Intersection of 2 Linestrings (not interpolated)

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I am struggling with a query in POSTGIS

I want to find linestring geometries where the geometries are containing the same point.

I don't want to calculate the intersection points. I only want to get a point, if the point is a real member of both geometries.

Example

SELECT ST_AsText(ST_Function(ST_GeomFromText('LINESTRING(1 2, 2 2, 0 0)'), ST_GeomFromText('LINESTRING(0 1, 2 2, 3 0)') ) )

should return

POINT(2 2)

and

SELECT ST_AsText(ST_Function(ST_GeomFromText('LINESTRING(1 2, 10 10)'), ST_GeomFromText('LINESTRING(1 1, 2 2, 3 3)') ) )

should return

EMPTY

or something similiar for empty.

How can I achieve that in a single query?

I tried to use ST_Intersection(), but this one calculates the point (which is wrong to my requirements).

Any help would be appreciated.



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