Merge branch 'Kernel_d-rewrite-glisse-old' into Kernel_d-rewrite-glisse

Hopefully the doc will be easier to build this way.

Kernel_23/include/CGAL/Dimension.h

@@ -23,9 +23,33 @@
 #include <CGAL/basic.h>
 #include <CGAL/Kernel_traits.h>
 #include <climits>
+#include <limits>
+#ifdef CGAL_EIGEN3_ENABLED
+#include <Eigen/Core>
+#endif
 
 namespace CGAL {
 
+#ifdef CGAL_EIGEN3_ENABLED
+const int UNKNOWN_DIMENSION=Eigen::Dynamic;
+#else
+const int UNKNOWN_DIMENSION=std::numeric_limits<int>::max();
+#endif
+
+// Check that dimension d1 is fine for a kernel of dimension d2.
+// If d2 is unknown, any d1 is fine.
+inline bool check_dimension_lt(int d1, int d2){
+	//return (d2==UNKNOWN_DIMENSION)||(d1<d2);
+	return d1<d2;
+}
+inline bool check_dimension_le(int d1, int d2){
+	//return (d2==UNKNOWN_DIMENSION)||(d1<=d2);
+	return d1<=d2;
+}
+inline bool check_dimension_eq(int d1, int d2){
+	return d2==UNKNOWN_DIMENSION || d1==d2;
+}
+
 // These tag classes help dispatching functions based on a geometric dimension.
 
 template < int dim >
@@ -34,7 +58,9 @@ struct Dimension_tag
   static const int value = dim;
 };
 
-struct Dynamic_dimension_tag {};
+struct Dynamic_dimension_tag {
+  static const int value = UNKNOWN_DIMENSION;
+};
 
 
 namespace internal {
@@ -69,6 +95,39 @@ struct Feature_dimension
   typedef typename K::template Feature_dimension<T>::type type;
 };
 
+// Change the dimension
+template<class D,int i=1>struct Increment_dimension {
+        typedef Dynamic_dimension_tag type;
+};
+template<int d,int i>struct Increment_dimension<Dimension_tag<d>,i> {
+        typedef Dimension_tag<d+i> type;
+};
+
+template<class D1,class D2>struct Product_dimension {
+        typedef Dynamic_dimension_tag type;
+};
+template<int d1,int d2>struct Product_dimension<Dimension_tag<d1>,Dimension_tag<d2> > {
+        typedef Dimension_tag<d1*d2> type;
+};
+
+#ifdef CGAL_EIGEN3_ENABLED
+// Convert to Eigen's notion of dimension
+template <class Dim_> struct Eigen_dimension {
+	enum { value=Eigen::Dynamic };
+};
+template <int d> struct Eigen_dimension<Dimension_tag<d> > {
+	enum { value=d };
+};
+
+// and convert back
+template <int d> struct Dimension_eigen {
+	typedef Dimension_tag<d> type;
+};
+template <> struct Dimension_eigen<Eigen::Dynamic> {
+	typedef Dynamic_dimension_tag type;
+};
+#endif
+
 } //namespace CGAL
 
 #endif // CGAL_DIMENSION_H

Kernel_d/doc/Kernel_d/CGAL/Cartesian_d.h

@@ -4,7 +4,7 @@ namespace CGAL {
 /*!
 \ingroup PkgKernelDKernels
 
-A model for `Kernel_d` that uses %Cartesian coordinates to represent the 
+A model for `Kernel_d` (and even `KernelWithLifting_d`) that uses %Cartesian coordinates to represent the 
 geometric objects. In order for `Cartesian_d` to model Euclidean geometry 
 in \f$ E^d\f$ , for some mathematical field \f$ E\f$ (<I>e.g.</I>, 
 the rationals \f$\mathbb{Q}\f$ or the reals \f$\mathbb{R}\f$), the template parameter `FieldNumberType` 
@@ -14,7 +14,7 @@ type provided as a model for `FieldNumberType` is only an approximation of a
 field (such as the built-in type `double`), then the geometry provided by 
 the kernel is only an approximation of Euclidean geometry. 
 
-\cgalModels `Kernel_d`
+\cgalModels `KernelWithLifting_d`
 
 \sa `CGAL::Homogeneous_d<RingNumberType>`
 

Kernel_d/doc/Kernel_d/CGAL/Epick_d.h

@@ -0,0 +1,72 @@
+
+namespace CGAL {
+
+/*!
+\ingroup PkgKernelDKernels
+
+A model for `Kernel_d` that uses %Cartesian coordinates to represent the
+geometric objects. The parameter `DimensionTag` is the dimension of the
+ambient Euclidean space. It may be either `Dimension_tag<d>` \cgalModifBegin where `d` is
+an integer \cgalModifEnd or
+`Dynamic_dimension_tag`. \cgalModifBegin In the later case, the dimension of the space is specified for each point when it is constructed, so it doesn't need to be known at compile-time. \cgalModifEnd This kernel supports construction of points from `double`
+%Cartesian coordinates. It provides exact geometric predicates, but
+the geometric constructions are not guaranteed to be exact. The geometric
+predicates are made exact without sacrificing speed thanks to the use of
+filters.
+
+This kernel is default constructible and copyable. It does not carry any
+state so it is possible to use objects created by one instance with
+functors created by another one.
+
+Note that this kernel does not completely conform to the `Kernel_d`
+concept: it is missing the constructions `Lift_to_paraboloid_d` and
+`Project_along_d_axis_d` which do not make sense with a single fixed
+dimension.
+
+Only the interfaces specific to this class are listed here, refer to the
+concepts for the rest.
+
+
+\cgalModels `Kernel_d`
+\cgalModels `DelaunayTriangulationTraits`
+
+\sa `CGAL::Cartesian_d<FieldNumberType>`
+\sa `CGAL::Homogeneous_d<RingNumberType>`
+
+*/
+template< typename DimensionTag >
+class Epick_d {
+public:
+/*!
+represents a point in the Euclidean space
+\cgalModels `DefaultConstructible`
+\cgalModels `Copyable`
+\cgalModels `Assignable`
+*/
+class Point_d {
+public:
+/*! introduces a point with coordinates (x0, x1, ...) where the number of
+    coordinates matches the dimension.
+    \pre `DimensionTag` is a fixed dimension, not `Dynamic_dimension_tag`. */
+Point_d(double x0, double x1, ...);
+
+/*! \cgalModifBegin introduces a point with coordinate set `[first,end)`.
+    \pre If `DimensionTag` is a fixed dimension, it matches `distance(first,end)`.
+    \cgalRequires The value type of `InputIterator` is convertible to `FT`.\cgalModifEnd
+    */
+template<typename InputIterator>
+Point_d(InputIterator first, InputIterator end);
+
+/*! returns the i'th coordinate of a point.
+    \pre `i` is non-negative and less than the dimension. */
+double operator[](int i)const;
+
+/*! \cgalModifBegin returns an iterator pointing to the zeroth Cartesian coordinate.\cgalModifEnd */
+Cartesian_const_iterator_d cartesian_begin()const;
+/*! \cgalModifBegin returns an iterator pointing beyond the last Cartesian coordinate.\cgalModifEnd */
+Cartesian_const_iterator_d cartesian_end()const;
+}
+/// @}
+
+}; /* end Epick_d */
+} /* end namespace CGAL */

Kernel_d/doc/Kernel_d/CGAL/Homogeneous_d.h

@@ -4,7 +4,7 @@ namespace CGAL {
 /*!
 \ingroup PkgKernelDKernels
 
-A model for a `Kernel_d` using homogeneous coordinates to represent the 
+A model for a `Kernel_d` (and even `KernelWithLifting_d`) using homogeneous coordinates to represent the 
 geometric objects. In order for `Homogeneous` to model Euclidean geometry 
 in \f$ E^d\f$, for some mathematical ring \f$ E\f$ (<I>e.g.</I>, 
 the integers \f$\mathbb{Z}\f$ or the rationals \f$\mathbb{Q}\f$), the template parameter `RT` 
@@ -14,7 +14,7 @@ type provided as a model for `RingNumberType` is only an approximation of a
 ring (such as the built-in type `double`), then the geometry provided by 
 the kernel is only an approximation of Euclidean geometry. 
 
-\cgalModels `Kernel_d`
+\cgalModels `KernelWithLifting_d`
 
 \sa `CGAL::Cartesian_d<FieldNumberType>`
 

Kernel_d/doc/Kernel_d/Concepts/Kernel--Lift_to_paraboloid_d.h

@@ -5,7 +5,7 @@
 
 */
 
-class Kernel_d::Lift_to_paraboloid_d {
+class KernelWithLifting_d::Lift_to_paraboloid_d {
 public:
 
 /// \name Operations
@@ -14,13 +14,13 @@ public:
 
 /*!
 returns \f$ p = (x_0,\ldots,x_{d-1})\f$ lifted to the paraboloid of 
-revolution which is the point \f$ (p_0, \ldots,p_{d-1},\sum_{0 \le i < 
+revolution which is the point \f$ (x_0, \ldots,x_{d-1},\sum_{0 \le i <
-d}p_i^2)\f$ in \f$ (d+1)\f$-space. 
+d}x_i^2)\f$ in \f$ (d+1)\f$-space.
 */ 
 Kernel_d::Point_d operator()(const Kernel_d::Point_d& 
 p); 
 
 /// @}
 
-}; /* end Kernel_d::Lift_to_paraboloid_d */
+}; /* end KernelWithLifting_d::Lift_to_paraboloid_d */
 

Kernel_d/doc/Kernel_d/Concepts/Kernel--Project_along_d_axis_d.h

@@ -5,7 +5,7 @@
 
 */
 
-class Kernel_d::Project_along_d_axis_d {
+class KernelWithLifting_d::Project_along_d_axis_d {
 public:
 
 /// \name Operations
@@ -20,5 +20,5 @@ Kernel_d::Point_d operator()(const Kernel_d::Point_d& p);
 
 /// @}
 
-}; /* end Kernel_d::Project_along_d_axis_d */
+}; /* end KernelWithLifting_d::Project_along_d_axis_d */
 

Kernel_d/doc/Kernel_d/Concepts/KernelWithLifting_d.h

@@ -0,0 +1,50 @@
+
+/*!
+\ingroup PkgKernelDKernelConcept
+\cgalConcept
+
+The concept of a <I>kernel with lifting</I> is a small refinement of the
+general kernel concept. It adds 2 functors, the meaning of which would be
+unclear in kernels of fixed dimension.
+
+\cgalRefines `Kernel_d`
+\cgalHasModel `CGAL::Cartesian_d<FieldNumberType>`
+\cgalHasModel `CGAL::Homogeneous_d<RingNumberType>` 
+*/
+class KernelWithLifting_d {
+public:
+
+/// \name Constructions 
+/// @{
+
+/*! 
+a model of `KernelWithLifting_d::Lift_to_paraboloid_d` 
+*/ 
+typedef unspecified_type Lift_to_paraboloid_d; 
+
+/*! 
+a model of `KernelWithLifting_d::Project_along_d_axis_d` 
+*/ 
+typedef unspecified_type Project_along_d_axis_d; 
+
+/// @} 
+
+/// \name Operations 
+/// The following member functions return function objects of the
+/// types listed above.
+/// @{
+
+/*! 
+
+*/ 
+Kernel_d::Lift_to_paraboloid_d lift_to_paraboloid_d_object() const; 
+
+/*! 
+
+*/ 
+Kernel_d::Project_along_d_axis_d project_along_d_axis_d_object() const; 
+
+/// @}
+
+}; /* end KernelWithLifting_d */
+

Kernel_d/doc/Kernel_d/Concepts/Kernel_d.h

@@ -20,6 +20,7 @@ replacing operators, especially for equality testing.
 
 \cgalHasModel `CGAL::Cartesian_d<FieldNumberType>`
 \cgalHasModel `CGAL::Homogeneous_d<RingNumberType>` 
+\cgalHasModel `CGAL::Epick_d<DimensionTag>` 
 */
 class Kernel_d {
 public:

Kernel_d/doc/Kernel_d/Kernel_d.txt

@@ -67,7 +67,7 @@ unordered set of elements of the corresponding tuple.
 
 This extends the syntax of random access iterators to input iterators.
 If we index the tuple as above then we require that
-\f$ ++^{(d+1)}\mathit{first} = \mathit{last}\f$.
+\f$ ++^{(d)}\mathit{first} = \mathit{last}\f$.
 
 \section Kernel_dKernel Kernel Representations
 
@@ -109,12 +109,14 @@ argument for this parameter must fulfill certain requirements on
 syntax and semantics. The list of requirements defines an abstract
 kernel concept. In \cgal such a kernel concept is often also called a
 <I>representation class</I> and denoted by `R`. A representation
-class provides the actual implementations of the kernel objects. For
+class provides the actual implementations of the kernel objects.
-all kernel objects `Kernel_object`, the types
+For all kernel objects `Kernel_object` of a representation class `R` based
-`CGAL::Kernel_object<R>` and `R::Kernel_object` are identical.
+on `Cartesian_d` or `Homogeneous_d`, the types `CGAL::Kernel_object<R>` and
+`R::Kernel_object` are identical.
 
-\cgal offers two families of concrete models for the concept
+
-representation class, one based on the %Cartesian
+\cgal offers three families of concrete models for the concept
+representation class, two based on the %Cartesian
 representation of points and one based on the homogeneous
 representation of points. The interface of the kernel objects is
 designed such that it works well with both
@@ -140,7 +142,7 @@ strictly speaking, the built-in type `int` does not fulfill the
 requirements on a field type, since `int`s correspond to elements
 of a ring rather than a field, especially operation \f$ /\f$ is not the
 inverse of \f$ *\f$. The requirements on the type `R::RT` are
-weaker. This type must fulfill the requirements on what is called an
+weaker. This type must fulfill the requirements on what is called a
 <I>Euclidean ring type</I> in \cgal. This roughly means that
 `R::RT` is a type for which operations \f$ +\f$, \f$ -\f$, \f$ *\f$ are
 defined with semantics (approximately) corresponding to those of a
@@ -205,10 +207,29 @@ circumvented. With `Homogeneous_d<RingNumberType>`,
 `Homogeneous_d<RingNumberType,LinearAlgebra>::%LA` is mapped to the
 type `LinearAlgebra`.
 
+\subsection Kernel_dEpickKernel Epick_d Kernel
+
+The kernel `Epick_d<DimensionTag>`, short for Exact Predicates Inexact
+Constructions Kernel is a kernel particularly useful when the dimension of
+the space is known at compile-time; \cgalModifBegin `DimensionTag` is then
+`Dimension_tag<d>` where `d` is an integer representing the dimension. It
+may also be used with parameter `Dynamic_dimension_tag`, in which case the
+dimension does not need to be known at compile-time.\cgalModifEnd
+It uses a Cartesian representation and
+supports construction of points from `double` coordinates. It provides exact
+geometric predicates, but the geometric constructions are not guaranteed to
+be exact.
+
+Note that it provides few interfaces in addition to those documented in the
+`Kernel_d` concept. In particular, the type of a point is only available as
+`Epick_d<DimensionTag>::Point_d`, <B>not</B> `Point_d<Epick_d<DimensionTag>>`.
+
+
 \subsection Kernel_dNamingconventions Naming conventions
 
 The use of representation classes not only avoids problems, it also
-makes all \cgal classes very uniform. They <B>always</B> consist of:
+makes all \cgal classes very uniform. Like `Cartesian_d<double>::Point_d`,
+they <B>always</B> consist of:
 <OL>
 
 <LI>The <I>capitalized base name</I> of the geometric object, such as
@@ -216,9 +237,10 @@ makes all \cgal classes very uniform. They <B>always</B> consist of:
 
 <LI>Followed by `_d`.
 
-<LI>A <I>representation class</I> as parameter, which itself is
+<LI>A <I>representation class</I>, which itself may be parameterized with a
-parameterized with a number type, such as
+number type, such as `Cartesian_d<double>` or `Homogeneous_d<leda_integer>`,
-`Cartesian_d<double>` or `Homogeneous_d<leda_integer>`.
+where the type can be found, \cgalModifBegin except for `Epick_d<DimensionTag>` where the
+number type is implicitly `double`\cgalModifEnd .
 </OL>
 
 \subsection Kernel_dKernelasaTraitsClass Kernel as a Traits Class
@@ -231,7 +253,7 @@ library you can use a kernel as a traits class. For some algorithms
 you even do not have to specify the kernel; it is detected
 automatically using the types of the geometric objects passed to the
 algorithm. In some other cases, the algorithms or data structures
-needs more than is provided by a kernel. In these cases, a kernel can
+need more than is provided by a kernel. In these cases, a kernel can
 not be used as a traits class.
 
 \subsection Kernel_dChoosingaKernel Choosing a Kernel
@@ -266,6 +288,11 @@ they need speed and can live with approximate results, or even
 algorithms that, from time to time, crash or compute incorrect results
 due to accumulated rounding errors.
 
+The `Epick_d` kernel provides a compromise using `double` coordinates. It
+evaluates predicates exactly, which is slower than plain `double`
+computations, but still faster than using an exact number type thanks to
+filtering techniques. Constructions are inexact, computed with `double`.
+
 \subsection Kernel_dInclusionofHeaderFiles Inclusion of Header Files
 
 You need just to include a representation class to obtain the
@@ -516,6 +543,10 @@ Stefan Schirra.
 This work was supported by ESPRIT IV Long Term Research Projects
 No. 21957 (CGAL) and No. 28155 (GALIA).
 
+The Epick_d kernel was partially supported by the IST Programme of the EU
+(FET Open) Project under Contract No IST-25582 – (CGL - Computational
+Geometric Learning).
+
 */ 
 } /* namespace CGAL */
 

Kernel_d/doc/Kernel_d/PackageDescription.txt

@@ -47,7 +47,8 @@
 
 ## Kernels ##
 - `CGAL::Cartesian_d<FieldNumberType>`
-- `CGAL::Homogeneous<RingNumberType>`
+- `CGAL::Homogeneous_d<RingNumberType>`
+- `CGAL::Epick_d<DimensionTag>`
 
 ## %Kernel Objects ##
 - `CGAL::Point_d<Kernel>`

Kernel_d/doc_tex/Kernel_d/kernel_representation_d.tex

@@ -132,6 +132,12 @@ circumvented.  With \ccc{Homogeneous_d<RingNumberType>},
 \ccc{Homogeneous_d<RingNumberType,LinearAlgebra>::LA} is mapped to the
 type \ccc{LinearAlgebra}.
 
