PCA: renamed example file for tetrahedra

started cleaning up the examples codes

.gitattributes

@@ -3036,7 +3036,7 @@ Principal_component_analysis/examples/Principal_component_analysis/linear_least_
 Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_segments_2.cpp -text
 Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_segments_3.cpp -text
 Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_spheres_3.cpp -text
-Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_tetrahedrons_3.cpp -text
+Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_tetrahedra_3.cpp -text
 Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_2.cpp -text
 Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_3.cpp -text
 Principal_component_analysis/include/CGAL/PCA_tags.h -text

Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_cuboids_3.cpp

@@ -14,21 +14,28 @@ typedef K::Iso_cuboid_3   Iso_cuboid_3;
 
 int main()
 {
-  std::list<Iso_cuboid_3> Iso_cuboids;
+  std::list<Iso_cuboid_3> cuboids;
-  Iso_cuboids.push_back(Iso_cuboid_3(Point_3(0.0,0.0,0.0),Point_3(1.0,1.0,1.0)));
+  cuboids.push_back(Iso_cuboid_3(Point_3(0.0,0.0,0.0),Point_3(1.0,1.0,1.0)));
-  Iso_cuboids.push_back(Iso_cuboid_3(Point_3(1.0,1.0,1.0),Point_3(6.0,6.0,6.0)));
+  cuboids.push_back(Iso_cuboid_3(Point_3(1.0,1.0,1.0),Point_3(6.0,6.0,6.0)));
 
   Line_3 line;
-  linear_least_squares_fitting_3(Iso_cuboids.begin(),Iso_cuboids.end(),line,CGAL::PCA_dimension_3_tag());
-
   Plane_3 plane;
-  linear_least_squares_fitting_3(Iso_cuboids.begin(),Iso_cuboids.end(),plane,CGAL::PCA_dimension_3_tag());
+
+	// fit volume
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),line,CGAL::PCA_dimension_3_tag());
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),plane,CGAL::PCA_dimension_3_tag());
   
+  // fit faces
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),line,CGAL::PCA_dimension_2_tag());
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),plane,CGAL::PCA_dimension_2_tag());
 
-  //Use only faces.
+	// fit edges
-  linear_least_squares_fitting_3(Iso_cuboids.begin(),Iso_cuboids.end(),line,CGAL::PCA_dimension_2_tag());
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),line,CGAL::PCA_dimension_1_tag());
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),plane,CGAL::PCA_dimension_1_tag());
 
-  linear_least_squares_fitting_3(Iso_cuboids.begin(),Iso_cuboids.end(),plane,CGAL::PCA_dimension_2_tag());
+	// fit vertices
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),line,CGAL::PCA_dimension_0_tag());
+  linear_least_squares_fitting_3(cuboids.begin(),cuboids.end(),plane,CGAL::PCA_dimension_0_tag());
 
   return 0;
 }

Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_tetrahedra_3.cpp

@@ -0,0 +1,36 @@
+// Example program for the linear_least_square_fitting function
+// on a set of tetrahedra in 3D
+
+#include <CGAL/Cartesian.h>
+#include <CGAL/linear_least_squares_fitting_3.h>
+#include <list>
+
+typedef double               FT;
+typedef CGAL::Cartesian<FT>  K;
+typedef K::Line_3            Line_3;
+typedef K::Plane_3           Plane_3;
+typedef K::Point_3           Point_3;
+typedef K::Tetrahedron_3     Tetrahedron_3;
+
+int main(void)
+{
+	Point a( 0.0,0.0,0.0);
+	Point b( 1.0,0.0,0.0);
+	Point c(-1.0,0.0,0.0);
+	Point d( 0.0,1.0,1.0);
+	Point e( 0.0,0.0,0.0);
+
+	std::list<Tetrahedron_3> tetrahedra;
+  tetrahedra.push_back(Tetrahedron_3(a,b,c,d));
+  tetrahedra.push_back(Tetrahedron_3(a,b,c,e));
+
+	// fit a line
+  Line_3 line;
+  linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),line,CGAL::PCA_dimension_3_tag());
+
+	// fit a plane
+  Plane_3 plane;
+  linear_least_squares_fitting_3(tetrahedra.begin(),tetrahedra.end(),plane,CGAL::PCA_dimension_3_tag());
+    
+  return 0;
+}

Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_tetrahedrons_3.cpp

@@ -1,28 +0,0 @@
-// Example program for the linear_least_square_fitting function on set of tetrahedrons in 3D
-
-#include <CGAL/Cartesian.h>
-#include <CGAL/linear_least_squares_fitting_3.h>
-
-#include <list>
-
-typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
-typedef K::Line_3            Line_3;
-typedef K::Plane_3           Plane_3;
-typedef K::Point_3           Point_3;
-typedef K::Tetrahedron_3          Tetrahedron_3;
-
-int main()
-{
-  std::list<Tetrahedron_3> tetrahedrons;
-  tetrahedrons.push_back(Tetrahedron_3(Point_3(0.0,0.0,0.0),Point_3(1.0,0.0,0.0),Point_3(0.0,1.0,0.0),Point_3(0.0,0.0,1.0)));
-  tetrahedrons.push_back(Tetrahedron_3(Point_3(0.0,0.0,0.0),Point_3(-1.0,0.0,0.0),Point_3(0.0,-1.0,0.0),Point_3(0.0,0.0,1.0)));
-
-  Line_3 line;
-  linear_least_squares_fitting_3(tetrahedrons.begin(),tetrahedrons.end(),line,CGAL::PCA_dimension_3_tag());
-
-  Plane_3 plane;
-  linear_least_squares_fitting_3(tetrahedrons.begin(),tetrahedrons.end(),plane,CGAL::PCA_dimension_3_tag());
-    
-  return 0;
-}

Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_3.cpp

@@ -10,9 +10,9 @@ typedef CGAL::Cartesian<FT>  K;
 typedef K::Line_3            Line_3;
 typedef K::Plane_3           Plane_3;
 typedef K::Point_3           Point_3;
-typedef K::Triangle_3          Triangle_3;
+typedef K::Triangle_3        Triangle_3;
 
-int main()
+int main(void)
 {
   std::list<Triangle_3> triangles;
   triangles.push_back(Triangle_3(Point_3(1.0,0.0,0.0),Point_3(0.0,1.0,0.0),Point_3(0.0,0.0,0.0)));

Principal_component_analysis/include/CGAL/PCA_tags.h

@@ -30,22 +30,10 @@ CGAL_BEGIN_NAMESPACE
 //::between these different types of the same geometry
 //::::::::::::::::::::::::::::::::::::::::::::::::::::::
 
-// Fully filled geometry object, such as disks in 2d and balls in 3d
-struct PCA_dimension_3_tag {};
-
-// Empty geometry objects, such as triangles in 2d and hollow cubes with just the planar facets in 3d
-struct PCA_dimension_2_tag {};
-
-// Only relevant for 3d objects, outlines of 3d geometry objects formed by just lines joing appropriate vetrices, such as outline of a cuboid.
-struct PCA_dimension_1_tag {};
-
-// For the vertices of objects.
 struct PCA_dimension_0_tag {};
-
+struct PCA_dimension_1_tag {};
-
+struct PCA_dimension_2_tag {};
-//::::::::::::::::::::::::::::::::::::::::::::::::::::::
+struct PCA_dimension_3_tag {};
-// Struct to denote dimension compile time decisions
-//::::::::::::::::::::::::::::::::::::::::::::::::::::::
 
 /*
 

Principal_component_analysis/include/CGAL/PCA_util.h

@@ -32,16 +32,16 @@ namespace CGALi {
 template <typename K>
 typename CGAL::Linear_algebraCd<typename K::FT>::Matrix
 init_matrix(const int n,
-						typename K::FT entries[])
+            typename K::FT entries[])
 {
   CGAL_assertion(n > 1); // dimension > 1
   typedef typename CGAL::Linear_algebraCd<typename K::FT>::Matrix Matrix;
 
