# 12.16.12 Spatial Convenience Functions

The functions in this section provide convenience operations on geometry values.

• Returns the mimimum spherical distance between two points and/or multipoints on a sphere, in meters, or `NULL` if any geometry argument is `NULL` or empty.

Calculations use a spherical earth and a configurable radius. The optional `radius` argument should be given in meters. If omitted, the default radius is 6,370,986 meters. An `ER_WRONG_ARGUMENTS` error occurs if the `radius` argument is present but not positive.

The geometry arguments should consist of points that specify (longitude, latitude) coordinate values:

• Longitude and latitude are the first and second coordinates of the point, respectively.

• Both coordinates are in degrees.

• Longitude values must be in the range (-180, 180]. Positive values are east of the prime meridian.

• Latitude values must be in the range [-90, 90]. Positive values are north of the equator.

Supported argument combinations are (`Point`, `Point`), (`Point`, `MultiPoint`), and (`MultiPoint`, `Point`). An `ER_GIS_UNSUPPORTED_ARGUMENT` error occurs for other combinations.

If any geometry argument is not a syntactically well-formed geometry byte string, an `ER_GIS_INVALID_DATA` error occurs.

``````mysql> SET @pt1 = ST_GeomFromText('POINT(0 0)');
mysql> SET @pt2 = ST_GeomFromText('POINT(180 0)');
mysql> SELECT ST_Distance_Sphere(@pt1, @pt2);
+--------------------------------+
| ST_Distance_Sphere(@pt1, @pt2) |
+--------------------------------+
|             20015042.813723423 |
+--------------------------------+``````
• Returns 1 if the argument is syntactically well-formed and is geometrically valid, 0 if the argument is not syntactically well-formed or is not geometrically valid. If the argument is `NULL`, the return value is `NULL`. Geometry validity is defined by the OGC specification.

The only valid empty geometry is represented in the form of an empty geometry collection value. `ST_IsValid()` returns 1 in this case.

`ST_IsValid()` works only for the Cartesian coordinate system and requires a geometry argument with an SRID of 0. An `ER_WRONG_ARGUMENTS` error occurs otherwise.

``````mysql> SET @ls1 = ST_GeomFromText('LINESTRING(0 0,-0.00 0,0.0 0)');
mysql> SET @ls2 = ST_GeomFromText('LINESTRING(0 0, 1 1)');
mysql> SELECT ST_IsValid(@ls1);
+------------------+
| ST_IsValid(@ls1) |
+------------------+
|                0 |
+------------------+
mysql> SELECT ST_IsValid(@ls2);
+------------------+
| ST_IsValid(@ls2) |
+------------------+
|                1 |
+------------------+``````
• Returns the rectangle that forms the envelope around two points, as a `Point`, `LineString`, or `Polygon`. If any argument is `NULL`, the return value is `NULL`.

Calculations are done using the Cartesian coordinate system rather than on a sphere, spheroid, or on earth.

Given two points `pt1` and `pt2`, `ST_MakeEnvelope()` creates the result geometry on an abstract plane like this:

• If `pt1` and `pt2` are equal, the result is the point `pt1`.

• Otherwise, if `(pt1, pt2)` is a vertical or horizontal line segment, the result is the line segment `(pt1, pt2)`.

• Otherwise, the result is a polygon using `pt1` and `pt2` as diagonal points.

The result geometry has an SRID of 0.

`ST_MakeEnvelope()` requires `Point` geometry arguments with an SRID of 0. An `ER_WRONG_ARGUMENTS` error occurs otherwise.

If any argument is not a syntactically well-formed geometry byte string, or if any coordinate value of the two points is infinite or `NaN`, an `ER_GIS_INVALID_DATA` error occurs.

``````mysql> SET @pt1 = ST_GeomFromText('POINT(0 0)');
mysql> SET @pt2 = ST_GeomFromText('POINT(1 1)');
mysql> SELECT ST_AsText(ST_MakeEnvelope(@pt1, @pt2));
+----------------------------------------+
| ST_AsText(ST_MakeEnvelope(@pt1, @pt2)) |
+----------------------------------------+
| POLYGON((0 0,1 0,1 1,0 1,0 0))         |
+----------------------------------------+``````
• Simplifies a geometry using the Douglas-Peucker algorithm and returns a simplified value of the same type. If any argument is `NULL`, the return value is `NULL`.

The geometry may be any geometry type, although the Douglas-Peucker algorithm may not actually process every type. A geometry collection is processed by giving its components one by one to the simplification algorithm, and the returned geometries are put into a geometry collection as result.

The `max_distance` argument is the distance (in units of the input coordinates) of a vertex to other segments to be removed. Vertices within this distance of the simplified linestring are removed. If the `max_distance` argument is not positive, or is `NaN`, an `ER_WRONG_ARGUMENTS` error occurs.

According to Boost.Geometry, geometries might become invalid as a result of the simplification process, and the process might create self-intersections. To check the validity of the result, pass it to `ST_IsValid()`.

If the geometry argument is not a syntactically well-formed geometry byte string, an `ER_GIS_INVALID_DATA` error occurs.

``````mysql> SET @g = ST_GeomFromText('LINESTRING(0 0,0 1,1 1,1 2,2 2,2 3,3 3)');
mysql> SELECT ST_AsText(ST_Simplify(@g, 0.5));
+---------------------------------+
| ST_AsText(ST_Simplify(@g, 0.5)) |
+---------------------------------+
| LINESTRING(0 0,0 1,1 1,2 3,3 3) |
+---------------------------------+
mysql> SELECT ST_AsText(ST_Simplify(@g, 1.0));
+---------------------------------+
| ST_AsText(ST_Simplify(@g, 1.0)) |
+---------------------------------+
| LINESTRING(0 0,3 3)             |
+---------------------------------+``````
• Validates a geometry according to the OGC specification. A geometry can be syntactically well-formed (WKB value plus SRID) but geometrically invalid. For example, this polygon is geometrically invalid: `POLYGON((0 0, 0 0, 0 0, 0 0, 0 0))`

`ST_Validate()` returns the geometry if it is syntactically well-formed and is geometrically valid, `NULL` if the argument is not syntactically well-formed or is not geometrically valid or is `NULL`.

`ST_Validate()` can be used to filter out invalid geometry data, although at a cost. For applications that require more precise results not tainted by invalid data, this penalty may be worthwhile.

If the geometry argument is valid, it is returned as is, except that if an input `Polygon` or `MultiPolygon` has clockwise rings, those rings are reversed before checking for validity. If the geometry is valid, the value with the reversed rings is returned.

The only valid empty geometry is represented in the form of an empty geometry collection value. `ST_Validate()` returns it directly without further checks in this case.

`ST_Validate()` works only for the Cartesian coordinate system and requires a geometry argument with an SRID of 0. An `ER_WRONG_ARGUMENTS` error occurs otherwise.

``````mysql> SET @ls1 = ST_GeomFromText('LINESTRING(0 0)');
mysql> SET @ls2 = ST_GeomFromText('LINESTRING(0 0, 1 1)');
mysql> SELECT ST_AsText(ST_Validate(@ls1));
+------------------------------+
| ST_AsText(ST_Validate(@ls1)) |
+------------------------------+
| NULL                         |
+------------------------------+
mysql> SELECT ST_AsText(ST_Validate(@ls2));
+------------------------------+
| ST_AsText(ST_Validate(@ls2)) |
+------------------------------+
| LINESTRING(0 0,1 1)          |
+------------------------------+``````