Name

ST_DelaunayTriangles — Return a Delaunay triangulation around the given input points.

Synopsis

geometry ST_DelaunayTriangles(geometry g1, float tolerance, int4 flags);

Description

Return a Delaunay triangulation around 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 togheter.

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))
:
:

3D Examples

-- 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)))

See Also

ST_ConcaveHull, ST_Dump