# Гео функции¶

## Geo utility functions¶

The following helper functions can use geo indexes, but do not have to in all cases. You can use all of these functions in combination with each other, and if you have configured a geo index it may be utilized, see Geo Indexing.

### DISTANCE()¶

`DISTANCE(latitude1, longitude1, latitude2, longitude2) → distance`

Calculate the distance between two arbitrary coordinates in meters (as birds would fly). The value is computed using the haversine formula, which is based on a spherical Earth model. It's fast to compute and is accurate to around 0.3%, which is sufficient for most use cases such as location-aware services.

• latitude1 (number): the latitude portion of the first coordinate
• longitude1 (number): the longitude portion of the first coordinate
• latitude2 (number): the latitude portion of the second coordinate
• longitude2 (number): the longitude portion of the second coordinate
• returns distance (number): the distance between both coordinates in meters
 ```1 2 3 4 5 6 7``` ``````// Distance from Brandenburg Gate (Berlin) to ArangoDB headquarters (Cologne) DISTANCE(52.5163, 13.3777, 50.9322, 6.94) // 476918.89688380965 (~477km) // Sort a small number of documents based on distance to Central Park (New York) FOR doc IN doc // e.g. documents returned by a traversal SORT DISTANCE(doc.latitude, doc.longitude, 40.78, -73.97) RETURN doc ``````

### GEO_CONTAINS()¶

`GEO_CONTAINS(geoJsonA, geoJsonB) → bool`

Checks whether the GeoJSON object `geoJsonA` fully contains `geoJsonB` (every point in B is also in A). The object `geoJsonA` has to be of type Polygon or MultiPolygon. For other types containment is not well-defined because of numerical stability problems.

• geoJsonA (object): first GeoJSON object or coordinate array (in longitude, latitude order)
• geoJsonB (object): second GeoJSON object or coordinate array (in longitude, latitude order)
• returns bool (bool): true if every point in B is also contained in A, false otherwise

{% hint 'info' %} ArangoDB follows and exposes the same behavior as the underlying S2 geometry library. As stated in the S2 documentation:

Point containment is defined such that if the sphere is subdivided into faces (loops), every point is contained by exactly one face. This implies that linear rings do not necessarily contain their vertices.

As a consequence, a linear ring or polygon does not necessarily contain its boundary edges!

You can optimize queries that contain a `FILTER` expression of the following form with an S2-based geospatial index:

 ```1 2 3``` ``````FOR doc IN coll FILTER GEO_CONTAINS(geoJson, doc.geo) ... ``````

In this example, you would create the index for the collection `coll`, on the attribute `geo`. You need to set the `geoJson` index option to `true`. The `geoJson` variable needs to evaluate to a valid GeoJSON object. Also note the argument order: the stored document attribute `doc.geo` is passed as the second argument. Passing it as the first argument, like `FILTER GEO_CONTAINS(doc.geo, geoJson)` to test whether `doc.geo` contains `geoJson`, cannot utilize the index.

### GEO_DISTANCE()¶

`GEO_DISTANCE(geoJsonA, geoJsonB, ellipsoid) → distance`

Return the distance between two GeoJSON objects, measured from the centroid of each shape. For a list of supported types see the geo index page.

• geoJsonA (object): first GeoJSON object
• geoJsonB (object): second GeoJSON object
• ellipsoid (string, optional): reference ellipsoid to use. Supported are `"sphere"` (default) and `"wgs84"`.
• returns distance (number): the distance between the centroid points of the two objects on the reference ellipsoid
 ```1 2 3 4 5 6 7``` ``````LET polygon = { type: "Polygon", coordinates: [[[-11.5, 23.5], [-10.5, 26.1], [-11.2, 27.1], [-11.5, 23.5]]] } FOR doc IN collectionName LET distance = GEO_DISTANCE(doc.geometry, polygon) // calculates the distance RETURN distance ``````

You can optimize queries that contain a `FILTER` expression of the following form with an S2-based geospatial index:

 ```1 2 3``` ``````FOR doc IN coll FILTER GEO_DISTANCE(geoJson, doc.geo) <= limit ... ``````

In this example, you would create the index for the collection `coll`, on the attribute `geo`. You need to set the `geoJson` index option to `true`. `geoJson` needs to evaluate to a valid GeoJSON object. `limit` must be a distance in meters; it cannot be an expression. An upper bound with `<`, a lower bound with `>` or `>=`, or both, are equally supported.

