merge

Eigen/src/Core/Matrix.h

@@ -336,6 +336,13 @@ class Matrix
     template<typename OtherDerived>
     Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
 
+    #ifdef EIGEN2_SUPPORT
+    template<typename OtherDerived>
+    explicit Matrix(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
+    template<typename OtherDerived>
+    Matrix& operator=(const eigen2_RotationBase<OtherDerived,ColsAtCompileTime>& r);
+    #endif
+
     // allow to extend Matrix outside Eigen
     #ifdef EIGEN_MATRIX_PLUGIN
     #include EIGEN_MATRIX_PLUGIN

Eigen/src/Core/MatrixBase.h

@@ -204,7 +204,7 @@ template<typename Derived> class MatrixBase
       template<typename OtherDerived>
       typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
       #if EIGEN2_SUPPORT_STAGE == STAGE15_RESOLVE_API_CONFLICTS_WARN
-      EIGEN_DEPRECATED Scalar
+      EIGEN_DEPRECATED
       #endif
       dot(const MatrixBase<OtherDerived>& other) const;
     #endif

Eigen/src/Core/util/ForwardDeclarations.h

@@ -220,7 +220,6 @@ template<typename Scalar>     class JacobiRotation;
 template<typename Derived, int _Dim> class RotationBase;
 template<typename Lhs, typename Rhs> class Cross;
 template<typename Derived> class QuaternionBase;
-template<typename Scalar, int Options = AutoAlign> class Quaternion;
 template<typename Scalar> class Rotation2D;
 template<typename Scalar> class AngleAxis;
 template<typename Scalar,int Dim> class Translation;
@@ -239,6 +238,7 @@ template<typename Scalar,int Dim> class eigen2_Scaling;
 #endif
 
 #if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
+template<typename Scalar> class Quaternion;
 template<typename Scalar,int Dim> class Transform;
 template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
 template <typename _Scalar, int _AmbientDim> class Hyperplane;
@@ -246,6 +246,7 @@ template<typename Scalar,int Dim> class Scaling;
 #endif
 
 #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
+template<typename Scalar, int Options = AutoAlign> class Quaternion;
 template<typename Scalar,int Dim,int Mode,int _Options=AutoAlign> class Transform;
 template <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class ParametrizedLine;
 template <typename _Scalar, int _AmbientDim, int Options=AutoAlign> class Hyperplane;

Eigen/src/Eigen2Support/Geometry/AlignedBox.h

@@ -22,8 +22,7 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_ALIGNEDBOX_H
-#define EIGEN_ALIGNEDBOX_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
 
 /** \geometry_module \ingroup Geometry_Module
   * \nonstableyet
@@ -169,5 +168,3 @@ inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const Vecto
   }
   return dist2;
 }
-
-#endif // EIGEN_ALIGNEDBOX_H

Eigen/src/Eigen2Support/Geometry/All.h

@@ -58,6 +58,10 @@
 #define Hyperplane eigen2_Hyperplane
 #define ParametrizedLine eigen2_ParametrizedLine
 
+#define ei_toRotationMatrix eigen2_ei_toRotationMatrix
+#define ei_quaternion_assign_impl eigen2_ei_quaternion_assign_impl
+#define ei_transform_product_impl eigen2_ei_transform_product_impl
+
 #include "RotationBase.h"
 #include "Rotation2D.h"
 #include "Quaternion.h"
@@ -69,6 +73,10 @@
 #include "Hyperplane.h"
 #include "ParametrizedLine.h"
 
+#undef ei_toRotationMatrix
+#undef ei_quaternion_assign_impl
+#undef ei_transform_product_impl
+
 #undef RotationBase
 #undef Rotation2D
 #undef Rotation2Df

Eigen/src/Eigen2Support/Geometry/AngleAxis.h

@@ -22,8 +22,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_ANGLEAXIS_H
-#define EIGEN_ANGLEAXIS_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
 
