# Geo functions

## 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**

```
// 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()

Introduced in: v3.4.0

`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

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:

```
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()

Introduced in: v3.4.0

`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

```
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:

```
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:

```
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

```
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()

Introduced in: v3.4.0

`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.

```
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
```

```
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()

Introduced in: v3.4.0

`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:

```
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.

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.

```
// 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.

```
// 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

Introduced in: v3.4.0

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

### 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

### 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

### 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

### 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:

Advanced Polygon with a hole inside:

### 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

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

## Geo Index Functions

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()

`NEAR`

is a deprecated AQL function from version 3.4.0 on. Use DISTANCE() in a query like this instead:

`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()

`WITHIN`

is a deprecated AQL function from version 3.4.0 on. Use DISTANCE() in a query like this instead:

`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**radius**(number): radius in meters**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()

`WITHIN_RECTANGLE`

is a deprecated AQL function from version 3.4.0 on. Use GEO_CONTAINS and a GeoJSON polygon instead:

`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