Why i did this silly change

.gitattributes

@@ -1877,6 +1877,8 @@ Principal_component_analysis/demo/Principal_component_analysis/windows/3d/res/id
 Principal_component_analysis/doc_tex/Principal_component_analysis/fit.eps -text svneol=unset#application/postscript
 Principal_component_analysis/doc_tex/Principal_component_analysis/fit.png -text svneol=unset#image/png
 Principal_component_analysis/doc_tex/Principal_component_analysis/teaserLeastSquaresFitting.png -text
+Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments.h -text
+Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles.h -text
 QP_solver/doc_tex/QP_solver/PkgDescription.tex -text
 QP_solver/doc_tex/QP_solver/closest_point.eps -text svneol=unset#application/postscript
 QP_solver/doc_tex/QP_solver/closest_point.fig -text svneol=unset#application/octet-stream

Principal_component_analysis/include/CGAL/centroid.h

@@ -88,6 +88,39 @@ centroid(InputIterator begin,
   return ORIGIN + v / (FT)nb_pts;
 }// end centroid of a 3D point set
 
+// computes the centroid of a 2D segment set
+// takes an iterator range over K::Segment_2
+template < typename InputIterator, 
+           typename K >
+typename K::Point_2
+centroid(InputIterator begin, 
+         InputIterator end, 
+         const K& ,
+         const typename K::Segment_2*)
+{
+  typedef typename K::FT       FT;
+  typedef typename K::Vector_2 Vector;
+  typedef typename K::Point_2  Point;
+  typedef typename K::Segment_2 Segment;
+
+  CGAL_precondition(begin != end);
+
+  Vector v = NULL_VECTOR;
+  FT sum_lengths = 0;
+  for(InputIterator it = begin;
+      it != end;
+      it++)
+  {
+    const Segment& s = *it;
+    FT length = std::sqrt(std::abs(s.squared_length()));
+    //    Point c = K().construct_centroid_2_object()(s[0],s[1]);??
+    v = v + length * (((s[0] - ORIGIN) + (s[1] - ORIGIN))/2);
+    sum_lengths += length;
+  }
+  CGAL_assertion(sum_lengths != 0.0);
+  return ORIGIN + v / sum_lengths;
+} // end centroid of a 2D triangle set
+
 // computes the centroid of a 2D triangle set
 // takes an iterator range over K::Triangle_2
 template < typename InputIterator, 
@@ -122,7 +155,7 @@ centroid(InputIterator begin,
 } // end centroid of a 2D triangle set
 
 // computes the centroid of a 3D triangle set
-// takes an iterator range over K::Triangle_2
+// takes an iterator range over K::Triangle_3
 template < typename InputIterator, 
            typename K >
 typename K::Point_3

Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h

@@ -23,10 +23,17 @@
 #include <CGAL/Object.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen_2.h>
+#include <CGAL/eigen.h>
+#include <CGAL/Linear_algebraCd.h>
+//#include <CGAL/Kernel_d/Matrix__.h>
+#include <CGAL/linear_least_squares_fitting_triangles.h>
+#include <CGAL/linear_least_squares_fitting_segments.h>
 
 #include <iterator>
 #include <list>
 #include <string>
+#include <vector>
+#include <cmath>
 
