CREATE TABLE linestring_test (line ST_LineString);

-- Create a U-shaped linestring:
INSERT INTO linestring_test VALUES (
   ST_LineFromText('linestring z (0 10 1, 0 0 3, 10 0 5, 10 10 7)', 0)
);

-- Perpendicular point is coincident with the input point,
-- on the base of the U:
SELECT SE_PerpendicularPoint(line, ST_PointFromText('point(5 0)', 0))
  FROM linestring_test;

-- Perpendicular points are located on all three segments of the U:
SELECT SE_PerpendicularPoint(line, ST_PointFromText('point(5 5)', 0))
  FROM linestring_test;

-- Perpendicular points are located at the endpoints of the U:
SELECT SE_PerpendicularPoint(line, ST_PointFromText('point(5 10)', 0))
  FROM linestring_test;

-- Perpendicular point is on the base of the U:
SELECT SE_PerpendicularPoint(line, ST_PointFromText('point(5 15)', 0))
  FROM linestring_test;

-- No perpendicular point can be constructed:
SELECT SE_PerpendicularPoint(line, ST_PointFromText('point(15 15)', 0))
  FROM linestring_test;