diff --git a/docs/source/nnls_modeling.rst b/docs/source/nnls_modeling.rst
index 2604027..0883c6d 100644
--- a/docs/source/nnls_modeling.rst
+++ b/docs/source/nnls_modeling.rst
@@ -1339,6 +1339,7 @@
    same update as :class:`QuaternionParameterization` but takes into
    account Eigen's internal memory element ordering.
 
+.. _`homogeneous_vector_parameterization`:
 .. class:: HomogeneousVectorParameterization
 
    In computer vision, homogeneous vectors are commonly used to
@@ -1362,6 +1363,27 @@
    last element of :math:`x` is the scalar component of the homogeneous
    vector.
 
+.. class:: LineParameterization
+
+   This class provides a parameterization for lines, where the line is
+   over-parameterized by an origin point and a direction vector. So the
+   parameter vector size needs to be two times the ambient space dimension,
+   where the first half is interpreted as the origin point and the second
+   half as the direction.
+
+   To give an example: Given n distinct points in 3D (measurements) we search
+   for the line which has the closest distance to all of these. We parameterize
+   the line with a 3D origin point and a 3D direction vector. As a cost
+   function the distance between the line and the given points is used.
+   We use six parameters for the line (two 3D vectors) but a line in 3D only
+   has four degrees of freedom. To make the over-parameterization visible to
+   the optimizer and covariance estimator this line parameterization can be
+   used.
+
+   The plus operator for the line direction is the same as for the
+   :ref:`HomogeneousVectorParameterization <homogeneous_vector_parameterization>`.
+   The update of the origin point is perpendicular to the line direction
+   before the update.
 
 .. class:: ProductParameterization
 
diff --git a/internal/ceres/householder_vector.h b/include/ceres/internal/householder_vector.h
similarity index 89%
rename from internal/ceres/householder_vector.h
rename to include/ceres/internal/householder_vector.h
index 6d85217..051a88d 100644
--- a/internal/ceres/householder_vector.h
+++ b/include/ceres/internal/householder_vector.h
@@ -28,8 +28,8 @@
 //
 // Author: vitus@google.com (Michael Vitus)
 
-#ifndef CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_
-#define CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_
+#ifndef CERES_PUBLIC_INTERNAL_HOUSEHOLDER_VECTOR_H_
+#define CERES_PUBLIC_INTERNAL_HOUSEHOLDER_VECTOR_H_
 
 #include "Eigen/Core"
 #include "glog/logging.h"
@@ -42,9 +42,9 @@
 // vector as pivot instead of first. This computes the vector v with v(n) = 1
 // and beta such that H = I - beta * v * v^T is orthogonal and
 // H * x = ||x||_2 * e_n.
-template <typename Scalar>
-void ComputeHouseholderVector(const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& x,
-                              Eigen::Matrix<Scalar, Eigen::Dynamic, 1>* v,
+template <typename Derived, typename Scalar, int N>
+void ComputeHouseholderVector(const Eigen::DenseBase<Derived>& x,
+                              Eigen::Matrix<Scalar, N, 1>* v,
                               Scalar* beta) {
   CHECK(beta != nullptr);
   CHECK(v != nullptr);
@@ -82,4 +82,4 @@
 }  // namespace internal
 }  // namespace ceres
 