-	Matrix m(n);
+  Matrix m(n);
-	int i,j;
+  int i,j;
   for(i = 0; i < n; i++) 
     for(j = 0; j < n; j++)
-			m[i][j] = entries[i*n+j];
+      m[i][j] = entries[i*n+j];
 
   return m;
 } // end initialization of matrix
@@ -56,7 +56,7 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& ,                    // kernel
                              const typename K::Point_3*,   // used for indirection
-			                       const CGAL::PCA_dimension_0_tag& tag)
+                             const CGAL::PCA_dimension_0_tag& tag)
 {
   typedef typename K::FT       FT;
   typedef typename K::Point_3  Point;
@@ -93,7 +93,7 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& k,                    // kernel
                              const typename K::Triangle_3*,// used for indirection
-			                       const CGAL::PCA_dimension_2_tag& tag)
+                             const CGAL::PCA_dimension_2_tag& tag)
 {
   typedef typename K::FT          FT;
   typedef typename K::Point_3     Point;
@@ -112,7 +112,7 @@ assemble_covariance_matrix_3(InputIterator first,
 
   // assemble 2nd order moment about the origin.  
   FT temp[9] = {1.0/12.0, 1.0/24.0, 1.0/24.0,
-		1.0/24.0, 1.0/12.0, 1.0/24.0,
+                1.0/24.0, 1.0/12.0, 1.0/24.0,
                 1.0/24.0, 1.0/24.0, 1.0/12.0};
   Matrix moment = init_matrix<K>(3,temp);
 
@@ -125,9 +125,8 @@ assemble_covariance_matrix_3(InputIterator first,
     const Triangle& t = *it;
 
     // defined for convenience.
-    // FT example = CGAL::to_double(t[0].x());
     FT delta[9] = {t[0].x(), t[1].x(), t[2].x(), 
-		   t[0].y(), t[1].y(), t[2].y(),
+                   t[0].y(), t[1].y(), t[2].y(),
                    t[0].z(), t[1].z(), t[2].z()};
     Matrix transformation = init_matrix<K>(3,delta);
     FT area = std::sqrt(t.squared_area());
@@ -170,7 +169,7 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& ,                    // kernel
                              const typename K::Iso_cuboid_3*,// used for indirection
-			     const CGAL::PCA_dimension_3_tag& tag)
+                             const CGAL::PCA_dimension_3_tag& tag)
 {
   typedef typename K::FT          FT;
   typedef typename K::Point_3     Point;
@@ -189,7 +188,7 @@ assemble_covariance_matrix_3(InputIterator first,
 
   // assemble 2nd order moment about the origin.  
   FT temp[9] = {1.0/3.0, 1.0/4.0, 1.0/4.0,
-		1.0/4.0, 1.0/3.0, 1.0/4.0,
+                1.0/4.0, 1.0/3.0, 1.0/4.0,
                 1.0/4.0, 1.0/4.0, 1.0/3.0};
   Matrix moment = init_matrix<K>(3,temp);
 
@@ -207,7 +206,7 @@ assemble_covariance_matrix_3(InputIterator first,
     FT y0 = t[0].y();
     FT z0 = t[0].z();
     FT delta[9] = {t[1].x()-x0, t[3].x()-x0, t[5].x()-x0, 
-		   t[1].y()-y0, t[3].y()-y0, t[5].y()-y0,
+                   t[1].y()-y0, t[3].y()-y0, t[5].y()-y0,
                    t[1].z()-z0, t[3].z()-z0, t[5].z()-z0};
     Matrix transformation = init_matrix<K>(3,delta);
     FT volume = t.volume();
@@ -255,12 +254,12 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& ,                    // kernel
                              const typename K::Iso_cuboid_3*,// used for indirection
-			                       const CGAL::PCA_dimension_2_tag& tag)
+                             const CGAL::PCA_dimension_2_tag& tag)
 {
-  typedef typename K::FT          FT;
+  typedef typename K::FT FT;
-  typedef typename K::Point_3     Point;
+  typedef typename K::Point_3 Point;
-  typedef typename K::Vector_3    Vector;
+  typedef typename K::Vector_3 Vector;
-  typedef typename K::Iso_cuboid_3    Iso_cuboid;
+  typedef typename K::Iso_cuboid_3 Iso_cuboid;
   typedef typename CGAL::Linear_algebraCd<FT> LA;
   typedef typename LA::Matrix Matrix;
 
