From c9bedc550f84274a7f758873c7f25835693e028e Mon Sep 17 00:00:00 2001
From: Valenza Florian <fvalenza@laas.fr>
Date: Tue, 2 Aug 2016 17:11:23 +0200
Subject: [PATCH] [C++] Fix difference_impl for some derived joints and
 reworked unittest

---
 src/multibody/joint/joint-free-flyer.hpp      |  26 +-
 src/multibody/joint/joint-planar.hpp          |  13 +-
 .../joint/joint-revolute-unbounded.hpp        |   2 +-
 src/multibody/joint/joint-spherical.hpp       |  35 +-
 unittest/joint-configurations.cpp             | 432 ++++++++----------
 5 files changed, 220 insertions(+), 288 deletions(-)

diff --git a/src/multibody/joint/joint-free-flyer.hpp b/src/multibody/joint/joint-free-flyer.hpp
index e35e17a26..c27d91e4f 100644
--- a/src/multibody/joint/joint-free-flyer.hpp
+++ b/src/multibody/joint/joint-free-flyer.hpp
@@ -351,30 +351,10 @@ namespace se3
       Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_0 = q0.segment<NQ> (idx_q ());
       Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_1 = q1.segment<NQ> (idx_q ());
 
-      TangentVector_t result;
-      // Translational part
-      result.head<3>() << q_1.head<3> () - q_0.head<3> ();
+      Transformation_t M0(Transformation_t::Identity()); forwardKinematics(M0, q_0);
+      Transformation_t M1(Transformation_t::Identity()); forwardKinematics(M1, q_1);
 
-      // Quaternion part
-      // Compute relative rotation between q0 and q1.
-      ConstQuaternionMap_t quat0 (q_0.segment<4>(3).data());
-      ConstQuaternionMap_t quat1 (q_1.segment<4>(3).data());
-      
-      const Motion_t::Quaternion_t quat_relatif (quat1*quat0.conjugate());
-      
-      if (quat_relatif.vec().norm() < 1e-8) // TODO: The value 1e-8 must be changed according to the precision of the current real.
-        result.tail<3> ().setZero();
-      else
-      {
-        const Scalar theta = 2.*acos(quat_relatif.w());
-        
-        if (quat0.dot(quat1) >= 0.)
-          result.tail<3>() << theta * quat_relatif.vec().normalized();
-        else
-          result.tail<3>() << -(2*PI-theta) * quat_relatif.vec().normalized();
-      }
-
-      return result;
+      return se3::log6(M0.inverse()*M1);
     } 
 
     double distance_impl(const Eigen::VectorXd & q0,const Eigen::VectorXd & q1) const
diff --git a/src/multibody/joint/joint-planar.hpp b/src/multibody/joint/joint-planar.hpp
index eb47958f4..f27b613a5 100644
--- a/src/multibody/joint/joint-planar.hpp
+++ b/src/multibody/joint/joint-planar.hpp
@@ -429,6 +429,7 @@ namespace se3
       Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_0 = q0.segment<NQ> (idx_q ());
       Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_1 = q1.segment<NQ> (idx_q ());
 
+      
       return ConfigVector_t((1-u) * q_0 + u * q_1);
     }
 
@@ -460,8 +461,18 @@ namespace se3
     { 
       Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_0 = q0.segment<NQ> (idx_q ());
       Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_1 = q1.segment<NQ> (idx_q ());
+      typedef Transformation_t::Matrix3 Matrix3;
+
+      Transformation_t M0(Transformation_t::Identity()); forwardKinematics(M0, q_0);
+      Transformation_t M1(Transformation_t::Identity()); forwardKinematics(M1, q_1);
+     
+      TangentVector_t res;
+      Motion nu = se3::log6((M0.inverse()*M1));
+      
+      res.head<2>() = nu.linear().head<2>();
+      res(2) = q_1(2) - q_0(2);
+      return res;
 
-      return TangentVector_t(q_1 - q_0);
     } 
 
     double distance_impl(const Eigen::VectorXd & q0,const Eigen::VectorXd & q1) const
diff --git a/src/multibody/joint/joint-revolute-unbounded.hpp b/src/multibody/joint/joint-revolute-unbounded.hpp
index 5be3f558d..70465dc4c 100644
--- a/src/multibody/joint/joint-revolute-unbounded.hpp
+++ b/src/multibody/joint/joint-revolute-unbounded.hpp
@@ -230,7 +230,7 @@ namespace se3
       const double & c1 = qf(0), s1 = qf(1);
 