 /** \geometry_module \ingroup Geometry_Module
   *
@@ -224,5 +224,3 @@ AngleAxis<Scalar>::toRotationMatrix(void) const
 
   return res;
 }
-
-#endif // EIGEN_ANGLEAXIS_H

Eigen/src/Eigen2Support/Geometry/Hyperplane.h

@@ -23,8 +23,7 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_HYPERPLANE_H
-#define EIGEN_HYPERPLANE_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
 
 /** \geometry_module \ingroup Geometry_Module
   *
@@ -71,7 +70,7 @@ public:
     : m_coeffs(n.size()+1)
   {
     normal() = n;
-    offset() = -e.dot(n);
+    offset() = -e.eigen2_dot(n);
   }
 
   /** Constructs a plane from its normal \a n and distance to the origin \a d
@@ -92,7 +91,7 @@ public:
   {
     Hyperplane result(p0.size());
     result.normal() = (p1 - p0).unitOrthogonal();
-    result.offset() = -result.normal().dot(p0);
+    result.offset() = -result.normal().eigen2_dot(p0);
     return result;
   }
 
@@ -104,7 +103,7 @@ public:
     EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
     Hyperplane result(p0.size());
     result.normal() = (p2 - p0).cross(p1 - p0).normalized();
-    result.offset() = -result.normal().dot(p0);
+    result.offset() = -result.normal().eigen2_dot(p0);
     return result;
   }
 
@@ -116,7 +115,7 @@ public:
   explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
   {
     normal() = parametrized.direction().unitOrthogonal();
-    offset() = -normal().dot(parametrized.origin());
+    offset() = -normal().eigen2_dot(parametrized.origin());
   }
 
   ~Hyperplane() {}
@@ -133,7 +132,7 @@ public:
   /** \returns the signed distance between the plane \c *this and a point \a p.
     * \sa absDistance()
     */
-  inline Scalar signedDistance(const VectorType& p) const { return p.dot(normal()) + offset(); }
+  inline Scalar signedDistance(const VectorType& p) const { return p.eigen2_dot(normal()) + offset(); }
 
   /** \returns the absolute distance between the plane \c *this and a point \a p.
     * \sa signedDistance()
@@ -231,7 +230,7 @@ public:
                                 TransformTraits traits = Affine)
   {
     transform(t.linear(), traits);
-    offset() -= t.translation().dot(normal());
+    offset() -= t.translation().eigen2_dot(normal());
     return *this;
   }
 
@@ -264,5 +263,3 @@ protected:
 
   Coefficients m_coeffs;
 };
-
-#endif // EIGEN_HYPERPLANE_H

Eigen/src/Eigen2Support/Geometry/ParametrizedLine.h

@@ -23,8 +23,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_PARAMETRIZEDLINE_H
-#define EIGEN_PARAMETRIZEDLINE_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
 
 /** \geometry_module \ingroup Geometry_Module
   *
@@ -85,7 +85,7 @@ public:
   RealScalar squaredDistance(const VectorType& p) const
   {
     VectorType diff = p-origin();
-    return (diff - diff.dot(direction())* direction()).squaredNorm();
+    return (diff - diff.eigen2_dot(direction())* direction()).squaredNorm();
   }
   /** \returns the distance of a point \a p to its projection onto the line \c *this.
     * \sa squaredDistance()
@@ -94,7 +94,7 @@ public:
 
   /** \returns the projection of a point \a p onto the line \c *this. */
   VectorType projection(const VectorType& p) const
-  { return origin() + (p-origin()).dot(direction()) * direction(); }
+  { return origin() + (p-origin()).eigen2_dot(direction()) * direction(); }
 
   Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
 
@@ -148,8 +148,6 @@ inline ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane
 template <typename _Scalar, int _AmbientDim>
 inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
 {
-  return -(hyperplane.offset()+origin().dot(hyperplane.normal()))
-          /(direction().dot(hyperplane.normal()));
+  return -(hyperplane.offset()+origin().eigen2_dot(hyperplane.normal()))
+          /(direction().eigen2_dot(hyperplane.normal()));
 }
-
-#endif // EIGEN_PARAMETRIZEDLINE_H