@@ -274,7 +273,7 @@ assemble_covariance_matrix_3(InputIterator first,
 
   // assemble 2nd order moment about the origin.  
   FT temp[9] = {7.0/3.0, 1.5, 1.5,
-		1.5, 7.0/3.0, 1.5,
+                1.5, 7.0/3.0, 1.5,
                 1.5, 1.5, 7.0/3.0};
   Matrix moment = init_matrix<K>(3,temp);
 
@@ -292,18 +291,18 @@ assemble_covariance_matrix_3(InputIterator first,
     FT y0 = t[0].y();
     FT z0 = t[0].z();
     FT delta[9] = {t[1].x()-x0, t[3].x()-x0, t[5].x()-x0, 
-		   t[1].y()-y0, t[3].y()-y0, t[5].y()-y0,
+                   t[1].y()-y0, t[3].y()-y0, t[5].y()-y0,
                    t[1].z()-z0, t[3].z()-z0, t[5].z()-z0};
     Matrix transformation = init_matrix<K>(3,delta);
     FT area = pow(delta[0]*delta[0] + delta[3]*delta[3] +
-			            delta[6]*delta[6],1/3.0)*pow(delta[1]*delta[1] +
+                  delta[6]*delta[6],1/3.0)*pow(delta[1]*delta[1] +
-									delta[4]*delta[4] + delta[7]*delta[7],1/3.0)*2 +
+                  delta[4]*delta[4] + delta[7]*delta[7],1/3.0)*2 +
-									pow(delta[0]*delta[0] + delta[3]*delta[3] +
+                  pow(delta[0]*delta[0] + delta[3]*delta[3] +
-									delta[6]*delta[6],1/3.0)*pow(delta[2]*delta[2] +
+                  delta[6]*delta[6],1/3.0)*pow(delta[2]*delta[2] +
-									delta[5]*delta[5] + delta[8]*delta[8],1/3.0)*2 +
+                  delta[5]*delta[5] + delta[8]*delta[8],1/3.0)*2 +
-									pow(delta[1]*delta[1] + delta[4]*delta[4] +
+                  pow(delta[1]*delta[1] + delta[4]*delta[4] +
-									delta[7]*delta[7],1/3.0)*pow(delta[2]*delta[2] +
+                  delta[7]*delta[7],1/3.0)*pow(delta[2]*delta[2] +
-									delta[5]*delta[5] + delta[8]*delta[8],1/3.0)*2;
+                  delta[5]*delta[5] + delta[8]*delta[8],1/3.0)*2;
     CGAL_assertion(area != 0.0);
 
     // Find the 2nd order moment for the cuboid wrt to the origin by an affine transformation.
@@ -348,7 +347,7 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& ,                    // kernel
                              const typename K::Sphere_3*,// used for indirection
-			     const CGAL::PCA_dimension_3_tag& tag)
+                             const CGAL::PCA_dimension_3_tag& tag)
 {
   typedef typename K::FT          FT;
   typedef typename K::Point_3     Point;
@@ -366,9 +365,9 @@ assemble_covariance_matrix_3(InputIterator first,
   FT mass = 0.0;
 
   // assemble 2nd order moment about the origin.  
-  FT temp[9] = {4.0/15.0, 0.0,     0.0,
+  FT temp[9] = {4.0/15.0, 0.0,      0.0,
-		0.0,     4.0/15.0, 0.0,
+                0.0,      4.0/15.0, 0.0,
-                0.0,     0.0,     4.0/15.0};
+                0.0,      0.0,      4.0/15.0};
   Matrix moment = init_matrix<K>(3,temp);
 
   for(InputIterator it = first;
@@ -380,10 +379,9 @@ assemble_covariance_matrix_3(InputIterator first,
     const Sphere& t = *it;
 
     // defined for convenience.
-    // FT example = CGAL::to_double(t[0].x());
     FT radius = std::sqrt(t.squared_radius());
     FT delta[9] = {radius, 0.0, 0.0, 
-		   0.0, radius, 0.0,
+                   0.0, radius, 0.0,
                    0.0, 0.0, radius};
     Matrix transformation = init_matrix<K>(3,delta);
     FT volume = 4/3.0 * radius*t.squared_radius();
@@ -430,7 +428,7 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& ,                    // kernel
                              const typename K::Sphere_3*,// used for indirection
-			     const CGAL::PCA_dimension_2_tag& tag)
+                             const CGAL::PCA_dimension_2_tag& tag)
 {
   typedef typename K::FT          FT;
   typedef typename K::Point_3     Point;
@@ -449,7 +447,7 @@ assemble_covariance_matrix_3(InputIterator first,
 