 CGAL_BEGIN_NAMESPACE
 

Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments.h

@@ -0,0 +1,138 @@
+// Copyright (c) 2005  INRIA Sophia-Antipolis (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you may redistribute it under
+// the terms of the Q Public License version 1.0.
+// See the file LICENSE.QPL distributed with CGAL.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL: svn+ssh://gankit@scm.gforge.inria.fr/svn/cgal/trunk/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles.h $
+// $Id: linear_least_squares_fitting_2.h 37882 2007-04-03 15:15:30Z spion $
+//
+// Author(s) : Pierre Alliez and Sylvain Pion and Ankit Gupta
+
+#ifndef CGAL_LINEAR_LEAST_SQUARES_FITTING_SEGMENTS_H
+#define CGAL_LINEAR_LEAST_SQUARES_FITTING_SEGMENTS_H
+
+#include <CGAL/basic.h>
+#include <CGAL/Object.h>
+#include <CGAL/centroid.h>
+#include <CGAL/eigen_2.h>
+#include <CGAL/eigen.h>
+#include <CGAL/Linear_algebraCd.h>
+
+#include <iterator>
+#include <vector>
+#include <cmath>
+
+CGAL_BEGIN_NAMESPACE
+
+namespace CGALi {
+// Fits a line to a 2D segment set.
+// Returns a fitting quality (1 - lambda_min/lambda_max):
+//  1 is best  (zero variance orthogonally to the fitting line);
+//  0 is worst (isotropic case, returns a line with horizontal
+//              direction by default)
+
+template < typename InputIterator, typename K >
+typename K::FT
+linear_least_squares_fitting_2(InputIterator first,
+                               InputIterator beyond, 
+                               typename K::Line_2& line,   // best fit line
+                               typename K::Point_2& c,     // centroid
+                               const K&,                   // kernel
+                               const typename K::Segment_2*) // used for indirection
+{
+  // types
+  typedef typename K::FT       FT;
+  typedef typename K::Line_2   Line;
+  typedef typename K::Point_2  Point;
+  typedef typename K::Vector_2 Vector;
+  typedef typename K::Segment_2 Segment;
+  typedef typename CGAL::Linear_algebraCd<FT> LA;
+  typedef typename LA::Matrix Matrix;
+
+  // precondition: at least one element in the container.
+  CGAL_precondition(first != beyond);
+
+  // compute centroid
+  c = centroid(first,beyond,K());
+
+  // assemble covariance matrix as a semi-definite matrix. 
+  // Matrix numbering:
+  // 0
+  // 1 2
+  //Final combined covariance matrix for all triangles and their combined mass
+  FT mass=0.0,cov[3]={0.0,0.0,0.0};
+
+  // step 1: assemble the 2nd order moment about the origin.  
+  FT cov_temp[4] = {1.0,0.5,0.5,1.0};
+  Matrix covariance = (std::sqrt(2)/3.0) * init_Matrix<K>(2,cov_temp);
+  for(InputIterator it = first;
+      it != beyond;
+      it++)
+  {
+    // Now for each triangle, construct the 2nd order moment about the origin.
+    // step 2: assemble the transformation matrix.
+    const Segment& t = *it;
+    // defined for convenience.
+    FT delta[4] = {t[0].x(), t[1].x(), t[0].y(), t[1].y()};
+
+    Matrix transformation = init_Matrix<K>(2,delta);
+    FT length = std::sqrt(t.squared_length());
+    CGAL_assertion(length!=0);
+    // step 3: Find the 2nd order moment for the triangle wrt to the origin by an affine transformation.
+    
+    // step 3.1: Transform the standard 2nd order moment using the transformation matrix
+    transformation = length*transformation*covariance*LA::transpose(transformation);
+    
+    //step 3.2: Translate the 2nd order moment to (x0,y0):Not Required Here
+    
+    cov[0]+=transformation[0][0];
+    cov[1]+=transformation[0][1];
+    cov[2]+=transformation[1][1];
+
+    mass+=length;
+  }
+  //step 4: Translace the 2nd order miment calculated about the origin to the center of mass to get the covariance.
+  cov[0]+=mass*(-1.0*c.x()*c.x());
+  cov[1]+=mass*(-1.0*c.x()*c.y());
+  cov[2]+=mass*(-1.0*c.y()*c.y());
+  std::cout<<cov[0]<<" "<<cov[1]<<" "<<cov[2]<<std::endl;
+
+  // solve for eigenvalues and eigenvectors.
+  // eigen values are sorted in descending order, 
+  // eigen vectors are sorted in accordance.
+  std::pair<FT,FT> eigen_values;
+  std::pair<Vector,Vector> eigen_vectors;
+  //  CGALi::eigen_symmetric_2<K>(final_cov, eigen_vectors, eigen_values);
+  FT eigen_vectors1[4];
+  FT eigen_values1[2];
+  eigen_symmetric<FT>(cov,2, eigen_vectors1, eigen_values1);
+  eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
+  eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
+  // check unicity and build fitting line accordingly
+  if(eigen_values.first != eigen_values.second)
+  {
+    // regular case
+    line = Line(c, eigen_vectors.first);
+    return (FT)1.0 - eigen_values.second / eigen_values.first;
+  } 
+  else
+  {
+    // isotropic case (infinite number of directions)
+    // by default: assemble a line that goes through 
+    // the centroid and with a default horizontal vector.
+    line = Line(c, Vector(1.0, 0.0));
+    return (FT)0.0;
+  } 
+} // end linear_least_squares_fitting_2 for triangle set
+
+} // end namespace CGALi
+CGAL_END_NAMESPACE
+#endif

Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles.h

@@ -0,0 +1,154 @@
+// Copyright (c) 2005  INRIA Sophia-Antipolis (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you may redistribute it under
+// the terms of the Q Public License version 1.0.
+// See the file LICENSE.QPL distributed with CGAL.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL: svn+ssh://gankit@scm.gforge.inria.fr/svn/cgal/trunk/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles.h $
+// $Id: linear_least_squares_fitting_2.h 37882 2007-04-03 15:15:30Z spion $
+//
+// Author(s) : Pierre Alliez and Sylvain Pion and Ankit Gupta
+
+#ifndef CGAL_LINEAR_LEAST_SQUARES_FITTING_TRIANGLES_H
+#define CGAL_LINEAR_LEAST_SQUARES_FITTING_TRIANGLES_H
+
+#include <CGAL/basic.h>
+#include <CGAL/Object.h>
+#include <CGAL/centroid.h>
+#include <CGAL/eigen_2.h>
+#include <CGAL/eigen.h>
+#include <CGAL/Linear_algebraCd.h>
+
+#include <iterator>
+#include <vector>
+#include <cmath>
+
+CGAL_BEGIN_NAMESPACE
+
+namespace CGALi {
+template<typename K>
+typename CGAL::Linear_algebraCd<typename K::FT>::Matrix
+init_Matrix(int n, typename K::FT entries[]) {
+  CGAL_assertion(n>1);
+  typedef typename CGAL::Linear_algebraCd<typename K::FT>::Matrix Matrix;
+  Matrix ret(n);
+  for(int i=0;i<n;i++) {
+    for(int j=0;j<n;j++) {
+      ret[i][j]=entries[i*n+j];
+    }
+  }
+  return ret;
+}
+// Fits a line to a 2D triangle set.
+// Returns a fitting quality (1 - lambda_min/lambda_max):
+//  1 is best  (zero variance orthogonally to the fitting line);
+//  0 is worst (isotropic case, returns a line with horizontal
+//              direction by default)
+
+template < typename InputIterator, typename K >
+typename K::FT
+linear_least_squares_fitting_2(InputIterator first,
+                               InputIterator beyond, 
+                               typename K::Line_2& line,   // best fit line
+                               typename K::Point_2& c,     // centroid
+                               const K&,                   // kernel
+                               const typename K::Triangle_2*) // used for indirection
+{
+  // types
+  typedef typename K::FT       FT;
+  typedef typename K::Line_2   Line;
+  typedef typename K::Point_2  Point;
+  typedef typename K::Vector_2 Vector;
+  typedef typename K::Triangle_2 Triangle;
+  typedef typename CGAL::Linear_algebraCd<FT> LA;
+  typedef typename LA::Matrix Matrix;
+
+  // precondition: at least one element in the container.
+  CGAL_precondition(first != beyond);
+
+  // compute centroid
+  c = centroid(first,beyond,K());
+
+  // assemble covariance matrix as a semi-definite matrix. 
+  // Matrix numbering:
+  // 0
+  // 1 2
+  //Final combined covariance matrix for all triangles and their combined mass
+  FT mass=0.0,cov[3]={0.0,0.0,0.0};
+
+  // step 1: assemble the 2nd order moment about the origin.  
+  FT cov_temp[4] = {1/12.0,1/24.0,1/24.0,1/12.0};
+  Matrix covariance = init_Matrix<K>(2,cov_temp);
+
+  for(InputIterator it = first;
+      it != beyond;
+      it++)
+  {
+    // Now for each triangle, construct the 2nd order moment about the origin.
+    // step 2: assemble the transformation matrix.
+    const Triangle& t = *it;
+    // defined for convenience.
+    FT x0 = t[0].x(), y0 = t[0].y();
+    FT delta[4] = {t[1].x() - x0,t[2].x() - x0,t[1].y() - y0,t[2].y() - y0};
+
+    Matrix transformation = init_Matrix<K>(2,delta);
+    FT detA = fabs(LA::determinant(transformation));
+    CGAL_assertion(detA!=0);
+    // step 3: Find the 2nd order moment for the triangle wrt to the origin by an affine transformation.
+    
+    // step 3.1: Transform the standard 2nd order moment using the transformation matrix
+    transformation = detA*transformation*covariance*LA::transpose(transformation);
+    
+    //step 3.2: Translate the 2nd order moment to (x0,y0).
+    FT xav0 = (delta[0]+delta[1])/3.0, yav0 = (delta[2]+delta[3])/3.0;
+    
+    cov[0]+=transformation[0][0]+0.5*detA*(x0*xav0*2+x0*x0);
+    cov[1]+=transformation[0][1]+0.5*detA*(x0*yav0+xav0*y0+x0*y0);
+    cov[2]+=transformation[1][1]+0.5*detA*(y0*yav0*2+y0*y0);
+
+    mass+=0.5*detA;
+  }
+  
+  //step 4: Translace the 2nd order miment calculated about the origin to the center of mass to get the covariance.
+  cov[0]+=mass*(-1.0*c.x()*c.x());
+  cov[1]+=mass*(-1.0*c.x()*c.y());
+  cov[2]+=mass*(-1.0*c.y()*c.y());
+
+  // solve for eigenvalues and eigenvectors.
+  // eigen values are sorted in descending order, 
+  // eigen vectors are sorted in accordance.
+  std::pair<FT,FT> eigen_values;
+  std::pair<Vector,Vector> eigen_vectors;
+  //  CGALi::eigen_symmetric_2<K>(final_cov, eigen_vectors, eigen_values);
+  FT eigen_vectors1[4];
+  FT eigen_values1[2];
+  eigen_symmetric<FT>(cov,2, eigen_vectors1, eigen_values1);
+  eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
+  eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
+  // check unicity and build fitting line accordingly
+  if(eigen_values.first != eigen_values.second)
+  {
+    // regular case
+    line = Line(c, eigen_vectors.first);
+    return (FT)1.0 - eigen_values.second / eigen_values.first;
+  } 
+  else
+  {
+    // isotropic case (infinite number of directions)
+    // by default: assemble a line that goes through 
+    // the centroid and with a default horizontal vector.
+    line = Line(c, Vector(1.0, 0.0));
+    return (FT)0.0;
+  } 
+} // end linear_least_squares_fitting_2 for triangle set
+
+} // end namespace CGALi
+CGAL_END_NAMESPACE
+#endif