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wm.sql
41
wm.sql
@ -1,9 +1,9 @@
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\set ON_ERROR_STOP on
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\set ON_ERROR_STOP on
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SET plpgsql.extra_errors TO 'all';
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SET plpgsql.extra_errors TO 'all';
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-- detect_bends detects bends using the inflection angles. No corrections.
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drop function if exists detect_bends;
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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 function detect_bends(line geometry, OUT bends geometry[]) as $$
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create or replace function detect_bends(line geometry, OUT bends geometry[]) as $$
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declare
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declare
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pi real;
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pi real;
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p geometry;
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p geometry;
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@ -16,8 +16,8 @@ declare
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begin
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begin
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pi = radians(180);
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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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-- the last vertex is iterated over twice, because the algorithm uses 3
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-- to calculate the angle between them.
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-- vertices to calculate the angle between them.
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--
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--
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-- Given 3 vertices p1, p2, p3:
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-- Given 3 vertices p1, p2, p3:
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--
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--
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@ -97,7 +97,8 @@ $$ language plpgsql;
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-- fix_gentle_inflections1 fixes gentle inflections of an array of lines in
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-- fix_gentle_inflections1 fixes gentle inflections of an array of lines in
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-- one direction. This is an implementation detail of fix_gentle_inflections.
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-- one direction. This is an implementation detail of fix_gentle_inflections.
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create or replace function fix_gentle_inflections1(INOUT bends geometry[]) as $$
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drop function if exists fix_gentle_inflections1;
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create function fix_gentle_inflections1(INOUT bends geometry[]) as $$
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declare
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declare
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pi real;
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pi real;
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small_angle real;
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small_angle real;
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@ -145,13 +146,14 @@ begin
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-- if the bend got too short, stop processing it
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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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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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-- inflection angle between ptail[1:3] is "large", stop processing
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exit when abs(st_angle(phead[1], phead[2], phead[3]) - pi) > small_angle;
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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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-- distance from head's 1st vertex should be larger than from 2nd vertex
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exit when st_distance(ptail, phead[2]) < st_distance(ptail, phead[3]);
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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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-- Detected a gentle inflection.
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-- 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] = st_removepoint(bends[i], 0);
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bends[i-1] = st_addpoint(bends[i-1], phead[3]);
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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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@ -162,7 +164,8 @@ $$ language plpgsql;
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-- self_crossing eliminates self-crossing from the bends, following the
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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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-- article's section "Self-line Crossing When Cutting a Bend".
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create or replace function self_crossing(INOUT bends geometry[]) as $$
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drop function if exists self_crossing;
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create function self_crossing(INOUT bends geometry[]) as $$
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declare
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declare
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i int4;
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i int4;
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j int4;
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j int4;
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@ -189,7 +192,9 @@ begin
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p1 = null;
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p1 = null;
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p2 = null;
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p2 = null;
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p3 = 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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for p0 in (
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select geom from st_dumppoints(bends[i]) order by path[1] asc
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) loop
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p3 = p2;
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p3 = p2;
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p2 = p1;
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p2 = p1;
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p1 = p0;
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p1 = p0;
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@ -219,8 +224,10 @@ begin
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-- are p2 and p3 on the different sides of line(p0,p1)? vector
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-- are p2 and p3 on the different sides of line(p0,p1)? vector
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-- multiplication; https://stackoverflow.com/questions/1560492/
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-- multiplication; 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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s2 = (st_x(p0)-st_x(p1)*(st_y(p2)-st_y(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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(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))-
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(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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continue when sign(s2) = sign(s3);
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-- do end vertices of bend[i] cross bend[j]?
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-- do end vertices of bend[i] cross bend[j]?
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@ -228,12 +235,13 @@ begin
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b = st_pointn(bends[i], -1);
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b = st_pointn(bends[i], -1);
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multi = st_split(bends[j], st_makeline(a, b));
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multi = st_split(bends[j], st_makeline(a, b));
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continue when st_numgeometries(multi) = 1;
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continue when st_numgeometries(multi) = 1;
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continue when st_numgeometries(multi) = 2 and (st_contains(bends[j], a) or st_contains(bends[j], b));
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continue when st_numgeometries(multi) = 2 and
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(st_contains(bends[j], a) or st_contains(bends[j], b));
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-- real self-crossing detected! Remove it.
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-- real self-crossing detected! Remove it.
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-- if j < i:
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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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-- bends[j] = multi[1][1...n-1]; that will have all the vertices of
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-- except the crossing and what comes after it.
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-- bends[j], except the crossing and what comes after it.
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-- bends[j] = append(bends[j], bends[i][-1])
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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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-- remove bends from bends[j+1] to bends[i] inclusive.
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-- j := i+1
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-- j := i+1
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@ -253,7 +261,8 @@ begin
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prev_length = array_length(bends, 1);
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prev_length = array_length(bends, 1);
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if j < i then
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if j < i then
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bends[j] = st_geometryn(multi, 1);
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bends[j] = st_geometryn(multi, 1);
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bends[j] = st_setpoint(bends[j], st_npoints(bends[j])-1, st_pointn(bends[i], st_npoints(bends[i])));
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bends[j] = st_setpoint(bends[j], st_npoints(bends[j])-1,
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st_pointn(bends[i], st_npoints(bends[i])));
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bends = bends[1:j] || bends[i+1:prev_length];
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bends = bends[1:j] || bends[i+1:prev_length];
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j = i;
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j = i;
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else
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else
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