CG_ConstrainedDelaunayTriangles
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Name

CG_ConstrainedDelaunayTriangles — Return a constrained Delaunay triangulation around the given input geometry.

Synopsis

geometry CG_ConstrainedDelaunayTriangles(geometry g1);

Description

Return a Constrained Delaunay triangulation around the vertices of the input geometry. Output is a TIN.

This method needs SFCGAL backend.

Availability: 3.0.0

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

Examples

Constrained Delaunay triangulation of the polygon and buffered point.

Code
SELECT
  CG_ConstrainedDelaunayTriangles(
    ST_Union(
      'POLYGON((175 150,20 40,50 60,125 100,175 150))'::geometry,
      ST_Buffer('POINT(110 170)'::geometry, 20)
    )
  );
Output
TIN(((50 60,175 150,20 40,50 60)),((125 100,50 60,20 40,125 100)),((50 60,125 100,175 150,50 60)),((130 170,129.6 166.1,175 150,130 170)),((128.5 162.3,175 150,129.6 166.1,128.5 162.3)),((130 170,124.1 155.9,129.6 166.1,130 170)),((126.6 158.9,175 150,128.5 162.3,126.6 158.9)),((129.6 166.1,126.6 158.9,128.5 162.3,129.6 166.1)),((124.1 155.9,175 150,126.6 158.9,124.1 155.9)),((129.6 166.1,124.1 155.9,126.6 158.9,129.6 166.1)),((121.1 153.4,175 150,124.1 155.9,121.1 153.4)),((110 150,121.1 153.4,124.1 155.9,110 150)),((117.7 151.5,175 150,121.1 153.4,117.7 151.5)),((113.9 150.4,117.7 151.5,121.1 153.4,113.9 150.4)),((113.9 150.4,175 150,117.7 151.5,113.9 150.4)),((20 40,113.9 150.4,110 150,20 40)),((20 40,175 150,113.9 150.4,20 40)),((20 40,110 150,106.1 150.4,20 40)),((113.9 150.4,121.1 153.4,110 150,113.9 150.4)),((20 40,106.1 150.4,102.3 151.5,20 40)),((110 150,124.1 155.9,128.5 177.7,110 150)),((20 40,102.3 151.5,98.9 153.4,20 40)),((106.1 150.4,110 150,98.9 153.4,106.1 150.4)),((20 40,98.9 153.4,95.9 155.9,20 40)),((102.3 151.5,106.1 150.4,98.9 153.4,102.3 151.5)),((20 40,95.9 155.9,93.4 158.9,20 40)),((98.9 153.4,110 150,95.9 155.9,98.9 153.4)),((20 40,93.4 158.9,91.5 162.3,20 40)),((95.9 155.9,110 150,102.3 188.5,95.9 155.9)),((20 40,91.5 162.3,90.4 166.1,20 40)),((93.4 158.9,95.9 155.9,91.5 162.3,93.4 158.9)),((20 40,90.4 166.1,90 170,20 40)),((91.5 162.3,95.9 155.9,90 170,91.5 162.3)),((20 40,90 170,90.4 173.9,20 40)),((90.4 166.1,91.5 162.3,90 170,90.4 166.1)),((20 40,90.4 173.9,91.5 177.7,20 40)),((90 170,95.9 155.9,102.3 188.5,90 170)),((90.4 173.9,90 170,91.5 177.7,90.4 173.9)),((91.5 177.7,90 170,102.3 188.5,91.5 177.7)),((93.4 181.1,91.5 177.7,95.9 184.1,93.4 181.1)),((95.9 184.1,91.5 177.7,102.3 188.5,95.9 184.1)),((98.9 186.6,95.9 184.1,102.3 188.5,98.9 186.6)),((102.3 188.5,110 150,128.5 177.7,102.3 188.5)),((106.1 189.6,102.3 188.5,110 190,106.1 189.6)),((110 190,102.3 188.5,117.7 188.5,110 190)),((113.9 189.6,110 190,117.7 188.5,113.9 189.6)),((117.7 188.5,102.3 188.5,128.5 177.7,117.7 188.5)),((121.1 186.6,124.1 184.1,175 150,121.1 186.6)),((121.1 186.6,117.7 188.5,124.1 184.1,121.1 186.6)),((124.1 184.1,126.6 181.1,175 150,124.1 184.1)),((124.1 184.1,117.7 188.5,128.5 177.7,124.1 184.1)),((126.6 181.1,128.5 177.7,175 150,126.6 181.1)),((126.6 181.1,124.1 184.1,128.5 177.7,126.6 181.1)),((128.5 177.7,129.6 173.9,175 150,128.5 177.7)),((128.5 177.7,124.1 155.9,130 170,128.5 177.7)),((129.6 173.9,130 170,175 150,129.6 173.9)),((129.6 173.9,128.5 177.7,130 170,129.6 173.9)))

ST_DelaunayTriangles applied to the same input. Triangle edges cross polygon boundaries.

