Geo-spatial functions in AQL

Geo-spatial data representations

You can model geo-spatial information in different ways using the data types available in ArangoDB. The recommended way is to use objects with GeoJSON geometry but you can also use longitude and latitude coordinate pairs for points. Both models are supported by Geo-Spatial Indexes.

Coordinate pairs

Longitude and latitude coordinates are numeric values and can be stored in the following ways:

• Coordinates using an array with two numbers in [longitude, latitude] order, for example, in a user-chosen attribute called location:

  {
    "location": [ -73.983, 40.764 ]
  }
  

• Coordinates using an array with two numbers in [latitude, longitude] order, for example, in a user-chosen attribute called location:

  {
    "location": [ 40.764, -73.983 ]
  }
  

• Coordinates using two separate numeric attributes, for example, in two user-chosen attributes called lat and lng as sub-attributes of a location attribute:

  {
    "location": {
      "lat": 40.764,
      "lng": -73.983
    }
  }
  

GeoJSON

GeoJSON is a geospatial data format based on JSON. It defines several different types of JSON objects and the way in which they can be combined to represent data about geographic shapes on the Earth surface.

Example of a document with a GeoJSON Point stored in a user-chosen attribute called location (with coordinates in [longitude, latitude] order):

{
  "location": {
    "type": "Point",
    "coordinates": [ -73.983, 40.764 ]
  }
}

GeoJSON uses a geographic coordinate reference system, World Geodetic System 1984 (WGS 84), and units of decimal degrees.

Internally, ArangoDB maps all coordinate pairs onto a unit sphere. Distances are projected onto a sphere with the Earth’s Volumetric mean radius of 6371 km. ArangoDB implements a useful subset of the GeoJSON format (RFC 7946) . Feature Objects and the GeometryCollection type are not supported. Supported geometry object types are:

• Point
• MultiPoint
• LineString
• MultiLineString
• Polygon
• MultiPolygon

Point

A GeoJSON Point  is a position  comprised of a longitude and a latitude:

{
  "type": "Point",
  "coordinates": [100.0, 0.0]
}

GeoJSON Points can optionally have a third coordinate for the elevation, but ArangoDB doesn’t use it in calculations:

{
  "location": {
    "type": "Point",
    "coordinates": [ 100.0, 0.0, 43.0 ]
  }
}

MultiPoint

A GeoJSON MultiPoint  is an array of positions:

{
  "type": "MultiPoint",
  "coordinates": [
    [100.0, 0.0],
    [101.0, 1.0]
  ]
}

LineString

A GeoJSON LineString  is an array of two or more positions:

{
  "type": "LineString",
  "coordinates": [
    [100.0, 0.0],
    [101.0, 1.0]
  ]
}

MultiLineString

A GeoJSON MultiLineString  is an array of LineString coordinate arrays:

{
  "type": "MultiLineString",
  "coordinates": [
    [
      [100.0, 0.0],
      [101.0, 1.0]
    ],
    [
      [102.0, 2.0],
      [103.0, 3.0]
    ]
  ]
}

Polygon

A GeoJSON Polygon  consists of a series of closed LineString objects (ring-like). These Linear Ring objects consist of four or more coordinate pairs with the first and last coordinate pair being equal. Coordinate pairs of a Polygon are an array of linear ring coordinate arrays. The first element in the array represents the exterior ring. Any subsequent elements represent interior rings (holes within the surface).

The orientation of the first linear ring is crucial: the right-hand-rule is applied, so that the area to the left of the path of the linear ring (when walking on the surface of the Earth) is considered to be the “interior” of the polygon. All other linear rings must be contained within this interior. According to the GeoJSON standard, the subsequent linear rings must be oriented following the right-hand-rule, too, that is, they must run clockwise around the hole (viewed from above). However, ArangoDB is tolerant here (as suggested by the GeoJSON standard ), all but the first linear ring are inverted if the orientation is wrong.

In the end, a point is considered to be in the interior of the polygon, if and only if one has to cross an odd number of linear rings to reach the exterior of the polygon prescribed by the first linear ring.

