beginnings of self-crossing

IV/notes.txt

@@ -27,13 +27,12 @@ after a few bends have been skipped. E.g. ends of A<->B cross the line, but
 
 
 
-If a bend with 180+ deg inflection is found, its line between inflection angles
+If a bend with 180+ deg sum of inflection angles is found, its line between
-(AB in our examples) must be crossed with all the other bends to detect a
+inflection angles (AB in our examples) must be crossed with all the other bends
-possible line-crossing. This is O(N*M), where N is the total number of line
+to detect a possible line-crossing. This is O(N*M), where N is the total number
-segments, and M is the number of qualifying bends. In other words, can be very
+of line segments, and M is the number of qualifying bends. It is expensive.
-computationally expensive.
 
 This may be simplified: if other bend's endpoints (A' and B') are in the same
 sub-plane as divided by AB, then the bend can be skipped from checking if it
-intersects with AB. Some intersections may be missed (see the example), but
+intersects with AB. Some intersections may be missed (see the last example),
-they will be eliminated by just joining A and B.
+but they will be eliminated by joining A and B anyway.

IV/tests.sql

@@ -47,7 +47,7 @@ drop table if exists inflections, demo_inflections;
 create table inflections (name text, ways geometry[]);
 insert into inflections select name, fix_gentle_inflections(ways) from bends;
 create table demo_inflections (name text, i bigint, way geometry);
-insert into demo_inflections select a.name, generate_subscripts(a.ways, 1), unnest(a.ways) from inflections a;
+insert into demo_inflections select name, generate_subscripts(ways, 1), unnest(ways) from inflections;
 
 do $$
 declare
@@ -67,3 +67,10 @@ begin
   perform assert_equals('LINESTRING(114 20,133 20,145 15,145 0,136 5,123 7,114 7)', st_astext(vinflections[2]));
   perform assert_equals('LINESTRING(123 7,114 7,111 2)', st_astext(vinflections[3]));
 end $$ language plpgsql;
+
+-- SELF-LINE CROSSING
+drop table if exists selfcrossing, demo_selfcrossing;
+create table selfcrossing (name text, ways geometry[]);
+insert into selfcrossing select name, self_crossing(ways) from inflections;
+create table demo_selfcrossing (name text, i bigint, way geometry);
+insert into demo_selfcrossing select name, generate_subscripts(ways, 1), unnest(ways) from selfcrossing;

IV/wm.sql

@@ -170,9 +170,35 @@ $$ language plpgsql;
 create or replace function self_crossing(INOUT bends geometry[]) as $$
 declare
   pi real;
+  angle real;
+  p geometry;
+  p1 geometry;
+  p2 geometry;
+  p3 geometry;
+  bend geometry;
 begin
+  pi = radians(180);
 
+  -- go through the bends and find one where sum of inflection angle is >180
+  foreach bend in array bends loop
+    angle = 0;
+    p3 = null;
+    p2 = null;
+    p1 = null;
+    for p in (select geom from st_dumppoints(bend) order by path[1] asc) loop
+      p3 = p2;
+      p2 = p1;
+      p1 = p;
+      if p3 is null then
+        continue;
+      end if;
+      angle = angle + abs(pi - st_angle(p1, p2, p3));
+    end loop;
 
+    if abs(angle) > pi then
+      raise notice 'maybe self-crossing bend %: %', st_astext(bend), round(degrees(abs(angle)));
+    end if;
+  end loop;
 
 end
 $$ language plpgsql;