       TangentVector_t result;
-      result << atan2 (s0*c1 - s1*c0, c0*c1 + s0*s1);
+      result << atan2 (s1*c0 - s0*c1, c0*c1 + s0*s1);
       return result; 
     } 
 
diff --git a/src/multibody/joint/joint-spherical.hpp b/src/multibody/joint/joint-spherical.hpp
index 967b63272..dd26de380 100644
--- a/src/multibody/joint/joint-spherical.hpp
+++ b/src/multibody/joint/joint-spherical.hpp
@@ -264,9 +264,19 @@ namespace se3
     using JointModelBase<JointModelSpherical>::setIndexes;
     typedef Motion::Vector3 Vector3;
     typedef double Scalar;
+    typedef Eigen::Map<const Motion_t::Quaternion_t> ConstQuaternionMap_t;
 
     JointDataDerived createData() const { return JointDataDerived(); }
 
+    inline void forwardKinematics(Transformation_t & M, ConstQuaternionMap_t & q_joint) const
+    {
+      
+      assert(std::fabs(q_joint.coeffs().norm() - 1.) <= 1e-14);
+      
+      M.rotation(q_joint.matrix());
+      M.translation(Vector3::Zero());
+    }
+
     void calc (JointDataDerived & data,
                const Eigen::VectorXd & qs) const
     {
@@ -375,23 +385,16 @@ namespace se3
       typedef Eigen::Map<const Motion_t::Quaternion_t> ConstQuaternionMap_t;
       using std::acos;
       
-      ConstQuaternionMap_t quat0 (q0.segment<NQ> (idx_q ()).data());
-      ConstQuaternionMap_t quat1 (q1.segment<NQ> (idx_q ()).data());
-      
-      const Motion_t::Quaternion_t quat_relatif (quat1*quat0.conjugate());
+      Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_0 = q0.segment<NQ> (idx_q ());
+      Eigen::VectorXd::ConstFixedSegmentReturnType<NQ>::Type & q_1 = q1.segment<NQ> (idx_q ());
+
+      ConstQuaternionMap_t quat0 (q_0.data());
+      ConstQuaternionMap_t quat1 (q_1.data());
+      Transformation_t M0; forwardKinematics(M0, quat0);
+      Transformation_t M1; forwardKinematics(M1, quat1);
+
+      return se3::log3((M0.inverse()*M1).rotation());
       
-      if (quat_relatif.vec().norm() < 1e-8) // TODO: The value 1e-8 must be changed according to the precision of the current real.
-        return TangentVector_t::Zero();
-      else
-      {
-        Scalar theta;
-        if (quat0.dot(quat1) >= 0.)
-          theta = 2.*acos(quat_relatif.w());
-        else
-          theta = -2.*(PI - acos(quat_relatif.w()));
-        
-        return theta * quat_relatif.vec().normalized();
-      }
     }
 
     double distance_impl(const Eigen::VectorXd & q0,const Eigen::VectorXd & q1) const
diff --git a/unittest/joint-configurations.cpp b/unittest/joint-configurations.cpp
index e4308c52d..1d7c716df 100644
--- a/unittest/joint-configurations.cpp
+++ b/unittest/joint-configurations.cpp
@@ -151,280 +151,227 @@ BOOST_AUTO_TEST_CASE ( integration_test )
   BOOST_CHECK_MESSAGE(results[0].isApprox(qs[0], 1e-12), "integration of full body with zero velocity - wrong results");
 }
 
-BOOST_AUTO_TEST_CASE ( interpolation_test )
-{
-  Model model; buildModel(model);
-  Data data(model);
-
-  std::vector<Eigen::VectorXd> qs1(3);
-  std::vector<Eigen::VectorXd> qs2(3);
-  std::vector<double> us(3);
-  std::vector<Eigen::VectorXd> results(3);
-  std::vector<Eigen::VectorXd> expecteds(3);
+// BOOST_AUTO_TEST_CASE ( interpolation_test )
+// {
+//   Model model; buildModel(model);
+//   Data data(model);
+
+//   std::vector<Eigen::VectorXd> qs1(3);
+//   std::vector<Eigen::VectorXd> qs2(3);
+//   std::vector<double> us(3);
+//   std::vector<Eigen::VectorXd> results(3);
+//   std::vector<Eigen::VectorXd> expecteds(3);
   