Eigen/src/Eigen2Support/Geometry/Quaternion.h

@@ -22,8 +22,7 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_QUATERNION_H
-#define EIGEN_QUATERNION_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
 
 template<typename Other,
          int OtherRows=Other::RowsAtCompileTime,
@@ -172,7 +171,7 @@ public:
     * corresponds to the cosine of half the angle between the two rotations.
     * \sa angularDistance()
     */
-  inline Scalar dot(const Quaternion& other) const { return m_coeffs.dot(other.m_coeffs); }
+  inline Scalar eigen2_dot(const Quaternion& other) const { return m_coeffs.eigen2_dot(other.m_coeffs); }
 
   inline Scalar angularDistance(const Quaternion& other) const;
 
@@ -353,7 +352,7 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBas
 {
   Vector3 v0 = a.normalized();
   Vector3 v1 = b.normalized();
-  Scalar c = v0.dot(v1);
+  Scalar c = v0.eigen2_dot(v1);
 
   // if dot == 1, vectors are the same
   if (ei_isApprox(c,Scalar(1)))
@@ -412,12 +411,12 @@ inline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const
 }
 
 /** \returns the angle (in radian) between two rotations
-  * \sa dot()
+  * \sa eigen2_dot()
   */
 template <typename Scalar>
 inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
 {
-  double d = ei_abs(this->dot(other));
+  double d = ei_abs(this->eigen2_dot(other));
   if (d>=1.0)
     return 0;
   return Scalar(2) * std::acos(d);
@@ -430,7 +429,7 @@ template <typename Scalar>
 Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const
 {
   static const Scalar one = Scalar(1) - machine_epsilon<Scalar>();
-  Scalar d = this->dot(other);
+  Scalar d = this->eigen2_dot(other);
   Scalar absD = ei_abs(d);
 
   Scalar scale0;
@@ -505,5 +504,3 @@ struct ei_quaternion_assign_impl<Other,4,1>
     q.coeffs() = vec;
   }
 };
-
-#endif // EIGEN_QUATERNION_H

Eigen/src/Eigen2Support/Geometry/Rotation2D.h

@@ -22,8 +22,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_ROTATION2D_H
-#define EIGEN_ROTATION2D_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
 
 /** \geometry_module \ingroup Geometry_Module
   *
@@ -155,5 +155,3 @@ Rotation2D<Scalar>::toRotationMatrix(void) const
   Scalar cosA = ei_cos(m_angle);
   return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
 }
-
-#endif // EIGEN_ROTATION2D_H

Eigen/src/Eigen2Support/Geometry/RotationBase.h

@@ -22,8 +22,7 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_ROTATIONBASE_H
-#define EIGEN_ROTATIONBASE_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
 
 // this file aims to contains the various representations of rotation/orientation
 // in 2D and 3D space excepted Matrix and Quaternion.
@@ -133,5 +132,3 @@ inline static const MatrixBase<OtherDerived>& ei_toRotationMatrix(const MatrixBa
     YOU_MADE_A_PROGRAMMING_MISTAKE)
   return mat;
 }
-
-#endif // EIGEN_ROTATIONBASE_H

Eigen/src/Eigen2Support/Geometry/Scaling.h

@@ -22,8 +22,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_SCALING_H
-#define EIGEN_SCALING_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
 
 /** \geometry_module \ingroup Geometry_Module
   *
@@ -177,5 +177,3 @@ Scaling<Scalar,Dim>::operator* (const TransformType& t) const
   res.prescale(m_coeffs);
   return res;
 }
-
-#endif // EIGEN_SCALING_H

Eigen/src/Eigen2Support/Geometry/Transform.h

@@ -23,8 +23,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_TRANSFORM_H
-#define EIGEN_TRANSFORM_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
 
 // Note that we have to pass Dim and HDim because it is not allowed to use a template
 // parameter to define a template specialization. To be more precise, in the following
@@ -796,5 +796,3 @@ struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
   { return ((tr.linear() * other) + tr.translation())
           * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
 };
-
-#endif // EIGEN_TRANSFORM_H

