diff --git a/gtsam/geometry/Point2.h b/gtsam/geometry/Point2.h
index 558c9b4fb..9d7190c8f 100644
--- a/gtsam/geometry/Point2.h
+++ b/gtsam/geometry/Point2.h
@@ -107,109 +107,17 @@ public:
   /// @{
 
   /// identity
-  inline static Point2 identity() {
-    return Point2();
-  }
-
-  /// "Inverse" - negates each coordinate such that compose(p,inverse(p)) == identity()
-  inline Point2 inverse(OptionalJacobian<2,2> H=boost::none) const {
-    if (H) *H = -I_2x2;
-    return Point2(-x_, -y_);
-  }
+  inline static Point2 identity() {return Point2();}
 
   /// syntactic sugar for inverse, i.e., -p == inverse(p)
   inline Point2 operator- () const {return Point2(-x_,-y_);}
 
-  /// "Compose", just adds the coordinates of two points. With optional derivatives
-  inline Point2 compose(const Point2& q,
-      OptionalJacobian<2,2> H1=boost::none,
-      OptionalJacobian<2,2> H2=boost::none) const {
-    if(H1) *H1 = I_2x2;
-    if(H2) *H2 = I_2x2;
-    return *this + q;
-  }
-
   /// syntactic sugar for adding two points, i.e., p+q == compose(p,q)
   inline Point2 operator + (const Point2& q) const {return Point2(x_+q.x_,y_+q.y_);}
 
-  /// "Between", subtracts point coordinates. between(p,q) == compose(inverse(p),q)
-  inline Point2 between(const Point2& q,
-      OptionalJacobian<2,2> H1=boost::none,
-      OptionalJacobian<2,2> H2=boost::none) const {
-    if(H1) *H1 = -I_2x2;
-    if(H2) *H2 = I_2x2;
-    return q - (*this);
-  }
-
   /// syntactic sugar for subtracting points, i.e., q-p == between(p,q)
   inline Point2 operator - (const Point2& q) const {return Point2(x_-q.x_,y_-q.y_);}
 
-  /// @}
-  /// @name Manifold
-  /// @{
-
-  /// dimension of the variable - used to autodetect sizes
-  inline static size_t Dim() { return 2; }
-
-  /// Dimensionality of tangent space = 2 DOF
-  inline size_t dim() const { return 2; }
-
-  /// Updates a with tangent space delta
-  inline Point2 retract(const Vector& v) const {
-    return *this + Point2(v);
-  }
-
-  /// Local coordinates of manifold neighborhood around current value
-  inline Vector localCoordinates(const Point2& t2) const {
-    Point2 dp = t2 - *this;
-    return Vector2(dp.x(), dp.y());
-  }
-
-  /// @}
-  /// @name Lie Group
-  /// @{
-
-  /// Exponential map around identity - just create a Point2 from a vector
-  static Point2 Expmap(const Vector2& v,
-      OptionalJacobian<2, 2> H = boost::none) {
-    if (H) *H = I_2x2;
-    return Point2(v);
-  }
-
-  /// Logmap around identity
-  static inline Vector2 Logmap(const Point2& dp,
-      OptionalJacobian<2, 2> H = boost::none) {
-    if (H) *H = I_2x2;
-    return Vector2(dp.x(), dp.y());
-  }
-
-  /// Left-trivialized derivative of the exponential map
-  static Matrix2 dexpL(const Vector2& v) {
-    return I_2x2;
-  }
-
-  /// Left-trivialized derivative inverse of the exponential map
-  static Matrix2 dexpInvL(const Vector2& v) {
-    return I_2x2;
-  }
-
-  /// Updates a with tangent space delta
-  inline Point2 retract(const Vector& v, OptionalJacobian<2, 2> H1,
-      OptionalJacobian<2, 2> H2 = boost::none) const {
-    if (H1) *H1 = I_2x2;
-    if (H2) *H2 = I_2x2;
-    return *this + Point2(v);
-  }
-
-  /// Local coordinates of manifold neighborhood around current value
-  inline Vector localCoordinates(const Point2& t2, OptionalJacobian<2, 2> H1,
-      OptionalJacobian<2, 2> H2 = boost::none) const {
-    if (H1) *H1 = - I_2x2;
-    if (H2) *H2 = I_2x2;
-    Point2 dp = t2 - *this;
-    return Vector2(dp.x(), dp.y());
-  }
-
   /// @}
   /// @name Vector Space
   /// @{
@@ -285,5 +193,5 @@ inline Point2 operator*(double s, const Point2& p) {return p*s;}
 template<>
 struct traits_x<Point2> : public internal::VectorSpace<Point2> {};
 
-}
+} // \ namespace gtsam
 
diff --git a/gtsam/geometry/tests/testPoint2.cpp b/gtsam/geometry/tests/testPoint2.cpp
index 1a11787fa..71524d25d 100644
--- a/gtsam/geometry/tests/testPoint2.cpp
+++ b/gtsam/geometry/tests/testPoint2.cpp
@@ -66,16 +66,16 @@ TEST(Point2, Lie) {
   Point2 p1(1, 2), p2(4, 5);
   Matrix H1, H2;
 
-  EXPECT(assert_equal(Point2(5,7), p1.compose(p2, H1, H2)));
+  EXPECT(assert_equal(Point2(5,7), traits_x<Point2>::Compose(p1, p2, H1, H2)));
   EXPECT(assert_equal(eye(2), H1));
   EXPECT(assert_equal(eye(2), H2));
 
-  EXPECT(assert_equal(Point2(3,3), p1.between(p2, H1, H2)));
+  EXPECT(assert_equal(Point2(3,3), traits_x<Point2>::Between(p1, p2, H1, H2)));
   EXPECT(assert_equal(-eye(2), H1));
   EXPECT(assert_equal(eye(2), H2));
 
-  EXPECT(assert_equal(Point2(5,7), p1.retract(Vector2(4., 5.))));
-  EXPECT(assert_equal(Vector2(3.,3.), p1.localCoordinates(p2)));
+  EXPECT(assert_equal(Point2(5,7), traits_x<Point2>::Retract(p1, Vector2(4., 5.))));
+  EXPECT(assert_equal(Vector2(3.,3.), traits_x<Point2>::Local(p1,p2)));
 }
 
 /* ************************************************************************* */
@@ -83,7 +83,7 @@ TEST( Point2, expmap) {
   Vector d(2);
   d(0) = 1;
   d(1) = -1;
-  Point2 a(4, 5), b = a.retract(d), c(5, 4);
+  Point2 a(4, 5), b = traits_x<Point2>::Retract(a,d), c(5, 4);
   EXPECT(assert_equal(b,c));
 }