+\subsection{Epick Kernel}
+
+The kernel \ccc{Epick_d<dimension>}, short for Exact Predicates Inexact Constructions Kernel is an experimental kernel useful when the dimension of the space is known at compile-time. It uses a Cartesian representation and supports construction of points from \ccc{double} coordinates. It provides exact geometric predicates, but inexact geometric constructions.
+
+Note that it is a rather strict model of the \ccc{Kernel_d} concept. The type of a point is \ccc{Epick_d<dimension>::Point_d}, {\bf not} \ccc{Point_d<Epick_d<dimension>>}.
+
 \subsection{Naming conventions}
 
 The use of representation classes not only avoids problems, it also

Kernel_d/doc_tex/Kernel_d_ref/Epick_d.tex

@@ -0,0 +1,36 @@
+\begin{ccRefClass}{Epick_d<dimension>}
+
+\ccInclude{CGAL/Epick_d.h}
+
+\ccDefinition
+A model for \ccc{Kernel_d} and \ccc{DelaunayTriangulationTraits} that
+uses Cartesian coordinates to represent the geometric objects.  The
+integer parameter \ccc{dimension} is the dimension of the ambient
+Euclidean space. It supports construction of points from \ccc{double}
+Cartesian coordinates. It provides exact geometric predicates, but
+inexact geometric constructions. The geometric predicates are made exact
+without sacrificing speed thanks to the use of filters.
+
+This kernel is default constructible and copyable. It does not carry any
+state so it is possible to use objects created by one instance with
+functors created by another one.
+
+Note that this kernel does not completely conform to the \ccc{Kernel_d}
+concept: it is missing the constructions \ccc{Lift_to_paraboloid_d} and
+\ccc{Project_along_d_axis_d} which do not make sense with a fixed
+dimension.
+
+\ccIsModel
+\ccRefConceptPage{Kernel_d}
+
+\ccRefConceptPage{DelaunayTriangulationTraits}
+
+\ccSeeAlso
+\ccRefIdfierPage{CGAL::Epick_d<dimension>::Point_d}
+
+\ccRefIdfierPage{CGAL::Cartesian_d<FieldNumberType>}
+
+\ccRefIdfierPage{CGAL::Homogeneous_d<RingNumberType>}
+
+
+\end{ccRefClass}

Kernel_d/doc_tex/Kernel_d_ref/Epick_d_Point_d.tex

@@ -0,0 +1,18 @@
+\begin{ccRefClass} {Epick_d<dimension>::Point_d}
+
+\ccDefinition
+An object of the class \ccRefName\ is a point in the Euclidean space $\E^{dimension}$.
+
+This class is DefaultConstructible, Copyable, Assignable, and provides the following additional interfaces:
+
+\ccCreation
+\ccCreationVariable{p}
+\ccConstructor{Point_d(double x_0, \ldots, double x_{dimension-1});}
+{introduces a point \ccVar\ initialized to $(x_0, \ldots, x_{dimension-1})$.}
+
+\ccOperations
+\ccMethod{double operator[](int i) const;}
+       {returns the i'th Cartesian coordinate of \ccVar.
+        \ccPrecond $0\leq i < dimension$.}
+
+\end{ccRefClass}

Kernel_d/doc_tex/Kernel_d_ref/Homogeneous_d.tex

@@ -1,4 +1,4 @@
-\begin{ccRefClass}{Homogeneous<RingNumberType>}
+\begin{ccRefClass}{Homogeneous_d<RingNumberType>}
 \ccInclude{CGAL/Homogeneous_d.h}
 
 \ccDefinition
@@ -16,6 +16,6 @@ the kernel is only an approximation of Euclidean geometry.
 \ccRefConceptPage{Kernel_d}
 
 \ccSeeAlso
-\ccRefIdfierPage{CGAL::Cartesian_d<FieldumberType>}
+\ccRefIdfierPage{CGAL::Cartesian_d<FieldNumberType>}
 
 \end{ccRefClass}

Kernel_d/doc_tex/Kernel_d_ref/Kernel.tex

@@ -170,6 +170,6 @@ corresponding functions are:
 
 \ccHasModels
 
-\ccc{Cartesian_d<FieldNumberType>}, \ccc{Homogeneous_d<RingNumberType>} 
+\ccc{Cartesian_d<FieldNumberType>}, \ccc{Homogeneous_d<RingNumberType>}, \ccc{Epick_d<dimension>}
 
 \end{ccRefConcept} 

Kernel_d/doc_tex/Kernel_d_ref/main.tex

@@ -20,6 +20,7 @@
 \input{Kernel_d_ref/Cartesian_d.tex}
 \gdef\ccRefPageBreak{\ccTrue}
 \input{Kernel_d_ref/Homogeneous_d.tex}
+\input{Kernel_d_ref/Epick_d.tex}
 
 \clearpage
 \section{Kernel Objects}
@@ -36,6 +37,7 @@
 \input{Kernel_d_ref/Sphere_d.tex}
 \input{Kernel_d_ref/Iso_box_d.tex}
 \input{Kernel_d_ref/Aff_transformation_d.tex}
+\input{Kernel_d_ref/Epick_d_Point_d.tex}
 
 
 

NewKernel_d/doc_tex/NewKernel_d_ref/Cartesian_complete.tex

@@ -0,0 +1,25 @@
+\begin{ccRefClass}{Cartesian_complete<Base,bool force=false,Derived=Default>}
+\ccInclude{CGAL/NewKernel_d/Cartesian_complete.h}
+
+\ccDefinition
+A model for \ccc{Kernel}, that takes a \ccc{Kernel} model \ccc{Base}
+which provides at least \ccc{Point} and extends it by defining a number
+of classical types and functors.  The \ccc{force} parameter says whether
+the class should override existing objects from \ccc{Base}.
+\ccc{Derived} is the name of the ``final'' class for CRTP patterns,
+which by default is \ccc{Cartesian_complete} itself.
+
+This is in particular expected to be enough for the \ccc{Triangulation}
+package.
+
+\ccIsModel
+\ccRefConceptPage{Kernel}
+
+\ccImplementation
+This is split in classes \ccc{Cartesian_complete_predicates},
+\ccc{Cartesian_complete_computations},
+\ccc{Cartesian_complete_constructions}, 
+\ccc{Cartesian_complete_functors} (a reunion of the previous three), 
+\ccc{Cartesian_complete_types}, all with the same parameters.
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Cartesian_filter_K.tex

@@ -0,0 +1,25 @@
+\begin{ccRefClass}{Cartesian_filter_K<Base,AK,EK>}
+\ccInclude{CGAL/NewKernel_d/Cartesian_filter_K.h}
+
+\ccDefinition
+A model for \ccc{Kernel} that derives from \ccc{Base} (already a
+\ccc{Kernel}) and redefines the predicates as filtered predicates
+using \ccc{AK} as the approximate kernel and \ccc{EK} as the exact
+kernel.
+
+\ccIsModel
+\ccRefConceptPage{Kernel}
+
+Constructors???
+
+NOTYET:
+\begin{itemize}
+  \item If \ccc{Base::Functor<Tag>::Is_exact::value} is true, don't filter.
+  \item \ccc{Functor<Tag,No_filter_tag>::type} is taken from Base.
+\end{itemize}
+
+\ccImplementation
+The implementation uses \ccc{CGAL::Filtered_predicate} and
+\ccc{CGAL::KernelD_converter}.
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Cartesian_mini_d.tex

@@ -0,0 +1,16 @@
+\begin{ccRefClass}{Cartesian_mini_d<FT,Dim>}
+\ccInclude{CGAL/NewKernel_d/Cartesian_mini_d.h}
+
+\ccDefinition
+A minimal model for \ccc{Kernel} where \ccc{FT} and
+\ccc{Default_ambient_dimension} are provided as template arguments.
+This kernel provides the \ccc{Point} concept and not much more.
+
+The class takes several other template parameters (in particular to
+specify \ccc{LA}) that are undocumented for now.
+
+\ccIsModel
+\ccRefConceptPage{Kernel}
+\ccRefConceptPage{Point}
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Cartesian_wrap.tex

@@ -0,0 +1,27 @@
+\begin{ccRefClass}{Cartesian_wrap<Base>}
+\ccInclude{CGAL/NewKernel_d/Cartesian_wrap.h}
+
+\ccDefinition
+This class derives from a \ccc{Kernel} \ccc{Base} and replaces a number
+of types (point, segment) with wrappers that have intuitive member
+functions that call the corresponding functors. For instance, the
+constructors forward to \ccc{Functor<Construct_ttag<Tag>>::type},
+\ccc{Point::operator[]} forwards to
+\ccc{Functor<Compute_cartesian_coordinate_tag>::type},
+\ccc{operator+(Vector,Vector)} forwards to
+\ccc{Functor<Construct_sum_of_vectors_tag>::type}, etc.
+
+For stateful kernels, the wrappers will store a pointer to the kernel
+instance. This means in particular that for such a kernel, one can't
+just create a point from its coordinates (like \ccc{Point M(1,2,3);}),
+they have to create it using some functor or an operation on existing
+objects.
+
+\ccIsModel
+\ccRefConceptPage{Kernel}
+
+\ccImplementation
+The implementation \emph{tries} to avoid any extra copying that could be
+caused by the wrapping.
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Define_segment.tex

@@ -0,0 +1,18 @@
+\begin{ccRefClass}{Define_segment<Base,Derived=Default>}
+\ccInclude{CGAL/NewKernel_d/Define_segment.h}
+
+\ccDefinition
+A model for \ccc{Kernel}, that takes a \ccc{Kernel} model \ccc{Base}
+which provides at least \ccc{Point} and extends it by providing
+\ccc{Segment}.
+\ccc{Derived} is the name of the ``final'' class for CRTP patterns,
+which by default is \ccc{Define_segment} itself.
+
+\ccIsModel
+\ccRefConceptPage{Kernel}
+\ccRefConceptPage{Segment}
+
+\ccImplementation
+The segment type is defined as an \ccc{std::pair} of points.
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/KernelD_converter.tex

@@ -0,0 +1,14 @@
+\begin{ccRefFunctionObjectClass}{KernelD_converter<K1,K2,List=K1::Object_list>}
+\ccInclude{CGAL/NewKernel_d/KernelD_converter.h}
+
+\ccDefinition
+A function object that converts objects from kernel \ccc{K1} to kernel \ccc{K2}. By default, it uses identity on \ccc{int}, \ccc{Origin} and \ccc{Null_vector}. It uses \ccc{NT_converter} for \ccc{RT} and \ccc{FT}. It uses \ccc{K1::Functor<Convert_ttag<Tag>::type} for \ccc{K1::Type<Tag>::type} (the list of possible \ccc{Tag} is taken from \ccc{List}). It can recursively convert iterators and \ccc{std::vector} of objects it already knows how to convert. It also unwraps a \ccc{CGAL::Object}, converts the content and rewraps it.
+
+\ccCreation
+\ccConstructor{KernelD_converter(K1 const&,K2 const&)}{main constructor}
+\ccConstructor{KernelD_converter()}{default constructor, only if \ccc{K1} and \ccc{K2} are stateless.}
+
+\ccOperations
+\ccMethod{K2::SomeThing operator()(K1::SomeThing) const;}{returns a converted object.}
+
+\end{ccRefFunctionObjectClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Kernel_2_interface.tex

@@ -0,0 +1,16 @@
+\begin{ccRefClass}{Kernel_2_interface<Base>}
+\ccInclude{CGAL/NewKernel_d/Kernel_2_interface.h}
+
+\ccDefinition
+This class derives from a \ccc{Kernel} \ccc{Base} and defines a number
+of typedefs and functions to give it an interface close to that of the
+classical \ccc{Kernel_23}, restricted to 2D. As an example, it contains:
+
+\ccc{typedef Type<Point_tag>::type Point_2}\\
+\ccc{struct Less_x_2}\\
+\ccc{Less_x_2 less_x_2_object()const}
+
+Assuming that \ccc{Base} provides everything required, this provides
+an interface suitable for the \ccc{Triangulation_2} package.
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Kernel_3_interface.tex

@@ -0,0 +1,16 @@
+\begin{ccRefClass}{Kernel_3_interface<Base>}
+\ccInclude{CGAL/NewKernel_d/Kernel_3_interface.h}
+
+\ccDefinition
+This class derives from a \ccc{Kernel} \ccc{Base} and defines a number
+of typedefs and functions to give it an interface close to that of the
+classical \ccc{Kernel_23}, restricted to 3D. As an example, it contains:
+
+\ccc{typedef Type<Point_tag>::type Point_3}\\
+\ccc{struct Side_of_oriented_sphere_3}\\
+\ccc{Side_of_oriented_sphere_3 side_of_oriented_sphere_3_object()const}
+
+Assuming that \ccc{Base} provides everything required, this provides
+an interface suitable for the \ccc{Triangulation_2} package.
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Kernel_d_interface.tex

@@ -0,0 +1,19 @@
+\begin{ccRefClass}{Kernel_d_interface<Base>}
+\ccInclude{CGAL/NewKernel_d/Kernel_d_interface.h}
+
+\ccDefinition
+This class derives from a \ccc{Kernel} \ccc{Base} and defines a number
+of typedefs and functions to give it an interface close to that of the
+classical \ccc{Kernel_d}. As an example, it contains:
+
+\ccc{typedef Type<Point_tag>::type Point_d}\\
+\ccc{typedef Functor<Compare_lexicographically_tag>::type Compare_lexicographically_d}\\
+\ccc{Compare_lexicographically_d compare_lexicographically_d_object()const{ return Compare_lexicographically_d(*this); }}
+
+Assuming that \ccc{Base} provides everything required, this provides
+an interface suitable for the \ccc{Triangulation} package.
+
+\ccIsModel
+\ccRefConceptPage{Triangulation_traits}
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/Kernel_functor.tex

@@ -0,0 +1,19 @@
+\begin{ccRefConcept}[Kernel::]{Functor<Tag,Option=Default>}
+Functors have a constructor that takes a \ccc{Kernel} as argument. If the kernel is stateless (as tested with \ccc{boost::is_empty<Kernel>}), functors may (must???) also have a default constructor. Functors follow the \ccc{result_of}-protocol.
+
+Member functions provided by each functor are described in their concept. Some special cases are:
+\begin{itemize}
+  \item A constructor is a functor represented by a tag \ccc{Construct_ttag<Some_tag>}. It contains member functions \ccc{Kernel::Type<Some_tag>::type operator()(Args...) const}.
+  \item A converter is a functor represented by a tag \ccc{Convert_ttag<Some_tag>}. It contains a member function \ccc{template <class K2, class Converter> K2::Type<Some_tag>::type operator()(K2 const&, Converter, Kernel::Type<Some_tag>::type) const}. As an example, a segment converter could first extract its extremities with \ccc{Kernel::Functor<Construct_segment_extremity_tag>}, then convert them to \ccc{K2::Type<Point_tag>} using \ccc{Converter} and finally build a \ccc{K2::Type<Segment_tag>} with \ccc{K2::Functor<Construct_segment_tag>}.
+    %TODO: clarify this Converter business
+\end{itemize}
+
+\ccc{Option} is used to specify a specific version of the functor. For instance, for a predicate, you might ask for a fast inexact version with \ccc{Fast_tag}.
+
+For each functor tag \ccc{Tag}, \ccc{map_functor_type<Tag>::type} shall be
+\ccc{Predicate_tag}, \ccc{Construct_tag}, \ccc{Compute_tag} or \ccc{Misc_tag}
+depending on the kind of functor it is. Predicates output a discrete value, for instance \ccc{Kernel::Boolean}. Computations output a number of type \ccc{Kernel::FT} or \ccc{Kernel::RT}. Constructions output an object of type \ccc{Kernel::Type<map_result_tag<Tag>::type>::type} where \ccc{map_result_tag} is specialized to specify the tag of the result. All others are miscellaneous.
+
+
+\end{ccRefConcept}
+

NewKernel_d/doc_tex/NewKernel_d_ref/Lazy_kernel.tex

@@ -0,0 +1,17 @@
+\begin{ccRefClass}{Lazy_kernel<EK,AK,E2A=KernelD_converter<EK,AK>>}
+\ccInclude{CGAL/NewKernel_d/Lazy_kernel.h}
+
+\ccDefinition
+A model for \ccc{Kernel}.
+\ccc{AK} is an approximate kernel (with an interval number type) and \ccc{EK}
+is an exact kernel.
+
+\ccIsModel
+\ccRefConceptPage{Kernel}
+
+\ccImplementation
+For each object, this kernel stores both an approximate object from
+\ccc{AK} and either an exact object from \ccc{EK} or a graph that
+allows it to compute such an exact object when needed.
+
+\end{ccRefClass}

NewKernel_d/doc_tex/NewKernel_d_ref/PkgDescription.tex

@@ -0,0 +1,8 @@
+\begin{ccPkgDescription}{dD Kernel}
+\ccPkgSummary{
+A new d-dimensional kernel.
+}
+\ccPkgIntroducedInCGAL{42.0}
+\ccPkgLicense{\ccLicenseLGPL}
+\end{ccPkgDescription}
+

NewKernel_d/doc_tex/NewKernel_d_ref/Point.tex

@@ -0,0 +1,27 @@
+\begin{ccRefConcept}{Point}
+The concept of a {\em Point} is defined by a set of requirements on
+the provision of certain types in a \ccc{Kernel}.
+
+\ccRefines
+\ccc{Kernel}
+
+\ccNestedType{Object_list}{shall contain at least \ccc{Point_tag} and \ccc{Point_cartesian_const_iterator_tag}.}
+
+\ccNestedType{Type<Point_tag>::type}{shall be CopyConstructible.}
+\ccNestedType{Type<Point_cartesian_const_iterator_tag>::type}{shall be a forward iterator (except that it may return an rvalue) whose \ccc{value_type} is \ccc{Kernel::Type<Point_tag>::type}.}
+
+\ccNestedType{Functor<Convert_ttag<Point_tag>>::type}{[Optional] A default converter it available to \ccc{Kernel_converter}, but may be unsuitable if your Point type is too original.}
+\ccNestedType{Functor<Construct_ttag<Point_cartesian_const_iterator_tag>>::type}{shall provide \ccc{Type<Point_cartesian_const_iterator_tag>::type operator()(Type<Point_tag>::type const&, Extremity_tag)const} where \ccc{Extemity_tag} is \ccc{Begin_tag} or \ccc{End_tag}.}
+\ccNestedType{Functor<Compute_cartesian_coordinate_tag>::type}{shall provide \ccc{FT operator()(Type<Point_tag>::type,int k)const} which returns the $k$th Cartesian coordinate of the point.}
+\ccNestedType{Functor<Point_dimension_tag>::type}{shall provide \ccc{int operator()(Type<Point_tag>::type)const} which returns the dimension of a point.}
+\ccNestedType{Functor<Construct_ttag<Point_tag>>::type}{shall provide:\\
+  \ccc{Type<Point_tag>::type operator()(int dim)const} which constructs a point at the origin;\\
+  \ccc{Type<Point_tag>::type operator()()const} the same, when \ccc{Default_ambient_dimension} is known;\\
+  \ccc{Type<Point_tag>::type operator()(Type<Point_tag>::type)const} which copies (???);\\
+  \ccc{Type<Point_tag>::type operator()(Iter, Iter, Cartesian_tag)const} which reads the Cartesian coordinates from the iterators;\\
+  \ccc{Type<Point_tag>::type operator()(Iter, Iter)const} same as above;\\
+  \ccc{Type<Point_tag>::type operator()(FT...)const} which reads the Cartesian coordinates from the arguments, when \ccc{Default_ambient_dimension} is known.
+}
+
+\end{ccRefConcept}
+

