> ## Documentation Index
> Fetch the complete documentation index at: https://docs.wherobots.com/llms.txt
> Use this file to discover all available pages before exploring further.

# ST_DelaunayTriangles

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.

<img src="https://mintcdn.com/wherobots/fqh3gPDE0J25Lra_/images/sql-functions/ST_DelaunayTriangles/ST_DelaunayTriangles.svg?fit=max&auto=format&n=fqh3gPDE0J25Lra_&q=85&s=04d05ae430c42f298b2864587e8c5b94" alt="ST_DelaunayTriangles" width="500" height="300" data-path="images/sql-functions/ST_DelaunayTriangles/ST_DelaunayTriangles.svg" />

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

## Signatures

```sql theme={"system"}
ST_DelaunayTriangles(geometry: Geometry)
```

```sql theme={"system"}
ST_DelaunayTriangles(geometry: Geometry, tolerance: Double)
```

```sql theme={"system"}
ST_DelaunayTriangles(geometry: Geometry, tolerance: Double, flag: Integer)
```

## Parameters

<ParamField body="geometry" type="Geometry" required>
  The input geometry.
</ParamField>

<ParamField body="tolerance" type="Double">
  The distance tolerance.
</ParamField>

<ParamField body="flag" type="Integer">
  The validation flag.
</ParamField>

## Return type

<ResponseField type="Geometry">
  The resulting geometry.
</ResponseField>

## Example

```sql theme={"system"}
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))')
)
```

```
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)))
```