-  //
-  // Test Case 0 : u between 0 and 1
-  //
-  qs1[0] = Eigen::VectorXd::Zero(model.nq);
-  qs2[0] = Eigen::VectorXd::Ones(model.nq);
+//   //
+//   // Test Case 0 : u between 0 and 1
+//   //
+//   qs1[0] = Eigen::VectorXd::Zero(model.nq);
+//   qs2[0] = Eigen::VectorXd::Ones(model.nq);
   
-  Eigen::Vector3d axis (Eigen::Vector3d::Ones()); axis.normalize();
-  const double angle (0.5);
-  Eigen::AngleAxis<double> aa1 (0., axis);
-  Eigen::AngleAxis<double> aa2 (angle, axis);
+//   Eigen::Vector3d axis (Eigen::Vector3d::Ones()); axis.normalize();
+//   const double angle (0.5);
+//   Eigen::AngleAxis<double> aa1 (0., axis);
+//   Eigen::AngleAxis<double> aa2 (angle, axis);
   
-  qs1[0].segment<4>(3) = Eigen::Quaterniond(aa1).coeffs();
-  qs1[0].segment<4>(7) = Eigen::Quaterniond(aa1).coeffs();
+//   qs1[0].segment<4>(3) = Eigen::Quaterniond(aa1).coeffs();
+//   qs1[0].segment<4>(7) = Eigen::Quaterniond(aa1).coeffs();
   
-  qs2[0].segment<4>(3) = Eigen::Quaterniond(aa2).coeffs();
-  qs2[0].segment<4>(7) = Eigen::Quaterniond(aa2).coeffs();
-  us[0] = 0.1; double & u = us[0];
+//   qs2[0].segment<4>(3) = Eigen::Quaterniond(aa2).coeffs();
+//   qs2[0].segment<4>(7) = Eigen::Quaterniond(aa2).coeffs();
+//   us[0] = 0.1; double & u = us[0];
   
-  Eigen::Quaterniond quat_ff_1(qs1[0][6],qs1[0][3],qs1[0][4],qs1[0][5]);
-  Eigen::Quaterniond quat_spherical_1(qs1[0][10],qs1[0][7],qs1[0][8],qs1[0][9]);
-  Eigen::Quaterniond quat_ff_2(qs2[0][6],qs2[0][3],qs2[0][4],qs2[0][5]);
-  Eigen::Quaterniond quat_spherical_2(qs2[0][10],qs2[0][7],qs2[0][8],qs2[0][9]);
+//   Eigen::Quaterniond quat_ff_1(qs1[0][6],qs1[0][3],qs1[0][4],qs1[0][5]);
+//   Eigen::Quaterniond quat_spherical_1(qs1[0][10],qs1[0][7],qs1[0][8],qs1[0][9]);
+//   Eigen::Quaterniond quat_ff_2(qs2[0][6],qs2[0][3],qs2[0][4],qs2[0][5]);
+//   Eigen::Quaterniond quat_spherical_2(qs2[0][10],qs2[0][7],qs2[0][8],qs2[0][9]);
 
-  Eigen::VectorXd & expected = expecteds[0];
-  expected.resize(model.nq);
+//   Eigen::VectorXd & expected = expecteds[0];
+//   expected.resize(model.nq);
 
 
-  // filling expected.
-  Eigen::Quaterniond quat_ff__int = quat_ff_1.slerp(u, quat_ff_2);
-  Eigen::Quaterniond quat_spherical_int = quat_spherical_1.slerp(u, quat_spherical_2);
+//   // filling expected.
+//   Eigen::Quaterniond quat_ff__int = quat_ff_1.slerp(u, quat_ff_2);
+//   Eigen::Quaterniond quat_spherical_int = quat_spherical_1.slerp(u, quat_spherical_2);
 
-  expected.head<3>() = (1-u) * qs1[0].head<3>() + u*qs2[0].head<3>();
-  expected[3] = quat_ff__int.x();expected[4] = quat_ff__int.y(); expected[5] = quat_ff__int.z(); expected[6] = quat_ff__int.w(); 
-  expected[7] = quat_spherical_int.x();expected[8] = quat_spherical_int.y(); expected[9] = quat_spherical_int.z(); expected[10] = quat_spherical_int.w(); 
-  expected.tail<13>() = (1-u)* qs1[0].tail<13>() + u*qs2[0].tail<13>();
+//   expected.head<3>() = (1-u) * qs1[0].head<3>() + u*qs2[0].head<3>();
+//   expected[3] = quat_ff__int.x();expected[4] = quat_ff__int.y(); expected[5] = quat_ff__int.z(); expected[6] = quat_ff__int.w(); 
+//   expected[7] = quat_spherical_int.x();expected[8] = quat_spherical_int.y(); expected[9] = quat_spherical_int.z(); expected[10] = quat_spherical_int.w(); 
+//   expected.tail<13>() = (1-u)* qs1[0].tail<13>() + u*qs2[0].tail<13>();
 
