mirror of https://github.com/CGAL/cgal
Why i did this silly change
This commit is contained in:
Ankit Gupta
parent
645aac9c61
commit
92ad068512
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@ -1877,6 +1877,8 @@ Principal_component_analysis/demo/Principal_component_analysis/windows/3d/res/id
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Principal_component_analysis/doc_tex/Principal_component_analysis/fit.eps -text svneol=unset#application/postscript
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Principal_component_analysis/doc_tex/Principal_component_analysis/fit.png -text svneol=unset#image/png
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Principal_component_analysis/doc_tex/Principal_component_analysis/teaserLeastSquaresFitting.png -text
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Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments.h -text
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Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles.h -text
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QP_solver/doc_tex/QP_solver/PkgDescription.tex -text
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QP_solver/doc_tex/QP_solver/closest_point.eps -text svneol=unset#application/postscript
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QP_solver/doc_tex/QP_solver/closest_point.fig -text svneol=unset#application/octet-stream
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@ -88,6 +88,39 @@ centroid(InputIterator begin,
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return ORIGIN + v / (FT)nb_pts;
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}// end centroid of a 3D point set
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// computes the centroid of a 2D segment set
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// takes an iterator range over K::Segment_2
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template < typename InputIterator,
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typename K >
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typename K::Point_2
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centroid(InputIterator begin,
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InputIterator end,
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const K& ,
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const typename K::Segment_2*)
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{
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typedef typename K::FT FT;
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typedef typename K::Vector_2 Vector;
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typedef typename K::Point_2 Point;
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typedef typename K::Segment_2 Segment;
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CGAL_precondition(begin != end);
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Vector v = NULL_VECTOR;
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FT sum_lengths = 0;
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for(InputIterator it = begin;
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it != end;
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it++)
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{
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const Segment& s = *it;
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FT length = std::sqrt(std::abs(s.squared_length()));
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// Point c = K().construct_centroid_2_object()(s[0],s[1]);??
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v = v + length * (((s[0] - ORIGIN) + (s[1] - ORIGIN))/2);
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sum_lengths += length;
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}
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CGAL_assertion(sum_lengths != 0.0);
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return ORIGIN + v / sum_lengths;
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} // end centroid of a 2D triangle set
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// computes the centroid of a 2D triangle set
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// takes an iterator range over K::Triangle_2
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template < typename InputIterator,
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@ -122,7 +155,7 @@ centroid(InputIterator begin,
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} // end centroid of a 2D triangle set
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// computes the centroid of a 3D triangle set
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// takes an iterator range over K::Triangle_2
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// takes an iterator range over K::Triangle_3
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template < typename InputIterator,
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typename K >
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typename K::Point_3
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@ -23,10 +23,17 @@
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#include <CGAL/Object.h>
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#include <CGAL/centroid.h>
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#include <CGAL/eigen_2.h>
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#include <CGAL/eigen.h>
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#include <CGAL/Linear_algebraCd.h>
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//#include <CGAL/Kernel_d/Matrix__.h>
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#include <CGAL/linear_least_squares_fitting_triangles.h>
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#include <CGAL/linear_least_squares_fitting_segments.h>
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#include <iterator>
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#include <list>
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#include <string>
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#include <vector>
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#include <cmath>
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CGAL_BEGIN_NAMESPACE
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@ -0,0 +1,138 @@
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// Copyright (c) 2005 INRIA Sophia-Antipolis (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you may redistribute it under
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// the terms of the Q Public License version 1.0.
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// See the file LICENSE.QPL distributed with CGAL.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL: svn+ssh://gankit@scm.gforge.inria.fr/svn/cgal/trunk/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles.h $
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// $Id: linear_least_squares_fitting_2.h 37882 2007-04-03 15:15:30Z spion $
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//
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// Author(s) : Pierre Alliez and Sylvain Pion and Ankit Gupta
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#ifndef CGAL_LINEAR_LEAST_SQUARES_FITTING_SEGMENTS_H
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#define CGAL_LINEAR_LEAST_SQUARES_FITTING_SEGMENTS_H
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#include <CGAL/basic.h>
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#include <CGAL/Object.h>
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#include <CGAL/centroid.h>
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#include <CGAL/eigen_2.h>
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#include <CGAL/eigen.h>
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#include <CGAL/Linear_algebraCd.h>
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#include <iterator>
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#include <vector>
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#include <cmath>
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CGAL_BEGIN_NAMESPACE
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namespace CGALi {
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// Fits a line to a 2D segment set.
