These functions compute geometric constructions, or alter geometry size or shape.

# Geometry Processing

ST_Buffer

Computes a geometry covering all points within a given distance from a geometry.

                        geometry ST_Buffer
                        geometry  g1
                        float  radius_of_buffer
                        text  buffer_style_parameters = ''

                        geometry ST_Buffer
                        geometry  g1
                        float  radius_of_buffer
                        integer  num_seg_quarter_circle

                        geography ST_Buffer
                        geography  g1
                        float  radius_of_buffer
                        text  buffer_style_parameters

                        geography ST_Buffer
                        geography  g1
                        float  radius_of_buffer
                        integer  num_seg_quarter_circle

### Description

Computes a POLYGON or MULTIPOLYGON that represents all points whose distance from a geometry/geography is less than or equal to a given distance. A negative distance shrinks the geometry rather than expanding it. A negative distance may shrink a polygon completely, in which case POLYGON EMPTY is returned. For points and lines negative distances always return empty results.

For geometry, the distance is specified in the units of the Spatial Reference System of the geometry. For geography, the distance is specified in meters.

The optional third parameter controls the buffer accuracy and style. The accuracy of circular arcs in the buffer is specified as the number of line segments used to approximate a quarter circle (default is 8). The buffer style can be specifed by providing a list of blank-separated key=value pairs as follows:

- 'quad_segs=#' : number of line segments used to approximate a quarter circle (default is 8).

- 'endcap=round|flat|square' : endcap style (defaults to "round"). 'butt' is accepted as a synonym for 'flat'.

- 'join=round|mitre|bevel' : join style (defaults to "round"). 'miter' is accepted as a synonym for 'mitre'.

- 'mitre_limit=#.#' : mitre ratio limit (only affects mitered join style). 'miter_limit' is accepted as a synonym for 'mitre_limit'.

- 'side=both|left|right' : 'left' or 'right' performs a single-sided buffer on the geometry, with the buffered side relative to the direction of the line. This is only applicable to LINESTRING geometry and does not affect POINT or POLYGON geometries. By default end caps are square.

For geography, this is a wrapper around the geometry implementation. It determines a planar spatial reference system that best fits the bounding box of the geography object (trying UTM, Lambert Azimuthal Equal Area (LAEA) North/South pole, and finally Mercator ). The buffer is computed in the planar space, and then transformed back to WGS84. This may not produce the desired behavior if the input object is much larger than a UTM zone or crosses the dateline

Buffer output is always a valid polygonal geometry. Buffer can handle invalid inputs, so buffering by distance 0 is sometimes used as a way of repairing invalid polygons. ST_MakeValid can also be used for this purpose.

Buffering is sometimes used to perform a within-distance search. For this use case it is more efficient to use ST_DWithin.

This function ignores the Z dimension. It always gives a 2D result even when used on a 3D geometry.

Enhanced: 2.5.0 - ST_Buffer geometry support was enhanced to allow for side buffering specification `side=both|left|right`.

Availability: 1.5 - ST_Buffer was enhanced to support different endcaps and join types. These are useful for example to convert road linestrings into polygon roads with flat or square edges instead of rounded edges. Thin wrapper for geography was added.

Performed by the GEOS module.

&sfs_compliant; s2.1.1.3

&sqlmm_compliant; SQL-MM 3: 5.1.17

### Examples

quad_segs=8 (default)
    SELECT ST_Buffer(
     ST_GeomFromText('POINT(100 90)'),
     50, 'quad_segs=8');
| quad_segs=2 (lame)
    SELECT ST_Buffer(
     ST_GeomFromText('POINT(100 90)'),
     50, 'quad_segs=2');
endcap=round join=round (default)
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'endcap=round join=round');
| endcap=square
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'endcap=square join=round');
| endcap=flat
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'endcap=flat join=round');
join=bevel
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'join=bevel');
| join=mitre mitre_limit=5.0 (default mitre limit)
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'join=mitre mitre_limit=5.0');
| join=mitre mitre_limit=1
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'join=mitre mitre_limit=1.0');
side=left
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'side=left');
| side=right
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'side=right');
| side=left join=mitre
    SELECT ST_Buffer(
     ST_GeomFromText(
      'LINESTRING(50 50,150 150,150 50)'
     ), 10, 'side=left join=mitre');
right-hand-winding, polygon boundary side=left
    SELECT ST_Buffer(
    ST_ForceRHR(
    ST_Boundary(
     ST_GeomFromText(
    'POLYGON ((50 50, 50 150, 150 150, 150 50, 50 50))'))),
     ), 20, 'side=left');
| right-hand-winding, polygon boundary side=right
    SELECT ST_Buffer(
    ST_ForceRHR(
    ST_Boundary(
     ST_GeomFromText(
    'POLYGON ((50 50, 50 150, 150 150, 150 50, 50 50))'))
    ), 20,'side=right')

    --A buffered point approximates a circle
    -- A buffered point forcing approximation of (see diagram)
    -- 2 points per quarter circle is poly with 8 sides (see diagram)
    SELECT ST_NPoints(ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50)) As promisingcircle_pcount,
    ST_NPoints(ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50, 2)) As lamecircle_pcount;

    promisingcircle_pcount | lamecircle_pcount
    ------------------------+-------------------
                 33 |                9

    --A lighter but lamer circle
    -- only 2 points per quarter circle is an octagon
    --Below is a 100 meter octagon
    -- Note coordinates are in NAD 83 long lat which we transform
    to Mass state plane meter and then buffer to get measurements in meters;
    SELECT ST_AsText(ST_Buffer(
    ST_Transform(
    ST_SetSRID(ST_Point(-71.063526, 42.35785),4269), 26986)
    ,100,2)) As octagon;
    ----------------------
    POLYGON((236057.59057465 900908.759918696,236028.301252769 900838.049240578,235
    957.59057465 900808.759918696,235886.879896532 900838.049240578,235857.59057465
    900908.759918696,235886.879896532 900979.470596815,235957.59057465 901008.759918
    696,236028.301252769 900979.470596815,236057.59057465 900908.759918696))

### See Also

ST_Collect, ST_DWithin, ST_SetSRID, ST_Transform, ST_Union, ST_MakeValid

ST_BuildArea

Creates a polygonal geometry formed by the linework of a geometry.

                    geometry ST_BuildArea
                    geometry  geom

### Description

Creates an areal geometry formed by the constituent linework of the input geometry. The input can be LINESTRINGS, MULTILINESTRINGS, POLYGONS, MULTIPOLYGONS, and GeometryCollections. The result is a Polygon or MultiPolygon, depending on input. If the input linework does not form polygons, NULL is returned.

This function assumes all inner geometries represent holes

Input linework must be correctly noded for this function to work properly

Availability: 1.1.0

### Examples

These will create a donut
    --using polygons
    SELECT ST_BuildArea(ST_Collect(smallc,bigc))
    FROM (SELECT
        ST_Buffer(
          ST_GeomFromText('POINT(100 90)'), 25) As smallc,
        ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50) As bigc) As foo;
    --using linestrings
    SELECT ST_BuildArea(ST_Collect(smallc,bigc))
    FROM (SELECT
        ST_ExteriorRing(ST_Buffer(
          ST_GeomFromText('POINT(100 90)'), 25)) As smallc,
        ST_ExteriorRing(ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50)) As bigc) As foo;

### See Also

ST_Node, ST_MakePolygon, ST_MakeValid, ST_BdPolyFromText, ST_BdMPolyFromText (wrappers to this function with standard OGC interface)

ST_Centroid

Returns the geometric center of a geometry.

              geometry ST_Centroid

              geometry
              g1

                    geography ST_Centroid

                    geography
                    g1
                    boolean
                    use_spheroid=true

### Description

Computes a point which is the geometric center of mass of a geometry. For [`MULTI`]`POINT`s, the centroid is the arithmetic mean of the input coordinates. For [`MULTI`]`LINESTRING`s, the centroid is computed using the weighted length of each line segment. For [`MULTI`]`POLYGON`s, the centroid is computed in terms of area. If an empty geometry is supplied, an empty `GEOMETRYCOLLECTION` is returned. If `NULL` is supplied, `NULL` is returned. If `CIRCULARSTRING` or `COMPOUNDCURVE` are supplied, they are converted to linestring with CurveToLine first, then same than for `LINESTRING`

For mixed-dimension input, the result is equal to the centroid of the component Geometries of highest dimension (since the lower-dimension geometries contribute zero "weight" to the centroid).

Note that for polygonal geometries the centroid does not necessarily lie in the interior of the polygon. For example, see the diagram below of the centroid of a C-shaped polygon. To construct a point guaranteed to lie in the interior of a polygon use ST_PointOnSurface.

New in 2.3.0 : supports `CIRCULARSTRING` and `COMPOUNDCURVE` (using CurveToLine)

Availability: 2.4.0 support for geography was introduced.

