wm/wm.sql

385 lines
12 KiB
PL/PgSQL

\set ON_ERROR_STOP on
SET plpgsql.extra_errors TO 'all';
-- detect_bends detects bends using the inflection angles. No corrections.
drop function if exists detect_bends;
create 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.
drop function if exists fix_gentle_inflections1;
create function fix_gentle_inflections1(INOUT bends geometry[]) as $$
declare
pi real;
small_angle real;
ptail geometry; -- tail point of tail bend
phead geometry[]; -- 3 tail points of head bend
i int4; -- bends[i] is the current head
begin
pi = radians(180);
-- the threshold when the angle is still "small", so gentle inflections can
-- be joined
small_angle := radians(30);
for i in 2..array_length(bends, 1) loop
-- Predicate: two bends will always share an edge. Assuming (A,B,C,D,E,F)
-- is a bend:
-- C________D
-- / \
-- \________/ \_______/
-- A B E F
--
-- Then edges (A,B) and (E,F) are shared with the neighboring bends.
--
--
-- Assume this curve (figure `inflection-1`), going clockwise from A:
--
-- \______B
-- A `-------. C
-- |
-- G___ F |
-- / `-----.____+ D
-- E
--
-- After processing the curve following the definition of a bend, the bend
-- [A-E] would be detected. Assuming inflection point E and F are "small",
-- the bend needs to be extended by two edges to [A,G].
select geom from st_dumppoints(bends[i-1])
order by path[1] asc limit 1 into ptail;
while true loop
-- copy last 3 points of bends[i-1] (tail) to ptail
select array(
select geom from st_dumppoints(bends[i]) order by path[1] asc limit 3
) into phead;
-- if the bend got too short, stop processing it
exit when array_length(phead, 1) < 3;
-- inflection angle between ptail[1:3] is "large", stop processing
exit when abs(st_angle(phead[1], phead[2], phead[3]) - pi) > small_angle;
-- distance from head's 1st vertex should be larger than from 2nd vertex
exit when st_distance(ptail, phead[2]) < st_distance(ptail, phead[3]);
-- Detected a gentle inflection.
-- Move head of the tail to the tail of head
bends[i] = st_removepoint(bends[i], 0);
bends[i-1] = st_addpoint(bends[i-1], phead[3]);
end loop;
end loop;
end
$$ language plpgsql;
-- self_crossing eliminates self-crossing from the bends, following the
-- article's section "Self-line Crossing When Cutting a Bend".
drop function if exists self_crossing;
create function self_crossing(
INOUT bends geometry[],
OUT mutated boolean
) as $$
declare
i int4;
j int4;
prev_length int4;
pi real;
angle real;
p0 geometry;
p1 geometry;
p2 geometry;
p3 geometry;
a geometry;
b geometry;
bend geometry;
multi geometry;
begin
pi = radians(180);
mutated = false;
-- 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 an imaginary line of end-vertices
p0 = st_pointn(bends[i], 1);
p1 = st_pointn(bends[i], -1);
-- go through each bend in the given 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.
j = 0;
while j < array_length(bends, 1) loop
j = j + 1;
continue when i = j;
p2 = st_pointn(bends[j], 1);
p3 = st_pointn(bends[j], -1);
-- do end vertices of bend[i] cross bend[j]?
a = st_pointn(bends[i], 1);
b = st_pointn(bends[i], -1);
multi = st_split(bends[j], st_makeline(a, b));
continue when st_numgeometries(multi) = 1;
continue when st_numgeometries(multi) = 2 and
(st_contains(bends[j], a) or st_contains(bends[j], b));
-- stars are aligned, we are changing the bend
mutated = true;
-- Sincere apologies to someone who will need to debug the block below.
