diff --git a/Principal_component_analysis/include/CGAL/PCA_tags.h b/Principal_component_analysis/include/CGAL/PCA_tags.h
index d7ac35e7791..ecf3ed1c50c 100644
--- a/Principal_component_analysis/include/CGAL/PCA_tags.h
+++ b/Principal_component_analysis/include/CGAL/PCA_tags.h
@@ -42,6 +42,30 @@ struct PCA_dimension_1_tag {};
 // For the vertices of objects.
 struct PCA_dimension_0_tag {};
 
+//::::::::::::::::::::::::::::::::::::::::::::::::::::::
+// Struct to denote dimension compile time decisions
+//::::::::::::::::::::::::::::::::::::::::::::::::::::::
+
+template <class Value_type /* type of fitted objects */,
+          class K>
+struct PCA_default_dimension{};
+
+template < typename K >
+struct PCA_default_dimension<typename K::Point_3> {
+  typedef CGAL::PCA_dimension_0_tag Tag;
+};
+
+template < typename K >
+struct PCA_default_dimension<typename K::Segment_3> {
+  typedef CGAL::PCA_dimension_1_tag Tag;
+};
+
+template < typename K >
+struct PCA_default_dimension<typename K::Triangle_3> {
+  typedef CGAL::PCA_dimension_2_tag Tag;
+};
+
+
 CGAL_END_NAMESPACE
 
 #endif // CGAL_LINEAR_LEAST_SQUARES_FITTING_TAGS_H
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
index 4f3ec979a37..acbe2fd29e7 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
@@ -43,10 +43,9 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename K::Line_2& line,
                                typename K::Point_2& centroid,
                                const K& k,
-			       const tag& t)
+			                         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));
   return CGALi::linear_least_squares_fitting_2(first, beyond, line,
                                                centroid, k, (Value_type*) NULL, t);
 }
@@ -59,7 +58,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
                                typename K::Line_2& line,
                                const K& k,
-			       const tag& t)
+			                         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));
@@ -71,37 +70,39 @@ linear_least_squares_fitting_2(InputIterator first,
 // deduces the kernel from the points in container.
 template < typename InputIterator, 
            typename Line,
-	   typename tag>
+	         typename tag>
 inline
 typename Kernel_traits<Line>::Kernel::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
                                Line& line,
                                typename Kernel_traits<Line>::Kernel::Point_2& centroid,
-			       const tag& t)
+			                         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_2(first,beyond,line,centroid,K(), t);
 }
 
 // does not return the centroid and deduces the kernel as well.
 template < typename InputIterator, 
-           typename Line, typename tag >
+           typename Line,
+           typename tag >
 inline
 typename Kernel_traits<Line>::Kernel::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
                                Line& line,
-			       const tag& t)
+			                         const tag& t)
 {
   typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
   typedef typename Kernel_traits<Value_type>::Kernel K;
-  //  BOOST_STATIC_ASSERT((boost::is_same<typename CGAL::Algebraic_structure_traits<Value_type>::Algebraic_category,CGAL::Field_with_sqrt_tag>::value));
   return CGAL::linear_least_squares_fitting_2(first,beyond,line,K(), t);
 }
 
 CGAL_END_NAMESPACE
 
+  //  BOOST_STATIC_ASSERT((boost::is_same<typename CGAL::Algebraic_structure_traits<Value_type>::Algebraic_category,CGAL::Field_with_sqrt_tag>::value));
+
+
 #endif // CGAL_LINEAR_LEAST_SQUARES_FITTING_2_H
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
index 756c2ca2c9d..990a6968675 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
@@ -46,10 +46,9 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Plane_3& plane,
                                typename K::Point_3& centroid,
                                const K& k,
-			       const tag& t)
+			                         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));
   return CGALi::linear_least_squares_fitting_3(first, beyond, plane,
                                                centroid, k, (Value_type*) NULL, t);
 }
@@ -63,7 +62,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Line_3& line,
                                typename K::Point_3& centroid,
                                const K& k,
-			       const tag& t)
+			                         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));
@@ -79,7 +78,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
                                typename K::Plane_3& plane,
                                const K& k,
-			       const tag& t)
+			                         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));
@@ -96,16 +95,15 @@ linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
                                typename K::Line_3& line,
                                const K& k,
-			       const tag& t)
+			                         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));
   typename K::Point_3 centroid;
   return CGALi::linear_least_squares_fitting_3(first, beyond, line,
                                                centroid, k,(Value_type*) NULL, t);
 }
 
-// deduces the kernel from the points in container.
+// deduces kernel 
 template < typename InputIterator, 
            typename Object,
            typename tag>
@@ -115,14 +113,14 @@ linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
                                Object& object,
                                typename Kernel_traits<Object>::Kernel::Point_3& centroid,
-			       const tag& t)
+			                         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,centroid,K(), t);
 }
 
