diff --git a/Line.h b/Line.h
index 8ff77cb..e198558 100644
--- a/Line.h
+++ b/Line.h
@@ -42,7 +42,8 @@ public:
         other -= from();
 
         // Cross product greater than zero?
-        if (m_to_from_origin.x() * other.y() - m_to_from_origin.y() * other.x() > 0)
+        // 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)
         {
             return true;
         }
diff --git a/Quickhull.h b/Quickhull.h
index 3490842..5cfac6a 100644
--- a/Quickhull.h
+++ b/Quickhull.h
@@ -132,24 +132,20 @@ private:
         //  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)
+            if (this_distance == furthest_distance)
             {
                 output.emplace_back(point);
             }
         }
+        // Remove the previously checked points from the input -- we can't do that in
+        //  the previous loop because we can't delete from the list we're iterating over
         input.remove_if([furthest_distance, line](Point point)
         {
             return furthest_distance == line.distance_squared_to(point);
         });
-        // Hotfix end
 
         output.emplace_back(furthest_point);
         input.remove(furthest_point);
@@ -173,12 +169,9 @@ private:
             new_line2 = Line(furthest_point, line.to());
         }
 
-        // TODO: Test if this improves performance
-        //Triangle triangle(a, b, c);
-        //input.remove_if([triangle](Point point)
-        //{
-        //    return triangle.is_point_inside(point);
-        //});
+        // We don't need to remove points inside the triangle created by those lines.
+        //  That happens implicitly since they are not handled further due to the
+        //  following step, which assigns each line its corresponding points to handle:
 
         // Get points right of new_line1 and 2
         std::list<Point> left_of_line1, left_of_line2;
@@ -189,8 +182,7 @@ private:
             {
                 left_of_line1.emplace_back(point);
             }
-            // TODO: Can we do else if here, or could we then miss out on points?
-            if (!new_line2.is_point_right(point))
+            else if (!new_line2.is_point_right(point))
             {
                 left_of_line2.emplace_back(point);
             }