OGRCoordinateTransformationH;

    OGRSpatialReferenceH OSRNewSpatialReference( const char * );
    void    OSRDestroySpatialReference( OGRSpatialReferenceH );

    int     OSRReference( OGRSpatialReferenceH );
    int     OSRDereference( OGRSpatialReferenceH );

    void OSRSetAxisMappingStrategy( OGRSpatialReferenceH,
                                    OSRAxisMappingStrategy );

    OGRErr  OSRImportFromEPSG( OGRSpatialReferenceH, int );
    OGRErr  OSRImportFromWkt( OGRSpatialReferenceH, char ** );
    OGRErr  OSRExportToWkt( OGRSpatialReferenceH, char ** );
    OGRErr  OSRExportToWktEx( OGRSpatialReferenceH, char **,
                            const char* const* papszOptions );

    OGRErr  OSRSetAttrValue( OGRSpatialReferenceH hSRS, const char * pszNodePath,
                            const char * pszNewNodeValue );
    const char *OSRGetAttrValue( OGRSpatialReferenceH hSRS,
                                const char * pszName, int iChild);

    OGRErr  OSRSetLinearUnits( OGRSpatialReferenceH, const char *, double );
    double  OSRGetLinearUnits( OGRSpatialReferenceH, char ** );

    int     OSRIsGeographic( OGRSpatialReferenceH );
    int     OSRIsProjected( OGRSpatialReferenceH );
    int     OSRIsSameGeogCS( OGRSpatialReferenceH, OGRSpatialReferenceH );
    int     OSRIsSame( OGRSpatialReferenceH, OGRSpatialReferenceH );

    OGRErr  OSRSetProjCS( OGRSpatialReferenceH hSRS, const char * pszName );
    OGRErr  OSRSetWellKnownGeogCS( OGRSpatialReferenceH hSRS,
                                const char * pszName );

    OGRErr  OSRSetGeogCS( OGRSpatialReferenceH hSRS,
                        const char * pszGeogName,
                        const char * pszDatumName,
                        const char * pszEllipsoidName,
                        double dfSemiMajor, double dfInvFlattening,
                        const char * pszPMName ,
                        double dfPMOffset ,
                        const char * pszUnits,
                        double dfConvertToRadians );

    double  OSRGetSemiMajor( OGRSpatialReferenceH, OGRErr * );
    double  OSRGetSemiMinor( OGRSpatialReferenceH, OGRErr * );
    double  OSRGetInvFlattening( OGRSpatialReferenceH, OGRErr * );

    OGRErr  OSRSetAuthority( OGRSpatialReferenceH hSRS,
                            const char * pszTargetKey,
                            const char * pszAuthority,
                            int nCode );
    OGRErr  OSRSetProjParm( OGRSpatialReferenceH, const char *, double );
    double  OSRGetProjParm( OGRSpatialReferenceH hSRS,
                            const char * pszParamName,
                            double dfDefault,
                            OGRErr * );

    OGRErr  OSRSetUTM( OGRSpatialReferenceH hSRS, int nZone, int bNorth );
    int     OSRGetUTMZone( OGRSpatialReferenceH hSRS, int *pbNorth );

    OGRCoordinateTransformationH
    OCTNewCoordinateTransformation( OGRSpatialReferenceH hSourceSRS,
                                    OGRSpatialReferenceH hTargetSRS );

    void OCTDestroyCoordinateTransformation( OGRCoordinateTransformationH );

    int OCTTransform( OGRCoordinateTransformationH hCT,
                    int nCount, double *x, double *y, double *z );

    OGRCoordinateTransformationOptionsH OCTNewCoordinateTransformationOptions(;

    int OCTCoordinateTransformationOptionsSetOperation(
        OGRCoordinateTransformationOptionsH hOptions,
        const char* pszCO, int bReverseCO);

    int OCTCoordinateTransformationOptionsSetAreaOfInterest(
        OGRCoordinateTransformationOptionsH hOptions,
        double dfWestLongitudeDeg,
        double dfSouthLatitudeDeg,
        double dfEastLongitudeDeg,
        double dfNorthLatitudeDeg);

    void OCTDestroyCoordinateTransformationOptions(OGRCoordinateTransformationOptionsH);

    OGRCoordinateTransformationH
    OCTNewCoordinateTransformationEx( OGRSpatialReferenceH hSourceSRS,
                                    OGRSpatialReferenceH hTargetSRS,
                                    OGRCoordinateTransformationOptionsH hOptions );

### Python bindings

    class osr.SpatialReference
        def __init__(self,obj=None):
        def SetAxisMappingStrategy( self, strategy ):
        def ImportFromWkt( self, wkt ):
        def ExportToWkt(self, options = None):
        def ImportFromEPSG(self,code):
        def IsGeographic(self):
        def IsProjected(self):
        def GetAttrValue(self, name, child = 0):
        def SetAttrValue(self, name, value):
        def SetWellKnownGeogCS(self, name):
        def SetProjCS(self, name = "unnamed" ):
        def IsSameGeogCS(self, other):
        def IsSame(self, other):
        def SetLinearUnits(self, units_name, to_meters ):
        def SetUTM(self, zone, is_north = 1):

    class CoordinateTransformation:
        def __init__(self,source,target):
        def TransformPoint(self, x, y, z = 0):
        def TransformPoints(self, points):

## History and implementation considerations

Before GDAL 3.0, the OGRSpatialReference class was strongly tied to OGC WKT (WKT 1) format specified by Coordinate Transformation Services (CT) specification (01-009), and the way it was interpreted by GDAL, which various caveats detailed in the OGC WKT Coordinate System Issues page. The class mostly contained an in-memory tree-like representation of WKT 1 strings. The class used to directly implement import and export to OGC WKT 1, WKT-ESRI and PROJ.4 formats. Reprojection services were only available if GDAL had been build against the PROJ library.

Starting with GDAL 3.0, the PROJ >= 6.0 library has become a required dependency of GDAL. PROJ 6 has built-in support for OGC WKT 1, ESRI WKT, OGC WKT 2:2015 and OGC WKT 2:2018 representations. PROJ 6 also implements a C++ object class hierarchy of the ISO-19111 / OGC Abstract Topic 2 "Referencing by coordinate" standard. Consequently the OGRSpatialReference class has been modified to act mostly as a wrapper on top of PROJ PJ* CRS objects, and tries to abstract away from the OGC WKT 1 representation as much as possible. However, for backward compatibility, some methods still expect arguments or return values that are specific of OGC WKT 1. The design of the OGRSpatialReference class is also still monolithic. Users wanting direct and fine grained access to CRS representations might want to directly use the PROJ 6 C or C++ API.