You can also optimize queries that use a `SORT` condition of the following form with a geospatial index:

 `1` `````` SORT GEO_DISTANCE(geoJson, doc.geo) ``````

The index covers returning matches from closest to furthest away, or vice versa. You may combine such a `SORT` with a `FILTER` expression that utilizes the geospatial index, too, via the `GEO_DISTANCE()`, `GEO_CONTAINS()`, and `GEO_INTERSECTS()` functions.

### GEO_AREA()¶

Introduced in: v3.5.1

`GEO_AREA(geoJson, ellipsoid) → area`

Return the area for a polygon or multi-polygon on a sphere with the average Earth radius, or an ellipsoid. For a list of supported types see the geo index page.

• geoJson (object): a GeoJSON object
• ellipsoid (string, optional): reference ellipsoid to use. Supported are `"sphere"` (default) and `"wgs84"`.
• returns area (number): the area in square meters of the polygon
 ```1 2 3 4 5``` ``````LET polygon = { type: "Polygon", coordinates: [[[-11.5, 23.5], [-10.5, 26.1], [-11.2, 27.1], [-11.5, 23.5]]] } RETURN GEO_AREA(polygon, "wgs84") ``````

### GEO_EQUALS()¶

`GEO_EQUALS(geoJsonA, geoJsonB) → bool`

Checks whether two GeoJSON objects are equal or not. For a list of supported types see the geo index page.

• geoJsonA (object): first GeoJSON object
• geoJsonB (object): second GeoJSON object.
• returns bool (bool): true for equality.
 ```1 2 3 4 5 6 7``` ``````LET polygonA = GEO_POLYGON([ [-11.5, 23.5], [-10.5, 26.1], [-11.2, 27.1], [-11.5, 23.5] ]) LET polygonB = GEO_POLYGON([ [-11.5, 23.5], [-10.5, 26.1], [-11.2, 27.1], [-11.5, 23.5] ]) RETURN GEO_EQUALS(polygonA, polygonB) // true ``````
 ```1 2 3 4 5 6 7``` ``````LET polygonA = GEO_POLYGON([ [-11.1, 24.0], [-10.5, 26.1], [-11.2, 27.1], [-11.1, 24.0] ]) LET polygonB = GEO_POLYGON([ [-11.5, 23.5], [-10.5, 26.1], [-11.2, 27.1], [-11.5, 23.5] ]) RETURN GEO_EQUALS(polygonA, polygonB) // false ``````

### GEO_INTERSECTS()¶

`GEO_INTERSECTS(geoJsonA, geoJsonB) → bool`

Checks whether the GeoJSON object `geoJsonA` intersects with `geoJsonB` (i.e. at least one point in B is also A or vice-versa).

• geoJsonA (object): first GeoJSON object
• geoJsonB (object): second GeoJSON object.
• returns bool (bool): true if B intersects A, false otherwise

You can optimize queries that contain a `FILTER` expression of the following form with an S2-based geospatial index:

 ```1 2 3``` ``````FOR doc IN coll FILTER GEO_INTERSECTS(geoJson, doc.geo) ... ``````

In this example, you would create the index for the collection `coll`, on the attribute `geo`. You need to set the `geoJson` index option to `true`. `geoJson` needs to evaluate to a valid GeoJSON object. Also note the argument order: the stored document attribute `doc.geo` is passed as the second argument. Passing it as the first argument, like `FILTER GEO_INTERSECTS(doc.geo, geoJson)` to test whether `doc.geo` intersects `geoJson`, cannot utilize the index.

### GEO_IN_RANGE()¶

Introduced in: v3.8.0

`GEO_IN_RANGE(geoJsonA, geoJsonB, low, high, includeLow, includeHigh) → bool`

Checks whether the distance between two GeoJSON objects lies within a given interval. The distance is measured from the centroid of each shape.

• geoJsonA (object|array): first GeoJSON object or coordinate array (in longitude, latitude order)
• geoJsonB (object|array): second GeoJSON object or coordinate array (in longitude, latitude order)
• low (number): minimum value of the desired range
• high (number): maximum value of the desired range
• includeLow (bool, optional): whether the minimum value shall be included in the range (left-closed interval) or not (left-open interval). The default value is `true`
• includeHigh (bool): whether the maximum value shall be included in the range (right-closed interval) or not (right-open interval). The default value is `true`
• returns bool (bool): whether the evaluated distance lies within the range

### IS_IN_POLYGON()¶

Determine whether a coordinate is inside a polygon.

