The ST_Intersection method finds the spatial intersection of two geometries.
A point is included in the intersection if it is present in both of the input geometries.
If the two geometries don't share any common points, the result is an empty geometry.
If the geometry-expression contains circular strings, then these are interpolated to line strings.
The following example shows the intersection (C) of a square (A) and a circle (B).
SELECT NEW ST_Polygon( 'Polygon( (-1 -0.25, 1 -0.25, 1 2.25, -1 2.25, -1 -0.25) )' ) AS A
, NEW ST_CurvePolygon( 'CurvePolygon( CircularString( 0 1, 1 2, 2 1, 1 0, 0 1 ) )' ) AS B
, A.ST_Intersection( B ) AS C
The intersection is shaded in the following picture. It is a single surface that includes
all of the points that are in the square and also in the circle.