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Функции для работы с многоугольниками

WKT​

Возвращает геометрический объект WKT (Well Known Text) из различных геометрических типов данных. Поддерживаемые WKT-объекты:

  • POINT
  • POLYGON
  • MULTIPOLYGON
  • LINESTRING
  • MULTILINESTRING

Синтаксис

WKT(geo_data)

Параметры

geo_data может быть одним из следующих геометрических типов Geo-данных или соответствующих им примитивных типов:

Возвращаемое значение

  • Для Point возвращается геометрический объект WKT POINT.
  • Для Polygon возвращается геометрический объект WKT POLYGON.
  • Для MultiPolygon возвращается геометрический объект WKT MULTIPOLYGON.
  • Для LineString возвращается геометрический объект WKT LINESTRING.
  • Для MultiLineString возвращается геометрический объект WKT MULTILINESTRING.

Примеры

POINT из кортежа:

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

POINT(0 0)

POLYGON из массива кортежей или массива массивов кортежей:

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

POLYGON((0 0,10 0,10 10,0 10))

MULTIPOLYGON из многомерного массива кортежей:

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)))

readWKTMultiPolygon​

Преобразует WKT (Well Known Text) MultiPolygon в тип MultiPolygon.

Пример​

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
типрезультат
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)]]]

Входные параметры​

Строка, начинающаяся с MULTIPOLYGON

Возвращаемое значение​

MultiPolygon

readWKTPolygon​

Преобразует WKT (Well Known Text) MultiPolygon в тип Polygon.

Пример​

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
typeoutput
Polygon[[(2,0),(10,0),(10,10),(0,10),(2,0)]]

Входные параметры​

Строка, начинающаяся с POLYGON.

Возвращаемое значение​

Тип Polygon.

readWKTPoint​

Функция readWKTPoint в ClickHouse разбирает представление геометрического объекта типа Point в формате Well-Known Text (WKT) и возвращает точку во внутреннем формате ClickHouse.

Синтаксис​

readWKTPoint(wkt_string)

Аргументы​

  • wkt_string: входная строка WKT, представляющая геометрию точки (Point).

Возвращаемое значение​

Функция возвращает внутреннее представление геометрии точки (Point) в ClickHouse.

Пример​

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

(1.2,3.4)

readWKTLineString​

Интерпретирует представление геометрии типа LineString в формате Well-Known Text (WKT) и возвращает его во внутреннем формате ClickHouse.

Синтаксис​

readWKTLineString(wkt_string)

Аргументы​

  • wkt_string: входная строка в формате WKT, представляющая геометрию LineString.

Возвращаемое значение​

Функция возвращает внутреннее представление геометрии типа LineString в ClickHouse.

Пример​

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

[(1,1),(2,2),(3,3),(1,1)]

readWKTMultiLineString​

Анализирует представление геометрии MultiLineString в формате Well-Known Text (WKT) и возвращает его во внутреннем формате ClickHouse.

Синтаксис​

readWKTMultiLineString(wkt_string)

Аргументы​

  • wkt_string: входная строка WKT, представляющая геометрию типа MultiLineString.

Возвращаемое значение​

Функция возвращает внутреннее представление геометрии типа MultiLineString в ClickHouse.

Пример​

SELECT readWKTMultiLineString('MULTILINESTRING ((1 1, 2 2, 3 3), (4 4, 5 5, 6 6))');

[[(1,1),(2,2),(3,3)],[(4,4),(5,5),(6,6)]]

readWKTRing​

Разбирает представление геометрии многоугольника в формате Well-Known Text (WKT) и возвращает кольцо (замкнутую ломаную линию, LineString) во внутреннем формате ClickHouse.

Синтаксис​

readWKTRing(wkt_string)

Аргументы​

  • wkt_string: входная строка в формате WKT, представляющая геометрию полигона.

Возвращаемое значение​

Функция возвращает внутреннее представление ClickHouse для геометрии кольца (замкнутой ломаной линии, closed linestring).

Пример​

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

[(1,1),(2,2),(3,3),(1,1)]

polygonsWithinSpherical​

Возвращает true или false в зависимости от того, расположен ли один многоугольник полностью внутри другого. См. документацию: https://www.boost.org/doc/libs/1_62_0/libs/geometry/doc/html/geometry/reference/algorithms/within/within_2.html

Пример​

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

readWKBMultiPolygon​

Преобразует мультиполигон в формате WKB (Well-Known Binary) в значение типа MultiPolygon.

