diff --git a/Line.h b/Line.h
index e198558..8ff77cb 100644
--- a/Line.h
+++ b/Line.h
@@ -42,8 +42,7 @@ public:
         other -= from();
 
         // Cross product greater than zero?
-        // Note: We need ">=" here so that we include points which are directly on the existing hull.
-        if (m_to_from_origin.x() * other.y() - m_to_from_origin.y() * other.x() >= 0)
+        if (m_to_from_origin.x() * other.y() - m_to_from_origin.y() * other.x() > 0)
         {
             return true;
         }
diff --git a/Quickhull.h b/Quickhull.h
index aada29b..f953ce9 100644
--- a/Quickhull.h
+++ b/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()) {
-                leftmost = point;
-            } else if (point.y() > rightmost.y()) {
-                rightmost = point;
-            }
-        }
-        // Add them to the output
-        output.emplace_back(leftmost);
-        output.emplace_back(rightmost);
+            // Also get highest and lowest point
+            Point lowest(0.0, -INFINITY), highest(0.0, INFINITY);
 
-        // Remove them from the input (as well as duplicates)
-        input.remove(leftmost);
-        input.remove(rightmost);
+            for (const Point &point : input)
+            {
+                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);