-#endif  // CERES_PUBLIC_HOUSEHOLDER_VECTOR_H_
+#endif  // CERES_PUBLIC_INTERNAL_HOUSEHOLDER_VECTOR_H_
diff --git a/include/ceres/internal/line_parameterization.h b/include/ceres/internal/line_parameterization.h
new file mode 100644
index 0000000..b2ec9e1
--- /dev/null
+++ b/include/ceres/internal/line_parameterization.h
@@ -0,0 +1,172 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2020 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: jodebo_beck@gmx.de (Johannes Beck)
+//
+
+#ifndef CERES_PUBLIC_INTERNAL_LINE_PARAMETERIZATION_H_
+#define CERES_PUBLIC_INTERNAL_LINE_PARAMETERIZATION_H_
+
+#include "householder_vector.h"
+
+namespace ceres {
+
+template <int AmbientSpaceDimension>
+bool LineParameterization<AmbientSpaceDimension>::Plus(
+    const double* x_ptr,
+    const double* delta_ptr,
+    double* x_plus_delta_ptr) const {
+  // We seek a box plus operator of the form
+  //
+  //   [o*, d*] = Plus([o, d], [delta_o, delta_d])
+  //
+  // where o is the origin point, d is the direction vector, delta_o is
+  // the delta of the origin point and delta_d the delta of the direction and
+  // o* and d* is the updated origin point and direction.
+  //
+  // We separate the Plus operator into the origin point and directional part
+  //   d* = Plus_d(d, delta_d)
+  //   o* = Plus_o(o, d, delta_o)
+  //
+  // The direction update function Plus_d is the same as for the homogeneous vector
+  // parameterization:
+  //
+  //   d* = H_{v(d)} [0.5 sinc(0.5 |delta_d|) delta_d, cos(0.5 |delta_d|)]^T
+  //
+  // where H is the householder matrix
+  //   H_{v} = I - (2 / |v|^2) v v^T
+  // and
+  //   v(d) = d - sign(d_n) |d| e_n.
+  //
+  // The origin point update function Plus_o is defined as
+  //
+  //   o* = o + H_{v(d)} [0.5 delta_o, 0]^T.
+
+  static constexpr int kDim = AmbientSpaceDimension;
+  using AmbientVector = Eigen::Matrix<double, kDim, 1>;
+  using AmbientVectorRef = Eigen::Map<Eigen::Matrix<double, kDim, 1>>;
+  using ConstAmbientVectorRef = Eigen::Map<const Eigen::Matrix<double, kDim, 1>>;
+  using ConstTangentVectorRef =
+      Eigen::Map<const Eigen::Matrix<double, kDim - 1, 1>>;
+  
+  
+  ConstAmbientVectorRef o(x_ptr);
+  ConstAmbientVectorRef d(x_ptr + kDim);
+
+  ConstTangentVectorRef delta_o(delta_ptr);
+  ConstTangentVectorRef delta_d(delta_ptr + kDim - 1);
+  AmbientVectorRef o_plus_delta(x_plus_delta_ptr);
+  AmbientVectorRef d_plus_delta(x_plus_delta_ptr + kDim);
+
+  const double norm_delta_d = delta_d.norm();
+
+  o_plus_delta = o;
+
+  // Shortcut for zero delta direction.
+  if (norm_delta_d == 0.0) {
+    d_plus_delta = d;
+
+    if (delta_o.isZero(0.0)) {
+      return true;
+    }
+  }
+
+  // Calculate the householder transformation which is needed for f_d and f_o.
+  AmbientVector v;
+  double beta;
+  internal::ComputeHouseholderVector(d, &v, &beta);
+
+  if (norm_delta_d != 0.0) {
+    // Map the delta from the minimum representation to the over parameterized
+    // homogeneous vector. See section A6.9.2 on page 624 of Hartley & Zisserman
+    // (2nd Edition) for a detailed description.  Note there is a typo on Page
+    // 625, line 4 so check the book errata.
+    const double norm_delta_div_2 = 0.5 * norm_delta_d;
+    const double sin_delta_by_delta =
+        std::sin(norm_delta_div_2) / norm_delta_div_2;
+
+    // Apply the delta update to remain on the unit sphere. See section A6.9.3
+    // on page 625 of Hartley & Zisserman (2nd Edition) for a detailed
+    // description.
+    AmbientVector y;
+    y.template head<kDim - 1>() = 0.5 * sin_delta_by_delta * delta_d;
+    y[kDim - 1] = std::cos(norm_delta_div_2);
+
+    d_plus_delta = d.norm() * (y - v * (beta * (v.transpose() * y)));
+  }
+
+  // The null space is in the direction of the line, so the tangent space is
+  // perpendicular to the line direction. This is achieved by using the
+  // householder matrix of the direction and allow only movements
+  // perpendicular to e_n.
+  //
+  // The factor of 0.5 is used to be consistent with the line direction
+  // update.
+  AmbientVector y;
+  y << 0.5 * delta_o, 0;
+  o_plus_delta += y - v * (beta * (v.transpose() * y));
+
+  return true;
+}
+
+template <int AmbientSpaceDimension>
+bool LineParameterization<AmbientSpaceDimension>::ComputeJacobian(
+    const double* x_ptr, double* jacobian_ptr) const {
+  static constexpr int kDim = AmbientSpaceDimension;
+  using AmbientVector = Eigen::Matrix<double, kDim, 1>;
+  using ConstAmbientVectorRef = Eigen::Map<const Eigen::Matrix<double, kDim, 1>>;  
+  using MatrixRef = Eigen::Map<
+      Eigen::Matrix<double, 2 * kDim, 2 * (kDim - 1), Eigen::RowMajor>>;
+
+  ConstAmbientVectorRef d(x_ptr + kDim);
+  MatrixRef jacobian(jacobian_ptr);
+
+  // Clear the Jacobian as only half of the matrix is not zero.
+  jacobian.setZero();
+
+  AmbientVector v;
+  double beta;
+  internal::ComputeHouseholderVector(d, &v, &beta);
+
+  // The Jacobian is equal to J = 0.5 * H.leftCols(kDim - 1) where H is
+  // the Householder matrix (H = I - beta * v * v') for the origin point. For
+  // the line direction part the Jacobian is scaled by the norm of the
+  // direction.
+  for (int i = 0; i < kDim - 1; ++i) {
+    jacobian.block(0, i, kDim, 1) = -0.5 * beta * v(i) * v;
+    jacobian.col(i)(i) += 0.5;
+  }
+
+  jacobian.template block<kDim, kDim - 1>(kDim, kDim - 1) =
+      jacobian.template block<kDim, kDim - 1>(0, 0) * d.norm();
+  return true;
+}
+
+}  // namespace ceres
+
+#endif  // CERES_PUBLIC_INTERNAL_LINE_PARAMETERIZATION_H_
diff --git a/include/ceres/local_parameterization.h b/include/ceres/local_parameterization.h
index 93c7973..0d7b507 100644
--- a/include/ceres/local_parameterization.h
+++ b/include/ceres/local_parameterization.h
@@ -262,6 +262,33 @@
   const int size_;
 };
 
