# Functions for Working with Polygons

## WKT​

Returns a WKT (Well Known Text) geometric object from various Geo Data Types. Supported WKT objects are:

• POINT
• POLYGON
• MULTIPOLYGON

Syntax

WKT(geo_data)

Parameters

geo_data can be one of the following Geo Data Types or their underlying primitive types:

Returned value

• WKT geometric object POINT is returned for a Point.
• WKT geometric object POLYGON is returned for a Polygon
• WKT geometric object MULTIPOLYGON is returned for a MultiPolygon.

Examples

POINT from tuple:

SELECT wkt((0., 0.));
POINT(0 0)

POLYGON from an array of tuples or an array of tuple arrays:

SELECT wkt([(0., 0.), (10., 0.), (10., 10.), (0., 10.)]);
POLYGON((0 0,10 0,10 10,0 10))

MULTIPOLYGON from an array of multi-dimensional tuple arrays:

SELECT wkt([[[(0., 0.), (10., 0.), (10., 10.), (0., 10.)], [(4., 4.), (5., 4.), (5., 5.), (4., 5.)]], [[(-10., -10.), (-10., -9.), (-9., 10.)]]]);
MULTIPOLYGON(((0 0,10 0,10 10,0 10,0 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))

Converts a WKT (Well Known Text) MultiPolygon into a MultiPolygon type.

### Example​

SELECT    toTypeName(readWKTMultiPolygon('MULTIPOLYGON(((2 0,10 0,10 10,0 10,2 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))')) AS type,    readWKTMultiPolygon('MULTIPOLYGON(((2 0,10 0,10 10,0 10,2 0),(4 4,5 4,5 5,4 5,4 4)),((-10 -10,-10 -9,-9 10,-10 -10)))') AS output FORMAT Markdown
typeoutput
MultiPolygon[[[(2,0),(10,0),(10,10),(0,10),(2,0)],[(4,4),(5,4),(5,5),(4,5),(4,4)]],[[(-10,-10),(-10,-9),(-9,10),(-10,-10)]]]

### Input parameters​

String starting with MULTIPOLYGON

### Returned value​

MultiPolygon

Converts a WKT (Well Known Text) MultiPolygon into a Polygon type.

### Example​

SELECT    toTypeName(readWKTPolygon('POLYGON((2 0,10 0,10 10,0 10,2 0))')) AS type,    readWKTPolygon('POLYGON((2 0,10 0,10 10,0 10,2 0))') AS outputFORMAT Markdown
typeoutput
Polygon[[(2,0),(10,0),(10,10),(0,10),(2,0)]]

### Input parameters​

String starting with POLYGON

### Returned value​

Polygon

The readWKTPoint function in ClickHouse parses a Well-Known Text (WKT) representation of a Point geometry and returns a point in the internal ClickHouse format.

### Syntax​

readWKTPoint(wkt_string)

### Arguments​

• wkt_string: The input WKT string representing a Point geometry.

### Returned value​

The function returns a ClickHouse internal representation of the Point geometry.

### Example​

SELECT readWKTPoint('POINT (1.2 3.4)');
(1.2,3.4)

Parses a Well-Known Text (WKT) representation of a LineString geometry and returns it in the internal ClickHouse format.

### Syntax​

readWKTLineString(wkt_string)

### Arguments​

• wkt_string: The input WKT string representing a LineString geometry.

### Returned value​

The function returns a ClickHouse internal representation of the linestring geometry.

### Example​

SELECT readWKTLineString('LINESTRING (1 1, 2 2, 3 3, 1 1)');
[(1,1),(2,2),(3,3),(1,1)]

Parses a Well-Known Text (WKT) representation of a Polygon geometry and returns a ring (closed linestring) in the internal ClickHouse format.

### Syntax​

readWKTRing(wkt_string)

### Arguments​

• wkt_string: The input WKT string representing a Polygon geometry.

### Returned value​

The function returns a ClickHouse internal representation of the ring (closed linestring) geometry.

