Функции для работы с полигонами

WKT

Возвращает геометрический объект WKT (Well Known Text) из различных гео-типов данных. Поддерживаются следующие WKT-объекты:

POINT
MULTIPOINT
POLYGON
MULTIPOLYGON
LINESTRING
MULTILINESTRING

Синтаксис

WKT(geo_data)

Параметры

geo_data может иметь один из следующих гео-типов данных или их базовых примитивных типов:

Возвращаемое значение

Для Point возвращается геометрический объект WKT POINT.
Для MultiPoint возвращается геометрический объект WKT MULTIPOINT.
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 Tuple или массива массивов Tuple:

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

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

MULTIPOLYGON из массива многомерных массивов 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 MultiPolygon в формате WKT (Well Known Text) 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

тип	результат
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 MultiPolygon в формате WKT (Well-Known Text) 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

тип	результат
Polygon	[[(2,0),(10,0),(10,10),(0,10),(2,0)]]

Входные параметры

Строка, начинающаяся с POLYGON

Возвращаемое значение

Polygon

readWKTPoint

Функция readWKTPoint в ClickHouse разбирает геометрию Point, представленную в формате Well-Known Text (WKT), и возвращает точку во внутреннем формате ClickHouse.

Синтаксис

readWKTPoint(wkt_string)

Аргументы

wkt_string: Входная строка WKT, описывающая геометрию Point.

Возвращаемое значение

Функция возвращает внутреннее представление геометрии Point, используемое в ClickHouse.

Пример

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

(1.2,3.4)

readWKTLineString

Разбирает геометрию LineString, представленную в формате Well-Known Text (WKT), и возвращает её во внутреннем формате ClickHouse.

Синтаксис

readWKTLineString(wkt_string)

Аргументы

wkt_string: Входная строка WKT, представляющая геометрический объект 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

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

Синтаксис

readWKTMultiLineString(wkt_string)

Аргументы

wkt_string: Входная WKT-строка, представляющая геометрию MultiLineString.

Возвращаемое значение

Функция возвращает внутреннее представление геометрии 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)]]

readWKTMultiPoint

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

Синтаксис

readWKTMultiPoint(wkt_string)

Аргументы

wkt_string: входная строка WKT, представляющая геометрию MultiPoint.

Возвращаемое значение

Функция возвращает внутреннее представление ClickHouse геометрии типа multipoint.

Пример

SELECT readWKTMultiPoint('MULTIPOINT (1 1, 2 2, 3 3)');

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

readWKTRing

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

Синтаксис

readWKTRing(wkt_string)

Аргументы

wkt_string: Входная строка WKT, представляющая геометрию типа Polygon.

Возвращаемое значение

Функция возвращает внутреннее представление ClickHouse для геометрии Ring (замкнутой линии).

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, находится ли один полигон целиком внутри другого полигона. См. 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)]]]);

readWKBMultiPolygon

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

Пример

SELECT
    toTypeName(readWKBMultiPolygon(unhex('0106000000020000000103000000020000000500000000000000000000400000000000000000000000000000244000000000000000000000000000002440000000000000244000000000000000000000000000002440000000000000004000000000000000000500000000000000000010400000000000001040000000000000144000000000000010400000000000001440000000000000144000000000000010400000000000001440000000000000104000000000000010400103000000010000000400000000000000000024c000000000000024c000000000000024c000000000000022c000000000000022c0000000000000244000000000000024c000000000000024c0'))) AS type,
    readWKBMultiPolygon(unhex('0106000000020000000103000000020000000500000000000000000000400000000000000000000000000000244000000000000000000000000000002440000000000000244000000000000000000000000000002440000000000000004000000000000000000500000000000000000010400000000000001040000000000000144000000000000010400000000000001440000000000000144000000000000010400000000000001440000000000000104000000000000010400103000000010000000400000000000000000024c000000000000024c000000000000024c000000000000022c000000000000022c0000000000000244000000000000024c000000000000024c0')) AS output FORMAT Markdown

тип	вывод
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 WKB (Well Known Binary) MultiPolygon в тип Polygon.

Пример

SELECT
    toTypeName(readWKBPolygon(unhex('010300000001000000050000000000000000000040000000000000000000000000000024400000000000000000000000000000244000000000000024400000000000000000000000000000244000000000000000400000000000000000'))) AS type,
    readWKBPolygon(unhex('010300000001000000050000000000000000000040000000000000000000000000000024400000000000000000000000000000244000000000000024400000000000000000000000000000244000000000000000400000000000000000')) AS output
FORMAT Markdown

тип	результат
Polygon	[[(2,0),(10,0),(10,10),(0,10),(2,0)]]

Входные параметры

Строка, начинающаяся с POLYGON

Возвращаемое значение

Polygon

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 внутреннее представление ClickHouse для геометрии Point.

Пример

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

(1.2,3.4)

readWKBLineString

Разбирает представление геометрии LineString в формате Well-Known Binary (WKB) и возвращает результат 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 LineString в ClickHouse.