-- To understand it, I suggest you take a pencil and paper, draw a
-- self-crossing bend (fig6 from the article works well), and figure out
-- what happens here, by hand.
prev_length = array_length(bends, 1);
if j < i then
-- remove first vertex of the following bend, because the last
-- segment is always duplicated with the i-th bend.
bends[i+1] = st_removepoint(bends[i+1], 0);
bends[j] = st_geometryn(multi, 1);
bends[j] = st_setpoint(
bends[j], st_npoints(bends[j])-1,
st_pointn(bends[i], st_npoints(bends[i]))
);
bends = bends[1:j] || bends[i+1:prev_length];
j = i;
else
-- remove last vertex of the previous bend, because the last
-- segment is duplicated with the i'th bend.
bends[i-1] = st_removepoint(bends[i-1], st_npoints(bends[i-1])-1);
bends[i] = st_makeline(
st_pointn(bends[i], 1),
st_removepoint(st_geometryn(multi, st_numgeometries(multi)), 0)
);
bends = bends[1:i] || bends[j+1:prev_length];
end if;
j = j - prev_length + array_length(bends, 1);
end loop;
end loop;
end
$$ language plpgsql;
drop function if exists bend_attrs;
create function bend_attrs(bends geometry[], dbg boolean default false) returns table(bend geometry, area real, cmp real, adjsize real) as $$
declare
i int4;
fourpi real;
polygon geometry;
begin
fourpi = 4*radians(180);
for i in 1..array_length(bends, 1) loop
bend = bends[i];
select st_makepolygon(st_addpoint(bend, st_startpoint(bend))) into polygon;
-- Compactness Index (cmp) is defined as "the ratio of the area of the
-- polygon over the circle whose circumference length is the same as the
-- length of the circumference of the polygon". I assume they meant the
-- area of the circle. So here goes:
-- 1. get polygon area P.
-- 2. get polygon perimeter = u. Pretend it's our circle's circumference.
-- 3. get A (area) of the circle from circumference u := (u^2)/(4*pi)
-- 4. divide area by A: cmp = P/((u^2)*4*pi) = 4*pi*P/u^2
select st_area(polygon) into area;
select fourpi*area/(st_perimeter(polygon)^2) into cmp;
if cmp > 0 then
select (area*(0.75/cmp)) into adjsize;
end if;
if dbg then
insert into debug_wm (name, way, props) values(
'bend_attrs_' || i,
polygon,
json_build_object('area', area, 'cmp', cmp, 'adjsize', adjsize)
);
end if;
return next;
end loop;
end;
$$ language plpgsql;
-- ST_SimplifyWM simplifies a given geometry using Wang & Müller's
-- "Line Generalization Based on Analysis of Shape Characteristics" algorithm,
-- 1998.
drop function if exists ST_SimplifyWM;
create function ST_SimplifyWM(geom geometry, dbg boolean default false) returns geometry as $$
declare
dbg_stage integer;
i integer;
line geometry;
lines geometry[];
bends geometry[];
mutated boolean;
l_type text;
begin
l_type = st_geometrytype(geom);
if l_type = 'ST_LineString' then
lines = array[geom];
elseif l_type = 'ST_MultiLineString' then
lines = array((select a.geom from st_dump(geom) a order by path[1] asc));
else
raise 'Unknown geometry type %', l_type;
end if;
for i in 1..array_length(lines, 1) loop
mutated = true;
dbg_stage = 1;
while mutated loop
if dbg then
insert into debug_wm (name, way) values(
dbg_stage || 'afigures_' || i,
lines[i]
);
end if;
bends = detect_bends(lines[i]);
if dbg then
insert into debug_wm(name, way) values(
dbg_stage || 'bbends_' || i || '_' || generate_subscripts(bends, 1),
unnest(bends)
);
end if;
bends = fix_gentle_inflections(bends);
if dbg then
insert into debug_wm(name, way) values(
dbg_stage || 'cinflections' || i || '_' || generate_subscripts(bends, 1),
unnest(bends)
);
end if;
select * from self_crossing(bends) into bends, mutated;
if dbg then
insert into debug_wm(name, way) values(
dbg_stage || 'dcrossings' || i || '_' || generate_subscripts(bends, 1),
unnest(bends)
);
end if;
if mutated then
lines[i] = st_linemerge(st_union(bends));
dbg_stage = dbg_stage + 1;
continue;
end if;
-- self-crossing mutations are done, calculate bend properties
perform bend_attrs(bends, true);
end loop;
end loop;
if l_type = 'ST_LineString' then
return st_linemerge(st_union(lines));
elseif l_type = 'ST_MultiLineString' then
return st_union(lines);
end if;
end
$$ language plpgsql;