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ClickHouse/docs/en/sql-reference/functions/geo/polygon.md

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---
slug: /en/sql-reference/functions/geo/polygons
sidebar_label: Polygons
title: "Functions for Working with Polygons"
---
## readWKTMultiPolygon
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Converts a WKT (Well Known Text) MultiPolygon into a MultiPolygon type.
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### Example
``` sql
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
```
| type | output |
|:-|:-|
| 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
## readWKTPolygon
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Converts a WKT (Well Known Text) MultiPolygon into a Polygon type.
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### Example
``` sql
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 output
FORMAT Markdown
```
| type | output |
|:-|:-|
| Polygon | [[(2,0),(10,0),(10,10),(0,10),(2,0)]] |
### Input parameters
String starting with `POLYGON`
### Returned value
Polygon
## polygonsWithinSpherical
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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
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### Example
``` sql
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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)]]]);
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```
```response
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0
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```
### Input parameters
### Returned value
UInt8, 0 for false, 1 for true
## polygonsDistanceSpherical
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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.
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### Example
``` sql
SELECT polygonsDistanceSpherical([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
```
```response
0.24372872211133834
```
### Input parameters
Two polygons
### Returned value
Float64
## polygonsDistanceCartesian
Calculates distance between two polygons
### Example
``` sql
SELECT polygonsDistanceCartesian([[[(0, 0), (0, 0.1), (0.1, 0.1), (0.1, 0)]]], [[[(10., 10.), (10., 40.), (40., 40.), (40., 10.), (10., 10.)]]])
```
```response
14.000714267493642
```
### Input parameters
Two polygons
### Returned value
Float64
## polygonsEqualsCartesian
Returns true if two polygons are equal
### Example
``` sql
SELECT polygonsEqualsCartesian([[[(1., 1.), (1., 4.), (4., 4.), (4., 1.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
```
```response
1
```
### Input parameters
Two polygons
### Returned value
UInt8, 0 for false, 1 for true
## polygonsSymDifferenceSpherical
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Calculates the spatial set theoretic symmetric difference (XOR) between two polygons
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### Example
``` sql
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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.)]])));
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```
```response
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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)))
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```
### Input parameters
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Polygons
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### Returned value
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MultiPolygon
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## polygonsSymDifferenceCartesian
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The same as `polygonsSymDifferenceSpherical`, but the coordinates are in the Cartesian coordinate system; which is more close to the model of the real Earth.
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### Example
``` sql
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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.)]]]))
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```
```response
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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)))
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```
### Input parameters
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Polygons
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### Returned value
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MultiPolygon
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## polygonsIntersectionSpherical
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Calculates the intersection (AND) between polygons, coordinates are spherical.
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### Example
``` sql
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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)]]])))
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```
```response
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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)))
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```
### Input parameters
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Polygons
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### Returned value
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MultiPolygon
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## polygonsWithinCartesian
Returns true if the second polygon is within the first polygon.
### Example
``` sql
SELECT polygonsWithinCartesian([[[(2., 2.), (2., 3.), (3., 3.), (3., 2.)]]], [[[(1., 1.), (1., 4.), (4., 4.), (4., 1.), (1., 1.)]]])
```
```response
1
```
### Input parameters
Two polygons
### Returned value
UInt8, 0 for false, 1 for true
## polygonConvexHullCartesian
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Calculates a convex hull. [Reference](https://www.boost.org/doc/libs/1_61_0/libs/geometry/doc/html/geometry/reference/algorithms/convex_hull.html)
Coordinates are in Cartesian coordinate system.
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### Example
``` sql
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SELECT wkt(polygonConvexHullCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.), (2., 3.)]]]))
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```
```response
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POLYGON((0 0,0 5,5 5,5 0,0 0))
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```
### Input parameters
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MultiPolygon
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### Returned value
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Polygon
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## polygonAreaSpherical
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Calculates the surface area of a polygon.
