Extrapolating a line in PostGIS

Question

I'm trying to extrapolate from a line segment to find a point on the line but a 3rd of the way 'back', i.e. trying to find point new, given points A and B below:

Given a line, I can interpolate it to get a position at any particular percentage along it:

=# select st_line_interpolate_point(
   st_makeline('0101000020E6100000300DC347C49418C03EE8D9ACFAA44A40', 
               '0101000020E6100000FB743C66A03218C0CDCCCCCCCC7C4A40'), 
   0.333);
0101000020E6100000ED45B41D537718C069C6A2E9EC984A40

I tried entering a negative number to find a point along the line in the opposite direction, but that fails as the interpolation argument has to be in the range [0, 1]

I thought about first scaling the line, but that doesn't use the centre of the line as the origin, so is useless for my purposes.

Answer 1

Another way I have solved a similar problem previously is to break it down into the following steps.

-- get the points A and B given a line L
A := ST_STARTPOINT(L);
B := ST_ENDPOINT(L);

-- get the bearing from point B --> A
azimuth := ST_AZIMUTH(B,A);

-- get the length of the line A --> B
length := ST_DISTANCE(A,B);
newlength := length + (length * (1/3));   -- increase the line length by 1/3

-- create a new point 1/3 as far away from A as B is from A
newpoint := ST_TRANSLATE(A, sin(azimuth) * newlength, cos(azimuth) * newlength);

EDIT: fixed the assignment of newlength so that it is 1 1/3 the length, rather than 1/3 and switched A & B around to match diagram.

Answer 2

Have solved it with:

F = 1.3333
st_affine(A, F, 0, 
             0, F, 
            (F-1)*-st_x(st_line_interpolate_point(st_makeline(A, B), 0.5)), 
            (F-1)*-st_y(st_line_interpolate_point(st_makeline(A, B), 0.5))
          )

Explanation:

(2-d) Scale the start point by a factor of 1.3333, taking the midpoint of the line segment as the origin for scaling.

Get out the graph paper!

http://en.wikipedia.org/wiki/Affine_transformation

Answer 3

I wrote a function for this:

CREATE OR REPLACE FUNCTION st_extend (
    geom geometry,
    head_rate double precision,
    head_constant double precision,
    tail_rate double precision,
    tail_constant double precision)
  RETURNS geometry AS
$BODY$
-- Extends a linestring.
-- First segment get extended by length * head_rate + head_constant.
-- Last segment get extended by length * tail_rate + tail_constant.
--
-- References:
-- http://blog.cleverelephant.ca/2015/02/breaking-linestring-into-segments.html
-- https://gis.stackexchange.com/a/104451/44921
-- https://gis.stackexchange.com/a/16701/44921
WITH segment_parts AS (
SELECT
(pt).path[1]-1 as segment_num
,
CASE
WHEN
  (nth_value((pt).path, 2) OVER ()) = (pt).path
AND
  (last_value((pt).path) OVER ()) = (pt).path
THEN
  3
WHEN
  (nth_value((pt).path, 2) OVER ()) = (pt).path
THEN
  1
WHEN
  (last_value((pt).path) OVER ()) = (pt).path
THEN
  2
ELSE
  0
END AS segment_flag
,
(pt).geom AS a
,
lag((pt).geom, 1, NULL) OVER () AS b
FROM ST_DumpPoints($1) pt
)
,
extended_segment_parts
AS
(
SELECT
  *
  ,
  ST_Azimuth(a,b) AS az1
  ,
  ST_Azimuth(b,a) AS az2
  ,
  ST_Distance(a,b) AS len
FROM
segment_parts
where b IS NOT NULL
)
,
expanded_segment_parts
AS
(
SELECT
  segment_num
  ,
  CASE
  WHEN
    bool(segment_flag & 2)
  THEN
    ST_Translate(b, sin(az2) * (len*tail_rate+tail_constant), cos(az2) * (len*tail_rate+tail_constant))
  ELSE
    a
  END
  AS a
  ,
  CASE
  WHEN
    bool(segment_flag & 1)
  THEN
    ST_Translate(a, sin(az1) * (len*head_rate+head_constant), cos(az1) * (len*head_rate+head_constant))
  ELSE
    b
  END
  AS b
FROM extended_segment_parts
)
,
expanded_segment_lines
AS
(
SELECT
  segment_num
  ,
  ST_MakeLine(a, b) as geom
FROM
expanded_segment_parts
)
SELECT
  ST_LineMerge(ST_Collect(geom ORDER BY segment_num)) AS geom
FROM expanded_segment_lines
;
$BODY$
LANGUAGE sql;

Usage:

SELECT st_extend(
st_makeline(
  '0101000020E6100000300DC347C49418C03EE8D9ACFAA44A40', 
  '0101000020E6100000FB743C66A03218C0CDCCCCCCCC7C4A40'
),
1.333::double precision,
0::double precision,
1::double precision,
0::double precision
);

Note that this yields the longer linestring but not the endpoint.

Code on GitHub Gist (if you upvote here I would appreciate a star there too)

Description of parameters (in case you missed them in the comment of the sql function):

• First segment length will be original_length * head_rate + head_constant.
• If you want it to get doubled then head rate is 2, constant is 0.
• We in hungary normally use EOV projection which is meter based. So if I want to add 2 meters to the end of the line, i set the tail:rate to 1 and the tail_constant to 2.