pgLatLon v0.12 documentation

pgLatLon is a spatial database extension for the PostgreSQL object-relational database management system providing geographic data types and spatial indexing for the WGS-84 spheroid.

While many other spatial databases still use imprecise bounding boxes for many operations, pgLatLon aims to support more precise calculations for all implemented geographic operators. Efficient indexing of geographic objects is provided using space-filling fractal curves. Optimizations on bit level (including logarithmic compression) allow for a highly memory-efficient non-overlapping index suitable for huge datasets.

pgLatLon is a lightweight solution as it only depends on PostgreSQL itself (and a C compiler for building).

Unlike competing spatial extensions for PostgreSQL, pgLatLon is available under the permissive MIT/X11 license to avoid problems with viral licenses like the GPLv2/v3.

Installation

Automatic installation

Prerequisites:

• Ensure that the pg_config binary is in your path (shipped with PostgreSQL).
• Ensure that GNU Make is available (either as make or gmake).

Then simply type:

make install

Manual installation

It is also possible to compile and install the extension without GNU Make as follows:

cc -Wall -O2 -fPIC -shared -I `pg_config --includedir-server` -o latlon-v0009.so latlon-v0009.c
cp latlon-v0009.so `pg_config --pkglibdir`
cp latlon.control `pg_config --sharedir`/extension/
cp latlon--*.sql `pg_config --sharedir`/extension/

Loading the extension

After installation, you can create a database and load the extension as follows:

% createdb test_database
% psql test_database
psql (9.5.4)
Type "help" for help.

test_database=# CREATE EXTENSION latlon;

Updating

Before updating your database cluster to a new version of pgLatLon, you may want to uninstall the old by calling "make uninstall" in the unpacked source code directory of your old pgLatLon version. You may also manually delete the latlon-v????.so files from your PostgreSQL library directory and the latlon.control and latlon--*.sql files from your PostgreSQL extension directory.

The new version can be installed as described above. For altering an existing database to use the installed new version (mandatory if you removed the old version), execute the following SQL command in the respective databases:

ALTER EXTENSION latlon UPDATE;

If the update contains modifications to operator classes, it may be necessary to drop all indices on geographic data types first (you will get an error message in this case). These indices can be re-created after the update.

Note that taking several update steps at once (e.g. updating from version 0.2 directly to version 0.4) requires the intermediate versions to be installed (i.e. in this example version 0.3 would need to be installed). Whenever you install or uninstall an intermediate or old version, make sure to afterwards re-install the latest pgLatLon version to ensure that the latlon.control file is available and points to the latest version.

If the update contains modifications to the internal data representation format, an update path might not be available. In this case, create a dump of your database, delete your database, and restore it from your dump.

Be sure to always keep backups of all your data before attempting to update.

Reference

1. Types

pgLatLon provides four geographic types: epoint, ebox, ecircle, and ecluster.

epoint

A point on the Earth spheroid (WGS-84).

The text input format is '[N|S]<float> [E|W]<float>', where each float is in degrees. Note the required white space between the latitude and longitude components. Each floating point number may have a sign, in which case N/S or E/W are switched respectively (e.g. E-5 is the same as W5).

An epoint may also be created from two floating point numbers by calling epoint(latitude, longitude), where positive latitudes are used for the northern hemisphere, negative latitudes are used for the southern hemisphere, positive longitudes indicate positions east of the prime meridian, and negative longitudes indicate positions west of the prime meridian.

Latitudes exceeding -90 or +90 degrees are truncated to -90 or +90 respectively, in which case a warning will be issued. Longitudes exceeding -180 or +180 degrees will be converted to values between -180 and +180 (both inclusive) by adding or substracting a multiple of 360 degrees, in which case a notice will be issued.

If the latitude is -90 or +90 (south pole or north pole), a longitude value is still stored in the datum, and if a point is on the prime meridian or the 180th meridian, the east/west bit is also stored in the datum. In case of the prime meridian, this is done by storing a floating point value of -0 for 0 degrees west and a value of +0 for 0 degrees east. In case of the 180th meridian, this is done by storing -180 or +180 respectively. The equality operator, however, returns true when the same points on Earth are described, i.e. the longitude is ignored for the poles, and 180 degrees west is considered to be equal to 180 degrees east.

ebox

An area on Earth demarcated by a southern and northern latitude, and a western and eastern longitude (all given in WGS-84).