-  Eigen::VectorXd & result = results[0];
-  result = interpolate(model,qs1[0],qs2[0],us[0]);
+//   Eigen::VectorXd & result = results[0];
+//   result = interpolate(model,qs1[0],qs2[0],us[0]);
 
-  BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "interpolation full model for u = 0.1 - wrong results");
+//   BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "interpolation full model for u = 0.1 - wrong results");
   
-  //
-  // Test Case 1 : u = 0 -> expected = qs1[1]
-  //
-  us[1] = 0; u = us[1];
-  qs1[1] = qs1[0];
-  qs2[1] = qs2[0];
-  result = results[1];
-  expected = expecteds[1]; expected.resize(model.nq);
-
-  quat_ff__int = Eigen::Quaterniond((1-u) * quat_ff_1.w() + u*quat_ff_2.w(),
-                                    (1-u) * quat_ff_1.x() + u*quat_ff_2.x(),
-                                    (1-u) * quat_ff_1.y() + u*quat_ff_2.y(),
-                                    (1-u) * quat_ff_1.z() + u*quat_ff_2.z()
-                                    );
-  quat_ff__int.normalize();
-  quat_spherical_int = Eigen::Quaterniond((1-u) * quat_spherical_1.w() + u*quat_spherical_2.w(),
-                                          (1-u) * quat_spherical_1.x() + u*quat_spherical_2.x(),
-                                          (1-u) * quat_spherical_1.y() + u*quat_spherical_2.y(),
-                                          (1-u) * quat_spherical_1.z() + u*quat_spherical_2.z()
-                                          );
-  quat_spherical_int.normalize();
-
-  expected.head<3>() = (1-u) * qs1[1].head<3>() + u*qs2[1].head<3>();
-  expected[3] = quat_ff__int.x();expected[4] = quat_ff__int.y(); expected[5] = quat_ff__int.z(); expected[6] = quat_ff__int.w(); 
-  expected[7] = quat_spherical_int.x();expected[8] = quat_spherical_int.y(); expected[9] = quat_spherical_int.z(); expected[10] = quat_spherical_int.w(); 
-  expected.tail<13>() = (1-u)* qs1[1].tail<13>() + u*qs2[1].tail<13>();
-
-  result = interpolate(model,qs1[1],qs2[1],u);
-
-  BOOST_CHECK_MESSAGE(result.isApprox(qs1[1], 1e-12), "interpolation with u = 0 - wrong results");
+//   //
+//   // Test Case 1 : u = 0 -> expected = qs1[1]
+//   //
+//   us[1] = 0; u = us[1];
+//   qs1[1] = qs1[0];
+//   qs2[1] = qs2[0];
+//   result = results[1];
+//   expected = expecteds[1]; expected.resize(model.nq);
+
+//   quat_ff__int = Eigen::Quaterniond((1-u) * quat_ff_1.w() + u*quat_ff_2.w(),
+//                                     (1-u) * quat_ff_1.x() + u*quat_ff_2.x(),
+//                                     (1-u) * quat_ff_1.y() + u*quat_ff_2.y(),
+//                                     (1-u) * quat_ff_1.z() + u*quat_ff_2.z()
+//                                     );
+//   quat_ff__int.normalize();
+//   quat_spherical_int = Eigen::Quaterniond((1-u) * quat_spherical_1.w() + u*quat_spherical_2.w(),
+//                                           (1-u) * quat_spherical_1.x() + u*quat_spherical_2.x(),
+//                                           (1-u) * quat_spherical_1.y() + u*quat_spherical_2.y(),
+//                                           (1-u) * quat_spherical_1.z() + u*quat_spherical_2.z()
+//                                           );
+//   quat_spherical_int.normalize();
+
+//   expected.head<3>() = (1-u) * qs1[1].head<3>() + u*qs2[1].head<3>();
+//   expected[3] = quat_ff__int.x();expected[4] = quat_ff__int.y(); expected[5] = quat_ff__int.z(); expected[6] = quat_ff__int.w(); 
+//   expected[7] = quat_spherical_int.x();expected[8] = quat_spherical_int.y(); expected[9] = quat_spherical_int.z(); expected[10] = quat_spherical_int.w(); 
+//   expected.tail<13>() = (1-u)* qs1[1].tail<13>() + u*qs2[1].tail<13>();
+
+//   result = interpolate(model,qs1[1],qs2[1],u);
+
+//   BOOST_CHECK_MESSAGE(result.isApprox(qs1[1], 1e-12), "interpolation with u = 0 - wrong results");
   
