diff --git a/gtsam/geometry/Cal3Bundler.cpp b/gtsam/geometry/Cal3Bundler.cpp
index 8b7771410..03071a4f2 100644
--- a/gtsam/geometry/Cal3Bundler.cpp
+++ b/gtsam/geometry/Cal3Bundler.cpp
@@ -152,7 +152,7 @@ Cal3Bundler Cal3Bundler::retract(const Vector& d) const {
 
 /* ************************************************************************* */
 Vector Cal3Bundler::localCoordinates(const Cal3Bundler& T2) const {
-  return vector() - T2.vector();
+  return T2.vector() - vector();
 }
 
 }
diff --git a/gtsam/geometry/Cal3DS2.cpp b/gtsam/geometry/Cal3DS2.cpp
index 0d263b625..e6c97cb1a 100644
--- a/gtsam/geometry/Cal3DS2.cpp
+++ b/gtsam/geometry/Cal3DS2.cpp
@@ -28,13 +28,20 @@ Cal3DS2::Cal3DS2(const Vector &v):
     fx_(v[0]), fy_(v[1]), s_(v[2]), u0_(v[3]), v0_(v[4]), k1_(v[5]), k2_(v[6]), k3_(v[7]), k4_(v[8]){}
 
 /* ************************************************************************* */
-Matrix Cal3DS2::K() const { return (Matrix(3, 3) <<  fx_, s_, u0_, 0.0, fy_, v0_, 0.0, 0.0, 1.0); }
+Matrix Cal3DS2::K() const {
+  return (Matrix(3, 3) << fx_, s_, u0_, 0.0, fy_, v0_, 0.0, 0.0, 1.0);
+}
 
 /* ************************************************************************* */
-Vector Cal3DS2::vector() const { return (Vector(9) << fx_, fy_, s_, u0_, v0_, k1_, k2_, k3_, k4_); }
+Vector Cal3DS2::vector() const {
+  return (Vector(9) << fx_, fy_, s_, u0_, v0_, k1_, k2_, k3_, k4_);
+}
 
 /* ************************************************************************* */
-void Cal3DS2::print(const std::string& s) const { gtsam::print(K(), s + ".K"); gtsam::print(Vector(k()), s + ".k"); }
+void Cal3DS2::print(const std::string& s) const {
+  gtsam::print(K(), s + ".K");
+  gtsam::print(Vector(k()), s + ".k");
+}
 
 /* ************************************************************************* */
 bool Cal3DS2::equals(const Cal3DS2& K, double tol) const {
@@ -173,10 +180,14 @@ Matrix Cal3DS2::D2d_calibration(const Point2& p) const {
 }
 
 /* ************************************************************************* */
-Cal3DS2 Cal3DS2::retract(const Vector& d) const { return Cal3DS2(vector() + d); }
+Cal3DS2 Cal3DS2::retract(const Vector& d) const {
+  return Cal3DS2(vector() + d);
+}
 
 /* ************************************************************************* */
-Vector Cal3DS2::localCoordinates(const Cal3DS2& T2) const { return vector() - T2.vector(); }
+Vector Cal3DS2::localCoordinates(const Cal3DS2& T2) const {
+  return T2.vector() - vector();
+}
 
 }
 /* ************************************************************************* */
diff --git a/gtsam/geometry/Cal3_S2.h b/gtsam/geometry/Cal3_S2.h
index a62266046..c134860bb 100644
--- a/gtsam/geometry/Cal3_S2.h
+++ b/gtsam/geometry/Cal3_S2.h
@@ -186,7 +186,7 @@ public:
 
   /// Unretraction for the calibration
   Vector localCoordinates(const Cal3_S2& T2) const {
-    return vector() - T2.vector();
+    return T2.vector() - vector();
   }
 
   /// @}
diff --git a/gtsam/geometry/tests/testCal3Bundler.cpp b/gtsam/geometry/tests/testCal3Bundler.cpp
index 7cec17b34..6e62d4be0 100644
--- a/gtsam/geometry/tests/testCal3Bundler.cpp
+++ b/gtsam/geometry/tests/testCal3Bundler.cpp
@@ -82,6 +82,7 @@ TEST( Cal3Bundler, retract)
   d << 10, 1e-3, 1e-3;
   Cal3Bundler actual = K.retract(d);
   CHECK(assert_equal(expected,actual,1e-7));
+  CHECK(assert_equal(d,K.localCoordinates(actual),1e-7));
 }
 
 /* ************************************************************************* */
diff --git a/gtsam/geometry/tests/testCal3DS2.cpp b/gtsam/geometry/tests/testCal3DS2.cpp
index 53a21a9fb..fc457767e 100644
--- a/gtsam/geometry/tests/testCal3DS2.cpp
+++ b/gtsam/geometry/tests/testCal3DS2.cpp
@@ -76,6 +76,18 @@ TEST( Cal3DS2, assert_equal)
   CHECK(assert_equal(K,K,1e-5));
 }
 
+/* ************************************************************************* */
+TEST( Cal3DS2, retract)
+{
+  Cal3DS2 expected(500 + 1, 100 + 2, 0.1 + 3, 320 + 4, 240 + 5, 1e-3 + 6,
+      2.0 * 1e-3 + 7, 3.0 * 1e-3 + 8, 4.0 * 1e-3 + 9);
+  Vector d(9);
+  d << 1,2,3,4,5,6,7,8,9;
+  Cal3DS2 actual = K.retract(d);
+  CHECK(assert_equal(expected,actual,1e-7));
+  CHECK(assert_equal(d,K.localCoordinates(actual),1e-7));
+}
+
 /* ************************************************************************* */
 int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
 /* ************************************************************************* */
diff --git a/gtsam/geometry/tests/testCal3_S2.cpp b/gtsam/geometry/tests/testCal3_S2.cpp
index e1dba2272..d77a534d6 100644
--- a/gtsam/geometry/tests/testCal3_S2.cpp
+++ b/gtsam/geometry/tests/testCal3_S2.cpp
@@ -82,6 +82,17 @@ TEST( Cal3_S2, assert_equal)
   CHECK(assert_equal(K,K1,1e-9));
 }
 
+/* ************************************************************************* */
+TEST( Cal3_S2, retract)
+{
+  Cal3_S2 expected(500+1, 500+2, 0.1+3, 640 / 2+4, 480 / 2+5);
+  Vector d(5);
+  d << 1,2,3,4,5;
+  Cal3_S2 actual = K.retract(d);
+  CHECK(assert_equal(expected,actual,1e-7));
+  CHECK(assert_equal(d,K.localCoordinates(actual),1e-7));
+}
+
 /* ************************************************************************* */
 int main() {
   TestResult tr;