diff --git a/gtsam/geometry/OrientedPlane3.cpp b/gtsam/geometry/OrientedPlane3.cpp
index fa92905ff..f3e3a039f 100644
--- a/gtsam/geometry/OrientedPlane3.cpp
+++ b/gtsam/geometry/OrientedPlane3.cpp
@@ -60,28 +60,21 @@ OrientedPlane3 OrientedPlane3::transform(const Pose3& xr,
 }
 
 /* ************************************************************************* */
-Vector3 OrientedPlane3::error(const OrientedPlane3& plane,
+Vector3 OrientedPlane3::error(const OrientedPlane3& other,
                               OptionalJacobian<3, 3> H1,
                               OptionalJacobian<3, 3> H2) const {
-  // Numerically calculate the derivative since this function doesn't provide
-  // one.
+  Vector2 n_error = -n_.localCoordinates(other.n_);
+  
   const auto f = boost::bind(&Unit3::localCoordinates, _1, _2);
-
-  Vector2 n_error = -n_.localCoordinates(plane.n_);
-
   if (H1) {
-    *H1 = I_3x3;
-    H1->block<2, 2>(0, 0) =
-        -numericalDerivative21<Vector2, Unit3, Unit3>(f, n_, plane.n_);
-    ;
+    Matrix2 H_n_error_this = -numericalDerivative21<Vector2, Unit3, Unit3>(f, n_, other.n_);
+    *H1 << H_n_error_this, Z_2x1, 0, 0, 1;
   }
   if (H2) {
-    *H2 = -I_3x3;
-    H2->block<2, 2>(0, 0) =
-        -numericalDerivative22<Vector2, Unit3, Unit3>(f, n_, plane.n_);
-    ;
+    Matrix H_n_error_other = -numericalDerivative22<Vector2, Unit3, Unit3>(f, n_, other.n_);
+    *H2 << H_n_error_other, Z_2x1, 0, 0, -1;
   }
-  return Vector3(n_error(0), n_error(1), d_ - plane.d_);
+  return Vector3(n_error(0), n_error(1), d_ - other.d_);
 }
 
 /* ************************************************************************* */
diff --git a/gtsam/geometry/OrientedPlane3.h b/gtsam/geometry/OrientedPlane3.h
index aaacca78a..2550761b1 100644
--- a/gtsam/geometry/OrientedPlane3.h
+++ b/gtsam/geometry/OrientedPlane3.h
@@ -96,9 +96,9 @@ public:
 
   /** Computes the error between two planes.
    *  The error is a norm 1 difference in tangent space.
-   * @param plane The other plane
+   * @param other The other plane
    */
-  Vector3 error(const OrientedPlane3& plane,
+  Vector3 error(const OrientedPlane3& other,
                 OptionalJacobian<3, 3> H1 = boost::none,
                 OptionalJacobian<3, 3> H2 = boost::none) const;
 
@@ -106,7 +106,7 @@ public:
    *  This uses Unit3::errorVector, as opposed to the other .error() in this class, which uses
    *  Unit3::localCoordinates. This one has correct derivatives.
    *  NOTE(hayk): The derivatives are zero when normals are exactly orthogonal.
-   * @param the other plane
+   * @param other the other plane
    */
   Vector3 errorVector(const OrientedPlane3& other, OptionalJacobian<3, 3> H1 = boost::none, //
                       OptionalJacobian<3, 3> H2 = boost::none) const;