The text input format is '{N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float>', where each float is in degrees. The ordering of the four white-space separated blocks is not significant. To include the 180th meridian, one longitude boundary must be equal to or exceed W180 or E180, e.g. 'N10 N20 E170 E190'.

A special value is the empty area, denoted by the text represenation 'empty'. Such an ebox does not contain any point.

An ebox may also be created from four floating point numbers by calling ebox(min_latitude, max_latitude, min_longitude, max_longitude), where positive values are used for north and east, and negative values are used for south and west. If min_latitude is strictly greater than max_latitude, an empty ebox is created. If min_longitude is greater than max_longitude and if both longitudes are between -180 and +180 degrees, then the area oriented in such way that the 180th meridian is included.

If the longitude span is less than 120 degrees, an ebox may be alternatively created from two epoints in the following way: ebox(epoint(lat1, lon1), epoint(lat2, lon2)). In this case lat1 and lat2 as well as lon1 and lon2 can be swapped without any impact.

ecircle

An area containing all points not farther away from a given center point (WGS-84) than a given radius.

The text input format is '{N|S}<float> {E|W}<float> <float>', where the first two floats denote the center point in degrees and the third float denotes the radius in meters. A radius equal to minus infinity denotes an empty circle which contains no point at all (despite having a center), while a radius equal to zero denotes a circle that includes a single point.

An ecircle may also be created by calling ecircle(epoint(...), radius) or from three floating point numbers by calling ecircle(latitude, longitude, radius).

ecluster

A collection of points, paths, polygons, and outlines on the WGS-84 spheroid. Each path, polygon, or outline must cover a longitude range of less than 180 degrees to avoid ambiguities.

The text input format is a white-space separated list of the following items:

• point ({N|S}<float> {E|W}<float>)
• path ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)
• outline ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)
• polygon ({N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> {N|S}<float> {E|W}<float> ...)

Paths are open by default (i.e. there is no connection from the last point in the list to the first point in the list). Outlines and polygons, in contrast, are automatically closed (i.e. there is a line segment from the last point in the list to the first point in the list) which means the first point should not be repeated as last point in the list. Polygons are filled, outlines are not.

2. Indices

Two kinds of indices are supported: B-tree and GiST indices.

B-tree indices

A B-tree index can be used for simple equality searches and is supported by the epoint, ebox, and ecircle data types. B-tree indices can not be used for geographic searches.

GiST indices

For geographic searches, GiST indices must be used. The epoint, ecircle, and ecluster data types support GiST indexing. A GiST index for geographic searches can be created as follows:

CREATE TABLE tbl (
        id              serial4         PRIMARY KEY,
        loc             epoint          NOT NULL );

CREATE INDEX name_of_index ON tbl USING gist (loc);

GiST indices also support nearest neighbor searches when using the distance operator (<->) in the ORDER BY clause.

Indices on other data types (e.g. GeoJSON)

Note that further types can be indexed by using an index on an expression with a conversion function. One conversion function provided by pgLatLon is the GeoJSON_to_ecluster(jsonb, text) function:

CREATE TABLE tbl (
        id              serial4         PRIMARY KEY,
        loc             jsonb           NOT NULL );

CREATE INDEX name_of_index ON tbl USING gist((GeoJSON_to_ecluster("loc")));

When using the conversion function in an expression, the index will be used automatically:

SELECT * FROM tbl WHERE GeoJSON_to_ecluster("loc") && 'N50 E10 10000'::ecircle;

3. Operators

Equality operator =

Tests if two geographic objects are equal.

The longitude is ignored for the poles, and 180 degrees west is considered to be equal to 180 degrees east.

For boxes and circles, two empty objects are considered equal. (Note that a circle is not empty if the radius is zero but only if it is negative infinity, i.e. smaller than zero.) Two circles with a positive infinite radius are also considered equal.

Implemented for:

• epoint = epoint
• ebox = ebox
• ecircle = ecircle

The negation is the inequality operator (<> or !=).

Linear ordering operators <<<, <<<=, >>>=, >>>

These operators create an arbitrary (but well-defined) linear ordering of geographic objects, which is used internally for B-tree indexing and merge joins. These operators will usually not be used by an application programmer.

Overlap operator &&

Tests if two geographic objects have at least one point in common. Currently implemented for:

• epoint && ebox
• epoint && ecircle
• epoint && ecluster
• ebox && ebox
• ebox && ecircle
• ebox && ecluster
• ecircle && ecircle
• ecircle && ecluster
• ecluster && ecluster

The && operator is commutative, i.e. "a && b" is the same as "b && a". Each commutation is supported as well.

