| 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 . 

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()  handles its arguments as described in the introduction to this section, with these exceptions: 

•If the arguments are not Point  values, an ER_WRONG_ARGUMENTS  error occurs. 

•An ER_GIS_INVALID_DATA  error occurs for the additional condition that any coordinate value of the two points is infinite or NaN . 

•If any geometry has an SRID value for a geographic spatial reference system (SRS), an ER_NOT_IMPLEMENTED_FOR_GEOGRAPHIC_SRS  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. 

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. 