+/*
 // does not return the centroid and deduces the kernel as well.
 template < typename InputIterator, 
            typename Object, typename tag >
@@ -131,7 +129,7 @@ typename Kernel_traits<Object>::Kernel::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
                                Object& object,
-			       const tag& t)
+			                         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));
@@ -139,6 +137,40 @@ linear_least_squares_fitting_3(InputIterator first,
   return CGAL::linear_least_squares_fitting_3(first,beyond,object,K(), t);
 }
 
+// default tag
+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 K;
+  return CGAL::linear_least_squares_fitting_3(first,beyond,object,K());
+}
+*/
+
+// does not return the centroid and deduces the kernel as well.
+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));
+
+
 CGAL_END_NAMESPACE
 
 #endif // CGAL_LINEAR_LEAST_SQUARES_FITTING_3_H
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
index 45da055a06a..c7b53572b08 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
@@ -41,7 +41,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& 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 = CGAL::PCA_dimension_3_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Iso_cuboid_3    Iso_cuboid;
@@ -72,7 +72,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& 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::Iso_cuboid_3    Iso_cuboid;
@@ -103,7 +103,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Iso_cuboid_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::Iso_cuboid_3    Iso_cuboid;
@@ -147,7 +147,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Iso_cuboid_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::Iso_cuboid_3    Iso_cuboid;
@@ -183,7 +183,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& 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 = CGAL::PCA_dimension_3_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Iso_cuboid_3    Iso_cuboid;
@@ -213,7 +213,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& 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::Iso_cuboid_3    Iso_cuboid;
@@ -244,7 +244,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Iso_cuboid_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::Iso_cuboid_3    Iso_cuboid;
@@ -288,7 +288,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Iso_cuboid_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::Iso_cuboid_3    Iso_cuboid;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
index 20810a10bda..d2592e62e9d 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
@@ -45,7 +45,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename K::Point_2& c,     // centroid
                                const K&,                   // kernel
                                const typename K::Point_2*,// used for indirection
-			       const CGAL::PCA_dimension_0_tag& t)   
+			                         const CGAL::PCA_dimension_0_tag& tag = CGAL::PCA_dimension_0_tag())   
 {
   // types
   typedef typename K::FT       FT;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
index 2b7ccd14c4e..5568c072179 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
@@ -43,7 +43,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,     // centroid
                                const K& k,                 // kernel
                                const typename K::Point_3*, // used for indirection
-			                         const CGAL::PCA_dimension_0_tag& tag)
+			                         const CGAL::PCA_dimension_0_tag& tag = CGAL::PCA_dimension_0_tag())
 {
   typedef typename K::FT       FT;
   typedef typename K::Point_3  Point;
@@ -77,7 +77,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,    // centroid
                                const K& k,                // kernel
                                const typename K::Point_3*, // used for indirection
-			       const CGAL::PCA_dimension_0_tag& tag)
+			                         const CGAL::PCA_dimension_0_tag& tag = CGAL::PCA_dimension_0_tag)
 {
   typedef typename K::FT       FT;
   typedef typename K::Point_3  Point;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
index 6f6e1574592..c347bb2ff66 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
@@ -48,7 +48,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename K::Point_2& c,     // centroid
                                const K&,                   // kernel
                                const typename K::Iso_rectangle_2*,// used for indirection
-			       const CGAL::PCA_dimension_2_tag& tag)
+			                         const CGAL::PCA_dimension_2_tag& tag = CGAL::PCA_dimension_2_tag())
 {
   // types
   typedef typename K::FT       FT;
@@ -124,20 +124,17 @@ linear_least_squares_fitting_2(InputIterator first,
   covariance[1] += mass * (-1.0 * c.x() * c.y());
   covariance[2] += mass * (-1.0 * c.y() * c.y());
 
-  // to remove later
-  //  std::cout<<covariance[0]<<" "<<covariance[1]<<" "<<covariance[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>(covariance,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)
   {
@@ -163,7 +160,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename K::Point_2& c,     // centroid
                                const K&,                   // kernel
                                const typename K::Iso_rectangle_2*,// used for indirection
-			       const CGAL::PCA_dimension_1_tag& tag)
+			                         const CGAL::PCA_dimension_1_tag& tag)
 {
   // types
   typedef typename K::Iso_rectangle_2 Iso_rectangle;
@@ -189,7 +186,9 @@ linear_least_squares_fitting_2(InputIterator first,
 
