diff --git a/gtsam/geometry/Cal3_S2.h b/gtsam/geometry/Cal3_S2.h
index 71adc58bc..120f8dc8b 100644
--- a/gtsam/geometry/Cal3_S2.h
+++ b/gtsam/geometry/Cal3_S2.h
@@ -34,11 +34,11 @@ namespace gtsam {
 	private:
 		double fx_, fy_, s_, u0_, v0_;
 
+	public:
+
     /// @name Standard Constructors
     /// @{
 
-	public:
-
 		/// Create a default calibration that leaves coordinates unchanged
 		Cal3_S2() :
 			fx_(1), fy_(1), s_(0), u0_(0), v0_(0) {
diff --git a/gtsam/geometry/Pose2.h b/gtsam/geometry/Pose2.h
index 9f83a3764..3a8f69899 100644
--- a/gtsam/geometry/Pose2.h
+++ b/gtsam/geometry/Pose2.h
@@ -177,23 +177,16 @@ public:
 				0., 0.,  0.);
 	}
 
-  /// @}
-	/// @name Standard Interface
+	/// @}
+	/// @name Group Action on Point2
 	/// @{
 
-	/** return transformation matrix */
-	Matrix matrix() const;
-
-	/**
-	 * Return point coordinates in pose coordinate frame
-	 */
+	/** Return point coordinates in pose coordinate frame */
 	Point2 transform_to(const Point2& point,
 			boost::optional<Matrix&> H1=boost::none,
 			boost::optional<Matrix&> H2=boost::none) const;
 
-	/**
-	 * Return point coordinates in global frame
-	 */
+	/** Return point coordinates in global frame */
 	Point2 transform_from(const Point2& point,
 			boost::optional<Matrix&> H1=boost::none,
 			boost::optional<Matrix&> H2=boost::none) const;
@@ -201,6 +194,34 @@ public:
 	/** syntactic sugar for transform_from */
 	inline Point2 operator*(const Point2& point) const { return transform_from(point);}
 
+  /// @}
+	/// @name Standard Interface
+	/// @{
+
+	/// get x
+	inline double x()     const { return t_.x(); }
+
+	/// get y
+	inline double y()     const { return t_.y(); }
+
+	/// get theta
+	inline double theta() const { return r_.theta(); }
+
+	/// translation
+	inline const Point2& t() const { return t_; }
+
+	/// rotation
+	inline const Rot2&   r() const { return r_; }
+
+	/// translation
+	inline const Point2& translation() const { return t_; }
+
+	/// rotation
+	inline const Rot2&   rotation() const { return r_; }
+
+	//// return transformation matrix
+	Matrix matrix() const;
+
 	/**
 	 * Calculate bearing to a landmark
 	 * @param point 2D location of landmark
@@ -237,26 +258,6 @@ public:
 			boost::optional<Matrix&> H1=boost::none,
 			boost::optional<Matrix&> H2=boost::none) const;
 
-	/** get functions for x, y, theta */
-
-	/// get x
-	inline double x()     const { return t_.x(); }
-
-	/// get y
-	inline double y()     const { return t_.y(); }
-
-	/// get theta
-	inline double theta() const { return r_.theta(); }
-
-	/** shorthand access functions */
-	inline const Point2& t() const { return t_; }
-	inline const Rot2&   r() const { return r_; }
-
-	/** full access functions required by Pose concept */
-
-	inline const Point2& translation() const { return t_; }
-	inline const Rot2&   rotation() const { return r_; }
-
 private:
 
 	/// @}
diff --git a/gtsam/geometry/Pose3.h b/gtsam/geometry/Pose3.h
index 7884e7912..640016970 100644
--- a/gtsam/geometry/Pose3.h
+++ b/gtsam/geometry/Pose3.h
@@ -165,6 +165,21 @@ namespace gtsam {
           0.,  0.,  0.,  0.);
     }
 
+  	/// @}
+  	/// @name Group Action on Point3
+  	/// @{
+
+    /** receives the point in Pose coordinates and transforms it to world coordinates */
+    Point3 transform_from(const Point3& p,
+        boost::optional<Matrix&> H1=boost::none, boost::optional<Matrix&> H2=boost::none) const;
+
+    /** syntactic sugar for transform_from */
+    inline Point3 operator*(const Point3& p) const { return transform_from(p); }
+
+    /** receives the point in world coordinates and transforms it to Pose coordinates */
+    Point3 transform_to(const Point3& p,
+        boost::optional<Matrix&> H1=boost::none, boost::optional<Matrix&> H2=boost::none) const;
+
     /// @}
   	/// @name Standard Interface
   	/// @{
@@ -187,19 +202,9 @@ namespace gtsam {
     /** convert to 4*4 matrix */
     Matrix matrix() const;
 
+    /** receives a pose in world coordinates and transforms it to local coordinates */
     Pose3 transform_to(const Pose3& pose) const;
 
-    /** receives the point in Pose coordinates and transforms it to world coordinates */
-    Point3 transform_from(const Point3& p,
-        boost::optional<Matrix&> H1=boost::none, boost::optional<Matrix&> H2=boost::none) const;
-
-    /** syntactic sugar for transform_from */
-    inline Point3 operator*(const Point3& p) const { return transform_from(p); }
-
-    /** receives the point in world coordinates and transforms it to Pose coordinates */
-    Point3 transform_to(const Point3& p,
-        boost::optional<Matrix&> H1=boost::none, boost::optional<Matrix&> H2=boost::none) const;
-
     /**
      * Calculate range to a landmark
      * @param point 3D location of landmark
@@ -230,6 +235,8 @@ namespace gtsam {
       ar & BOOST_SERIALIZATION_NVP(R_);
       ar & BOOST_SERIALIZATION_NVP(t_);
     }
+  	/// @}
+
   }; // Pose3 class
 
