docs/api/sql/Geometry-Processing/ST_DelaunayTriangles.md

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# ST_DelaunayTriangles

Introduction: This function computes the [Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation) for the set of vertices in the input geometry. An optional `tolerance` parameter allows snapping nearby input vertices together prior to triangulation and can improve robustness in certain scenarios by handling near-coincident vertices. The default for  `tolerance` is 0. The Delaunay triangulation geometry is bounded by the convex hull of the input vertex set.

![ST_DelaunayTriangles](../../../image/ST_DelaunayTriangles/ST_DelaunayTriangles.svg "ST_DelaunayTriangles")

The output geometry representation depends on the provided `flag`:

- `0` - a GeometryCollection of triangular Polygons (default option)
- `1` - a MultiLinestring of the edges of the triangulation

Format:

`ST_DelaunayTriangles(geometry: Geometry)`

`ST_DelaunayTriangles(geometry: Geometry, tolerance: Double)`

`ST_DelaunayTriangles(geometry: Geometry, tolerance: Double, flag: Integer)`

Return type: `Geometry`

Since: `v1.6.1`

SQL Example

```sql
SELECT ST_DelaunayTriangles(
        ST_GeomFromWKT('POLYGON ((10 10, 15 30, 20 25, 25 35, 30 20, 40 30, 50 10, 45 5, 35 15, 30 5, 25 15, 20 10, 15 20, 10 10))')
)
```

Output:

```
GEOMETRYCOLLECTION (POLYGON ((15 30, 10 10, 15 20, 15 30)), POLYGON ((15 30, 15 20, 20 25, 15 30)), POLYGON ((15 30, 20 25, 25 35, 15 30)), POLYGON ((25 35, 20 25, 30 20, 25 35)), POLYGON ((25 35, 30 20, 40 30, 25 35)), POLYGON ((40 30, 30 20, 35 15, 40 30)), POLYGON ((40 30, 35 15, 50 10, 40 30)), POLYGON ((50 10, 35 15, 45 5, 50 10)), POLYGON ((30 5, 45 5, 35 15, 30 5)), POLYGON ((30 5, 35 15, 25 15, 30 5)), POLYGON ((30 5, 25 15, 20 10, 30 5)), POLYGON ((30 5, 20 10, 10 10, 30 5)), POLYGON ((10 10, 20 10, 15 20, 10 10)), POLYGON ((15 20, 20 10, 25 15, 15 20)), POLYGON ((15 20, 25 15, 20 25, 15 20)), POLYGON ((20 25, 25 15, 30 20, 20 25)), POLYGON ((30 20, 25 15, 35 15, 30 20)))
```