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

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 in meters, 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 in meters

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 of the polygon in square meters

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.

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

RETURN GEO_LINESTRING([
  [35, 10], [45, 45]
])

[
  {
    "type": "LineString",
    "coordinates": [
      [
        35,
        10
      ],
      [
        45,
        45
      ]
    ]
  }
]

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

RETURN GEO_MULTILINESTRING([
  [[100.0, 0.0], [101.0, 1.0]],
  [[102.0, 2.0], [101.0, 2.3]]
])

[
  {
    "type": "MultiLineString",
    "coordinates": [
      [
        [
          100,
          0
        ],
        [
          101,
          1
        ]
      ],
      [
        [
          102,
          2
        ],
        [
          101,
          2.3
        ]
      ]
    ]
  }
]

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

RETURN GEO_MULTIPOINT([
  [35, 10], [45, 45]
])

[
  {
    "type": "MultiPoint",
    "coordinates": [
      [
        35,
        10
      ],
      [
        45,
        45
      ]
    ]
  }
]

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

RETURN GEO_POINT(1.0, 2.0)

[
  {
    "type": "Point",
    "coordinates": [
      1,
      2
    ]
  }
]

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:

RETURN GEO_POLYGON([
  [0.0, 0.0], [7.5, 2.5], [0.0, 5.0]
])

[
  {
    "type": "Polygon",
    "coordinates": [
      [
        [
          0,
          0
        ],
        [
          7.5,
          2.5
        ],
        [
          0,
          5
        ]
      ]
    ]
  }
]

Advanced Polygon with a hole inside:

RETURN GEO_POLYGON([
  [[35, 10], [45, 45], [15, 40], [10, 20], [35, 10]],
  [[20, 30], [30, 20], [35, 35], [20, 30]]
])

[
  {
    "type": "Polygon",
    "coordinates": [
      [
        [
          35,
          10
        ],
        [
          45,
          45
        ],
        [
          15,
          40
        ],
        [
          10,
          20
        ],
        [
          35,
          10
        ]
      ],
      [
        [
          20,
          30
        ],
        [
          30,
          20
        ],
        [
          35,
          35
        ],
        [
          20,
          30
        ]
      ]
    ]
  }
]

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:

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]]
  ]
])

[
  {
    "type": "MultiPolygon",
    "coordinates": [
      [
        [
          [
            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
          ]
        ]
      ]
    ]
  }
]

Geo Index Functions

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()

FOR doc IN doc
  SORT DISTANCE(doc.latitude, doc.longitude, paramLatitude, paramLongitude) ASC
  RETURN doc

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()

FOR doc IN doc
  LET d = DISTANCE(doc.latitude, doc.longitude, paramLatitude, paramLongitude)
  FILTER d <= radius
  SORT d ASC
  RETURN doc

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()

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

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