NewKernel_d/doc_tex/NewKernel_d_ref/PreKernel.tex

@@ -0,0 +1,150 @@
+% +------------------------------------------------------------------------+
+% | Reference manual page: PreKernel.tex
+% +------------------------------------------------------------------------+
+% | 21.05.2012   Marc Glisse
+% | Package: NewKernel_d
+% |
+\RCSdef{\RCSPreKernelRev}{$Id$}
+\RCSdefDate{\RCSPreKernelDate}{$Date$}
+% |
+\ccRefPageBegin
+%%RefPage: end of header, begin of main body
+% +------------------------------------------------------------------------+
+
+
+\begin{ccRefConcept}{PreKernel}
+
+%% \ccHtmlCrossLink{}     %% add further rules for cross referencing links
+%% \ccHtmlIndexC[concept]{} %% add further index entries
+
+\ccDefinition
+  
+%copied from Kernel_23
+The concept of a {\em prekernel} is defined by a set of requirements on
+the provision of certain types and access member functions to create
+objects of these types. The types are function object classes to be used
+within the algorithms and data structures of \cgal. This allows you to
+use any model of a kernel as a traits class in the Cgal algorithms and
+data structures, unless they require types beyond those provided by a
+kernel.
+
+A kernel provides types, construction objects, and generalized
+predicates. The former replace constructors of the kernel classes and
+constructive procedures in the kernel. There are also function objects
+replacing operators, especially for equality testing. 
+
+Types and functors are identified by tags, which may be any type (like
+\ccc{CGAL::Segment_tag}). As a special case, the construction functor of
+a type identified by \ccc{Some_tag} is identified by the tag
+\ccc{Construct_ttag<Some_tag>}, and the conversion functor by
+\ccc{Convert_ttag<Some_tag>}.
+
+Depending on \ccc{Default_ambient_dimension}, a kernel has 2
+constructors, a default constructor and a constructor that takes as
+argument an \ccc{int} for the dimension.
+
+
+%\ccGeneralizes
+%
+%ThisConcept \\
+%ThatConcept
+
+\ccTypes
+
+\ccNestedType{Default_ambient_dimension}{\ccc{Dimension_tag<d>} where \ccc{d} is the ambient dimension or \ccc{Dynamic_dimension_tag} if the dimension is unknown.}
+\ccGlue
+\ccNestedType{Max_ambient_dimension}{\ccc{Dimension_tag<d>} where \ccc{d} is an upper bound on the ambient dimension or \ccc{Dynamic_dimension_tag}.}
+
+\ccNestedType{FT}{a model of \ccc{FieldNumberType}}
+\ccGlue
+\ccNestedType{RT}{a model of \ccc{RingNumberType}}
+
+% Not documented in the first version
+\ccNestedType{LA}{a model of \ccc{LinearAlgebraSomething} using \ccc{RT}}
+
+The following types describe the return types of predicates.  They typically
+map to \ccc{bool} and \cgal\ kernel enum types, except when an interval arithmetic
+number type is used such as within the filtering kernels, in which case it is
+\ccc{Uncertain<bool>} or similar.
+
+\ccNestedType{Boolean}{\ccc{bool} or \ccc{Uncertain<bool>}}
+\ccGlue
+\ccNestedType{Sign}{\ccc{CGAL::Sign} or \ccc{Uncertain<CGAL::Sign>}}
+\ccGlue
+\ccNestedType{Comparison_result}{\ccc{CGAL::Comparison_result} or \ccc{Uncertain<CGAL::Comparison_result>}}
+\ccGlue
+\ccNestedType{Orientation}{\ccc{CGAL::Orientation} or \ccc{Uncertain<CGAL::Orientation>}}
+\ccGlue
+\ccNestedType{Oriented_side}{\ccc{CGAL::Oriented_side} or \ccc{Uncertain<CGAL::Oriented_side>}}
+\ccGlue
+\ccNestedType{Bounded_side}{\ccc{CGAL::Bounded_side} or \ccc{Uncertain<CGAL::Bounded_side>}}
+\ccGlue
+\ccNestedType{Angle}{\ccc{CGAL::Angle} or \ccc{Uncertain<CGAL::Angle>}}
+
+\ccHeading{Geometric Objects}
+
+%\ccNestedType{template <class Tag> struct Type<Tag>}{This nested template class defines an object type \ccc{type}. For instance, \ccc{Type<Point_tag>::type} is the type of points.}
+\ccNestedType{Point, \ldots}{Geometric object type}
+
+\ccNestedType{Object_list}{A typedef for \ccc{typeset<Point_tag,...>}
+with the list of tags corresponding to the provided geometric object
+types.}
+
+\ccHeading{Iterators}
+
+\ccNestedType{Point_cartesian_const_iterator, \ldots}{Iterator}
+
+\ccNestedType{Iterator_list}{A typedef for
+\ccc{typeset<Point_cartesian_const_iterator_tag,...>} with the list of
+tags corresponding to the provided iterators.}
+
+
+\ccHeading{Function objects}
+
+\ccNestedType{template <class Tag, class Option> struct Functor<Tag,Option=Default>}{This nested template class defines a functor type \ccc{type}. For instance, \ccc{Functor<Orientation_tag>::type} is the orientation predicate. Functors that are not provided should all be \ccc{Null_functor}.}
+
+
+\ccCreation
+\ccCreationVariable{kernel}  %% choose variable name
+
+\ccConstructor{PreKernel();}{default constructor.}
+\ccConstructor{PreKernel(int d);}{constructor for dimension $d$.}
+
+\ccOperations
+
+\ccMethod{int dimension();}{returns the dimension (or UNKNOWN\_DIMENSION)}
+
+\ccHasModels
+
+\ccc{Some_class},
+\ccc{Some_other_class}.
+
+\ccSeeAlso
+
+Kernel\_d
+%Some\_other\_concept,
+%%\ccc{some_other_function}.
+
+%\ccExample
+%
+%A short example program.
+%Instead of a short program fragment, a full running program can be
+%included using the 
+%\verb|\ccIncludeExampleCode{Package/PreKernel.C}| 
+%macro. The program example would be part of the source code distribution and
+%also part of the automatic test suite.
+%
+%\begin{ccExampleCode}
+%void your_example_code() {
+%}
+%\end{ccExampleCode}
+
+%% \ccIncludeExampleCode{Package/PreKernel.C}
+
+\end{ccRefConcept}
+
+% +------------------------------------------------------------------------+
+%%RefPage: end of main body, begin of footer
+\ccRefPageEnd
+% EOF
+% +------------------------------------------------------------------------+

NewKernel_d/doc_tex/NewKernel_d_ref/Segment.tex

@@ -0,0 +1,28 @@
+\begin{ccRefConcept}{Segment}
+The concept of a {\em Segment} is defined by a set of requirements on
+the provision of certain types in a \ccc{Kernel} that already provides
+the concept of a \ccc{Point}.
+
+\ccRefines
+\ccc{Point}
+
+\ccNestedType{Object_list}{shall contain at least \ccc{Segment_tag}.}
+
+\ccNestedType{Type<Segment_tag>::type}{shall be CopyConstructible.}
+
+\ccNestedType{Functor<Convert_ttag<Segment_tag>>::type}{[Optional] A default converter it available to \ccc{Kernel_converter}, but may be unsuitable if your Segment type is too original.}
+\ccNestedType{Functor<Construct_segment_extremity_tag>::type}{shall
+provide \ccc{Type<Point_tag>::type operator()(Type<Segment_tag>::type,
+int k)const} which returns the $k$th ($0$ or $1$) extremity of the segment.}
+\ccNestedType{Functor<Construct_ttag<Segment_tag>>::type}{shall provide:\\
+  \ccc{Type<Segment_tag>::type
+  operator()(Type<Point_tag>::type,Type<Point_tag>::type)const} which
+  constructs a segment from its extremities;\\
+  \ccc{Type<Segment_tag>::type operator()(piecewise_construct_t,
+  tuple<U...> u, tuple<V...> v)const} which calls
+  \ccc{Functor<Construct_ttag<Point_tag>>::type} on the content of each
+  tuple to create the extremities.
+}
+
+\end{ccRefConcept}
+

NewKernel_d/doc_tex/NewKernel_d_ref/main.tex

@@ -0,0 +1,25 @@
+% +------------------------------------------------------------------------+
+% | CBP Reference Manual:  main.tex
+% +------------------------------------------------------------------------+
+% | Automatically generated driver file for the reference manual chapter
+% | of this package. Do not edit manually, you may loose your changes.
+% +------------------------------------------------------------------------+
+
+\input{NewKernel_d_ref/Cartesian_complete.tex}
+\input{NewKernel_d_ref/Cartesian_filter_K.tex}
+\input{NewKernel_d_ref/Cartesian_mini_d.tex}
+\input{NewKernel_d_ref/Cartesian_wrap.tex}
+\input{NewKernel_d_ref/Define_segment.tex}
+\input{NewKernel_d_ref/KernelD_converter.tex}
+\input{NewKernel_d_ref/Kernel_2_interface.tex}
+\input{NewKernel_d_ref/Kernel_3_interface.tex}
+\input{NewKernel_d_ref/Kernel_d_interface.tex}
+\input{NewKernel_d_ref/Kernel_functor.tex}
+\input{NewKernel_d_ref/Lazy_kernel.tex}
+\input{NewKernel_d_ref/PkgDescription.tex}
+\input{NewKernel_d_ref/Point.tex}
+\input{NewKernel_d_ref/PreKernel.tex}
+\input{NewKernel_d_ref/Segment.tex}
+\input{NewKernel_d_ref/typeset.tex}
+
+%% EOF

NewKernel_d/doc_tex/NewKernel_d_ref/typeset.tex

@@ -0,0 +1,17 @@
+\begin{ccRefClass}{typeset<...>}
+\ccInclude{CGAL/typeset.h}
+
+\ccDefinition
+This class provides a set of types, where each type appears at most once. Iterating through the set should be done by looking at \ccc{head} and recursing on \ccc{tail}, testing whether a set is empty by comparing it to \ccc{typeset<>}.
+
+\ccNestedType{head}{One element from the list.}
+\ccNestedType{tail}{A typeset of the other elements from list.}
+\ccNestedType{add<X>::type}{A typeset with \ccc{X} added to the list.}
+\ccNestedType{contains<X>::value}{A boolean that says whether \ccc{X} is in the list.}
+
+In C++11, \ccc{add<X>} is already a typeset so one can omit \ccc{::type}, and \ccc{contains<X>} derives from \ccc{true_type} or \ccc{false_type}.
+
+\ccImplementation
+In C++11, the list looks like \ccc{typeset<type1,type2,type3>} whereas in C++03 it looks like \ccc{typeset<type1,typeset<type2,typeset<type3,typeset<> > > >} (an alternative would have been \ccc{typeset<type1,type2,type3,void,void,void,void>}, as in \ccc{boost::tuple}).
+
+\end{ccRefClass}

NewKernel_d/include/CGAL/Epick_d.h

@@ -0,0 +1,51 @@
+#ifndef CGAL_EPICK_D_H
+#define CGAL_EPICK_D_H
+#include <CGAL/Kernel_d/Cartesian_base.h>
+#include <CGAL/Kernel_d/Cartesian_static_filters.h>
+#include <CGAL/Kernel_d/Cartesian_filter_K.h>
+#include <CGAL/Kernel_d/Wrapper/Cartesian_wrap.h>
+#include <CGAL/Kernel_d/Kernel_d_interface.h>
+#include <CGAL/Gmpq.h>
+#include <CGAL/Interval_nt.h>
+
+
+namespace CGAL {
+#define CGAL_BASE \
+  Cartesian_filter_K< \
+    Cartesian_base_d<double, Dim>, \
+    Cartesian_base_d<Interval_nt_advanced, Dim>, \
+    Cartesian_base_d<Gmpq, Dim> \
+  >
+template<class Dim>
+struct Epick_d_help1
+: CGAL_BASE
+{
+  CGAL_CONSTEXPR Epick_d_help1(){}
+  CGAL_CONSTEXPR Epick_d_help1(int d):CGAL_BASE(d){}
+};
+#undef CGAL_BASE
+#define CGAL_BASE \
+  Cartesian_static_filters<Dim,Epick_d_help1<Dim>,Epick_d_help2<Dim> >
+template<class Dim>
+struct Epick_d_help2
+: CGAL_BASE
+{
+  CGAL_CONSTEXPR Epick_d_help2(){}
+  CGAL_CONSTEXPR Epick_d_help2(int d):CGAL_BASE(d){}
+};
+#undef CGAL_BASE
+#define CGAL_BASE \
+  Kernel_d_interface< \
+    Cartesian_wrap< \
+      Epick_d_help2<Dim>, \
+      Epick_d<Dim> > >
+template<class Dim>
+struct Epick_d
+: CGAL_BASE
+{
+  CGAL_CONSTEXPR Epick_d(){}
+  CGAL_CONSTEXPR Epick_d(int d):CGAL_BASE(d){}
+};
+#undef CGAL_BASE
+}
+#endif

NewKernel_d/include/CGAL/Filtered_predicate2.h

@@ -0,0 +1,137 @@
+// Copyright (c) 2001-2005  INRIA Sophia-Antipolis (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; version 2.1 of the License.
+// See the file LICENSE.LGPL 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.
+//
+// $URL$
+// $Id$
+// 
+//
+// Author(s)     : Sylvain Pion
+
+#ifndef CGAL_FILTERED_PREDICATE_H
+#define CGAL_FILTERED_PREDICATE_H
+
+#include <string>
+#include <CGAL/config.h>
+#include <CGAL/Interval_nt.h>
+#include <CGAL/Uncertain.h>
+#include <CGAL/Profile_counter.h>
+#include <CGAL/store_kernel.h>
+#include <boost/preprocessor.hpp>
+
+namespace CGAL {
+
+// This template class is a wrapper that implements the filtering for any
+// predicate (dynamic filters with IA).
+
+// TODO :
+// - each predicate in the default kernel should define a tag that says if it
+//   wants to be filtered or not (=> all homogeneous predicate define this
+//   tag).  We could even test-suite that automatically.  It makes a strong
+//   new requirement on the kernel though...
+//   Could be done with a traits mechanism ?
+//   A default template could use the current IA, but other tags or whatever
+//   could specify no filtering at all, or static filtering...
+// - same thing for constructions => virtual operator() ?
+// - similarly, constructions should have a tag saying if they can throw or
+//   not, or we let all this up to the compiler optimizer to figure out ?
+// - Some caching could be done at the Point_2 level.
+
+
+template <class EP, class AP, class C2E, class C2A, bool Protection = true>
+class Filtered_predicate2
+{
+//TODO: pack (at least use a tuple)
+//FIXME: is it better to store those, or just store enough to recreate them
+//(i.e. possibly references to the kernels)?
+  EP  ep;
+  AP  ap;
+  C2E c2e;
+  C2A c2a;
+
+  typedef typename AP::result_type  Ares;
+
+public:
+
+  typedef AP    Approximate_predicate;
+  typedef EP    Exact_predicate;
+  typedef C2E   To_exact_converter;
+  typedef C2A   To_approximate_converter;
+
+  // FIXME: should use result_of, see emails by Nico
+  typedef typename EP::result_type  result_type;
+  // AP::result_type must be convertible to EP::result_type.
+
+  Filtered_predicate2()
+  {}
+
+  template <class K>
+  Filtered_predicate2(const K& k)
+    : ep(k.exact_kernel()), ap(k.approximate_kernel()), c2e(k,k.exact_kernel()), c2a(k,k.approximate_kernel())
+  {}
+
+#ifdef CGAL_CXX0X
+  template <typename... Args>
+  result_type
+  operator()(Args&&... args) const
+  {
+    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
+    // Protection is outside the try block as VC8 has the CGAL_CFG_FPU_ROUNDING_MODE_UNWINDING_VC_BUG
+    {
+      Protect_FPU_rounding<Protection> p;
+      try
+	{
+	  // No forward here, the arguments may still be needed
+	  Ares res = ap(c2a(args)...);
+	  if (is_certain(res))
+	    return get_certain(res);
+	}
+      catch (Uncertain_conversion_exception) {}
+    }
+    CGAL_BRANCH_PROFILER_BRANCH(tmp);
+    Protect_FPU_rounding<!Protection> p(CGAL_FE_TONEAREST);
+    return ep(c2e(std::forward<Args>(args))...);
+  }
+#else
+
+#define VAR(Z,N,C) C(a##N)
+#define CODE(Z,N,_) \
+  template <BOOST_PP_ENUM_PARAMS(N,class A)> \
+  result_type \
+  operator()(BOOST_PP_ENUM_BINARY_PARAMS(N, A, const& a)) const \
+  { \
+    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp); \
+    { \
+      Protect_FPU_rounding<Protection> p; \
+      try \
+	{ \
+	  Ares res = ap(BOOST_PP_ENUM(N,VAR,c2a)); \
+	  if (is_certain(res)) \
+	    return get_certain(res); \
+	} \
+      catch (Uncertain_conversion_exception) {} \
+    } \
+    CGAL_BRANCH_PROFILER_BRANCH(tmp); \
+    Protect_FPU_rounding<!Protection> p(CGAL_FE_TONEAREST); \
+    return ep(BOOST_PP_ENUM(N,VAR,c2e)); \
+  }
+  BOOST_PP_REPEAT_FROM_TO(1, 10, CODE, _ )
+#undef CODE
+#undef VAR
+
+#endif
+};
+
+} //namespace CGAL
+
+#endif // CGAL_FILTERED_PREDICATE_H

NewKernel_d/include/CGAL/Handle_for.h

@@ -0,0 +1,323 @@
+// Copyright (c) 1999,2001,2003  Utrecht University (The Netherlands),
+// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
+// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
+// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
+// and Tel-Aviv University (Israel).  All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; version 2.1 of the License.
+// See the file LICENSE.LGPL 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.
+//
+// $URL$
+// $Id$
+// 
+//
+// Author(s)     : Stefan Schirra, Sylvain Pion
+ 
+#ifndef CGAL_HANDLE_FOR_H
+#define CGAL_HANDLE_FOR_H
+
+#include <boost/config.hpp>
+#include <CGAL/memory.h>
+#include <algorithm>
+#include <cstddef>
+#include <CGAL/marcutils.h>
+#include <boost/preprocessor/repetition.hpp>
+
+#if defined(BOOST_MSVC)
+#  pragma warning(push)
+#  pragma warning(disable:4345) // Avoid warning  http://msdn.microsoft.com/en-us/library/wewb47ee(VS.80).aspx
+#endif
+namespace CGAL {
+
+template <class T, class Alloc = CGAL_ALLOCATOR(T) >
+class Handle_for
+{
+    // Wrapper that adds the reference counter.
+    struct RefCounted {
+        T t;
+        unsigned int count;
+    };
+
+    typedef typename Alloc::template rebind<RefCounted>::other  Allocator;
+    typedef typename Allocator::pointer                         pointer_;
+
+    static Allocator   allocator;
+    pointer_            ptr_;
+
+public:
+
+    typedef T element_type;
+    
+    typedef std::ptrdiff_t Id_type ;
+
+    Handle_for()
+      : ptr_(allocator.allocate(1))
+    {
+        new (&(ptr_->t)) element_type(); // we get the warning here 
+        ptr_->count = 1;
+    }
+
+    Handle_for(const element_type& t)
+      : ptr_(allocator.allocate(1))
+    {
+        new (&(ptr_->t)) element_type(t);
+        ptr_->count = 1;
+    }
+
+#ifndef CGAL_CFG_NO_CPP0X_RVALUE_REFERENCE
+    Handle_for(element_type && t)
+      : ptr_(allocator.allocate(1))
+    {
+        new (&(ptr_->t)) element_type(std::move(t));
+        ptr_->count = 1;
+    }
+#endif
+
+/* I comment this one for now, since it's preventing the automatic conversions
+   to take place.  We'll see if it's a problem later.
+    template < typename T1 >
+    Handle_for(const T1& t1)
+      : ptr_(allocator.allocate(1))
+    {
+        new (&(ptr_->t)) T(t1);
+        ptr_->count = 1;
+    }
+*/
+
+#if !defined CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES && !defined CGAL_CFG_NO_CPP0X_RVALUE_REFERENCE
+    template < typename T1, typename T2, typename... Args >
+    Handle_for(T1 && t1, T2 && t2, Args && ... args)
+      : ptr_(allocator.allocate(1))
+    {
+        new (&(ptr_->t)) element_type(std::forward<T1>(t1), std::forward<T2>(t2), std::forward<Args>(args)...);
+        ptr_->count = 1;
+    }
+
+    template < typename F, typename... Args >
+    Handle_for(Eval_functor &&, F && f, Args && ... args)
+      : ptr_(allocator.allocate(1))
+    {
+        new (&(ptr_->t)) element_type(std::forward<F>(f)(std::forward<Args>(args)...));
+        ptr_->count = 1;
+    }
+#else
+#define CODE(Z,N,_) template <BOOST_PP_ENUM_PARAMS(N,class T)> \
+    Handle_for(BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+      : ptr_(allocator.allocate(1)) \
+    { \
+        new (&(ptr_->t)) element_type(BOOST_PP_ENUM_PARAMS(N,t)); \
+        ptr_->count = 1; \
+    }
+    BOOST_PP_REPEAT_FROM_TO(2,11,CODE,_)
+#undef CODE
+#define CODE(Z,N,_) template <class F,BOOST_PP_ENUM_PARAMS(N,class T)> \
+    Handle_for(Eval_functor,F const&f,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+      : ptr_(allocator.allocate(1)) \
+    { \
+        new (&(ptr_->t)) element_type(f(BOOST_PP_ENUM_PARAMS(N,t))); \
+        ptr_->count = 1; \
+    }
+    BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+    template <class F>
+    Handle_for(Eval_functor,F const&f)
+      : ptr_(allocator.allocate(1))
+    {
+        new (&(ptr_->t)) element_type(f());
+        ptr_->count = 1;
+    }
+#endif // CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
+
+    Handle_for(const Handle_for& h)
+      : ptr_(h.ptr_)
+    {
+        ++(ptr_->count);
+    }
+
+    Handle_for&
+    operator=(const Handle_for& h)
+    {
+        Handle_for tmp = h;
+        swap(tmp);
+        return *this;
+    }
+
+    Handle_for&
+    operator=(const element_type &t)
+    {
+        if (is_shared())
+            *this = Handle_for(t);
+        else
+            ptr_->t = t;
+
+        return *this;
+    }
+
+#ifndef CGAL_CFG_NO_CPP0X_RVALUE_REFERENCE
+    // Note : I don't see a way to make a useful move constructor, apart
+    //        from e.g. using NULL as a ptr value, but this is drastic.
+
+    Handle_for&
+    operator=(Handle_for && h)
+    {
+        swap(h);
+        return *this;
+    }
+
+    Handle_for&
+    operator=(element_type && t)
+    {
+        if (is_shared())
+            *this = Handle_for(std::move(t));
+        else
+            ptr_->t = std::move(t);
+
+        return *this;
+    }
+#endif
+
+    ~Handle_for()
+    {
+      if (! is_shared() ) {
+          allocator.destroy( ptr_);
+          allocator.deallocate( ptr_, 1);
+      }
+      else
+	  --(ptr_->count);
+    }
+
+    void
+    initialize_with(const element_type& t)
+    {
+        // kept for backward compatibility.  Use operator=(t) instead.
+        *this = t;
+    }
+
+    Id_type id() const { return Ptr() - static_cast<T const*>(0); }
+    
+    bool identical(const Handle_for& h) const { return Ptr() == h.Ptr(); }
+
+
+    // Ptr() is the "public" access to the pointer to the object.
+    // The non-const version asserts that the instance is not shared.
+    const element_type *
+    Ptr() const
+    {
+       return &(ptr_->t);
+    }
+
+    /*
+    // The assertion triggers in a couple of places, so I comment it for now.
+    T *
+    Ptr()
+    {
+      CGAL_assertion(!is_shared());
+      return &(ptr_->t);
+    }
+    */
+
+    bool
+    is_shared() const
+    {
+	return ptr_->count > 1;
+    }
+
+    bool
+    unique() const
+    {
+	return !is_shared();
+    }
+
+    long
+    use_count() const
+    {
+	return ptr_->count;
+    }
+
+    void
+    swap(Handle_for& h)
+    {
+      std::swap(ptr_, h.ptr_);
+    }
+
+protected:
+
+    void
+    copy_on_write()
+    {
+      if ( is_shared() )
+      {
+        pointer_ tmp_ptr = allocator.allocate(1);
+        new (&(tmp_ptr->t)) element_type(ptr_->t);
+        tmp_ptr->count = 1;
+        --(ptr_->count);
+        ptr_ = tmp_ptr;
+      }
+    }
+
+    // ptr() is the protected access to the pointer.  Both const and non-const.
+    // Redundant with Ptr().
+    element_type *
+    ptr()
+    { return &(ptr_->t); }
+
+    const element_type *
+    ptr() const
+    { return &(ptr_->t); }
+};
+
+
+template <class T, class Allocator>
+typename Handle_for<T, Allocator>::Allocator
+Handle_for<T, Allocator>::allocator;
+
+template <class T, class Allocator>
+inline
+void
+swap(Handle_for<T, Allocator> &h1, Handle_for<T, Allocator> &h2)
+{
+    h1.swap(h2);
+}
+
+template <class T, class Allocator>
+inline
+bool
+identical(const Handle_for<T, Allocator> &h1,
+          const Handle_for<T, Allocator> &h2)
+{
+    return h1.identical(h2);
+}
+
+template <class T> inline bool identical(const T &t1, const T &t2) { return &t1 == &t2; }
+
+template <class T, class Allocator>
+inline
+const T&
+get(const Handle_for<T, Allocator> &h)
+{
+    return *(h.Ptr());
+}
+
+template <class T>
+inline
+const T&
+get(const T &t)
+{
+    return t;
+}
+
+} //namespace CGAL
+
+#if defined(BOOST_MSVC)
+#  pragma warning(pop)
+#endif
+
+#endif // CGAL_HANDLE_FOR_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_LA_base.h