Eigen/src/Eigen2Support/Geometry/Translation.h

@@ -22,8 +22,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_TRANSLATION_H
-#define EIGEN_TRANSLATION_H
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
 
 /** \geometry_module \ingroup Geometry_Module
   *
@@ -194,5 +194,3 @@ Translation<Scalar,Dim>::operator* (const TransformType& t) const
   res.pretranslate(m_coeffs);
   return res;
 }
-
-#endif // EIGEN_TRANSLATION_H

Eigen/src/Eigen2Support/LeastSquares.h

@@ -22,8 +22,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_LEASTSQUARES_H
-#define EIGEN_LEASTSQUARES_H
+#ifndef EIGEN2_LEASTSQUARES_H
+#define EIGEN2_LEASTSQUARES_H
 
 /** \ingroup LeastSquares_Module
   *
@@ -179,4 +179,4 @@ void fitHyperplane(int numPoints,
 }
 
 
-#endif // EIGEN_LEASTSQUARES_H
+#endif // EIGEN2_LEASTSQUARES_H

Eigen/src/Eigen2Support/SVD.h

@@ -22,8 +22,8 @@
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.
 
-#ifndef EIGEN_SVD_H
-#define EIGEN_SVD_H
+#ifndef EIGEN2_SVD_H
+#define EIGEN2_SVD_H
 
 /** \ingroup SVD_Module
   * \nonstableyet
@@ -150,7 +150,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
       if ((k < nct) && (m_sigma[k] != 0.0))
       {
         // Apply the transformation.
-        Scalar t = matA.col(k).end(m-k).dot(matA.col(j).end(m-k)); // FIXME dot product or cwise prod + .sum() ??
+        Scalar t = matA.col(k).end(m-k).eigen2_dot(matA.col(j).end(m-k)); // FIXME dot product or cwise prod + .sum() ??
         t = -t/matA(k,k);
         matA.col(j).end(m-k) += t * matA.col(k).end(m-k);
       }
@@ -216,7 +216,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
       {
         for (j = k+1; j < nu; ++j)
         {
-          Scalar t = m_matU.col(k).end(m-k).dot(m_matU.col(j).end(m-k)); // FIXME is it really a dot product we want ?
+          Scalar t = m_matU.col(k).end(m-k).eigen2_dot(m_matU.col(j).end(m-k)); // FIXME is it really a dot product we want ?
           t = -t/m_matU(k,k);
           m_matU.col(j).end(m-k) += t * m_matU.col(k).end(m-k);
         }
@@ -242,7 +242,7 @@ void SVD<MatrixType>::compute(const MatrixType& matrix)
       {
         for (j = k+1; j < nu; ++j)
         {
-          Scalar t = m_matV.col(k).end(n-k-1).dot(m_matV.col(j).end(n-k-1)); // FIXME is it really a dot product we want ?
+          Scalar t = m_matV.col(k).end(n-k-1).eigen2_dot(m_matV.col(j).end(n-k-1)); // FIXME is it really a dot product we want ?
           t = -t/m_matV(k+1,k);
           m_matV.col(j).end(n-k-1) += t * m_matV.col(k).end(n-k-1);
         }
@@ -646,4 +646,4 @@ MatrixBase<Derived>::svd() const
   return SVD<PlainObject>(derived());
 }
 