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### Example
``` sql
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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)
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```
```response
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9.387704e-8
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```
### Input parameters
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Polygon
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### Returned value
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Float
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## polygonsUnionSpherical
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Calculates a union (OR).
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### Example
``` sql
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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)]]]))
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```
```response
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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)))
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```
### Input parameters
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Polygons
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### Returned value
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MultiPolygon
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## polygonPerimeterSpherical
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Calculates the perimeter of the polygon.
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### Example
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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 -16.1677,31.4806 -16.178,31.5192 -16.1965,31.6861 -16.2072,31.7107 -16.2179,31.7382 -16.2398,31.7988 -16.3037,31.8181 -16.3196,31.8601 -16.3408,31.8719 -16.3504,31.8807 -16.368,31.8856 -16.4063,31.8944 -16.4215,31.9103 -16.4289,32.0141 -16.4449,32.2118 -16.4402,32.2905 -16.4518,32.3937 -16.4918,32.5521 -16.5534,32.6718 -16.5998,32.6831 -16.6099,32.6879 -16.6243,32.6886 -16.6473,32.6987 -16.6868,32.7252 -16.7064,32.7309 -16.7087,32.7313 -16.7088,32.7399 -16.7032,32.7538 -16.6979,32.7693 -16.6955,32.8007 -16.6973,32.862 -16.7105,32.8934 -16.7124,32.9096 -16.7081,32.9396 -16.6898,32.9562 -16.6831,32.9685 -16.6816,32.9616 -16.7103,32.9334 -16.8158,32.9162 -16.8479,32.9005 -16.8678,32.8288 -16.9351,32.8301 -16.9415,32.8868 -17.0382,32.9285 -17.1095,32.9541 -17.1672,32.9678 -17.2289,32.9691 -17.2661,32.9694 -17.2761,32.9732 -17.2979,32.9836 -17.3178,32.9924 -17.3247,33.0147 -17.3367,33.0216 -17.3456,33.0225 -17.3615,33.0163 -17.3772,33.0117 -17.384,32.9974 -17.405,32.9582 -17.4785,32.9517 -17.4862,32.943 -17.4916,32.9366 -17.4983,32.9367 -17.5094,32.9472 -17.5432,32.9517 -17.5514,32.9691 -17.5646,33.0066 -17.581,33.0204 -17.5986,33.0245 -17.6192,33.0206 -17.6385,33.0041 -17.6756,33.0002 -17.7139,33.0032 -17.7577,32.9991 -17.7943,32.9736 -17.8106,32.957 -17.818,32.9461 -17.8347,32.9397 -17.8555,32.9369 -17.875,32.9384 -17.8946,32.9503 -17.9226,32.9521 -17.9402,32.9481 -17.9533,32.9404 -17.96,32.9324 -17.9649,32.9274 -17.9729,32.929 -17.9823,32.9412 -17.9963,32.9403 -18.0048,32.9349 -18.0246,32.9371 -18.0471,32.9723 -18.1503,32.9755 -18.1833,32.9749 -18.1908,32.9659 -18.2122,32.9582 -18.2254,32.9523 -18.233,32.9505 -18.2413,32.955 -18.2563,32.9702 -18.2775,33.0169 -18.3137,33.035 -18.3329,33.0428 -18.352,33.0381 -18.3631,33.0092 -18.3839,32.9882 -18.4132,32.9854 -18.4125,32.9868 -18.4223,32.9995 -18.4367,33.003 -18.4469,32.9964 -18.4671,32.9786 -18.4801,32.9566 -18.4899,32.9371 -18.501,32.9193 -18.51,32.9003 -18.5153,32.8831 -18.5221,32.8707 -18.5358,32.8683 -18.5526,32.8717 -18.5732,32.8845 -18.609,32.9146 -18.6659,32.9223 -18.6932,32.9202 -18.7262,32.9133 -18.753,32.9025 -18.7745,32.8852 -18.7878,32.8589 -18.79,32.8179 -18.787,32.7876 -18.7913,32.6914 -18.8343,32.6899 -18.8432,32.6968 -18.8972,32.7032 -18.9119,32.7158 -18.9198,32.7051 -18.9275,32.6922 -18.9343,32.6825 -18.9427,32.6811 -18.955,32.6886 -18.9773,32.6903 -18.9882,32.6886 -19.001,32.6911 -19.0143,32.699 -19.0222,32.7103 -19.026,32.7239 -19.0266,32.786 -19.0177,32.8034 -19.0196,32.8142 -19.0238,32.82 -19.0283,32.823 -19.0352,32.8253 -19.0468,32.8302 -19.0591,32.8381 -19.0669,32.8475 -19.0739,32.8559 -19.0837,32.8623 -19.1181,32.8332 -19.242,32.8322 -19.2667,32.8287 -19.2846,32.8207 -19.3013,32.8061 -19.3234,32.7688 -19.3636,32.7665 -19.3734,32.7685 -19.4028,32.7622 -19.4434,32.7634 -19.464,32.7739 -19.4759,32.7931 -19.4767,32.8113 -19.4745,32.8254 -19.4792,32.8322 -19.5009,32.8325 -19.5193,32.8254 -19.5916,32.8257 -19.6008,32.8282 -19.6106,32.8296 -19.6237,32.8254 -19.6333,32.8195 -19.642,32.8163 -19.6521,32.8196 -19.6743,32.831 -19.6852,32.8491 -19.6891,32.8722 -19.6902,32.8947 -19.
```
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``` sql
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SELECT round(polygonPerimeterSpherical([(30.010654, -15.646227), (30.050238, -15.640129), (30.090029, -15.629381), (30.130129, -15.623696), (30.16992, -15.632171), (30.195552, -15.649121), (30.207231, -15.653152), (30.223147, -15.649741), (30.231002, -15.644677), (30.246091, -15.632068), (30.254876, -15.628864), (30.280094, -15.632275), (30.296196, -15.639042), (30.32805, -15.652428), (30.356679, -15.651498), (30.396263, -15.635995), (30.39771, -15.716817), (30.39926, -15.812005), (30.401327, -15.931688), (30.402568, -16.001244), (30.514809, -16.000418), (30.586587, -16.000004), (30.74973, -15.998867), (30.857424, -15.998144), (30.901865, -16.007136), (30.942173, -16.034524), (30.958296, -16.05106), (30.973075, -16.062016), (30.989767, -16.06429), (31.012039, -16.054885), (31.023718, -16.045169), (31.042218, -16.024912), (31.056895, -16.017574), (31.065421, -16.019641), (31.073328, -16.025532), (31.080872, -16.025946), (31.089037, -16.01189), (31.1141, -15.996904), (31.15849, -16.000211), (31.259983, -16.023465), (31.278897, -16.030287), (31.29533, -16.041655), (31.309592, -16.059019), (31.328351, -16.092815), (31.340908, -16.106664), (31.360339, -16.116896), (31.37026, -16.123718), (31.374601, -16.132916), (31.377754, -16.142218), (31.384006, -16.148832), (31.387727, -16.149556), (31.395582, -16.147695), (31.399613, -16.147282), (31.404315, -16.149866), (31.404057, -16.154517), (31.402713, -16.159374), (31.404574, -16.162268), (31.424107, -16.164749), (31.445708, -16.164955), (31.465655, -16.167746), (31.480641, -16.177978), (31.519192, -16.196478), (31.686107, -16.207227), (31.710705, -16.217872), (31.738197, -16.239783), (31.798761, -16.303655), (31.818088, -16.319571), (31.86005, -16.340759), (31.871935, -16.35037), (31.88072, -16.368044), (31.88563, -16.406284), (31.894363, -16.421477), (31.910279, -16.428919), (32.014149, -16.444938), (32.211759, -16.440184), (32.290463, -16.45176), (32.393661, -16.491757), (32.5521, -16.553355), (32.671783, -16.599761), (32.6831, -16.609889), (32.687906, -16.624255), (32.68863, -16.647303), (32.698655, -16.686784), (32.725217, -16.706421), (32.73095, -16.708656), (32.731314, -16.708798), (32.739893, -16.703217), (32.753845, -16.697946), (32.769348, -16.695466), (32.800664, -16.697326), (32.862004, -16.710452), (32.893372, -16.712415), (32.909598, -16.708075), (32.93957, -16.689781), (32.95621, -16.683063), (32.968509, -16.681615999999998), (32.961585, -16.710348), (32.933369, -16.815768), (32.916213, -16.847911), (32.900503, -16.867755), (32.828776, -16.935141), (32.83012, -16.941549), (32.886757, -17.038184), (32.928512, -17.109497), (32.954143, -17.167168), (32.967786, -17.22887), (32.96909, -17.266115), (32.969439, -17.276102), (32.973212, -17.297909), (32.983599, -17.317753), (32.992384, -17.324678), (33.014656, -17.336667), (33.021633, -17.345555), (33.022459, -17.361471), (33.016258, -17.377181), (33.011651, -17.383991), (32.997448, -17.404983), (32.958174, -17.478467), (32.951663, -17.486218), (32.942981, -17.491593), (32.936573, -17.498311), (32.936676, -17.509369), (32.947218, -17.543166), (32.951663