@@ -0,0 +1,135 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_LA_BASE_H
+#define CGAL_KERNEL_D_CARTESIAN_LA_BASE_H
+
+#include <CGAL/basic.h>
+#include <CGAL/Origin.h>
+
+#include <CGAL/representation_tags.h>
+#include <CGAL/functor_tags.h>
+#include <CGAL/Uncertain.h>
+#include <CGAL/typeset.h>
+#include <CGAL/Kernel_d/Dimension_base.h>
+#include <CGAL/Kernel_d/Cartesian_LA_functors.h>
+#include <CGAL/Vector/array.h>
+#ifdef CGAL_EIGEN3_ENABLED
+#include <CGAL/LA_eigen/LA.h>
+#else
+#include <CGAL/LA_default/LA.h>
+#endif
+
+namespace CGAL {
+
+template < typename FT_, typename Dim_,
+#if 0
+	 typename Vec_=Array_vector<FT_, Dim_>,
+#else
+	 typename Vec_=LA_eigen<FT_, Dim_>,
+#endif
+	 typename LA_=LA_eigen<FT_,Dim_> >
+  /* Default LA to Vec or to LA_eigen? */
+struct Cartesian_LA_base_d : public Dimension_base<Dim_>
+{
+    typedef Cartesian_LA_base_d<FT_,Dim_>               Self;
+    typedef Cartesian_tag                               Rep_tag;
+    typedef Cartesian_tag                               Kernel_tag;
+    typedef Dim_              Default_ambient_dimension;
+    typedef Dim_              Max_ambient_dimension;
+    typedef LA_               LA;
+
+    typedef Vec_     LA_vector;
+    typedef typename LA_vector::Vector Point;
+    typedef typename LA_vector::Vector Vector;
+    typedef typename LA_vector::Vector Vector_;
+    typedef typename LA_vector::Construct_vector Constructor;
+    typedef typename LA_vector::Vector_const_iterator Point_cartesian_const_iterator;
+    typedef typename LA_vector::Vector_const_iterator Vector_cartesian_const_iterator;
+
+    template<class, class=void> struct Type {};
+    template<class D> struct Type< Point_tag, D> { typedef Vector_ type; };
+    template<class D> struct Type<Vector_tag, D> { typedef Vector_ type; };
+    template<class D> struct Type<    FT_tag, D> { typedef     FT_ type; };
+    template<class D> struct Type<    RT_tag, D> { typedef     FT_ type; };
+
+    typedef typeset<Point_tag>
+      ::add<Vector_tag>::type
+    // FIXME: Segment has nothing to do here.
+      ::add<Segment_tag>::type
+      Object_list;
+
+    typedef typeset< Point_cartesian_const_iterator_tag>::type
+      ::add<Vector_cartesian_const_iterator_tag>::type
+      Iterator_list;
+
+    template<class, class=void, bool=true> struct Functor {
+	    typedef Null_functor type;
+    };
+    template<class D> struct Functor<Construct_ttag<Vector_tag>,D> {
+	    typedef CartesianDVectorBase::Construct_LA_vector<Self,Null_vector> type;
+    };
+    template<class D> struct Functor<Construct_ttag<Point_tag>,D> {
+	    typedef CartesianDVectorBase::Construct_LA_vector<Self,Origin> type;
+    };
+    template<class D> struct Functor<Construct_ttag<Point_cartesian_const_iterator_tag>,D> {
+	    typedef CartesianDVectorBase::Construct_cartesian_const_iterator<Self> type;
+    };
+    template<class D> struct Functor<Construct_ttag<Vector_cartesian_const_iterator_tag>,D> {
+	    typedef CartesianDVectorBase::Construct_cartesian_const_iterator<Self> type;
+    };
+    template<class D> struct Functor<Sum_of_vectors_tag,D,
+      LA_vector::template Property<Has_vector_plus_minus_tag>::value> {
+	    typedef CartesianDVectorBase::Sum_of_vectors<Self> type;
+    };
+    template<class D> struct Functor<Difference_of_vectors_tag,D,
+      LA_vector::template Property<Has_vector_plus_minus_tag>::value> {
+	    typedef CartesianDVectorBase::Difference_of_vectors<Self> type;
+    };
+    template<class D> struct Functor<Opposite_vector_tag,D,
+      LA_vector::template Property<Has_vector_plus_minus_tag>::value> {
+	    typedef CartesianDVectorBase::Opposite_vector<Self> type;
+    };
+    template<class D> struct Functor<Midpoint_tag,D,
+      LA_vector::template Property<Has_vector_plus_minus_tag>::value &&
+      LA_vector::template Property<Has_vector_scalar_ops_tag>::value> {
+	    typedef CartesianDVectorBase::Midpoint<Self> type;
+    };
+    template<class D> struct Functor<Compute_point_cartesian_coordinate_tag,D> {
+	    typedef CartesianDVectorBase::Compute_cartesian_coordinate<Self> type;
+    };
+    template<class D> struct Functor<Compute_vector_cartesian_coordinate_tag,D> {
+	    typedef CartesianDVectorBase::Compute_cartesian_coordinate<Self> type;
+    };
+    template<class D> struct Functor<Point_dimension_tag,D> {
+	    typedef CartesianDVectorBase::PV_dimension<Self> type;
+    };
+    template<class D> struct Functor<Vector_dimension_tag,D> {
+	    typedef CartesianDVectorBase::PV_dimension<Self> type;
+    };
+    template<class D> struct Functor<Orientation_of_vectors_tag,D,
+      LA_vector::template Property<Has_determinant_of_iterator_to_vectors_tag>::value> {
+	    typedef CartesianDVectorBase::Orientation_of_vectors<Self> type;
+    };
+    template<class D> struct Functor<Orientation_of_points_tag,D,
+      LA_vector::template Property<Has_determinant_of_iterator_to_points_tag>::value> {
+	    typedef CartesianDVectorBase::Orientation_of_points<Self> type;
+    };
+    template<class D> struct Functor<Scalar_product_tag,D,
+      LA_vector::template Property<Has_dot_product_tag>::value> {
+	    typedef CartesianDVectorBase::Scalar_product<Self> type;
+    };
+    template<class D> struct Functor<Squared_distance_to_origin_tag,D,
+      LA_vector::template Property<Stores_squared_norm_tag>::value> {
+	    typedef CartesianDVectorBase::Squared_distance_to_origin_stored<Self> type;
+    };
+    template<class D> struct Functor<Squared_distance_to_origin_tag,D,
+      !LA_vector::template Property<Stores_squared_norm_tag>::value &&
+      LA_vector::template Property<Has_dot_product_tag>::value> {
+	    typedef CartesianDVectorBase::Squared_distance_to_origin_via_dotprod<Self> type;
+    };
+
+    CGAL_CONSTEXPR Cartesian_LA_base_d(){}
+    CGAL_CONSTEXPR Cartesian_LA_base_d(int d):Dimension_base<Dim_>(d){}
+};
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_CARTESIAN_LA_BASE_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_LA_functors.h

@@ -0,0 +1,313 @@
+#ifndef CGAL_CARTESIAN_LA_FUNCTORS_H
+#define CGAL_CARTESIAN_LA_FUNCTORS_H
+
+#include <CGAL/marcutils.h>
+#include <CGAL/is_iterator.h>
+#include <CGAL/argument_swaps.h>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/store_kernel.h>
+
+namespace CGAL {
+namespace CartesianDVectorBase {
+#ifndef CGAL_CXX0X
+namespace internal {
+template<class R_,int dim_> struct Construct_LA_vector_ {
+	struct Never_use {};
+	void operator()(Never_use)const;
+};
+#define CODE(Z,N,_) template<class R> struct Construct_LA_vector_<R,N> { \
+	typedef typename R::Constructor Constructor; \
+	typedef typename Get_type<R, RT_tag>::type RT; \
+	typedef typename R::Vector_ result_type; \
+	result_type operator() \
+	(BOOST_PP_ENUM_PARAMS(N,RT const& t)) const { \
+	return typename Constructor::Values()(BOOST_PP_ENUM_PARAMS(N,t)); \
+	} \
+	result_type operator() \
+	(BOOST_PP_ENUM_PARAMS(BOOST_PP_INC(N),RT const& t)) const { \
+	return typename Constructor::Values_divide()(t##N,BOOST_PP_ENUM_PARAMS(N,t)); \
+	} \
+	};
+BOOST_PP_REPEAT_FROM_TO(2, 11, CODE, _ )
+#undef CODE
+}
+#endif
+
+template<class R_,class Zero_> struct Construct_LA_vector
+: private Store_kernel<R_>
+#ifndef CGAL_CXX0X
+, public internal::Construct_LA_vector_<R_,R_::Default_ambient_dimension::value>
+#endif
+{
+	//CGAL_FUNCTOR_INIT_IGNORE(Construct_LA_vector)
+	CGAL_FUNCTOR_INIT_STORE(Construct_LA_vector)
+	typedef R_ R;
+	typedef typename R::Constructor Constructor;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, FT_tag>::type FT;
+	typedef typename R::Vector_ result_type;
+	typedef typename R_::Default_ambient_dimension Dimension;
+	static const int static_dim=Dimension::value;
+	result_type operator()(int d)const{
+		CGAL_assertion(check_dimension_eq(d,this->kernel().dimension()));
+		return typename Constructor::Dimension()(d);
+	}
+	result_type operator()()const{
+		return typename Constructor::Dimension()(this->kernel().dimension());
+	}
+	result_type operator()(Zero_ const&)const{
+		return typename Constructor::Dimension()(this->kernel().dimension());
+	}
+	result_type operator()(result_type const& v)const{
+		return v;
+	}
+#ifdef CGAL_CXX0X
+	result_type operator()(result_type&& v)const{
+		return std::move(v);
+	}
+#endif
+#ifdef CGAL_CXX0X
+	template<class...U>
+	typename std::enable_if<Constructible_from_each<RT,U...>::value &&
+		(sizeof...(U)==static_dim), result_type>::type
+	operator()(U&&...u)const{
+		return typename Constructor::Values()(std::forward<U>(u)...);
+	}
+	//template<class...U,class=typename std::enable_if<Constructible_from_each<RT,U...>::value>::type,class=typename std::enable_if<(sizeof...(U)==static_dim+1)>::type,class=void>
+	template<class...U>
+	typename std::enable_if<Constructible_from_each<RT,U...>::value &&
+		(sizeof...(U)==static_dim+1), result_type>::type
+	operator()(U&&...u)const{
+		return Apply_to_last_then_rest()(typename Constructor::Values_divide(),std::forward<U>(u)...);
+	}
+#else
+	using internal::Construct_LA_vector_<R_,R::Default_ambient_dimension::value>::operator();
+#endif
+	template<class Iter> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::forward_iterator_tag>,result_type>::type operator()
+		(Iter f,Iter g,Cartesian_tag t)const
+	{
+		return this->operator()(std::distance(f,g),f,g,t);
+	}
+	template<class Iter> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::forward_iterator_tag>,result_type>::type operator()
+		(int d,Iter f,Iter g,Cartesian_tag)const
+	{
+		CGAL_assertion(d==std::distance(f,g));
+		CGAL_assertion(check_dimension_eq(d,this->kernel().dimension()));
+		return typename Constructor::Iterator()(d,f,g);
+	}
+	template<class Iter> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::bidirectional_iterator_tag>,result_type>::type operator()
+		(Iter f,Iter g,Homogeneous_tag)const
+	{
+		--g;
+		return this->operator()(std::distance(f,g),f,g,*g);
+	}
+	template<class Iter> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::bidirectional_iterator_tag>,result_type>::type operator()
+		(int d,Iter f,Iter g,Homogeneous_tag)const
+	{
+		--g;
+		return this->operator()(d,f,g,*g);
+	}
+	template<class Iter> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::forward_iterator_tag>,result_type>::type operator()
+		(Iter f,Iter g)const
+	{
+	  // Shouldn't it try comparing dist(f,g) to the dimension if it is known?
+		return this->operator()(f,g,typename R::Rep_tag());
+	}
+	template<class Iter> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::forward_iterator_tag>,result_type>::type operator()
+		(int d,Iter f,Iter g)const
+	{
+		return this->operator()(d,f,g,typename R::Rep_tag());
+	}
+
+	// Last homogeneous coordinate given separately
+	template<class Iter,class NT> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::forward_iterator_tag>,result_type>::type operator()
+		(int d,Iter f,Iter g,NT const&l)const
+	{
+		CGAL_assertion(d==std::distance(f,g));
+		CGAL_assertion(check_dimension_eq(d,this->kernel().dimension()));
+		// RT? better be safe for now
+		return typename Constructor::Iterator()(d,CGAL::make_transforming_iterator(f,Divide<FT,NT>(l)),CGAL::make_transforming_iterator(g,Divide<FT,NT>(l)));
+	}
+	template<class Iter,class NT> inline
+	  typename boost::enable_if<is_iterator_type<Iter,std::forward_iterator_tag>,result_type>::type operator()
+		(Iter f,Iter g,NT const&l)const
+	{
+		return this->operator()(std::distance(f,g),f,g,l);
+	}
+};
+
+template<class R_> struct Compute_cartesian_coordinate {
+	CGAL_FUNCTOR_INIT_IGNORE(Compute_cartesian_coordinate)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename R::Vector_ first_argument_type;
+	typedef int second_argument_type;
+	typedef Tag_true Is_exact;
+#ifdef CGAL_CXX0X
+	typedef decltype(std::declval<const first_argument_type>()[0]) result_type;
+#else
+	typedef RT const& result_type;
+	// RT const& doesn't work with some LA (Eigen2 for instance) so we
+	// should use plain RT or find a way to detect this.
+#endif
+
+	result_type operator()(first_argument_type const& v,int i)const{
+		return v[i];
+	}
+};
+
+template<class R_> struct Construct_cartesian_const_iterator {
+	CGAL_FUNCTOR_INIT_IGNORE(Construct_cartesian_const_iterator)
+	typedef R_ R;
+	typedef typename R::Vector_ argument_type;
+	typedef typename R::LA_vector S_;
+	typedef typename R::Point_cartesian_const_iterator result_type;
+	// same as Vector
+	typedef Tag_true Is_exact;
+
+	result_type operator()(argument_type const& v,Begin_tag)const{
+		return S_::vector_begin(v);
+	}
+	result_type operator()(argument_type const& v,End_tag)const{
+		return S_::vector_end(v);
+	}
+};
+
+template<class R_> struct Midpoint {
+	CGAL_FUNCTOR_INIT_IGNORE(Midpoint)
+	typedef R_ R;
+	typedef typename Get_type<R, Point_tag>::type first_argument_type;
+	typedef typename Get_type<R, Point_tag>::type second_argument_type;
+	typedef typename Get_type<R, Point_tag>::type result_type;
+
+	result_type operator()(result_type const& a, result_type const& b)const{
+		return (a+b)/2;
+	}
+};
+
+template<class R_> struct Sum_of_vectors {
+	CGAL_FUNCTOR_INIT_IGNORE(Sum_of_vectors)
+	typedef R_ R;
+	typedef typename Get_type<R, Vector_tag>::type first_argument_type;
+	typedef typename Get_type<R, Vector_tag>::type second_argument_type;
+	typedef typename Get_type<R, Vector_tag>::type result_type;
+
+	result_type operator()(result_type const& a, result_type const& b)const{
+		return a+b;
+	}
+};
+
+template<class R_> struct Difference_of_vectors {
+	CGAL_FUNCTOR_INIT_IGNORE(Difference_of_vectors)
+	typedef R_ R;
+	typedef typename Get_type<R, Vector_tag>::type first_argument_type;
+	typedef typename Get_type<R, Vector_tag>::type second_argument_type;
+	typedef typename Get_type<R, Vector_tag>::type result_type;
+
+	result_type operator()(result_type const& a, result_type const& b)const{
+		return a-b;
+	}
+};
+
+template<class R_> struct Opposite_vector {
+	CGAL_FUNCTOR_INIT_IGNORE(Opposite_vector)
+	typedef R_ R;
+	typedef typename Get_type<R, Vector_tag>::type result_type;
+	typedef typename Get_type<R, Vector_tag>::type argument_type;
+
+	result_type operator()(result_type const& v)const{
+		return -v;
+	}
+};
+
+template<class R_> struct Scalar_product {
+	CGAL_FUNCTOR_INIT_IGNORE(Scalar_product)
+	typedef R_ R;
+	typedef typename R::LA_vector LA;
+	typedef typename Get_type<R, RT_tag>::type result_type;
+	typedef typename Get_type<R, Vector_tag>::type first_argument_type;
+	typedef typename Get_type<R, Vector_tag>::type second_argument_type;
+
+	result_type operator()(first_argument_type const& a, second_argument_type const& b)const{
+		return LA::dot_product(a,b);
+	}
+};
+
+template<class R_> struct Squared_distance_to_origin_stored {
+	CGAL_FUNCTOR_INIT_IGNORE(Squared_distance_to_origin_stored)
+	typedef R_ R;
+	typedef typename R::LA_vector LA;
+	typedef typename Get_type<R, RT_tag>::type result_type;
+	typedef typename Get_type<R, Point_tag>::type argument_type;
+
+	result_type operator()(argument_type const& a)const{
+		return LA::squared_norm(a);
+	}
+};
+
+template<class R_> struct Squared_distance_to_origin_via_dotprod {
+	CGAL_FUNCTOR_INIT_IGNORE(Squared_distance_to_origin_via_dotprod)
+	typedef R_ R;
+	typedef typename R::LA_vector LA;
+	typedef typename Get_type<R, RT_tag>::type result_type;
+	typedef typename Get_type<R, Point_tag>::type argument_type;
+
+	result_type operator()(argument_type const& a)const{
+		return LA::dot_product(a,a);
+	}
+};
+
+template<class R_> struct Orientation_of_vectors {
+	CGAL_FUNCTOR_INIT_IGNORE(Orientation_of_vectors)
+	typedef R_ R;
+	typedef typename R::Vector_cartesian_const_iterator first_argument_type;
+	typedef typename R::Vector_cartesian_const_iterator second_argument_type;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename R::LA_vector LA;
+
+	template<class Iter>
+	result_type operator()(Iter const& f, Iter const& e) const {
+		return LA::determinant_of_iterators_to_vectors(f,e);
+	}
+};
+
+template<class R_> struct Orientation_of_points {
+	CGAL_FUNCTOR_INIT_IGNORE(Orientation_of_points)
+	typedef R_ R;
+	typedef typename R::Point_cartesian_const_iterator first_argument_type;
+	typedef typename R::Point_cartesian_const_iterator second_argument_type;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename R::LA_vector LA;
+
+	template<class Iter>
+	result_type operator()(Iter const& f, Iter const& e) const {
+		return LA::determinant_of_iterators_to_points(f,e);
+	}
+};
+
+template<class R_> struct PV_dimension {
+	CGAL_FUNCTOR_INIT_IGNORE(PV_dimension)
+	typedef R_ R;
+	typedef typename R::Vector_ argument_type;
+	typedef int result_type;
+	typedef typename R::LA_vector LA;
+	typedef Tag_true Is_exact;
+
+	template<class T>
+	result_type operator()(T const& v) const {
+		return LA::size_of_vector(v);
+	}
+};
+
+
+}
+} // namespace CGAL
+#endif // CGAL_CARTESIAN_LA_FUNCTORS_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_base.h

