# constructors

This module contains functions that create new geographies from coordinates or already existing geographies.

## ST\_BEZIERSPLINE <a href="#st_bezierspline" id="st_bezierspline"></a>

```sql
ST_BEZIERSPLINE(geog, resolution, sharpness)
```

**Description**

Takes a line and returns a curved version of it by applying a Bezier spline algorithm. Note that the resulting geography will be a LineString with additional points inserted.

**Input parameters**

* `geog`: `GEOGRAPHY` input LineString.
* `resolution`: `INT64`|`NULL` total time in milliseconds assigned to the line. If `NULL` the default value `10000` is used. Internal curve vertices are generated in 10 ms increments, so the maximum number of resulting points will be `resolution/10` (close points may be merged resulting in less points). A higher number will increase the accuracy of the result but will increase the computation time and number of points.
* `sharpness`: `FLOAT64`|`NULL` a measure of how curvy the path should be between splines. If `NULL` the default value `0.85` is used.

**Example**

{% tabs %}
{% tab title="carto-un" %}

```sql
SELECT `carto-un`.carto.ST_BEZIERSPLINE(
  ST_GEOGFROMTEXT(
    "LINESTRING (-76.091308 18.427501,-76.695556 18.729501,-76.552734 19.40443,-74.61914 19.134789,-73.652343 20.07657,-73.157958 20.210656)"
  ),
  10000,
  0.9
);
-- LINESTRING(-76.091308 18.427501, -76.0916216712943 ...
```

{% endtab %}

{% tab title="carto-un-eu" %}

```sql
SELECT `carto-un-eu`.carto.ST_BEZIERSPLINE(
  ST_GEOGFROMTEXT(
    "LINESTRING (-76.091308 18.427501,-76.695556 18.729501,-76.552734 19.40443,-74.61914 19.134789,-73.652343 20.07657,-73.157958 20.210656)"
  ),
  10000,
  0.9
);
-- LINESTRING(-76.091308 18.427501, -76.0916216712943 ...
```

{% endtab %}

{% tab title="manual" %}

```sql
SELECT carto.ST_BEZIERSPLINE(
  ST_GEOGFROMTEXT(
    "LINESTRING (-76.091308 18.427501,-76.695556 18.729501,-76.552734 19.40443,-74.61914 19.134789,-73.652343 20.07657,-73.157958 20.210656)"
  ),
  10000,
  0.9
);
-- LINESTRING(-76.091308 18.427501, -76.0916216712943 ...
```

{% endtab %}
{% endtabs %}

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

* [Identifying earthquake-prone areas in the state of California](https://academy.carto.com/advanced-spatial-analytics/spatial-analytics-for-bigquery/step-by-step-tutorials/identifying-earthquake-prone-areas-in-the-state-of-california)
  {% endhint %}

## ST\_MAKEELLIPSE <a href="#st_makeellipse" id="st_makeellipse"></a>

```sql
ST_MAKEELLIPSE(geog, xSemiAxis, ySemiAxis, angle, units, steps)
```

**Description**

Takes a Point and calculates the ellipse polygon given two semi-axes expressed in variable units and steps for precision.

**Input parameters**

* `center`: `GEOGRAPHY` center point.
* `xSemiAxis`: `FLOAT64` semi (major) axis of the ellipse along the x-axis.
* `ySemiAxis`: `FLOAT64` semi (minor) axis of the ellipse along the y-axis.
* `angle`: `FLOAT64`|`NULL` angle of rotation (along the horizontal axis), from East in decimal degrees, positive clockwise. If `NULL` the default value `0` is used.
* `units`: `STRING`|`NULL` units of length, the supported options are: miles, kilometers, and degrees. If `NULL`the default value `kilometers` is used.
* `steps`: `INT64`|`NULL` number of steps. If `NULL` the default value `64` is used.

**Example**

{% tabs %}
{% tab title="carto-un" %}

```sql
SELECT `carto-un`.carto.ST_MAKEELLIPSE(
  ST_GEOGPOINT(-73.9385,40.6643),
  5,
  3,
  -30,
  "miles",
  80
);
-- POLYGON((-73.8558575786687 40.7004828957859 ...
```

{% endtab %}

{% tab title="carto-un-eu" %}

```sql
SELECT `carto-un-eu`.carto.ST_MAKEELLIPSE(
  ST_GEOGPOINT(-73.9385,40.6643),
  5,
  3,
  -30,
  "miles",
  80
);
-- POLYGON((-73.8558575786687 40.7004828957859 ...
```

