Remove intersecting chains

Removed intersecting chains using a greedy method
Fixed issue where chains found after splitting partitions do not get checked for intersection

src/main/java/com/aaaaahhhhhhh/bananapuncher714/mesh/Mesh.java

@@ -1390,7 +1390,13 @@ public class Mesh< T extends Region > {
             }
             
             /*
-             * Check all previous chains for intersections and stuff
+             * Check all previous chains for intersections and stuff. This method
+             * is unfortunately polynomial time(O(n^2)) and there's not much we can do about it.
+             * 
+             * Maybe parallelize the intersection checking though? We'd need to ensure that the
+             * intersection collection for each chain is synchronized, but otherwise entirely possible.
+             * 
+             * TODO Good idea, now someone needs to implement that.
              */
             void addChain( final Chain chain ) {
                 final Vertex chainOrigin = chain.getOrigin();
@@ -1582,8 +1588,9 @@ public class Mesh< T extends Region > {
                     
                     final Partition copy = new Partition( lower, newUpper );
                     
-                    // Copy all chains from the previous region in case of intersection
-                    copy.chains.addAll( toSplit.chains );
+                    // Share chains since new chains from one region may intersect
+                    // with chains from another region
+                    copy.chains = toSplit.chains;
                     
                     toSplit.lower = newLower;
 
@@ -1724,6 +1731,7 @@ public class Mesh< T extends Region > {
                 }
                 
                 top.chains.addAll( bottom.chains );
+                
                 lowerEdgeMap.remove( bottom.upper );
                 
                 // Merge the top and bottom partition
@@ -1848,10 +1856,54 @@ public class Mesh< T extends Region > {
                 System.out.println( "DUPLICATE!" );
             }
         }
-        return chains;
         
         // Given a chain link, select the links which intersect the least, and remove any that it intersects with from the
         // queue. Essentially, a greedy method, which is more or less guaranteed optimal results.
+        // This is also unfortunately an O(n^2) time algorithm that can't be simplified.
+        
+        // Keep track of all chains that we want
+        final Collection< Chain > selectedChains = new HashSet< Chain >();
+        // Keep track of all remaining chains that needs to be scanned
+        final Collection< Chain > remainingChains = new HashSet< Chain >( chains );
+        
+        // Do a quick scan and remove any chains that have 0 intersections, since we can get
+        // this done in linear time and all at once
+        for ( final Iterator< Chain > it = remainingChains.iterator(); it.hasNext(); ) {
+            final Chain chain = it.next();
+            
+            if ( chain.intersections.size() == 0 ) {
+                selectedChains.add( chain );
+                it.remove();
+            }
+        }
+        
+        while ( !remainingChains.isEmpty() ) {
+            // Find the chain with the least amount of intersections
+            final Chain least = remainingChains.parallelStream().min( ( c1, c2 ) -> {
+                return Integer.compare( c1.intersections.size(), c2.intersections.size() );
+            } ).get();
+            
+            System.out.println( "Removing chain " + least.getOrigin() + ",\t" + least.getDest() );
+            System.out.println( "Intersection with " + least.intersections.size() );
+            for ( Chain c : least.intersections ) {
+                System.out.println( "\t" + c.getOrigin() + ",\t" + c.getDest() );
+            }
+            
+            // Now remove this chain and all other chains that it intersects with
+            remainingChains.remove( least );
+            if ( !least.intersections.isEmpty() ) {
+                remainingChains.removeAll( least.intersections );
+                
+                // Remove all intersected chains from other chains
+                remainingChains.parallelStream().forEach( c -> c.intersections.removeAll( least.intersections ) );
+            }
+            
+            selectedChains.add( least );
+        }
+        
+        System.out.println( "After reducing the amount of intersecting chains: " + selectedChains.size() );
+        
+        return selectedChains;
     }
     
     private static Collection< EdgePolygon > partitionMonotone( final TreeSet< Vertex > vertices, final Collection< HalfEdge > interior ) {