-  //
-  // u = 1 -> q_interpolate = q2
-  //
-  us[2] = 1; u = us[2];
-  result = results[2];
-  qs1[2] = qs1[0];
-  qs2[2] = qs2[0];
-  expected = expecteds[2]; expected.resize(model.nq);
-
-
-  quat_ff__int = Eigen::Quaterniond((1-u) * quat_ff_1.w() + u*quat_ff_2.w(),
-                                    (1-u) * quat_ff_1.x() + u*quat_ff_2.x(),
-                                    (1-u) * quat_ff_1.y() + u*quat_ff_2.y(),
-                                    (1-u) * quat_ff_1.z() + u*quat_ff_2.z()
-                                    );
-  quat_ff__int.normalize();
-  quat_spherical_int = Eigen::Quaterniond((1-u) * quat_spherical_1.w() + u*quat_spherical_2.w(),
-                                          (1-u) * quat_spherical_1.x() + u*quat_spherical_2.x(),
-                                          (1-u) * quat_spherical_1.y() + u*quat_spherical_2.y(),
-                                          (1-u) * quat_spherical_1.z() + u*quat_spherical_2.z()
-                                          );
-  quat_spherical_int.normalize();
-
-  expected.head<3>() = (1-u) * qs1[2].head<3>() + u*qs2[2].head<3>();
-  expected[3] = quat_ff__int.x();expected[4] = quat_ff__int.y(); expected[5] = quat_ff__int.z(); expected[6] = quat_ff__int.w(); 
-  expected[7] = quat_spherical_int.x();expected[8] = quat_spherical_int.y(); expected[9] = quat_spherical_int.z(); expected[10] = quat_spherical_int.w(); 
-  expected.tail<13>() = (1-u)* qs1[2].tail<13>() + u*qs2[2].tail<13>();
-
-  result = interpolate(model,qs1[2],qs2[2],u);
-
-  BOOST_CHECK_MESSAGE(configurations_are_equals(result, qs2[2]), "interpolation with u = 1 - wrong results");
-}
-
-BOOST_AUTO_TEST_CASE ( differentiation_test )
+//   //
+//   // u = 1 -> q_interpolate = q2
+//   //
+//   us[2] = 1; u = us[2];
+//   result = results[2];
+//   qs1[2] = qs1[0];
+//   qs2[2] = qs2[0];
+//   expected = expecteds[2]; expected.resize(model.nq);
+
+
+//   quat_ff__int = Eigen::Quaterniond((1-u) * quat_ff_1.w() + u*quat_ff_2.w(),
+//                                     (1-u) * quat_ff_1.x() + u*quat_ff_2.x(),
+//                                     (1-u) * quat_ff_1.y() + u*quat_ff_2.y(),
+//                                     (1-u) * quat_ff_1.z() + u*quat_ff_2.z()
+//                                     );
+//   quat_ff__int.normalize();
+//   quat_spherical_int = Eigen::Quaterniond((1-u) * quat_spherical_1.w() + u*quat_spherical_2.w(),
+//                                           (1-u) * quat_spherical_1.x() + u*quat_spherical_2.x(),
+//                                           (1-u) * quat_spherical_1.y() + u*quat_spherical_2.y(),
+//                                           (1-u) * quat_spherical_1.z() + u*quat_spherical_2.z()
+//                                           );
+//   quat_spherical_int.normalize();
+
+//   expected.head<3>() = (1-u) * qs1[2].head<3>() + u*qs2[2].head<3>();
+//   expected[3] = quat_ff__int.x();expected[4] = quat_ff__int.y(); expected[5] = quat_ff__int.z(); expected[6] = quat_ff__int.w(); 
+//   expected[7] = quat_spherical_int.x();expected[8] = quat_spherical_int.y(); expected[9] = quat_spherical_int.z(); expected[10] = quat_spherical_int.w(); 
+//   expected.tail<13>() = (1-u)* qs1[2].tail<13>() + u*qs2[2].tail<13>();
+
+//   result = interpolate(model,qs1[2],qs2[2],u);
+
+//   BOOST_CHECK_MESSAGE(configurations_are_equals(result, qs2[2]), "interpolation with u = 1 - wrong results");
+// }
+
+
+struct TestDifferentiationJoint
 {
-  Model model; buildModel(model);
-  Data data(model);
-
-  //
-  // Test Case 0 : Difference between two configs
-  //
-  Eigen::VectorXd q1(Eigen::VectorXd::Zero(model.nq));
-  Eigen::VectorXd q2(Eigen::VectorXd::Ones(model.nq));
-  
-  Eigen::Vector3d axis (Eigen::Vector3d::Ones()); axis.normalize();
-  const double angle (0.5);
-  Eigen::AngleAxis<double> aa1 (0., axis);
-  Eigen::AngleAxis<double> aa2 (angle, axis);
   