&sfs_compliant;

&sqlmm_compliant; SQL-MM 3: 8.1.4, 9.5.5

### Examples

In the following illustrations the red dot is the centroid of the source geometry.

Centroid of a `MULTIPOINT` | Centroid of a `LINESTRING`
Centroid of a `POLYGON` | Centroid of a `GEOMETRYCOLLECTION`

    SELECT ST_AsText(ST_Centroid('MULTIPOINT ( -1 0, -1 2, -1 3, -1 4, -1 7, 0 1, 0 3, 1 1, 2 0, 6 0, 7 8, 9 8, 10 6 )'));
                    st_astext
    ------------------------------------------
     POINT(2.30769230769231 3.30769230769231)
    (1 row)

    SELECT ST_AsText(ST_centroid(g))
    FROM  ST_GeomFromText('CIRCULARSTRING(0 2, -1 1,0 0, 0.5 0, 1 0, 2 1, 1 2, 0.5 2, 0 2)')  AS g ;
    ------------------------------------------
    POINT(0.5 1)

    SELECT ST_AsText(ST_centroid(g))
    FROM  ST_GeomFromText('COMPOUNDCURVE(CIRCULARSTRING(0 2, -1 1,0 0),(0 0, 0.5 0, 1 0),CIRCULARSTRING( 1 0, 2 1, 1 2),(1 2, 0.5 2, 0 2))' ) AS g;
    ------------------------------------------
    POINT(0.5 1)

### See Also

ST_PointOnSurface, ST_GeometricMedian

ST_ChaikinSmoothing

Returns a smoothed version of a geometry, using the Chaikin algorithm

                geometry ST_ChaikinSmoothing
                geometry geom
                integer nIterations = 1
                boolean preserveEndPoints = false

### Description

Returns a "smoothed" version of the given geometry using the Chaikin algorithm. See Chaikins-Algorithm for an explanation of the process. For each iteration the number of vertex points will double. The function puts new vertex points at 1/4 of the line before and after each point and removes the original point. To reduce the number of points use one of the simplification functions on the result. The new points gets interpolated values for all included dimensions, also z and m.

Second argument, number of iterations is limited to max 5 iterations

Note third argument is only valid for polygons, and will be ignored for linestrings

This function handles 3D and the third dimension will affect the result.

Note that returned geometry will get more points than the original. To reduce the number of points again use one of the simplification functions on the result. (see ST_Simplify and ST_SimplifyVW)

Availability: 2.5.0

### Examples

A triangle is smoothed

    select ST_AsText(ST_ChaikinSmoothing(geom)) smoothed
    FROM (SELECT  'POLYGON((0 0, 8 8, 0 16, 0 0))'::geometry geom) As foo;
    ┌───────────────────────────────────────────┐
    │                 smoothed                  │
    ├───────────────────────────────────────────┤
    │ POLYGON((2 2,6 6,6 10,2 14,0 12,0 4,2 2)) │
    └───────────────────────────────────────────┘

### See Also

ST_Simplify, ST_SimplifyVW

ST_ConcaveHull

Computes a possibly concave geometry that encloses all input geometry vertices

                geometry ST_ConcaveHull
                geometry  param_geom
                float  param_pctconvex
                boolean  param_allow_holes = false

### Description

A concave hull of a geometry is a possibly concave geometry that encloses the vertices of the input geometry. In the general case the concave hull is a Polygon. The polygon will not contain holes unless the optional `param_allow_holes` argument is specified as true. The concave hull of two or more collinear points is a two-point LineString. The concave hull of one or more identical points is a Point.

One can think of a concave hull as "shrink-wrapping" a set of points. This is different to the convex hull, which is more like wrapping a rubber band around the points. The concave hull generally has a smaller area and represents a more natural boundary for the input points. Like the convex hull, the vertices of a concave hull are a subset of the input points, and all other input points are contained within it.

The `param_pctconvex` controls the concaveness of the computed hull. A value of 1 produces the convex hull. A value of 0 produces a hull of maximum concaveness (but still a single polygon). Values between 1 and 0 produce hulls of increasing concaveness. Choosing a suitable value depends on the nature of the input data, but often values between 0.3 and 0.1 produce reasonable results.

Technically, the `param_pctconvex` determines a length as a fraction of the difference between the longest and shortest edges in the Delaunay Triangulation of the input points. Edges longer than this length are "eroded" from the triangulation. The triangles remaining form the concave hull.

For point and linear inputs, the hull will enclose all the points of the inputs. For polygonal inputs, the hull will enclose all the points of the input and also all the areas covered by the input. If you want a point-wise hull of a polygonal input, convert it to points first, using ST_Points.

This is not an aggregate function. To compute the concave hull of a set of geometries use ST_Collect (e.g. `ST_ConcaveHull( ST_Collect( geom ), 0.80)`.

Availability: 2.0.0

Enhanced: 3.3.0, GEOS native implementation enabled for GEOS 3.11+

### Examples

Concave Hull of a MultiPoint

    SELECT ST_AsText( ST_ConcaveHull(
            'MULTIPOINT ((10 72), (53 76), (56 66), (63 58), (71 51), (81 48), (91 46), (101 45), (111 46), (121 47), (131 50), (140 55), (145 64), (144 74), (135 80), (125 83), (115 85), (105 87), (95 89), (85 91), (75 93), (65 95), (55 98), (45 102), (37 107), (29 114), (22 122), (19 132), (18 142), (21 151), (27 160), (35 167), (44 172), (54 175), (64 178), (74 180), (84 181), (94 181), (104 181), (114 181), (124 181), (134 179), (144 177), (153 173), (162 168), (171 162), (177 154), (182 145), (184 135), (139 132), (136 142), (128 149), (119 153), (109 155), (99 155), (89 155), (79 153), (69 150), (61 144), (63 134), (72 128), (82 125), (92 123), (102 121), (112 119), (122 118), (132 116), (142 113), (151 110), (161 106), (170 102), (178 96), (185 88), (189 78), (190 68), (189 58), (185 49), (179 41), (171 34), (162 29), (153 25), (143 23), (133 21), (123 19), (113 19), (102 19), (92 19), (82 19), (72 21), (62 22), (52 25), (43 29), (33 34), (25 41), (19 49), (14 58), (21 73), (31 74), (42 74), (173 134), (161 134), (150 133), (97 104), (52 117), (157 156), (94 171), (112 106), (169 73), (58 165), (149 40), (70 33), (147 157), (48 153), (140 96), (47 129), (173 55), (144 86), (159 67), (150 146), (38 136), (111 170), (124 94), (26 59), (60 41), (71 162), (41 64), (88 110), (122 34), (151 97), (157 56), (39 146), (88 33), (159 45), (47 56), (138 40), (129 165), (33 48), (106 31), (169 147), (37 122), (71 109), (163 89), (37 156), (82 170), (180 72), (29 142), (46 41), (59 155), (124 106), (157 80), (175 82), (56 50), (62 116), (113 95), (144 167))',
             0.1 ) );
    ---st_astext--
    POLYGON ((18 142, 21 151, 27 160, 35 167, 44 172, 54 175, 64 178, 74 180, 84 181, 94 181, 104 181, 114 181, 124 181, 134 179, 144 177, 153 173, 162 168, 171 162, 177 154, 182 145, 184 135, 173 134, 161 134, 150 133, 139 132, 136 142, 128 149, 119 153, 109 155, 99 155, 89 155, 79 153, 69 150, 61 144, 63 134, 72 128, 82 125, 92 123, 102 121, 112 119, 122 118, 132 116, 142 113, 151 110, 161 106, 170 102, 178 96, 185 88, 189 78, 190 68, 189 58, 185 49, 179 41, 171 34, 162 29, 153 25, 143 23, 133 21, 123 19, 113 19, 102 19, 92 19, 82 19, 72 21, 62 22, 52 25, 43 29, 33 34, 25 41, 19 49, 14 58, 10 72, 21 73, 31 74, 42 74, 53 76, 56 66, 63 58, 71 51, 81 48, 91 46, 101 45, 111 46, 121 47, 131 50, 140 55, 145 64, 144 74, 135 80, 125 83, 115 85, 105 87, 95 89, 85 91, 75 93, 65 95, 55 98, 45 102, 37 107, 29 114, 22 122, 19 132, 18 142))