### Example​

SELECT readWKTRing('POLYGON ((1 1, 2 2, 3 3, 1 1))');
[(1,1),(2,2),(3,3),(1,1)]

## polygonsWithinSpherical​

Returns true or false depending on whether or not one polygon lies completely inside another polygon. Reference https://www.boost.org/doc/libs/1_62_0/libs/geometry/doc/html/geometry/reference/algorithms/within/within_2.html

### Example​

select polygonsWithinSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]);
0

### Returned value​

UInt8, 0 for false, 1 for true

## polygonsDistanceSpherical​

Calculates the minimal distance between two points where one point belongs to the first polygon and the second to another polygon. Spherical means that coordinates are interpreted as coordinates on a pure and ideal sphere, which is not true for the Earth. Using this type of coordinate system speeds up execution, but of course is not precise.

### Example​

SELECT polygonsDistanceSpherical([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
0.24372872211133834

Two polygons

Float64

## polygonsDistanceCartesian​

Calculates distance between two polygons

### Example​

SELECT polygonsDistanceCartesian([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
14.000714267493642

Two polygons

Float64

## polygonsEqualsCartesian​

Returns true if two polygons are equal

### Example​

SELECT polygonsEqualsCartesian([[[(1., 1.), (1., 4.), (4., 4.), (4., 1.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
1

Two polygons

### Returned value​

UInt8, 0 for false, 1 for true

## polygonsSymDifferenceSpherical​

Calculates the spatial set theoretic symmetric difference (XOR) between two polygons

### Example​

SELECT wkt(arraySort(polygonsSymDifferenceSpherical([[(50., 50.), (50., -50.), (-50., -50.), (-50., 50.), (50., 50.)], [(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)], [(-10., -10.), (-10., -40.), (-40., -40.), (-40., -10.), (-10., -10.)]], [[(-20., -20.), (-20., 20.), (20., 20.), (20., -20.), (-20., -20.)]])));
MULTIPOLYGON(((-20 -10.3067,-10 -10,-10 -20.8791,-20 -20,-20 -10.3067)),((10 20.8791,20 20,20 10.3067,10 10,10 20.8791)),((50 50,50 -50,-50 -50,-50 50,50 50),(20 10.3067,40 10,40 40,10 40,10 20.8791,-20 20,-20 -10.3067,-40 -10,-40 -40,-10 -40,-10 -20.8791,20 -20,20 10.3067)))

Polygons

MultiPolygon

## polygonsSymDifferenceCartesian​

The same as polygonsSymDifferenceSpherical, but the coordinates are in the Cartesian coordinate system; which is more close to the model of the real Earth.

### Example​

SELECT wkt(polygonsSymDifferenceCartesian([[[(0, 0), (0, 3), (1, 2.9), (2, 2.6), (2.6, 2), (2.9, 1), (3, 0), (0, 0)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
MULTIPOLYGON(((1 2.9,1 1,2.9 1,3 0,0 0,0 3,1 2.9)),((1 2.9,1 4,4 4,4 1,2.9 1,2.6 2,2 2.6,1 2.9)))

Polygons

MultiPolygon

## polygonsIntersectionSpherical​

Calculates the intersection (AND) between polygons, coordinates are spherical.

### Example​

SELECT wkt(arrayMap(a -> arrayMap(b -> arrayMap(c -> (round(c.1, 6), round(c.2, 6)), b), a), polygonsIntersectionSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]])))
MULTIPOLYGON(((4.3666 50.8434,4.36024 50.8436,4.34956 50.8536,4.35268 50.8567,4.36794 50.8525,4.3666 50.8434)))

Polygons

MultiPolygon

## polygonsWithinCartesian​

Returns true if the second polygon is within the first polygon.

### Example​

SELECT polygonsWithinCartesian([[[(2., 2.), (2., 3.), (3., 3.), (3., 2.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
1

Two polygons

### Returned value​

UInt8, 0 for false, 1 for true

## polygonConvexHullCartesian​

Calculates a convex hull. Reference

Coordinates are in Cartesian coordinate system.