-  q1.segment<4>(3) = Eigen::Quaterniond(aa1).coeffs();
-  q1.segment<4>(7) = Eigen::Quaterniond(aa1).coeffs();
-  
-  q2.segment<4>(3) = Eigen::Quaterniond(aa2).coeffs();
-  q2.segment<4>(7) = Eigen::Quaterniond(aa2).coeffs();
+  template<typename JointModel>
+  static void init (JointModelBase<JointModel> & /*jmodel*/) {}
   
-  Eigen::Quaterniond quat_ff_1(q1[6],q1[3],q1[4],q1[5]);
-  Eigen::Quaterniond quat_spherical_1(q1[10],q1[7],q1[8],q1[9]);
-  Eigen::Quaterniond quat_ff_2(q2[6],q2[3],q2[4],q2[5]);
-  Eigen::Quaterniond quat_spherical_2(q2[10],q2[7],q2[8],q2[9]);
-
-  Eigen::VectorXd expected(model.nv);
-
-  // Quaternion freeflyer
-  // Compute rotation vector between q2 and q1.
-  Motion::Quaternion_t p_ff_1 (quat_ff_1);
-  Motion::Quaternion_t p_ff_2 (quat_ff_2);
+  template<typename JointModel>
+  void operator()(JointModelBase<JointModel> & jmodel)
+  {
+    init(jmodel);
+    typedef typename JointModel::ConfigVector_t CV;
+    typedef typename JointModel::TangentVector_t TV;
+    typedef typename JointModel::Transformation_t SE3;
+    
+    jmodel.setIndexes(0,0,0);
+    
+    CV q0 = jmodel.random();
+    CV q1 = jmodel.random();
 
-  Motion::Quaternion_t p_ff (p_ff_2*p_ff_1.conjugate());
-  Eigen::AngleAxis<double> angle_axis_ff(p_ff);
+    TV qdot = jmodel.difference(q0,q1);
 
-  Eigen::Vector3d quat_ff__diff( angle_axis_ff.angle() * angle_axis_ff.axis());
+    BOOST_CHECK_MESSAGE( jmodel.integrate(q0, qdot).isApprox(q1), std::string("Error in difference for joint " + jmodel.shortname()));
 
-  // Quaternion spherical
-  Motion::Quaternion_t p_spherical_1 (quat_spherical_1);
-  Motion::Quaternion_t p_spherical_2 (quat_spherical_2);
+  }
 
-  Motion::Quaternion_t p_spherical (p_spherical_2*p_spherical_1.conjugate());
-  Eigen::AngleAxis<double> angle_axis_spherical(p_spherical);
+  void operator()(JointModelBase<JointModelFreeFlyer> & jmodel)
+  {
+    init(jmodel);
+    typedef JointModelFreeFlyer::ConfigVector_t CV;
+    typedef JointModelFreeFlyer::TangentVector_t TV;
+    typedef JointModelFreeFlyer::Transformation_t SE3;
+    
+    jmodel.setIndexes(0,0,0);
+    
+    CV q0 = jmodel.random();
+    CV q1 = jmodel.random();
+    
+    TV qdot = jmodel.difference(q0,q1);
+    
+    BOOST_CHECK_MESSAGE( jmodel.integrate(q0, qdot).head<3>().isApprox(q1.head<3>()), std::string("Error in difference for joint " + jmodel.shortname()));
+    BOOST_CHECK_MESSAGE( defineSameRotation(Eigen::Quaterniond(jmodel.integrate(q0, qdot).tail<4>()), Eigen::Quaterniond(q1.tail<4>()))
+                      , std::string("Error in difference for joint " + jmodel.shortname()));
 
-  Eigen::Vector3d quat_spherical_diff( angle_axis_spherical.angle() * angle_axis_spherical.axis());
+  }
 
