How to find LINESTRINGs that touch in a begin/ending node - postgresql

Question

In PostGIS you can intersect two geometries using:
geometry ST_Intersection (geometry geomA, geometry geomB);
In my case both geomA and geomB are LINESTRING so ST_Intersection() returns a POINT geometry.
I want to know if the intersection occurs in a begin/end node (the geometries touch) or in the middle (the geometries intersect).
I can compare the (Point.X, Point.Y) with each ending node:
geomA.nodes(0) - geomA.nodes(len-1)
geomB.nodes(0) - geomB.nodes(len-1)
But is very complex. And I would like a simple solution.
There are 3 intersect cases.
Example 1: Two lines in a "L" shape intersect in an end node on both lines on the bottom left.
Example 2: Two lines in a "T" shape where the vertical line intersects in the middle of the horizontal line. In this case the vertical line end node touches a non-end node of the horizontal line.
Example 3: Two lines in a "X" shape. Intersection point isn't an end node for either line.
For my problem I'm only interested in finding the touching scenario like Example 2.
NOTE
This is the pseudo code I use now.
geomM, geomN Linestring
a, b, c, d, z Points.
(a,b) begin/end node for geomM ST_StartPoint(geom) and ST_EndPoint(geom)
(c,d) begin/end node for geomN
z = ST_Intersect(geomM, geomN)
SELECT geomM, geomN, z
FROM Table
WHERE
(A and not ( B or C or D))
OR (B and not ( A or C or D))
OR (C and not ( A or B or D))
OR (D and not ( A or B or C))
A, B, C, D replace ( a=z ) ( b=z ) ( c=z ) ( d=z )
This mean one node {a,b,c,d} is equal to intersection z. But only one
This return all "T" shape intersections.

Answer 1

You need the PostGIS function ST_Touches() here. The function returns true if the geometries touch on their boundaries, but false if they intersect. In terms of your examples, Example 1 and 2 return true, Example 3 returns false.
Relaxed solution
To select the IDs of all pairs of touching geometry(LINESTRING, xxx) records from a single table use this:
SELECT x.id AS idA, y.id AS idB
FROM my_table x
JOIN my_table y ON ST_Touches(y.the_geom, x.the_geom)
WHERE x.id < y.id;
(The WHERE clause avoids duplicate results like (132, 254) and (254, 132).)
Note that the linestrings can also touch on any of their non-node vertices. If you want to strictly follow Example 2 then you have to compare every point on every linestring against every point on all other linestrings, which is obviously going to be a very intensive operation. Example 2 is basically only feasible when you know that the linestrings are very short, preferably just straight lines.
Strict solution, straight lines only
If all LINESTRINGs are straight, i.e. composed of a starting and an ending node only, then this is your solution:
SELECT h.id AS touched, v.id AS touching, ST_Intersection(h.the_geom, v.the_geom) AS touch_point
FROM my_table h -- "horizontal" T bar, being touched
JOIN my_table v ON -- "vertical" T bar, touching
(
-- The "vertical" start node touches, but not on either of the "horizonal" nodes
ST_Equals(ST_Intersection(h.the_geom, v.the_geom), ST_StartPoint(v.the_geom))
AND NOT ST_Equals(ST_StartPoint(h.the_geom), ST_StartPoint(v.the_geom))
AND NOT ST_Equals(ST_EndPoint(h.the_geom), ST_StartPoint(v.the_geom))
) OR (
-- The "vertical" end node touches, but not on either of the "horizonal" nodes
ST_Equals(ST_Intersection(h.the_geom, v.the_geom), ST_EndPoint(v.the_geom))
AND NOT ST_Equals(ST_StartPoint(h.the_geom), ST_EndPoint(v.the_geom))
AND NOT ST_Equals(ST_EndPoint(h.the_geom), ST_EndPoint(v.the_geom))
);
All the requirements are checked in the JOIN ON clause. This will also return the location where the "vertical" bar of the T touches the "horizontal" bar. Note that the conditions are short-circuited when being evaluated and repeated calls to a function with the same input data are optimized to a single call.