> For the complete documentation index, see [llms.txt](https://docs.carto.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.carto.com/data-and-analysis/analytics-toolbox-for-redshift/sql-reference/processing.md).

# processing

This module contains functions that computes new geographies by processing existing geographies.

## ST\_DELAUNAYLINES <a href="#st_delaunaylines" id="st_delaunaylines"></a>

```sql
ST_DELAUNAYLINES(points)
```

**Description**

Calculates the Delaunay triangulation of the points provided. A MultiLineString object is returned.

**Input parameters**

* `points`: `GEOMETRY` MultiPoint input to the Delaunay triangulation.

{% hint style="warning" %}
**warning**

The maximum number of points typically used to compute Delaunay diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.
{% endhint %}

**Return type**

`VARCHAR(MAX)`

**Example**

{% code overflow="wrap" lineNumbers="true" %}

```sql
SELECT carto.ST_DELAUNAYLINES(
  ST_GEOMFROMTEXT(
    'MULTIPOINT((-70.3894720672732 42.9988854818585),(-71.1048188482079 42.6986831053718),(-72.6818783178395 44.1191152795997),(-73.8221894711314 35.1057463244819))'
  )
);
-- {"type": "MultiLineString", "coordinates": [[[-71.1048188482, 42.6986831054], [-70.3894720673, 42.9988854819], [-73.8221894711, 35.1057463245], [-71.1048188482, 42.6986831054]], ...
```

{% endcode %}

## ST\_DELAUNAYPOLYGONS <a href="#st_delaunaypolygons" id="st_delaunaypolygons"></a>

```sql
ST_DELAUNAYPOLYGONS(points)
```

**Description**

Calculates the Delaunay triangulation of the points provided. A MultiPolygon object is returned.

**Input parameters**

* `points`: `GEOMETRY` MultiPoint input to the Delaunay triangulation.

{% hint style="warning" %}
**warning**

The maximum number of points typically used to compute Delaunay diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.
{% endhint %}

**Return type**

`VARCHAR(MAX)`

**Example**

{% code overflow="wrap" lineNumbers="true" %}

```sql
SELECT carto.ST_DELAUNAYPOLYGONS(
  ST_GEOMFROMTEXT(
    'MULTIPOINT((-70.3894720672732 42.9988854818585),(-71.1048188482079 42.6986831053718),(-72.6818783178395 44.1191152795997),(-73.8221894711314 35.1057463244819))'
  )
);
-- {"type": "MultiPolygon", "coordinates": [[[[-71.1048188482, 42.6986831054], [-70.3894720673, 42.9988854819], [-73.8221894711, 35.1057463245], [-71.1048188482, 42.6986831054]]], ...
```

{% endcode %}

## ST\_POLYGONIZE <a href="#st_polygonize" id="st_polygonize"></a>

```sql
ST_POLYGONIZE(lines)
```

**Description**

Creates a polygon from a geography which contains lines that represent its edges.

**Input parameters**

* `line`: `GEOMETRY` lines which represent the polygon edges.

**Return type**

`GEOMETRY`

**Example**

{% code overflow="wrap" lineNumbers="true" %}

```sql
SELECT carto.ST_POLYGONIZE(
  ST_GEOMFROMTEXT(
    'LINESTRING(-74.5366825512491 43.6889777784079, -70.7632814028801 42.9679602005825, -70.2005131676838 43.8455720129728, -74.5366825512491 43.6889777784079)'
  )
);
-- POLYGON ((-74.5366825512491 43.6889777784079, -70.7632814028801 42.9679602005825, -70.2005131676838 43.8455720129728, -74.5366825512491 43.6889777784079))
```

{% endcode %}

## ST\_VORONOILINES <a href="#st_voronoilines" id="st_voronoilines"></a>

```sql
ST_VORONOILINES(points)
```

**Description**

Calculates the Voronoi diagram of the points provided. A MultiLineString object is returned.

**Input parameters**

* `points`: `GEOMETRY` MultiPoint input to the Voronoi diagram.

{% hint style="warning" %}
**warning**

The maximum number of points typically used to compute Voronoi diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.
{% endhint %}

**Return type**

`VARCHAR(MAX)`

**Example**

{% code overflow="wrap" lineNumbers="true" %}

```sql
SELECT carto.ST_VORONOILINES(
  ST_GEOMFROMTEXT(
    'MULTIPOINT((-74.5366825512491 43.6889777784079),(-74.4821382017478 43.3096147774153),(-70.7632814028801 42.9679602005825))'
  )
);
-- {"type": "MultiLineString", "coordinates": [[[-72.563891028, 43.7790206765], [-72.6715241053, 42.6074514117]], [[-72.563891028, 43.7790206765], ...
```

{% endcode %}

## ST\_VORONOIPOLYGONS <a href="#st_voronoipolygons" id="st_voronoipolygons"></a>

```sql
ST_VORONOIPOLYGONS(points)
```

**Description**

Calculates the Voronoi diagram of the points provided. A MultiPolygon object is returned.

**Input parameters**

* `points`: `GEOMETRY` MultiPoint input to the Voronoi diagram.

{% hint style="warning" %}
**warning**

The maximum number of points typically used to compute Voronoi diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.
{% endhint %}

**Return type**

`VARCHAR(MAX)`

**Example**

{% code overflow="wrap" lineNumbers="true" %}

```sql
SELECT carto.ST_VORONOIPOLYGONS(
  ST_GEOMFROMTEXT(
    'MULTIPOINT((-74.5366825512491 43.6889777784079),(-74.4821382017478 43.3096147774153),(-70.7632814028801 42.9679602005825))'
  )
);
-- {"type": "MultiPolygon", "coordinates": [[[[-74.8971913401, 43.443541604], [-72.563891028, 43.7790206765], [-72.5122106861, 44.0494865673], [-74.8971913401, 44.0494865673], ...
```

{% endcode %}


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