   // assemble 2nd order moment about the origin.  
   FT temp[9] = {4.0/3.0, 0.0,     0.0,
-		0.0,     4.0/3.0, 0.0,
+                0.0,     4.0/3.0, 0.0,
                 0.0,     0.0,     4.0/3.0};
   Matrix moment = init_matrix<K>(3,temp);
 
@@ -464,9 +462,9 @@ assemble_covariance_matrix_3(InputIterator first,
     // defined for convenience.
     // FT example = CGAL::to_double(t[0].x());
     FT radius = std::sqrt(t.squared_radius());
-    FT delta[9] = {radius, 0.0, 0.0, 
+    FT delta[9] = {radius, 0.0,    0.0, 
-		   0.0, radius, 0.0,
+                   0.0,    radius, 0.0,
-                   0.0, 0.0, radius};
+                   0.0,    0.0,    radius};
     Matrix transformation = init_matrix<K>(3,delta);
     FT area = 4 * t.squared_radius();
     CGAL_assertion(area != 0.0);
@@ -513,7 +511,7 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& ,                    // kernel
                              const typename K::Tetrahedron_3*,// used for indirection
-			     const CGAL::PCA_dimension_3_tag& tag)
+                             const CGAL::PCA_dimension_3_tag& tag)
 {
   typedef typename K::FT          FT;
   typedef typename K::Point_3     Point;
@@ -532,8 +530,8 @@ assemble_covariance_matrix_3(InputIterator first,
 
   // assemble 2nd order moment about the origin.  
   FT temp[9] = {1.0/60.0,  1.0/120.0, 1.0/120.0,
-		1.0/120.0, 1.0/60.0,  1.0/120.0,
+                1.0/120.0, 1.0/60.0,  1.0/120.0,
-		1.0/120.0, 1.0/120.0, 1.0/60.0};
+                1.0/120.0, 1.0/120.0, 1.0/60.0};
   Matrix moment = init_matrix<K>(3,temp);
 
   for(InputIterator it = first;
@@ -545,13 +543,12 @@ assemble_covariance_matrix_3(InputIterator first,
     const Tetrahedron& t = *it;
 
     // defined for convenience.
-    // FT example = CGAL::to_double(t[0].x());
     FT x0 = t[0].x();
     FT y0 = t[0].y();
     FT z0 = t[0].z();
 
     FT delta[9] = {t[1].x()-x0, t[2].x()-x0, t[3].x()-x0, 
-		   t[1].y()-y0, t[2].y()-y0, t[3].y()-y0,
+                   t[1].y()-y0, t[2].y()-y0, t[3].y()-y0,
                    t[1].z()-z0, t[2].z()-z0, t[3].z()-z0};
     Matrix transformation = init_matrix<K>(3,delta);
     FT volume = t.volume();
@@ -599,7 +596,7 @@ assemble_covariance_matrix_3(InputIterator first,
                              const typename K::Point_3& c, // centroid
                              const K& ,                    // kernel
                              const typename K::Segment_3*,// used for indirection
-			     const CGAL::PCA_dimension_1_tag& tag)
+                             const CGAL::PCA_dimension_1_tag& tag)
 {
   typedef typename K::FT          FT;
   typedef typename K::Point_3     Point;
@@ -618,7 +615,7 @@ assemble_covariance_matrix_3(InputIterator first,
 
   // assemble 2nd order moment about the origin.  
   FT temp[9] = {1.0, 0.5, 0.0,
-		0.5, 1.0, 0.0,
+                0.5, 1.0, 0.0,
                 0.0, 0.0, 0.0};
   Matrix moment = 1.0/3.0 * init_matrix<K>(3,temp);
 
