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