   /**
@@ -243,6 +250,5 @@ namespace gtsam {
   inline Matrix wedge<Pose3>(const Vector& xi) {
     return Pose3::wedge(xi(0),xi(1),xi(2),xi(3),xi(4),xi(5));
   }
-	/// @}
 
 } // namespace gtsam
diff --git a/gtsam/geometry/Rot2.h b/gtsam/geometry/Rot2.h
index 7dbac4593..f3062f5c1 100644
--- a/gtsam/geometry/Rot2.h
+++ b/gtsam/geometry/Rot2.h
@@ -44,9 +44,6 @@ namespace gtsam {
 		/** normalize to make sure cos and sin form unit vector */
 		Rot2& normalize();
 
-		/// @name Standard Constructors
-		/// @{
-
 		/** private constructor from cos/sin */
 		inline Rot2(double c, double s) :
 				c_(c), s_(s) {
@@ -54,6 +51,9 @@ namespace gtsam {
 
 	public:
 
+    /// @name Constructors and named constructors
+    /// @{
+
 		/** default constructor, zero rotation */
 		Rot2() :
 				c_(1.0), s_(0.0) {
@@ -171,21 +171,36 @@ namespace gtsam {
 			return Vector_(1, r.theta());
 		}
 
-		/// @}
-	  /// @name Vector Space
-		/// @{
+  	/// @}
+  	/// @name Group Action on Point2
+  	/// @{
+
+    /**
+		 * rotate point from rotated coordinate frame to world \f$ p^w = R_c^w p^c \f$
+		 */
+		Point2 rotate(const Point2& p, boost::optional<Matrix&> H1 = boost::none,
+				boost::optional<Matrix&> H2 = boost::none) const;
+
+		/** syntactic sugar for rotate */
+		inline Point2 operator*(const Point2& p) const {
+			return rotate(p);
+		}
 
 		/**
-		 * Creates a unit vector as a Point2
+		 * rotate point from world to rotated frame \f$ p^c = (R_c^w)^T p^w \f$
 		 */
-		inline Point2 unit() const {
-			return Point2(c_, s_);
-		}
+		Point2 unrotate(const Point2& p, boost::optional<Matrix&> H1 = boost::none,
+				boost::optional<Matrix&> H2 = boost::none) const;
 
 		/// @}
 		/// @name Standard Interface
 		/// @{
 
+		/// Creates a unit vector as a Point2
+		inline Point2 unit() const {
+			return Point2(c_, s_);
+		}
+
 		/** return angle (RADIANS) */
 		double theta() const {
 			return ::atan2(s_, c_);
@@ -213,25 +228,6 @@ namespace gtsam {
 		/** return 2*2 transpose (inverse) rotation matrix   */
 		Matrix transpose() const;
 
-		/**
-		 * rotate point from rotated coordinate frame to
-		 * world = R*p
-		 */
-		Point2 rotate(const Point2& p, boost::optional<Matrix&> H1 = boost::none,
-				boost::optional<Matrix&> H2 = boost::none) const;
-
-		/** syntactic sugar for rotate */
-		inline Point2 operator*(const Point2& p) const {
-			return rotate(p);
-		}
-
-		/**
-		 * rotate point from world to rotated
-		 * frame = R'*p
-		 */
-		Point2 unrotate(const Point2& p, boost::optional<Matrix&> H1 = boost::none,
-				boost::optional<Matrix&> H2 = boost::none) const;
-
 		/// @}
 		/// @name Advanced Interface
 		/// @{
diff --git a/gtsam/geometry/Rot3.h b/gtsam/geometry/Rot3.h
index 456546a21..2e16f869c 100644
--- a/gtsam/geometry/Rot3.h
+++ b/gtsam/geometry/Rot3.h
@@ -266,27 +266,28 @@ namespace gtsam {
      */
     static Vector Logmap(const Rot3& R);
 
-    /// @}
-  	/// @name Standard Interface
+  	/// @}
+  	/// @name Group Action on Point3
   	/// @{
 
     /**
-     * rotate point from rotated coordinate frame to
-     * world = R*p
-     */
-    Point3 rotate(const Point3& p,
-    boost::optional<Matrix&> H1=boost::none,  boost::optional<Matrix&> H2=boost::none) const;
+		 * rotate point from rotated coordinate frame to world \f$ p^w = R_c^w p^c \f$
+		 */
+		Point3 rotate(const Point3& p, boost::optional<Matrix&> H1 = boost::none,
+				boost::optional<Matrix&> H2 = boost::none) const;
 
-    /// rotate point from rotated coordinate frame to world = R*p
-    Point3 operator*(const Point3& p) const;
+		/// rotate point from rotated coordinate frame to world = R*p
+		Point3 operator*(const Point3& p) const;
 
-    /**
-     * rotate point from world to rotated
-     * frame = R'*p
-     */
-    Point3 unrotate(const Point3& p,
-      boost::optional<Matrix&> H1=boost::none, boost::optional<Matrix&> H2=boost::none) const;
+		/**
+		 * rotate point from world to rotated frame \f$ p^c = (R_c^w)^T p^w \f$
+		 */
+		Point3 unrotate(const Point3& p, boost::optional<Matrix&> H1 = boost::none,
+				boost::optional<Matrix&> H2 = boost::none) const;
 
+    /// @}
+  	/// @name Standard Interface
+  	/// @{
 
     /** return 3*3 rotation matrix */
     Matrix matrix() const;