wm/wm.sql

242 lines
7.5 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 $$
declare
pi real;
p geometry;
p1 geometry;
p2 geometry;
p3 geometry;
bend geometry;
prev_sign int4;
cur_sign int4;
begin
pi = radians(180);
-- the last vertex is iterated over twice, because the algorithm uses 3 vertices
-- to calculate the angle between them.
--
-- Given 3 vertices p1, p2, p3:
--
-- p1___ ...
-- /
-- ... _____/
-- p3 p2
--
-- When looping over the line, p1 will be head (lead) vertex, p2 will be the
-- measured angle, and p3 will be trailing. The line that will be added to
-- the bend will always be [p3,p2].
-- So once the p1 becomes the last vertex, the loop terminates, and the
-- [p2,p1] line will not have a chance to be added. So the loop adds the last
-- vertex twice, so it has a chance to become p2, and be added to the bend.
--
for p in (
(select geom from st_dumppoints(line) order by path[1] asc)
union all
(select geom from st_dumppoints(line) order by path[1] desc limit 1)
) loop
p3 = p2;
p2 = p1;
p1 = p;
continue when p3 is null;
cur_sign = sign(pi - st_angle(p1, p2, p2, p3));
if bend is null then
bend = st_makeline(p3, p2);
else
bend = st_linemerge(st_union(bend, st_makeline(p3, p2)));
end if;
if prev_sign + cur_sign = 0 then
if bend is not null then
bends = bends || bend;
end if;
bend = st_makeline(p3, p2);
end if;
prev_sign = cur_sign;
end loop;
-- the last line may be lost if there is no "final" inflection angle. Add it.
if (select count(1) >= 2 from st_dumppoints(bend)) then
bends = bends || bend;
end if;
end
$$ 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).
--
-- The implementation could be significantly optimized to avoid `st_reverse`
-- and array reversals, trading for complexity in fix_gentle_inflections1.
create or replace function fix_gentle_inflections(INOUT bends geometry[]) as $$
declare
len int4;
bends1 geometry[];
begin
len = array_length(bends, 1);
bends = fix_gentle_inflections1(bends);
for i in 1..len loop
bends1[i] = st_reverse(bends[len-i+1]);
end loop;
bends1 = fix_gentle_inflections1(bends1);
for i in 1..len loop
bends[i] = st_reverse(bends1[len-i+1]);
end loop;
end
$$ language plpgsql;
-- fix_gentle_inflections1 fixes gentle inflections of an array of lines in
-- one direction. This is an implementation detail of fix_gentle_inflections.
create or replace function fix_gentle_inflections1(INOUT bends geometry[]) as $$
declare
pi real;
small_angle real;
ptail geometry; -- tail point of tail bend
phead geometry[]; -- 3 tail points of head bend
i int4; -- bends[i] is the current head
begin
pi = radians(180);
-- the threshold when the angle is still "small", so gentle inflections can
-- be joined
small_angle := radians(30);
for i in 2..array_length(bends, 1) loop
-- Predicate: two bends will always share an edge. Assuming (A,B,C,D,E,F)
-- is a bend:
-- C________D
-- / \
-- \________/ \_______/
-- A B E F
--
-- Then edges (A,B) and (E,F) are shared with the neighboring bends.
--
--
-- Assume this curve (figure `inflection-1`), going clockwise from A:
--
-- \______B
-- A `-------. C
-- |
-- G___ F |
-- / `-----.____+ D
-- E
--
-- After processing the curve following the definition of a bend, the bend
-- [A-E] would be detected. Assuming inflection point E and F are "small",
-- the bend needs to be extended by two edges to [A,G].
select geom from st_dumppoints(bends[i-1])
order by path[1] asc limit 1 into ptail;
while true loop
-- copy last 3 points of bends[i-1] (tail) to ptail
select array(
select geom from st_dumppoints(bends[i]) order by path[1] asc limit 3
) into phead;
-- if the bend got too short, stop processing it
exit when array_length(phead, 1) < 3;
-- if inflection angle between ptail[1:3] "large", stop processing this bend
exit when abs(st_angle(phead[1], phead[2], phead[3]) - pi) > small_angle;
-- distance from head's first vertex should be larger than from second vertex
exit when st_distance(ptail, phead[2]) < st_distance(ptail, phead[3]);
-- detected a gentle inflection. Move head of the tail to the tail of head
bends[i] = st_removepoint(bends[i], 0);
bends[i-1] = st_addpoint(bends[i-1], phead[3]);
end loop;
end loop;
end
$$ language plpgsql;
-- self_crossing eliminates self-crossing from the bends, following the
-- article's section "Self-line Crossing When Cutting a Bend".
create or replace function self_crossing(INOUT bends geometry[]) as $$
declare
i int4;
j int4;
pi real;
angle real;
p0 geometry;
p1 geometry;
p2 geometry;
p3 geometry;
s2 real;
s3 real;
bend geometry;
this geometry;
multi geometry;
begin
pi = radians(180);
-- go through the bends and find one where sum of inflection angle is >180
for i in 1..array_length(bends, 1) loop
angle = 0;
p1 = null;
p2 = null;
p3 = null;
for p0 in (select geom from st_dumppoints(bends[i]) order by path[1] asc) loop
p3 = p2;
p2 = p1;
p1 = p0;
continue when p3 is null;
angle = angle + abs(pi - st_angle(p1, p2, p3));
end loop;
continue when abs(angle) <= pi;
-- sum of inflection angles for this bend is >180, so it may be self-crossing.
-- now try to find another bend in this line that crosses this one.
p0 = st_pointn(bends[i], 1);
p1 = st_pointn(bends[i], -1);
-- go through each bend in this line, and see if has a potential to cross bends[i].
-- optimization: we care only about bends which beginning and end start at different
-- sides of the plane, separated by endpoints p0 and p1.
for j in 1..array_length(bends, 1) loop
continue when i = j;
p2 = st_pointn(bends[j], 1);
p3 = st_pointn(bends[j], -1);
-- are p2 and p3 on the same side of (p0,p1)? vector multiplication
-- https://stackoverflow.com/questions/1560492/
s2 = (st_x(p0)-st_x(p1)*(st_y(p2)-st_y(p1))-(st_y(p0)-st_y(p1))*(st_x(p2)-st_x(p1)));
s3 = (st_x(p0)-st_x(p1)*(st_y(p3)-st_y(p1))-(st_y(p0)-st_y(p1))*(st_x(p3)-st_x(p1)));
continue when sign(s2) = sign(s3);
-- do end vertices of bend[i] cross bend[j]?
this = st_makeline(st_pointn(bends[i], 1), st_pointn(bends[i], -1));
multi = st_split(bends[j], this);
continue when st_numgeometries(multi) = 1;
-- self-crossing detected!
-- if j < i:
-- bends[j] = multi[1][1...n-1]; that will have all the vertices of bends[j],
-- except the crossing itself.
-- bends[j] = append(bends[j], bends[i][-1])
-- remove bends from bends[j+1] to bends[i] inclusive.
-- elif j > i:
-- remove bends from bends[i+1] to bends[j-1] inclusive.
-- bends[j] = multi[2][2..n]
-- bends[i]
end loop;
end loop;
end
$$ language plpgsql;