@@ -633,7 +630,7 @@ assemble_covariance_matrix_3(InputIterator first,
     // defined for convenience.
     // FT example = CGAL::to_double(t[0].x());
     FT delta[9] = {t[0].x(), t[1].x(), 0.0, 
-		   t[0].y(), t[1].y(), 0.0,
+       t[0].y(), t[1].y(), 0.0,
                    t[0].z(), t[1].z(), 1.0};
     Matrix transformation = init_matrix<K>(3,delta);
     FT length = std::sqrt(t.squared_length());
@@ -719,7 +716,7 @@ typename K::FT
 fitting_line_3(const typename K::FT covariance[6], // covariance matrix
                const typename K::Point_3& c,       // centroid
                typename K::Line_3& line,           // best fit line
-               const K&  )                         // kernel
+               const K&)                           // kernel
 {
   typedef typename K::FT       FT;
   typedef typename K::Point_3  Point;

Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h

@@ -23,12 +23,14 @@
 #include <CGAL/Object.h>
 #include <CGAL/Algebraic_structure_traits.h>
 #include <CGAL/IO/io.h>
+
 #include <CGAL/linear_least_squares_fitting_points_3.h>
-#include <CGAL/linear_least_squares_fitting_segments_3.h>
-#include <CGAL/linear_least_squares_fitting_triangles_3.h>
 #include <CGAL/linear_least_squares_fitting_spheres_3.h>
 #include <CGAL/linear_least_squares_fitting_cuboids_3.h>
+#include <CGAL/linear_least_squares_fitting_segments_3.h>
+#include <CGAL/linear_least_squares_fitting_triangles_3.h>
 #include <CGAL/linear_least_squares_fitting_tetrahedra_3.h>
+
 #include <CGAL/PCA_tags.h>
 
 #include <iterator>
@@ -46,9 +48,9 @@ inline
 typename Kernel::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
-                               typename Object& object, // plane or line (result)
+                               typename Object& object, // plane or line
-                               typename Kernel::Point_3& centroid,
+                               typename Kernel::Point_3& centroid, 
-                               const Tag& tag,
+                               const Tag& tag, // dimension tag, ranges from 0 to 3
 			                         const Kernel& kernel)
 {
   typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
@@ -56,7 +58,6 @@ linear_least_squares_fitting_3(InputIterator first,
                                                centroid, (Value_type*) NULL, kernel, tag);
 }
 
-
 // deduces kernel from value type of input iterator
 template < typename InputIterator, 
            typename Object,
@@ -66,16 +67,16 @@ inline
 typename Kernel_traits<Object>::Kernel::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
-                               Object& object,
+                               Object& object,  // plane or line
                                Point& centroid,
-			                         const Tag& tag)
+			                         const Tag& tag) // dimension tag, ranges from 0 to 3
 {
   typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
   typedef typename Kernel_traits<Value_type>::Kernel Kernel;
   return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag,Kernel());
 }
 
-// does not writes centroid and deduces kernel
+// deduces kernel and does not write centroid
 template < typename InputIterator, 
            typename Object,
            typename Tag>
@@ -83,108 +84,15 @@ inline
 typename Kernel_traits<Object>::Kernel::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
-                               Object& object,
+                               Object& object, // plane or line
-			                         const Tag& tag)
+			                         const Tag& tag) // dimension tag, ranges from 0 to 3
 {
   typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
   typedef typename Kernel_traits<Value_type>::Kernel Kernel;
-  typename Kernel::Point_3 centroid; // unused by caller
+  typename Kernel::Point_3 centroid; // not used by caller
   return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag);
 }
 
