diff --git a/gtsam/geometry/CalibratedCamera.cpp b/gtsam/geometry/CalibratedCamera.cpp
index 86e01d71e..026becebe 100644
--- a/gtsam/geometry/CalibratedCamera.cpp
+++ b/gtsam/geometry/CalibratedCamera.cpp
@@ -24,7 +24,7 @@ using namespace std;
 namespace gtsam {
 
 /* ************************************************************************* */
-Matrix26 PinholeBase::Dpose(const Vector2& pn, double d) {
+Matrix26 PinholeBase::Dpose(const Point2& pn, double d) {
   // optimized version of derivatives, see CalibratedCamera.nb
   const double u = pn.x(), v = pn.y();
   double uv = u * v, uu = u * u, vv = v * v;
@@ -34,7 +34,7 @@ Matrix26 PinholeBase::Dpose(const Vector2& pn, double d) {
 }
 
 /* ************************************************************************* */
-Matrix23 PinholeBase::Dpoint(const Vector2& pn, double d, const Matrix3& Rt) {
+Matrix23 PinholeBase::Dpoint(const Point2& pn, double d, const Matrix3& Rt) {
   // optimized version of derivatives, see CalibratedCamera.nb
   const double u = pn.x(), v = pn.y();
   Matrix23 Dpn_point;
@@ -85,20 +85,20 @@ const Pose3& PinholeBase::getPose(OptionalJacobian<6, 6> H) const {
 }
 
 /* ************************************************************************* */
-Vector2 PinholeBase::Project(const Point3& pc, OptionalJacobian<2, 3> Dpoint) {
+Point2 PinholeBase::Project(const Point3& pc, OptionalJacobian<2, 3> Dpoint) {
   double d = 1.0 / pc.z();
   const double u = pc.x() * d, v = pc.y() * d;
   if (Dpoint)
     *Dpoint << d, 0.0, -u * d, 0.0, d, -v * d;
-  return Vector2(u, v);
+  return Point2(u, v);
 }
 
 /* ************************************************************************* */
-Vector2 PinholeBase::Project(const Unit3& pc, OptionalJacobian<2, 2> Dpoint) {
+Point2 PinholeBase::Project(const Unit3& pc, OptionalJacobian<2, 2> Dpoint) {
   if (Dpoint) {
     Matrix32 Dpoint3_pc;
     Matrix23 Duv_point3;
-    Vector2 uv = Project(pc.point3(Dpoint3_pc), Duv_point3);
+    Point2 uv = Project(pc.point3(Dpoint3_pc), Duv_point3);
     *Dpoint = Duv_point3 * Dpoint3_pc;
     return uv;
   } else
@@ -106,14 +106,14 @@ Vector2 PinholeBase::Project(const Unit3& pc, OptionalJacobian<2, 2> Dpoint) {
 }
 
 /* ************************************************************************* */
-pair<Vector2, bool> PinholeBase::projectSafe(const Point3& pw) const {
+pair<Point2, bool> PinholeBase::projectSafe(const Point3& pw) const {
   const Point3 pc = pose().transform_to(pw);
-  const Vector2 pn = Project(pc);
+  const Point2 pn = Project(pc);
   return make_pair(pn, pc.z() > 0);
 }
 
 /* ************************************************************************* */
-Vector2 PinholeBase::project2(const Point3& point, OptionalJacobian<2, 6> Dpose,
+Point2 PinholeBase::project2(const Point3& point, OptionalJacobian<2, 6> Dpose,
     OptionalJacobian<2, 3> Dpoint) const {
 
   Matrix3 Rt; // calculated by transform_to if needed
@@ -122,7 +122,7 @@ Vector2 PinholeBase::project2(const Point3& point, OptionalJacobian<2, 6> Dpose,
   if (q.z() <= 0)
     throw CheiralityException();
 #endif
-  const Vector2 pn = Project(q);
+  const Point2 pn = Project(q);
 
   if (Dpose || Dpoint) {
     const double d = 1.0 / q.z();
@@ -135,7 +135,7 @@ Vector2 PinholeBase::project2(const Point3& point, OptionalJacobian<2, 6> Dpose,
 }
 