Concave Hull of a MultiPoint, allowing holes

    SELECT ST_AsText( ST_ConcaveHull(
            'MULTIPOINT ((132 64), (114 64), (99 64), (81 64), (63 64), (57 49), (52 36), (46 20), (37 20), (26 20), (32 36), (39 55), (43 69), (50 84), (57 100), (63 118), (68 133), (74 149), (81 164), (88 180), (101 180), (112 180), (119 164), (126 149), (132 131), (139 113), (143 100), (150 84), (157 69), (163 51), (168 36), (174 20), (163 20), (150 20), (143 36), (139 49), (132 64), (99 151), (92 138), (88 124), (81 109), (74 93), (70 82), (83 82), (99 82), (112 82), (126 82), (121 96), (114 109), (110 122), (103 138), (99 151), (34 27), (43 31), (48 44), (46 58), (52 73), (63 73), (61 84), (72 71), (90 69), (101 76), (123 71), (141 62), (166 27), (150 33), (159 36), (146 44), (154 53), (152 62), (146 73), (134 76), (143 82), (141 91), (130 98), (126 104), (132 113), (128 127), (117 122), (112 133), (119 144), (108 147), (119 153), (110 171), (103 164), (92 171), (86 160), (88 142), (79 140), (72 124), (83 131), (79 118), (68 113), (63 102), (68 93), (35 45))',
             0.15, true ) );
    ---st_astext--
    POLYGON ((43 69, 50 84, 57 100, 63 118, 68 133, 74 149, 81 164, 88 180, 101 180, 112 180, 119 164, 126 149, 132 131, 139 113, 143 100, 150 84, 157 69, 163 51, 168 36, 174 20, 163 20, 150 20, 143 36, 139 49, 132 64, 114 64, 99 64, 81 64, 63 64, 57 49, 52 36, 46 20, 37 20, 26 20, 32 36, 35 45, 39 55, 43 69), (88 124, 81 109, 74 93, 83 82, 99 82, 112 82, 121 96, 114 109, 110 122, 103 138, 92 138, 88 124))

Using with ST_Collect to compute the concave hull of a geometry set.

    -- Compute estimate of infected area based on point observations
    SELECT disease_type,
        ST_ConcaveHull( ST_Collect(obs_pnt), 0.3 ) AS geom
      FROM disease_obs
      GROUP BY disease_type;

### See Also

ST_ConvexHull, ST_Collect, ST_AlphaShape, ST_OptimalAlphaShape

ST_ConvexHull

Computes the convex hull of a geometry.

                geometry ST_ConvexHull
                geometry  geomA

### Description

Computes the convex hull of a geometry. The convex hull is the smallest convex geometry that encloses all geometries in the input.

One can think of the convex hull as the geometry obtained by wrapping an rubber band around a set of geometries. This is different from a concave hull which is analogous to "shrink-wrapping" the geometries. A convex hull is often used to determine an affected area based on a set of point observations.

In the general case the convex hull is a Polygon. The convex hull of two or more collinear points is a two-point LineString. The convex hull of one or more identical points is a Point.

This is not an aggregate function. To compute the convex hull of a set of geometries, use ST_Collect to aggregate them into a geometry collection (e.g. `ST_ConvexHull(ST_Collect(geom))`.

Performed by the GEOS module

&sfs_compliant; s2.1.1.3

&sqlmm_compliant; SQL-MM 3: 5.1.16

&Z_support;

### Examples

Convex Hull of a MultiLinestring and a MultiPoint

    SELECT ST_AsText(ST_ConvexHull(
        ST_Collect(
            ST_GeomFromText('MULTILINESTRING((100 190,10 8),(150 10, 20 30))'),
                ST_GeomFromText('MULTIPOINT(50 5, 150 30, 50 10, 10 10)')
                )) );
    ---st_astext--
    POLYGON((50 5,10 8,10 10,100 190,150 30,150 10,50 5))

Using with ST_Collect to compute the convex hulls of geometry sets.

    --Get estimate of infected area based on point observations
    SELECT d.disease_type,
        ST_ConvexHull(ST_Collect(d.geom)) As geom
        FROM disease_obs As d
        GROUP BY d.disease_type;

### See Also

ST_Collect, ST_ConcaveHull, ST_MinimumBoundingCircle

ST_DelaunayTriangles

Returns the Delaunay triangulation of the vertices of a geometry.

                    geometry ST_DelaunayTriangles
                    geometry  g1
                    float  tolerance
                    int4  flags

### Description

Return the Delaunay triangulation of the vertices of the input geometry. Output is a COLLECTION of polygons (for flags=0) or a MULTILINESTRING (for flags=1) or TIN (for flags=2). The tolerance, if any, is used to snap input vertices together.

Performed by the GEOS module.

Availability: 2.1.0

&Z_support;

&T_support;

### 2D Examples

Original polygons
    -- our original geometry --
        ST_Union(ST_GeomFromText('POLYGON((175 150, 20 40,
                50 60, 125 100, 175 150))'),
            ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
            )
ST_DelaunayTriangles of 2 polygons: delaunay triangle polygons each triangle themed in different color
    -- geometries overlaid multilinestring triangles
    SELECT
        ST_DelaunayTriangles(
            ST_Union(ST_GeomFromText('POLYGON((175 150, 20 40,
                50 60, 125 100, 175 150))'),
            ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
            ))
         As  dtriag;
-- delaunay triangles as multilinestring
    SELECT
        ST_DelaunayTriangles(
            ST_Union(ST_GeomFromText('POLYGON((175 150, 20 40,
                50 60, 125 100, 175 150))'),
            ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
            ),0.001,1)
         As  dtriag;
-- delaunay triangles of 45 points as 55 triangle polygons
    -- this produces a table of 42 points that form an L shape
    SELECT (ST_DumpPoints(ST_GeomFromText(
    'MULTIPOINT(14 14,34 14,54 14,74 14,94 14,114 14,134 14,
    150 14,154 14,154 6,134 6,114 6,94 6,74 6,54 6,34 6,
    14 6,10 6,8 6,7 7,6 8,6 10,6 30,6 50,6 70,6 90,6 110,6 130,
    6 150,6 170,6 190,6 194,14 194,14 174,14 154,14 134,14 114,
    14 94,14 74,14 54,14 34,14 14)'))).geom
        INTO TABLE l_shape;
    -- output as individual polygon triangles
    SELECT ST_AsText((ST_Dump(geom)).geom) As wkt
    FROM ( SELECT ST_DelaunayTriangles(ST_Collect(geom)) As geom
    FROM l_shape) As foo;

    ---wkt ---
    POLYGON((6 194,6 190,14 194,6 194))
    POLYGON((14 194,6 190,14 174,14 194))
    POLYGON((14 194,14 174,154 14,14 194))
    POLYGON((154 14,14 174,14 154,154 14))
    POLYGON((154 14,14 154,150 14,154 14))
    POLYGON((154 14,150 14,154 6,154 14))
    :
    :

### Example 1

    -- 3D multipoint --
    SELECT ST_AsText(ST_DelaunayTriangles(ST_GeomFromText(
    'MULTIPOINT Z(14 14 10,
    150 14 100,34 6 25, 20 10 150)'))) As wkt;

    -----wkt----
    GEOMETRYCOLLECTION Z (POLYGON Z ((14 14 10,20 10 150,34 6 25,14 14 10))
     ,POLYGON Z ((14 14 10,34 6 25,150 14 100,14 14 10)))

ST_FilterByM

Removes vertices based on their M value

                geometry ST_FilterByM
                geometry geom
                double precision min
                double precision max = null
                boolean returnM = false

### Description

Filters out vertex points based on their M-value. Returns a geometry with only vertex points that have a M-value larger or equal to the min value and smaller or equal to the max value. If max-value argument is left out only min value is considered. If fourth argument is left out the m-value will not be in the resulting geometry. If resulting geometry have too few vertex points left for its geometry type an empty geometry will be returned. In a geometry collection geometries without enough points will just be left out silently.

This function is mainly intended to be used in conjunction with ST_SetEffectiveArea. ST_EffectiveArea sets the effective area of a vertex in its m-value. With ST_FilterByM it then is possible to get a simplified version of the geometry without any calculations, just by filtering

There is a difference in what ST_SimplifyVW returns when not enough points meet the criteria compared to ST_FilterByM. ST_SimplifyVW returns the geometry with enough points while ST_FilterByM returns an empty geometry

Note that the returned geometry might be invalid

This function returns all dimensions, including the Z and M values

Availability: 2.5.0

### Examples

A linestring is filtered

    SELECT ST_AsText(ST_FilterByM(geom,30)) simplified
    FROM (SELECT  ST_SetEffectiveArea('LINESTRING(5 2, 3 8, 6 20, 7 25, 10 10)'::geometry) geom) As foo;
    -result
             simplified
    ----------------------------
     LINESTRING(5 2,7 25,10 10)

### See Also

ST_SetEffectiveArea, ST_SimplifyVW

ST_GeneratePoints

Generates random points contained in a Polygon or MultiPolygon.

                geometry ST_GeneratePoints

                    g
                    geometry

                    npoints
                    integer

                geometry ST_GeneratePoints
                 geometry g
                 integer npoints
                 integer seed

### Description

ST_GeneratePoints generates a given number of pseudo-random points which lie within the input area. The optional `seed` is used to regenerate a deterministic sequence of points, and must be greater than zero.