-// does not return the centroid, deduces kernel, and default tag
-// simplest (default) call of the function
-/*
-template < typename InputIterator, 
-           typename Object>
-inline
-typename Kernel_traits<Object>::Kernel::FT
-linear_least_squares_fitting_3(InputIterator first,
-                               InputIterator beyond, 
-                               Object& object)
-{
-  typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
-  typedef typename Kernel_traits<Value_type>::Kernel Kernel;
-  typename Kernel::Point_3 centroid; // unused by caller
-  return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,(Value_type *)NULL,K());
-}*/
-
-/*
-template < typename InputIterator, 
-           typename Object, typename tag >
-inline
-typename Kernel_traits<Object>::Kernel::FT
-linear_least_squares_fitting_3(InputIterator first,
-                               InputIterator beyond, 
-                               Object& object,
-			                         const tag& t)
-{
-  typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
-  //   BOOST_STATIC_ASSERT((boost::is_same<typename CGAL::Algebraic_structure_traits<Value_type>::Algebraic_category,CGAL::Field_with_sqrt_tag>::value));
-  typedef typename Kernel_traits<Value_type>::Kernel K;
-  return CGAL::linear_least_squares_fitting_3(first,beyond,object,K(), t);
-}
-
-template < typename InputIterator, 
-           typename Object, 
-           typename tag = typename PCA_default_dimension< typename std::iterator_traits<InputIterator>::value_type >::Tag>
-inline
-typename Kernel_traits<Object>::Kernel::FT
-linear_least_squares_fitting_3(InputIterator first,
-                               InputIterator beyond, 
-                               Object& object,
-			                         const tag& t = tag())
-{
-  typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
-  typedef typename Kernel_traits<Value_type>::Kernel K;
-  return CGAL::linear_least_squares_fitting_3(first,beyond,object,K(), t);
-}
-
-  //   BOOST_STATIC_ASSERT((boost::is_same<typename CGAL::Algebraic_structure_traits<Value_type>::Algebraic_category,CGAL::Field_with_sqrt_tag>::value));
-
-	// default tag (dimension of fitted objects, ie 1 for segments, 2 for triangles, 3 for tets, etc.)
-template < typename InputIterator, 
-           typename Object,
-           typename Kernel >
-inline
-typename Kernel::FT
-linear_least_squares_fitting_3(InputIterator first,
-                               InputIterator beyond, 
-                               typename Object& object, // plane or line
-                               typename Kernel::Point_3& centroid,
-			                         const Kernel& kernel)
-{
-  typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
-  return CGALi::linear_least_squares_fitting_3(first, beyond, object,
-                                               centroid, (Value_type*) NULL, kernel);
-}
-
-
-
-// omits centroid
-template < typename InputIterator, 
-           typename Object,
-           typename Kernel,
-           typename Tag >
-inline
-typename Kernel::FT
-linear_least_squares_fitting_3(InputIterator first,
-                               InputIterator beyond, 
-                               Object& object,
-			                         const Kernel& kernel,
-                               const Tag& tag)
-{
-  typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
-  typename Kernel::Point_3 centroid; // unused by caller
-  return CGALi::linear_least_squares_fitting_3(first, beyond, object,
-                                               centroid, (Value_type*) NULL, kernel, tag);
-}
-
-
-	
-	*/
-
-
 CGAL_END_NAMESPACE
 
 #endif // CGAL_LINEAR_LEAST_SQUARES_FITTING_3_H

Principal_component_analysis/test/Principal_component_analysis/linear_least_squares_fitting_spheres_3.cpp

@@ -6,22 +6,31 @@
 #include <list>
 
 typedef double               FT;
-typedef CGAL::Cartesian<FT>  K;
+typedef CGAL::Cartesian<FT>  Kernel;
-typedef K::Line_3            Line_3;
+typedef Kernel::Line_3       Line_3;
-typedef K::Plane_3           Plane_3;
+typedef Kernel::Plane_3      Plane_3;
-typedef K::Point_3           Point_3;
+typedef Kernel::Point_3      Point_3;
-typedef K::Sphere_3          Sphere_3;
+typedef Kernel::Sphere_3     Sphere_3;
 
-int main()
+int main(void)
 {
-  std::list<Sphere_3> spheres;
+	// centers
-  spheres.push_back(Sphere_3(Point_3(0.0,0.0,0.0),9));
+	Point c1(0.0,0.0,0.0);
-  spheres.push_back(Sphere_3(Point_3(0.0,10.0,0.0),25));
+	Point c2(1.0,1.0,1.0);
 
+	// radii
+	FT sqr1 = 0.1;
+	FT sqr2 = 0.5;
+
+	// add two spheres
+  std::list<Sphere_3> spheres;
+  spheres.push_back(Sphere_3(c1,sqr1));
+  spheres.push_back(Sphere_3(c2,sqr2));
+
+  Kernel k;
+  Point_3 c;
   Line_3 line;
   Plane_3 plane;
-  K k;
-  Point_3 c;
 
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,CGAL::PCA_dimension_3_tag());
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,CGAL::PCA_dimension_2_tag());