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  #ifndef PCL_COMMON_EIGEN_IMPL_HPP_
  #define PCL_COMMON_EIGEN_IMPL_HPP_
  
  #include <pcl/pcl_macros.h>
  
  //////////////////////////////////////////////////////////////////////////////////////////
  void 
  pcl::getTransFromUnitVectorsZY (const Eigen::Vector3f& z_axis, 
                                  const Eigen::Vector3f& y_direction, 
                                  Eigen::Affine3f& transformation)
  {
    Eigen::Vector3f tmp0 = (y_direction.cross(z_axis)).normalized();
    Eigen::Vector3f tmp1 = (z_axis.cross(tmp0)).normalized();
    Eigen::Vector3f tmp2 = z_axis.normalized();
    
    transformation(0,0)=tmp0[0]; transformation(0,1)=tmp0[1]; transformation(0,2)=tmp0[2]; transformation(0,3)=0.0f;
    transformation(1,0)=tmp1[0]; transformation(1,1)=tmp1[1]; transformation(1,2)=tmp1[2]; transformation(1,3)=0.0f;
    transformation(2,0)=tmp2[0]; transformation(2,1)=tmp2[1]; transformation(2,2)=tmp2[2]; transformation(2,3)=0.0f;
    transformation(3,0)=0.0f;    transformation(3,1)=0.0f;    transformation(3,2)=0.0f;    transformation(3,3)=1.0f;
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  Eigen::Affine3f 
  pcl::getTransFromUnitVectorsZY (const Eigen::Vector3f& z_axis, 
                                  const Eigen::Vector3f& y_direction)
  {
    Eigen::Affine3f transformation;
    getTransFromUnitVectorsZY (z_axis, y_direction, transformation);
    return (transformation);
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  void 
  pcl::getTransFromUnitVectorsXY (const Eigen::Vector3f& x_axis, 
                                  const Eigen::Vector3f& y_direction, 
                                  Eigen::Affine3f& transformation)
  {
    Eigen::Vector3f tmp2 = (x_axis.cross(y_direction)).normalized();
    Eigen::Vector3f tmp1 = (tmp2.cross(x_axis)).normalized();
    Eigen::Vector3f tmp0 = x_axis.normalized();
    
    transformation(0,0)=tmp0[0]; transformation(0,1)=tmp0[1]; transformation(0,2)=tmp0[2]; transformation(0,3)=0.0f;
    transformation(1,0)=tmp1[0]; transformation(1,1)=tmp1[1]; transformation(1,2)=tmp1[2]; transformation(1,3)=0.0f;
    transformation(2,0)=tmp2[0]; transformation(2,1)=tmp2[1]; transformation(2,2)=tmp2[2]; transformation(2,3)=0.0f;
    transformation(3,0)=0.0f;    transformation(3,1)=0.0f;    transformation(3,2)=0.0f;    transformation(3,3)=1.0f;
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  Eigen::Affine3f 
  pcl::getTransFromUnitVectorsXY (const Eigen::Vector3f& x_axis, 
                                  const Eigen::Vector3f& y_direction)
  {
    Eigen::Affine3f transformation;
    getTransFromUnitVectorsXY (x_axis, y_direction, transformation);
    return (transformation);
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  void 
  pcl::getTransformationFromTwoUnitVectors (const Eigen::Vector3f& y_direction, 
                                            const Eigen::Vector3f& z_axis, 
                                            Eigen::Affine3f& transformation)
  {
    getTransFromUnitVectorsZY (z_axis, y_direction, transformation);
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  Eigen::Affine3f 
  pcl::getTransformationFromTwoUnitVectors (const Eigen::Vector3f& y_direction, 
                                            const Eigen::Vector3f& z_axis)
  {
    Eigen::Affine3f transformation;
    getTransformationFromTwoUnitVectors (y_direction, z_axis, transformation);
    return (transformation);
  }
  