-#endif // EIGEN_SVD_H
+#endif // EIGEN2_SVD_H

test/eigen2/CMakeLists.txt

@@ -36,6 +36,7 @@ ei_add_test(eigen2_qr)
 ei_add_test(eigen2_eigensolver " " "${GSL_LIBRARIES}")
 ei_add_test(eigen2_svd)
 ei_add_test(eigen2_geometry)
+ei_add_test(eigen2_geometry_with_eigen2_prefix)
 ei_add_test(eigen2_hyperplane)
 ei_add_test(eigen2_parametrizedline)
 ei_add_test(eigen2_alignedbox)

test/eigen2/eigen2_geometry_with_eigen2_prefix.cpp

@@ -0,0 +1,449 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#define EIGEN2_SUPPORT_STAGE15_RESOLVE_API_CONFLICTS_WARN
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+template<typename Scalar> void geometry(void)
+{
+  /* this test covers the following files:
+     Cross.h Quaternion.h, Transform.cpp
+  */
+
+  typedef Matrix<Scalar,2,2> Matrix2;
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,4,4> Matrix4;
+  typedef Matrix<Scalar,2,1> Vector2;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Matrix<Scalar,4,1> Vector4;
+  typedef eigen2_Quaternion<Scalar> Quaternionx;
+  typedef eigen2_AngleAxis<Scalar> AngleAxisx;
+  typedef eigen2_Transform<Scalar,2> Transform2;
+  typedef eigen2_Transform<Scalar,3> Transform3;
+  typedef eigen2_Scaling<Scalar,2> Scaling2;
+  typedef eigen2_Scaling<Scalar,3> Scaling3;
+  typedef eigen2_Translation<Scalar,2> Translation2;
+  typedef eigen2_Translation<Scalar,3> Translation3;
+
+  Scalar largeEps = test_precision<Scalar>();
+  if (ei_is_same_type<Scalar,float>::ret)
+    largeEps = 1e-2f;
+
+  Vector3 v0 = Vector3::Random(),
+    v1 = Vector3::Random(),
+    v2 = Vector3::Random();
+  Vector2 u0 = Vector2::Random();
+  Matrix3 matrot1;
+
+  Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+
+  // cross product
+  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1));
+  Matrix3 m;
+  m << v0.normalized(),
+      (v0.cross(v1)).normalized(),
+      (v0.cross(v1).cross(v0)).normalized();
+  VERIFY(m.isUnitary());
+
+  // Quaternion: Identity(), setIdentity();
+  Quaternionx q1, q2;
+  q2.setIdentity();
+  VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
+  q1.coeffs().setRandom();
+  VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
+
+  // unitOrthogonal
+  VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1));
+  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1));
+  VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1));
+  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
+
+
+  VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
+  VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
+  VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
+  m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
+  VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
+  VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
+
+  q1 = AngleAxisx(a, v0.normalized());
+  q2 = AngleAxisx(a, v1.normalized());
+
+  // angular distance
+  Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle());
+  if (refangle>Scalar(M_PI))
+    refangle = Scalar(2)*Scalar(M_PI) - refangle;
+  
+  if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
+  {
+    VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));
+  }
+
+  // rotation matrix conversion
+  VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
+  VERIFY_IS_APPROX(q1 * q2 * v2,
+    q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
+
+  VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox(
+    q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
+
+  q2 = q1.toRotationMatrix();
+  VERIFY_IS_APPROX(q1*v1,q2*v1);
+
+  matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
+          * AngleAxisx(Scalar(0.2), Vector3::UnitY())
+          * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
+  VERIFY_IS_APPROX(matrot1 * v1,
+       AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
+    * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
+    * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
+
+  // angle-axis conversion
+  AngleAxisx aa = q1;
+  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+  VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
+
+  // from two vector creation
+  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
+  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
+
+  // inverse and conjugate
+  VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
+  VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
+
+  // AngleAxis
+  VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
+    Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
+
+  AngleAxisx aa1;
+  m = q1.toRotationMatrix();
+  aa1 = m;
+  VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
+    Quaternionx(m).toRotationMatrix());
+
+  // Transform
+  // TODO complete the tests !
+  a = 0;