Пример​

SELECT
    toTypeName(readWKBMultiPolygon(unhex('0106000000020000000103000000020000000500000000000000000000400000000000000000000000000000244000000000000000000000000000002440000000000000244000000000000000000000000000002440000000000000004000000000000000000500000000000000000010400000000000001040000000000000144000000000000010400000000000001440000000000000144000000000000010400000000000001440000000000000104000000000000010400103000000010000000400000000000000000024c000000000000024c000000000000024c000000000000022c000000000000022c0000000000000244000000000000024c000000000000024c0'))) AS type,
    readWKBMultiPolygon(unhex('0106000000020000000103000000020000000500000000000000000000400000000000000000000000000000244000000000000000000000000000002440000000000000244000000000000000000000000000002440000000000000004000000000000000000500000000000000000010400000000000001040000000000000144000000000000010400000000000001440000000000000144000000000000010400000000000001440000000000000104000000000000010400103000000010000000400000000000000000024c000000000000024c000000000000024c000000000000022c000000000000022c0000000000000244000000000000024c000000000000024c0')) 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)]]]

Входные параметры​

Строка, начинающаяся с MULTIPOLYGON

Возвращаемое значение​

MultiPolygon

readWKBPolygon​

Преобразует объект типа MultiPolygon в формате WKB (Well Known Binary) в объект типа Polygon.

Пример​

SELECT
    toTypeName(readWKBPolygon(unhex('010300000001000000050000000000000000000040000000000000000000000000000024400000000000000000000000000000244000000000000024400000000000000000000000000000244000000000000000400000000000000000'))) AS type,
    readWKBPolygon(unhex('010300000001000000050000000000000000000040000000000000000000000000000024400000000000000000000000000000244000000000000024400000000000000000000000000000244000000000000000400000000000000000')) AS output
FORMAT Markdown
типвывод
Полигон[[(2,0),(10,0),(10,10),(0,10),(2,0)]]

Входные параметры​

Строка, начинающаяся с POLYGON.

Возвращаемое значение​

Полигон

readWKBPoint​

Функция readWKBPoint в ClickHouse разбирает представление геометрии Point в формате Well-Known Binary (WKB) и возвращает точку во внутреннем формате ClickHouse.

Синтаксис​

readWKBPoint(wkb_string)

Аргументы​

  • wkb_string: входная строка WKB, представляющая геометрию типа Point.

Возвращаемое значение​

Функция возвращает геометрию Point во внутреннем формате ClickHouse.

Пример​

SELECT readWKBPoint(unhex('0101000000333333333333f33f3333333333330b40'));

(1.2,3.4)

readWKBLineString​

Парсит бинарное представление геометрии LineString в формате Well-Known Binary (WKB) и возвращает его во внутреннем формате ClickHouse.

Синтаксис​

readWKBLineString(wkb_string)

Аргументы​

  • wkb_string: входная строка WKB, представляющая геометрию типа LineString.

Возвращаемое значение​

Функция возвращает внутреннее представление геометрии типа LineString в ClickHouse.

Пример​

SELECT readWKBLineString(unhex('010200000004000000000000000000f03f000000000000f03f0000000000000040000000000000004000000000000008400000000000000840000000000000f03f000000000000f03f'));

[(1,1),(2,2),(3,3),(1,1)]

readWKBMultiLineString​

Выполняет разбор представления геометрии MultiLineString в формате Well-Known Binary (WKB) и возвращает его во внутреннем формате ClickHouse.

Синтаксис​

readWKBMultiLineString(wkb_string)

Аргументы​

  • wkb_string: Входная строка в формате WKB, представляющая геометрию MultiLineString.

Возвращаемое значение​

Функция возвращает внутреннее представление ClickHouse для геометрии типа MultiLineString.

Пример​

SELECT readWKBMultiLineString(unhex('010500000002000000010200000003000000000000000000f03f000000000000f03f0000000000000040000000000000004000000000000008400000000000000840010200000003000000000000000000104000000000000010400000000000001440000000000000144000000000000018400000000000001840'));

[[(1,1),(2,2),(3,3)],[(4,4),(5,5),(6,6)]]

Входные параметры​

Возвращаемое значение​

UInt8, 0 — ложь, 1 — истина

polygonsDistanceSpherical​

Вычисляет минимальное расстояние между двумя точками, где одна точка принадлежит первому полигону, а вторая — другому полигону. Spherical в названии функции означает, что координаты интерпретируются как координаты на идеальной сфере, что не соответствует форме Земли. Использование такой системы координат ускоряет выполнение, но, разумеется, снижает точность.