Code
SELECT
  ST_DelaunayTriangles(
    ST_Union(
      'POLYGON((175 150,20 40,50 60,125 100,175 150))'::geometry,
      ST_Buffer('POINT(110 170)'::geometry, 20)
    )
  );
Output
GEOMETRYCOLLECTION(POLYGON((95.9 184.1,93.4 181.1,95.9 155.9,95.9 184.1)), POLYGON((95.9 184.1,95.9 155.9,102.3 188.5,95.9 184.1)), POLYGON((95.9 184.1,102.3 188.5,98.9 186.6,95.9 184.1)), POLYGON((102.3 188.5,95.9 155.9,98.9 153.4,102.3 188.5)), POLYGON((102.3 188.5,98.9 153.4,102.3 151.5,102.3 188.5)), POLYGON((102.3 188.5,102.3 151.5,106.1 189.6,102.3 188.5)), POLYGON((106.1 189.6,102.3 151.5,106.1 150.4,106.1 189.6)), POLYGON((106.1 189.6,106.1 150.4,110 190,106.1 189.6)), POLYGON((110 190,106.1 150.4,110 150,110 190)), POLYGON((110 190,110 150,117.7 188.5,110 190)), POLYGON((110 190,117.7 188.5,113.9 189.6,110 190)), POLYGON((117.7 188.5,110 150,121.1 153.4,117.7 188.5)), POLYGON((117.7 188.5,121.1 153.4,121.1 186.6,117.7 188.5)), POLYGON((121.1 186.6,121.1 153.4,124.1 155.9,121.1 186.6)), POLYGON((121.1 186.6,124.1 155.9,124.1 184.1,121.1 186.6)), POLYGON((121.1 186.6,124.1 184.1,175 150,121.1 186.6)), POLYGON((175 150,124.1 184.1,126.6 181.1,175 150)), POLYGON((175 150,126.6 181.1,128.5 177.7,175 150)), POLYGON((175 150,128.5 177.7,129.6 173.9,175 150)), POLYGON((175 150,129.6 173.9,130 170,175 150)), POLYGON((175 150,130 170,129.6 166.1,175 150)), POLYGON((175 150,129.6 166.1,128.5 162.3,175 150)), POLYGON((175 150,128.5 162.3,126.6 158.9,175 150)), POLYGON((175 150,126.6 158.9,124.1 155.9,175 150)), POLYGON((175 150,124.1 155.9,125 100,175 150)), POLYGON((125 100,124.1 155.9,121.1 153.4,125 100)), POLYGON((125 100,121.1 153.4,117.7 151.5,125 100)), POLYGON((125 100,117.7 151.5,113.9 150.4,125 100)), POLYGON((125 100,113.9 150.4,110 150,125 100)), POLYGON((125 100,110 150,106.1 150.4,125 100)), POLYGON((125 100,106.1 150.4,102.3 151.5,125 100)), POLYGON((125 100,102.3 151.5,98.9 153.4,125 100)), POLYGON((125 100,98.9 153.4,50 60,125 100)), POLYGON((125 100,50 60,20 40,125 100)), POLYGON((20 40,50 60,90.4 166.1,20 40)), POLYGON((20 40,90.4 166.1,90 170,20 40)), POLYGON((20 40,90 170,90.4 173.9,20 40)), POLYGON((20 40,90.4 173.9,91.5 177.7,20 40)), POLYGON((91.5 177.7,90.4 173.9,90 170,91.5 177.7)), POLYGON((91.5 177.7,90 170,91.5 162.3,91.5 177.7)), POLYGON((91.5 177.7,91.5 162.3,93.4 158.9,91.5 177.7)), POLYGON((91.5 177.7,93.4 158.9,93.4 181.1,91.5 177.7)), POLYGON((93.4 181.1,93.4 158.9,95.9 155.9,93.4 181.1)), POLYGON((95.9 155.9,93.4 158.9,50 60,95.9 155.9)), POLYGON((95.9 155.9,50 60,98.9 153.4,95.9 155.9)), POLYGON((50 60,93.4 158.9,91.5 162.3,50 60)), POLYGON((50 60,91.5 162.3,90.4 166.1,50 60)), POLYGON((90.4 166.1,91.5 162.3,90 170,90.4 166.1)), POLYGON((110 150,113.9 150.4,121.1 153.4,110 150)), POLYGON((121.1 153.4,113.9 150.4,117.7 151.5,121.1 153.4)), POLYGON((124.1 155.9,126.6 158.9,129.6 166.1,124.1 155.9)), POLYGON((124.1 155.9,129.6 166.1,128.5 177.7,124.1 155.9)), POLYGON((124.1 155.9,128.5 177.7,124.1 184.1,124.1 155.9)), POLYGON((124.1 184.1,128.5 177.7,126.6 181.1,124.1 184.1)), POLYGON((128.5 177.7,129.6 166.1,130 170,128.5 177.7)), POLYGON((128.5 177.7,130 170,129.6 173.9,128.5 177.7)), POLYGON((129.6 166.1,126.6 158.9,128.5 162.3,129.6 166.1)))