A number of additional rules apply (and are enforced by the GeoJSON parser):

• A polygon must contain at least one linear ring, i.e., it must not be empty.
• A linear ring may not be empty, it needs at least three distinct coordinate pairs, that is, at least 4 coordinate pairs (since the first and last must be the same).
• No two edges of linear rings in the polygon must intersect, in particular, no linear ring may be self-intersecting.
• Within the same linear ring, consecutive coordinate pairs may be the same, otherwise all coordinate pairs need to be distinct (except the first and last one).
• Linear rings of a polygon must not share edges, but they may share coordinate pairs.
• A linear ring defines two regions on the sphere. ArangoDB always interprets the region that lies to the left of the boundary ring (in the direction of its travel on the surface of the Earth) as the interior of the ring. This is in contrast to earlier versions of ArangoDB before 3.10, which always took the smaller of the two regions as the interior. Therefore, from 3.10 on one can now have polygons whose outer ring encloses more than half the Earth’s surface.
• The interior rings must be contained in the (interior) of the outer ring.
• Interior rings should follow the above rule for orientation (counterclockwise external rings, clockwise internal rings, interior always to the left of the line).

Here is an example with no holes:

{
  "type": "Polygon",
    "coordinates": [
    [
      [100.0, 0.0],
      [101.0, 0.0],
      [101.0, 1.0],
      [100.0, 1.0],
      [100.0, 0.0]
    ]
  ]
}

Here is an example with a hole:

{
  "type": "Polygon",
  "coordinates": [
    [
      [100.0, 0.0],
      [101.0, 0.0],
      [101.0, 1.0],
      [100.0, 1.0],
      [100.0, 0.0]
    ],
    [
      [100.8, 0.8],
      [100.8, 0.2],
      [100.2, 0.2],
      [100.2, 0.8],
      [100.8, 0.8]
    ]
  ]
}

MultiPolygon

A GeoJSON MultiPolygon  consists of multiple polygons. The “coordinates” member is an array of Polygon coordinate arrays. See above for the rules and the meaning of polygons.

If the polygons in a MultiPolygon are disjoint, then a point is in the interior of the MultiPolygon if and only if it is contained in one of the polygons. If some polygon P2 in a MultiPolygon is contained in another polygon P1, then P2 is treated like a hole in P1 and containment of points is defined with the even-odd-crossings rule (see Polygon).

Additionally, the following rules apply and are enforced for MultiPolygons:

• No two edges in the linear rings of the polygons of a MultiPolygon may intersect.
• Polygons in the same MultiPolygon may not share edges, but they may share coordinate pairs.

Example with two polygons, the second one with a hole:

{
    "type": "MultiPolygon",
    "coordinates": [
        [
            [
                [102.0, 2.0],
                [103.0, 2.0],
                [103.0, 3.0],
                [102.0, 3.0],
                [102.0, 2.0]
            ]
        ],
        [
            [
                [100.0, 0.0],
                [101.0, 0.0],
                [101.0, 1.0],
                [100.0, 1.0],
                [100.0, 0.0]
            ],
            [
                [100.2, 0.2],
                [100.2, 0.8],
                [100.8, 0.8],
                [100.8, 0.2],
                [100.2, 0.2]
            ]
        ]
    ]
}

GeoJSON interpretation

Note the following technical detail about GeoJSON: The GeoJSON standard, Section 3.1.1 Position  prescribes that lines are cartesian lines in cylindrical coordinates (longitude/latitude). However, this definition is inconvenient in practice, since such lines are not geodesic on the surface of the Earth. Furthermore, the best available algorithms for geospatial computations on Earth typically use geodesic lines as the boundaries of polygons on Earth.

Therefore, ArangoDB uses the syntax of the GeoJSON standard, but then interprets lines (and boundaries of polygons) as geodesic lines (pieces of great circles) on Earth. This is a violation of the GeoJSON standard, but serving a practical purpose.

Note in particular that this can sometimes lead to unexpected results. Consider the following polygon (remember that GeoJSON has longitude before latitude in coordinate pairs):

{ "type": "Polygon", "coordinates": [[
  [4, 54], [4, 47], [16, 47], [16, 54], [4, 54]
]] }

It does not contain the point [10, 47] since the shortest path (geodesic) from [4, 47] to [16, 47] lies North relative to the parallel of latitude at 47 degrees. On the contrary, the polygon does contain the point [10, 54] as it lies South of the parallel of latitude at 54 degrees.

