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ST_ConstrainedDelaunay

Signature

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

Description

Returns a MULTIPOLYGON (or a MULTILINESTRING) that represent a Constrained Delaunay Triangulation from a geometry.

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.

Remark

If the input geometry does not contain any lines, a Delaunay triangulation will be computed.

Examples

1rst signature, with POLYGON
SELECT ST_ConstrainedDelaunay('POLYGON ((4 8, 5 6, 9 6, 7 5, 2 6, 2 5, 
					 1 3, 3 2, 5 1, 3 0, 0 2, 0 4, 
					 1 7, 4 8), 
  			                (4 7, 3 7, 4 6, 4 7))');
-- Answer: 
MULTIPOLYGON (((0 4, 0 2, 1 3, 0 4)), ((0 4, 2 5, 1 3, 0 4)), ((0 4, 2 5, 1 7, 0 4)), ((2 5, 1 7, 2 6, 2 5)), 
	      ((0 2, 3 2, 3 0, 0 2)), ((0 2, 3 2, 1 3, 0 2)), ((1 3, 2 5, 3 2, 1 3)), ((7 5, 3 2, 5 1, 7 5)), 
	      ((2 6, 1 7, 3 7, 2 6)), ((2 6, 3 7, 4 6, 2 6)), ((4 6, 3 7, 4 7, 4 6)), ((4 7, 3 7, 4 8, 4 7)), 
	      ((3 7, 1 7, 4 8, 3 7)), ((3 0, 3 2, 5 1, 3 0)), ((7 5, 3 2, 2 5, 7 5)), ((4 6, 4 7, 5 6, 4 6)),
	      ((4 7, 4 8, 5 6, 4 7)), ((2 5, 7 5, 2 6, 2 5)), ((2 6, 4 6, 7 5, 2 6)), ((4 6, 5 6, 7 5, 4 6)),
	      ((5 1, 7 5, 9 6, 5 1)), ((7 5, 5 6, 9 6, 7 5)), ((5 6, 4 8, 9 6, 5 6)))

1rst signature, with LINESTRING
SELECT ST_ConstrainedDelaunay('MULTILINESTRING ((1 1, 0 4, 1 6, 2 8, 4 8, 7 8, 9 7, 9 6), 
  						(3 6, 2 5, 2 3, 2 1), 
  						(5 6, 7 6, 8 5, 8 4, 7 3))');
-- Answer: 
MULTIPOLYGON (((2 3, 1 1, 2 1, 2 3)), ((2 3, 1 1, 0 4, 2 3)), ((0 4, 2 5, 2 3, 0 4)), ((0 4, 2 5, 1 6, 0 4)),
	      ((1 6, 3 6, 2 5, 1 6)), ((2 3, 7 3, 2 1, 2 3)), ((2 3, 2 5, 3 6, 2 3)), ((1 6, 3 6, 2 8, 1 6)),
	      ((2 3, 5 6, 3 6, 2 3)), ((3 6, 2 8, 4 8, 3 6)), ((3 6, 5 6, 4 8, 3 6)), ((2 3, 7 3, 5 6, 2 3)),
	      ((7 3, 5 6, 7 6, 7 3)), ((5 6, 7 8, 7 6, 5 6)), ((5 6, 7 8, 4 8, 5 6)), ((7 3, 7 6, 8 4, 7 3)),
	      ((8 4, 7 6, 8 5, 8 4)), ((7 6, 9 6, 8 5, 7 6)), ((8 4, 8 5, 9 6, 8 4)), ((7 6, 9 7, 9 6, 7 6)),
	      ((7 6, 9 7, 7 8, 7 6)))

2nd signature, with flag parameter
SELECT ST_ConstrainedDelaunay('POLYGON ((4 8, 5 6, 9 6, 7 5, 2 6, 2 5, 
					 1 3, 3 2, 5 1, 3 0, 0 2, 0 4, 
					 1 7, 4 8), 
  			                (4 7, 3 7, 4 6, 4 7))'
			       , 1);
-- Answer: 
MULTILINESTRING ((0 2, 0 4), (0 2, 1 3), (0 4, 1 3), (0 4, 2 5), (0 4, 1 7), (1 3, 2 5), (1 7, 2 5), (2 5, 2 6),
		 (1 7, 2 6), (0 2, 3 0), (0 2, 3 2), (3 0, 3 2), (1 3, 3 2), (2 5, 3 2), (3 2, 7 5), (2 6, 3 7),
		 (1 7, 3 7), (2 6, 4 6), (3 7, 4 6), (4 6, 4 7), (3 7, 4 7), (4 7, 4 8), (3 7, 4 8), (1 7, 4 8),
		 (3 0, 5 1), (3 2, 5 1), (2 5, 7 5), (4 6, 5 6), (4 7, 5 6), (4 8, 5 6), (5 1, 7 5), (2 6, 7 5),
		 (4 6, 7 5), (5 6, 7 5), (5 1, 9 6), (7 5, 9 6), (5 6, 9 6), (4 8, 9 6))

See also