docs and inflections

IV/tests.sql

@@ -16,8 +16,9 @@ create table figures (name text, way geometry);
 insert into figures (name, way) values ('fig3',ST_GeomFromText('LINESTRING(0 0,12 0,13 4,20 2,20 0,32 0,33 10,38 16,43 15,44 10,44 0,60 0)'));
 insert into figures (name, way) values ('fig3-1',ST_GeomFromText('LINESTRING(0 0,12 0,13 4,20 2,20 0,32 0,33 10,38 16,43 15,44 10,44 0)'));
 insert into figures (name, way) values ('fig5',ST_GeomFromText('LINESTRING(0 39,19 52,27 77,26 104,41 115,49 115,65 103,65 75,53 45,63 15,91 0,91 0)'));
-insert into figures (name, way) values ('inflection-1',ST_GeomFromText('LINESTRING(100 14,114 20,133 20,145 15,145 0,136 5,123 7,114 7,111 2)'));
+insert into figures (name, way) values ('inflection-1',ST_GeomFromText('LINESTRING(110 24,114 20,133 20,145 15,145 0,136 5,123 7,114 7,111 2)'));
 
+-- `bends` is for manual inspection using, say, qgis
 drop table if exists bends;
 create table bends (way geometry);
 insert into bends select unnest(detect_bends((select way from figures where name='fig3')));
@@ -26,17 +27,27 @@ insert into bends select unnest(detect_bends((select way from figures where name
 
 do $$
 declare
-  bends geometry[];
+  vbends geometry[];
 begin
-  select detect_bends((select way from figures where name='fig3')) into bends;
+  -- DETECT BENDS
-  perform assert_equals(5, array_length(bends, 1));
+  select detect_bends((select way from figures where name='fig3')) into vbends;
-  perform assert_equals('LINESTRING(0 0,12 0,13 4)', st_astext(bends[1]));
+  perform assert_equals(5, array_length(vbends, 1));
-  perform assert_equals('LINESTRING(12 0,13 4,20 2,20 0)', st_astext(bends[2]));
+  perform assert_equals('LINESTRING(0 0,12 0,13 4)', st_astext(vbends[1]));
-  perform assert_equals('LINESTRING(20 2,20 0,32 0,33 10)', st_astext(bends[3]));
+  perform assert_equals('LINESTRING(12 0,13 4,20 2,20 0)', st_astext(vbends[2]));
-  perform assert_equals('LINESTRING(32 0,33 10,38 16,43 15,44 10,44 0)', st_astext(bends[4]));
+  perform assert_equals('LINESTRING(20 2,20 0,32 0,33 10)', st_astext(vbends[3]));
+  perform assert_equals('LINESTRING(32 0,33 10,38 16,43 15,44 10,44 0)', st_astext(vbends[4]));
 
   perform assert_equals(4, array_length(detect_bends((select way from figures where name='fig3-1')), 1));
 
-  select detect_bends((select way from figures where name='fig5')) into bends;
+  select detect_bends((select way from figures where name='fig5')) into vbends;
-  perform assert_equals(3, array_length(bends, 1));
+  perform assert_equals(3, array_length(vbends, 1));
+
+  -- FIX BEND INFLECTIONS
+  select detect_bends((select way from figures where name='inflection-1')) into vbends;
+
+  drop table if exists inflections;
+  create table inflections (way geometry);
+  --insert into inflections select unnest(fix_gentle_inflections(vbends));
+  select fix_gentle_inflections(vbends);
+
 end $$ language plpgsql;

IV/wm.sql

@@ -73,19 +73,21 @@ $$ language plpgsql;
 --
 -- The text does not specify how many vertices can be "adjusted"; it can
 -- equally be one or many. This function is adjusting many, as long as the
--- commulative inflection angle is less than pi/6 (30 deg).
+-- commulative inflection angle small (see variable below).
 create or replace function fix_gentle_inflections(INOUT bends geometry[]) as $$
 declare
-  prev_bend geometry;
+  small_angle real;
-  bend geometry;
+  phead geometry; -- head point of head bend
-  p geometry;
+  ptail geometry[]; -- 3 head points of tail bend
-  p1 geometry;
+  i int4; -- bends[i] is the current head
-  p2 geometry;
-  p3 geometry;
 begin
-  foreach bend in array bends loop
+  -- the threshold when the angle is still "small", so gentle inflections can
-    if prev_bend is null  then
+  -- be joined
-      prev_bend = bend;
+  small_angle := radians(30);
+
+  <<bend_loop>>
+  for i in select generate_subscripts(bends, 1) loop
+    if i = 1 then
       continue;
     end if;
 
@@ -101,31 +103,36 @@ begin
     --
     -- Assume this curve (figure `inflection-1`):
     --
-    --        A______B
+    --    \______B
-    --     ---'      `-------. C
+    --    A      `-------. C
-    --                       |
+    --                   |
-    --        G___ F         |
+    --    G___ F         |
-    --        /   `-----.____+ D
+    --    /   `-----.____+ D
-    --                  E
+    --              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;
-    -- Assuming the direction in this example is clock-wise, the first set of
+    while true loop
-    -- `p` variables will be: p1=C, p2=B, p3=A.
+      -- copy last 3 points of bends[i-1] (tail) to ptail
-    for p in (select geom from st_dumppoints(prev_bend) order by path[1] desc) loop
+      select array_agg(geom) from st_dumppoints(bends[i-1]) order by path[1] desc limit 3 into ptail;
-      p3 = p2;
+
-      p2 = p1;
+      -- if inflection angle between ptail[1:3] "large", stop processing this bend
-      p1 = p;
+      if abs(st_angle(ptail[1], ptail[2], ptail[2], ptail[3]) - pi) > small_angle then
-      if p3 is null then
+        exit bend_loop;
-        continue;
       end if;
 
-      -- (p2, p1) is shared with the current bend.
+      -- 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;
 
-    prev_bend = bend;
   end loop;
 end
 $$ language plpgsql;