@@ -0,0 +1,21 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_BASE_H
+#define CGAL_KERNEL_D_CARTESIAN_BASE_H
+
+#include <CGAL/basic.h>
+#include <CGAL/Kernel_d/Cartesian_complete.h>
+#include <CGAL/Kernel_d/Cartesian_LA_base.h>
+
+namespace CGAL {
+#define CGAL_BASE \
+  Cartesian_LA_base_d< FT_, Dim_ >
+template < typename FT_, typename Dim_, typename Derived_=Default>
+struct Cartesian_base_d : public CGAL_BASE
+{
+    CGAL_CONSTEXPR Cartesian_base_d(){}
+    CGAL_CONSTEXPR Cartesian_base_d(int d):CGAL_BASE(d){}
+};
+#undef CGAL_BASE
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_CARTESIAN_BASE_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_change_FT.h

@@ -0,0 +1,98 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_CHANGE_FT_H
+#define CGAL_KERNEL_D_CARTESIAN_CHANGE_FT_H
+
+#include <CGAL/basic.h>
+#include <CGAL/NT_converter.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/Kernel_d/Cartesian_complete.h>
+
+namespace CGAL {
+
+template < typename Base_, typename FT_, typename LA_=CGAL::LA_eigen<FT_,typename Base_::Default_ambient_dimension> >
+struct Cartesian_change_FT_base : public
+	Base_
+{
+    CGAL_CONSTEXPR Cartesian_change_FT_base(){}
+    CGAL_CONSTEXPR Cartesian_change_FT_base(int d):Base_(d){}
+
+    typedef Cartesian_change_FT_base Self;
+    typedef Base_ Kernel_base;
+    typedef LA_ LA;
+
+    template <class T, class D=void> struct Type : Inherit_type<Base_, T> {};
+    template <class D> struct Type <FT_tag, D> { typedef FT_ type; };
+    template <class D> struct Type <RT_tag, D> { typedef FT_ type; };
+
+    typedef NT_converter<typename Get_type<Kernel_base, FT_tag>::type,FT_> FT_converter;
+    typedef transforming_iterator<FT_converter,typename Kernel_base::Point_cartesian_const_iterator> Point_cartesian_const_iterator;
+    typedef transforming_iterator<FT_converter,typename Kernel_base::Vector_cartesian_const_iterator> Vector_cartesian_const_iterator;
+    //FIXME: use Iterator_list!
+    /*
+    template<class T,bool=BOOSTD is_same<typename iterator_tag_traits<T>::value_tag,FT_tag>::value>
+    struct Iterator : Get_type<Kernel_base,T> {};
+    template<class T> struct Iterator<T,true> {
+      typedef transforming_iterator<FT_converter,typename Get_type<Kernel_base,T>::type> type;
+    };
+    */
+
+    template<class Tag_,class Type_>
+    struct Construct_cartesian_const_iterator_ {
+	    typedef typename Get_functor<Kernel_base, Tag_>::type Functor_base;
+	    Construct_cartesian_const_iterator_(){}
+	    Construct_cartesian_const_iterator_(Self const&r):f(r){}
+	    Functor_base f;
+	    typedef Type_ result_type;
+	    template<class T>
+	    result_type operator()(T const& v, Begin_tag)const{
+		    return make_transforming_iterator(f(v,Begin_tag()),FT_converter());
+	    }
+	    template<class T>
+	    result_type operator()(T const& v, End_tag)const{
+		    return make_transforming_iterator(f(v,End_tag()),FT_converter());
+	    }
+    };
+    typedef Construct_cartesian_const_iterator_<Construct_ttag<Point_cartesian_const_iterator_tag>,Point_cartesian_const_iterator> Construct_point_cartesian_const_iterator;
+    typedef Construct_cartesian_const_iterator_<Construct_ttag<Vector_cartesian_const_iterator_tag>,Vector_cartesian_const_iterator> Construct_vector_cartesian_const_iterator;
+
+    template<class Tag_>
+    struct Compute_cartesian_coordinate {
+	    typedef typename Get_functor<Kernel_base, Tag_>::type Functor_base;
+	    Compute_cartesian_coordinate(){}
+	    Compute_cartesian_coordinate(Self const&r):f(r){}
+	    Functor_base f;
+	    typedef FT_ result_type;
+	    template<class Obj_>
+	    result_type operator()(Obj_ const& v,int i)const{
+		    return FT_converter()(f(v,i));
+	    }
+    };
+
+    template<class T,class U=void,class=typename Get_functor_category<Cartesian_change_FT_base,T>::type> struct Functor :
+	    Inherit_functor<Kernel_base,T,U> { };
+    template<class T,class U> struct Functor<T,U,Compute_tag> { };
+    template<class T,class U> struct Functor<T,U,Predicate_tag> { };
+    template<class D> struct Functor<Compute_point_cartesian_coordinate_tag,D,Compute_tag> {
+	    typedef Compute_cartesian_coordinate<Compute_point_cartesian_coordinate_tag> type;
+    };
+    template<class D> struct Functor<Compute_vector_cartesian_coordinate_tag,D,Compute_tag> {
+	    typedef Compute_cartesian_coordinate<Compute_vector_cartesian_coordinate_tag> type;
+    };
+    template<class D> struct Functor<Construct_ttag<Point_cartesian_const_iterator_tag>,D,Construct_iterator_tag> {
+	    typedef Construct_point_cartesian_const_iterator type;
+    };
+    template<class D> struct Functor<Construct_ttag<Vector_cartesian_const_iterator_tag>,D,Construct_iterator_tag> {
+	    typedef Construct_vector_cartesian_const_iterator type;
+    };
+};
+
+template < typename Base_, typename FT_>
+struct Cartesian_change_FT : public
+	Cartesian_change_FT_base<Base_,FT_>
+{
+    CGAL_CONSTEXPR Cartesian_change_FT(){}
+    CGAL_CONSTEXPR Cartesian_change_FT(int d):Cartesian_change_FT_base<Base_,FT_>(d){}
+};
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_CARTESIAN_CHANGE_FT_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_complete.h

@@ -0,0 +1,14 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_COMPLETE_H
+#define CGAL_KERNEL_D_CARTESIAN_COMPLETE_H
+
+#include <CGAL/Kernel_d/function_objects_cartesian.h>
+#include <CGAL/Kernel_d/Cartesian_per_dimension.h>
+#include <CGAL/Kernel_d/Types/Segment.h>
+#include <CGAL/Kernel_d/Types/Sphere.h>
+#include <CGAL/Kernel_d/Types/Hyperplane.h>
+#include <CGAL/Kernel_d/Types/Aff_transformation.h>
+#include <CGAL/Kernel_d/Types/Line.h>
+#include <CGAL/Kernel_d/Types/Ray.h>
+#include <CGAL/Kernel_d/Types/Iso_box.h>
+
+#endif // CGAL_KERNEL_D_CARTESIAN_COMPLETE_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_filter_K.h

@@ -0,0 +1,49 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_FILTER_K_H
+#define CGAL_KERNEL_D_CARTESIAN_FILTER_K_H
+
+#include <CGAL/basic.h>
+#include <CGAL/Kernel_d/KernelD_converter.h>
+#include <CGAL/Filtered_predicate2.h>
+#include <boost/mpl/if.hpp>
+
+namespace CGAL {
+
+template < typename Base_, typename AK_, typename EK_ >
+struct Cartesian_filter_K : public Base_,
+	private Store_kernel<AK_>, private Store_kernel2<EK_>
+{
+    CGAL_CONSTEXPR Cartesian_filter_K(){}
+    CGAL_CONSTEXPR Cartesian_filter_K(int d):Base_(d){}
+    //FIXME: or do we want an instance of AK and EK belonging to this kernel,
+    //instead of a reference to external ones?
+    CGAL_CONSTEXPR Cartesian_filter_K(AK_ const&a,EK_ const&b):Base_(),Store_kernel<AK_>(a),Store_kernel2<EK_>(b){}
+    CGAL_CONSTEXPR Cartesian_filter_K(int d,AK_ const&a,EK_ const&b):Base_(d),Store_kernel<AK_>(a),Store_kernel2<EK_>(b){}
+    typedef Base_ Kernel_base;
+    typedef AK_ AK;
+    typedef EK_ EK;
+    typedef typename Store_kernel<AK_>::reference_type AK_rt;
+    AK_rt approximate_kernel()const{return this->kernel();}
+    typedef typename Store_kernel2<EK_>::reference2_type EK_rt;
+    EK_rt exact_kernel()const{return this->kernel2();}
+
+    //TODO: C2A/C2E could be able to convert *this into this->kernel() or this->kernel2().
+    typedef KernelD_converter<Kernel_base,AK> C2A;
+    typedef KernelD_converter<Kernel_base,EK> C2E;
+
+    template<class T,class D=void,class=typename Get_functor_category<Cartesian_filter_K,T>::type> struct Functor :
+	    Inherit_functor<Kernel_base,T,D> {};
+    template<class T,class D> struct Functor<T,D,Predicate_tag> {
+	    typedef typename Get_functor<AK, T>::type AP;
+	    typedef typename Get_functor<EK, T>::type EP;
+	    typedef Filtered_predicate2<EP,AP,C2E,C2A> type;
+    };
+// TODO:
+//    template<class T> struct Functor<T,No_filter_tag,Predicate_tag> :
+//	    Kernel_base::template Functor<T,No_filter_tag> {};
+// TODO:
+// detect when Less_cartesian_coordinate doesn't need filtering
+};
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_CARTESIAN_FILTER_K_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_filter_NT.h

@@ -0,0 +1,74 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_FILTER_NT_H
+#define CGAL_KERNEL_D_CARTESIAN_FILTER_NT_H
+
+#include <CGAL/basic.h>
+#include <CGAL/Kernel_d/Cartesian_change_FT.h>
+#include <CGAL/internal/Exact_type_selector.h>
+
+namespace CGAL {
+
+template < typename Base_ >
+struct Cartesian_filter_NT : public Base_
+{
+    CGAL_CONSTEXPR Cartesian_filter_NT(){}
+    CGAL_CONSTEXPR Cartesian_filter_NT(int d):Base_(d){}
+    typedef Base_ Kernel_base;
+    typedef Cartesian_change_FT<Kernel_base,Interval_nt_advanced> K1;
+    typedef typename internal::Exact_field_selector<typename Get_type<Kernel_base, FT_tag>::type>::Type  Exact_nt;
+    typedef Cartesian_change_FT<Kernel_base,Exact_nt> K2;
+
+    template<class T,class D=void,class=typename Get_functor_category<Cartesian_filter_NT,T>::type> struct Functor :
+       Inherit_functor<Kernel_base,T,D> {};
+    template<class T,class D> struct Functor<T,D,Predicate_tag> {
+	    struct type {
+		    //TODO: use compression (derive from a compressed_pair?)
+		    typedef typename Get_functor<K1, T>::type P1; P1 p1;
+		    typedef typename Get_functor<K2, T>::type P2; P2 p2;
+		    typedef typename P2::result_type result_type;
+		    type(){}
+		    type(Cartesian_filter_NT const&k):p1(reinterpret_cast<K1 const&>(k)),p2(reinterpret_cast<K2 const&>(k)){}
+		    //FIXME: if predicate's constructor takes a kernel as argument, how do we translate that? reinterpret_cast is really ugly and possibly unsafe.
+
+#ifdef CGAL_CXX0X
+		    template<class...U> result_type operator()(U&&...u)const{
+			    {
+			          Protect_FPU_rounding<true> p;
+				  try {
+					  typename P1::result_type res=p1(u...); // don't forward as u may be reused
+					  if(is_certain(res)) return get_certain(res);
+				  } catch (Uncertain_conversion_exception) {}
+			    }
+			    return p2(std::forward<U>(u)...);
+		    }
+#else
+		    result_type operator()()const{ // does it make sense to have 0 argument?
+			    {
+			          Protect_FPU_rounding<true> p;
+				  try {
+					  typename P1::result_type res=p1();
+					  if(is_certain(res)) return get_certain(res);
+				  } catch (Uncertain_conversion_exception) {}
+			    }
+			    return p2();
+		    }
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class T)> result_type operator()(BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t))const{ \
+			    { \
+			          Protect_FPU_rounding<true> p; \
+				  try { \
+					  typename P1::result_type res=p1(BOOST_PP_ENUM_PARAMS(N,t)); \
+					  if(is_certain(res)) return get_certain(res); \
+				  } catch (Uncertain_conversion_exception) {} \
+			    } \
+			    return p2(BOOST_PP_ENUM_PARAMS(N,t)); \
+		    }
+		    BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+
+#endif
+	    };
+    };
+};
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_CARTESIAN_FILTER_NT_H

NewKernel_d/include/CGAL/Kernel_d/Cartesian_per_dimension.h

@@ -0,0 +1,14 @@
+#ifndef CGAL_KD_CARTESIAN_PER_DIM_H
+#define CGAL_KD_CARTESIAN_PER_DIM_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/predicates/sign_of_determinant.h>
+
+// Should probably disappear.
+
+namespace CGAL {
+template <class Dim_, class R_, class Derived_>
+struct Cartesian_per_dimension : public R_ {};
+}
+
+#endif

NewKernel_d/include/CGAL/Kernel_d/Cartesian_static_filters.h

@@ -0,0 +1,76 @@
+#ifndef CGAL_KD_CARTESIAN_STATIC_FILTERS_H
+#define CGAL_KD_CARTESIAN_STATIC_FILTERS_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/internal/Static_filters/tools.h> // bug, should be included by the next one
+#include <CGAL/internal/Static_filters/Orientation_2.h>
+#include <boost/type_traits/conditional.hpp>
+
+namespace CGAL {
+namespace SFA { // static filter adapter
+// Note that this would be quite a bit simpler without stateful kernels
+template <class Base_,class R_> struct Orientation_of_points_2 : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Orientation_of_points_2);
+	typedef typename Get_type<R_, Point_tag>::type	Point;
+	typedef typename Get_type<R_, Orientation_tag>::type result_type;
+	typedef typename Get_type<R_, FT_tag>::type FT;
+	typedef typename Get_functor<R_, Compute_point_cartesian_coordinate_tag>::type CC;
+	typedef typename Get_functor<Base_, Orientation_of_points_tag>::type Orientation_base;
+	// TODO: Move this out for easy reuse
+	struct Adapter {
+		struct Point_2 {
+			R_ const&r; CC const&c; Point const& p;
+			Point_2(R_ const&r_, CC const&c_, Point const&p_):r(r_),c(c_),p(p_){}
+			// use result_of instead?
+			typename CC::result_type x()const{return c(p,0);}
+			typename CC::result_type y()const{return c(p,1);}
+		};
+		struct Vector_2 {};
+		struct Circle_2 {};
+		struct Orientation_2 {
+			typedef Orientation_of_points_2::result_type result_type;
+			result_type operator()(Point_2 const&A, Point_2 const&B, Point_2 const&C)const{
+				Point const* t[3]={&A.p,&B.p,&C.p};
+				return Orientation_base(A.r)(make_transforming_iterator<Dereference_functor>(t+0),make_transforming_iterator<Dereference_functor>(t+3));
+			}
+		};
+	};
+	template<class Iter> result_type operator()(Iter f, Iter CGAL_assertion_code(e))const{
+		CC c(this->kernel());
+		Point const& A=*f;
+		Point const& B=*++f;
+		Point const& C=*++f;
+		CGAL_assertion(++f==e);
+		typedef typename Adapter::Point_2 P;
+		return typename internal::Static_filters_predicates::Orientation_2<Adapter>()(P(this->kernel(),c,A),P(this->kernel(),c,B),P(this->kernel(),c,C));
+	}
+};
+}
+
+template <class Dim_ /* should be implicit */, class R_, class Derived_=Default>
+struct Cartesian_static_filters : public R_ {
+  CGAL_CONSTEXPR Cartesian_static_filters(){}
+  CGAL_CONSTEXPR Cartesian_static_filters(int d):R_(d){}
+};
+
+template <class R_, class Derived_>
+struct Cartesian_static_filters<Dimension_tag<2>, R_, Derived_> : public R_ {
+  CGAL_CONSTEXPR Cartesian_static_filters(){}
+  CGAL_CONSTEXPR Cartesian_static_filters(int d):R_(d){}
+	typedef Cartesian_static_filters<Dimension_tag<2>, R_, Derived_> Self;
+	typedef typename Default::Get<Derived_,Self>::type Derived;
+	template <class T, class=void> struct Functor : Inherit_functor<R_, T> {};
+	template <class D> struct Functor <Orientation_of_points_tag,D> {
+		typedef
+			//typename boost::conditional<
+			//boost::is_same<D,No_filter_tag>::value,
+			//typename Get_functor<R_, Orientation_of_points_tag>::type,
+			SFA::Orientation_of_points_2<R_,Derived>
+			//	>::type
+				type;
+	};
+};
+
+}
+
+#endif

