wm/wm.sql

139 lines
4.3 KiB
PL/PgSQL

\set ON_ERROR_STOP on
SET plpgsql.extra_errors TO 'all';
drop function if exists detect_bends;
-- detect_bends detects bends using the inflection angles. It does not do corrections.
create or replace function detect_bends(line geometry, OUT bends geometry[]) as $$
declare
pi real;
p geometry;
p1 geometry;
p2 geometry;
p3 geometry;
bend geometry;
prev_sign int4;
cur_sign int4;
begin
pi = radians(180);
-- the last vertex is iterated over twice, because the algorithm uses 3 vertices
-- to calculate the angle between them.
--
-- Given 3 vertices p1, p2, p3:
--
-- p1___ ...
-- /
-- ... _____/
-- p3 p2
--
-- When looping over the line, p1 will be head (lead) vertex, p2 will be the
-- measured angle, and p3 will be trailing. The line that will be added to
-- the bend will always be [p3,p2].
-- So once the p1 becomes the last vertex, the loop terminates, and the
-- [p2,p1] line will not have a chance to be added. So the loop adds the last
-- vertex twice, so it has a chance to become p2, and be added to the bend.
--
for p in (
(select geom from st_dumppoints(line) order by path[1] asc)
union all
(select geom from st_dumppoints(line) order by path[1] desc limit 1)
) loop
p3 = p2;
p2 = p1;
p1 = p;
if p3 is null then
continue;
end if;
cur_sign = sign(pi - st_angle(p1, p2, p2, p3));
if bend is null then
bend = st_makeline(p3, p2);
else
bend = st_linemerge(st_union(bend, st_makeline(p3, p2)));
end if;
if prev_sign + cur_sign = 0 then
if bend is not null then
bends = bends || bend;
end if;
bend = st_makeline(p3, p2);
end if;
prev_sign = cur_sign;
end loop;
-- the last line may be lost if there is no "final" inflection angle. Add it.
if (select count(1) >= 2 from st_dumppoints(bend)) then
bends = bends || bend;
end if;
end
$$ language plpgsql;
-- fix_gentle_inflections moves bend endpoints following "Gentle Inflection at
-- End of a Bend" section.
--
-- The text does not specify how many vertices can be "adjusted"; it can
-- equally be one or many. This function is adjusting many, as long as the
-- commulative inflection angle small (see variable below).
create or replace function fix_gentle_inflections(INOUT bends geometry[]) as $$
declare
small_angle real;
phead geometry; -- head point of head bend
ptail geometry[]; -- 3 head points of tail bend
i int4; -- bends[i] is the current head
begin
-- the threshold when the angle is still "small", so gentle inflections can
-- be joined
small_angle := radians(30);
<<bend_loop>>
for i in select generate_subscripts(bends, 1) loop
if i = 1 then
continue;
end if;
-- Predicate: two bends will always share an edge. Assuming (A,B,C,D,E,F)
-- is a bend:
-- C________D
-- / \
-- \________/ \_______/
-- A B E F
--
-- Then edges (A,B) and (E,F) are shared with the neighboring bends.
--
--
-- Assume this curve (figure `inflection-1`):
--
-- \______B
-- A `-------. C
-- |
-- G___ F |
-- / `-----.____+ D
-- E
--
-- After processing the curve following the definition of a bend, the bend
-- [A-E] would be detected. Assuming inflection point E and F are "small",
-- the bend needs to be extended by two edges to [A,G].
select geom from st_dumppoints(bends[i]) order by path[1] desc limit 1 into phead;
while true loop
-- copy last 3 points of bends[i-1] (tail) to ptail
select array_agg(geom) from st_dumppoints(bends[i-1]) order by path[1] desc limit 3 into ptail;
-- if inflection angle between ptail[1:3] "large", stop processing this bend
if abs(st_angle(ptail[1], ptail[2], ptail[2], ptail[3]) - pi) > small_angle then
exit bend_loop;
end if;
-- distance from last vertex should be larger than second-last vertex
if st_distance(phead, ptail[2]) < st_distance(phead, ptail[3]) then
exit bend_loop;
end if;
-- detected a gentle inflection. Move head of the tail to the tail of head
bends[i] = st_addpoint(bends[i], ptail[3]);
bends[i-1] = st_removepoint(bends[i-1], st_npoints(bends[i-1])-1);
end loop;
end loop;
end
$$ language plpgsql;