diff --git a/test/geo_hyperplane.cpp b/test/geo_hyperplane.cpp
new file mode 100644
index 0000000..3275378
--- /dev/null
+++ b/test/geo_hyperplane.cpp
@@ -0,0 +1,185 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/QR>
+
+template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
+{
+  /* this test covers the following files:
+     Hyperplane.h
+  */
+  typedef typename HyperplaneType::Index Index;
+  const Index dim = _plane.dim();
+  enum { Options = HyperplaneType::Options };
+  typedef typename HyperplaneType::Scalar Scalar;
+  typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
+                         HyperplaneType::AmbientDimAtCompileTime> MatrixType;
+
+  VectorType p0 = VectorType::Random(dim);
+  VectorType p1 = VectorType::Random(dim);
+
+  VectorType n0 = VectorType::Random(dim).normalized();
+  VectorType n1 = VectorType::Random(dim).normalized();
+
+  HyperplaneType pl0(n0, p0);
+  HyperplaneType pl1(n1, p1);
+  HyperplaneType pl2 = pl1;
+
+  Scalar s0 = internal::random<Scalar>();
+  Scalar s1 = internal::random<Scalar>();
+
+  VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
+
+  VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
+  VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0 );
+  VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
+  VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 +  pl1.normal().unitOrthogonal() * s1), Scalar(1) );
+
+  // transform
+  if (!NumTraits<Scalar>::IsComplex)
+  {
+    MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();
+    DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
+    Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
+
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
+                                 .absDistance((rot*scaling*translation) * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
+                                 .absDistance((rot*translation) * p1), Scalar(1) );
+  }
+
+  // casting
+  const int Dim = HyperplaneType::AmbientDimAtCompileTime;
+  typedef typename GetDifferentType<Scalar>::type OtherScalar;
+  Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>();
+  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
+  Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();
+  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
+}
+
+template<typename Scalar> void lines()
+{
+  using std::abs;
+  typedef Hyperplane<Scalar, 2> HLine;
+  typedef ParametrizedLine<Scalar, 2> PLine;
+  typedef Matrix<Scalar,2,1> Vector;
+  typedef Matrix<Scalar,3,1> CoeffsType;
+
+  for(int i = 0; i < 10; i++)
+  {
+    Vector center = Vector::Random();
+    Vector u = Vector::Random();
+    Vector v = Vector::Random();
+    Scalar a = internal::random<Scalar>();
+    while (abs(a-1) < 1e-4) a = internal::random<Scalar>();
+    while (u.norm() < 1e-4) u = Vector::Random();
+    while (v.norm() < 1e-4) v = Vector::Random();
+
+    HLine line_u = HLine::Through(center + u, center + a*u);
+    HLine line_v = HLine::Through(center + v, center + a*v);
+
+    // the line equations should be normalized so that a^2+b^2=1
+    VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
+    VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
+
+    Vector result = line_u.intersection(line_v);
+
+    // the lines should intersect at the point we called "center"
+    VERIFY_IS_APPROX(result, center);
+
+    // check conversions between two types of lines
+    PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable
+    CoeffsType converted_coeffs = HLine(pl).coeffs();
+    converted_coeffs *= (line_u.coeffs()[0])/(converted_coeffs[0]);
+    VERIFY(line_u.coeffs().isApprox(converted_coeffs));
+  }
+}
+
+template<typename Scalar> void planes()
+{
+  using std::abs;
+  typedef Hyperplane<Scalar, 3> Plane;
+  typedef Matrix<Scalar,3,1> Vector;
+
+  for(int i = 0; i < 10; i++)
+  {
+    Vector v0 = Vector::Random();
+    Vector v1(v0), v2(v0);
+    if(internal::random<double>(0,1)>0.25)
+      v1 += Vector::Random();
+    if(internal::random<double>(0,1)>0.25)
+      v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
+    if(internal::random<double>(0,1)>0.25)
+      v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
+
+    Plane p0 = Plane::Through(v0, v1, v2);
+
+    VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
+    VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
+    VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
+    VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
+  }
+}
+
+template<typename Scalar> void hyperplane_alignment()
+{
+  typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;
+  typedef Hyperplane<Scalar,3,DontAlign> Plane3u;
+
+  EIGEN_ALIGN16 Scalar array1[4];
+  EIGEN_ALIGN16 Scalar array2[4];
+  EIGEN_ALIGN16 Scalar array3[4+1];
+  Scalar* array3u = array3+1;
+
+  Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a;
+  Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u;
+  Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u;
+  
+  p1->coeffs().setRandom();
+  *p2 = *p1;
+  *p3 = *p1;
+
+  VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
+  VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
+  
+  #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
+  if(internal::packet_traits<Scalar>::Vectorizable)
+    VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a));
+  #endif
+}
+
+
+void test_geo_hyperplane()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );
+    CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );
+    CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) );
+    CALL_SUBTEST_2( hyperplane_alignment<float>() );
+    CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );
+    CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );
+    CALL_SUBTEST_1( lines<float>() );
+    CALL_SUBTEST_3( lines<double>() );
+    CALL_SUBTEST_2( planes<float>() );
+    CALL_SUBTEST_5( planes<double>() );
+  }
+}