NewKernel_d/include/CGAL/Kernel_d/Coaffine.h

@@ -0,0 +1,248 @@
+#ifndef CGAL_KD_COAFFINE_H
+#define CGAL_KD_COAFFINE_H
+#include <vector>
+#include <algorithm>
+#include <iterator>
+#include <CGAL/Dimension.h>
+#include <CGAL/functor_tags.h>
+
+namespace CGAL {
+namespace CartesianDKernelFunctors {
+struct Flat_orientation {
+	std::vector<int> proj;
+	std::vector<int> rest;
+};
+
+// For debugging purposes
+inline std::ostream& operator<< (std::ostream& o, Flat_orientation const& f) {
+  o << "Proj: ";
+  for(std::vector<int>::const_iterator i=f.proj.begin();
+      i!=f.proj.end(); ++i)
+    o << *i << ' ';
+  o << "\nRest: ";
+  for(std::vector<int>::const_iterator i=f.rest.begin();
+      i!=f.rest.end(); ++i)
+    o << *i << ' ';
+  return o << '\n';
+}
+
+namespace internal {
+namespace coaffine {
+template<class Mat>
+inline void debug_matrix(std::ostream& o, Mat const&mat) {
+  for(int i=0;i<mat.rows();++i){
+  for(int j=0;j<mat.cols();++j){
+    o<<mat(i,j)<<' ';
+  }
+  o<<'\n';
+  }
+}
+}
+}
+
+template<class R_> struct Construct_flat_orientation : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Construct_flat_orientation)
+	typedef R_ R;
+	typedef typename Get_type<R, FT_tag>::type FT;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type Dplusone;
+	typedef typename R::LA::template Rebind_dimension<Dynamic_dimension_tag,Dplusone>::Other LA;
+	typedef typename LA::Square_matrix Matrix;
+	typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type CCC;
+	typedef typename Get_functor<R, Point_dimension_tag>::type PD;
+	typedef Flat_orientation result_type;
+
+	// This implementation is going to suck. Maybe we should push the
+	// functionality into LA.
+	template<class Iter>
+	result_type operator()(Iter f, Iter e)const{
+		PD pd (this->kernel());
+		CCC ccc (this->kernel());
+		int dim = pd(*f);
+		Matrix coord (dim+1, dim+1); // use distance(f,e)? This matrix doesn't need to be square.
+		int col = 0;
+		Flat_orientation o;
+		std::vector<int>& proj=o.proj;
+		std::vector<int>& rest=o.rest; rest.reserve(dim+1);
+		for(int i=0; i<dim+1; ++i) rest.push_back(i);
+		for( ; f != e ; ++col, ++f ) {
+			Point const&p=*f;
+			// use a coordinate iterator instead?
+			for(int i=0; i<dim; ++i) coord(col, i) = ccc(p, i);
+			coord(col,dim)=1;
+			int d = proj.size()+1;
+			Matrix m (d, d);
+			// Fill the matrix with what we already have
+			for(int i=0; i<d; ++i)
+			for(int j=0; j<d-1; ++j)
+				m(i,j) = coord(i, proj[j]);
+			// Try to complete with any other coordinate
+			// TODO: iterate on rest by the end, or use a (forward_)list.
+			for(std::vector<int>::iterator it=rest.begin();;++it) {
+				CGAL_assertion(it!=rest.end());
+				for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
+				if(LA::sign_of_determinant(m)!=0) {
+					proj.push_back(*it);
+					rest.erase(it);
+					break;
+				}
+			}
+		}
+		std::sort(proj.begin(),proj.end());
+		return o;
+	}
+};
+
+template<class R_> struct Contained_in_affine_hull : private Store_kernel<R_> {
+        CGAL_FUNCTOR_INIT_STORE(Contained_in_affine_hull)
+        typedef R_ R;
+	typedef typename Get_type<R, FT_tag>::type FT;
+        typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Bool_tag>::type result_type;
+	typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type CCC;
+	typedef typename Get_functor<R, Point_dimension_tag>::type PD;
+	//typedef typename Increment_dimension<typename R::Default_ambient_dimension>::type D1;
+	//typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type D2;
+	//typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
+	typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type Dplusone;
+	typedef typename R::LA::template Rebind_dimension<Dynamic_dimension_tag,Dplusone>::Other LA;
+	typedef typename LA::Square_matrix Matrix;
+
+	// mostly copied from Construct_flat_orientation. TODO: dedup this code.
+        template<class Iter>
+        result_type operator()(Iter f, Iter e, Point const&x) const {
+		PD pd (this->kernel());
+		CCC ccc (this->kernel());
+		int dim=pd(*f);
+		Matrix coord (dim+1, dim+1); // use distance
+		int col = 0;
+		std::vector<int> proj;
+		std::vector<int> rest; rest.reserve(dim+1);
+		for(int i=0; i<dim+1; ++i) rest.push_back(i);
+		for( ; f != e ; ++col, ++f ) {
+			Point const&p=*f;
+			for(int i=0; i<dim; ++i) coord(col, i) = ccc(p, i);
+			coord(col,dim)=1;
+			int d = proj.size()+1;
+			Matrix m (d, d);
+			for(int i=0; i<d; ++i)
+			for(int j=0; j<d-1; ++j)
+				m(i,j) = coord(i, proj[j]);
+			for(std::vector<int>::iterator it=rest.begin();it!=rest.end();++it) {
+				for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
+				if(LA::sign_of_determinant(m)!=0) {
+					proj.push_back(*it);
+					rest.erase(it);
+					break;
+				}
+			}
+		}
+			for(int i=0; i<dim; ++i) coord(col, i) = ccc(x, i);
+			coord(col,dim)=1;
+			int d = proj.size()+1;
+			Matrix m (d, d);
+			for(int i=0; i<d; ++i)
+			for(int j=0; j<d-1; ++j)
+				m(i,j) = coord(i, proj[j]);
+			for(std::vector<int>::iterator it=rest.begin();it!=rest.end();++it) {
+				for(int i=0; i<d; ++i) m(i,d-1) = coord(i, *it);
+				if(LA::sign_of_determinant(m)!=0) return false;
+			}
+			return true;
+        }
+};
+
+template<class R_> struct In_flat_orientation : private Store_kernel<R_> {
+        CGAL_FUNCTOR_INIT_STORE(In_flat_orientation)
+        typedef R_ R;
+	typedef typename Get_type<R, FT_tag>::type FT;
+        typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename Increment_dimension<typename R::Default_ambient_dimension>::type D1;
+	typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type D2;
+	typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
+	typedef typename LA::Square_matrix Matrix;
+
+        template<class Iter>
+        result_type operator()(Flat_orientation const&o, Iter f, Iter e) const {
+		// TODO: work in the projection instead of the ambient space.
+                typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+                typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+                int d=pd(*f);
+                Matrix m(d+1,d+1);
+                int i=0;
+		for(;f!=e;++f,++i) {
+			Point const& p=*f;
+			m(i,0)=1;
+			for(int j=0;j<d;++j){
+				m(i,j+1)=c(p,j);
+			}
+		}
+		for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
+			m(i,0)=1;
+			for(int j=0;j<d;++j){
+				m(i,j+1)=0; // unneeded if the matrix is initialized to 0
+			}
+			if(*it != d) m(i,1+*it)=1;
+		}
+
+                return LA::sign_of_determinant(CGAL_MOVE(m));
+        }
+};
+
+template<class R_> struct In_flat_side_of_oriented_sphere : private Store_kernel<R_> {
+        CGAL_FUNCTOR_INIT_STORE(In_flat_side_of_oriented_sphere)
+        typedef R_ R;
+	typedef typename Get_type<R, FT_tag>::type FT;
+        typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename Increment_dimension<typename R::Default_ambient_dimension,2>::type D1;
+	typedef typename Increment_dimension<typename R::Max_ambient_dimension,2>::type D2;
+	typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
+	typedef typename LA::Square_matrix Matrix;
+
+        template<class Iter>
+        result_type operator()(Flat_orientation const&o, Iter f, Iter e, Point const&x) const {
+		// TODO: can't work in the projection, but we should at least remove the row of 1s.
+                typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+                typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+                int d=pd(*f);
+                Matrix m(d+2,d+2);
+                int i=0;
+		for(;f!=e;++f,++i) {
+			Point const& p=*f;
+			m(i,0)=1;
+			m(i,d+1)=0;
+			for(int j=0;j<d;++j){
+				m(i,j+1)=c(p,j);
+				m(i,d+1)+=CGAL_NTS square(m(i,j+1));
+			}
+		}
+		for(std::vector<int>::const_iterator it = o.rest.begin(); it != o.rest.end() /* i<d+1 */; ++i, ++it) {
+			m(i,0)=1;
+			for(int j=0;j<d;++j){
+				m(i,j+1)=0; // unneeded if the matrix is initialized to 0
+			}
+			if(*it != d) m(i,d+1)=m(i,1+*it)=1;
+			else m(i,d+1)=0;
+		}
+		m(d+1,0)=1;
+		m(d+1,d+1)=0;
+		for(int j=0;j<d;++j){
+			m(d+1,j+1)=c(x,j);
+			m(d+1,d+1)+=CGAL_NTS square(m(d+1,j+1));
+		}
+
+                return -LA::sign_of_determinant(CGAL_MOVE(m));
+        }
+};
+
+
+}
+CGAL_KD_DEFAULT_TYPE(Flat_orientation_tag,(CGAL::CartesianDKernelFunctors::Flat_orientation),(),());
+CGAL_KD_DEFAULT_FUNCTOR(In_flat_orientation_tag,(CartesianDKernelFunctors::In_flat_orientation<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
+CGAL_KD_DEFAULT_FUNCTOR(In_flat_side_of_oriented_sphere_tag,(CartesianDKernelFunctors::In_flat_side_of_oriented_sphere<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
+CGAL_KD_DEFAULT_FUNCTOR(Construct_flat_orientation_tag,(CartesianDKernelFunctors::Construct_flat_orientation<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
+CGAL_KD_DEFAULT_FUNCTOR(Contained_in_affine_hull_tag,(CartesianDKernelFunctors::Contained_in_affine_hull<K>),(Point_tag),(Compute_point_cartesian_coordinate_tag,Point_dimension_tag));
+}
+#endif

NewKernel_d/include/CGAL/Kernel_d/Define_kernel_types.h

@@ -0,0 +1,30 @@
+#ifndef CGAL_DEFINE_KERNEL_TYPES_H
+#define CGAL_DEFINE_KERNEL_TYPES_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/typeset.h>
+#ifdef CGAL_CXX0X
+#include <type_traits>
+#else
+#include <boost/type_traits.hpp>
+#endif
+
+namespace CGAL {
+  namespace internal {
+    template<class K,class Tag_,bool=iterator_tag_traits<Tag_>::is_iterator>
+      struct Type_or_iter : K::template Type<Tag_> {};
+    template<class K,class Tag_>
+      struct Type_or_iter<K, Tag_, true> : K::template Iterator<Tag_> {};
+  }
+  template<class K, class Base=K, class List=typename typeset_union<typename K::Object_list,typename K::Iterator_list>::type> struct Define_kernel_types;
+  template<class K, class Base>
+    struct Define_kernel_types <K, Base, typeset<> > : Base {};
+  template<class K>
+    struct Define_kernel_types <K, void, typeset<> > {};
+  template<class K, class Base, class List>
+    struct Define_kernel_types :
+      Typedef_tag_type<typename List::head,
+        typename internal::Type_or_iter<K,typename List::head>::type,
+	Define_kernel_types<K, Base, typename List::tail>
+      > {};
+}
+#endif

NewKernel_d/include/CGAL/Kernel_d/Dimension_base.h

@@ -0,0 +1,30 @@
+#ifndef bd_h
+#define db_h
+#include <CGAL/Dimension.h>
+#include <CGAL/assertions.h>
+#include <CGAL/marcutils.h>
+namespace CGAL {
+struct Store_dimension_base {
+	//TODO: add some assertions
+	Store_dimension_base(int dim=UNKNOWN_DIMENSION):dim_(dim){}
+	int dimension()const{return dim_;}
+	void set_dimension(int dim){dim_=dim;}
+	private:
+	int dim_;
+};
+template<class=Dynamic_dimension_tag>
+struct Dimension_base {
+	Dimension_base(int = UNKNOWN_DIMENSION){}
+	int dimension() const { return UNKNOWN_DIMENSION; }
+	void set_dimension(int) {}
+};
+template<int dim_>
+struct Dimension_base<Dimension_tag<dim_> > {
+	Dimension_base(){}
+	Dimension_base(int dim){CGAL_assertion(dim_==dim);}
+	int dimension()const{return dim_;}
+	void set_dimension(int dim){CGAL_assertion(dim_==dim);}
+};
+}
+#endif
+

NewKernel_d/include/CGAL/Kernel_d/KernelD_converter.h

@@ -0,0 +1,175 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_CONVERTER_H
+#define CGAL_KERNEL_D_CARTESIAN_CONVERTER_H
+
+#include <CGAL/basic.h>
+#include <CGAL/tuple.h>
+#include <CGAL/typeset.h>
+#include <CGAL/Object.h>
+#include <CGAL/NT_converter.h>
+#include <CGAL/functor_tags.h>
+#include <CGAL/Kernel/mpl.h>
+#include <CGAL/is_iterator.h>
+#include <CGAL/transforming_iterator.h>
+#include <boost/utility/enable_if.hpp>
+#include <CGAL/store_kernel.h>
+#include <CGAL/Kernel_d/Kernel_object_converter.h>
+
+namespace CGAL {
+namespace internal {
+// Reverses order, but that shouldn't matter.
+template<class K,class T> struct Map_taglist_to_typelist :
+  Map_taglist_to_typelist<K,typename T::tail>::type
+  ::template add<typename Get_type<K, typename T::head>::type>
+{};
+template<class K> struct Map_taglist_to_typelist<K,typeset<> > : typeset<> {};
+}
+
+template<class List = typeset<> >
+struct Object_converter {
+	typedef Object result_type;
+	template<class F>
+	result_type operator()(Object const& o, F const& f) const {
+	  typedef typename List::head H;
+		if (H const* ptr = object_cast<H>(&o))
+			return make_object(f(*ptr));
+		else
+			return Object_converter<typename List::tail>()(o,f);
+	}
+};
+template<>
+struct Object_converter <typeset<> > {
+	typedef Object result_type;
+	template<class F>
+	result_type operator()(Object const&,F const&)const {
+		CGAL_error_msg("Cartesiand_converter is unable to determine what is wrapped in the Object");
+		return Object();
+	}
+};
+
+
+	//TODO: special case when K1==K2 (or they are very close?)
+template<class Final_, class K1, class K2, class List>
+class KernelD_converter_
+: public KernelD_converter_<Final_,K1,K2,typename List::tail>
+{
+	typedef typename List::head Tag_;
+	typedef typename List::tail Rest;
+	typedef KernelD_converter_<Final_,K1,K2,Rest> Base;
+	typedef typename Get_type<K1,Tag_>::type K1_Obj;
+	typedef typename Get_type<K2,Tag_>::type K2_Obj;
+	typedef typename Get_functor<K1, Convert_ttag<Tag_> >::type K1_Conv;
+	typedef KO_converter<Tag_,K1,K2> KOC;
+	typedef BOOSTD is_same<K1_Conv, Null_functor> no_converter;
+	typedef typename internal::Map_taglist_to_typelist<K1,Rest>::type::template contains<K1_Obj> duplicate;
+
+	// Disable the conversion in some cases:
+	struct Do_not_use{};
+	typedef typename BOOSTD conditional<
+	  // If Point==Vector, keep only one conversion
+	  duplicate::value ||
+	  // For iterator objects, the default is make_transforming_iterator
+	  (iterator_tag_traits<Tag_>::is_iterator && no_converter::value),
+	  Do_not_use,K1_Obj>::type argument_type;
+	//typedef typename KOC::argument_type K1_Obj;
+	//typedef typename KOC::result_type K2_Obj;
+	public:
+	using Base::operator(); // don't use directly, just make it accessible to the next level
+	K2_Obj helper(K1_Obj const& o,BOOSTD true_type)const{
+		return KOC()(this->myself().kernel(),this->myself().kernel2(),this->myself(),o);
+	}
+	K2_Obj helper(K1_Obj const& o,BOOSTD false_type)const{
+		return K1_Conv(this->myself().kernel())(this->myself().kernel2(),this->myself(),o);
+	}
+	K2_Obj operator()(argument_type const& o)const{
+	  return helper(o,no_converter());
+	}
+	template<class X,int=0> struct result:Base::template result<X>{};
+	template<int i> struct result<Final_(argument_type),i> {typedef K2_Obj type;};
+};
+
+template<class Final_, class K1, class K2>
+class KernelD_converter_<Final_,K1,K2,typeset<> > {
+	public:
+	struct Do_not_use{};
+	void operator()(Do_not_use)const{}
+	template<class T> struct result;
+	Final_& myself(){return *static_cast<Final_*>(this);}
+	Final_ const& myself()const{return *static_cast<Final_ const*>(this);}
+};
+
+
+// TODO: use the intersection of Kn::Object_list.
+template<class K1, class K2, class List_=
+typename typeset_intersection<typename K1::Object_list, typename K2::Object_list>::type
+//typeset<Point_tag>::add<Vector_tag>::type/*::add<Segment_tag>::type*/
+> class KernelD_converter
+	: public Store_kernel<K1>, public Store_kernel2<K2>,
+	public KernelD_converter_<KernelD_converter<K1,K2,List_>,K1,K2,List_>
+{
+	typedef KernelD_converter Self;
+	typedef Self Final_;
+	typedef KernelD_converter_<Self,K1,K2,List_> Base;
+	typedef typename Get_type<K1, FT_tag>::type FT1;
+	typedef typename Get_type<K2, FT_tag>::type FT2;
+	typedef NT_converter<FT1, FT2> NTc;
+	NTc c; // TODO: compressed storage as this is likely empty and the converter gets passed around (and stored in iterators)
+
+	public:
+	KernelD_converter(){}
+	KernelD_converter(K1 const&a,K2 const&b):Store_kernel<K1>(a),Store_kernel2<K2>(b){}
+
+	// For boost::result_of, used in transforming_iterator
+	template<class T,int i=is_iterator<T>::value?42:0> struct result:Base::template result<T>{};
+	template<class T> struct result<Final_(T),42> {
+		typedef transforming_iterator<Final_,T> type;
+	};
+	template<int i> struct result<Final_(K1),i>{typedef K2 type;};
+	template<int i> struct result<Final_(int),i>{typedef int type;};
+	// Ideally the next 2 would come with Point_tag and Vector_tag, but that's hard...
+	template<int i> struct result<Final_(Origin),i>{typedef Origin type;};
+	template<int i> struct result<Final_(Null_vector),i>{typedef Null_vector type;};
+	template<int i> struct result<Final_(Object),i>{typedef Object type;};
+	template<int i> struct result<Final_(FT1),i>{typedef FT2 type;};
+
+	using Base::operator();
+	typename Store_kernel2<K2>::reference2_type operator()(K1 const&)const{return this->kernel2();}
+	int operator()(int i)const{return i;}
+	Origin operator()(Origin const&o)const{return o;}
+	Null_vector operator()(Null_vector const&v)const{return v;}
+	FT2 operator()(FT1 const&x)const{return c(x);}
+	//RT2 operator()(typename First_if_different<RT1,FT1>::Type const&x)const{return cr(x);}
+
+	typename Get_type<K2, Flat_orientation_tag>::type const&
+	operator()(typename Get_type<K1, Flat_orientation_tag>::type const&o)const
+	{ return o; } // Both kernels should have the same, returning a reference should warn if not.
+
+	template<class It>
+	transforming_iterator<Final_,typename boost::enable_if<is_iterator<It>,It>::type>
+	operator()(It const& it) const {
+		return make_transforming_iterator(it,*this);
+	}
+
+	template<class T>
+	//TODO: use decltype in C++11 instead of result
+	std::vector<typename result<Final_(T)>::type>
+	operator()(const std::vector<T>& v) const {
+		return std::vector<typename result<Final_(T)>::type>(operator()(v.begin()),operator()(v.begin()));
+	}
+
+	//TODO: convert std::list and other containers?
+
+	Object
+	operator()(const Object &obj) const
+	{
+		typedef typename internal::Map_taglist_to_typelist<K1,List_>::type Possibilities;
+		//TODO: add Empty, vector<Point>, etc to the list.
+		return Object_converter<Possibilities>()(obj,*this);
+	}
+
+	//TODO: convert boost::variant
+
+};
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_CARTESIAN_CONVERTER_H

NewKernel_d/include/CGAL/Kernel_d/Kernel_2_interface.h

@@ -0,0 +1,85 @@
+#ifndef CGAL_KD_KERNEL_2_INTERFACE_H
+#define CGAL_KD_KERNEL_2_INTERFACE_H
+
+#include <CGAL/functor_tags.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/marcutils.h>
+#include <CGAL/tuple.h>
+
+
+namespace CGAL {
+template <class Base_> struct Kernel_2_interface : public Base_ {
+	typedef Base_ Base;
+	typedef Kernel_2_interface<Base> Kernel;
+        typedef typename Get_type<Base, RT_tag>::type RT;
+        typedef typename Get_type<Base, FT_tag>::type FT;
+        typedef typename Get_type<Base, Bool_tag>::type Boolean;
+        typedef typename Get_type<Base, Sign_tag>::type Sign;
+        typedef typename Get_type<Base, Comparison_result_tag>::type Comparison_result;
+        typedef typename Get_type<Base, Orientation_tag>::type Orientation;
+        typedef typename Get_type<Base, Oriented_side_tag>::type Oriented_side;
+        typedef typename Get_type<Base, Bounded_side_tag>::type Bounded_side;
+        typedef typename Get_type<Base, Angle_tag>::type Angle;
+	typedef typename Get_type<Base, Point_tag>::type  Point_2;
+	typedef typename Get_type<Base, Vector_tag>::type Vector_2;
+	typedef typename Get_type<Base, Segment_tag>::type Segment_2;
+	typedef cpp0x::tuple<Point_2,Point_2,Point_2> Triangle_2; // triangulation insists...
+	template <class T,int i> struct Help_2p_i {
+		typedef typename Get_functor<Base, T>::type LT;
+		typedef typename LT::result_type result_type;
+		LT lt;
+		Help_2p_i(Kernel const&k):lt(k){}
+		result_type operator()(Point_2 const&a, Point_2 const&b) {
+			return lt(a,b,i);
+		}
+	};
+	typedef Help_2p_i<Less_point_cartesian_coordinate_tag,0> Less_x_2;
+	typedef Help_2p_i<Less_point_cartesian_coordinate_tag,1> Less_y_2;
+	typedef Help_2p_i<Compare_point_cartesian_coordinate_tag,0> Compare_x_2;
+	typedef Help_2p_i<Compare_point_cartesian_coordinate_tag,1> Compare_y_2;
+	struct Compare_distance_2 {
+		typedef typename Get_functor<Base, Compare_distance_tag>::type CD;
+		typedef typename CD::result_type result_type;
+		CD cd;
+		Compare_distance_2(Kernel const&k):cd(k){}
+		result_type operator()(Point_2 const&a, Point_2 const&b, Point_2 const&c) {
+			return cd(a,b,c);
+		}
+		result_type operator()(Point_2 const&a, Point_2 const&b, Point_2 const&c, Point_2 const&d) {
+			return cd(a,b,c,d);
+		}
+	};
+	struct Orientation_2 {
+		typedef typename Get_functor<Base, Orientation_of_points_tag>::type O;
+		typedef typename O::result_type result_type;
+		O o;
+		Orientation_2(Kernel const&k):o(k){}
+		result_type operator()(Point_2 const&a, Point_2 const&b, Point_2 const&c) {
+			//return o(a,b,c);
+			Point_2 const* t[3]={&a,&b,&c};
+			return o(make_transforming_iterator<Dereference_functor>(t+0),make_transforming_iterator<Dereference_functor>(t+3));
+
+		}
+	};
+	struct Side_of_oriented_circle_2 {
+		typedef typename Get_functor<Base, Side_of_oriented_sphere_tag>::type SOS;
+		typedef typename SOS::result_type result_type;
+		SOS sos;
+		Side_of_oriented_circle_2(Kernel const&k):sos(k){}
+		result_type operator()(Point_2 const&a, Point_2 const&b, Point_2 const&c, Point_2 const&d) {
+			//return sos(a,b,c,d);
+			Point_2 const* t[4]={&a,&b,&c,&d};
+			return sos(make_transforming_iterator<Dereference_functor>(t+0),make_transforming_iterator<Dereference_functor>(t+4));
+		}
+	};
+	Less_x_2 less_x_2_object()const{ return Less_x_2(*this); }
+	Less_y_2 less_y_2_object()const{ return Less_y_2(*this); }
+	Compare_x_2 compare_x_2_object()const{ return Compare_x_2(*this); }
+	Compare_y_2 compare_y_2_object()const{ return Compare_y_2(*this); }
+	Compare_distance_2 compare_distance_2_object()const{ return Compare_distance_2(*this); }
+	Orientation_2 orientation_2_object()const{ return Orientation_2(*this); }
+	Side_of_oriented_circle_2 side_of_oriented_circle_2_object()const{ return Side_of_oriented_circle_2(*this); }
+};
+}
+
+#endif