{% hint 'warning' %} The IS_IN_POLYGON AQL function is deprecated as of ArangoDB 3.4.0 in favor of the new `GEO_CONTAINS` AQL function, which works with GeoJSON Polygons and MultiPolygons.

`IS_IN_POLYGON(polygon, latitude, longitude) → bool`

• polygon (array): an array of arrays with 2 elements each, representing the points of the polygon in the format [lat, lon]
• latitude (number): the latitude portion of the search coordinate
• longitude (number): the longitude portion of the search coordinate
• returns bool (bool): true if the point (latitude, longitude) is inside the polygon or false if it's not. The result is undefined (can be true or false) if the specified point is exactly on a boundary of the polygon.
 ```1 2``` ``````// will check if the point (lat 4, lon 7) is contained inside the polygon IS_IN_POLYGON( [ [ 0, 0 ], [ 0, 10 ], [ 10, 10 ], [ 10, 0 ] ], 4, 7 ) ``````

`IS_IN_POLYGON(polygon, coord, useLonLat) → bool`

The 2nd parameter can alternatively be specified as an array with two values.

By default, each array element in polygon is expected to be in the format [lat, lon]. This can be changed by setting the 3rd parameter to true to interpret the points as [lon, lat]. coord will then also be interpreted in the same way.

• polygon (array): an array of arrays with 2 elements each, representing the points of the polygon
• coord (array): the search coordinate as a number array with two elements
• useLonLat (bool, optional): if set to true, the coordinates in polygon and the search coordinate coord will be interpreted as [lon, lat] (GeoJSON). The default is false and the format [lat, lon] is expected.
• returns bool (bool): true if the point coord is inside the polygon or false if it's not. The result is undefined (can be true or false) if the specified point is exactly on a boundary of the polygon.
 ```1 2 3 4 5``` ``````// will check if the point (lat 4, lon 7) is contained inside the polygon IS_IN_POLYGON( [ [ 0, 0 ], [ 0, 10 ], [ 10, 10 ], [ 10, 0 ] ], [ 4, 7 ] ) // will check if the point (lat 4, lon 7) is contained inside the polygon IS_IN_POLYGON( [ [ 0, 0 ], [ 10, 0 ], [ 10, 10 ], [ 0, 10 ] ], [ 7, 4 ], true ) ``````

## GeoJSON Constructors¶

The following helper functions are available to easily create valid GeoJSON output. In all cases you can write equivalent JSON yourself, but these functions will help you to make all your AQL queries shorter and easier to read.

### GEO_LINESTRING()¶

`GEO_LINESTRING(points) → geoJson`

Construct a GeoJSON LineString. Needs at least two longitude/latitude pairs.

• points (array): number array of longitude/latitude pairs
• returns geoJson (object): a valid GeoJSON LineString

{% aqlexample examplevar="examplevar" type="type" query="query" bind="bind" result="result" %} @startDocuBlockInline aqlGeoLineString_1 @EXAMPLE_AQL{aqlGeoLineString_1} RETURN GEO_LINESTRING([ [35, 10], [45, 45] ]) @END_EXAMPLE_AQL @endDocuBlock aqlGeoLineString_1 {% endaqlexample %}

### GEO_MULTILINESTRING()¶

`GEO_MULTILINESTRING(points) → geoJson`

Construct a GeoJSON MultiLineString. Needs at least two elements consisting valid LineStrings coordinate arrays.

• points (array): array of LineStrings
• returns geoJson (object): a valid GeoJSON MultiLineString

{% aqlexample examplevar="examplevar" type="type" query="query" bind="bind" result="result" %} @startDocuBlockInline aqlGeoMultiLineString_1 @EXAMPLE_AQL{aqlGeoMultiLineString_1} RETURN GEO_MULTILINESTRING([ [[100.0, 0.0], [101.0, 1.0]], [[102.0, 2.0], [101.0, 2.3]] ]) @END_EXAMPLE_AQL @endDocuBlock aqlGeoMultiLineString_1 {% endaqlexample %}

### GEO_MULTIPOINT()¶

`GEO_MULTIPOINT(points) → geoJson`

Construct a GeoJSON LineString. Needs at least two longitude/latitude pairs.

