postgresql - Get the lines between all points of a polygon in PostGis : avoid nested loop?

I am trying to get all the lines between the points of a polygon, by writing PostGreSQL functions. I have written the two following functions that do the job fine :

• the first function to get all the points from the polygon

CREATE OR REPLACE FUNCTION PointsFromPolygon(polygon geometry) 
RETURNS SETOF geometry AS
$$
DECLARE
    point geometry;
BEGIN

FOR point IN SELECT DISTINCT points.geom FROM ( SELECT (ST_DumpPoints(polygon)).* ) AS points LOOP
    RETURN NEXT point;
END LOOP;
END;
$$
LANGUAGE plpgsql ;

• the second function to create all segments between these points.

CREATE OR REPLACE FUNCTION AllSegmentsFromPoints(polygon geometry)
RETURNS SETOF geometry AS
$$
DECLARE
    point1 geometry;
    point2 geometry;
    i integer;
BEGIN
i:=1;

    FOR point1 IN SELECT * FROM PointsFromPolygon(polygon) LOOP
        FOR point2 IN SELECT * FROM PointsFromPolygon(polygon) OFFSET i LOOP
            RETURN NEXT ST_MakeLine(point1,point2);
        END LOOP;
    i:= i+1;
    END LOOP;
END;
$$
LANGUAGE plpgsql;

Is there a better way to perform this ? Perhaps by doing a cartesian product between the points ?

Answer

I think I found my answer :

 WITH poly_geom1 AS (SELECT way FROM planet_osm_polygon WHERE id=1),
      poly_geom2 AS (SELECT way FROM planet_osm_polygon WHERE id=1),
      points1 AS (SELECT (ST_DumpPoints(poly_geom1.way)).* FROM poly_geom1),
      points2 AS (SELECT (ST_DumpPoints(poly_geom2.way)).* FROM poly_geom2)
 SELECT DISTINCT ST_MakeLine(points1.geom, points2.geom)
 FROM points1,points2
 WHERE points1.path <> points2.path;

Execution time for a 40 points polygon goes down from 135ms to 115ms.

Update

Thank to simplexio, the following query does exactly the same and is shorter :

WITH poly_geom AS (SELECT way FROM planet_osm_polygon WHERE id=1),
     points1 AS (SELECT (ST_DumpPoints(poly_geom.way)).* FROM poly_geom),
     points2 AS (SELECT (ST_DumpPoints(poly_geom.way)).* FROM poly_geom)
SELECT DISTINCT ST_MakeLine(points1.geom, points2.geom)
FROM points1,points2
WHERE points1.path <> points2.path;