Пример

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

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

readWKBMultiLineString

Разбирает геометрию MultiLineString, представленную в формате Well-Known Binary (WKB), и возвращает её во внутреннем формате ClickHouse.

Синтаксис

readWKBMultiLineString(wkb_string)

Аргументы

wkb_string: Входная строка WKB, представляющая геометрию типа MultiLineString.

Возвращаемое значение

Функция возвращает внутреннее представление геометрии multilinestring в ClickHouse.

Пример

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

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

Входные параметры

Возвращаемое значение

UInt8, 0 — для false, 1 — для true

readWKBMultiPoint

Разбирает представление геометрии MultiPoint в формате Well-Known Binary (WKB) и возвращает его во внутреннем формате ClickHouse.

Синтаксис

readWKBMultiPoint(wkb_string)

Аргументы

wkb_string: Входная WKB-строка, представляющая геометрию MultiPoint.

Возвращаемое значение

Функция возвращает внутреннее представление ClickHouse геометрии типа multipoint.

Пример

SELECT readWKBMultiPoint(unhex('0104000000020000000101000000000000000000f03f000000000000f03f010100000000000000000000400000000000000040'));

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

polygonsDistanceSpherical

Вычисляет минимальное расстояние между двумя точками, одна из которых принадлежит первому полигону, а вторая — другому. Сферическое означает, что координаты интерпретируются как координаты на идеальной сфере, что для Земли неверно. Использование такой системы координат ускоряет вычисления, но, разумеется, не дает точного результата.

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 полигонами

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 полигона

Возвращаемое значение

Float64

polygonsEqualsCartesian

Возвращает true, если два полигона равны

Пример

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

Входные параметры

Два многоугольника

Возвращаемое значение

UInt8: 0 — для false, 1 — для true

polygonsSymDifferenceSpherical

Вычисляет пространственную симметрическую разность (XOR) двух полигонов

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

Полигоны

Возвращаемое значение

MultiPolygon

polygonsSymDifferenceCartesian

То же, что и polygonsSymDifferenceSpherical, но координаты заданы 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

Полигоны

Возвращаемое значение

MultiPolygon

polygonsIntersectionSpherical

Вычисляет пересечение (побитовое И) полигонов; координаты — 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)))

В отличие от polygonsIntersectCartesian, функция принимает любой геометрический тип данных (Point, MultiPoint, LineString, MultiLineString, Ring, Polygon, MultiPolygon), включая универсальный тип Geometry, при этом оба аргумента могут быть разных типов.

Координаты заданы в декартовой системе координат.

Пример

SELECT geometryIntersectCartesian([(2., 2.), (2., 3.), (3., 3.), (3., 2.)]::Ring, [(1., 1.), (1., 4.), (4., 4.), (4., 1.)]::Ring)

Входные параметры

Две геометрии любого геометрического типа данных (или Geometry).

Возвращаемое значение

UInt8, 0 для false, 1 для true

geometryIntersectSpherical

Возвращает true, если две геометрии пересекаются (то есть имеют хотя бы одну общую точку, линию или область).

В отличие от polygonsIntersectSpherical, принимает любой геометрический тип данных (Point, MultiPoint, LineString, MultiLineString, Ring, Polygon, MultiPolygon), включая универсальный тип Geometry, при этом оба аргумента могут быть разных типов.

Координаты интерпретируются как расположенные на идеальной сфере.

Пример

SELECT geometryIntersectSpherical([[[(4.3613577, 50.8651821), (4.349556, 50.8535879), (4.3602419, 50.8435626), (4.3830299, 50.8428851), (4.3904543, 50.8564867), (4.3613148, 50.8651279)]]]::MultiPolygon, (4.36, 50.85)::Point)

Входные параметры

Две геометрии любого геометрического типа данных (или Geometry).

Возвращаемое значение

UInt8: 0 для false, 1 для true

polygonConvexHullCartesian

Вычисляет выпуклую оболочку. Справочник

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 полигона.

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 объединение (операцию 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

Полигоны

Возвращаемое значение

MultiPolygon

polygonPerimeterSpherical

Вычисляет периметр полигона.

Пример

Полигон, представляющий Зимбабве

Вот полигон, представляющий 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

Параметры

Возвращаемое значение

polygonsIntersectionCartesian

Вычисляет пересечение полигонов.

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

Полигоны

Возвращаемое значение

MultiPolygon

polygonAreaCartesian

Вычисляет площадь полигона

Пример

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

Входные параметры

Polygon

Возвращаемое значение

Float64

polygonPerimeterCartesian

Вычисляет периметр полигона.

Пример

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

Входные параметры

Polygon

Возвращаемое значение

Float64

polygonsUnionCartesian

Вычисляет объединение полигонов.

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

Полигоны

Возвращаемое значение

MultiPolygon

Подробнее о геометрических системах см. в этой презентации о библиотеке Boost, которую использует ClickHouse.