Lossy overlap operator &&+

Tests if two geographic objects may have at least one point in common. Opposed to the && operator, the &&+ operator may return false positives and is currently implemented for:

• epoint &&+ ecluster
• ebox &&+ ecircle
• ebox &&+ ecluster
• ecircle &&+ ecluster
• ecluster &&+ ecluster

The &&+ operator is commutative, i.e. "a &&+ b" is the same as "b &&+ a". Each commutation is supported as well.

Where two data types support both the && and the &&+ operator, the &&+ operator computes faster.

Contains operator @>

Tests if the object right of the operator is contained in the object left of the operator. Currently implemented for:

• ebox @> epoint (alias for &&)
• ebox @> ebox
• ebox @> ecluster
• ecluster @> epoint (alias for &&)
• ecluster @> ebox
• ecluster @> ecluster

The commutator of @> ("contains") is <@ ("is contained in"), i.e. "a @> b" is the same as "b <@ a".

Whether the perimeter of an object is taken into account is undefined and may differ between the left and the right hand side of the operator. The current implementation returns true only if an object is contained completely within the other object, not touching its perimeter, paths, outlines, or any singular points.

Distance operator <->

Calculates the shortest distance between two geographic objects in meters (zero if the objects are overlapping). Currently implemented for:

• epoint <-> epoint
• epoint <-> ebox
• epoint <-> ecircle
• epoint <-> ecluster
• ebox <-> ebox
• ebox <-> ecircle
• ebox <-> ecluster
• ecircle <-> ecircle
• ecircle <-> ecluster
• ecluster <-> ecluster

The <-> operator is commutative, i.e. "a <-> b" is the same as "b <-> a". Each commutation is supported as well.

For short distances, the result is very accurate (i.e. respects the dimensions of the WGS-84 spheroid). For longer distances in the order of magnitude of Earth's radius or greater, the value is only approximate (but the error is still less than 0.2% as long as no polygons with very long edges are involved).

The functions distance(epoint, epoint) and distance(ecluster, epoint) can be used as an alias for this operator.

Note: In case of radial searches with a fixed radius, this operator should not be used. Instead, an ecircle should be created and used in combination with the overlap operator (&&). Alternatively, the functions distance_within(epoint, epoint, float8) or distance_within(ecluster, epoint, float8) can be used for fixed-radius searches.

4. Functions

center(circle)

Returns the center of an ecircle as an epoint.

distance(epoint, epoint)

Calculates the distance between two epoint datums in meters. This function is an alias for the distance operator <->.

Note: In case of radial searches with a fixed radius, this function should not be used. Use distance_within(epoint, epoint, float8) instead.

distance(ecluster, epoint)

Calculates the distance from an ecluster to an epoint in meters. This function is an alias for the distance operator <->.

Note: In case of radial searches with a fixed radius, this function should not be used. Use distance_within(epoint, epoint, float8) instead.

distance_within(variable epoint, fixed epoint, radius float8)

Checks if the distance between two epoint datums is not greater than a given value (search radius).

Note: In case of radial searches with a fixed radius, the first argument must be used for the table column, while the second argument must be used for the search center. Otherwise an existing index cannot be used.

distance_within(variable ecluster, fixed epoint, radius float8)

Checks if the distance from an ecluster to an epoint is not greater than a given value (search radius).

ebox(latmin float8, latmax float8, lonmin float8, lonmax float8)

Creates a new ebox with the given boundaries. See "1. Types", subsection ebox for details.

ebox(epoint, epoint)

Creates a new ebox. This function may only be used if the longitude difference is less than or equal to 120 degrees. See "1. Types", subsection ebox for details.

ecircle(epoint, float8)

Creates an ecircle with the given center point and radius.

ecircle(latitude float8, longitude float8, radius float8)

Creates an ecircle with the given center point and radius.

ecluster_concat(ecluster, ecluster)

Combines two clusters to form a new ecluster by uniting all entries of both clusters. Note that two overlapping areas of polygons annihilate each other (which may be used to create polygons with holes).

ecluster_concat(ecluster[])

Creates a new ecluster that unites all entries of all clusters in the passed array. Note that two overlapping areas of polygons annihilate each other (which may be used to create polygons with holes).

ecluster_create_multipoint(epoint[])

Creates a new ecluster which contains multiple points.

ecluster_create_outline(epoint[])

Creates a new ecluster that is an outline given by the passed points.

