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

저렇게 긍정적으로 생각해야겠지? 

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)]

Nikola Tesla

“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”


― Nikola Tesla

ARCBALL

회전축과 회전각도를 결정하여 회전 Quaternion 을 구해냄.

마우스 입력으로 3차원 회전축과 각도를 어떻게 결정하는지 알면 끝.

현재점과 anchor 점을 결정할 때 2D 입력을 spherical mapping을 사용하여 3D Vector로 mapping.

본 논문 : 

ARCBALL: a user interface for specifying three-dimensional orientation using a mouse
http://dl.acm.org/citation.cfm?id=155312

예쁜 구름

지난 10월초 유럽의 어느 하늘 위. 

#pragma warning(disable : 4244)

#if (_MSC_VER)      
// make microsoft visual studio complain less about double / float conversion.
#pragma warning(disable : 4244)
#endif

ofQuaternion.h 에서 참고

Take Screenshot After Some Delay: gnome-screenshot

$ gnome-screenshot -w -d 2

 -d 2 is used for delaying the screenshot for 2 seconds. So within the 2 seconds, we can make the window which we want to take screenshot as active.

Lifelines

Lifelines of referenced historical figures

꼭지점 필터

솔리드 웍스 작업중에 자꾸 켜지는 꼭지점 필터.

Curvature

Geometry perception 과 관련하여:

Larger curves explored by touching multiple points, whether statically or dynamically, appear to be judged by the difference in local slope at different points of contact (Pont, 1997; Pont, Kappers, & Koenderink, 1999).

from Lederman, Susan J., and Roberta L. Klatzky. "Haptic perception: A tutorial." Attention, Perception, & Psychophysics 71.7 (2009): 1439-1459.

Pont, S. C. (1997). Haptic curvature comparison. Unpublished doctoral

dissertation, Helmholz Instituut, Utrecht.

Pont, S. C., Kappers, A. M. L., & Koenderink, J. J. (1999). Similar mechanisms underlie curvature comparison by static and dynamic touch. Perception & Psychophysics, 61, 874-894.

수요일 알리미

"매번 벌써 수요일인가?" 라는 생각을 하게하는 수요일 알리미. 

myDAQ

좋은 세상이구나~

Eigenvalues of rotation matrix : 0~180 degrees

Eigenvalue의 의미를 보여주는 그래프. y축은 imaginary axis.

추가 1)

When an n×n rotation matrix, Q, does not include −1 as an eigenvalue, so that none of the planar rotations of which it is composed are 180° rotations, then Q+I is an invertible matrix. Most rotation matrices fit this description.

http://en.wikipedia.org/wiki/Rotation_matrix