+// This provides a parameterization for lines, where the line is
+// over-parameterized by an origin point and a direction vector. So the
+// parameter vector size needs to be two times the ambient space dimension,
+// where the first half is interpreted as the origin point and the second half
+// as the direction.
+//
+// The plus operator for the line direction is the same as for the
+// HomogeneousVectorParameterization. The update of the origin point is
+// perpendicular to the line direction before the update.
+//
+// This local parameterization is a special case of the affine Grassmannian
+// manifold (see https://en.wikipedia.org/wiki/Affine_Grassmannian_(manifold))
+// for the case Graff_1(R^n).
+template <int AmbientSpaceDimension>
+class CERES_EXPORT LineParameterization : public LocalParameterization {
+ public:
+  static_assert(AmbientSpaceDimension >= 2,
+                "The ambient space must be at least 2");
+
+  bool Plus(const double* x,
+            const double* delta,
+            double* x_plus_delta) const override;
+  bool ComputeJacobian(const double* x, double* jacobian) const override;
+  int GlobalSize() const override { return 2 * AmbientSpaceDimension; }
+  int LocalSize() const override { return 2 * (AmbientSpaceDimension - 1); }
+};
+
 // Construct a local parameterization by taking the Cartesian product
 // of a number of other local parameterizations. This is useful, when
 // a parameter block is the cartesian product of two or more
@@ -328,5 +355,7 @@
 }  // namespace ceres
 
 #include "ceres/internal/reenable_warnings.h"
+#include "ceres/internal/line_parameterization.h"
 
 #endif  // CERES_PUBLIC_LOCAL_PARAMETERIZATION_H_
+
diff --git a/internal/ceres/householder_vector_test.cc b/internal/ceres/householder_vector_test.cc
index 69a6d3c..9eaca75 100644
--- a/internal/ceres/householder_vector_test.cc
+++ b/internal/ceres/householder_vector_test.cc
@@ -28,7 +28,7 @@
 //
 // Author: vitus@google.com (Michael Vitus)
 
-#include "ceres/householder_vector.h"
+#include "ceres/internal/householder_vector.h"
 #include "ceres/internal/eigen.h"
 #include "glog/logging.h"
 #include "gtest/gtest.h"
diff --git a/internal/ceres/local_parameterization.cc b/internal/ceres/local_parameterization.cc
index b6316f1..5fedefa 100644
--- a/internal/ceres/local_parameterization.cc
+++ b/internal/ceres/local_parameterization.cc
@@ -32,7 +32,7 @@
 
 #include <algorithm>
 #include "Eigen/Geometry"
-#include "ceres/householder_vector.h"
+#include "ceres/internal/householder_vector.h"
 #include "ceres/internal/eigen.h"
 #include "ceres/internal/fixed_array.h"
 #include "ceres/rotation.h"
@@ -248,16 +248,16 @@
   // (2nd Edition) for a detailed description.  Note there is a typo on Page
   // 625, line 4 so check the book errata.
   const double norm_delta_div_2 = 0.5 * norm_delta;
-  const double sin_delta_by_delta = sin(norm_delta_div_2) /
+  const double sin_delta_by_delta = std::sin(norm_delta_div_2) /
       norm_delta_div_2;
 
