ST_DelaunayTriangles
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## Name

ST_DelaunayTriangles — Returns the Delaunay triangulation of the vertices of a geometry.

## Synopsis

`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

This function supports 3d and will not drop the z-index.

This function supports Triangles and Triangulated Irregular Network Surfaces (TIN).

## 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)))

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