# 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. An array of linestrings in GeoJSON format is returned.

**Input parameters**

* `points`: `ARRAY` array of points in GeoJSON format casted to STRING.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting polygons (about 1 meter). This can also result in some points being merged together, so that fewer polygons than expected may result.

{% 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**

`ARRAY`

**Examples**

```sql
SELECT CARTO.CARTO.ST_DELAUNAYLINES(
  ARRAY_CONSTRUCT(
    ST_ASGEOJSON(ST_POINT(-75.833, 39.284))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.6, 39.984))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.221, 39.125))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.521, 39.325))::STRING
  )
);
--  "{\"coordinates\":[[-75.833,39.284],[-75.221,39.125],[-75.6,39.984],[-75.833,39.284]],\"type\":\"LineString\"}",
--  "{\"coordinates\":[[-75.833,39.284],[-75.521,39.325],[-75.6,39.984],[-75.833,39.284]],\"type\":\"LineString\"}",
--  "{\"coordinates\":[[-75.833,39.284],[-75.521,39.325],[-75.221,39.125],[-75.833,39.284]],\"type\":\"LineString\"}",
--  "{\"coordinates\":[[-75.521,39.325],[-75.221,39.125],[-75.6,39.984],[-75.521,39.325]],\"type\":\"LineString\"}"
```

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer lines than expected, for example these four points result in two lines:

```sql
SELECT CARTO.CARTO.ST_DELAUNAYLINES(
  ARRAY_CONSTRUCT(
    '{"coordinates":[4.1829523,43.6347910],"type":"Point"}',
    '{"coordinates":[4.1829967,43.6347137],"type":"Point"}',
    '{"coordinates":[4.1829955,43.6347143],"type":"Point"}',
    '{"coordinates":[4.1829321,43.6347500],"type":"Point"}'
  )
);
-- [
--   "{\"coordinates\":[[4.18293,43.63475],[4.183,43.63471],[4.18295,43.63479],[4.18293,43.63475]],\"type\":\"LineString\"}"
-- ]
```

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

```sql
ST_DELAUNAYLINES(points)
```

**Description**

Calculates the Delaunay triangulation of the points provided. An array of polygons in GeoJSON format is returned.

**Input parameters**

* `points`: `ARRAY` array of points in GeoJSON format casted to STRING.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting polygons (about 1 meter). This can also result in some points being merged together, so that fewer polygons than expected may result.

{% 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**

`ARRAY`

**Examples**

```sql
SELECT CARTO.CARTO.ST_DELAUNAYPOLYGONS(
  ARRAY_CONSTRUCT(
    ST_ASGEOJSON(ST_POINT(-75.833, 39.284))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.6, 39.984))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.221, 39.125))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.521, 39.325))::STRING
  )
);
-- "{\"coordinates\":[[[-75.833,39.284],[-75.221,39.125],[-75.6,39.984],[-75.833,39.284]]],\"type\":\"Polygon\"}",
-- "{\"coordinates\":[[[-75.833,39.284],[-75.521,39.325],[-75.6,39.984],[-75.833,39.284]]],\"type\":\"Polygon\"}",
-- "{\"coordinates\":[[[-75.833,39.284],[-75.521,39.325],[-75.221,39.125],[-75.833,39.284]]],\"type\":\"Polygon\"}",
-- "{\"coordinates\":[[[-75.521,39.325],[-75.221,39.125],[-75.6,39.984],[-75.521,39.325]]],\"type\":\"Polygon\"}"
```

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer triangles than expected, for example these four points result in one triangle:

```sql
SELECT CARTO.CARTO.ST_DELAUNAYPOLYGONS(
  ARRAY_CONSTRUCT(
    '{"coordinates":[4.1829523,43.6347910],"type":"Point"}',
    '{"coordinates":[4.1829967,43.6347137],"type":"Point"}',
    '{"coordinates":[4.1829955,43.6347143],"type":"Point"}',
    '{"coordinates":[4.1829321,43.6347500],"type":"Point"}'
  )
);
-- [
--   "{\"coordinates\":[[[4.18293,43.63475],[4.183,43.63471],[4.18295,43.63479],[4.18293,43.63475]]],\"type\":\"Polygon\"}"
-- ]
```

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

```sql
ST_POLYGONIZE(lines)
```

**Description**

Creates a set of polygons from geographies which contain lines that represent the their edges.

**Input parameters**

* `lines`: `ARRAY` array of lines which represent the polygons edges in GeoJSON format casted to STRING.