Availability: 2.3.0

Enhanced: 3.0.0, added seed parameter

### Examples

Generated 12 Points overlaid on top of original polygon using a random seed value 1996

    SELECT ST_GeneratePoints(geom, 12, 1996)
    FROM (
        SELECT ST_Buffer(
            ST_GeomFromText(
            'LINESTRING(50 50,150 150,150 50)'),
            10, 'endcap=round join=round') AS geom
    ) AS s;

ST_GeometricMedian

Returns the geometric median of a MultiPoint.

                geometry ST_GeometricMedian

                 geometry geom
                float8 tolerance = NULL
                int max_iter = 10000
                boolean fail_if_not_converged = false

### Description

Computes the approximate geometric median of a MultiPoint geometry using the Weiszfeld algorithm. The geometric median is the point minimizing the sum of distances to the input points. It provides a centrality measure that is less sensitive to outlier points than the centroid (center of mass).

The algorithm iterates until the distance change between successive iterations is less than the supplied `tolerance` parameter. If this condition has not been met after `max_iterations` iterations, the function produces an error and exits, unless `fail_if_not_converged` is set to `false` (the default).

If a `tolerance` argument is not provided, the tolerance value is calculated based on the extent of the input geometry.

If present, the input point M values are interpreted as their relative weights.

Availability: 2.3.0

Enhanced: 2.5.0 Added support for M as weight of points.

&Z_support;

&M_support;

### Examples

Comparison of the geometric median (red) and centroid (turquoise) of a MultiPoint.

    WITH test AS (
    SELECT 'MULTIPOINT((10 10), (10 40), (40 10), (190 190))'::geometry geom)
    SELECT
      ST_AsText(ST_Centroid(geom)) centroid,
      ST_AsText(ST_GeometricMedian(geom)) median
    FROM test;

          centroid      |                 median
    --------------------+----------------------------------------
       POINT(62.5 62.5) | POINT(25.01778421249728 25.01778421249728)
    (1 row)

### See Also

ST_Centroid

ST_LineMerge

Return the lines formed by sewing together a MultiLineString.

    				geometry ST_LineMerge
    				geometry  amultilinestring

    				geometry ST_LineMerge
    				geometry  amultilinestring
    				boolean  directed

### Description

Returns a LineString or MultiLineString formed by joining together the line elements of a MultiLineString. Lines are joined at their endpoints at 2-way intersections. Lines are not joined across intersections of 3-way or greater degree.

If directed is TRUE, then ST_LineMerge will not change point order within LineStrings, so lines with opposite directions will not be merged

Only use with MultiLineString/LineStrings. Other geometry types return an empty GeometryCollection

Performed by the GEOS module.

Enhanced: 3.3.0 accept a directed parameter - requires GEOS >= 3.11.0

Availability: 1.1.0

This function strips the M dimension.

### Examples

Merging lines with different orientation.

    SELECT ST_AsText(ST_LineMerge(
    'MULTILINESTRING((10 160, 60 120), (120 140, 60 120), (120 140, 180 120))'
    		));
    --------------------------------------------
     LINESTRING(10 160,60 120,120 140,180 120)

Lines are not merged across intersections with degree > 2.

    SELECT ST_AsText(ST_LineMerge(
    'MULTILINESTRING((10 160, 60 120), (120 140, 60 120), (120 140, 180 120), (100 180, 120 140))'
    		));
    --------------------------------------------
     MULTILINESTRING((10 160,60 120,120 140),(100 180,120 140),(120 140,180 120))

If merging is not possible due to non-touching lines, the original MultiLineString is returned.

    SELECT ST_AsText(ST_LineMerge(
    'MULTILINESTRING((-29 -27,-30 -29.7,-36 -31,-45 -33),(-45.2 -33.2,-46 -32))'
    ));
    ----------------
    MULTILINESTRING((-45.2 -33.2,-46 -32),(-29 -27,-30 -29.7,-36 -31,-45 -33))

Lines with opposite directions are not merged if directed = TRUE.

    SELECT ST_AsText(ST_LineMerge(
    'MULTILINESTRING((60 30, 10 70), (120 50, 60 30), (120 50, 180 30))',
    TRUE));
    -------------------------------------------------------
     MULTILINESTRING((120 50,60 30,10 70),(120 50,180 30))

Example showing Z-dimension handling.

    SELECT ST_AsText(ST_LineMerge(
          'MULTILINESTRING((-29 -27 11,-30 -29.7 10,-36 -31 5,-45 -33 6), (-29 -27 12,-30 -29.7 5), (-45 -33 1,-46 -32 11))'
            ));
    --------------------------------------------------------------------------------------------------
    LINESTRING Z (-30 -29.7 5,-29 -27 11,-30 -29.7 10,-36 -31 5,-45 -33 1,-46 -32 11)

### See Also

ST_Segmentize, ST_LineSubstring

ST_MaximumInscribedCircle

Computes the largest circle contained within a geometry.

                (geometry, geometry, double precision) ST_MaximumInscribedCircle
                geometry  geom

### Description

Finds the largest circle that is contained within a (multi)polygon, or which does not overlap any lines and points. Returns a record with fields:

- `center` - center point of the circle

- `nearest` - a point on the geometry nearest to the center

- `radius` - radius of the circle

For polygonal inputs, the circle is inscribed within the boundary rings, using the internal rings as boundaries. For linear and point inputs, the circle is inscribed within the convex hull of the input, using the input lines and points as further boundaries.

Availability: 3.1.0 - requires GEOS >= 3.9.0.

### See Also

ST_MinimumBoundingCircle

### Examples

Maximum inscribed circle of a polygon. Center, nearest point, and radius are returned.

    SELECT radius, ST_AsText(center) AS center, ST_AsText(nearest) AS nearest
        FROM ST_MaximumInscribedCircle(
            'POLYGON ((40 180, 110 160, 180 180, 180 120, 140 90, 160 40, 80 10, 70 40, 20 50, 40 180),
            (60 140, 50 90, 90 140, 60 140))');

         radius      |           center           |    nearest
    -----------------+----------------------------+---------------
     45.165845650018 | POINT(96.953125 76.328125) | POINT(140 90)

Maximum inscribed circle of a multi-linestring. Center, nearest point, and radius are returned.

### See Also

ST_MinimumBoundingRadius

ST_MinimumBoundingCircle

Returns the smallest circle polygon that contains a geometry.

                geometry ST_MinimumBoundingCircle
                geometry  geomA
                integer  num_segs_per_qt_circ=48

### Description

Returns the smallest circle polygon that contains a geometry.

The bounding circle is approximated by a polygon with a default of 48 segments per quarter circle. Because the polygon is an approximation of the minimum bounding circle, some points in the input geometry may not be contained within the polygon. The approximation can be improved by increasing the number of segments. For applications where an approximation is not suitable ST_MinimumBoundingRadius may be used.

This function is not an aggregate. It can be used with ST_Collect to get the minimum bounding circle of a set of geometries.

The ratio of the area of a polygon divided by the area of its Minimum Bounding Circle is referred to as the Reock compactness score.

Performed by the GEOS module.

Availability: 1.4.0

### See Also

ST_Collect, ST_MinimumBoundingRadius

### Examples

    SELECT d.disease_type,
        ST_MinimumBoundingCircle(ST_Collect(d.geom)) As geom
        FROM disease_obs As d
        GROUP BY d.disease_type;

Minimum bounding circle of a point and linestring. Using 8 segs to approximate a quarter circle

    SELECT ST_AsText(ST_MinimumBoundingCircle(
            ST_Collect(
                ST_GeomFromText('LINESTRING(55 75,125 150)'),
                    ST_Point(20, 80)), 8
                    )) As wktmbc;
    wktmbc
    -----------
    POLYGON((135.59714732062 115,134.384753327498 102.690357210921,130.79416296937 90.8537670908995,124.963360620072 79.9451031602111,117.116420743937 70.3835792560632,107.554896839789 62.5366393799277,96.6462329091006 56.70583703063,84.8096427890789 53.115246672502,72.5000000000001 51.9028526793802,60.1903572109213 53.1152466725019,48.3537670908996 56.7058370306299,37.4451031602112 62.5366393799276,27.8835792560632 70.383579256063,20.0366393799278 79.9451031602109,14.20583703063 90.8537670908993,10.615246672502 102.690357210921,9.40285267938019 115,10.6152466725019 127.309642789079,14.2058370306299 139.1462329091,20.0366393799275 150.054896839789,27.883579256063 159.616420743937,
    37.4451031602108 167.463360620072,48.3537670908992 173.29416296937,60.190357210921 176.884753327498,
    72.4999999999998 178.09714732062,84.8096427890786 176.884753327498,96.6462329091003 173.29416296937,107.554896839789 167.463360620072,
    117.116420743937 159.616420743937,124.963360620072 150.054896839789,130.79416296937 139.146232909101,134.384753327498 127.309642789079,135.59714732062 115))

### See Also

ST_Collect, ST_MinimumBoundingRadius

ST_MinimumBoundingRadius

Returns the center point and radius of the smallest circle that contains a geometry.

