# 16. Projecting Data¶

The earth is not flat, and there is no simple way of putting it down on a flat paper map (or computer screen), so people have come up with all sorts of ingenious solutions, each with pros and cons. Some projections preserve area, so all objects have a relative size to each other; other projections preserve angles (conformal) like the Mercator projection; some projections try to find a good intermediate mix with only little distortion on several parameters. Common to all projections is that they transform the (spherical) world onto a flat Cartesian coordinate system, and which projection to choose depends on how you will be using the data.

We’ve already encountered projections when we loaded our nyc data. (Recall that pesky SRID 26918). Sometimes, however, you need to transform and re-project between spatial reference systems. PostGIS includes built-in support for changing the projection of data, using the ST_Transform(geometry, srid) function. For managing the spatial reference identifiers on geometries, PostGIS provides the ST_SRID(geometry) and ST_SetSRID(geometry, srid) functions.

We can confirm the SRID of our data with the ST_SRID function:

```SELECT ST_SRID(geom) FROM nyc_streets LIMIT 1;
```
```26918
```

And what is definition of “26918”? As we saw in “loading data section”, the definition is contained in the `spatial_ref_sys` table. In fact, two definitions are there. The “well-known text” (WKT) definition is in the `srtext` column, and there is a second definition in “proj.4” format in the `proj4text` column.

```SELECT * FROM spatial_ref_sys WHERE srid = 26918;
```

The PostGIS reprojection engine will attempt to find the best projection from the `spatial_ref_sys` table:

• auth_name / auth_srid If proj can find a valid “authority name” and “authority srid” in its internal catalogue, it will use that to generate a projection definition.

• srtext If proj can parse and form a definition object from the `srtext` it will use that.

• proj4text Finally, proj will attempt to process the `proj4text`.

All this redundancy means that all you need to create a new projection in PostGIS is either a valid `srtext` string or `proj4text` string. All the common authority name/code pairs are already loaded in the table by default.

If you have a choice when creating a custom projection, fill out the `srtext` column, since that column is also used by external programs like GeoServer, QGIS, and FME and others.

## 16.1. Comparing Data¶

Taken together, a coordinate and an SRID define a location on the globe. Without an SRID, a coordinate is just an abstract notion. A “Cartesian” coordinate plane is defined as a “flat” coordinate system placed on the surface of Earth. Because PostGIS functions work on such a plane, comparison operations require that both geometries be represented in the same SRID.

If you feed in geometries with differing SRIDs you will just get an error:

```SELECT ST_Equals(
ST_GeomFromText('POINT(0 0)', 4326),
ST_GeomFromText('POINT(0 0)', 26918)
);
```
```ERROR:  ST_Equals: Operation on mixed SRID geometries (Point, 4326) != (Point, 26918)
```

Note

Be careful of getting too happy with using ST_Transform for on-the-fly conversion. Spatial indexes are built using SRID of the stored geometries. If comparison are done in a different SRID, spatial indexes are (often) not used. It is best practice to choose one SRID for all the tables in your database. Only use the transformation function when you are reading or writing data to external applications.

## 16.2. Transforming Data¶

If we return to our proj4 definition for SRID 26918, we can see that our working projection is UTM (Universal Transverse Mercator) of zone 18, with meters as the unit of measurement.

```SELECT srtext FROM spatial_ref_sys WHERE srid = 26918;
```
```PROJCS["NAD83 / UTM zone 18N",
DATUM["North_American_Datum_1983",
SPHEROID["GRS 1980",6378137,298.257222101,AUTHORITY["EPSG","7019"]],
TOWGS84[0,0,0,0,0,0,0],
AUTHORITY["EPSG","6269"]],
PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],
UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4269"]],
PROJECTION["Transverse_Mercator"],
PARAMETER["latitude_of_origin",0],
PARAMETER["central_meridian",-75],
PARAMETER["scale_factor",0.9996],
PARAMETER["false_easting",500000],
PARAMETER["false_northing",0],
UNIT["metre",1,AUTHORITY["EPSG","9001"]],
AXIS["Easting",EAST],AXIS["Northing",NORTH],
AUTHORITY["EPSG","26918"]]
```

Let’s convert some data from our working projection to geographic coordinates – also known as “longitude/latitude”.

To convert data from one SRID to another, you must first verify that your geometry has a valid SRID. Since we have already confirmed a valid SRID, we next need the SRID of the projection to transform into. In other words, what is the SRID of geographic coordinates?

The most common SRID for geographic coordinates is 4326, which corresponds to “longitude/latitude on the WGS84 spheroid”. You can see the definition here:

You can also pull the definitions from the `spatial_ref_sys` table:

```SELECT srtext FROM spatial_ref_sys WHERE srid = 4326;
```
```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",0.01745329251994328,AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4326"]]
```

Let’s convert the coordinates of the ‘Broad St’ subway station into geographics:

```SELECT ST_AsText(ST_Transform(geom,4326))
FROM nyc_subway_stations
```
```POINT(-74.01067146887341 40.70710481558761)
```

If you load data or create a new geometry without specifying an SRID, the SRID value will be 0. Recall in Geometries, that when we created our `geometries` table we didn’t specify an SRID. If we query our database, we should expect all the `nyc_` tables to have an SRID of 26918, while the `geometries` table defaulted to an SRID of 0.

To view a table’s SRID assignment, query the database’s `geometry_columns` table.

```SELECT f_table_name AS name, srid
FROM geometry_columns;
```
```        name         | srid
---------------------+-------
nyc_census_blocks   | 26918
nyc_homicides       | 26918
nyc_neighborhoods   | 26918
nyc_streets         | 26918
nyc_subway_stations | 26918
geometries          |     0
```

However, if you know what the SRID of the coordinates is supposed to be, you can set it post-facto, using ST_SetSRID on the geometry. Then you will be able to transform the geometry into other systems.

```SELECT ST_AsText(
ST_Transform(
ST_SetSRID(geom,26918),
4326)
)
FROM geometries;
```

## 16.3. Function List¶

ST_AsText: Returns the Well-Known Text (WKT) representation of the geometry/geography without SRID metadata.

ST_SetSRID(geometry, srid): Sets the SRID on a geometry to a particular integer value.

ST_SRID(geometry): Returns the spatial reference identifier for the ST_Geometry as defined in spatial_ref_sys table.

ST_Transform(geometry, srid): Returns a new geometry with its coordinates transformed to the SRID referenced by the integer parameter.