ST_ConvexHull
ST_ConvexHull returns a geometry that represents the convex hull of the nonempty points contained in the input geometry.
For empty input, the resulting geometry is the same as the input geometry.
For all nonempty input, the function operates on the 2D projection of the input geometry.
However, the dimension of the output geometry depends on the dimension of the input geometry.
More specifically, when the input geometry is a nonempty 3DM or 3D geometry, m
coordinates are dropped.
That is, the dimension of the returned geometry is 2D or 3DZ, respectively.
If the input is a nonempty 2D or 3DZ geometry, the resulting geometry has the same dimension.
Syntax
ST_ConvexHull(geom)
Arguments
 geom

A value of data type
GEOMETRY
or an expression that evaluates to aGEOMETRY
type.
Return type
GEOMETRY
The spatial reference system identifier (SRID) value of the returned geometry is the SRID value of the input geometry.
If geom is null, then null is returned.
The values returned are as follows.
Number of points on the convex hull  Geometry subtype 

0 
A copy of geom is returned. 
1 
A 
2 
A 
3 or greater 
A 
Examples
The following SQL returns the extended wellknown text (EWKT) representation of a linestring. In this case, the convex hull returned is a polygon.
SELECT ST_AsEWKT(ST_ConvexHull(ST_GeomFromText('LINESTRING(0 0,1 0,0 1,1 1,0.5 0.5)'))) as output;
output

POLYGON((0 0,0 1,1 1,1 0,0 0))
The following SQL returns the EWKT representation of a linestring. In this case, the convex hull returned is a linestring.
SELECT ST_AsEWKT(ST_ConvexHull(ST_GeomFromText('LINESTRING(0 0,1 1,0.2 0.2,0.6 0.6,0.5 0.5)'))) as output;
output

LINESTRING(0 0,1 1)
The following SQL returns the EWKT representation of a multipoint. In this case, the convex hull returned is a point.
SELECT ST_AsEWKT(ST_ConvexHull(ST_GeomFromText('MULTIPOINT(0 0,0 0,0 0)'))) as output;
output

POINT(0 0)