                    (geometry, double precision) ST_MinimumBoundingRadius
                    geometry geom

### Description

Computes the center point and radius of the smallest circle that contains a geometry. Returns a record with fields:

- `center` - center point of the circle

- `radius` - radius of the circle

Use in conjunction with ST_Collect to get the minimum bounding circle of a set of geometries.

Availability - 2.3.0

### See Also

ST_Collect, ST_MinimumBoundingCircle

### Examples

    SELECT ST_AsText(center), radius FROM ST_MinimumBoundingRadius('POLYGON((26426 65078,26531 65242,26075 65136,26096 65427,26426 65078))');

                    st_astext                 |      radius
    ------------------------------------------+------------------
     POINT(26284.8418027133 65267.1145090825) | 247.436045591407

ST_OrientedEnvelope

Returns a minimum-area rectangle containing a geometry.

                        geometry ST_OrientedEnvelope

                            geometry
                            geom

### Description

Returns the minimum-area rotated rectangle enclosing a geometry. Note that more than one such rectangle may exist. May return a Point or LineString in the case of degenerate inputs.

Availability: 2.5.0

### See Also

ST_Envelope ST_MinimumBoundingCircle

### Examples

                    SELECT ST_AsText(ST_OrientedEnvelope('MULTIPOINT ((0 0), (-1 -1), (3 2))'));

                    st_astext
                    ------------------------------------------------
                    POLYGON((3 2,2.88 2.16,-1.12 -0.84,-1 -1,3 2))

Oriented envelope of a point and linestring.

    SELECT ST_AsText(ST_OrientedEnvelope(
            ST_Collect(
                ST_GeomFromText('LINESTRING(55 75,125 150)'),
                    ST_Point(20, 80))
                    )) As wktenv;
    wktenv
    -----------
    POLYGON((19.9999999999997 79.9999999999999,33.0769230769229 60.3846153846152,138.076923076924 130.384615384616,125.000000000001 150.000000000001,19.9999999999997 79.9999999999999))

ST_OffsetCurve

Returns an offset line at a given distance and side from an input line.

                    geometry ST_OffsetCurve
                    geometry  line
                    float  signed_distance
                    text  style_parameters=''

### Description

Return an offset line at a given distance and side from an input line. All points of the returned geometries are not further than the given distance from the input geometry. Useful for computing parallel lines about a center line.

For positive distance the offset is on the left side of the input line and retains the same direction. For a negative distance it is on the right side and in the opposite direction.

Units of distance are measured in units of the spatial reference system.

Note that output may be a MULTILINESTRING or EMPTY for some jigsaw-shaped input geometries.

The optional third parameter allows specifying a list of blank-separated key=value pairs to tweak operations as follows:

- 'quad_segs=#' : number of segments used to approximate a quarter circle (defaults to 8).

- 'join=round|mitre|bevel' : join style (defaults to "round"). 'miter' is also accepted as a synonym for 'mitre'.

- 'mitre_limit=#.#' : mitre ratio limit (only affects mitred join style). 'miter_limit' is also accepted as a synonym for 'mitre_limit'.

Performed by the GEOS module.

Availability: 2.0

Enhanced: 2.5 - added support for GEOMETRYCOLLECTION and MULTILINESTRING

This function ignores the Z dimension. It always gives a 2D result even when used on a 3D geometry.

### Examples

Compute an open buffer around roads

    SELECT ST_Union(
     ST_OffsetCurve(f.geom,  f.width/2, 'quad_segs=4 join=round'),
     ST_OffsetCurve(f.geom, -f.width/2, 'quad_segs=4 join=round')
    ) as track
    FROM someroadstable;

15, 'quad_segs=4 join=round' original line and its offset 15 units.
    SELECT ST_AsText(ST_OffsetCurve(ST_GeomFromText(
    'LINESTRING(164 16,144 16,124 16,104 16,84 16,64 16,
        44 16,24 16,20 16,18 16,17 17,
        16 18,16 20,16 40,16 60,16 80,16 100,
        16 120,16 140,16 160,16 180,16 195)'),
        15, 'quad_segs=4 join=round'));
    --output --
    LINESTRING(164 1,18 1,12.2597485145237 2.1418070123307,
        7.39339828220179 5.39339828220179,
        5.39339828220179 7.39339828220179,
        2.14180701233067 12.2597485145237,1 18,1 195)
| -15, 'quad_segs=4 join=round' original line and its offset -15 units
    SELECT ST_AsText(ST_OffsetCurve(geom,
        -15, 'quad_segs=4 join=round')) As notsocurvy
        FROM ST_GeomFromText(
    'LINESTRING(164 16,144 16,124 16,104 16,84 16,64 16,
        44 16,24 16,20 16,18 16,17 17,
        16 18,16 20,16 40,16 60,16 80,16 100,
        16 120,16 140,16 160,16 180,16 195)') As geom;
    -- notsocurvy --
    LINESTRING(31 195,31 31,164 31)
double-offset to get more curvy, note the first reverses direction, so -30 + 15 = -15
    SELECT ST_AsText(ST_OffsetCurve(ST_OffsetCurve(geom,
        -30, 'quad_segs=4 join=round'), -15, 'quad_segs=4 join=round')) As morecurvy
        FROM ST_GeomFromText(
    'LINESTRING(164 16,144 16,124 16,104 16,84 16,64 16,
        44 16,24 16,20 16,18 16,17 17,
        16 18,16 20,16 40,16 60,16 80,16 100,
        16 120,16 140,16 160,16 180,16 195)') As geom;
    -- morecurvy --
    LINESTRING(164 31,46 31,40.2597485145236 32.1418070123307,
    35.3933982822018 35.3933982822018,
    32.1418070123307 40.2597485145237,31 46,31 195)
| double-offset to get more curvy,combined with regular offset 15 to get parallel lines. Overlaid with original.
    SELECT ST_AsText(ST_Collect(
        ST_OffsetCurve(geom, 15, 'quad_segs=4 join=round'),
        ST_OffsetCurve(ST_OffsetCurve(geom,
        -30, 'quad_segs=4 join=round'), -15, 'quad_segs=4 join=round')
        )
    ) As parallel_curves
        FROM ST_GeomFromText(
    'LINESTRING(164 16,144 16,124 16,104 16,84 16,64 16,
        44 16,24 16,20 16,18 16,17 17,
        16 18,16 20,16 40,16 60,16 80,16 100,
        16 120,16 140,16 160,16 180,16 195)') As geom;
    -- parallel curves  --
    MULTILINESTRING((164 1,18 1,12.2597485145237 2.1418070123307,
    7.39339828220179 5.39339828220179,5.39339828220179 7.39339828220179,
    2.14180701233067 12.2597485145237,1 18,1 195),
    (164 31,46 31,40.2597485145236 32.1418070123307,35.3933982822018 35.3933982822018,
    32.1418070123307 40.2597485145237,31 46,31 195))
15, 'quad_segs=4 join=bevel' shown with original line
    SELECT ST_AsText(ST_OffsetCurve(ST_GeomFromText(
    'LINESTRING(164 16,144 16,124 16,104 16,84 16,64 16,
        44 16,24 16,20 16,18 16,17 17,
        16 18,16 20,16 40,16 60,16 80,16 100,
        16 120,16 140,16 160,16 180,16 195)'),
            15, 'quad_segs=4 join=bevel'));
    -- output --
    LINESTRING(164 1,18 1,7.39339828220179 5.39339828220179,
        5.39339828220179 7.39339828220179,1 18,1 195)
| 15,-15 collected, join=mitre mitre_limit=2.1
    SELECT ST_AsText(ST_Collect(
        ST_OffsetCurve(geom, 15, 'quad_segs=4 join=mitre mitre_limit=2.2'),
        ST_OffsetCurve(geom, -15, 'quad_segs=4 join=mitre mitre_limit=2.2')
        ) )
        FROM ST_GeomFromText(
    'LINESTRING(164 16,144 16,124 16,104 16,84 16,64 16,
        44 16,24 16,20 16,18 16,17 17,
        16 18,16 20,16 40,16 60,16 80,16 100,
        16 120,16 140,16 160,16 180,16 195)') As geom;
    -- output --
    MULTILINESTRING((164 1,11.7867965644036 1,1 11.7867965644036,1 195),
        (31 195,31 31,164 31))

### See Also

ST_Buffer

ST_PointOnSurface

Computes a point guaranteed to lie in a polygon, or on a geometry.

                geometry ST_PointOnSurface

                geometry
                g1

### Description

Returns a `POINT` which is guaranteed to lie in the interior of a surface (POLYGON, MULTIPOLYGON, and CURVED POLYGON). In PostGIS this function also works on line and point geometries.