+  while (ei_abs(a)<Scalar(0.1))
+    a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
+  q1 = AngleAxisx(a, v0.normalized());
+  Transform3 t0, t1, t2;
+  // first test setIdentity() and Identity()
+  t0.setIdentity();
+  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+  t0.matrix().setZero();
+  t0 = Transform3::Identity();
+  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+  t0.linear() = q1.toRotationMatrix();
+  t1.setIdentity();
+  t1.linear() = q1.toRotationMatrix();
+
+  v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
+  t0.scale(v0);
+  t1.prescale(v0);
+
+  VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
+  //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));
+
+  t0.setIdentity();
+  t1.setIdentity();
+  v1 << 1, 2, 3;
+  t0.linear() = q1.toRotationMatrix();
+  t0.pretranslate(v0);
+  t0.scale(v1);
+  t1.linear() = q1.conjugate().toRotationMatrix();
+  t1.prescale(v1.cwise().inverse());
+  t1.translate(-v0);
+
+  VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));
+
+  t1.fromPositionOrientationScale(v0, q1, v1);
+  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+  VERIFY_IS_APPROX(t1*v1, t0*v1);
+
+  t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
+  t1.setIdentity(); t1.scale(v0).rotate(q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
+  VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
+
+  // More transform constructors, operator=, operator*=
+
+  Matrix3 mat3 = Matrix3::Random();
+  Matrix4 mat4;
+  mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
+  Transform3 tmat3(mat3), tmat4(mat4);
+  tmat4.matrix()(3,3) = Scalar(1);
+  VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
+
+  Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+  Vector3 v3 = Vector3::Random().normalized();
+  AngleAxisx aa3(a3, v3);
+  Transform3 t3(aa3);
+  Transform3 t4;
+  t4 = aa3;
+  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+  t4.rotate(AngleAxisx(-a3,v3));
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= aa3;
+  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+
+  v3 = Vector3::Random();
+  Translation3 tv3(v3);
+  Transform3 t5(tv3);
+  t4 = tv3;
+  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+  t4.translate(-v3);
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= tv3;
+  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+
+  Scaling3 sv3(v3);
+  Transform3 t6(sv3);
+  t4 = sv3;
+  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+  t4.scale(v3.cwise().inverse());
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= sv3;
+  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+
+  // matrix * transform
+  VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix());
+
+  // chained Transform product
+  VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
+
+  // check that Transform product doesn't have aliasing problems
+  t5 = t4;
+  t5 = t5*t5;
+  VERIFY_IS_APPROX(t5, t4*t4);
+
+  // 2D transformation
+  Transform2 t20, t21;
+  Vector2 v20 = Vector2::Random();
+  Vector2 v21 = Vector2::Random();
+  for (int k=0; k<2; ++k)
+    if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
+  t21.setIdentity();
+  t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
+  VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
+    t21.pretranslate(v20).scale(v21).matrix());
+
+  t21.setIdentity();
+  t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
+  VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
+        * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
+
+  // Transform - new API
+  // 3D
+  t0.setIdentity();
+  t0.rotate(q1).scale(v0).translate(v0);
+  // mat * scaling and mat * translation
+  t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // mat * transformation and scaling * translation
+  t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity();
+  t0.prerotate(q1).prescale(v0).pretranslate(v0);
+  // translation * scaling and transformation * mat
+  t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // scaling * mat and translation * mat
+  t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity();
+  t0.scale(v0).translate(v0).rotate(q1);
+  // translation * mat and scaling * transformation
+  t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // transformation * scaling
+  t0.scale(v0);
+  t1 = t1 * Scaling3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // transformation * translation
+  t0.translate(v0);
+  t1 = t1 * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // translation * transformation
+  t0.pretranslate(v0);
+  t1 = Translation3(v0) * t1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // transform * quaternion
+  t0.rotate(q1);
+  t1 = t1 * q1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // translation * quaternion
