diff --git a/gtsam/geometry/tests/testQuaternion.cpp b/gtsam/geometry/tests/testQuaternion.cpp
index 22a96f4a3..8c8f9354f 100644
--- a/gtsam/geometry/tests/testQuaternion.cpp
+++ b/gtsam/geometry/tests/testQuaternion.cpp
@@ -33,9 +33,19 @@ namespace manifold {
 
 /// Chart for Eigen Quaternions
 template<typename S, int O>
-class QuaternionChart: public manifold::Chart<Eigen::Quaternion<S, O>,
+struct QuaternionChart: public manifold::Chart<Eigen::Quaternion<S, O>,
     QuaternionChart<S, O> > {
-
+  typedef Eigen::Quaternion<S, O> Q;
+  typedef typename traits::TangentVector<Q>::type V;
+  static V local(const Q& p, const Q& q) {
+    return V();
+  }
+  static Q retract(const Q& p, const V& v) {
+    double theta = v.norm();
+    if (std::abs(theta) < 1e-10)
+      return p;
+    return p * Q(Eigen::AngleAxisd(theta, v / theta));
+  }
 };
 
 namespace traits {
@@ -49,13 +59,13 @@ struct dimension<Eigen::Quaternion<S, O> > : public boost::integral_constant<
 /// Define the trait that asserts Quaternion TangentVector is Vector3
 template<typename S, int O>
 struct TangentVector<Eigen::Quaternion<S, O> > {
-  typedef Eigen::Matrix<S,3,1,O,3,1> type;
+  typedef Eigen::Matrix<S, 3, 1, O, 3, 1> type;
 };
 
 /// Define the trait that asserts Quaternion TangentVector is Vector3
 template<typename S, int O>
 struct DefaultChart<Eigen::Quaternion<S, O> > {
-  typedef QuaternionChart<S,O> type;
+  typedef QuaternionChart<S, O> type;
 };
 
 } // \namespace gtsam::manifold::traits
@@ -129,21 +139,45 @@ typedef Quaternion Q; // Typedef
 
 //******************************************************************************
 TEST(Quaternion , Concept) {
-  //  BOOST_CONCEPT_ASSERT((IsGroup<Quaternion >));
-  //  BOOST_CONCEPT_ASSERT((IsManifold<Quaternion >));
-  //  BOOST_CONCEPT_ASSERT((IsLieGroup<Quaternion >));
+  BOOST_CONCEPT_ASSERT((IsGroup<Quaternion >)); // not strictly needed
+  BOOST_CONCEPT_ASSERT((IsManifold<Quaternion >)); // not strictly needed
+  BOOST_CONCEPT_ASSERT((IsLieGroup<Quaternion >));
 }
 
 //******************************************************************************
 TEST(Quaternion , Constructor) {
-  Q g(Eigen::AngleAxisd(1, Vector3(0, 0, 1)));
+  Q q(Eigen::AngleAxisd(1, Vector3(0, 0, 1)));
 }
 
 //******************************************************************************
 TEST(Quaternion , Invariants) {
-  Q g(Eigen::AngleAxisd(1, Vector3(0, 0, 1)));
-  Q h(Eigen::AngleAxisd(2, Vector3(0, 1, 0)));
-  // group::check_invariants(g,h); Does not satisfy Testable concept (yet!)
+  Q q1(Eigen::AngleAxisd(1, Vector3(0, 0, 1)));
+  Q q2(Eigen::AngleAxisd(2, Vector3(0, 1, 0)));
+  // group::check_invariants(q1,q2); Does not satisfy Testable concept (yet!)
+}
+
+//******************************************************************************
+TEST(Quaternion , Local) {
+  Vector3 z_axis(0,0,1);
+  Q q1(Eigen::AngleAxisd(0,z_axis));
+  Q q2(Eigen::AngleAxisd(0.1, z_axis));
+  typedef manifold::traits::DefaultChart<Q>::type Chart;
+  Vector3 expected(0,0,0.1);
+  Vector3 actual = Chart::Local(q1,q2);
+  cout << expected << endl;
+  cout << actual << endl;
+  EXPECT(assert_equal((Vector)expected,actual));
+}
+
+//******************************************************************************
+TEST(Quaternion , Retract) {
+  Vector3 z_axis(0,0,1);
+  Q q(Eigen::AngleAxisd(0,z_axis));
+  Q expected(Eigen::AngleAxisd(0.1, z_axis));
+  typedef manifold::traits::DefaultChart<Q>::type Chart;
+  Vector3 v(0,0,0.1);
+  Q actual = Chart::Retract(q,v);
+  EXPECT(actual.isApprox(expected));
 }
 
 //******************************************************************************
@@ -155,7 +189,7 @@ TEST(Quaternion , Between) {
 }
 
 //******************************************************************************
-TEST(Quaternion , Ivnverse) {
+TEST(Quaternion , Inverse) {
 }
 
 //******************************************************************************