### Example​

SELECT wkt(polygonConvexHullCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.), (2., 3.)]]]))
POLYGON((0 0,0 5,5 5,5 0,0 0))

MultiPolygon

Polygon

## polygonAreaSpherical​

Calculates the surface area of a polygon.

### Example​

SELECT round(polygonAreaSpherical([[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]), 14)
9.387704e-8

Polygon

Float

## polygonsUnionSpherical​

Calculates a union (OR).

### Example​

SELECT wkt(polygonsUnionSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]], [[[(4.346693, 50.858306), (4.367945, 50.852455), (4.366227, 50.840809), (4.344961, 50.833264), (4.338074, 50.848677), (4.346693, 50.858306)]]]))
MULTIPOLYGON(((4.36661 50.8434,4.36623 50.8408,4.34496 50.8333,4.33807 50.8487,4.34669 50.8583,4.35268 50.8567,4.36136 50.8652,4.36131 50.8651,4.39045 50.8565,4.38303 50.8429,4.36661 50.8434)))

Polygons

MultiPolygon

## polygonPerimeterSpherical​

Calculates the perimeter of the polygon.

### Example​

This is the polygon representing Zimbabwe:

POLYGON((30.0107 -15.6462,30.0502 -15.6401,30.09 -15.6294,30.1301 -15.6237,30.1699 -15.6322,30.1956 -15.6491,30.2072 -15.6532,30.2231 -15.6497,30.231 -15.6447,30.2461 -15.6321,30.2549 -15.6289,30.2801 -15.6323,30.2962 -15.639,30.3281 -15.6524,30.3567 -15.6515,30.3963 -15.636,30.3977 -15.7168,30.3993 -15.812,30.4013 -15.9317,30.4026 -16.0012,30.5148 -16.0004,30.5866 -16,30.7497 -15.9989,30.8574 -15.9981,30.9019 -16.0071,30.9422 -16.0345,30.9583 -16.0511,30.9731 -16.062,30.9898 -16.0643,31.012 -16.0549,31.0237 -16.0452,31.0422 -16.0249,31.0569 -16.0176,31.0654 -16.0196,31.0733 -16.0255,31.0809 -16.0259,31.089 -16.0119,31.1141 -15.9969,31.1585 -16.0002,31.26 -16.0235,31.2789 -16.0303,31.2953 -16.0417,31.3096 -16.059,31.3284 -16.0928,31.3409 -16.1067,31.3603 -16.1169,31.3703 -16.1237,31.3746 -16.1329,31.3778 -16.1422,31.384 -16.1488,31.3877 -16.1496,31.3956 -16.1477,31.3996 -16.1473,31.4043 -16.1499,31.4041 -16.1545,31.4027 -16.1594,31.4046 -16.1623,31.4241 -16.1647,31.4457 -16.165,31.4657 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0.45539

## polygonsIntersectionCartesian​

Calculates the intersection of polygons.

### Example​

SELECT wkt(polygonsIntersectionCartesian([[[(0., 0.), (0., 3.), (1., 2.9), (2., 2.6), (2.6, 2.), (2.9, 1.), (3., 0.), (0., 0.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
MULTIPOLYGON(((1 2.9,2 2.6,2.6 2,2.9 1,1 1,1 2.9)))

Polygons

MultiPolygon

## polygonAreaCartesian​

Calculates the area of a polygon

### Example​

SELECT polygonAreaCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
25

Polygon

Float64

## polygonPerimeterCartesian​

Calculates the perimeter of a polygon.

### Example​

SELECT polygonPerimeterCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
15

Polygon

Float64

## polygonsUnionCartesian​

Calculates the union of polygons.

### Example​

SELECT wkt(polygonsUnionCartesian([[[(0., 0.), (0., 3.), (1., 2.9), (2., 2.6), (2.6, 2.), (2.9, 1), (3., 0.), (0., 0.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]]))
MULTIPOLYGON(((1 2.9,1 4,4 4,4 1,2.9 1,3 0,0 0,0 3,1 2.9)))

Polygons

### Returned value​

MultiPolygon

For more information on geometry systems, see this presentation about the Boost library, which is what ClickHouse uses.