ST_Distance_Sphere(g1, g2 [, radius])

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:

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 |
+--------------------------------+

ST_IsValid(g)

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 |
+------------------+

ST_MakeEnvelope(pt1, pt2)

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:

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))         |
+----------------------------------------+

ST_Simplify(g, max_distance)

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)             |
+---------------------------------+

ST_Validate(g)

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)          |
+------------------------------+