&sfs_compliant; s3.2.14.2 // s3.2.18.2

&sqlmm_compliant; SQL-MM 3: 8.1.5, 9.5.6. The specifications define ST_PointOnSurface for surface geometries only. PostGIS extends the function to support all common geometry types. Other databases (Oracle, DB2, ArcSDE) seem to support this function only for surfaces. SQL Server 2008 supports all common geometry types.

&Z_support;

### Examples

PointOnSurface of a `MULTIPOINT` | PointOnSurface of a `LINESTRING`
PointOnSurface of a `POLYGON` | PointOnSurface of a `GEOMETRYCOLLECTION`

    SELECT ST_AsText(ST_PointOnSurface('POINT(0 5)'::geometry));
    ------------
     POINT(0 5)

    SELECT ST_AsText(ST_PointOnSurface('LINESTRING(0 5, 0 10)'::geometry));
    ------------
     POINT(0 5)

    SELECT ST_AsText(ST_PointOnSurface('POLYGON((0 0, 0 5, 5 5, 5 0, 0 0))'::geometry));
    ----------------
     POINT(2.5 2.5)

    SELECT ST_AsEWKT(ST_PointOnSurface(ST_GeomFromEWKT('LINESTRING(0 5 1, 0 0 1, 0 10 2)')));
    ----------------
     POINT(0 0 1)

Example: The result of ST_PointOnSurface is guaranteed to lie within polygons, whereas the point computed by ST_Centroid may be outside.

Red: point on surface; Green: centroid

    SELECT ST_AsText(ST_PointOnSurface(geom)) AS pt_on_surf,
           ST_AsText(ST_Centroid(geom)) AS centroid
        FROM (SELECT 'POLYGON ((130 120, 120 190, 30 140, 50 20, 190 20,
                          170 100, 90 60, 90 130, 130 120))'::geometry AS geom) AS t;

       pt_on_surf    |                  centroid
    -----------------+---------------------------------------------
     POINT(62.5 110) | POINT(100.18264840182648 85.11415525114155)

### See Also

ST_Centroid, ST_MaximumInscribedCircle

ST_Polygonize

Computes a collection of polygons formed from the linework of a set of geometries.

                geometry ST_Polygonize
                geometry set geomfield

                geometry ST_Polygonize
                geometry[] geom_array

### Description

Creates a GeometryCollection containing the polygons formed by the constituent linework of a set of geometries. Input linework must be correctly noded for this function to work properly.

To ensure input is fully noded use ST_Node on the input geometry before polygonizing.

GeometryCollections are often difficult to deal with with third party tools. Use ST_Dump to convert the polygonize result into separate polygons.

Performed by the GEOS module.

Availability: 1.0.0RC1

### Examples: Polygonizing single linestrings

    SELECT ST_AsEWKT(ST_Polygonize(geom_4269)) As geomtextrep
    FROM (SELECT geom_4269 FROM ma.suffolk_edges ORDER BY tlid LIMIT 45) As foo;

    geomtextrep
    -------------------------------------
     SRID=4269;GEOMETRYCOLLECTION(POLYGON((-71.040878 42.285678,-71.040943 42.2856,-71.04096 42.285752,-71.040878 42.285678)),
     POLYGON((-71.17166 42.353675,-71.172026 42.354044,-71.17239 42.354358,-71.171794 42.354971,-71.170511 42.354855,
     -71.17112 42.354238,-71.17166 42.353675)))
    (1 row)

    --Use ST_Dump to dump out the polygonize geoms into individual polygons
    SELECT ST_AsEWKT((ST_Dump(foofoo.polycoll)).geom) As geomtextrep
    FROM (SELECT ST_Polygonize(geom_4269) As polycoll
        FROM (SELECT geom_4269 FROM ma.suffolk_edges
            ORDER BY tlid LIMIT 45) As foo) As foofoo;

    geomtextrep
    ------------------------
     SRID=4269;POLYGON((-71.040878 42.285678,-71.040943 42.2856,-71.04096 42.285752,
    -71.040878 42.285678))
     SRID=4269;POLYGON((-71.17166 42.353675,-71.172026 42.354044,-71.17239 42.354358
    ,-71.171794 42.354971,-71.170511 42.354855,-71.17112 42.354238,-71.17166 42.353675))
    (2 rows)

### See Also

ST_Node, ST_Dump

ST_ReducePrecision

Returns a valid geometry with points rounded to a grid tolerance.

                geometry ST_ReducePrecision

                geometry
                g
                float8
                gridsize

### Description

Returns a valid geometry with all points rounded to the provided grid tolerance, and features below the tolerance removed.

Unlike ST_SnapToGrid the returned geometry will be valid, with no ring self-intersections or collapsed components.

Precision reduction can be used to:

- match coordinate precision to the data accuracy

- reduce the number of coordinates needed to represent a geometry

- ensure valid geometry output to formats which use lower precision (e.g. text formats such as WKT, GeoJSON or KML when the number of output decimal places is limited).

- export valid geometry to systems which use lower or limited precision (e.g. SDE, Oracle tolerance value)

Availability: 3.1.0 - requires GEOS >= 3.9.0.

### Examples

    SELECT ST_AsText(ST_ReducePrecision('POINT(1.412 19.323)', 0.1));
        st_astext
    -----------------
     POINT(1.4 19.3)

    SELECT ST_AsText(ST_ReducePrecision('POINT(1.412 19.323)', 1.0));
      st_astext
    -------------
     POINT(1 19)

    SELECT ST_AsText(ST_ReducePrecision('POINT(1.412 19.323)', 10));
      st_astext
    -------------
     POINT(0 20)

Precision reduction can reduce number of vertices

    SELECT ST_AsText(ST_ReducePrecision('LINESTRING (10 10, 19.6 30.1, 20 30, 20.3 30, 40 40)', 1));
      st_astext
    -------------
     LINESTRING (10 10, 20 30, 40 40)

Precision reduction splits polygons if needed to ensure validity

    SELECT ST_AsText(ST_ReducePrecision('POLYGON ((10 10, 60 60.1, 70 30, 40 40, 50 10, 10 10))', 10));
      st_astext
    -------------
     MULTIPOLYGON (((60 60, 70 30, 40 40, 60 60)), ((40 40, 50 10, 10 10, 40 40)))

### See Also

ST_SnapToGrid, ST_Simplify, ST_SimplifyVW

ST_SharedPaths

Returns a collection containing paths shared by the two input linestrings/multilinestrings.

                geometry ST_SharedPaths
                geometry lineal1
                geometry lineal2

### Description

Returns a collection containing paths shared by the two input geometries. Those going in the same direction are in the first element of the collection, those going in the opposite direction are in the second element. The paths themselves are given in the direction of the first geometry.

Performed by the GEOS module.

Availability: 2.0.0

### Examples: Finding shared paths

A multilinestring and a linestring
The shared path of multilinestring and linestring overlaid with original geometries.
     SELECT ST_AsText(
      ST_SharedPaths(
        ST_GeomFromText('MULTILINESTRING((26 125,26 200,126 200,126 125,26 125),
           (51 150,101 150,76 175,51 150))'),
        ST_GeomFromText('LINESTRING(151 100,126 156.25,126 125,90 161, 76 175)')
        )
      ) As wkt

                                    wkt
    -------------------------------------------------------------
    GEOMETRYCOLLECTION(MULTILINESTRING((126 156.25,126 125),
     (101 150,90 161),(90 161,76 175)),MULTILINESTRING EMPTY)
    -- same example but linestring orientation flipped
    SELECT ST_AsText(
      ST_SharedPaths(
       ST_GeomFromText('LINESTRING(76 175,90 161,126 125,126 156.25,151 100)'),
       ST_GeomFromText('MULTILINESTRING((26 125,26 200,126 200,126 125,26 125),
           (51 150,101 150,76 175,51 150))')
        )
      ) As wkt

                                    wkt
    -------------------------------------------------------------
    GEOMETRYCOLLECTION(MULTILINESTRING EMPTY,
    MULTILINESTRING((76 175,90 161),(90 161,101 150),(126 125,126 156.25)))

### See Also

ST_Dump, ST_GeometryN, ST_NumGeometries

ST_Simplify

Returns a simplified version of a geometry, using the Douglas-Peucker algorithm.

                geometry ST_Simplify
                geometry geomA
                float tolerance

                geometry ST_Simplify
                geometry geomA
                float tolerance
                boolean preserveCollapsed

### Description

Returns a "simplified" version of the given geometry using the Douglas-Peucker algorithm. Will actually do something only with (multi)lines and (multi)polygons but you can safely call it with any kind of geometry. Since simplification occurs on a object-by-object basis you can also feed a GeometryCollection to this function.

The "preserve collapsed" flag will retain objects that would otherwise be too small given the tolerance. For example, a 1m long line simplified with a 10m tolerance. If `preserveCollapsed` argument is specified as true, the line will not disappear. This flag is useful for rendering engines, to avoid having large numbers of very small objects disappear from a map leaving surprising gaps.