, -17.551434), (32.969129, -17.56456), (33.006646, -17.580993), (33.020392, -17.598563), (33.024526, -17.619233), (33.020599, -17.638457), (33.004063, -17.675561), (33.000238, -17.713905), (33.003184, -17.757726), (32.999102, -17.794313), (32.973573, -17.810643), (32.957037, -17.817981), (32.946082, -17.834724), (32.939674, -17.855498), (32.936883, -17.875032), (32.938433, -17.894566), (32.950267, -17.922574), (32.952128, -17.940247), (32.948149, -17.95327), (32.940397, -17.959988), (32.932439, -17.964949), (32.927375, -17.972907), (32.928977, -17.982312), (32.941224, -17.996265), (32.940294, -18.004843), (32.934919, -18.024583), (32.93709, -18.047114), (32.972282, -18.150261), (32.975537, -18.183333), (32.974865, -18.190775), (32.965925, -18.212169), (32.958174, -18.225398), (32.952283, -18.233046), (32.950525999999996, -18.241314), (32.95497, -18.256301), (32.970163, -18.277488), (33.016878, -18.313661), (33.034965, -18.332885), (33.042768, -18.352005), (33.038066, -18.3630
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```
```response
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0.45539
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```
### Input parameters
### Returned value
## polygonsIntersectionCartesian
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Calculates the intersection of polygons.
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### Example
``` sql
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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.)]]]))
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```
```response
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MULTIPOLYGON(((1 2.9,2 2.6,2.6 2,2.9 1,1 1,1 2.9)))
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```
### Input parameters
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Polygons
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### Returned value
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MultiPolygon
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## polygonAreaCartesian
Calculates the area of a polygon
### Example
``` sql
SELECT polygonAreaCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
25
```
### Input parameters
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Polygon
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### Returned value
Float64
## polygonPerimeterCartesian
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Calculates the perimeter of a polygon.
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### Example
``` sql
SELECT polygonPerimeterCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
15
```
### Input parameters
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Polygon
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### Returned value
Float64
## polygonsUnionCartesian
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Calculates the union of polygons.
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### Example
``` sql
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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.)]]]))
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```
```response
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MULTIPOLYGON(((1 2.9,1 4,4 4,4 1,2.9 1,3 0,0 0,0 3,1 2.9)))
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```
### Input parameters
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Polygons
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### Returned value
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MultiPolygon
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For more information on geometry systems, see this [presentation](https://archive.fosdem.org/2020/schedule/event/working_with_spatial_trajectories_in_boost_geometry/attachments/slides/3988/export/events/attachments/working_with_spatial_trajectories_in_boost_geometry/slides/3988/FOSDEM20_vissarion.pdf) about the Boost library, which is what ClickHouse uses.
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