Functions for Working with Geographical Coordinates 

greatCircleDistance 

Calculate the distance between two points on the Earth’s surface using the great-circle formula.

greatCircleDistance(lon1Deg, lat1Deg, lon2Deg, lat2Deg)

Input parameters

  • lon1Deg — Longitude of the first point in degrees. Range: [-180°, 180°].
  • lat1Deg — Latitude of the first point in degrees. Range: [-90°, 90°].
  • lon2Deg — Longitude of the second point in degrees. Range: [-180°, 180°].
  • lat2Deg — Latitude of the second point in degrees. Range: [-90°, 90°].

Positive values correspond to North latitude and East longitude, and negative values correspond to South latitude and West longitude.

Returned value

The distance between two points on the Earth’s surface, in meters.

Generates an exception when the input parameter values fall outside of the range.

Example

SELECT greatCircleDistance(55.755831, 37.617673, -55.755831, -37.617673)
┌─greatCircleDistance(55.755831, 37.617673, -55.755831, -37.617673)─┐
│                                                14132374.194975413 │
└───────────────────────────────────────────────────────────────────┘

pointInEllipses 

Checks whether the point belongs to at least one of the ellipses.
Coordinates are geometric in the Cartesian coordinate system.

pointInEllipses(x, y, x₀, y₀, a₀, b₀,...,xₙ, yₙ, aₙ, bₙ)

Input parameters

  • x, y — Coordinates of a point on the plane.
  • xᵢ, yᵢ — Coordinates of the center of the i-th ellipsis.
  • aᵢ, bᵢ — Axes of the i-th ellipsis in units of x, y coordinates.

The input parameters must be 2+4⋅n, where n is the number of ellipses.

Returned values

1 if the point is inside at least one of the ellipses; 0if it is not.

Example

SELECT pointInEllipses(10., 10., 10., 9.1, 1., 0.9999)
┌─pointInEllipses(10., 10., 10., 9.1, 1., 0.9999)─┐
│                                               1 │
└─────────────────────────────────────────────────┘

pointInPolygon 

Checks whether the point belongs to the polygon on the plane.

pointInPolygon((x, y), [(a, b), (c, d) ...], ...)

Input values

  • (x, y) — Coordinates of a point on the plane. Data type — Tuple — A tuple of two numbers.
  • [(a, b), (c, d) ...] — Polygon vertices. Data type — Array. Each vertex is represented by a pair of coordinates (a, b). Vertices should be specified in a clockwise or counterclockwise order. The minimum number of vertices is 3. The polygon must be constant.
  • The function also supports polygons with holes (cut out sections). In this case, add polygons that define the cut out sections using additional arguments of the function. The function does not support non-simply-connected polygons.

Returned values

1 if the point is inside the polygon, 0 if it is not.
If the point is on the polygon boundary, the function may return either 0 or 1.

Example

SELECT pointInPolygon((3., 3.), [(6, 0), (8, 4), (5, 8), (0, 2)]) AS res
┌─res─┐
│   1 │
└─────┘

geohashEncode 

Encodes latitude and longitude as a geohash-string, please see (http://geohash.org/, https://en.wikipedia.org/wiki/Geohash).

geohashEncode(longitude, latitude, [precision])

Input values

  • longitude - longitude part of the coordinate you want to encode. Floating in range[-180°, 180°]
  • latitude - latitude part of the coordinate you want to encode. Floating in range [-90°, 90°]
  • precision - Optional, length of the resulting encoded string, defaults to 12. Integer in range [1, 12]. Any value less than 1 or greater than 12 is silently converted to 12.

Returned values

  • alphanumeric String of encoded coordinate (modified version of the base32-encoding alphabet is used).

Example

SELECT geohashEncode(-5.60302734375, 42.593994140625, 0) AS res
┌─res──────────┐
│ ezs42d000000 │
└──────────────┘

geohashDecode 

Decodes any geohash-encoded string into longitude and latitude.

Input values

  • encoded string - geohash-encoded string.

Returned values

  • (longitude, latitude) - 2-tuple of Float64 values of longitude and latitude.

Example

SELECT geohashDecode('ezs42') AS res
┌─res─────────────────────────────┐
│ (-5.60302734375,42.60498046875) │
└─────────────────────────────────┘

geoToH3 

Returns H3 point index (lon, lat) with specified resolution.

H3 is a geographical indexing system where Earth’s surface divided into even hexagonal tiles. This system is hierarchical, i. e. each hexagon on the top level can be splitted into seven even but smaller ones and so on.

This index is used primarily for bucketing locations and other geospatial manipulations.

Syntax

geoToH3(lon, lat, resolution)

Parameters

  • lon — Longitude. Type: Float64.
  • lat — Latitude. Type: Float64.
  • resolution — Index resolution. Range: [0, 15]. Type: UInt8.

Returned values

  • Hexagon index number.
  • 0 in case of error.

Type: UInt64.