 /* ************************************************************************* */
-Vector2 PinholeBase::project2(const Unit3& pw, OptionalJacobian<2, 6> Dpose,
+Point2 PinholeBase::project2(const Unit3& pw, OptionalJacobian<2, 6> Dpose,
     OptionalJacobian<2, 2> Dpoint) const {
 
   // world to camera coordinate
@@ -146,7 +146,7 @@ Vector2 PinholeBase::project2(const Unit3& pw, OptionalJacobian<2, 6> Dpose,
 
   // camera to normalized image coordinate
   Matrix2 Dpn_pc;
-  const Vector2 pn = Project(pc, Dpose || Dpoint ? &Dpn_pc : 0);
+  const Point2 pn = Project(pc, Dpose || Dpoint ? &Dpn_pc : 0);
 
   // chain the Jacobian matrices
   if (Dpose) {
@@ -161,7 +161,7 @@ Vector2 PinholeBase::project2(const Unit3& pw, OptionalJacobian<2, 6> Dpose,
   return pn;
 }
 /* ************************************************************************* */
-Point3 PinholeBase::backproject_from_camera(const Vector2& p,
+Point3 PinholeBase::backproject_from_camera(const Point2& p,
     const double depth) {
   return Point3(p.x() * depth, p.y() * depth, depth);
 }
@@ -178,7 +178,7 @@ CalibratedCamera CalibratedCamera::Lookat(const Point3& eye,
 }
 
 /* ************************************************************************* */
-Vector2 CalibratedCamera::project(const Point3& point,
+Point2 CalibratedCamera::project(const Point3& point,
     OptionalJacobian<2, 6> Dcamera, OptionalJacobian<2, 3> Dpoint) const {
   return project2(point, Dcamera, Dpoint);
 }
diff --git a/gtsam/geometry/CalibratedCamera.h b/gtsam/geometry/CalibratedCamera.h
index bba438e70..81f448a7c 100644
--- a/gtsam/geometry/CalibratedCamera.h
+++ b/gtsam/geometry/CalibratedCamera.h
@@ -54,7 +54,7 @@ public:
    *  Some classes template on either PinholeCamera or StereoCamera,
    *  and this typedef informs those classes what "project" returns.
    */
-  typedef Vector2 Measurement;
+  typedef Point2 Measurement;
 
 private:
 
@@ -70,7 +70,7 @@ protected:
    * @param pn projection in normalized coordinates
    * @param d disparity (inverse depth)
    */
-  static Matrix26 Dpose(const Vector2& pn, double d);
+  static Matrix26 Dpose(const Point2& pn, double d);
 
   /**
    * Calculate Jacobian with respect to point
@@ -78,7 +78,7 @@ protected:
    * @param d disparity (inverse depth)
    * @param Rt transposed rotation matrix
    */
-  static Matrix23 Dpoint(const Vector2& pn, double d, const Matrix3& Rt);
+  static Matrix23 Dpoint(const Point2& pn, double d, const Matrix3& Rt);
 
   /// @}
 
@@ -169,7 +169,7 @@ public:
    * Does *not* throw a CheiralityException, even if pc behind image plane
    * @param pc point in camera coordinates
    */
-  static Vector2 Project(const Point3& pc, //
+  static Point2 Project(const Point3& pc, //
       OptionalJacobian<2, 3> Dpoint = boost::none);
 
   /**
@@ -177,18 +177,18 @@ public:
    * Does *not* throw a CheiralityException, even if pc behind image plane
    * @param pc point in camera coordinates
    */
-  static Vector2 Project(const Unit3& pc, //
+  static Point2 Project(const Unit3& pc, //
       OptionalJacobian<2, 2> Dpoint = boost::none);
 
