diff --git a/cartographer/common/math.h b/cartographer/common/math.h
index ea96c0b..f0ae9e2 100644
--- a/cartographer/common/math.h
+++ b/cartographer/common/math.h
@@ -51,14 +51,6 @@ constexpr T Pow2(T a) {
   return Power(a, 2);
 }
 
-// Calculates the real part of the square root of 'a'. This is helpful when
-// rounding errors generate a small negative argument. Otherwise std::sqrt
-// returns NaN if its argument is negative.
-template <typename T>
-constexpr T RealSqrt(T a) {
-  return sqrt(std::max(T(0.), a));
-}
-
 // Converts from degrees to radians.
 constexpr double DegToRad(double deg) { return M_PI * deg / 180.; }
 
diff --git a/cartographer/mapping_3d/scan_matching/fast_correlative_scan_matcher.cc b/cartographer/mapping_3d/scan_matching/fast_correlative_scan_matcher.cc
index 8a8b8a4..b8875c1 100644
--- a/cartographer/mapping_3d/scan_matching/fast_correlative_scan_matcher.cc
+++ b/cartographer/mapping_3d/scan_matching/fast_correlative_scan_matcher.cc
@@ -249,9 +249,9 @@ std::vector<DiscreteScan> FastCorrelativeScanMatcher::GenerateDiscreteScans(
     // and rotation of the 'initial_pose', so that the rotation is around the
     // origin of the range data, and yaw is in map frame.
     const transform::Rigid3f pose(
-        Eigen::Translation3f(initial_pose.translation()) *
+        initial_pose.translation(),
         transform::AngleAxisVectorToRotationQuaternion(angle_axis) *
-        Eigen::Quaternionf(initial_pose.rotation()));
+            initial_pose.rotation());
     result.push_back(
         DiscretizeScan(search_parameters, coarse_point_cloud, pose));
   }
diff --git a/cartographer/transform/rigid_transform.h b/cartographer/transform/rigid_transform.h
index 5a45fb3..16779fb 100644
--- a/cartographer/transform/rigid_transform.h
+++ b/cartographer/transform/rigid_transform.h
@@ -32,7 +32,6 @@ namespace transform {
 template <typename FloatType>
 class Rigid2 {
  public:
-  using Affine = Eigen::Transform<FloatType, 2, Eigen::Affine>;
   using Vector = Eigen::Matrix<FloatType, 2, 1>;
   using Rotation2D = Eigen::Rotation2D<FloatType>;
 
@@ -125,16 +124,12 @@ using Rigid2f = Rigid2<float>;
 template <typename FloatType>
 class Rigid3 {
  public:
-  using Affine = Eigen::Transform<FloatType, 3, Eigen::Affine>;
   using Vector = Eigen::Matrix<FloatType, 3, 1>;
   using Quaternion = Eigen::Quaternion<FloatType>;
   using AngleAxis = Eigen::AngleAxis<FloatType>;
 
   Rigid3()
       : translation_(Vector::Identity()), rotation_(Quaternion::Identity()) {}
-  // TODO(damonkohler): Remove
-  explicit Rigid3(const Affine& affine)
-      : translation_(affine.translation()), rotation_(affine.rotation()) {}
   Rigid3(const Vector& translation, const Quaternion& rotation)
       : translation_(translation), rotation_(rotation) {}
   Rigid3(const Vector& translation, const AngleAxis& rotation)