Пример​

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

Входные параметры​

Два полигона

Возвращаемое значение​

Float64

polygonsDistanceCartesian​

Вычисляет расстояние между двумя многоугольниками

Пример​

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

Входные параметры​

Два многоугольника

Возвращаемое значение​

Float64

polygonsEqualsCartesian​

Возвращает значение true, если два многоугольника равны

Пример​

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

1

Входные параметры​

Два многоугольника

Возвращаемое значение​

UInt8, 0 — ложь, 1 — истина

polygonsSymDifferenceSpherical​

Вычисляет теоретико-множественную симметрическую разность (XOR) двух полигонов в пространстве

Пример​

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)))

Входные параметры​

Polygons

Возвращаемое значение​

MultiPolygon

polygonsSymDifferenceCartesian​

То же, что и polygonsSymDifferenceSpherical, но используются координаты в декартовой системе координат, которая ближе к модели реальной Земли.

Пример​

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)))

Входные параметры​

Polygons

Возвращаемое значение​

MultiPolygon

polygonsIntersectionSpherical​

Вычисляет пересечение (логическая операция AND) между полигонами, при этом координаты интерпретируются как сферические.

Пример​

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)))

Входные параметры​

Polygons

Возвращаемое значение​

MultiPolygon

polygonsWithinCartesian​

Возвращает true, если второй многоугольник находится внутри первого многоугольника.

Пример​

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

1

Входные параметры​

Два многоугольника

Возвращаемое значение​

UInt8, 0 — ложь, 1 — истина

polygonsIntersectCartesian​

Возвращает true, если два многоугольника пересекаются (имеют общую область или границу).

Пример​

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

1

Входные параметры​

Два полигона

Возвращаемое значение​

UInt8: 0 — ложь, 1 — истина

polygonsIntersectSpherical​

Возвращает true, если два многоугольника пересекаются (имеют общую площадь или общую границу). См. документацию: https://www.boost.org/doc/libs/1_62_0/libs/geometry/doc/html/geometry/reference/algorithms/intersects.html

Пример​

SELECT polygonsIntersectSpherical([[[(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)]]]);

1

Входные параметры​

Два многоугольника

Возвращаемое значение​

UInt8: 0 — ложь, 1 — истина

polygonConvexHullCartesian​

Вычисляет выпуклую оболочку. Справка

Координаты заданы в декартовой системе координат.

Пример​

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

POLYGON((0 0,0 5,5 5,5 0,0 0))

Входные параметры​

MultiPolygon

Возвращаемое значение​

Polygon

polygonAreaSpherical​

Вычисляет площадь поверхности многоугольника.

Пример​

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

Входные параметры​

Polygon

Возвращаемое значение​

Float

polygonsUnionSpherical​

Вычисляет операцию объединения (OR).

Пример​

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)))

Входные параметры​

Polygons

Возвращаемое значение​

MultiPolygon

polygonPerimeterSpherical​

Вычисляет периметр многоугольника.

Пример​

Многоугольник, описывающий территорию Зимбабве​

Это многоугольник, описывающий территорию Зимбабве:

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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Использование функции polygonPerimeterSpherical​

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, 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0.45539

Входные параметры​

Возвращаемое значение​

polygonsIntersectionCartesian​

Вычисляет пересечение многоугольников.

Пример​

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)))

Входные параметры​

Polygons

Возвращаемое значение​

MultiPolygon

polygonAreaCartesian​

Вычисляет площадь многоугольника

Пример​

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

25

Входные параметры​

Polygon

Возвращаемое значение​

Float64

polygonPerimeterCartesian​

Вычисляет периметр многоугольника.

Пример​

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

15

Входные параметры​

Polygon

Возвращаемое значение​

Float64

polygonsUnionCartesian​

Вычисляет объединение многоугольников.

Пример​

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)))

Входные параметры​

Polygons

Возвращаемое значение​

MultiPolygon

Дополнительные сведения о системах геометрии см. в этой презентации о библиотеке Boost, которую использует ClickHouse.