   Vector y(size_);
   y.head(size_ - 1) = 0.5 * sin_delta_by_delta * delta;
-  y(size_ - 1) = cos(norm_delta_div_2);
+  y(size_ - 1) = std::cos(norm_delta_div_2);
 
   Vector v(size_);
   double beta;
-  internal::ComputeHouseholderVector<double>(x, &v, &beta);
+  internal::ComputeHouseholderVector(x, &v, &beta);
 
   // Apply the delta update to remain on the unit sphere. See section A6.9.3
   // on page 625 of Hartley & Zisserman (2nd Edition) for a detailed
@@ -274,7 +274,7 @@
 
   Vector v(size_);
   double beta;
-  internal::ComputeHouseholderVector<double>(x, &v, &beta);
+  internal::ComputeHouseholderVector(x, &v, &beta);
 
   // The Jacobian is equal to J = 0.5 * H.leftCols(size_ - 1) where H is the
   // Householder matrix (H = I - beta * v * v').
diff --git a/internal/ceres/local_parameterization_test.cc b/internal/ceres/local_parameterization_test.cc
index 9334287..f165049 100644
--- a/internal/ceres/local_parameterization_test.cc
+++ b/internal/ceres/local_parameterization_test.cc
@@ -36,9 +36,9 @@
 
 #include "Eigen/Geometry"
 #include "ceres/autodiff_local_parameterization.h"
-#include "ceres/householder_vector.h"
 #include "ceres/internal/autodiff.h"
 #include "ceres/internal/eigen.h"
+#include "ceres/internal/householder_vector.h"
 #include "ceres/random.h"
 #include "ceres/rotation.h"
 #include "gtest/gtest.h"
@@ -418,45 +418,41 @@
 }
 
 // Functor needed to implement automatically differentiated Plus for
-// homogeneous vectors. Note this explicitly defined for vectors of size 4.
+// homogeneous vectors.
+template <int Dim>
 struct HomogeneousVectorParameterizationPlus {
   template <typename Scalar>
   bool operator()(const Scalar* p_x,
                   const Scalar* p_delta,
                   Scalar* p_x_plus_delta) const {
-    Eigen::Map<const Eigen::Matrix<Scalar, 4, 1>> x(p_x);
-    Eigen::Map<const Eigen::Matrix<Scalar, 3, 1>> delta(p_delta);
-    Eigen::Map<Eigen::Matrix<Scalar, 4, 1>> x_plus_delta(p_x_plus_delta);
+    Eigen::Map<const Eigen::Matrix<Scalar, Dim, 1>> x(p_x);
+    Eigen::Map<const Eigen::Matrix<Scalar, Dim - 1, 1>> delta(p_delta);
+    Eigen::Map<Eigen::Matrix<Scalar, Dim, 1>> x_plus_delta(p_x_plus_delta);
 
-    const Scalar squared_norm_delta =
-        delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2];
+    const Scalar squared_norm_delta = delta.squaredNorm();
 
-    Eigen::Matrix<Scalar, 4, 1> y;
+    Eigen::Matrix<Scalar, Dim, 1> y;
     Scalar one_half(0.5);
     if (squared_norm_delta > Scalar(0.0)) {
       Scalar norm_delta = sqrt(squared_norm_delta);
       Scalar norm_delta_div_2 = 0.5 * norm_delta;
       const Scalar sin_delta_by_delta =
           sin(norm_delta_div_2) / norm_delta_div_2;
-      y[0] = sin_delta_by_delta * delta[0] * one_half;
-      y[1] = sin_delta_by_delta * delta[1] * one_half;
-      y[2] = sin_delta_by_delta * delta[2] * one_half;
-      y[3] = cos(norm_delta_div_2);
+      y.template head<Dim - 1>() = sin_delta_by_delta * one_half * delta;
+      y[Dim - 1] = cos(norm_delta_div_2);
 
     } else {
       // We do not just use y = [0,0,0,1] here because that is a
       // constant and when used for automatic differentiation will
       // lead to a zero derivative. Instead we take a first order
       // approximation and evaluate it at zero.
-      y[0] = delta[0] * one_half;
-      y[1] = delta[1] * one_half;
-      y[2] = delta[2] * one_half;
-      y[3] = Scalar(1.0);
+      y.template head<Dim - 1>() = delta * one_half;
+      y[Dim - 1] = Scalar(1.0);
     }
 