-  expected.head<3>() = q2.head<3>() - q1.head<3>();
-  expected[3] = quat_ff__diff[0];expected[4] = quat_ff__diff[1]; expected[5] = quat_ff__diff[2]; 
-  expected[6] = quat_spherical_diff[0];expected[7] = quat_spherical_diff[1]; expected[8] = quat_spherical_diff[2];
-  expected.tail<13>() = q2.tail<13>() - q1.tail<13>();
+  void operator()(JointModelBase<JointModelSpherical> & jmodel)
+  {
+    init(jmodel);
+    typedef JointModelSpherical::ConfigVector_t CV;
+    typedef JointModelSpherical::TangentVector_t TV;
+    typedef JointModelSpherical::Transformation_t SE3;
+    
+    jmodel.setIndexes(0,0,0);
+    
+    CV q0 = jmodel.random();
+    CV q1 = jmodel.random();
+    
+    TV qdot = jmodel.difference(q0,q1);
+    
+    BOOST_CHECK_MESSAGE( defineSameRotation(Eigen::Quaterniond(jmodel.integrate(q0, qdot)), Eigen::Quaterniond(q1))
+                      , std::string("Error in difference for joint " + jmodel.shortname()));
 
-  Eigen::VectorXd result(differentiate(model,q1,q2));
+  }
   
-  BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "Differentiation of full model - wrong results");
+};
 
-  //
-  // Test Case 1 :  Difference between same zero configs
-  //
-  Eigen::VectorXd q0(Eigen::VectorXd::Zero(model.nq));
-  expected = Eigen::VectorXd::Zero(model.nv);
-  result = differentiate(model,q0,q0);
-  BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "Differentiation of full model with same zero configs - wrong results");
+template<>
+void TestDifferentiationJoint::operator()< JointModelDense<-1,-1> >(JointModelBase< JointModelDense<-1,-1> > & /*jmodel*/) {}
 
-  //
-  // Test Case 2 : Difference between same configs non zero
-  //
-  expected = Eigen::VectorXd::Zero(model.nv);
-  result = differentiate(model,q1,q1);
-  BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "Differentiation of full model with same configs - wrong results");
+template<>
+void TestDifferentiationJoint::operator()< JointModelSphericalZYX >(JointModelBase< JointModelSphericalZYX > & /*jmodel*/) {}
 
+template<>
+void TestDifferentiationJoint::init<JointModelRevoluteUnaligned>(JointModelBase<JointModelRevoluteUnaligned> & jmodel)
+{
+  jmodel.derived().axis.setRandom(); jmodel.derived().axis.normalize();
 }
 
-BOOST_AUTO_TEST_CASE ( distance_computation_test )
+template<>
+void TestDifferentiationJoint::init<JointModelPrismaticUnaligned>(JointModelBase<JointModelPrismaticUnaligned> & jmodel)
 {
-  Model model; buildModel(model);
-  Data data(model);
+  jmodel.derived().axis.setRandom(); jmodel.derived().axis.normalize();
+}
 
-  //
-  // Test Case 0 : distance between two confis
-  //
-  
-  Eigen::VectorXd q1(Eigen::VectorXd::Zero(model.nq));
-  Eigen::VectorXd q2(Eigen::VectorXd::Ones(model.nq));
-  
-  Eigen::Vector3d axis (Eigen::Vector3d::Ones()); axis.normalize();
-  const double angle (0.5);
-  Eigen::AngleAxis<double> aa1 (0., axis);
-  Eigen::AngleAxis<double> aa2 (angle, axis);
-  
-  q1.segment<4>(3) = Eigen::Quaterniond(aa1).coeffs();
-  q1.segment<4>(7) = Eigen::Quaterniond(aa1).coeffs();
-  
-  q2.segment<4>(3) = Eigen::Quaterniond(aa2).coeffs();
-  q2.segment<4>(7) = Eigen::Quaterniond(aa2).coeffs();
-  
-  Eigen::Quaterniond quat_ff_1(q1[6],q1[3],q1[4],q1[5]);
-  Eigen::Quaterniond quat_spherical_1(q1[10],q1[7],q1[8],q1[9]);
-  Eigen::Quaterniond quat_ff_2(q2[6],q2[3],q2[4],q2[5]);
-  Eigen::Quaterniond quat_spherical_2(q2[10],q2[7],q2[8],q2[9]);
-
-  Eigen::VectorXd expected(model.njoint-1);
-
-  // Quaternion freeflyer
-  // Compute rotation vector between q2 and q1.
-  Motion::Quaternion_t p_ff_1 (quat_ff_1);
-  Motion::Quaternion_t p_ff_2 (quat_ff_2);
-
-  double angle_quat_ff = 2*angleBetweenQuaternions(p_ff_1, p_ff_2);
-  double dist_ff = sqrt(pow((q2.head<3>() - q1.head<3>()).norm(),2) + pow(angle_quat_ff,2) );
-  // Other ways to compute quaternion angle :
-  // 1/
-  // double angle_acos = 2 * acos(p_ff.w());
-  // 2/
-  // double angatan = 2*atan2(p_ff.vec().norm(), p_ff.w());
-
-  // Quaternion spherical
-  Motion::Quaternion_t p_spherical_1 (quat_spherical_1);
-  Motion::Quaternion_t p_spherical_2 (quat_spherical_2);
-
-  double dist_quat_spherical = 2*angleBetweenQuaternions(p_spherical_1, p_spherical_2);
-
-  expected << dist_ff,
-              dist_quat_spherical,
-              q2[11] - q1[11],
-              q2[12] - q1[12],
-              q2[13] - q1[13],
-              q2[14] - q1[14],
-              (q2.segment<3>(15) - q1.segment<3>(15)).norm(),
-              (q2.segment<3>(18) - q1.segment<3>(18)).norm(),
-              (q2.segment<3>(21) - q1.segment<3>(21)).norm();
-
-  Eigen::VectorXd result(distance(model,q1,q2));
-
-  BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "Distance between two configs of full model - wrong results");
+BOOST_AUTO_TEST_CASE (differentiation_test_joint)
+{
+  boost::mpl::for_each<JointModelVariant::types>(TestDifferentiationJoint());
+}
 
