PCA in PCL

/////////////////////////////////////////////////////////////////////////////////////////
template bool
pcl::PCA::initCompute ()
{
  if(!Base::initCompute ())
  {
    PCL_THROW_EXCEPTION (InitFailedException, "[pcl::PCA::initCompute] failed");
    return (false);
  }
  if(indices_->size () < 3)
  {
    PCL_THROW_EXCEPTION (InitFailedException, "[pcl::PCA::initCompute] number of points < 3");
    return (false);
  }

  // Compute mean
  mean_ = Eigen::Vector4f::Zero ();
  compute3DCentroid (*input_, *indices_, mean_);
  // Compute demeanished cloud
  Eigen::MatrixXf cloud_demean;
  demeanPointCloud (*input_, *indices_, mean_, cloud_demean);
  assert (cloud_demean.cols () == int (indices_->size ()));
  // Compute the product cloud_demean * cloud_demean^T
  Eigen::Matrix3f alpha = cloud_demean.topRows<3> () * cloud_demean.topRows<3> ().transpose ();

  // Compute eigen vectors and values
  Eigen::SelfAdjointEigenSolver evd (alpha);
  // Organize eigenvectors and eigenvalues in ascendent order
  for (int i = 0; i < 3; ++i)
  {
    eigenvalues_[i] = evd.eigenvalues () [2-i];
    eigenvectors_.col (i) = evd.eigenvectors ().col (2-i);
  }
  // If not basis only then compute the coefficients

  if (!basis_only_)
    coefficients_ = eigenvectors_.transpose() * cloud_demean.topRows<3> ();
  compute_done_ = true;
  return (true);
}



from /opt/ros/fuerte/include/pcl-1.5/pcl/common/impl/pca.hpp

생각대로

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Z-Y-X Euler Angles

Z-Y-X Euler Angles

Z-Y-X Euler Angles (or X-Y-Z fixed angles)
Rx'y'z' (a,b,c) =

[ cos(a)*cos(b), cos(a)*sin(b)*sin(c) - cos(c)*sin(a), sin(a)*sin(c) + cos(a)*cos(c)*sin(b)]
[ cos(b)*sin(a), cos(a)*cos(c) + sin(a)*sin(b)*sin(c), cos(c)*sin(a)*sin(b) - cos(a)*sin(c)]
[       -sin(b),                        cos(b)*sin(c),                        cos(b)*cos(c)]



X-Y-Z Euler Angles
Rz'y'x' (a,b,c) =

[                        cos(b)*cos(c),                       -cos(b)*sin(c),         sin(b)]
[ cos(a)*sin(c) + cos(c)*sin(a)*sin(b), cos(a)*cos(c) - sin(a)*sin(b)*sin(c), -cos(b)*sin(a)]
[ sin(a)*sin(c) - cos(a)*cos(c)*sin(b), cos(c)*sin(a) + cos(a)*sin(b)*sin(c),  cos(a)*cos(b)]

Rz'y'x' (c,b,a) =
[                        cos(a)*cos(b),                       -cos(b)*sin(a),         sin(b)]
[ cos(c)*sin(a) + cos(a)*sin(b)*sin(c), cos(a)*cos(c) - sin(a)*sin(b)*sin(c), -cos(b)*sin(c)]
[ sin(a)*sin(c) - cos(a)*cos(c)*sin(b), cos(a)*sin(c) + cos(c)*sin(a)*sin(b),  cos(b)*cos(c)]