  void 
  pcl::getTransformationFromTwoUnitVectorsAndOrigin (const Eigen::Vector3f& y_direction, 
                                                     const Eigen::Vector3f& z_axis,
                                                     const Eigen::Vector3f& origin, 
                                                     Eigen::Affine3f& transformation)
  {
    getTransformationFromTwoUnitVectors(y_direction, z_axis, transformation);
    Eigen::Vector3f translation = transformation*origin;
    transformation(0,3)=-translation[0];  transformation(1,3)=-translation[1];  transformation(2,3)=-translation[2];
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  void 
  pcl::getEulerAngles (const Eigen::Affine3f& t, float& roll, float& pitch, float& yaw)
  {
    roll  = atan2f(t(2,1), t(2,2));
    pitch = asinf(-t(2,0));
    yaw   = atan2f(t(1,0), t(0,0));
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  void 
  pcl::getTranslationAndEulerAngles (const Eigen::Affine3f& t, 
                                     float& x, float& y, float& z, 
                                     float& roll, float& pitch, float& yaw)
  {
    x = t(0,3);
    y = t(1,3);
    z = t(2,3);
    roll  = atan2f(t(2,1), t(2,2));
    pitch = asinf(-t(2,0));
    yaw   = atan2f(t(1,0), t(0,0));
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  template <typename Scalar> void 
  pcl::getTransformation (Scalar x, Scalar y, Scalar z, 
                          Scalar roll, Scalar pitch, Scalar yaw, 
                          Eigen::Transform<Scalar, 3, Eigen::Affine> &t)
  {
    Scalar A = cos (yaw),  B = sin (yaw),  C  = cos (pitch), D  = sin (pitch),
           E = cos (roll), F = sin (roll), DE = D*E,         DF = D*F;
  
    t (0, 0) = A*C;  t (0, 1) = A*DF - B*E;  t (0, 2) = B*F + A*DE;  t (0, 3) = x;
    t (1, 0) = B*C;  t (1, 1) = A*E + B*DF;  t (1, 2) = B*DE - A*F;  t (1, 3) = y;
    t (2, 0) = -D;   t (2, 1) = C*F;         t (2, 2) = C*E;         t (2, 3) = z;
    t (3, 0) = 0;    t (3, 1) = 0;           t (3, 2) = 0;           t (3, 3) = 1;
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  Eigen::Affine3f 
  pcl::getTransformation (float x, float y, float z, float roll, float pitch, float yaw)
  {
    Eigen::Affine3f t;
    getTransformation (x, y, z, roll, pitch, yaw, t);
    return (t);
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  template <typename Derived> void 
  pcl::saveBinary (const Eigen::MatrixBase<Derived>& matrix, std::ostream& file)
  {
    uint32_t rows = static_cast<uint32_t> (matrix.rows ()), cols = static_cast<uint32_t> (matrix.cols ());
    file.write (reinterpret_cast<char*> (&rows), sizeof (rows));
    file.write (reinterpret_cast<char*> (&cols), sizeof (cols));
    for (uint32_t i = 0; i < rows; ++i)
      for (uint32_t j = 0; j < cols; ++j)
      {
        typename Derived::Scalar tmp = matrix(i,j);
        file.write (reinterpret_cast<const char*> (&tmp), sizeof (tmp));
      }
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  template <typename Derived> void 
  pcl::loadBinary (Eigen::MatrixBase<Derived> const & matrix_, std::istream& file)
  {
    Eigen::MatrixBase<Derived> &matrix = const_cast<Eigen::MatrixBase<Derived> &> (matrix_);
  
    uint32_t rows, cols;
    file.read (reinterpret_cast<char*> (&rows), sizeof (rows));
    file.read (reinterpret_cast<char*> (&cols), sizeof (cols));
    if (matrix.rows () != static_cast<int>(rows) || matrix.cols () != static_cast<int>(cols))
      matrix.derived().resize(rows, cols);
    
    for (uint32_t i = 0; i < rows; ++i)
      for (uint32_t j = 0; j < cols; ++j)
      {
        typename Derived::Scalar tmp;
        file.read (reinterpret_cast<char*> (&tmp), sizeof (tmp));
        matrix (i, j) = tmp;
      }
  }
  