**Return type**

`ARRAY`

**Example**

```sql
SELECT CARTO.CARTO.ST_POLYGONIZE(
  ARRAY_CONSTRUCT(
    ST_ASGEOJSON(
      ST_GEOGRAPHYFROMWKT(
        'LINESTRING(-74.5366825512491 43.6889777784079, -70.7632814028801 42.9679602005825, -70.2005131676838 43.8455720129728, -74.5366825512491 43.6889777784079)'
      )
    )::STRING,
    ST_ASGEOJSON(
      ST_GEOGRAPHYFROMWKT(
        'LINESTRING(-73.9704330709753 35.3953164724094, -72.514071762468 36.5823995124737, -73.3262122666779 41.2706174323278, -73.9704330709753 35.3953164724094)'
      )
    )::STRING
  )
);
-- "{\"coordinates\":[[[-74.5366825512491,43.6889777784079],[-70.7632814028801,42.9679602005825],[-70.2005131676838,43.8455720129728],[-74.5366825512491,43.6889777784079]]],\"type\":\"Polygon\"}",
-- "{\"coordinates\":[[[-73.9704330709753,35.3953164724094],[-72.514071762468,36.5823995124737],[-73.3262122666779,41.2706174323278],[-73.9704330709753,35.3953164724094]]],\"type\":\"Polygon\"}"
```

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

```sql
ST_VORONOILINES(points [, bbox])
```

**Description**

Calculates the Voronoi diagram of the points provided. An array of linestrings in GeoJSON format is returned.

**Input parameters**

* `points`: `ARRAY` array of points in GeoJSON format casted to STRING.
* `bbox` (optional): `ARRAY` clipping bounding box. By default the \[-180,-85,180,85] bbox will be used.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting lines (about 1 meter). This can also result in some points being merged together, so that fewer lines than input points may result.

{% 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**

`ARRAY`

**Examples**

```sql
SELECT CARTO.CARTO.ST_VORONOILINES(
  ARRAY_CONSTRUCT(
    ST_ASGEOJSON(ST_POINT(-75.833, 39.284))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.6, 39.984))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.221, 39.125))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.521, 39.325))::STRING
  )
);
--  "{\"type\":\"LineString\",\"coordinates\":[[-180,74.34550785714367],[-75.72047348298037,39.63532260219203],[-75.6178875502008,38.854668674698786],[-107.79581617647065,-85],[-180,-85],[-180,74.34550785714367]]}",
--  "{\"type\":\"LineString\",\"coordinates\":[[27.59130606860346,85],[-75.04333534909291,39.716496976360624],[-75.72047348298037,39.63532260219203],[-180,74.34550785714367],[-180,85],[27.59130606860346,85]]}",
--  "{\"type\":\"LineString\",\"coordinates\":[[-107.79581617647065,-85],[-75.6178875502008,38.854668674698786],[-75.04333534909291,39.716496976360624],[27.59130606860346,85],[180,85],[180,-85],[-107.79581617647065,-85]]}",
--  "{\"type\":\"LineString\",\"coordinates\":[[-75.72047348298037,39.63532260219203],[-75.04333534909291,39.716496976360624],[-75.6178875502008,38.854668674698786],[-75.72047348298037,39.63532260219203]]}"
```

```sql
SELECT CARTO.CARTO.ST_VORONOILINES(
  ARRAY_CONSTRUCT(
    ST_ASGEOJSON(ST_POINT(-75.833, 39.284))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.6, 39.984))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.221, 39.125))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.521, 39.325))::STRING
  ),
  ARRAY_CONSTRUCT(-76.0, 35.0, -70.0, 45.0)
);
--  "{\"type\":\"LineString\",\"coordinates\":[[-76,39.728365000000004],[-75.72047348298037,39.63532260219203],[-75.6178875502008,38.854668674698786],[-76,37.38389622641511],[-76,39.728365000000004]]}",
--  "{\"type\":\"LineString\",\"coordinates\":[[-70,41.941670547147794],[-75.04333534909291,39.716496976360624],[-75.72047348298037,39.63532260219203],[-76,39.728365000000004],[-76,45],[-70,45],[-70,41.941670547147794]]}",
--  "{\"type\":\"LineString\",\"coordinates\":[[-76,37.38389622641511],[-75.6178875502008,38.854668674698786],[-75.04333534909291,39.716496976360624],[-70,41.941670547147794],[-70,35],[-76,35],[-76,37.38389622641511]]}",
--  "{\"type\":\"LineString\",\"coordinates\":[[-75.72047348298037,39.63532260219203],[-75.04333534909291,39.716496976360624],[-75.6178875502008,38.854668674698786],[-75.72047348298037,39.63532260219203]]}"
```

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer lines than points, for example these three points result in two lines

```sql
SELECT CARTO.CARTO.ST_VORONOILINES(
  ARRAY_CONSTRUCT(
    '{"coordinates":[4.1829523,43.6347910],"type":"Point"}',
    '{"coordinates":[4.1829967,43.6347137],"type":"Point"}',
    '{"coordinates":[4.1829955,43.6347143],"type":"Point"}'
  ),
  ARRAY_CONSTRUCT(4.182, 43.634, 4.183, 43.635)
);
-- [
--   "{\"type\":\"LineString\",\"coordinates\":[[4.183,43.634765625],[4.182,43.63414062499997],[4.182,43.635],[4.183,43.635],[4.183,43.634765625]]}",
--   "{\"type\":\"LineString\",\"coordinates\":[[4.182,43.63414062499997],[4.183,43.634765625],[4.183,43.634],[4.182,43.634],[4.182,43.63414062499997]]}"
-- ]
```

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

```sql
ST_VORONOIPOLYGONS(points [, bbox])
```

**Description**

Calculates the Voronoi diagram of the points provided. An array of polygons in GeoJSON format is returned.