Furthermore, there is an issue with the interpretation of linear rings (boundaries of polygons) according to GeoJSON standard, Section 3.1.6 Polygon . This section states explicitly:

A linear ring MUST follow the right-hand rule with respect to the area it bounds, i.e., exterior rings are counter-clockwise, and holes are clockwise.

This rather misleading phrase means that when a linear ring is used as the boundary of a polygon, the “interior” of the polygon lies to the left of the boundary when one travels on the surface of the Earth and along the linear ring. For example, the polygon below travels counter-clockwise around the point [10, 50], and thus the interior of the polygon contains this point and its surroundings, but not, for example, the North Pole and the South Pole.

{ "type": "Polygon", "coordinates": [[
  [4, 54], [4, 47], [16, 47], [16, 54], [4, 54]
]] }

On the other hand, the following polygon travels clockwise around the point [10, 50], and thus its “interior” does not contain [10, 50], but does contain the North Pole and the South Pole:

{ "type": "Polygon", "coordinates": [[
  [4, 54], [16, 54], [16, 47], [4, 47], [4, 54]
]] }

Remember that the “interior” is to the left of the given linear ring, so this second polygon is basically the complement on Earth of the previous polygon!

ArangoDB versions before 3.10 did not follow this rule and always took the “smaller” connected component of the surface as the “interior” of the polygon. This made it impossible to specify polygons which covered more than half of the sphere. From version 3.10 onward, ArangoDB recognizes this correctly. See Legacy Polygons for how to deal with this issue.

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 points 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 of the first point
• longitude1 (number): the longitude of the first point
• latitude2 (number): the latitude of the second point
• longitude2 (number): the longitude of the second point
• returns distance (number): the distance between both points 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 coll // 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.
• geoJsonB (object): Second GeoJSON object, or a coordinate array in [longitude, latitude] order.
• returns bool (bool): true if every point in B is also contained in A, otherwise false.

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()

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, or a coordinate array in [longitude, latitude] order.
• geoJsonB (object): Second GeoJSON object, or a coordinate array in [longitude, latitude] order.
• 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()

GEO_AREA(geoJson, ellipsoid) → area

Return the area for a Polygon or MultiPolygon on a sphere with the average Earth radius, or an ellipsoid.

• 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()

GEO_EQUALS(geoJsonA, geoJsonB) → bool

Checks whether two GeoJSON objects are equal or not.

• geoJsonA (object): First GeoJSON object.
• geoJsonB (object): Second GeoJSON object.
• returns bool (bool): true if they are equal, otherwise false.

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()

GEO_INTERSECTS(geoJsonA, geoJsonB) → bool

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

• geoJsonA (object): First GeoJSON object.
• geoJsonB (object): Second GeoJSON object, or a coordinate array in [longitude, latitude] order.
• 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()

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 a coordinate array in [longitude, latitude] order.
• geoJsonB (object|array): Second GeoJSON object, or a 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.

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): An array of [longitude, latitude] pairs, or optionally [longitude, latitude, elevation].
• 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): An array of arrays of [longitude, latitude] pairs, or optionally [longitude, latitude, elevation].
• 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): An array of [longitude, latitude] pairs, or optionally [longitude, latitude, elevation].
• 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, elevation) → geoJson

Construct a valid GeoJSON Point.

• longitude (number): The longitude portion of the point.
• latitude (number): The latitude portion of the point.
• elevation (number, optional): The elevation portion of the point (introduced in v3.11.14-2 and v3.12.6).
• returns geoJson (object): A valid 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): An array of (arrays of) [longitude, latitude] pairs, or optionally [longitude, latitude, elevation].
• 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], [0.0, 0.0]
])

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

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 MultiPolygon for the rules of Polygon and MultiPolygon construction.

• polygons (array): An array of arrays of arrays of [longitude, latitude] pairs, or optionally [longitude, latitude, elevation].
• 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:

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 
          ] 
        ] 
      ] 
    ] 
  } 
]