diff --git a/shapes/Extrude.cc b/shapes/Extrude.cc
index 7924d2b..9fb697b 100644
--- a/shapes/Extrude.cc
+++ b/shapes/Extrude.cc
@@ -35,12 +35,43 @@ Shape::IntersectionList Extrude::intersect(refptr<Shape> _this, const Ray & ray)
 {
     Ray ray_inv = m_inverse.transform_ray(ray);
     IntersectionList res;
+
+    /*** optimization ***/
+    if (ray_inv.getOrigin()[0] > m_aabb.max[0])
+    {
+        if (ray_inv.getDirection() % Vector::X > 0)
+            return res;
+    }
+    else if (ray_inv.getOrigin()[0] < m_aabb.min[0])
+    {
+        if (ray_inv.getDirection() % Vector::X < 0)
+            return res;
+    }
+    if (ray_inv.getOrigin()[1] > m_aabb.max[1])
+    {
+        if (ray_inv.getDirection() % Vector::Y > 0)
+            return res;
+    }
+    else if (ray_inv.getOrigin()[1] < m_aabb.min[1])
+    {
+        if (ray_inv.getDirection() % Vector::Y < 0)
+            return res;
+    }
+    if (ray_inv.getOrigin()[2] > m_aabb.max[2])
+    {
+        if (ray_inv.getDirection() % Vector::Z > 0)
+            return res;
+    }
+    else if (ray_inv.getOrigin()[2] < m_aabb.min[2])
+    {
+        if (ray_inv.getDirection() % Vector::Z < 0)
+            return res;
+    }
+    /*** end optimization ***/
+
     int n_polygons = m_polygons.size();
     int n_offsets = m_offsets.size();
 
-    if (n_polygons < 1 || n_offsets < 1)
-        return res;
-
     double distance = 0.0;
     Vector scale(1.0, 1.0, 1.0);
     Vector shift(0.0, 0.0, 0.0);
@@ -159,12 +190,75 @@ Shape::IntersectionList Extrude::intersect(refptr<Shape> _this, const Ray & ray)
 void Extrude::addPolygon(refptr<Polygon> polygon)
 {
     m_polygons.push_back(polygon);
+    updateAABB();
 }
 
 void Extrude::addOffset(double distance,
         const Vector & scale, const Vector & shift)
 {
     m_offsets.push_back(Offset(distance, scale, shift));
+    updateAABB();
+}
+
+void Extrude::updateAABB()
+{
+    int n_polygons = m_polygons.size();
+    int n_offsets = m_offsets.size();
+    bool first = true;
+    double distance = 0.0;
+    Vector scale(1.0, 1.0, 1.0);
+    Vector shift(0.0, 0.0, 0.0);
+    for (int p = 0; p < n_polygons; p++)
+    {
+        refptr<Polygon> polygon = m_polygons[p];
+        for (int o = 0; o < n_offsets; o++)
+        {
+            Offset & offset = m_offsets[o];
+            for (int pt = 0, n_pts = polygon->size(); pt < n_pts; pt++)
+            {
+                Vector p1 = scale.mult(*(*polygon)[pt]) + shift;
+                Vector p2 = scale.mult(*(*polygon)[(pt+1) % n_pts]) + shift;
+                Vector p3 = scale.mult(offset.scale)
+                    .mult(*(*polygon)[(pt+1) % n_pts])
+                    + shift + offset.shift;
+                Vector p4 = scale.mult(offset.scale).mult(*(*polygon)[pt])
+                    + shift + offset.shift;
+                p1[2] += distance;
+                p2[2] += distance;
+                p3[2] += distance + offset.distance;
+                p4[2] += distance + offset.distance;
+                if (first)
+                {
+                    m_aabb.min = p1;
+                    m_aabb.max = p1;
+                    first = false;
+                }
+                expandAABB(p1);
+                expandAABB(p2);
+                expandAABB(p3);
+                expandAABB(p4);
+            }
+            distance += offset.distance;
+            scale = scale.mult(offset.scale);
+            shift += offset.shift;
+        }
+    }
+}
+
+void Extrude::expandAABB(const Vector & v)
+{
+    if (v[0] < m_aabb.min[0])
+        m_aabb.min[0] = v[0];
+    if (v[0] > m_aabb.max[0])
+        m_aabb.max[0] = v[0];
+    if (v[1] < m_aabb.min[1])
+        m_aabb.min[1] = v[1];
+    if (v[1] > m_aabb.max[1])
+        m_aabb.max[1] = v[1];
+    if (v[2] < m_aabb.min[2])
+        m_aabb.min[2] = v[2];
+    if (v[2] > m_aabb.max[2])
+        m_aabb.max[2] = v[2];
 }
 
 refptr<Shape> Extrude::clone()
diff --git a/shapes/Extrude.h b/shapes/Extrude.h
index ac9c9a5..93e63bf 100644
--- a/shapes/Extrude.h
+++ b/shapes/Extrude.h
@@ -5,6 +5,8 @@
 #include <vector>
 
 #include "util/Polygon.h"
+#include "util/AABB.h"
+
 #include "Shape.h"
 
 class Extrude : public Shape
@@ -31,6 +33,10 @@ class Extrude : public Shape
     protected:
         std::vector< refptr<Polygon> > m_polygons;
         std::vector<Offset> m_offsets;
+        AABB m_aabb;
+
+        void updateAABB();
+        void expandAABB(const Vector & v);
 };
 
 #endif
diff --git a/util/AABB.h b/util/AABB.h
new file mode 100644
index 0000000..b953dda
--- /dev/null
+++ b/util/AABB.h
@@ -0,0 +1,21 @@
+
+#ifndef AABB_H
+#define AABB_H
+
+class AABB
+{
+    public:
+        Vector min;
+        Vector max;
+
+        AABB()
+        {
+        }
+
+        AABB(const Vector & min, const Vector & max)
+            : min(min), max(max)
+        {
+        }
+};
+
+#endif /* AABB_H */