ecluster_create_path(epoint[])

Creates a new ecluster that is a path given by the passed points.

ecluster_create_polygon(epoint[])

Creates a new ecluster that is a polygon given by the passed points.

ecluster_extract_outlines(ecluster)

Set-returning function that returns the outlines of an ecluster as epoint[] rows.

ecluster_extract_paths(ecluster)

Set-returning function that returns the paths of an ecluster as epoint[] rows.

ecluster_extract_points(ecluster)

Set-returning function that returns the points of an ecluster as epoint rows.

ecluster_extract_polygons(ecluster)

Set-returning function that returns the polygons of an ecluster as epoint[] rows.

empty_ebox()

Returns the empty ebox. See "1. Types", subsection ebox for details.

epoint(latitude float8, longitude float8)

Returns an epoint with the given latitude and longitude.

epoint_latlon(latitude float8, longitude float8)

Alias for epoint(float8, float8).

epoint_lonlat(longitude float8, latitude float8)

Same as epoint(float8, float8) but with arguments reversed.

fair_distance(ecluster, epoint, samples int4 = 10000)

When working with user-generated content, users may be tempted to create intentionally oversized objects in order to optimize search results in an unfair manner. The fair_distance function aims to handle this by returning an adjusted distance (i.e. distance increased by a penalty) if a geographic object (the ecluster) consists of more than one point.

The first argument to this function is an ecluster, the second argument is a search point (epoint), and the third argument is an interger related to the precision (higher precision will require more computation time).

The penalty by which the returned distance is increased fulfills (at least) the following properties:

• The penalty function is continuous (except noise created by numerical integration, see paragraph after this list) as long as no objects are added to or removed from the ecluster. That particularly means: small changes in the search point (second argument) cause only small changes in the result.
• For search points far away from the ecluster (i.e. large distances compared to the dimensions of the ecluster), the penalty approaches zero, i.e. the behavior of the fair_distance function approaches the behavior of the distance function.
• If the ecluster consists of a set of points, the penalty for a search point close to one of those points (closer than half of the minimum distance between each pair of points in the ecluster) is chosen in such a way that the adjusted distance is equal to the distance from the search point to the closest point in the ecluster multiplied by the square root of the count of points in the ecluster.
• If the ecluster does not cover any area (i.e. only consists of points, paths, and/or outlines), and if the search point (second argument) overlaps with the ecluster, then the penalty (and thus the result) is zero.
• The integral (or average) of the square of the fair distance value (result of this function) over all possible search points is independent of the ecluster as long as the ecluster does not cover more than a half of earth's surface.

The function uses numerical integration to compute the result. The third parameter (which defaults to 10000) can be used to adjust the number of samples taken. A higher sample count increases precision as well as execution time of the function. Because this function internally uses a spherical model of earth for certain steps of the calculation, the precision cannot be increased unboundedly.

Despite the limitations explained above, it is ensured that the penalty is always positive, i.e. results returned by the fair_distance function are always equal to or greater than the results returned by the distance function regardless of stochastic effects. Furthermore, all results are deterministic and reproducible with the same version of pgLatLon.

GeoJSON_to_epoint(jsonb, text)

Maps a GeoJSON object of type "Point" or "Feature" (which contains a "Point") to an epoint datum. For any other JSON objects, NULL is returned.

The second parameter (which defaults to epoint_lonlat) may be set to a name of a conversion function that transforms two coordinates (two float8 parameters) to an epoint.

GeoJSON_to_ecluster(jsonb, text)

Maps a (valid) GeoJSON object to an ecluster. Note that this function does not check whether the JSONB object is a valid GeoJSON object.

The second parameter (which defaults to epoint_lonlat) may be set to a name of a conversion function that transforms two coordinates (two float8 parameters) to an epoint.

max_latitude(ebox)

Returns the northern boundary of a given ebox in degrees between -90 and +90.

max_longitude(ebox)

Returns the eastern boundary of a given ebox in degrees between -180 and +180 (both inclusive).

min_latitude(ebox)

Returns the southern boundary of a given ebox in degrees between -90 and +90.

min_longitude(ebox)

Returns the western boundary of a given ebox in degrees between -180 and +180 (both inclusive).

latitude(epoint)

Returns the latitude value of an epoint in degrees between -90 and +90.

longitude(epoint)

Returns the longitude value of an epoint in degrees between -180 and +180 (both inclusive).

radius(ecircle)

Returns the radius of an ecircle in meters.