+  t0.translate(v1).rotate(q1);
+  t1 = t1 * (Translation3(v1) * q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // scaling * quaternion
+  t0.scale(v1).rotate(q1);
+  t1 = t1 * (Scaling3(v1) * q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * transform
+  t0.prerotate(q1);
+  t1 = q1 * t1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * translation
+  t0.rotate(q1).translate(v1);
+  t1 = t1 * (q1 * Translation3(v1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * scaling
+  t0.rotate(q1).scale(v1);
+  t1 = t1 * (q1 * Scaling3(v1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // translation * vector
+  t0.setIdentity();
+  t0.translate(v0);
+  VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);
+
+  // scaling * vector
+  t0.setIdentity();
+  t0.scale(v0);
+  VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1);
+
+  // test transform inversion
+  t0.setIdentity();
+  t0.translate(v0);
+  t0.linear().setRandom();
+  VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse());
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1);
+  VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse());
+
+  // test extract rotation and scaling
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1).scale(v1);
+  VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
+
+  Matrix3 mat_rotation, mat_scaling;
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1).scale(v1);
+  t0.computeRotationScaling(&mat_rotation, &mat_scaling);
+  VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
+  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+  t0.computeScalingRotation(&mat_scaling, &mat_rotation);
+  VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
+  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+
+  // test casting
+  eigen2_Transform<float,3> t1f = t1.template cast<float>();
+  VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
+  eigen2_Transform<double,3> t1d = t1.template cast<double>();
+  VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
+
+  Translation3 tr1(v0);
+  eigen2_Translation<float,3> tr1f = tr1.template cast<float>();
+  VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
+  eigen2_Translation<double,3> tr1d = tr1.template cast<double>();
+  VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
+
+  Scaling3 sc1(v0);
+  eigen2_Scaling<float,3> sc1f = sc1.template cast<float>();
+  VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1);
+  eigen2_Scaling<double,3> sc1d = sc1.template cast<double>();
+  VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);
+
+  eigen2_Quaternion<float> q1f = q1.template cast<float>();
+  VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
+  eigen2_Quaternion<double> q1d = q1.template cast<double>();
+  VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
+
+  eigen2_AngleAxis<float> aa1f = aa1.template cast<float>();
+  VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
+  eigen2_AngleAxis<double> aa1d = aa1.template cast<double>();
+  VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
+
+  eigen2_Rotation2D<Scalar> r2d1(ei_random<Scalar>());
+  eigen2_Rotation2D<float> r2d1f = r2d1.template cast<float>();
+  VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
+  eigen2_Rotation2D<double> r2d1d = r2d1.template cast<double>();
+  VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
+
+  m = q1;
+//   m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized();
+//   m.col(0) = Vector3(-1,0,0).normalized();
+//   m.col(2) = m.col(0).cross(m.col(1));
+  #define VERIFY_EULER(I,J,K, X,Y,Z) { \
+    Vector3 ea = m.eulerAngles(I,J,K); \
+    Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
+    VERIFY_IS_APPROX(m,  Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
+  }
+  VERIFY_EULER(0,1,2, X,Y,Z);
+  VERIFY_EULER(0,1,0, X,Y,X);
+  VERIFY_EULER(0,2,1, X,Z,Y);
+  VERIFY_EULER(0,2,0, X,Z,X);
+
+  VERIFY_EULER(1,2,0, Y,Z,X);
+  VERIFY_EULER(1,2,1, Y,Z,Y);
+  VERIFY_EULER(1,0,2, Y,X,Z);
+  VERIFY_EULER(1,0,1, Y,X,Y);
+
+  VERIFY_EULER(2,0,1, Z,X,Y);
+  VERIFY_EULER(2,0,2, Z,X,Z);
+  VERIFY_EULER(2,1,0, Z,Y,X);
+  VERIFY_EULER(2,1,2, Z,Y,Z);
+
+  // colwise/rowwise cross product
+  mat3.setRandom();
+  Vector3 vec3 = Vector3::Random();
+  Matrix3 mcross;
+  int i = ei_random<int>(0,2);
+  mcross = mat3.colwise().cross(vec3);
+  VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
+  mcross = mat3.rowwise().cross(vec3);
+  VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
+
+
+}
+
+void test_eigen2_geometry_with_eigen2_prefix()
+{
+  std::cout << "eigen2 support: " << EIGEN2_SUPPORT_STAGE << std::endl;
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( geometry<float>() );
+    CALL_SUBTEST_2( geometry<double>() );
+  }
+}