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// Returns a fitting quality (1 - lambda_min/lambda_max):
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// 1 is best (zero variance orthogonally to the fitting line);
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// 0 is worst (isotropic case, returns a line with horizontal
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// direction by default)
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template < typename InputIterator, typename K >
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typename K::FT
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linear_least_squares_fitting_2(InputIterator first,
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InputIterator beyond,
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typename K::Line_2& line, // best fit line
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typename K::Point_2& c, // centroid
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const K&, // kernel
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const typename K::Segment_2*) // used for indirection
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{
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// types
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typedef typename K::FT FT;
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typedef typename K::Line_2 Line;
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typedef typename K::Point_2 Point;
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typedef typename K::Vector_2 Vector;
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typedef typename K::Segment_2 Segment;
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typedef typename CGAL::Linear_algebraCd<FT> LA;
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typedef typename LA::Matrix Matrix;
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// precondition: at least one element in the container.
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CGAL_precondition(first != beyond);
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// compute centroid
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c = centroid(first,beyond,K());
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// assemble covariance matrix as a semi-definite matrix.
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// Matrix numbering:
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// 0
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// 1 2
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//Final combined covariance matrix for all triangles and their combined mass
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FT mass=0.0,cov[3]={0.0,0.0,0.0};
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// step 1: assemble the 2nd order moment about the origin.
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FT cov_temp[4] = {1.0,0.5,0.5,1.0};
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Matrix covariance = (std::sqrt(2)/3.0) * init_Matrix<K>(2,cov_temp);
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for(InputIterator it = first;
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it != beyond;
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it++)
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{
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// Now for each triangle, construct the 2nd order moment about the origin.
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// step 2: assemble the transformation matrix.
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const Segment& t = *it;
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// defined for convenience.
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FT delta[4] = {t[0].x(), t[1].x(), t[0].y(), t[1].y()};
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Matrix transformation = init_Matrix<K>(2,delta);
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FT length = std::sqrt(t.squared_length());
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CGAL_assertion(length!=0);
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// step 3: Find the 2nd order moment for the triangle wrt to the origin by an affine transformation.
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// step 3.1: Transform the standard 2nd order moment using the transformation matrix
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transformation = length*transformation*covariance*LA::transpose(transformation);
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//step 3.2: Translate the 2nd order moment to (x0,y0):Not Required Here
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cov[0]+=transformation[0][0];
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cov[1]+=transformation[0][1];
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cov[2]+=transformation[1][1];
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mass+=length;
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}
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//step 4: Translace the 2nd order miment calculated about the origin to the center of mass to get the covariance.
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cov[0]+=mass*(-1.0*c.x()*c.x());
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cov[1]+=mass*(-1.0*c.x()*c.y());
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cov[2]+=mass*(-1.0*c.y()*c.y());
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std::cout<<cov[0]<<" "<<cov[1]<<" "<<cov[2]<<std::endl;
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// solve for eigenvalues and eigenvectors.
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// eigen values are sorted in descending order,
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// eigen vectors are sorted in accordance.
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std::pair<FT,FT> eigen_values;
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std::pair<Vector,Vector> eigen_vectors;
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// CGALi::eigen_symmetric_2<K>(final_cov, eigen_vectors, eigen_values);
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FT eigen_vectors1[4];
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FT eigen_values1[2];
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eigen_symmetric<FT>(cov,2, eigen_vectors1, eigen_values1);
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eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
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eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
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// check unicity and build fitting line accordingly
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if(eigen_values.first != eigen_values.second)
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{
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// regular case
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line = Line(c, eigen_vectors.first);
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return (FT)1.0 - eigen_values.second / eigen_values.first;
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}
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else
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{
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// isotropic case (infinite number of directions)
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// by default: assemble a line that goes through
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// the centroid and with a default horizontal vector.
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line = Line(c, Vector(1.0, 0.0));
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return (FT)0.0;
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}
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} // end linear_least_squares_fitting_2 for triangle set
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} // end namespace CGALi
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CGAL_END_NAMESPACE
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#endif
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@ -0,0 +1,154 @@
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// Copyright (c) 2005 INRIA Sophia-Antipolis (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you may redistribute it under
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// the terms of the Q Public License version 1.0.
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// See the file LICENSE.QPL distributed with CGAL.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL: svn+ssh://gankit@scm.gforge.inria.fr/svn/cgal/trunk/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles.h $
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// $Id: linear_least_squares_fitting_2.h 37882 2007-04-03 15:15:30Z spion $
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//
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// Author(s) : Pierre Alliez and Sylvain Pion and Ankit Gupta
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#ifndef CGAL_LINEAR_LEAST_SQUARES_FITTING_TRIANGLES_H
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#define CGAL_LINEAR_LEAST_SQUARES_FITTING_TRIANGLES_H
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#include <CGAL/basic.h>
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#include <CGAL/Object.h>
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#include <CGAL/centroid.h>
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#include <CGAL/eigen_2.h>
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#include <CGAL/eigen.h>
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#include <CGAL/Linear_algebraCd.h>
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#include <iterator>
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#include <vector>
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#include <cmath>
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CGAL_BEGIN_NAMESPACE
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namespace CGALi {
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template<typename K>
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typename CGAL::Linear_algebraCd<typename K::FT>::Matrix
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init_Matrix(int n, typename K::FT entries[]) {
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CGAL_assertion(n>1);
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typedef typename CGAL::Linear_algebraCd<typename K::FT>::Matrix Matrix;
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Matrix ret(n);
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for(int i=0;i<n;i++) {
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for(int j=0;j<n;j++) {
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ret[i][j]=entries[i*n+j];
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}
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}
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return ret;
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}
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// Fits a line to a 2D triangle set.
