# Spatial functions

These functions are used to specify 2D or 3D points in a Coordinate Reference System (CRS) and to calculate the geodesic distance between two points.

Functions:

The following graph is used for some of the examples below. ## 1. distance()

`distance()` returns a floating point number representing the geodesic distance between two points in the same Coordinate Reference System (CRS).

• If the points are in the Cartesian CRS (2D or 3D), then the units of the returned distance will be the same as the units of the points, calculated using Pythagoras' theorem.

• If the points are in the WGS-84 CRS (2D), then the units of the returned distance will be meters, based on the haversine formula over a spherical earth approximation.

• If the points are in the WGS-84 CRS (3D), then the units of the returned distance will be meters.

• The distance is calculated in two steps.

• First, a haversine formula over a spherical earth is used, at the average height of the two points.

• To account for the difference in height, Pythagoras' theorem is used, combining the previously calculated spherical distance with the height difference.

• This formula works well for points close to the earth’s surface; for instance, it is well-suited for calculating the distance of an airplane flight. It is less suitable for greater heights, however, such as when calculating the distance between two satellites.

Syntax: `distance(point1, point2)`

Returns:

 A Float.

Arguments:

Name Description

`point1`

A point in either a geographic or cartesian coordinate system.

`point2`

A point in the same CRS as 'point1'.

Considerations:

 `distance(null, null)`, `distance(null, point2)` and `distance(point1, null)` all return `null`. Attempting to use points with different Coordinate Reference Systems (such as WGS 84 2D and WGS 84 3D) will return `null`.
Query
``````WITH point({ x: 2.3, y: 4.5, crs: 'cartesian' }) AS p1, point({ x: 1.1, y: 5.4, crs: 'cartesian' }) AS p2
RETURN distance(p1,p2) AS dist``````

The distance between two 2D points in the Cartesian CRS is returned.

Table 1. Result
dist

`1.5`

1 row

Query
``````WITH point({ longitude: 12.78, latitude: 56.7, height: 100 }) AS p1, point({ latitude: 56.71, longitude: 12.79, height: 100 }) AS p2
RETURN distance(p1,p2) AS dist``````

The distance between two 3D points in the WGS 84 CRS is returned.

Table 2. Result
dist

`1269.9148706779097`

1 row

Query
``````MATCH (t:TrainStation)-[:TRAVEL_ROUTE]->(o:Office)
WITH point({ longitude: t.longitude, latitude: t.latitude }) AS trainPoint, point({ longitude: o.longitude, latitude: o.latitude }) AS officePoint
RETURN round(distance(trainPoint, officePoint)) AS travelDistance``````

The distance between the train station in Copenhagen and the Neo4j office in Malmo is returned.

Table 3. Result
travelDistance

`27842.0`

1 row

Query
``RETURN distance(NULL , point({ longitude: 56.7, latitude: 12.78 })) AS d``

If `null` is provided as one or both of the arguments, `null` is returned.

Table 4. Result
d

`<null>`

1 row

## 2. point() - WGS 84 2D

`point({longitude | x, latitude | y [, crs][, srid]})` returns a 2D point in the WGS 84 CRS corresponding to the given coordinate values.

Syntax: `point({longitude | x, latitude | y [, crs][, srid]})`

Returns:

 A 2D point in WGS 84.

Arguments:

Name Description

`A single map consisting of the following:`

`longitude/x`

A numeric expression that represents the longitude/x value in decimal degrees

`latitude/y`

A numeric expression that represents the latitude/y value in decimal degrees

`crs`

The optional string 'WGS-84'

`srid`

The optional number 4326

Considerations:

 If any argument provided to `point()` is `null`, `null` will be returned. If the coordinates are specified using `latitude` and `longitude`, the `crs` or `srid` fields are optional and inferred to be `'WGS-84'` (srid=4326). If the coordinates are specified using `x` and `y`, then either the `crs` or `srid` field is required if a geographic CRS is desired.
Query
``RETURN point({ longitude: 56.7, latitude: 12.78 }) AS point``

A 2D point with a `longitude` of `56.7` and a `latitude` of `12.78` in the WGS 84 CRS is returned.

Table 5. Result
point

`point({x: 56.7, y: 12.78, crs: 'wgs-84'})`

1 row

Query
``RETURN point({ x: 2.3, y: 4.5, crs: 'WGS-84' }) AS point``

`x` and `y` coordinates may be used in the WGS 84 CRS instead of `longitude` and `latitude`, respectively, providing `crs` is set to `'WGS-84'`, or `srid` is set to `4326`.

Table 6. Result
point

`point({x: 2.3, y: 4.5, crs: 'wgs-84'})`

1 row

Query
``````MATCH (p:Office)
RETURN point({ longitude: p.longitude, latitude: p.latitude }) AS officePoint``````

A 2D point representing the coordinates of the city of Malmo in the WGS 84 CRS is returned.