• points (array): number array of longitude/latitude pairs
• returns geoJson (object): a valid GeoJSON Point

{% aqlexample examplevar="examplevar" type="type" query="query" bind="bind" result="result" %} @startDocuBlockInline aqlGeoMultiPoint_1 @EXAMPLE_AQL{aqlGeoMultiPoint_1} RETURN GEO_MULTIPOINT([ [35, 10], [45, 45] ]) @END_EXAMPLE_AQL @endDocuBlock aqlGeoMultiPoint_1 {% endaqlexample %}

### GEO_POINT()¶

`GEO_POINT(longitude, latitude) → geoJson`

Construct a valid GeoJSON Point.

• longitude (number): the longitude portion of the point
• latitude (number): the latitude portion of the point
• returns geoJson (object): a GeoJSON Point

{% aqlexample examplevar="examplevar" type="type" query="query" bind="bind" result="result" %} @startDocuBlockInline aqlGeoPoint_1 @EXAMPLE_AQL{aqlGeoPoint_1} RETURN GEO_POINT(1.0, 2.0) @END_EXAMPLE_AQL @endDocuBlock aqlGeoPoint_1 {% endaqlexample %}

### GEO_POLYGON()¶

`GEO_POLYGON(points) → geoJson`

Construct a GeoJSON Polygon. Needs at least one array representing a linear ring. Each linear ring consists of an array with at least four longitude/latitude pairs. The first linear ring must be the outermost, while any subsequent linear ring will be interpreted as holes.

For details about the rules, see GeoJSON polygons.

• points (array): array of (arrays of) longitude/latitude pairs
• returns geoJson (object|null): a valid GeoJSON Polygon

A validation step is performed using the S2 geometry library. If the validation is not successful, an AQL warning is issued and `null` is returned.

Simple Polygon:

{% aqlexample examplevar="examplevar" type="type" query="query" bind="bind" result="result" %} @startDocuBlockInline aqlGeoPolygon_1 @EXAMPLE_AQL{aqlGeoPolygon_1} RETURN GEO_POLYGON([ [0.0, 0.0], [7.5, 2.5], [0.0, 5.0] ]) @END_EXAMPLE_AQL @endDocuBlock aqlGeoPolygon_1 {% endaqlexample %}

Advanced Polygon with a hole inside:

{% aqlexample examplevar="examplevar" type="type" query="query" bind="bind" result="result" %} @startDocuBlockInline aqlGeoPolygon_2 @EXAMPLE_AQL{aqlGeoPolygon_2} RETURN GEO_POLYGON([ [[35, 10], [45, 45], [15, 40], [10, 20], [35, 10]], [[20, 30], [30, 20], [35, 35], [20, 30]] ]) @END_EXAMPLE_AQL @endDocuBlock aqlGeoPolygon_2 {% endaqlexample %}

### GEO_MULTIPOLYGON()¶

`GEO_MULTIPOLYGON(polygons) → geoJson`

Construct a GeoJSON MultiPolygon. Needs at least two Polygons inside. See GEO_POLYGON() and GeoJSON MultiPolygons for the rules of Polygon and MultiPolygon construction.

• polygons (array): array of arrays of array of longitude/latitude pairs
• returns geoJson (object|null): a valid GeoJSON MultiPolygon

A validation step is performed using the S2 geometry library, if the validation is not successful, an AQL warning is issued and `null` is returned.

MultiPolygon comprised of a simple Polygon and a Polygon with hole:

{% aqlexample examplevar="examplevar" type="type" query="query" bind="bind" result="result" %} @startDocuBlockInline aqlGeoMultiPolygon_1 @EXAMPLE_AQL{aqlGeoMultiPolygon_1} RETURN GEO_MULTIPOLYGON([ [ [[40, 40], [20, 45], [45, 30], [40, 40]] ], [ [[20, 35], [10, 30], [10, 10], [30, 5], [45, 20], [20, 35]], [[30, 20], [20, 15], [20, 25], [30, 20]] ] ]) @END_EXAMPLE_AQL @endDocuBlock aqlGeoMultiPolygon_1 {% endaqlexample %}

## Geo Index Functions¶

{% hint 'warning' %} The AQL functions `NEAR()`, `WITHIN()` and `WITHIN_RECTANGLE()` are deprecated starting from version 3.4.0. Please use the Geo utility functions instead.