Note that returned geometry might lose its simplicity (see ST_IsSimple)

Note topology may not be preserved and may result in invalid geometries. Use (see ST_SimplifyPreserveTopology) to preserve topology.

Availability: 1.2.2

### Examples

A circle simplified too much becomes a triangle, medium an octagon,

    SELECT ST_Npoints(geom) AS np_before,
           ST_NPoints(ST_Simplify(geom,0.1)) AS np01_notbadcircle,
           ST_NPoints(ST_Simplify(geom,0.5)) AS np05_notquitecircle,
           ST_NPoints(ST_Simplify(geom,1)) AS np1_octagon,
           ST_NPoints(ST_Simplify(geom,10)) AS np10_triangle,
           (ST_Simplify(geom,100) is null) AS  np100_geometrygoesaway
      FROM
        (SELECT ST_Buffer('POINT(1 3)', 10,12) As geom) AS foo;

     np_before | np01_notbadcircle | np05_notquitecircle | np1_octagon | np10_triangle | np100_geometrygoesaway
    -----------+-------------------+---------------------+-------------+---------------+------------------------
            49 |                33 |                  17 |           9 |             4 | t

### See Also

ST_IsSimple, ST_SimplifyPreserveTopology, ST_SimplifyVW, Topology TP_ST_Simplify

ST_SimplifyPreserveTopology

Returns a simplified and valid version of a geometry, using the Douglas-Peucker algorithm.

                geometry ST_SimplifyPreserveTopology
                geometry geomA
                float tolerance

### Description

Returns a "simplified" version of the given geometry using the Douglas-Peucker algorithm. Will avoid creating derived geometries (polygons in particular) that are invalid. Will actually do something only with (multi)lines and (multi)polygons but you can safely call it with any kind of geometry. Since simplification occurs on a object-by-object basis you can also feed a GeometryCollection to this function.

Performed by the GEOS module.

Availability: 1.3.3

### Examples

Same example as Simplify, but we see Preserve Topology prevents oversimplification. The circle can at most become a square.

    SELECT ST_Npoints(geom) As np_before, ST_NPoints(ST_SimplifyPreserveTopology(geom,0.1)) As np01_notbadcircle, ST_NPoints(ST_SimplifyPreserveTopology(geom,0.5)) As np05_notquitecircle,
    ST_NPoints(ST_SimplifyPreserveTopology(geom,1)) As np1_octagon, ST_NPoints(ST_SimplifyPreserveTopology(geom,10)) As np10_square,
    ST_NPoints(ST_SimplifyPreserveTopology(geom,100)) As  np100_stillsquare
    FROM (SELECT ST_Buffer('POINT(1 3)', 10,12) As geom) As foo;

    --result--
     np_before | np01_notbadcircle | np05_notquitecircle | np1_octagon | np10_square | np100_stillsquare
    -----------+-------------------+---------------------+-------------+---------------+-------------------
            49 |                33 |                  17 |           9 |             5 |                 5

### See Also

ST_Simplify

ST_SimplifyPolygonHull

Computes a simplifed topology-preserving outer or inner hull of a polygonal geometry.

                geometry ST_SimplifyPolygonHull
                geometry  param_geom
                float  vertex_fraction
                boolean  is_outer = true

### Description

Computes a simplified topology-preserving outer or inner hull of a polygonal geometry. An outer hull completely covers the input geometry. An inner hull is completely covered by the input geometry. The result is a polygonal geometry formed by a subset of the input vertices. MultiPolygons and holes are handled and produce a result with the same structure as the input.

The reduction in vertex count is controlled by the `vertex_fraction` parameter, which is a number in the range 0 to 1. Lower values produce simpler results, with smaller vertex count and less concaveness. For both outer and inner hulls a vertex fraction of 1.0 produces the orginal geometry. For outer hulls a value of 0.0 produces the convex hull (for a single polygon); for inner hulls it produces a triangle.

The simplification process operates by progressively removing concave corners that contain the least amount of area, until the vertex count target is reached. It prevents edges from crossing, so the result is always a valid polygonal geometry.

To get better results with geometries that contain relatively long line segments, it might be necessary to "segmentize" the input, as shown below.

Performed by the GEOS module.

Availability: 3.3.0 - requires GEOS >= 3.11.0

### Examples

Outer hull of a Polygon

    SELECT ST_SimplifyPolygonHull(
      'POLYGON ((131 158, 136 163, 161 165, 173 156, 179 148, 169 140, 186 144, 190 137, 185 131, 174 128, 174 124, 166 119, 158 121, 158 115, 165 107, 161 97, 166 88, 166 79, 158 57, 145 57, 112 53, 111 47, 93 43, 90 48, 88 40, 80 39, 68 32, 51 33, 40 31, 39 34, 49 38, 34 38, 25 34, 28 39, 36 40, 44 46, 24 41, 17 41, 14 46, 19 50, 33 54, 21 55, 13 52, 11 57, 22 60, 34 59, 41 68, 75 72, 62 77, 56 70, 46 72, 31 69, 46 76, 52 82, 47 84, 56 90, 66 90, 64 94, 56 91, 33 97, 36 100, 23 100, 22 107, 29 106, 31 112, 46 116, 36 118, 28 131, 53 132, 59 127, 62 131, 76 130, 80 135, 89 137, 87 143, 73 145, 80 150, 88 150, 85 157, 99 162, 116 158, 115 165, 123 165, 122 170, 134 164, 131 158))',
        0.3);

Inner hull of a Polygon

    SELECT ST_SimplifyPolygonHull(
      'POLYGON ((131 158, 136 163, 161 165, 173 156, 179 148, 169 140, 186 144, 190 137, 185 131, 174 128, 174 124, 166 119, 158 121, 158 115, 165 107, 161 97, 166 88, 166 79, 158 57, 145 57, 112 53, 111 47, 93 43, 90 48, 88 40, 80 39, 68 32, 51 33, 40 31, 39 34, 49 38, 34 38, 25 34, 28 39, 36 40, 44 46, 24 41, 17 41, 14 46, 19 50, 33 54, 21 55, 13 52, 11 57, 22 60, 34 59, 41 68, 75 72, 62 77, 56 70, 46 72, 31 69, 46 76, 52 82, 47 84, 56 90, 66 90, 64 94, 56 91, 33 97, 36 100, 23 100, 22 107, 29 106, 31 112, 46 116, 36 118, 28 131, 53 132, 59 127, 62 131, 76 130, 80 135, 89 137, 87 143, 73 145, 80 150, 88 150, 85 157, 99 162, 116 158, 115 165, 123 165, 122 170, 134 164, 131 158))',
        0.3, false);

Outer hull simplification of a MultiPolygon, with segmentization

    SELECT ST_SimplifyPolygonHull(
      ST_Segmentize(ST_Letters('xt'), 2.0),
        0.1);

### See Also

ST_ConvexHull, ST_SimplifyVW, ST_ConcaveHull, ST_Segmentize

ST_SimplifyVW

Returns a simplified version of a geometry, using the Visvalingam-Whyatt algorithm

                geometry ST_SimplifyVW
                geometry geomA
                float tolerance

### Description

Returns a "simplified" version of the given geometry using the Visvalingam-Whyatt algorithm. Will actually do something only with (multi)lines and (multi)polygons but you can safely call it with any kind of geometry. Since simplification occurs on a object-by-object basis you can also feed a GeometryCollection to this function.

Note that returned geometry might lose its simplicity (see ST_IsSimple)

Note topology may not be preserved and may result in invalid geometries. Use (see ST_SimplifyPreserveTopology) to preserve topology.

This function handles 3D and the third dimension will affect the result.

Availability: 2.2.0

### Examples

A LineString is simplified with a minimum area threshold of 30.

    select ST_AsText(ST_SimplifyVW(geom,30)) simplified
    FROM (SELECT  'LINESTRING(5 2, 3 8, 6 20, 7 25, 10 10)'::geometry geom) As foo;
    -result
     simplified
    ------------------------------
    LINESTRING(5 2,7 25,10 10)

### See Also

ST_SetEffectiveArea, ST_Simplify, ST_SimplifyPreserveTopology, Topology TP_ST_Simplify

ST_SetEffectiveArea

Sets the effective area for each vertex, using the Visvalingam-Whyatt algorithm.

                geometry ST_SetEffectiveArea
                geometry geomA
                float threshold = 0
                integer set_area = 1

### Description

Sets the effective area for each vertex, using the Visvalingam-Whyatt algorithm. The effective area is stored as the M-value of the vertex. If the optional "theshold" parameter is used, a simplified geometry will be returned, containing only vertices with an effective area greater than or equal to the threshold value.

This function can be used for server-side simplification when a threshold is specified. Another option is to use a threshold value of zero. In this case, the full geometry will be returned with effective areas as M-values, which can be used by the client to simplify very quickly.

