Update Makefile

Doesn't seem to make much of a difference though :(

but another issue was fixed in the meantime (we weren't actually usign the leftmost and rightmost points!)

Makefile

@@ -1,5 +1,5 @@
 CXX = g++
-CXXFLAGS = -Wall -O3 -g
+CXXFLAGS = -Wall -O3
 SFMLFLAGS = -lsfml-system -lsfml-window -lsfml-graphics
 
 # In case you installed SFML to a non-standard path, you'll need to tell the compiler where to find the SFML headers (.hpp files):
@@ -20,5 +20,5 @@ main.o: main.cpp
 
 Display.o: Display.h
 
-clean :
+clean:
-	-rm *.o quickhull performance
+	-rm *.o quickhull

Quickhull.h

@@ -8,6 +8,7 @@
 
 #include "Display.h"
 #include "Triangle.h"
+#include "Utility.h"  // For IsPointInRectangle
 
 class Quickhull
 {
@@ -19,21 +20,56 @@ public:
         // Get leftmost and rightmost point
         Point leftmost(INFINITY, 0.0), rightmost(-INFINITY, 0.0);
 
-        for (const Point &point : input)
+        if (akl)
         {
-            if (point.x() < leftmost.x()) {
+            // Also get highest and lowest point
-                leftmost = point;
+            Point lowest(0.0, -INFINITY), highest(0.0, INFINITY);
-            } else if (point.y() > rightmost.y()) {
-                rightmost = point;
-            }
-        }
-        // Add them to the output
-        output.emplace_back(leftmost);
-        output.emplace_back(rightmost);
 
-        // Remove them from the input (as well as duplicates)
+            for (const Point &point : input)
-        input.remove(leftmost);
+            {
-        input.remove(rightmost);
+                if (point.x() < leftmost.x()) {
+                    leftmost = point;
+                } else if (point.x() > rightmost.x()) {
+                    rightmost = point;
+                }
+
+                if (point.y() < highest.y()) {
+                    highest = point;
+                } else if (point.y() > lowest.y()) {
+                    lowest = point;
+                }
+            }
+
+            Triangle t1(highest, rightmost, lowest);
+            Triangle t2(lowest, leftmost, highest);
+
+            // Remove all points in this rectangle
+            input.remove_if([highest, leftmost, lowest, rightmost](const Point &point)
+            {
+                return IsPointInRectangle(point, highest, leftmost, lowest, rightmost);
+            });
+
+            output.emplace_back(leftmost);
+            output.emplace_back(rightmost);
+            output.emplace_back(highest);
+            output.emplace_back(lowest);
+        } else {
+            for (const Point &point : input)
+            {
+                if (point.x() < leftmost.x()) {
+                    leftmost = point;
+                } else if (point.x() > rightmost.x()) {
+                    rightmost = point;
+                }
+            }
+            // Add them to the output
+            output.emplace_back(leftmost);
+            output.emplace_back(rightmost);
+
+            // Remove them from the input (as well as duplicates)
+            input.remove(leftmost);
+            input.remove(rightmost);
+        }
 
         // Create a line from leftmost to rightmost
         Line line = Line(leftmost, rightmost);
@@ -113,46 +149,38 @@ private:
         // If the input vector is empty, we're done
         if (input.empty()) return;
 
-        // Find the point which is furthest away from the line, add it to the output
+        // Find the points which are furthest away from the line
-        Point furthest_point;
         float furthest_distance = -1.0;
 
+        std::list<Point> furthest_points;
+
         for (const Point &point : input)
         {
             float this_distance = line.distance_squared_to(point);
+            // It's possible for there to be multiple closests points (e.g. in the case)
+            //  of a rectangle). We need to handle all these properly, so we make a list
+            //  of all points at the furthest distance.
             if (this_distance > furthest_distance)
             {
                 furthest_distance = this_distance;
-                furthest_point = point;
+                furthest_points.clear();
+                furthest_points.emplace_back(point);
             }
-        }
+            else if (this_distance == furthest_distance)
-
-        // TODO: e.g. in the case of a rectangle, it's possible for there to be
-        //  multiple closest points (sometimes all at distance 0). How do we handle
-        //  these properly? We definitely need to remove them all from input later;
-        //  do we also need to handle them all further? This hotfix works, but seems
-        //  like an unnecessarily big performance hit for that edge case.
-        // FIXME: This workaround also causes problems with extremely large numbers
-        //  of randomly generated numbers, causing random lines within the data!
-        //  Points inside the hull are added because of random lines.
-        for (const Point &point : input)
-        {
-            float this_distance = line.distance_squared_to(point);
-            // TODO: Both are required, otherwise only one side of the rectangle is
-            //  taken -- why?
-            if (this_distance == furthest_distance || line.distance_squared_to(point) == 0)
             {
-                output.emplace_back(point);
+                furthest_points.emplace_back(point);
             }
         }
-        input.remove_if([furthest_distance, line](Point point)
-        {
-            return furthest_distance == line.distance_squared_to(point);
-        });
-        // Hotfix end
 
-        output.emplace_back(furthest_point);
+        for (const Point &point : furthest_points)
-        input.remove(furthest_point);
+        {
+            // All furthest points we found are part of the hull, so add them to the output
+            //  and remove them from the input.
+            output.emplace_back(point);
+            input.remove(point);
+        }
+
+        Point furthest_point = furthest_points.front();
 
         // Build a triangle with these 3 points
 
@@ -163,7 +191,6 @@ private:
 
         if (line.is_point_right(furthest_point))
         {
-            // TOOD: It's probably more efficient to set the fields?
             new_line1 = Line(line.to(), furthest_point);
             new_line2 = Line(furthest_point, line.from());
         }
@@ -173,12 +200,9 @@ private:
             new_line2 = Line(furthest_point, line.to());
         }
 
-        // TODO: Test if this improves performance
+        // We don't need to remove points inside the triangle created by those lines.
-        //Triangle triangle(a, b, c);
+        //  That happens implicitly since they are not handled further due to the
-        //input.remove_if([triangle](Point point)
+        //  following step, which assigns each line its corresponding points to handle:
-        //{
-        //    return triangle.is_point_inside(point);
-        //});
 
         // Get points right of new_line1 and 2
         std::list<Point> left_of_line1, left_of_line2;
@@ -189,15 +213,15 @@ private:
             {
                 left_of_line1.emplace_back(point);
             }
-            // TODO: Can we do else if here, or could we then miss out on points?
+            // TODO: Are there any possible edge cases where this 'else if' won't work,
-            if (!new_line2.is_point_right(point))
+            //  and we need an 'if' instead?
+            else if (!new_line2.is_point_right(point))
             {
                 left_of_line2.emplace_back(point);
             }
         }
 
         // Recursively call get_hull_with_line for each side of the triangle
-        // TODO: We can skip the original one
         get_hull_with_line(left_of_line1, output, new_line1);
         get_hull_with_line(left_of_line2, output, new_line2);
     }