   /// Project a point into the image and check depth
-  std::pair<Vector2, bool> projectSafe(const Point3& pw) const;
+  std::pair<Point2, bool> projectSafe(const Point3& pw) const;
 
   /** Project point into the image
    * Throws a CheiralityException if point behind image plane iff GTSAM_THROW_CHEIRALITY_EXCEPTION
    * @param point 3D point in world coordinates
    * @return the intrinsic coordinates of the projected point
    */
-  Vector2 project2(const Point3& point, OptionalJacobian<2, 6> Dpose =
+  Point2 project2(const Point3& point, OptionalJacobian<2, 6> Dpose =
       boost::none, OptionalJacobian<2, 3> Dpoint = boost::none) const;
 
   /** Project point at infinity into the image
@@ -196,12 +196,12 @@ public:
    * @param point 3D point in world coordinates
    * @return the intrinsic coordinates of the projected point
    */
-  Vector2 project2(const Unit3& point,
+  Point2 project2(const Unit3& point,
       OptionalJacobian<2, 6> Dpose = boost::none,
       OptionalJacobian<2, 2> Dpoint = boost::none) const;
 
   /// backproject a 2-dimensional point to a 3-dimensional point at given depth
-  static Point3 backproject_from_camera(const Vector2& p, const double depth);
+  static Point3 backproject_from_camera(const Point2& p, const double depth);
 
   /// @}
   /// @name Advanced interface
@@ -325,11 +325,11 @@ public:
    * @deprecated
    * Use project2, which is more consistently named across Pinhole cameras
    */
-  Vector2 project(const Point3& point, OptionalJacobian<2, 6> Dcamera =
+  Point2 project(const Point3& point, OptionalJacobian<2, 6> Dcamera =
       boost::none, OptionalJacobian<2, 3> Dpoint = boost::none) const;
 
   /// backproject a 2-dimensional point to a 3-dimensional point at given depth
-  Point3 backproject(const Vector2& pn, double depth) const {
+  Point3 backproject(const Point2& pn, double depth) const {
     return pose().transform_from(backproject_from_camera(pn, depth));
   }
 
diff --git a/gtsam/geometry/Point2.cpp b/gtsam/geometry/Point2.cpp
index dbbe898ef..e1c5b4c4a 100644
--- a/gtsam/geometry/Point2.cpp
+++ b/gtsam/geometry/Point2.cpp
@@ -63,7 +63,7 @@ bool Point2::equals(const Point2& q, double tol) const {
 
 /* ************************************************************************* */
 double Point2::norm(OptionalJacobian<1,2> H) const {
-  return norm(*this, H);
+  return gtsam::norm2(*this, H);
 }
 
 /* ************************************************************************* */
@@ -78,6 +78,18 @@ ostream &operator<<(ostream &os, const Point2& p) {
   return os;
 }
 
+#ifdef GTSAM_ALLOW_DEPRECATED_SINCE_V4
+boost::optional<Point2> CircleCircleIntersection(double R_d, double r_d, double tol) {
+  return circleCircleIntersection(R_d, r_d, tol);
+}
+std::list<Point2> CircleCircleIntersection(Point2 c1, Point2 c2, boost::optional<Point2> fh) {
+  return circleCircleIntersection(c1, c2, fh);
+}
+std::list<Point2> CircleCircleIntersection(Point2 c1, double r1, Point2 c2, double r2, double tol) {
+  return circleCircleIntersection(c1, r1, c2, r2, tol);
+}
+#endif
+
 #endif // GTSAM_TYPEDEF_POINTS_TO_VECTORS
 
 /* ************************************************************************* */
diff --git a/gtsam/geometry/Point2.h b/gtsam/geometry/Point2.h
index 8d75c805b..fb250df6d 100644
--- a/gtsam/geometry/Point2.h
+++ b/gtsam/geometry/Point2.h
@@ -61,14 +61,6 @@ public:
 