Table 7. Result
officePoint

`point({x: 12.994341, y: 55.611784, crs: 'wgs-84'})`

1 row

Query
``RETURN point(NULL ) AS p``

If `null` is provided as the argument, `null` is returned.

Table 8. Result
p

`<null>`

1 row

## 3. point() - WGS 84 3D

`point({longitude | x, latitude | y, height | z, [, crs][, srid]})` returns a 3D point in the WGS 84 CRS corresponding to the given coordinate values.

Syntax: `point({longitude | x, latitude | y, height | z, [, crs][, srid]})`

Returns:

 A 3D point in WGS 84.

Arguments:

Name Description

`A single map consisting of the following:`

`longitude/x`

A numeric expression that represents the longitude/x value in decimal degrees

`latitude/y`

A numeric expression that represents the latitude/y value in decimal degrees

`height/z`

A numeric expression that represents the height/z value in meters

`crs`

The optional string 'WGS-84-3D'

`srid`

The optional number 4979

Considerations:

 If any argument provided to `point()` is `null`, `null` will be returned. If the `height/z` key and value is not provided, a 2D point in the WGS 84 CRS will be returned. If the coordinates are specified using `latitude` and `longitude`, the `crs` or `srid` fields are optional and inferred to be `'WGS-84-3D'` (srid=4979). If the coordinates are specified using `x` and `y`, then either the `crs` or `srid` field is required if a geographic CRS is desired.
Query
``RETURN point({ longitude: 56.7, latitude: 12.78, height: 8 }) AS point``

A 3D point with a `longitude` of `56.7`, a `latitude` of `12.78` and a height of `8` meters in the WGS 84 CRS is returned.

Table 9. Result
point

`point({x: 56.7, y: 12.78, z: 8.0, crs: 'wgs-84-3d'})`

1 row

## 4. point() - Cartesian 2D

`point({x, y [, crs][, srid]})` returns a 2D point in the Cartesian CRS corresponding to the given coordinate values.

Syntax: `point({x, y [, crs][, srid]})`

Returns:

 A 2D point in Cartesian.

Arguments:

Name Description

`A single map consisting of the following:`

`x`

A numeric expression

`y`

A numeric expression

`crs`

The optional string 'cartesian'

`srid`

The optional number 7203

Considerations:

 If any argument provided to `point()` is `null`, `null` will be returned. The `crs` or `srid` fields are optional and default to the Cartesian CRS (which means `srid:7203`).
Query
``RETURN point({ x: 2.3, y: 4.5 }) AS point``

A 2D point with an `x` coordinate of `2.3` and a `y` coordinate of `4.5` in the Cartesian CRS is returned.

Table 10. Result
point

`point({x: 2.3, y: 4.5, crs: 'cartesian'})`

1 row

## 5. point() - Cartesian 3D

`point({x, y, z, [, crs][, srid]})` returns a 3D point in the Cartesian CRS corresponding to the given coordinate values.

Syntax: `point({x, y, z, [, crs][, srid]})`

Returns:

 A 3D point in Cartesian.

Arguments:

Name Description

`A single map consisting of the following:`

`x`

A numeric expression

`y`

A numeric expression

`z`

A numeric expression

`crs`

The optional string 'cartesian-3D'

`srid`

The optional number 9157

Considerations:

 If any argument provided to `point()` is `null`, `null` will be returned. If the `z` key and value is not provided, a 2D point in the Cartesian CRS will be returned. The `crs` or `srid` fields are optional and default to the 3D Cartesian CRS (which means `srid:9157`).
Query
``RETURN point({ x: 2.3, y: 4.5, z: 2 }) AS point``

A 3D point with an `x` coordinate of `2.3`, a `y` coordinate of `4.5` and a `z` coordinate of `2` in the Cartesian CRS is returned.

Table 11. Result
point

`point({x: 2.3, y: 4.5, z: 2.0, crs: 'cartesian-3d'})`

1 row