Example

Query:

SELECT geoToH3(37.79506683, 55.71290588, 15) as h3Index

Result:

┌────────────h3Index─┐
│ 644325524701193974 │
└────────────────────┘

geohashesInBox 

Returns an array of geohash-encoded strings of given precision that fall inside and intersect boundaries of given box, basically a 2D grid flattened into array.

Input values

  • longitude_min - min longitude, floating value in range [-180°, 180°]
  • latitude_min - min latitude, floating value in range [-90°, 90°]
  • longitude_max - max longitude, floating value in range [-180°, 180°]
  • latitude_max - max latitude, floating value in range [-90°, 90°]
  • precision - geohash precision, UInt8 in range [1, 12]

Please note that all coordinate parameters should be of the same type: either Float32 or Float64.

Returned values

  • array of precision-long strings of geohash-boxes covering provided area, you should not rely on order of items.
  • [] - empty array if min values of latitude and longitude aren’t less than corresponding max values.

Please note that function will throw an exception if resulting array is over 10’000’000 items long.

Example

SELECT geohashesInBox(24.48, 40.56, 24.785, 40.81, 4) AS thasos
┌─thasos──────────────────────────────────────┐
│ ['sx1q','sx1r','sx32','sx1w','sx1x','sx38'] │
└─────────────────────────────────────────────┘

h3GetBaseCell 

Returns the base cell number of the index.

Syntax

h3GetBaseCell(index)

Parameters

  • index — Hexagon index number. Type: UInt64.

Returned values

  • Hexagon base cell number. Type: UInt8.

Example

Query:

SELECT h3GetBaseCell(612916788725809151) as basecell

Result:

┌─basecell─┐
│       12 │
└──────────┘

h3HexAreaM2 

Average hexagon area in square meters at the given resolution.

Syntax

h3HexAreaM2(resolution)

Parameters

  • resolution — Index resolution. Range: [0, 15]. Type: UInt8.

Returned values

Example

Query:

SELECT h3HexAreaM2(13) as area

Result:

┌─area─┐
│ 43.9 │
└──────┘

h3IndexesAreNeighbors 

Returns whether or not the provided H3Indexes are neighbors.

Syntax

h3IndexesAreNeighbors(index1, index2)

Parameters

  • index1 — Hexagon index number. Type: UInt64.
  • index2 — Hexagon index number. Type: UInt64.

Returned values

  • Returns 1 if the indexes are neighbors, 0 otherwise. Type: UInt8.

Example

Query:

SELECT h3IndexesAreNeighbors(617420388351344639, 617420388352655359) AS n

Result:

┌─n─┐
│ 1 │
└───┘

h3ToChildren 

Returns an array with the child indexes of the given index.

Syntax

h3ToChildren(index, resolution)

Parameters

  • index — Hexagon index number. Type: UInt64.
  • resolution — Index resolution. Range: [0, 15]. Type: UInt8.

Returned values

  • Array with the child H3 indexes. Array of type: UInt64.

Example

Query:

SELECT h3ToChildren(599405990164561919, 6) AS children

Result:

┌─children───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ [603909588852408319,603909588986626047,603909589120843775,603909589255061503,603909589389279231,603909589523496959,603909589657714687] │
└────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┘

h3ToParent 

Returns the parent (coarser) index containing the given index.

Syntax

h3ToParent(index, resolution)

Parameters

  • index — Hexagon index number. Type: UInt64.
  • resolution — Index resolution. Range: [0, 15]. Type: UInt8.

Returned values

  • Parent H3 index. Type: UInt64.

Example

Query:

SELECT h3ToParent(599405990164561919, 3) as parent

Result:

┌─────────────parent─┐
│ 590398848891879423 │
└────────────────────┘

h3ToString 

Converts the H3Index representation of the index to the string representation.

h3ToString(index)

Parameters

  • index — Hexagon index number. Type: UInt64.

Returned values

  • String representation of the H3 index. Type: String.

Example

Query:

SELECT h3ToString(617420388352917503) as h3_string

Result:

┌─h3_string───────┐
│ 89184926cdbffff │
└─────────────────┘

stringToH3 

Converts the string representation to H3Index (UInt64) representation.

stringToH3(index_str)

Parameters

  • index_str — String representation of the H3 index. Type: String.

Returned values

  • Hexagon index number. Returns 0 on error. Type: UInt64.

Example

Query:

SELECT stringToH3('89184926cc3ffff') as index

Result:

┌──────────────index─┐
│ 617420388351344639 │
└────────────────────┘

h3GetResolution 

Returns the resolution of the index.

Syntax

h3GetResolution(index)

Parameters

  • index — Hexagon index number. Type: UInt64.

Returned values

  • Index resolution. Range: [0, 15]. Type: UInt8.

Example

Query:

SELECT h3GetResolution(617420388352917503) as res

Result:

┌─res─┐
│   9 │
└─────┘

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