{% endtab %}

{% tab title="manual" %}

```sql
SELECT carto.ST_MAKEELLIPSE(
  ST_GEOGPOINT(-73.9385,40.6643),
  5,
  3,
  -30,
  "miles",
  80
);
-- POLYGON((-73.8558575786687 40.7004828957859 ...
```

{% endtab %}
{% endtabs %}

## ST\_MAKEENVELOPE <a href="#st_makeenvelope" id="st_makeenvelope"></a>

```sql
ST_MAKEENVELOPE(xmin, ymin, xmax, ymax)
```

**Description** Creates a rectangular Polygon from the minimum and maximum values for X and Y.

**Input parameters**

* `xmin`: `FLOAT64` minimum value for X.
* `ymin`: `FLOAT64` minimum value for Y.
* `xmax`: `FLOAT64` maximum value for X.
* `ymax`: `FLOAT64` maximum value for Y.

**Return type**

`GEOGRAPHY`

**Example**

{% tabs %}
{% tab title="carto-un" %}

```sql
SELECT `carto-un`.carto.ST_MAKEENVELOPE(0,0,1,1);
-- POLYGON((1 0, 1 1, 0 1, 0 0, 1 0))
```

{% endtab %}

{% tab title="carto-un-eu" %}

```sql
SELECT `carto-un-eu`.carto.ST_MAKEENVELOPE(0,0,1,1);
-- POLYGON((1 0, 1 1, 0 1, 0 0, 1 0))
```

{% endtab %}

{% tab title="manual" %}

```sql
SELECT carto.ST_MAKEENVELOPE(0,0,1,1);
-- POLYGON((1 0, 1 1, 0 1, 0 0, 1 0))
```

{% endtab %}
{% endtabs %}

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

* [Identifying earthquake-prone areas in the state of California](https://academy.carto.com/advanced-spatial-analytics/spatial-analytics-for-bigquery/step-by-step-tutorials/identifying-earthquake-prone-areas-in-the-state-of-california)
  {% endhint %}

## ST\_TILEENVELOPE <a href="#st_tileenvelope" id="st_tileenvelope"></a>

```sql
ST_TILEENVELOPE(zoomLevel, xTile, yTile)
```

**Description** Returns the boundary polygon of a [tile](https://wiki.openstreetmap.org/wiki/Slippy_map_tilenames) given its zoom level and its X and Y indices.

**Input parameters**

* `zoomLevel`: `INT64` zoom level of the tile.
* `xTile`: `INT64` X index of the tile.
* `yTile`: `INT64` Y index of the tile.

**Return type**

`GEOGRAPHY`

**Example**

{% tabs %}
{% tab title="carto-un" %}

```sql
SELECT `carto-un`.carto.ST_TILEENVELOPE(10,384,368);
-- POLYGON((-45 45.089035564831, -45 44.840290651398, -44.82421875 44.840290651398, -44.6484375 44.840290651398, -44.6484375 45.089035564831, -44.82421875 45.089035564831, -45 45.089035564831))
```

{% endtab %}

{% tab title="carto-un-eu" %}

```sql
SELECT `carto-un-eu`.carto.ST_TILEENVELOPE(10,384,368);
-- POLYGON((-45 45.089035564831, -45 44.840290651398, -44.82421875 44.840290651398, -44.6484375 44.840290651398, -44.6484375 45.089035564831, -44.82421875 45.089035564831, -45 45.089035564831))
```

{% endtab %}

{% tab title="manual" %}

```sql
SELECT carto.ST_TILEENVELOPE(10,384,368);
-- POLYGON((-45 45.089035564831, -45 44.840290651398, -44.82421875 44.840290651398, -44.6484375 44.840290651398, -44.6484375 45.089035564831, -44.82421875 45.089035564831, -45 45.089035564831))
```

{% endtab %}
{% endtabs %}

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

* [Census areas in the UK within tiles of multiple resolutions](https://academy.carto.com/advanced-spatial-analytics/spatial-analytics-for-bigquery/step-by-step-tutorials/census-areas-in-the-uk-within-tiles-of-multiple-resolutions)
  {% endhint %}

<img src="https://3029946802-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FybPdpmLltPkzGFvz7m8A%2Fuploads%2Fgit-blob-1c82685e4e434438152a8e3d867df996413489fe%2Feu-flag-website.png?alt=media&#x26;token=4343f6e5-973a-4e9a-8e14-50366a086f72" alt="EU flag" data-size="line">This project has received funding from the [European Union’s Horizon 2020](https://ec.europa.eu/programmes/horizon2020/en) research and innovation programme under grant agreement No 960401.