NewKernel_d/include/CGAL/Kernel_d/Kernel_3_interface.h

@@ -0,0 +1,83 @@
+#ifndef CGAL_KD_KERNEL_3_INTERFACE_H
+#define CGAL_KD_KERNEL_3_INTERFACE_H
+
+#include <CGAL/functor_tags.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/marcutils.h>
+#include <CGAL/tuple.h>
+
+
+namespace CGAL {
+template <class Base_> struct Kernel_3_interface : public Base_ {
+	typedef Base_ Base;
+	typedef Kernel_3_interface<Base> Kernel;
+        typedef typename Get_type<Base, RT_tag>::type RT;
+        typedef typename Get_type<Base, FT_tag>::type FT;
+        typedef typename Get_type<Base, Bool_tag>::type Boolean;
+        typedef typename Get_type<Base, Sign_tag>::type Sign;
+        typedef typename Get_type<Base, Comparison_result_tag>::type Comparison_result;
+        typedef typename Get_type<Base, Orientation_tag>::type Orientation;
+        typedef typename Get_type<Base, Oriented_side_tag>::type Oriented_side;
+        typedef typename Get_type<Base, Bounded_side_tag>::type Bounded_side;
+        typedef typename Get_type<Base, Angle_tag>::type Angle;
+	typedef typename Get_type<Base, Point_tag>::type	Point_3;
+	typedef typename Get_type<Base, Vector_tag>::type	Vector_3;
+	typedef typename Get_type<Base, Segment_tag>::type	Segment_3;
+	typedef cpp0x::tuple<Point_3,Point_3,Point_3>		Triangle_3; // placeholder
+	typedef cpp0x::tuple<Point_3,Point_3,Point_3,Point_3>	Tetrahedron_3; // placeholder
+	struct Compare_xyz_3 {
+		typedef typename Get_functor<Base, Compare_lexicographically_tag>::type CL;
+		typedef typename CL::result_type result_type;
+		CL cl;
+		Compare_xyz_3(Kernel const&k):cl(k){}
+		result_type operator()(Point_3 const&a, Point_3 const&b) {
+			return cl(a,b);
+		}
+	};
+	struct Compare_distance_3 {
+		typedef typename Get_functor<Base, Compare_distance_tag>::type CD;
+		typedef typename CD::result_type result_type;
+		CD cd;
+		Compare_distance_3(Kernel const&k):cd(k){}
+		result_type operator()(Point_3 const&a, Point_3 const&b, Point_3 const&c) {
+			return cd(a,b,c);
+		}
+		result_type operator()(Point_3 const&a, Point_3 const&b, Point_3 const&c, Point_3 const&d) {
+			return cd(a,b,c,d);
+		}
+	};
+	struct Orientation_3 {
+		typedef typename Get_functor<Base, Orientation_of_points_tag>::type O;
+		typedef typename O::result_type result_type;
+		O o;
+		Orientation_3(Kernel const&k):o(k){}
+		result_type operator()(Point_3 const&a, Point_3 const&b, Point_3 const&c, Point_3 const&d) {
+			//return o(a,b,c,d);
+			Point_3 const* t[4]={&a,&b,&c,&d};
+			return o(make_transforming_iterator<Dereference_functor>(t+0),make_transforming_iterator<Dereference_functor>(t+4));
+
+		}
+	};
+	struct Side_of_oriented_sphere_3 {
+		typedef typename Get_functor<Base, Side_of_oriented_sphere_tag>::type SOS;
+		typedef typename SOS::result_type result_type;
+		SOS sos;
+		Side_of_oriented_sphere_3(Kernel const&k):sos(k){}
+		result_type operator()(Point_3 const&a, Point_3 const&b, Point_3 const&c, Point_3 const&d, Point_3 const&e) {
+			//return sos(a,b,c,d);
+			Point_3 const* t[5]={&a,&b,&c,&d,&e};
+			return sos(make_transforming_iterator<Dereference_functor>(t+0),make_transforming_iterator<Dereference_functor>(t+5));
+		}
+	};
+
+	// I don't have the Coplanar predicates (yet)
+
+
+	Compare_xyz_3 compare_xyz_3_object()const{ return Compare_xyz_3(*this); }
+	Compare_distance_3 compare_distance_3_object()const{ return Compare_distance_3(*this); }
+	Orientation_3 orientation_3_object()const{ return Orientation_3(*this); }
+	Side_of_oriented_sphere_3 side_of_oriented_sphere_3_object()const{ return Side_of_oriented_sphere_3(*this); }
+};
+}
+
+#endif

NewKernel_d/include/CGAL/Kernel_d/Kernel_d_interface.h

@@ -0,0 +1,173 @@
+#ifndef CGAL_KD_KERNEL_D_INTERFACE_H
+#define CGAL_KD_KERNEL_D_INTERFACE_H
+
+#include <CGAL/functor_tags.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/marcutils.h>
+#include <CGAL/tuple.h>
+
+
+namespace CGAL {
+template <class Base_> struct Kernel_d_interface : public Base_ {
+  CGAL_CONSTEXPR Kernel_d_interface(){}
+  CGAL_CONSTEXPR Kernel_d_interface(int d):Base_(d){}
+
+	typedef Base_ Base;
+	typedef Kernel_d_interface<Base> Kernel;
+	typedef Base_ R_; // for the macros
+	typedef typename Get_type<Base, RT_tag>::type RT;
+	typedef typename Get_type<Base, FT_tag>::type FT;
+	typedef typename Get_type<Base, Bool_tag>::type Boolean;
+	typedef typename Get_type<Base, Sign_tag>::type Sign;
+	typedef typename Get_type<Base, Comparison_result_tag>::type Comparison_result;
+	typedef typename Get_type<Base, Orientation_tag>::type Orientation;
+	typedef typename Get_type<Base, Oriented_side_tag>::type Oriented_side;
+	typedef typename Get_type<Base, Bounded_side_tag>::type Bounded_side;
+	typedef typename Get_type<Base, Angle_tag>::type Angle;
+	typedef typename Get_type<Base, Flat_orientation_tag>::type Flat_orientation_d;
+	typedef typename Get_type<Base, Point_tag>::type	Point_d;
+	typedef typename Get_type<Base, Vector_tag>::type	Vector_d;
+	typedef typename Get_type<Base, Segment_tag>::type	Segment_d;
+	typedef typename Get_type<Base, Sphere_tag>::type	Sphere_d;
+	typedef typename Get_type<Base, Hyperplane_tag>::type	Hyperplane_d;
+	typedef Vector_d Direction_d;
+	typedef typename Get_type<Base, Line_tag>::type	Line_d;
+	typedef typename Get_type<Base, Ray_tag>::type	Ray_d;
+	typedef typename Get_type<Base, Iso_box_tag>::type	Iso_box_d;
+	typedef typename Get_type<Base, Aff_transformation_tag>::type	Aff_transformation_d;
+	typedef typename Get_functor<Base, Compute_point_cartesian_coordinate_tag>::type Compute_coordinate_d;
+	typedef typename Get_functor<Base, Compare_lexicographically_tag>::type Compare_lexicographically_d;
+	typedef typename Get_functor<Base, Equal_points_tag>::type Equal_d;
+	typedef typename Get_functor<Base, Less_lexicographically_tag>::type Less_lexicographically_d;
+	typedef typename Get_functor<Base, Less_or_equal_lexicographically_tag>::type Less_or_equal_lexicographically_d;
+	// FIXME: and vectors?
+	typedef typename Get_functor<Base, Orientation_of_points_tag>::type Orientation_d;
+	typedef typename Get_functor<Base, Less_point_cartesian_coordinate_tag>::type Less_coordinate_d;
+	typedef typename Get_functor<Base, Point_dimension_tag>::type Point_dimension_d;
+	typedef typename Get_functor<Base, Side_of_oriented_sphere_tag>::type Side_of_oriented_sphere_d;
+	typedef typename Get_functor<Base, Contained_in_affine_hull_tag>::type Contained_in_affine_hull_d;
+	typedef typename Get_functor<Base, Construct_flat_orientation_tag>::type Construct_flat_orientation_d;
+	typedef typename Get_functor<Base, In_flat_orientation_tag>::type In_flat_orientation_d;
+	typedef typename Get_functor<Base, In_flat_side_of_oriented_sphere_tag>::type In_flat_side_of_oriented_sphere_d;
+	typedef typename Get_functor<Base, Point_to_vector_tag>::type Point_to_vector_d;
+	typedef typename Get_functor<Base, Vector_to_point_tag>::type Vector_to_point_d;
+	typedef typename Get_functor<Base, Construct_ttag<Point_tag> >::type Construct_point_d;
+	typedef typename Get_functor<Base, Construct_ttag<Vector_tag> >::type Construct_vector_d;
+	typedef typename Get_functor<Base, Construct_ttag<Segment_tag> >::type Construct_segment_d;
+	typedef typename Get_functor<Base, Construct_ttag<Sphere_tag> >::type Construct_sphere_d;
+	typedef typename Get_functor<Base, Construct_ttag<Hyperplane_tag> >::type Construct_hyperplane_d;
+	typedef Construct_vector_d Construct_direction_d;
+	typedef typename Get_functor<Base, Construct_ttag<Line_tag> >::type Construct_line_d;
+	typedef typename Get_functor<Base, Construct_ttag<Ray_tag> >::type Construct_ray_d;
+	typedef typename Get_functor<Base, Construct_ttag<Iso_box_tag> >::type Construct_iso_box_d;
+	typedef typename Get_functor<Base, Construct_ttag<Aff_transformation_tag> >::type Construct_aff_transformation_d;
+	typedef typename Get_functor<Base, Midpoint_tag>::type Midpoint_d;
+	struct Component_accessor_d : private Store_kernel<R_> {
+	  CGAL_FUNCTOR_INIT_STORE(Component_accessor_d)
+	  int dimension(Point_d const&p){
+	    return this->kernel().point_dimension_d_object()(p);
+	  }
+	  FT cartesian(Point_d const&p, int i){
+	    return this->kernel().compute_coordinate_d_object()(p);
+	  }
+	  RT homogeneous(Point_d const&p, int i){
+	    throw "not implemented yet";
+	    return 0;
+	    // FIXME
+	    //return this->kernel().compute_coordinate_d_object()(p);
+	  }
+	};
+	struct Construct_cartesian_const_iterator_d : private Store_kernel<R_> {
+	  CGAL_FUNCTOR_INIT_STORE(Construct_cartesian_const_iterator_d)
+	  typedef typename Get_functor<Base, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CPI;
+	  typedef typename Get_functor<Base, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CVI;
+	  typedef typename CGAL::decay<typename boost::result_of<CPI(Point_d,CGAL::Begin_tag)>::type>::type result_type;
+	  // Kernel_d requires a common iterator type for points and vectors
+	  // TODO: provide this mixed functor in preKernel?
+	  CGAL_static_assertion((boost::is_same<typename CGAL::decay<typename boost::result_of<CVI(Vector_d,CGAL::Begin_tag)>::type>::type, result_type>::value));
+	  template <class Tag_>
+	  result_type operator()(Point_d const&p, Tag_ t)const{
+	    return CPI(this->kernel())(p,t);
+	  }
+	  template <class Tag_>
+	  result_type operator()(typename First_if_different<Vector_d,Point_d>::Type const&v, Tag_ t)const{
+	    return CVI(this->kernel())(v,t);
+	  }
+
+	  template <class Obj>
+	  result_type operator()(Obj const&o)const{
+	    return operator()(o, Begin_tag());
+	  }
+	  result_type operator()(Point_d const&p, int)const{
+	    return operator()(p, End_tag());
+	  }
+	  result_type operator()(typename First_if_different<Vector_d,Point_d>::Type const&v, int)const{
+	    return operator()(v, End_tag());
+	  }
+	};
+	typedef typename Construct_cartesian_const_iterator_d::result_type Cartesian_const_iterator_d;
+	typedef typename Get_functor<Base, Squared_distance_tag>::type Squared_distance_d;
+	//typedef typename Get_functor<Base, Affine_rank_tag>::type Affine_rank_d;
+	//typedef typename Get_functor<Base, Affinely_independent_tag>::type Affinely_independent_d;
+	//typedef typename Get_functor<Base, Contained_in_linear_hull_tag>::type Contained_in_linear_hull_d;
+	//typedef typename Get_functor<Base, Contained_in_simplex_tag>::type Contained_in_simplex_d;
+	typedef typename Get_functor<Base, Has_on_positive_side_tag>::type Has_on_positive_side_d;
+	//typedef typename Get_functor<Base, Linear_rank_tag>::type Linear_rank_d;
+	//typedef typename Get_functor<Base, Linearly_independent_tag>::type Linearly_independent_d;
+	typedef typename Get_functor<Base, Oriented_side_tag>::type Oriented_side_d;
+	//typedef typename Get_functor<Base, Side_of_bounded_sphere_tag>::type Side_of_bounded_sphere_d;
+
+	typedef typename Get_functor<Base, Center_of_sphere_tag>::type Center_of_sphere_d;
+	typedef typename Get_functor<Base, Value_at_tag>::type Value_at_d;
+	typedef typename Get_functor<Base, Point_of_sphere_tag>::type Point_of_sphere_d;
+	typedef typename Get_functor<Base, Orthogonal_vector_tag>::type Orthogonal_vector_d;
+	//typedef typename Get_functor<Base, Linear_base_tag>::type Linear_base_d;
+
+	//typedef ??? Intersect_d;
+
+
+	Compute_coordinate_d compute_coordinate_d_object()const{ return Compute_coordinate_d(*this); }
+	Compare_lexicographically_d compare_lexicographically_d_object()const{ return Compare_lexicographically_d(*this); }
+	Equal_d equal_d_object()const{ return Equal_d(*this); }
+	Less_lexicographically_d less_lexicographically_d_object()const{ return Less_lexicographically_d(*this); }
+	Less_or_equal_lexicographically_d less_or_equal_lexicographically_d_object()const{ return Less_or_equal_lexicographically_d(*this); }
+	Less_coordinate_d less_coordinate_d_object()const{ return Less_coordinate_d(*this); }
+	Orientation_d orientation_d_object()const{ return Orientation_d(*this); }
+	Point_dimension_d point_dimension_d_object()const{ return Point_dimension_d(*this); }
+	Side_of_oriented_sphere_d side_of_oriented_sphere_d_object()const{ return Side_of_oriented_sphere_d(*this); }
+	Contained_in_affine_hull_d contained_in_affine_hull_d_object()const{ return Contained_in_affine_hull_d(*this); }
+	Construct_flat_orientation_d construct_flat_orientation_d_object()const{ return Construct_flat_orientation_d(*this); }
+	In_flat_orientation_d in_flat_orientation_d_object()const{ return In_flat_orientation_d(*this); }
+	In_flat_side_of_oriented_sphere_d in_flat_side_of_oriented_sphere_d_object()const{ return In_flat_side_of_oriented_sphere_d(*this); }
+	Point_to_vector_d point_to_vector_d_object()const{ return Point_to_vector_d(*this); }
+	Vector_to_point_d vector_to_point_d_object()const{ return Vector_to_point_d(*this); }
+	Midpoint_d midpoint_d_object()const{ return Midpoint_d(*this); }
+	Component_accessor_d component_accessor_d_object()const{ return Component_accessor_d(*this); }
+	Orthogonal_vector_d orthogonal_vector_d_object()const{ return Orthogonal_vector_d(*this); }
+	Construct_cartesian_const_iterator_d construct_cartesian_const_iterator_d_object()const{ return Construct_cartesian_const_iterator_d(*this); }
+	Construct_point_d construct_point_d_object()const{ return Construct_point_d(*this); }
+	Construct_vector_d construct_vector_d_object()const{ return Construct_vector_d(*this); }
+	Construct_segment_d construct_segment_d_object()const{ return Construct_segment_d(*this); }
+	Construct_sphere_d construct_sphere_d_object()const{ return Construct_sphere_d(*this); }
+	Construct_hyperplane_d construct_hyperplane_d_object()const{ return Construct_hyperplane_d(*this); }
+	Squared_distance_d squared_distance_d_object()const{ return Squared_distance_d(*this); }
+	Construct_direction_d construct_direction_d_object()const{ return Construct_direction_d(*this); }
+	Construct_line_d construct_line_d_object()const{ return Construct_line_d(*this); }
+	Construct_ray_d construct_ray_d_object()const{ return Construct_ray_d(*this); }
+	Construct_iso_box_d construct_iso_box_d_object()const{ return Construct_iso_box_d(*this); }
+	Construct_aff_transformation_d construct_aff_transformation_d_object()const{ return Construct_aff_transformation_d(*this); }
+
+	// Dummies for those required functors missing a concept.
+	typedef Null_functor Position_on_line_d;
+	Position_on_line_d position_on_line_d_object()const{return Null_functor();}
+	typedef Null_functor Barycentric_coordinates_d;
+	Barycentric_coordinates_d barycentric_coordinates_d_object()const{return Null_functor();}
+
+	/* Not provided because they don't make sense here:
+	   Lift_to_paraboloid_d
+	   Project_along_d_axis_d
+	 */
+};
+}
+
+#endif // CGAL_KD_KERNEL_D_INTERFACE_H