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// Returns a fitting quality (1 - lambda_min/lambda_max):
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// 1 is best (zero variance orthogonally to the fitting line);
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// 0 is worst (isotropic case, returns a line with horizontal
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// direction by default)
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template < typename InputIterator, typename K >
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typename K::FT
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linear_least_squares_fitting_2(InputIterator first,
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InputIterator beyond,
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typename K::Line_2& line, // best fit line
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typename K::Point_2& c, // centroid
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const K&, // kernel
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const typename K::Triangle_2*) // used for indirection
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{
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// types
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typedef typename K::FT FT;
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typedef typename K::Line_2 Line;
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typedef typename K::Point_2 Point;
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typedef typename K::Vector_2 Vector;
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typedef typename K::Triangle_2 Triangle;
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typedef typename CGAL::Linear_algebraCd<FT> LA;
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typedef typename LA::Matrix Matrix;
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// precondition: at least one element in the container.
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CGAL_precondition(first != beyond);
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// compute centroid
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c = centroid(first,beyond,K());
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// assemble covariance matrix as a semi-definite matrix.
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// Matrix numbering:
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// 0
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// 1 2
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//Final combined covariance matrix for all triangles and their combined mass
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FT mass=0.0,cov[3]={0.0,0.0,0.0};
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// step 1: assemble the 2nd order moment about the origin.
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FT cov_temp[4] = {1/12.0,1/24.0,1/24.0,1/12.0};
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Matrix covariance = init_Matrix<K>(2,cov_temp);
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for(InputIterator it = first;
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it != beyond;
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it++)
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{
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// Now for each triangle, construct the 2nd order moment about the origin.
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// step 2: assemble the transformation matrix.
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const Triangle& t = *it;
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// defined for convenience.
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FT x0 = t[0].x(), y0 = t[0].y();
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FT delta[4] = {t[1].x() - x0,t[2].x() - x0,t[1].y() - y0,t[2].y() - y0};
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Matrix transformation = init_Matrix<K>(2,delta);
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FT detA = fabs(LA::determinant(transformation));
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CGAL_assertion(detA!=0);
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// step 3: Find the 2nd order moment for the triangle wrt to the origin by an affine transformation.
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// step 3.1: Transform the standard 2nd order moment using the transformation matrix
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transformation = detA*transformation*covariance*LA::transpose(transformation);
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//step 3.2: Translate the 2nd order moment to (x0,y0).
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FT xav0 = (delta[0]+delta[1])/3.0, yav0 = (delta[2]+delta[3])/3.0;
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cov[0]+=transformation[0][0]+0.5*detA*(x0*xav0*2+x0*x0);
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cov[1]+=transformation[0][1]+0.5*detA*(x0*yav0+xav0*y0+x0*y0);
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cov[2]+=transformation[1][1]+0.5*detA*(y0*yav0*2+y0*y0);
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mass+=0.5*detA;
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}
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//step 4: Translace the 2nd order miment calculated about the origin to the center of mass to get the covariance.
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cov[0]+=mass*(-1.0*c.x()*c.x());
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cov[1]+=mass*(-1.0*c.x()*c.y());
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cov[2]+=mass*(-1.0*c.y()*c.y());
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// solve for eigenvalues and eigenvectors.
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// eigen values are sorted in descending order,
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// eigen vectors are sorted in accordance.
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std::pair<FT,FT> eigen_values;
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std::pair<Vector,Vector> eigen_vectors;
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// CGALi::eigen_symmetric_2<K>(final_cov, eigen_vectors, eigen_values);
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FT eigen_vectors1[4];
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FT eigen_values1[2];
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eigen_symmetric<FT>(cov,2, eigen_vectors1, eigen_values1);
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eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
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eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
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// check unicity and build fitting line accordingly
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if(eigen_values.first != eigen_values.second)
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{
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// regular case
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line = Line(c, eigen_vectors.first);
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return (FT)1.0 - eigen_values.second / eigen_values.first;
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}
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else
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{
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// isotropic case (infinite number of directions)
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// by default: assemble a line that goes through
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// the centroid and with a default horizontal vector.
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line = Line(c, Vector(1.0, 0.0));
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return (FT)0.0;
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}
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} // end linear_least_squares_fitting_2 for triangle set
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} // end namespace CGALi
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CGAL_END_NAMESPACE
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#endif
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