   /// construct from 2D vector
   explicit Point2(const Vector2& v):Vector2(v) {}
-  /// @}
-  /// @name Declare circle intersection functionality
-  /// @{
-
-  friend boost::optional<Point2> circleCircleIntersection(double R_d, double r_d, double tol);
-  friend std::list<Point2> circleCircleIntersection(Point2 c1, Point2 c2, boost::optional<Point2> fh);
-  friend std::list<Point2> circleCircleIntersection(Point2 c1, double r1, Point2 c2, double r2, double tol);
-
   /// @}
   /// @name Testable
   /// @{
@@ -132,15 +124,9 @@ public:
   static Vector2 Logmap(const Point2& p) { return p;}
   static Point2 Expmap(const Vector2& v) { return Point2(v);}
   inline double dist(const Point2& p2) const {return distance(p2);}
-  static boost::optional<Point2> CircleCircleIntersection(double R_d, double r_d, double tol = 1e-9) {
-    return circleCircleIntersection( R_d,  r_d,  tol);
-  }
-  static std::list<Point2> CircleCircleIntersection(Point2 c1, Point2 c2, boost::optional<Point2>) {
-    return circleCircleIntersection( c1,  c2, boost::optional<Point2>);
-  }
-  static std::list<Point2> CircleCircleIntersection(Point2 c1, double r1, Point2 c2, double r2, double tol = 1e-9) {
-    return CircleCircleIntersection(Point2 c1, double r1, Point2 c2, double r2, double tol = 1e-9);
-  }
+  static boost::optional<Point2> CircleCircleIntersection(double R_d, double r_d, double tol = 1e-9);
+  static std::list<Point2> CircleCircleIntersection(Point2 c1, Point2 c2, boost::optional<Point2> fh);
+  static std::list<Point2> CircleCircleIntersection(Point2 c1, double r1, Point2 c2, double r2, double tol = 1e-9);
   /// @}
 #endif
 
diff --git a/gtsam/geometry/Point3.cpp b/gtsam/geometry/Point3.cpp
index d158c91f0..7dc6bd704 100644
--- a/gtsam/geometry/Point3.cpp
+++ b/gtsam/geometry/Point3.cpp
@@ -34,11 +34,11 @@ void Point3::print(const string& s) const {
 /* ************************************************************************* */
 double Point3::distance(const Point3 &q, OptionalJacobian<1, 3> H1,
                         OptionalJacobian<1, 3> H2) const {
-  return gtsam::distance(*this,q,H1,H2);
+  return gtsam::distance3(*this,q,H1,H2);
 }
 
 double Point3::norm(OptionalJacobian<1,3> H) const {
-  return gtsam::norm(*this, H);
+  return gtsam::norm3(*this, H);
 }
 
 Point3 Point3::normalized(OptionalJacobian<3,3> H) const {
diff --git a/gtsam/geometry/tests/testPoint2.cpp b/gtsam/geometry/tests/testPoint2.cpp
index 7ed8cfc6e..e2a5bcdea 100644
--- a/gtsam/geometry/tests/testPoint2.cpp
+++ b/gtsam/geometry/tests/testPoint2.cpp
@@ -111,9 +111,9 @@ TEST( Point2, arithmetic) {
 /* ************************************************************************* */
 TEST( Point2, unit) {
   Point2 p0(10, 0), p1(0, -10), p2(10, 10);
-  EXPECT(assert_equal(Point2(1, 0), p0.normalized(), 1e-6));
-  EXPECT(assert_equal(Point2(0,-1), p1.normalized(), 1e-6));
-  EXPECT(assert_equal(Point2(sqrt(2.0)/2.0, sqrt(2.0)/2.0), p2.normalized(), 1e-6));
+  EXPECT(assert_equal(Point2(1, 0), Point2(p0.normalized()), 1e-6));
+  EXPECT(assert_equal(Point2(0,-1), Point2(p1.normalized()), 1e-6));
+  EXPECT(assert_equal(Point2(sqrt(2.0)/2.0, sqrt(2.0)/2.0), Point2(p2.normalized()), 1e-6));
 }
 
 namespace {