## Name

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

## Synopsis

`geometry ST_DelaunayTriangles(`geometry g1, float tolerance = 0.0, int4 flags = 0`)`;

## Descrição

Computes the Delaunay triangulation of the vertices of the input geometry. The optional `tolerance` can be used to snap nearby input vertices together, which improves robustness in some situations. The result geometry is bounded by the convex hull of the input vertices. The result geometry representation is determined by the `flags` code:

• `0` - a GEOMETRYCOLLECTION of triangular POLYGONs (default)

• `1` - a MULTILINESTRING of the edges of the triangulation

• `2` - A TIN of the triangulation

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

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

## Exemplos

 Polígonos originais ```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 de 2 polígonos: polígonos da triangulação de Delaunay, cada triângulo de uma cor diferente ``` 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; ``` -- triângulos de Delaunay como 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;``` -- triângulos delaunay de 45 pontos como 55 polígonos triangulares ``` 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 using vertices with Z values.

```
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)))```