AQL offers the following functions to filter data based on geo indexes. These functions require the collection to have at least one geo index. If no geo index can be found, calling this function will fail with an error at runtime. There is no error when explaining the query however.

### NEAR()¶

{% hint 'warning' %} `NEAR` is a deprecated AQL function from version 3.4.0 on. Use DISTANCE() in a query like this instead:

 ```1 2 3``` ``````FOR doc IN doc SORT DISTANCE(doc.latitude, doc.longitude, paramLatitude, paramLongitude) ASC RETURN doc ``````

Assuming there exists a geo-type index on `latitude` and `longitude`, the optimizer will recognize it and accelerate the query.

`NEAR(coll, latitude, longitude, limit, distanceName) → docArray`

Return at most limit documents from collection coll that are near latitude and longitude. The result contains at most limit documents, returned sorted by distance, with closest distances being returned first. Optionally, the distances in meters between the specified coordinate (latitude and longitude) and the document coordinates can be returned as well. To make use of that, the desired attribute name for the distance result has to be specified in the distanceName argument. The result documents will contain the distance value in an attribute of that name.

• coll (collection): a collection
• latitude (number): the latitude portion of the search coordinate
• longitude (number): the longitude portion of the search coordinate
• limit (number, optional): cap the result to at most this number of documents. The default is 100. If more documents than limit are found, it is undefined which ones will be returned.
• distanceName (string, optional): include the distance to the search coordinate in each document in the result (in meters), using the attribute name distanceName
• returns docArray (array): an array of documents, sorted by distance (shortest distance first)

### WITHIN()¶

{% hint 'warning' %} `WITHIN` is a deprecated AQL function from version 3.4.0 on. Use DISTANCE() in a query like this instead:

 ```1 2 3 4 5``` ``````FOR doc IN doc LET d = DISTANCE(doc.latitude, doc.longitude, paramLatitude, paramLongitude) FILTER d <= radius SORT d ASC RETURN doc ``````

Assuming there exists a geo-type index on `latitude` and `longitude`, the optimizer will recognize it and accelerate the query.

`WITHIN(coll, latitude, longitude, radius, distanceName) → docArray`

Return all documents from collection coll that are within a radius of radius around the specified coordinate (latitude and longitude). The documents returned are sorted by distance to the search coordinate, with the closest distances being returned first. Optionally, the distance in meters between the search coordinate and the document coordinates can be returned as well. To make use of that, an attribute name for the distance result has to be specified in the distanceName argument. The result documents will contain the distance value in an attribute of that name.

• coll (collection): a collection
• latitude (number): the latitude portion of the search coordinate
• longitude (number): the longitude portion of the search coordinate
• distanceName (string, optional): include the distance to the search coordinate in each document in the result (in meters), using the attribute name distanceName
• returns docArray (array): an array of documents, sorted by distance (shortest distance first)

### WITHIN_RECTANGLE()¶

{% hint 'warning' %} `WITHIN_RECTANGLE` is a deprecated AQL function from version 3.4.0 on. Use GEO_CONTAINS and a GeoJSON polygon instead:

 ```1 2 3 4``` ``````LET rect = {type: "Polygon", coordinates: [[[longitude1, latitude1], ...]]]} FOR doc IN doc FILTER GEO_CONTAINS(poly, [doc.longitude, doc.latitude]) RETURN doc ``````

Assuming there exists a geo-type index on `latitude` and `longitude`, the optimizer will recognize it and accelerate the query.

`WITHIN_RECTANGLE(coll, latitude1, longitude1, latitude2, longitude2) → docArray`

Return all documents from collection coll that are positioned inside the bounding rectangle with the points (latitude1, longitude1) and (latitude2, longitude2). There is no guaranteed order in which the documents are returned.

• coll (collection): a collection
• latitude1 (number): the bottom-left latitude portion of the search coordinate
• longitude1 (number): the bottom-left longitude portion of the search coordinate
• latitude2 (number): the top-right latitude portion of the search coordinate
• longitude2 (number): the top-right longitude portion of the search coordinate
• returns docArray (array): an array of documents, in random order