diff --git a/util/Matrix.cc b/util/Matrix.cc
index 62744cf..39a9ae3 100644
--- a/util/Matrix.cc
+++ b/util/Matrix.cc
@@ -214,10 +214,11 @@ Matrix operator*(const Matrix & m1, const Matrix & m2)
     return res;
 }
 
+/* transform a point */
 Vector operator*(const Matrix & m, const Vector & v)
 {
     Vector res;
-    for (int i = 0; i < 4; i++)
+    for (int i = 0; i < 3; i++)
     {
         res[i] = m[i][0] * v[0]
                + m[i][1] * v[1]
@@ -227,6 +228,19 @@ Vector operator*(const Matrix & m, const Vector & v)
     return res;
 }
 
+/* transform a direction */
+Vector operator%(const Matrix & m, const Vector & v)
+{
+    Vector res;
+    for (int i = 0; i < 3; i++)
+    {
+        res[i] = m[i][0] * v[0]
+               + m[i][1] * v[1]
+               + m[i][2] * v[2];
+    }
+    return res;
+}
+
 bool operator==(const Matrix & m1, const Matrix & m2)
 {
     for (int i = 0; i < 4; i++)
diff --git a/util/Matrix.h b/util/Matrix.h
index 84b780e..5ccd23f 100644
--- a/util/Matrix.h
+++ b/util/Matrix.h
@@ -26,7 +26,8 @@ class Matrix
 };
 
 Matrix operator*(const Matrix & m1, const Matrix & m2);
-Vector operator*(const Matrix & m, const Vector & v);
+Vector operator*(const Matrix & m, const Vector & v); /* transform point */
+Vector operator%(const Matrix & m, const Vector & v); /* transform direction */
 bool operator==(const Matrix & m1, const Matrix & m2);
 std::ostream & operator<<(std::ostream & out, const Matrix & m);