Will actually do something only with (multi)lines and (multi)polygons but you can safely call it with any kind of geometry. Since simplification occurs on a object-by-object basis you can also feed a GeometryCollection to this function.

Note that returned geometry might lose its simplicity (see ST_IsSimple)

Note topology may not be preserved and may result in invalid geometries. Use (see ST_SimplifyPreserveTopology) to preserve topology.

The output geometry will lose all previous information in the M-values

This function handles 3D and the third dimension will affect the effective area

Availability: 2.2.0

### Examples

Calculating the effective area of a LineString. Because we use a threshold value of zero, all vertices in the input geometry are returned.

    select ST_AsText(ST_SetEffectiveArea(geom)) all_pts, ST_AsText(ST_SetEffectiveArea(geom,30) ) thrshld_30
    FROM (SELECT  'LINESTRING(5 2, 3 8, 6 20, 7 25, 10 10)'::geometry geom) As foo;
    -result
     all_pts | thrshld_30
    -----------+-------------------+
    LINESTRING M (5 2 3.40282346638529e+38,3 8 29,6 20 1.5,7 25 49.5,10 10 3.40282346638529e+38) | LINESTRING M (5 2 3.40282346638529e+38,7 25 49.5,10 10 3.40282346638529e+38)

### See Also

ST_SimplifyVW

ST_TriangulatePolygon

Computes the constrained Delaunay triangulation of polygons

                geometry ST_TriangulatePolygon
                geometry geom

### Description

Computes the constrained Delaunay triangulation of polygons. Holes and Multipolygons are supported.

The "constrained Delaunay triangulation" of a polygon is a set of triangles formed from the vertices of the polygon, and covering it exactly, with the maximum total interior angle over all possible triangulations. It provides the "best quality" triangulation of the polygon.

Availability: 3.3.0

### Example

Triangulation of a square.

    SELECT ST_AsText(
        ST_TriangulatePolygon('POLYGON((0 0, 0 1, 1 1, 1 0, 0 0))'));

                                     st_astext
    ---------------------------------------------------------------------------
     GEOMETRYCOLLECTION(POLYGON((0 0,0 1,1 1,0 0)),POLYGON((1 1,1 0,0 0,1 1)))

### Example

Triangulation of the letter P.

    SELECT ST_AsText(ST_TriangulatePolygon(
        'POLYGON ((26 17, 31 19, 34 21, 37 24, 38 29, 39 43, 39 161, 38 172, 36 176, 34 179, 30 181, 25 183, 10 185, 10 190, 100 190, 121 189, 139 187, 154 182, 167 177, 177 169, 184 161, 189 152, 190 141, 188 128, 186 123, 184 117, 180 113, 176 108, 170 104, 164 101, 151 96, 136 92, 119 89, 100 89, 86 89, 73 89, 73 39, 74 32, 75 27, 77 23, 79 20, 83 18, 89 17, 106 15, 106 10, 10 10, 10 15, 26 17), (152 147, 151 152, 149 157, 146 162, 142 166, 137 169, 132 172, 126 175, 118 177, 109 179, 99 180, 89 180, 80 179, 76 178, 74 176, 73 171, 73 100, 85 99, 91 99, 102 99, 112 100, 121 102, 128 104, 134 107, 139 110, 143 114, 147 118, 149 123, 151 128, 153 141, 152 147))'
        ));

Polygon Triangulation

### See Also

ST_DelaunayTriangles, ST_ConstrainedDelaunayTriangles, ST_Tesselate

ST_VoronoiLines

Returns the boundaries of the Voronoi diagram of the vertices of a geometry.

                geometry ST_VoronoiLines

                    g1
                    geometry

                    tolerance
                    float8

                    extend_to
                    geometry

### Description

ST_VoronoiLines computes a two-dimensional Voronoi diagram from the vertices of the supplied geometry and returns the boundaries between cells in that diagram as a MultiLineString. Returns null if input geometry is null. Returns an empty geometry collection if the input geometry contains only one vertex. Returns an empty geometry collection if the extend_to envelope has zero area.

Optional parameters:

- 'tolerance' : The distance within which vertices will be considered equivalent. Robustness of the algorithm can be improved by supplying a nonzero tolerance distance. (default = 0.0)

- 'extend_to' : If a geometry is supplied as the "extend_to" parameter, the diagram will be extended to cover the envelope of the "extend_to" geometry, unless that envelope is smaller than the default envelope (default = NULL, default envelope is boundingbox of input geometry extended by about 50% in each direction).

Performed by the GEOS module.

Availability: 2.3.0

### Examples

Voronoi lines with tolerance of 30 units
    SELECT ST_VoronoiLines(geom, 30) As geom
    FROM (SELECT 'MULTIPOINT (50 30, 60 30, 100 100,10 150, 110 120)'::geometry As geom ) As g
     -- ST_AsText output
    MULTILINESTRING((135.555555555556 270,36.8181818181818 92.2727272727273),(36.8181818181818 92.2727272727273,-110 43.3333333333333),(230 -45.7142857142858,36.8181818181818 92.2727272727273))

### See Also

ST_DelaunayTriangles, ST_VoronoiPolygons, ST_Collect

ST_VoronoiPolygons

Returns the cells of the Voronoi diagram of the vertices of a geometry.

                geometry ST_VoronoiPolygons

                    g1
                    geometry

                    tolerance
                    float8

                    extend_to
                    geometry

### Description

ST_VoronoiPolygons computes a two-dimensional Voronoi diagram from the vertices of the supplied geometry. The result is a GeometryCollection of Polygons that covers an envelope larger than the extent of the input vertices. Returns null if input geometry is null. Returns an empty geometry collection if the input geometry contains only one vertex. Returns an empty geometry collection if the extend_to envelope has zero area.

Optional parameters:

- 'tolerance' : The distance within which vertices will be considered equivalent. Robustness of the algorithm can be improved by supplying a nonzero tolerance distance. (default = 0.0)

- 'extend_to' : If a geometry is supplied as the "extend_to" parameter, the diagram will be extended to cover the envelope of the "extend_to" geometry, unless that envelope is smaller than the default envelope (default = NULL, default envelope is boundingbox of input geometry extended by about 50% in each direction).

Performed by the GEOS module.

Availability: 2.3.0

### Examples

Points overlaid on top of Voronoi diagram
    SELECT
        ST_VoronoiPolygons(geom) As geom
    FROM (SELECT 'MULTIPOINT (50 30, 60 30, 100 100,10 150, 110 120)'::geometry As geom ) As g;
     -- ST_AsText output
    GEOMETRYCOLLECTION(POLYGON((-110 43.3333333333333,-110 270,100.5 270,59.3478260869565 132.826086956522,36.8181818181818 92.2727272727273,-110 43.3333333333333)),
    POLYGON((55 -90,-110 -90,-110 43.3333333333333,36.8181818181818 92.2727272727273,55 79.2857142857143,55 -90)),
    POLYGON((230 47.5,230 -20.7142857142857,55 79.2857142857143,36.8181818181818 92.2727272727273,59.3478260869565 132.826086956522,230 47.5)),POLYGON((230 -20.7142857142857,230 -90,55 -90,55 79.2857142857143,230 -20.7142857142857)),
    POLYGON((100.5 270,230 270,230 47.5,59.3478260869565 132.826086956522,100.5 270)))
Voronoi with tolerance of 30 units
    SELECT ST_VoronoiPolygons(geom, 30) As geom
    FROM (SELECT 'MULTIPOINT (50 30, 60 30, 100 100,10 150, 110 120)'::geometry As geom ) As g;
     -- ST_AsText output
    GEOMETRYCOLLECTION(POLYGON((-110 43.3333333333333,-110 270,100.5 270,59.3478260869565 132.826086956522,36.8181818181818 92.2727272727273,-110 43.3333333333333)),
    POLYGON((230 47.5,230 -45.7142857142858,36.8181818181818 92.2727272727273,59.3478260869565 132.826086956522,230 47.5)),POLYGON((230 -45.7142857142858,230 -90,-110 -90,-110 43.3333333333333,36.8181818181818 92.2727272727273,230 -45.7142857142858)),
    POLYGON((100.5 270,230 270,230 47.5,59.3478260869565 132.826086956522,100.5 270)))
Voronoi with tolerance of 30 units as MultiLineString
    SELECT ST_VoronoiLines(geom, 30) As geom
    FROM (SELECT 'MULTIPOINT (50 30, 60 30, 100 100,10 150, 110 120)'::geometry As geom ) As g
     -- ST_AsText output
    MULTILINESTRING((135.555555555556 270,36.8181818181818 92.2727272727273),(36.8181818181818 92.2727272727273,-110 43.3333333333333),(230 -45.7142857142858,36.8181818181818 92.2727272727273))

### See Also

ST_DelaunayTriangles, ST_VoronoiLines, ST_Collect