 } // end linear_least_squares_fitting_2 for rectangle set with 1D tag
 
-template < typename InputIterator, typename K >
+
+template < typename InputIterator,
+           typename K >
 typename K::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -197,7 +196,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename K::Point_2& c,     // centroid
                                const K&,                   // kernel
                                const typename K::Iso_rectangle_2*,// used for indirection
-			       const CGAL::PCA_dimension_0_tag& tag)
+			                         const CGAL::PCA_dimension_0_tag& tag)
 {
   // types
   typedef typename K::Iso_rectangle_2 Iso_rectangle;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
index 2880c85c07c..c97e57e2f75 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
@@ -48,7 +48,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename K::Point_2& c,     // centroid
                                const K&,                   // kernel
                                const typename K::Segment_2*,// used for indirection
-			       const CGAL::PCA_dimension_1_tag& tag)   
+			                         const CGAL::PCA_dimension_1_tag& tag = CGAL::PCA_dimension_1_tag())   
 {
   // types
   typedef typename K::FT       FT;
@@ -73,8 +73,7 @@ linear_least_squares_fitting_2(InputIterator first,
   FT covariance[3] = {0.0,0.0,0.0};
 
   // assemble 2nd order moment about the origin.  
-  FT temp[4] = {1.0, 0.5,
-		0.5, 1.0};
+  FT temp[4] = {1.0, 0.5, 0.5, 1.0};
   Matrix moment = (1.0/3.0) * init_matrix<K>(2,temp);
 
   for(InputIterator it = first;
@@ -148,7 +147,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename K::Point_2& c,     // centroid
                                const K& k,                   // kernel
                                const typename K::Segment_2*,// used for indirection
-			       const CGAL::PCA_dimension_0_tag& tag)   
+			                         const CGAL::PCA_dimension_0_tag& tag)   
 {
   // types
   typedef typename K::Point_2  Point;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
index 59651a5d839..cace4d3d298 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
@@ -41,7 +41,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Segment_3*,  // used for indirection
-			       const CGAL::PCA_dimension_1_tag& tag)
+			                         const CGAL::PCA_dimension_1_tag& tag = CGAL::PCA_dimension_1_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Segment_3  Segment;
@@ -71,7 +71,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Segment_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::Segment_3  Segment;
@@ -105,7 +105,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Segment_3*,  // used for indirection
-			       const CGAL::PCA_dimension_1_tag& tag)
+			                         const CGAL::PCA_dimension_1_tag& tag = CGAL::PCA_dimension_1_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Segment_3  Segment;
@@ -135,7 +135,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Segment_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::Segment_3  Segment;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
index 3b558095098..d4529fa23f6 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
@@ -31,7 +31,7 @@ CGAL_BEGIN_NAMESPACE
 
 namespace CGALi {
 
-// fits a plane to a 3D sphere set
+// fits a plane to a set of 3D balls (3D)
 template < typename InputIterator, 
            typename K >
 typename K::FT
@@ -41,7 +41,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Sphere_3*,  // used for indirection
-			       const CGAL::PCA_dimension_3_tag& tag)
+			                         const CGAL::PCA_dimension_3_tag& tag = CGAL::PCA_dimension_3_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Sphere_3    Sphere;
@@ -71,7 +71,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& 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::Sphere_3    Sphere;
@@ -91,7 +91,8 @@ linear_least_squares_fitting_3(InputIterator first,
 
 } // end linear_least_squares_fitting_spheres_3
 
-// fits a line to a 3D sphere set
+
+// fits a line to a 3D ball set
 template < typename InputIterator, 
            typename K >
 typename K::FT
@@ -101,7 +102,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Sphere_3*,  // used for indirection
-			       const CGAL::PCA_dimension_3_tag& tag)
+			                         const CGAL::PCA_dimension_3_tag& tag = CGAL::PCA_dimension_3_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Sphere_3  Sphere;
@@ -132,7 +133,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& 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::Sphere_3  Sphere;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
index 451a933f067..f343882861c 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
@@ -41,7 +41,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Tetrahedron_3*,  // used for indirection
-			                         const CGAL::PCA_dimension_3_tag& tag)
+			                         const CGAL::PCA_dimension_3_tag& tag = CGAL::PCA_dimension_3_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Tetrahedron_3    Tetrahedron;
@@ -72,7 +72,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Tetrahedron_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::Tetrahedron_3    Tetrahedron;
@@ -182,7 +182,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Tetrahedron_3*,  // used for indirection
-			       const CGAL::PCA_dimension_3_tag& tag)
+			                         const CGAL::PCA_dimension_3_tag& tag = CGAL::PCA_dimension_3_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Tetrahedron_3    Tetrahedron;
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
index 977df79b9ea..2b15bb8f397 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
@@ -41,7 +41,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                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 = CGAL::PCA_dimension_2_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Triangle_3  Triangle;
@@ -71,7 +71,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Triangle_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::Triangle_3  Triangle;
@@ -106,7 +106,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Triangle_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::Triangle_3  Triangle;
@@ -141,7 +141,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                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 = CGAL::PCA_dimension_2_tag())
 {
   typedef typename K::FT          FT;
   typedef typename K::Triangle_3  Triangle;
@@ -171,7 +171,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Triangle_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::Triangle_3  Triangle;
@@ -206,7 +206,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename K::Point_3& c,       // centroid
                                const K& k,                   // kernel
                                const typename K::Triangle_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::Triangle_3  Triangle;