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Functions for Working with Polygons

readWKTMultiPolygon​

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

Example​

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

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)]]]

Input parameters​

String starting with MULTIPOLYGON

Returned value​

MultiPolygon

readWKTPolygon​

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

Example​

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)]]

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​

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

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​

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

Input parameters​

Two polygons

Returned value​

Float64

polygonsDistanceCartesian​

Calculates distance between two polygons

Example​

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

Input parameters​

Two polygons

Returned value​

Float64

polygonsEqualsCartesian​

Returns true if two polygons are equal

Example​

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

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)))

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​

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)))

Input parameters​

Polygons

Returned value​

MultiPolygon

polygonsIntersectionSpherical​

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

Example​

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)))

Input parameters​

Polygons

Returned value​

MultiPolygon

polygonsWithinCartesian​

Returns true if the second polygon is within the first polygon.

Example​

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

Input parameters​

Two polygons

Returned value​

UInt8, 0 for false, 1 for true

polygonConvexHullCartesian​

Calculates a convex hull. Reference

Coordinates are in Cartesian coordinate system.

Example​

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

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

Input parameters​

Polygon

Returned value​

Float

polygonsUnionSpherical​

Calculates a union (OR).

Example​

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)))

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 -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 -19.6843,32.9246 -19.6553,32.9432 -19.6493,32.961 -19.6588,32.9624 -19.6791,32.9541 -19.7178,32.9624 -19.7354,32.9791 -19.7514,33.0006 -19.7643,33.0228 -19.7731,33.0328 -19.7842,33.0296 -19.8034,33.0229 -19.8269,33.0213 -19.8681,33.002 -19.927,32.9984 -20.0009,33.0044 -20.0243,33.0073 -20.032,32.9537 -20.0302,32.9401 -20.0415,32.9343 -20.0721,32.9265 -20.0865,32.9107 -20.0911,32.8944 -20.094,32.8853 -20.103,32.8779 -20.1517,32.8729 -20.1672,32.8593 -20.1909,32.8571 -20.2006,32.8583 -20.2075,32.8651 -20.2209,32.8656 -20.2289,32.8584 -20.2595,32.853 -20.2739,32.8452 -20.2867,32.8008 -20.3386,32.7359 -20.4142,32.7044 -20.4718,32.6718 -20.5318,32.6465 -20.558,32.6037 -20.5648,32.5565 -20.5593,32.5131 -20.5646,32.4816 -20.603,32.4711 -20.6455,32.4691 -20.6868,32.4835 -20.7942,32.4972 -20.8981,32.491 -20.9363,32.4677 -20.9802,32.4171 -21.0409,32.3398 -21.1341,32.3453 -21.1428,32.3599 -21.1514,32.3689 -21.163,32.3734 -21.1636,32.3777 -21.1634,32.3806 -21.1655,32.3805 -21.1722,32.3769 -21.1785,32.373 -21.184,32.3717 -21.1879,32.4446 -21.3047,32.4458 -21.309,32.4472 -21.3137,32.4085 -21.2903,32.373 -21.3279,32.3245 -21.3782,32.2722 -21.4325,32.2197 -21.4869,32.1673 -21.5413,32.1148 -21.5956,32.0624 -21.65,32.01 -21.7045,31.9576 -21.7588,31.9052 -21.8132,31.8527 -21.8676,31.8003 -21.922,31.7478 -21.9764,31.6955 -22.0307,31.6431 -22.0852,31.5907 -22.1396,31.5382 -22.1939,31.4858 -22.2483,31.4338 -22.302,31.3687 -22.345,31.2889 -22.3973,31.2656 -22.3655,31.2556 -22.358,31.2457 -22.3575,31.2296 -22.364,31.2215 -22.3649,31.2135 -22.3619,31.1979 -22.3526,31.1907 -22.3506,31.1837 -22.3456,31.1633 -22.3226,31.1526 -22.3164,31.1377 -22.3185,31.1045 -22.3334,31.097 -22.3349,31.0876 -22.3369,31.0703 -22.3337,31.0361 -22.3196,30.9272 -22.2957,30.8671 -22.2896,30.8379 -22.2823,30.8053 -22.2945,30.6939 -22.3028,30.6743 -22.3086,30.6474 -22.3264,30.6324 -22.3307,30.6256 -22.3286,30.6103 -22.3187,30.6011 -22.3164,30.5722 -22.3166,30.5074 -22.3096,30.4885 -22.3102,30.4692 -22.3151,30.4317 -22.3312,30.4127 -22.3369,30.3721 -22.3435,30.335 -22.3447,30.3008 -22.337,30.2693 -22.3164,30.2553 -22.3047,30.2404 -22.2962,30.2217 -22.2909,30.197 -22.2891,30.1527 -22.2948,30.1351 -22.2936,30.1111 -22.2823,30.0826 -22.2629,30.0679 -22.2571,30.0381 -22.2538,30.0359 -22.2506,30.0345 -22.2461,30.0155 -22.227,30.0053 -22.2223,29.9838 -22.2177,29.974 -22.214,29.9467 -22.1983,29.9321 -22.1944,29.896 -22.1914,29.8715 -22.1793,29.8373 -22.1724,29.7792 -22.1364,29.7589 -22.1309,29.6914 -22.1341,29.6796 -22.1383,29.6614 -22.1265,29.6411 -22.1292,29.604 -22.1451,29.5702 -22.142,29.551 -22.146,29.5425 -22.1625,29.5318 -22.1724,29.5069 -22.1701,29.4569 -22.1588,29.4361 -22.1631,29.3995 -22.1822,29.378 -22.1929,29.3633 -22.1923,29.3569 -22.1909,29.3501 -22.1867,29.2736 -22.1251,29.2673 -22.1158,29.2596 -22.0961,29.2541 -22.0871,29.2444 -22.0757,29.2393 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(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)
0.45539

Input parameters​

Returned value​

polygonsIntersectionCartesian​

Calculates the intersection of polygons.

Example​

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)))

Input parameters​

Polygons

Returned value​

MultiPolygon

polygonAreaCartesian​

Calculates the area of a polygon

Example​

SELECT polygonAreaCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
25

Input parameters​

Polygon

Returned value​

Float64

polygonPerimeterCartesian​

Calculates the perimeter of a polygon.

Example​

SELECT polygonPerimeterCartesian([[[(0., 0.), (0., 5.), (5., 5.), (5., 0.)]]])
15

Input parameters​

Polygon

Returned value​

Float64

polygonsUnionCartesian​

Calculates the union of polygons.

Example​

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)))

Input parameters​

Polygons

Returned value​

MultiPolygon

For more information on geometry systems, see this presentation about the Boost library, which is what ClickHouse uses.