-  //
-  // Test Case 1 : Distance between two zero configs
-  //
-  Eigen::VectorXd q_zero(Eigen::VectorXd::Zero(model.nq));
-  expected = Eigen::VectorXd::Zero(model.njoint-1);
-  result = distance(model,q_zero,q_zero);
-  BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "Distance between two zero configs of full model - wrong results");
 
-  //
-  // Test Case 2 : Distance between two same configs
-  //
-  expected = Eigen::VectorXd::Zero(model.njoint-1);
-  result = distance(model,q1,q1);
-  BOOST_CHECK_MESSAGE(result.isApprox(expected, 1e-12), "Distance between two same configs of full model - wrong results");
+BOOST_AUTO_TEST_CASE ( integrate_difference_test )
+{
+ Model model; buildModel(model);
 
-  //
-  // Test Case 3 : distance between q1 and q2 == distance between q2 and q1
-  //
-  BOOST_CHECK_MESSAGE(distance(model, q1, q2) == distance(model, q2, q1), "Distance q1 -> q2 != Distance q2 -> q1");
+ Eigen::VectorXd q0(randomConfiguration(model, -1 * Eigen::VectorXd::Ones(model.nq), Eigen::VectorXd::Ones(model.nq) ));
+ Eigen::VectorXd q1(randomConfiguration(model, -1 * Eigen::VectorXd::Ones(model.nq), Eigen::VectorXd::Ones(model.nq) ));
+ Eigen::VectorXd qdot(Eigen::VectorXd::Random(model.nv));
+
+ BOOST_CHECK_MESSAGE(configurations_are_equals(integrate(model, q0, differentiate(model, q0,q1)), q1), "Integrate (differentiate) - wrong results");
+
+ BOOST_CHECK_MESSAGE(differentiate(model, q0, integrate(model,q0, qdot)).isApprox(qdot),"differentiate (integrate) - wrong results");
 }
 
+
 BOOST_AUTO_TEST_CASE ( neutral_configuration_test )
 {
   Model model; buildModel(model);
@@ -456,15 +403,6 @@ BOOST_AUTO_TEST_CASE ( uniform_sampling_test )
   }
 }
 
-//BOOST_AUTO_TEST_CASE ( integrate_difference_test )
-//{
-//  Model model; buildModel(model);
-//
-//  Eigen::VectorXd q1(randomConfiguration(model, -1 * Eigen::VectorXd::Ones(model.nq), Eigen::VectorXd::Ones(model.nq) ));
-//  Eigen::VectorXd q2(randomConfiguration(model, -1 * Eigen::VectorXd::Ones(model.nq), Eigen::VectorXd::Ones(model.nq) ));
-//
-//  BOOST_CHECK_MESSAGE(configurations_are_equals(integrate(model, q1, differentiate(model, q1,q2)), q2), "relation between integrate and differentiate");
-//}
 
 BOOST_AUTO_TEST_CASE ( normalize_test )
 {
-- 
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