-    Eigen::Matrix<Scalar, Eigen::Dynamic, 1> v(4);
+    Eigen::Matrix<Scalar, Dim, 1> v;
     Scalar beta;
-    internal::ComputeHouseholderVector<Scalar>(x, &v, &beta);
+    internal::ComputeHouseholderVector(x, &v, &beta);
 
     x_plus_delta = x.norm() * (y - v * (beta * v.dot(y)));
 
@@ -484,7 +480,7 @@
   EXPECT_NEAR(x_plus_delta_norm, x_norm, kTolerance);
 
   // Autodiff jacobian at delta_x = 0.
-  AutoDiffLocalParameterization<HomogeneousVectorParameterizationPlus, 4, 3>
+  AutoDiffLocalParameterization<HomogeneousVectorParameterizationPlus<4>, 4, 3>
       autodiff_jacobian;
 
   double jacobian_autodiff[12];
@@ -565,6 +561,177 @@
   EXPECT_DEATH_IF_SUPPORTED(HomogeneousVectorParameterization x(1), "size");
 }
 
+// Functor needed to implement automatically differentiated Plus for
+// line parameterization.
+template <int AmbientSpaceDim>
+struct LineParameterizationPlus {
+  template <typename Scalar>
+  bool operator()(const Scalar* p_x,
+                  const Scalar* p_delta,
+                  Scalar* p_x_plus_delta) const {
+    static constexpr int kTangetSpaceDim = AmbientSpaceDim - 1;
+    Eigen::Map<const Eigen::Matrix<Scalar, AmbientSpaceDim, 1>> origin_point(
+        p_x);
+    Eigen::Map<const Eigen::Matrix<Scalar, AmbientSpaceDim, 1>> dir(
+        p_x + AmbientSpaceDim);
+    Eigen::Map<const Eigen::Matrix<Scalar, kTangetSpaceDim, 1>>
+        delta_origin_point(p_delta);
+    Eigen::Map<Eigen::Matrix<Scalar, AmbientSpaceDim, 1>>
+        origin_point_plus_delta(p_x_plus_delta);
+
+    HomogeneousVectorParameterizationPlus<AmbientSpaceDim> dir_plus;
+    dir_plus(dir.data(),
+             p_delta + kTangetSpaceDim,
+             p_x_plus_delta + AmbientSpaceDim);
+
+    Eigen::Matrix<Scalar, AmbientSpaceDim, 1> v;
+    Scalar beta;
+    internal::ComputeHouseholderVector(dir, &v, &beta);
+
+    Eigen::Matrix<Scalar, AmbientSpaceDim, 1> y;
+    y << 0.5 * delta_origin_point, Scalar(0.0);
+    origin_point_plus_delta = origin_point + y - v * (beta * v.dot(y));
+
+    return true;
+  }
+};
+
+template <int AmbientSpaceDim>
+static void LineParameterizationHelper(const double* x_ptr,
+                                       const double* delta) {
+  const double kTolerance = 1e-14;
+
+  static constexpr int ParameterDim = 2 * AmbientSpaceDim;
+  static constexpr int TangientParameterDim = 2 * (AmbientSpaceDim - 1);
+
+  LineParameterization<AmbientSpaceDim> line_parameterization;
+
+  using ParameterVector = Eigen::Matrix<double, ParameterDim, 1>;
+  ParameterVector x_plus_delta = ParameterVector::Zero();
+  line_parameterization.Plus(x_ptr, delta, x_plus_delta.data());
+
+  // Ensure the update maintains the norm for the line direction.
+  Eigen::Map<const ParameterVector> x(x_ptr);
+  const double dir_plus_delta_norm =
+      x_plus_delta.template tail<AmbientSpaceDim>().norm();
+  const double dir_norm = x.template tail<AmbientSpaceDim>().norm();
+  EXPECT_NEAR(dir_plus_delta_norm, dir_norm, kTolerance);
+
+  // Ensure the update of the origin point is perpendicular to the line
+  // direction.
+  const double dot_prod_val = x.template tail<AmbientSpaceDim>().dot(
+      x_plus_delta.template head<AmbientSpaceDim>() -
+      x.template head<AmbientSpaceDim>());
+  EXPECT_NEAR(dot_prod_val, 0.0, kTolerance);
+
+  // Autodiff jacobian at delta_x = 0.
+  AutoDiffLocalParameterization<LineParameterizationPlus<AmbientSpaceDim>,