**Input parameters**

* `points`: `ARRAY` array of points in GeoJSON format casted to STRING.
* `bbox` (optional): `ARRAY` clipping bounding box. By default the \[-180,-85,180,85] bbox will be used.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting polygons (about 1 meter). This can also result in some points being merged together, so that fewer polygons than input points may result.

{% 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**

`ARRAY`

**Examples**

```sql
SELECT CARTO.CARTO.ST_VORONOIPOLYGONS(
  ARRAY_CONSTRUCT(
    ST_ASGEOJSON(ST_POINT(-75.833, 39.284))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.6, 39.984))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.221, 39.125))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.521, 39.325))::STRING
  )
);
--  "{\"type\":\"Polygon\",\"coordinates\":[[[-180,74.34550785714367],[-75.72047348298037,39.63532260219203],[-75.6178875502008,38.854668674698786],[-107.79581617647065,-85],[-180,-85],[-180,74.34550785714367]]]}",
--  "{\"type\":\"Polygon\",\"coordinates\":[[[27.59130606860346,85],[-75.04333534909291,39.716496976360624],[-75.72047348298037,39.63532260219203],[-180,74.34550785714367],[-180,85],[27.59130606860346,85]]]}",
--  "{\"type\":\"Polygon\",\"coordinates\":[[[-107.79581617647065,-85],[-75.6178875502008,38.854668674698786],[-75.04333534909291,39.716496976360624],[27.59130606860346,85],[180,85],[180,-85],[-107.79581617647065,-85]]]}",
--  "{\"type\":\"Polygon\",\"coordinates\":[[[-75.72047348298037,39.63532260219203],[-75.04333534909291,39.716496976360624],[-75.6178875502008,38.854668674698786],[-75.72047348298037,39.63532260219203]]]}"
```

```sql
SELECT CARTO.CARTO.ST_VORONOIPOLYGONS(
  ARRAY_CONSTRUCT(
    ST_ASGEOJSON(ST_POINT(-75.833, 39.284))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.6, 39.984))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.221, 39.125))::STRING,
    ST_ASGEOJSON(ST_POINT(-75.521, 39.325))::STRING
  ),
  ARRAY_CONSTRUCT(-76.0, 35.0, -70.0, 45.0)
);
--  "{\"type\":\"Polygon\",\"coordinates\":[[[-76,39.728365000000004],[-75.72047348298037,39.63532260219203],[-75.6178875502008,38.854668674698786],[-76,37.38389622641511],[-76,39.728365000000004]]]}",
--  "{\"type\":\"Polygon\",\"coordinates\":[[[-70,41.941670547147794],[-75.04333534909291,39.716496976360624],[-75.72047348298037,39.63532260219203],[-76,39.728365000000004],[-76,45],[-70,45],[-70,41.941670547147794]]]}",
--  "{\"type\":\"Polygon\",\"coordinates\":[[[-76,37.38389622641511],[-75.6178875502008,38.854668674698786],[-75.04333534909291,39.716496976360624],[-70,41.941670547147794],[-70,35],[-76,35],[-76,37.38389622641511]]]}",
--  "{\"type\":\"Polygon\",\"coordinates\":[[[-75.72047348298037,39.63532260219203],[-75.04333534909291,39.716496976360624],[-75.6178875502008,38.854668674698786],[-75.72047348298037,39.63532260219203]]]}"
```

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer polygons than points, for example these three points result in two polygons:

```sql
SELECT CARTO.CARTO.ST_VORONOIPOLYGONS(
  ARRAY_CONSTRUCT(
    '{"coordinates":[4.1829523,43.6347910],"type":"Point"}',
    '{"coordinates":[4.1829967,43.6347137],"type":"Point"}',
    '{"coordinates":[4.1829955,43.6347143],"type":"Point"}'
  ),
  ARRAY_CONSTRUCT(4.182, 43.634, 4.183, 43.635)
);
-- [
--  "{\"type\":\"Polygon\",\"coordinates\":[[[4.183,43.634765625],[4.182,43.63414062499997],[4.182,43.635],[4.183,43.635],[4.183,43.634765625]]]}",
--   "{\"type\":\"Polygon\",\"coordinates\":[[[4.182,43.63414062499997],[4.183,43.634765625],[4.183,43.634],[4.182,43.634],[4.-- 182,43.63414062499997]]]}"
-- ]
```

{% hint style="info" %}
**Additional examples**

* [Analyzing store location coverage using a Voronoi diagram](https://academy.carto.com/advanced-spatial-analytics/spatial-analytics-for-snowflake/step-by-step-tutorials/analyzing-store-location-coverage-using-a-voronoi-diagram)
  {% endhint %}