diff --git a/shapes/Box.cc b/shapes/Box.cc
index 5a77263..12d0a75 100644
--- a/shapes/Box.cc
+++ b/shapes/Box.cc
@@ -20,6 +20,40 @@ Shape::IntersectionList Box::intersect(refptr<Shape> _this, const Ray & ray)
     Ray ray_inv = m_inverse.transform_ray(ray);
 
     IntersectionList res;
+
+    /*** optimization ***/
+    if (ray_inv.getOrigin()[0] > m_size[0])
+    {
+        if (ray_inv.getDirection() % Vector::X > 0)
+            return res;
+    }
+    else if (ray_inv.getOrigin()[0] < -m_size[0])
+    {
+        if (ray_inv.getDirection() % Vector::X < 0)
+            return res;
+    }
+    if (ray_inv.getOrigin()[1] > m_size[1])
+    {
+        if (ray_inv.getDirection() % Vector::Y > 0)
+            return res;
+    }
+    else if (ray_inv.getOrigin()[1] < -m_size[1])
+    {
+        if (ray_inv.getDirection() % Vector::Y < 0)
+            return res;
+    }
+    if (ray_inv.getOrigin()[2] > m_size[2])
+    {
+        if (ray_inv.getDirection() % Vector::Z > 0)
+            return res;
+    }
+    else if (ray_inv.getOrigin()[2] < -m_size[2])
+    {
+        if (ray_inv.getDirection() % Vector::Z < 0)
+            return res;
+    }
+    /*** end optimization ***/
+
     /*
      * Ray equation:   R = R0 + tRd
      *                 x = R0x + tRdx
diff --git a/shapes/Intersect.cc b/shapes/Intersect.cc
index 2546c1c..e0d2dc8 100644
--- a/shapes/Intersect.cc
+++ b/shapes/Intersect.cc
@@ -33,8 +33,12 @@ Shape::IntersectionList Intersect::intersect(refptr<Shape> _this, const Ray & ra
 {
     Ray ray_inv = m_inverse.transform_ray(ray);
     IntersectionList res1 = m_shape1->intersect(m_shape1, ray_inv);
-    if (res1.size() == 0)           /* optimization */
+
+    /*** optimization ***/
+    if (res1.size() == 0)
         return res1;
+    /*** end optimization ***/
+
     IntersectionList res2 = m_shape2->intersect(m_shape2, ray_inv);
     BoolIntersectionList merged(res1, res2, ray_inv.getOrigin());
 
diff --git a/shapes/Sphere.cc b/shapes/Sphere.cc
index 1f6925a..c8794bd 100644
--- a/shapes/Sphere.cc
+++ b/shapes/Sphere.cc
@@ -16,6 +16,7 @@ Shape::IntersectionList Sphere::intersect(refptr<Shape> _this, const Ray & ray)
     Ray ray_inv = m_inverse.transform_ray(ray);
 
     IntersectionList res;
+
     QuadraticSolver solver(1.0,
                            2 * ( ray_inv.getOrigin()[0] * ray_inv.getDirection()[0]
                                + ray_inv.getOrigin()[1] * ray_inv.getDirection()[1]
diff --git a/shapes/Subtract.cc b/shapes/Subtract.cc
index dd7a646..5b4eed1 100644
--- a/shapes/Subtract.cc
+++ b/shapes/Subtract.cc
@@ -33,8 +33,12 @@ Shape::IntersectionList Subtract::intersect(refptr<Shape> _this, const Ray & ray
 {
     Ray ray_inv = m_inverse.transform_ray(ray);
     IntersectionList res1 = m_shape1->intersect(m_shape1, ray_inv);
-    if (res1.size() == 0)           /* optimization */
+
+    /*** optimization ***/
+    if (res1.size() == 0)
         return res1;
+    /*** end optimization ***/
+
     IntersectionList res2 = m_shape2->intersect(m_shape2, ray_inv);
     BoolIntersectionList merged(res1, res2, ray_inv.getOrigin());
 
diff --git a/util/Vector.cc b/util/Vector.cc
index 3c5065e..d0328ae 100644
--- a/util/Vector.cc
+++ b/util/Vector.cc
@@ -6,6 +6,10 @@
 
 #include "Vector.h"
 
+const Vector Vector::X(1, 0, 0);
+const Vector Vector::Y(0, 1, 0);
+const Vector Vector::Z(0, 0, 1);
+
 Vector::Vector()
 {
     m_array[0] = 0.0;
diff --git a/util/Vector.h b/util/Vector.h
index 7993441..3c4f7cd 100644
--- a/util/Vector.h
+++ b/util/Vector.h
@@ -32,6 +32,10 @@ class Vector
         Vector & operator+=(const Vector & v2);
         Vector & operator-=(const Vector & v2);
 
+        static const Vector X;
+        static const Vector Y;
+        static const Vector Z;
+
     protected:
         double  m_array[3];
 };