  //////////////////////////////////////////////////////////////////////////////////////////
  template <typename Derived, typename OtherDerived> 
  typename Eigen::internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type
  pcl::umeyama (const Eigen::MatrixBase<Derived>& src, const Eigen::MatrixBase<OtherDerived>& dst, bool with_scaling)
  {
    typedef typename Eigen::internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType;
    typedef typename Eigen::internal::traits<TransformationMatrixType>::Scalar Scalar;
    typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
    typedef typename Derived::Index Index;
  
    EIGEN_STATIC_ASSERT (!Eigen::NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
    EIGEN_STATIC_ASSERT ((Eigen::internal::is_same<Scalar, typename Eigen::internal::traits<OtherDerived>::Scalar>::value),
      YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
  
    enum { Dimension = PCL_EIGEN_SIZE_MIN_PREFER_DYNAMIC (Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
  
    typedef Eigen::Matrix<Scalar, Dimension, 1> VectorType;
    typedef Eigen::Matrix<Scalar, Dimension, Dimension> MatrixType;
    typedef typename Eigen::internal::plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;
  
    const Index m = src.rows (); // dimension
    const Index n = src.cols (); // number of measurements
  
    // required for demeaning ...
    const RealScalar one_over_n = 1 / static_cast<RealScalar> (n);
  
    // computation of mean
    const VectorType src_mean = src.rowwise ().sum () * one_over_n;
    const VectorType dst_mean = dst.rowwise ().sum () * one_over_n;
  
    // demeaning of src and dst points
    const RowMajorMatrixType src_demean = src.colwise () - src_mean;
    const RowMajorMatrixType dst_demean = dst.colwise () - dst_mean;
  
    // Eq. (36)-(37)
    const Scalar src_var = src_demean.rowwise ().squaredNorm ().sum () * one_over_n;
  
    // Eq. (38)
    const MatrixType sigma (one_over_n * dst_demean * src_demean.transpose ());
  
    Eigen::JacobiSVD<MatrixType> svd (sigma, Eigen::ComputeFullU | Eigen::ComputeFullV);
  
    // Initialize the resulting transformation with an identity matrix...
    TransformationMatrixType Rt = TransformationMatrixType::Identity (m + 1, m + 1);
  
    // Eq. (39)
    VectorType S = VectorType::Ones (m);
    if (sigma.determinant () < 0) 
      S (m - 1) = -1;
  
    // Eq. (40) and (43)
    const VectorType& d = svd.singularValues ();
    Index rank = 0; 
    for (Index i = 0; i < m; ++i) 
      if (!Eigen::internal::isMuchSmallerThan (d.coeff (i), d.coeff (0))) 
        ++rank;
    if (rank == m - 1) 
    {
      if (svd.matrixU ().determinant () * svd.matrixV ().determinant () > 0) 
        Rt.block (0, 0, m, m).noalias () = svd.matrixU () * svd.matrixV ().transpose ();
      else 
      {
        const Scalar s = S (m - 1); 
        S (m - 1) = -1;
        Rt.block (0, 0, m, m).noalias () = svd.matrixU () * S.asDiagonal () * svd.matrixV ().transpose ();
        S (m - 1) = s;
      }
    } 
    else 
    {
      Rt.block (0, 0, m, m).noalias () = svd.matrixU () * S.asDiagonal () * svd.matrixV ().transpose ();
    }
  
    // Eq. (42)
    if (with_scaling)
    {
      // Eq. (42)
      const Scalar c = 1 / src_var * svd.singularValues ().dot (S);
  
      // Eq. (41)
      Rt.col (m).head (m) = dst_mean;
      Rt.col (m).head (m).noalias () -= c * Rt.topLeftCorner (m, m) * src_mean;
      Rt.block (0, 0, m, m) *= c;
    }
    else
    {
      Rt.col (m).head (m) = dst_mean;
      Rt.col (m).head (m).noalias () -= Rt.topLeftCorner (m, m) * src_mean;
    }
  
    return (Rt);
  }
  
  #endif  //PCL_COMMON_EIGEN_IMPL_HPP_
  