--- slug: /en/sql-reference/functions/geo/polygons sidebar_label: Polygons title: "Functions for Working with Polygons" --- ## WKT Returns a WKT (Well Known Text) geometric object from various [Geo Data Types](../../data-types/geo.md). Supported WKT objects are: - POINT - POLYGON - MULTIPOLYGON **Syntax** ```sql WKT(geo_data) ``` **Parameters** `geo_data` can be one of the following [Geo Data Types](../../data-types/geo.md) or their underlying primitive types: - [Point](../../data-types/geo.md#point) - [Ring](../../data-types/geo.md#ring) - [Polygon](../../data-types/geo.md#polygon) - [MultiPolygon](../../data-types/geo.md#multipolygon) **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: ```sql SELECT wkt((0., 0.)); ``` ```response POINT(0 0) ``` POLYGON from an array of tuples or an array of tuple arrays: ```sql SELECT wkt([(0., 0.), (10., 0.), (10., 10.), (0., 10.)]); ``` ```response POLYGON((0 0,10 0,10 10,0 10)) ``` MULTIPOLYGON from an array of multi-dimensional tuple arrays: ```sql SELECT wkt([[[(0., 0.), (10., 0.), (10., 10.), (0., 10.)], [(4., 4.), (5., 4.), (5., 5.), (4., 5.)]], [[(-10., -10.), (-10., -9.), (-9., 10.)]]]); ``` ```response 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))) ``` ## 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 ## readWKTPoint 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 ```sql 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 ```sql SELECT readWKTPoint('POINT (1.2 3.4)'); ``` ```response (1.2,3.4) ``` ## readWKTRing Parses a Well-Known Text (WKT) representation of a Polygon geometry and returns a ring (closed linestring) in the internal ClickHouse format. ### Syntax ```sql 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 ```sql SELECT readWKTRing('LINESTRING (1 1, 2 2, 3 3, 1 1)'); ``` ```response [(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 ``` 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 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.)]]))); ``` ```response 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))) ``` ### Input parameters Polygons ### Returned value 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 ``` sql 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.)]]])) ``` ```response 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))) ``` ### Input parameters Polygons ### Returned value MultiPolygon ## polygonsIntersectionSpherical Calculates the intersection (AND) between polygons, coordinates are spherical. ### Example ``` sql 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)]]]))) ``` ```response 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))) ``` ### Input parameters Polygons ### Returned value MultiPolygon ## 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 wkt(polygonConvexHullCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.), (2., 3.)]]])) ``` ```response POLYGON((0 0,0 5,5 5,5 0,0 0)) ``` ### Input parameters MultiPolygon ### Returned value Polygon ## polygonAreaSpherical Calculates the surface area of a polygon. ### Example ``` sql 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) ``` ```response 9.387704e-8 ``` ### Input parameters Polygon ### Returned value Float ## polygonsUnionSpherical Calculates a union (OR). ### Example ``` sql 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)]]])) ``` ```response 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))) ``` ### Input parameters Polygons ### Returned value 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 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(27.604495, -17.312792), (27.624856, -17.233314), (27.641186, -17.198484), (27.777301, -17.001183), (27.816886, -16.959636), (27.868562, -16.929663), (28.022993, -16.865393), (28.113922, -16.827551), (28.21252, -16.748589), (28.280113, -16.706524), (28.643295, -16.568755), (28.690734, -16.56028), (28.718794, -16.56028), (28.73285, -16.55811), (28.741377, -16.550668), (28.761117, -16.532271), (28.769282, -16.515218), (28.808866, -16.486279), (28.822509, -16.470776), (28.829124, -16.434603), (28.833051, -16.426438), (28.857236, -16.388198), (28.857029, -16.36546), (28.840492, -16.323602), (28.836772, -16.306342), (28.840286, -16.284741), (28.86416, -16.231205), (28.847107, -16.202679), (28.852481, -16.162785), (28.8654, -16.121237), (28.870981, -16.087234), (28.868501, -16.08217), (28.86385, -16.076589), (28.859303, -16.069561), (28.857236, -16.060466), (28.860336, -16.049407), (28.874082, -16.028943), (28.877183, -16.022018), (28.898887, -15.995457), (28.932373, -15.963727), (28.946862, -15.957235), (28.951287, -15.955252), (28.972784, -15.951428), (29.018053, -15.950602), (29.042341, -15.946261), (29.055053, -15.934375), (29.076344, -15.895411), (29.086162, -15.884559), (29.102182, -15.870916), (29.121716, -15.859341), (29.141869, -15.854483), (29.150964, -15.848799), (29.186311, -15.812832), (29.406969, -15.714233), (29.422059, -15.711030000000001), (29.508462, -15.703588), (29.526239, -15.692839), (29.563446, -15.662144), (29.587217, -15.655736), (29.608559, -15.658422999999999), (29.62799, -15.663591), (29.648505, -15.666588), (29.672793, -15.663281), (29.73005, -15.644677), (29.773252, -15.638062), (29.814283, -15.619666), (29.837331, -15.614808), (29.881773, -15.618839), (29.967504, -15.641473), (30.010654, -15.646227)]), 6) ``` ```response 0.45539 ``` ### Input parameters ### Returned value ## polygonsIntersectionCartesian Calculates the intersection of polygons. ### Example ``` sql 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.)]]])) ``` ```response MULTIPOLYGON(((1 2.9,2 2.6,2.6 2,2.9 1,1 1,1 2.9))) ``` ### Input parameters Polygons ### Returned value MultiPolygon ## polygonAreaCartesian Calculates the area of a polygon ### Example ``` sql SELECT polygonAreaCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]]) ``` ```response 25 ``` ### Input parameters Polygon ### Returned value Float64 ## polygonPerimeterCartesian Calculates the perimeter of a polygon. ### Example ``` sql SELECT polygonPerimeterCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]]) ``` ```response 15 ``` ### Input parameters Polygon ### Returned value Float64 ## polygonsUnionCartesian Calculates the union of polygons. ### Example ``` sql 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.)]]])) ``` ```response MULTIPOLYGON(((1 2.9,1 4,4 4,4 1,2.9 1,3 0,0 0,0 3,1 2.9))) ``` ### Input parameters Polygons ### Returned value MultiPolygon 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.