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

---
slug: /en/sql-reference/functions/geo/polygons
sidebar_label: Polygons
title: "Functions for Working with Polygons"
---

## readWKTMultiPolygon

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

### 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

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

### 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

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

``` sql
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)]]]);
```
```response
0
```

### Input parameters

### 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

``` 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

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

### Example

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

## 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

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

## polygonsIntersectionSpherical

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

### Example

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

## 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

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.

### Example

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

## polygonAreaSpherical

Calculates the surface area of a polygon.

### Example

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

MultiPolygon

## polygonsUnionSpherical

Calculates a union (OR).

### Example

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

## polygonPerimeterSpherical

Calculates

### Example

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

## polygonsIntersectionCartesian

Calculates

### Example

``` sql
SELECT
```
```response
```

### Input parameters


### Returned value

## polygonAreaCartesian

Calculates the area of a polygon

### Example

``` sql
SELECT polygonAreaCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
25
```

### Input parameters

One polygon

### Returned value

Float64

## polygonPerimeterCartesian

Calculates

### Example

``` sql
SELECT polygonPerimeterCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
```
```response
15
```

### Input parameters

One polygon

### Returned value

Float64

## polygonsUnionCartesian

Calculates

### Example

``` sql
SELECT
```
```response
```

### Input parameters

### Returned value

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.