self-crossing bugfix

IV/notes.txt

@@ -52,6 +52,20 @@ To:
 But perhaps it doesn't look quite as natural. I will trust the original
 article to do the right thing here and remove the bend altogether.
 
+ALSO: the bends should be iterated from different directions:
+
+for i := 0; i < len(bends); i++ {
+  for j := 0; j < i; j++ {
+    ...
+  }
+  for j := len(bends); j > i; j-- {
+    ...
+  }
+}
+
+So if there are multiple bends between the baseline, they will be cut
+correctly.
+
 The Context of a Bend
 ---------------------
 

IV/tests.sql

@@ -53,7 +53,9 @@ insert into wm_figures (name, way) values ('inflection-1',ST_GeomFromText('LINES
 insert into wm_figures (name, way) values ('multi-island',ST_GeomFromText('MULTILINESTRING((-15 10,-10 10,-5 11,0 11,5 11,10 10,11 9,13 10,15 9),(-5 11,-2 15,0 16,2 15,5 11))'));
 
 -- TODO: there is a bug and it does not go through `self_crossing` function.
---insert into wm_figures (name, way) values ('selfcrossing-1',ST_GeomFromText('LINESTRING(-27 180,-20 166,-21 142,-18 136,55 136,55 136,71 145,44 165,37 146,22 145,14 164,11 164,3 146,-12 146,-13 176,-18 184)'));
+insert into wm_figures (name, way) values ('selfcrossing-1',ST_GeomFromText('LINESTRING(-27 180,-20 166,-21 142,-18 136,55 136,55 136,71 145,44 165,37 146,22 145,14 164,11 164,3 146,-12 146,-13 176,-18 184)'));
+insert into wm_figures (name, way) values ('selfcrossing-1-rev',ST_Reverse(ST_Translate((select way from wm_figures where name='selfcrossing-1'), 60, 0)));
+
 
 -- Run ST_SimplifyWM in debug mode, so `wm_debug` is populated. That table
 -- is used for geometric assertions later in the file.

IV/wm.sql

@@ -236,12 +236,7 @@ begin
 
     -- go through each bend in the given line, and see if has a potential to
     -- cross bends[i].
-    j = 0;
-    while j < array_length(bends, 1) loop
-      j = j + 1;
-      continue when i = j;
-
-      -- do end vertices of bend[i] cross bend[j]?
+    for j in 1..i-1 loop
       a = st_pointn(bends[i], 1);
       b = st_pointn(bends[i], -1);
       multi = st_split(bends[j], st_makeline(a, b));
@@ -257,7 +252,7 @@ begin
       -- figure out what happens here, by hand. I know it's hard to follow.
       -- Apologies.
       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);
@@ -268,24 +263,35 @@ begin
         st_pointn(bends[i], st_npoints(bends[i]))
       );
       bends = bends[1:j] || bends[i+1:prev_length];
-        j = i;
-      else
+      exit;
+    end loop;
+
+    for j in reverse array_length(bends, 1)..i+1 loop
+      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));
+
+      -- vertices, segments and stars are aligned, we are changing the bend
+      mutated = true;
+
+      -- To understand the block below, 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. I know it's hard to follow.
+      -- Apologies.
+      prev_length = array_length(bends, 1);
       -- 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);
       -- continue debugging the selfcrossing-1 here.
-        --raise notice 'previous bend: %', st_astext(bends[i-1]);
-        --raise notice 'multi: %', st_astext(multi);
-        --raise notice '2: removing first point from %', st_astext(st_geometryn(multi, st_numgeometries(multi)));
-        --mutated = false;
-        --return;
       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);
+      exit;
     end loop;
   end loop;
 end