+                                ParameterDim,
+                                TangientParameterDim>
+      autodiff_jacobian;
+
+  using JacobianMatrix = Eigen::
+      Matrix<double, ParameterDim, TangientParameterDim, Eigen::RowMajor>;
+  constexpr double kNaN = std::numeric_limits<double>::quiet_NaN();
+  JacobianMatrix jacobian_autodiff = JacobianMatrix::Constant(kNaN);
+  JacobianMatrix jacobian_analytic = JacobianMatrix::Constant(kNaN);
+
+  autodiff_jacobian.ComputeJacobian(x_ptr, jacobian_autodiff.data());
+  line_parameterization.ComputeJacobian(x_ptr, jacobian_analytic.data());
+
+  EXPECT_FALSE(jacobian_autodiff.hasNaN());
+  EXPECT_FALSE(jacobian_analytic.hasNaN());
+  EXPECT_TRUE(jacobian_autodiff.isApprox(jacobian_analytic))
+      << "auto diff:\n"
+      << jacobian_autodiff << "\n"
+      << "analytic diff:\n"
+      << jacobian_analytic;
+}
+
+TEST(LineParameterization, ZeroTest3D) {
+  double x[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 1.0};
+  double delta[4] = {0.0, 0.0, 0.0, 0.0};
+
+  LineParameterizationHelper<3>(x, delta);
+}
+
+TEST(LineParameterization, ZeroTest4D) {
+  double x[8] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0};
+  double delta[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
+
+  LineParameterizationHelper<4>(x, delta);
+}
+
+TEST(LineParameterization, ZeroOriginPointTest3D) {
+  double x[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 1.0};
+  double delta[4] = {0.0, 0.0, 1.0, 2.0};
+
+  LineParameterizationHelper<3>(x, delta);
+}
+
+TEST(LineParameterization, ZeroOriginPointTest4D) {
+  double x[8] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0};
+  double delta[6] = {0.0, 0.0, 0.0, 1.0, 2.0, 3.0};
+
+  LineParameterizationHelper<4>(x, delta);
+}
+
+TEST(LineParameterization, ZeroDirTest3D) {
+  double x[6] = {0.0, 0.0, 0.0, 0.0, 0.0, 1.0};
+  double delta[4] = {3.0, 2.0, 0.0, 0.0};
+
+  LineParameterizationHelper<3>(x, delta);
+}
+
+TEST(LineParameterization, ZeroDirTest4D) {
+  double x[8] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0};
+  double delta[6] = {3.0, 2.0, 1.0, 0.0, 0.0, 0.0};
+
+  LineParameterizationHelper<4>(x, delta);
+}
+
+TEST(LineParameterization, AwayFromZeroTest3D1) {
+  Eigen::Matrix<double, 6, 1> x;
+  x.head<3>() << 1.54, 2.32, 1.34;
+  x.tail<3>() << 0.52, 0.25, 0.15;
+  x.tail<3>().normalize();
+
+  double delta[4] = {4.0, 7.0, 1.0, -0.5};
+
+  LineParameterizationHelper<3>(x.data(), delta);
+}
+
+TEST(LineParameterization, AwayFromZeroTest4D1) {
+  Eigen::Matrix<double, 8, 1> x;
+  x.head<4>() << 1.54, 2.32, 1.34, 3.23;
+  x.tail<4>() << 0.52, 0.25, 0.15, 0.45;
+  x.tail<4>().normalize();
+
+  double delta[6] = {4.0, 7.0, -3.0, 0.0, 1.0, -0.5};
+
+  LineParameterizationHelper<4>(x.data(), delta);
+}
+
+TEST(LineParameterization, AwayFromZeroTest3D2) {
+  Eigen::Matrix<double, 6, 1> x;
+  x.head<3>() << 7.54, -2.81, 8.63;
+  x.tail<3>() << 2.52, 5.25, 4.15;
+
+  double delta[4] = {4.0, 7.0, 1.0, -0.5};
+
+  LineParameterizationHelper<3>(x.data(), delta);
+}
+
+TEST(LineParameterization, AwayFromZeroTest4D2) {
+  Eigen::Matrix<double, 8, 1> x;
+  x.head<4>() << 7.54, -2.81, 8.63, 6.93;
+  x.tail<4>() << 2.52, 5.25, 4.15, 1.45;
+
+  double delta[6] = {4.0, 7.0, -3.0, 2.0, 1.0, -0.5};
+
+  LineParameterizationHelper<4>(x.data(), delta);
+}
+
 class ProductParameterizationTest : public ::testing::Test {
  protected:
   void SetUp() final {