ST_Delaunay

Signatures

GEOMETRY ST_Delaunay(GEOMETRY geom)
GEOMETRY ST_Delaunay(GEOMETRY geom, INTEGER flag)
GEOMETRY ST_Delaunay(GEOMETRY geom, INTEGER flag, DOUBLE quality)

Description

Returns a MULTIPOLYGON (or a MULTILINESTRING) that represent a Delaunay triangulation constructed from a collection of POINTs.

If flag=0 (default value) the output is a collection of POLYGON. If flag=1, a MULTILINESTRING is returned.

The last argument can be set to improve the quality of the triangulation. The value must be comprised between 0 and 1. If quality > 0.6, we assume that the triangle’s quality is acceptable.

Remarks

Input geometry (geom) can be a POINT, a LINESTRING or a POLYGON. Nevertheless, for good practice reasons, the user may use this function only with POINTs. To process LINESTRINGs and POLYGONs it’s preferable to use ST_ConstrainedDelaunay.
Note that the triangulation doesn’t compute the intersections between lines; it takes only existing coordinates.

Examples

1rst signature

SELECT ST_Delaunay('MULTIPOINT((1 1), (0 4), (3 2), (3 7), (4 5),
                               (5 2), (7 1), (7 6), (8 4), (5 8),
                               (1 8), (4 0))');
-- Answer: 
MULTIPOLYGON (((1 8, 0 4, 3 7, 1 8)), ((1 8, 3 7, 5 8, 1 8)),
	      ((5 8, 3 7, 4 5, 5 8)), ((5 8, 4 5, 7 6, 5 8)),
	      ((7 6, 4 5, 8 4, 7 6)), ((8 4, 4 5, 5 2, 8 4)),
	      ((8 4, 5 2, 7 1, 8 4)), ((4 0, 7 1, 5 2, 4 0)),
	      ((4 0, 5 2, 3 2, 4 0)), ((4 0, 3 2, 1 1, 4 0)),
	      ((1 1, 3 2, 0 4, 1 1)), ((0 4, 3 2, 4 5, 0 4)),
	      ((0 4, 4 5, 3 7, 0 4)), ((4 5, 3 2, 5 2, 4 5)))

2nd signature with `flag` parameter

SELECT ST_Delaunay('MULTIPOINT((1 1), (0 4), (3 2), (3 7), (4 5),
                               (5 2), (7 1), (7 6), (8 4), (5 8),
                               (1 8), (4 0))'
		    ,1);
-- Answer: 
MULTILINESTRING ((7 6, 8 4), (5 8, 7 6), (1 8, 5 8), (0 4, 1 8), 
		 (0 4, 1 1), (1 1, 4 0), (4 0, 7 1), (7 1, 8 4),
		 (5 2, 7 1), (5 2, 8 4), (4 5, 5 2), (4 5, 8 4),
		 (4 5, 7 6), (4 5, 5 8), (3 7, 4 5), (3 7, 5 8),
		 (1 8, 3 7), (0 4, 3 7), (0 4, 4 5), (3 2, 4 5),
		 (0 4, 3 2), (1 1, 3 2), (3 2, 4 0), (3 2, 5 2),
		 (4 0, 5 2))

3rd signature with `flag` and `quality` parameters

SELECT ST_Delaunay('MULTIPOINT((1 1), (0 4), (3 2), (3 7), (4 5),
                               (5 2), (7 1), (7 6), (8 4), (5 8),
                               (1 8), (4 0))'
		    , 1, 0.5);
-- Answer: 
MULTILINESTRING ((0 4, 1 1), (0 4, 1 8), (0 4, 3 2), (1 1, 3 2), 
		 (0 4, 3 7), (0 4, 4 5), (1 8, 3 7), (1 1, 4 0),
		 (3 2, 4 0), (3 2, 4 5), (3 2, 5 2), (3 7, 4 5),
		 (4 0, 5 2), (4 5, 5 2), (4 5, 8 4), (4 5, 5 8),
		 (3 7, 5 8), (3 8, 5 8), (4 0, 7 1), (5 2, 7 1),
		 (4 5, 7 6), (5 2, 8 4), (5 8, 7 6), (7 1, 8 4),
		 (7 6, 8 4), (3 7, 3 8), (1 8, 3 8))

See also