STIntersection (geometry Data Type)
Applies to: 
SQL Server
Azure SQL Database
Azure SQL Managed Instance
Returns an object that represents the points where a geometry instance intersects another geometry instance.
Syntax
.STIntersection ( other_geometry )
Arguments
other_geometry
Is another geometry instance to compare with the instance on which STIntersection() is being invoked, to determine where they intersect.
Return Types
SQL Server return type: geometry
CLR return type: SqlGeometry
Remarks
STIntersection() always returns null if the spatial reference IDs (SRIDs) of the geometry instances do not match. The result may contain circular arc segments only if the input instances contain them.
Examples
A. Using STIntersection() on Polygon instances
The following example uses STIntersection() to compute the intersection of two polygons.
DECLARE @g geometry;
DECLARE @h geometry;
SET @g = geometry::STGeomFromText('POLYGON((0 0, 0 2, 2 2, 2 0, 0 0))', 0);
SET @h = geometry::STGeomFromText('POLYGON((1 1, 3 1, 3 3, 1 3, 1 1))', 0);
SELECT @g.STIntersection(@h).ToString();
B. Using STIntersection() with CurvePolygon instance
The following example returns an instance that contains a circular arc segment.
DECLARE @g geometry = 'CURVEPOLYGON (CIRCULARSTRING (0 -4, 4 0, 0 4, -4 0, 0 -4))';
DECLARE @h geometry = 'POLYGON ((1 -1, 5 -1, 5 3, 1 3, 1 -1))';
SELECT @h.STIntersection(@g).ToString();