NewKernel_d/include/CGAL/Kernel_d/Kernel_object_converter.h

@@ -0,0 +1,78 @@
+#ifndef CGAL_KD_KO_CONVERTER_H
+#define CGAL_KD_KO_CONVERTER_H
+#include <CGAL/marcutils.h>
+#include <CGAL/functor_tags.h>
+#include <CGAL/Kernel/mpl.h> // First_if_different
+namespace CGAL {
+template <class Tag_, class K1, class K2> struct KO_converter;
+//TODO: It would probably be better if this was a Misc Functor in K1.
+// This way K1 could chose how it wants to present its points (sparse
+// iterator?) and derived classes would inherit it.
+
+namespace internal {
+template <class D /*=Dynamic_dimension_tag*/, class K1, class K2>
+struct Point_converter_help {
+	typedef typename Get_type<K1, Point_tag>::type	argument_type;
+	typedef typename Get_type<K2, Point_tag>::type	result_type;
+	template <class C>
+	result_type operator()(K1 const& k1, K2 const& k2, C const& conv, argument_type const& p) const {
+		typename Get_functor<K1, Construct_ttag<Point_cartesian_const_iterator_tag> >::type i(k1);
+		typename Get_functor<K2, Construct_ttag<Point_tag> >::type cp(k2);
+		return cp(conv(i(p,Begin_tag())),conv(i(p,End_tag())));
+	}
+};
+#ifdef CGAL_CXX0X
+// This doesn't seem so useful, the compiler should be able to handle
+// the iterators just as efficiently.
+template <int d, class K1, class K2>
+struct Point_converter_help<Dimension_tag<d>,K1,K2> {
+	typedef typename Get_type<K1, Point_tag>::type	argument_type;
+	typedef typename Get_type<K2, Point_tag>::type	result_type;
+	template <class C,int...I>
+	result_type help(Indices<I...>, K1 const& k1, K2 const& k2, C const& conv, argument_type const& p) const {
+		typename Get_functor<K1, Compute_point_cartesian_coordinate_tag>::type cc(k1);
+		typename Get_functor<K2, Construct_ttag<Point_tag> >::type cp(k2);
+		return cp(conv(cc(p,I))...);
+	}
+	template <class C>
+	result_type operator()(K1 const& k1, K2 const& k2, C const& conv, argument_type const& p) const {
+		return help(typename N_increasing_indices<d>::type(),k1,k2,conv,p);
+	}
+};
+#endif
+}
+template <class K1, class K2> struct KO_converter<Point_tag,K1,K2>
+: internal::Point_converter_help<typename K1::Default_ambient_dimension,K1,K2>
+{};
+
+template <class K1, class K2> struct KO_converter<Vector_tag,K1,K2>{
+	typedef typename Get_type<K1, Vector_tag>::type	K1_Vector;
+	
+	// Disabling is now done in KernelD_converter
+	// // can't use vector without at least a placeholder point because of this
+	// typedef typename K1:: Point K1_Point;
+	// typedef typename First_if_different<K1_Vector,K1_Point>::Type argument_type;
+
+	typedef K1_Vector argument_type;
+	typedef typename Get_type<K2, Vector_tag>::type	result_type;
+	template <class C>
+	result_type operator()(K1 const& k1, K2 const& k2, C const& conv, argument_type const& v) const {
+		typename Get_functor<K1, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type i(k1);
+		typename Get_functor<K2, Construct_ttag<Vector_tag> >::type cp(k2);
+		return cp(conv(i(v,Begin_tag())),conv(i(v,End_tag())));
+	}
+};
+
+template <class K1, class K2> struct KO_converter<Segment_tag,K1,K2>{
+	typedef typename Get_type<K1, Segment_tag>::type	argument_type;
+	typedef typename Get_type<K2, Segment_tag>::type	result_type;
+	template <class C>
+	result_type operator()(K1 const& k1, K2 const& k2, C const& conv, argument_type const& s) const {
+		typename Get_functor<K1, Segment_extremity_tag>::type f(k1);
+		typename Get_functor<K2, Construct_ttag<Segment_tag> >::type cs(k2);
+		return cs(conv(f(s,0)),conv(f(s,1)));
+	}
+};
+
+}
+#endif

NewKernel_d/include/CGAL/Kernel_d/Lazy_cartesian.h

@@ -0,0 +1,169 @@
+#ifndef CGAL_KERNEL_D_LAZY_CARTESIAN_H
+#define CGAL_KERNEL_D_LAZY_CARTESIAN_H
+
+#include <CGAL/basic.h>
+#include <CGAL/algorithm.h>
+#include <CGAL/Lazy.h>
+#include <CGAL/Default.h>
+#include <CGAL/Filtered_predicate2.h>
+#include <CGAL/iterator_from_indices.h>
+#include <CGAL/Kernel_d/Define_kernel_types.h>
+
+namespace CGAL {
+
+template<class K,class T>
+struct Nth_iterator_element : private Store_kernel<K> {
+  Nth_iterator_element(){}
+  Nth_iterator_element(K const&k):Store_kernel<K>(k){}
+  typedef typename Get_type<K, typename iterator_tag_traits<T>::value_tag>::type result_type;
+  template<class U> result_type operator()(CGAL_FORWARDABLE(U) u, int i) const {
+    typename Get_functor<K, Construct_ttag<T> >::type ci(this->kernel());
+    return *cpp0x::next(ci(CGAL_FORWARD(U,u),Begin_tag()),i);
+  }
+};
+      //typedef typename Functor<typename iterator_tag_traits<T>::nth_element>::type nth_elem;
+template<class K, class T, bool = iterator_tag_traits<T>::has_nth_element>
+struct Select_nth_element_functor {
+  typedef Nth_iterator_element<K, T> type;
+};
+template<class K, class T>
+struct Select_nth_element_functor <K, T, true> :
+  Get_functor<K, typename iterator_tag_traits<T>::nth_element> {};
+
+namespace internal {
+  template<class A,class B,class C,bool/*is_NT=false*/>
+    struct Lazy_construction_maybe_nt {
+      typedef Lazy_construction<A,B,C> type;
+    };
+  template<class A,class B,class C>
+    struct Lazy_construction_maybe_nt<A,B,C,true> {
+      typedef Lazy_construction_nt<A,B,C> type;
+    };
+}
+
+template <class EK_, class AK_, class E2A_, class Kernel_>
+struct Lazy_cartesian_types
+{
+    typedef typename typeset_intersection<
+      typename AK_::Object_list,
+      typename EK_::Object_list
+	>::type Object_list;
+
+    typedef typename typeset_intersection<
+      typename AK_::Iterator_list,
+      typename EK_::Iterator_list
+	>::type Iterator_list;
+
+    template <class T,class=typename Get_type_category<Kernel_,T>::type> struct Type {};
+    template <class T> struct Type<T,Object_tag> {
+	    typedef Lazy<
+		    typename Get_type<AK_,T>::type,
+		    typename Get_type<EK_,T>::type,
+		    typename Get_type<EK_, FT_tag>::type,
+		    E2A_> type;
+    };
+    template <class T> struct Type<T,Number_tag> {
+      typedef CGAL::Lazy_exact_nt<typename Get_type<EK_,T>::type>  type;
+    };
+
+    template <class T> struct Iterator {
+      typedef typename iterator_tag_traits<T>::value_tag Vt;
+      typedef typename Type<Vt>::type V;
+      typedef typename Select_nth_element_functor<AK_,T>::type AF;
+      typedef typename Select_nth_element_functor<EK_,T>::type EF;
+
+      typedef typename internal::Lazy_construction_maybe_nt<
+	Kernel_, AF, EF, is_NT_tag<Vt>::value
+	>::type nth_elem;
+
+      typedef Iterator_from_indices<
+	const typename Type<typename iterator_tag_traits<T>::container>::type,
+	const V, V, nth_elem
+      > type;
+    };
+};
+
+template <class EK_, class AK_, class E2A_/*, class Kernel_=Default*/>
+struct Lazy_cartesian : Dimension_base<typename EK_::Default_ambient_dimension>,
+  Lazy_cartesian_types<EK_,AK_,E2A_,Lazy_cartesian<EK_,AK_,E2A_> >
+{
+    //CGAL_CONSTEXPR Lazy_cartesian(){}
+    //CGAL_CONSTEXPR Lazy_cartesian(int d):Base_(d){}
+
+    //TODO: Do we want to store an AK and an EK? Or just references?
+    //FIXME: references would be better I guess.
+    //TODO: In any case, make sure that we don't end up storing this kernel for
+    //nothing (it is not empty but references empty kernels or something)
+    AK_ ak; EK_ ek;
+    AK_ const& approximate_kernel()const{return ak;}
+    EK_ const& exact_kernel()const{return ek;}
+
+    typedef Lazy_cartesian Self;
+    typedef Lazy_cartesian_types<EK_,AK_,E2A_,Self> Base;
+    //typedef typename Default::Get<Kernel_,Self>::type Kernel;
+    typedef Self  Kernel;
+    typedef AK_   Approximate_kernel;
+    typedef EK_   Exact_kernel;
+    typedef E2A_  E2A;
+    typedef Approx_converter<Kernel, Approximate_kernel>   C2A;
+    typedef Exact_converter<Kernel, Exact_kernel>    C2E;
+
+    typedef typename Exact_kernel::Rep_tag Rep_tag;
+    typedef typename Exact_kernel::Kernel_tag Kernel_tag;
+    typedef typename Exact_kernel::Default_ambient_dimension Default_ambient_dimension;
+    typedef typename Exact_kernel::Max_ambient_dimension Max_ambient_dimension;
+    //typedef typename Exact_kernel::Flat_orientation Flat_orientation;
+    // Check that Approximate_kernel agrees with all that...
+
+    template<class T,class D=void,class=typename Get_functor_category<Lazy_cartesian,T,D>::type> struct Functor {
+	    typedef Null_functor type;
+    };
+	    //FIXME: what do we do with D here?
+    template<class T,class D> struct Functor<T,D,Predicate_tag> {
+	    typedef typename Get_functor<Approximate_kernel, T>::type FA;
+	    typedef typename Get_functor<Exact_kernel, T>::type FE;
+	    typedef Filtered_predicate2<FE,FA,C2E,C2A> type;
+    };
+    template<class T,class D> struct Functor<T,D,Compute_tag> {
+	    typedef typename Get_functor<Approximate_kernel, T>::type FA;
+	    typedef typename Get_functor<Exact_kernel, T>::type FE;
+	    typedef Lazy_construction_nt<Kernel,FA,FE> type;
+    };
+    template<class T,class D> struct Functor<T,D,Construct_tag> {
+	    typedef typename Get_functor<Approximate_kernel, T>::type FA;
+	    typedef typename Get_functor<Exact_kernel, T>::type FE;
+	    typedef Lazy_construction<Kernel,FA,FE> type;
+    };
+
+    //typedef typename Iterator<Point_cartesian_const_iterator_tag>::type Point_cartesian_const_iterator;
+    //typedef typename Iterator<Vector_cartesian_const_iterator_tag>::type Vector_cartesian_const_iterator;
+
+    template<class U>
+    struct Construct_iter : private Store_kernel<Kernel> {
+	    Construct_iter(){}
+	    Construct_iter(Kernel const&k):Store_kernel<Kernel>(k){}
+	    //FIXME: pass the kernel to the functor in the iterator
+	    typedef U result_type;
+	    template<class T>
+	    result_type operator()(T const& t,Begin_tag)const{
+		    return result_type(t,0,this->kernel());
+	    }
+	    template<class T>
+	    result_type operator()(T const& t,End_tag)const{
+		    return result_type(t,Self().dimension(),this->kernel());
+	    }
+    };
+    template<class T,class D> struct Functor<T,D,Construct_iterator_tag> {
+	    typedef Construct_iter<typename Base::template Iterator<typename map_result_tag<T>::type>::type> type;
+    };
+
+
+    //TODO: what about other functors of the Misc category?
+    // for Point_dimension, we should apply it to the approximate point
+    // for printing, we should??? just not do printing this way?
+};
+
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_LAZY_CARTESIAN_H

NewKernel_d/include/CGAL/Kernel_d/Types/Aff_transformation.h

@@ -0,0 +1,39 @@
+#ifndef CGAL_KD_TYPE_AFF_TRANSFORMATION_H
+#define CGAL_KD_TYPE_AFF_TRANSFORMATION_H
+#include <CGAL/store_kernel.h>
+#include <boost/preprocessor/repetition.hpp>
+
+// Dummy, that's all the Kernel_d concept requires, so a useful class will wait.
+
+namespace CGAL {
+template<class R_>
+struct Aff_transformation {
+  typedef R_ R;
+};
+namespace CartesianDKernelFunctors {
+template<class R_> struct Construct_aff_transformation {
+  CGAL_FUNCTOR_INIT_IGNORE(Construct_aff_transformation)
+  typedef R_ R;
+  typedef typename Get_type<R, Aff_transformation_tag>::type result_type;
+#ifdef CGAL_CXX0X
+  template<class...T>
+  result_type operator()(T&&...)const{return result_type();}
+#else
+  result_type operator()()const{
+    return result_type();
+  }
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class U)> \
+  result_type operator()(BOOST_PP_ENUM_BINARY_PARAMS(N,U,const& BOOST_PP_INTERCEPT))const{ \
+    return result_type(); \
+  }
+  BOOST_PP_REPEAT_FROM_TO(1, 9, CODE, _ )
+#undef CODE
+
+#endif
+};
+}
+CGAL_KD_DEFAULT_TYPE(Aff_transformation_tag,(CGAL::Aff_transformation<K>),(),());
+CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Aff_transformation_tag>,(CartesianDKernelFunctors::Construct_aff_transformation<K>),(Aff_transformation_tag),());
+
+}
+#endif

NewKernel_d/include/CGAL/Kernel_d/Types/Hyperplane.h

@@ -0,0 +1,79 @@
+#ifndef CGAL_KD_TYPE_HYPERPLANE_H
+#define CGAL_KD_TYPE_HYPERPLANE_H
+#include <CGAL/store_kernel.h>
+namespace CGAL {
+template <class R_> class Hyperplane {
+	typedef typename Get_type<R_, FT_tag>::type FT_;
+	typedef typename Get_type<R_, Vector_tag>::type	Vector_;
+	Vector_ v_;
+	FT_ s_;
+
+	public:
+	Hyperplane(Vector_ const&v, FT_ const&s): v_(v), s_(s) {}
+	// TODO: Add a piecewise constructor?
+
+	Vector_ orthogonal_vector()const{return v_;}
+	FT_ translation()const{return s_;}
+};
+namespace CartesianDKernelFunctors {
+template <class R_> struct Construct_hyperplane : Store_kernel<R_> {
+  CGAL_FUNCTOR_INIT_STORE(Construct_hyperplane)
+  typedef typename Get_type<R_, Hyperplane_tag>::type	result_type;
+  typedef typename Get_type<R_, Vector_tag>::type	Vector;
+  typedef typename Get_type<R_, FT_tag>::type FT;
+  typedef typename R_::LA LA;
+  result_type operator()(Vector const&a, FT const&b)const{
+    return result_type(a,b);
+  }
+  template <class Iter>
+  result_type operator()(Iter f, Iter e)const{
+    throw "not implemented yet!";
+  }
+};
+template <class R_> struct Orthogonal_vector {
+  CGAL_FUNCTOR_INIT_IGNORE(Orthogonal_vector)
+  typedef typename Get_type<R_, Hyperplane_tag>::type	Hyperplane;
+  typedef typename Get_type<R_, Vector_tag>::type	result_type;
+  result_type operator()(Hyperplane const&s)const{
+    return s.orthogonal_vector();
+  }
+};
+template <class R_> struct Hyperplane_translation {
+  CGAL_FUNCTOR_INIT_IGNORE(Hyperplane_translation)
+  typedef typename Get_type<R_, Hyperplane_tag>::type	Hyperplane;
+  typedef typename Get_type<R_, FT_tag>::type result_type;
+  // TODO: Is_exact?
+  result_type operator()(Hyperplane const&s)const{
+    return s.translation();
+  }
+};
+template <class R_> struct Value_at : Store_kernel<R_> {
+  CGAL_FUNCTOR_INIT_STORE(Value_at)
+  typedef typename Get_type<R_, Hyperplane_tag>::type	Hyperplane;
+  typedef typename Get_type<R_, Vector_tag>::type	Vector;
+  typedef typename Get_type<R_, Point_tag>::type	Point;
+  typedef typename Get_type<R_, FT_tag>::type		FT;
+  typedef FT result_type;
+  typedef typename Get_functor<R_, Scalar_product_tag>::type	Dot;
+  typedef typename Get_functor<R_, Point_to_vector_tag>::type	P2V;
+  result_type operator()(Hyperplane const&h, Point const&p)const{
+    Dot dot(this->kernel());
+    P2V p2v(this->kernel());
+    return dot(h.orthogonal_vector(),p2v(p));
+    // Use Orthogonal_vector to make it generic?
+    // Copy the code from Scalar_product to avoid p2v?
+  }
+  template <class Iter>
+  result_type operator()(Iter f, Iter e)const{
+    throw "not implemented yet!";
+  }
+};
+}
+//TODO: Add a condition that the hyperplane type is the one from this file.
+CGAL_KD_DEFAULT_TYPE(Hyperplane_tag,(CGAL::Hyperplane<K>),(Vector_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Hyperplane_tag>,(CartesianDKernelFunctors::Construct_hyperplane<K>),(Vector_tag,Hyperplane_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Orthogonal_vector_tag,(CartesianDKernelFunctors::Orthogonal_vector<K>),(Vector_tag,Hyperplane_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Hyperplane_translation_tag,(CartesianDKernelFunctors::Hyperplane_translation<K>),(Hyperplane_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Value_at_tag,(CartesianDKernelFunctors::Value_at<K>),(Point_tag,Vector_tag,Hyperplane_tag),(Scalar_product_tag,Point_to_vector_tag));
+} // namespace CGAL
+#endif

NewKernel_d/include/CGAL/Kernel_d/Types/Iso_box.h

@@ -0,0 +1,49 @@
+#ifndef CGAL_KERNELD_TYPES_ISO_BOX_H
+#define CGAL_KERNELD_TYPES_ISO_BOX_H
+#include <utility>
+#include <CGAL/basic.h>
+#include <CGAL/functor_tags.h>
+#include <CGAL/Kernel/mpl.h>
+#include <CGAL/transforming_pair_iterator.h>
+namespace CGAL {
+template <class R_> class Iso_box {
+	typedef typename Get_type<R_, FT_tag>::type FT_;
+	typedef typename Get_type<R_, Point_tag>::type	Point_;
+	typedef std::pair<Point_,Point_> Data_;
+	Data_ data;
+	public:
+	Iso_box(){}
+	Iso_box(Point_ const&a, Point_ const&b): data(a,b) {}
+	Point_ min()const{
+	  return data.first;
+	}
+	Point_ max()const{
+	  return data.second;
+	}
+};
+namespace CartesianDKernelFunctors {
+  template <class R_> struct Construct_iso_box : Store_kernel<R_> {
+    CGAL_FUNCTOR_INIT_STORE(Construct_iso_box)
+    typedef typename Get_type<R_, Iso_box_tag>::type	result_type;
+    typedef typename Get_type<R_, RT_tag>::type RT;
+    typedef typename Get_type<R_, Point_tag>::type	Point;
+    typedef typename Get_functor<R_, Construct_ttag<Point_tag> >::type Cp_;
+    typedef typename Get_functor<R_, Construct_ttag<Point_cartesian_const_iterator_tag> >::type Ci_;
+    result_type operator()(Point const&a, Point const&b)const{
+      Cp_ cp(this->kernel());
+      Ci_ ci(this->kernel());
+      return result_type(cp(
+	  make_transforming_pair_iterator(ci(a,Begin_tag()), ci(b,Begin_tag()), Min<RT>()),
+	  make_transforming_pair_iterator(ci(a,End_tag()), ci(b,End_tag()), Min<RT>())),
+      cp(
+	  make_transforming_pair_iterator(ci(a,Begin_tag()), ci(b,Begin_tag()), Max<RT>()),
+	  make_transforming_pair_iterator(ci(a,End_tag()), ci(b,End_tag()), Max<RT>())));
+    }
+  };
+}
+CGAL_KD_DEFAULT_TYPE(Iso_box_tag,(CGAL::Iso_box<K>),(Point_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Iso_box_tag>,(CartesianDKernelFunctors::Construct_iso_box<K>),(Iso_box_tag,Point_tag),(Construct_ttag<Point_cartesian_const_iterator_tag>,Construct_ttag<Point_tag>));
+
+} // namespace CGAL
+
+#endif // CGAL_KERNELD_TYPES_ISO_BOX_H

NewKernel_d/include/CGAL/Kernel_d/Types/Line.h

@@ -0,0 +1,47 @@
+#ifndef CGAL_KERNELD_TYPES_LINE_H
+#define CGAL_KERNELD_TYPES_LINE_H
+#include <utility>
+#include <CGAL/functor_tags.h>
+#include <CGAL/Kernel/mpl.h>
+namespace CGAL {
+template <class R_> class Line {
+	typedef typename Get_type<R_, FT_tag>::type FT_;
+	typedef typename Get_type<R_, Point_tag>::type	Point_;
+	typedef std::pair<Point_,Point_> Data_;
+	Data_ data;
+	public:
+	Line(){}
+	Line(Point_ const&a, Point_ const&b): data(a,b) {}
+	Point_ point(int i)const{
+	  if(i==0) return data.first;
+	  if(i==1) return data.second;
+	  throw "not implemented";
+	}
+	Line opposite()const{
+		return Line(data.second,data.first);
+	}
+};
+namespace CartesianDKernelFunctors {
+  template <class R_> struct Construct_line : Store_kernel<R_> {
+    CGAL_FUNCTOR_INIT_STORE(Construct_line)
+    typedef typename Get_type<R_, Line_tag>::type	result_type;
+    typedef typename Get_type<R_, Point_tag>::type	Point;
+    typedef typename Get_type<R_, Vector_tag>::type	Vector;
+    typedef typename Get_functor<R_, Translated_point_tag>::type Tp_;
+    //typedef typename Get_functor<R_, Difference_of_points_tag>::type Dp_;
+    //typedef typename Get_functor<R_, Scaled_vector_tag>::type Sv_;
+    result_type operator()(Point const&a, Point const&b)const{
+      return result_type(a,b);
+    }
+    result_type operator()(Point const&a, typename First_if_different<Vector,Point>::Type const&b)const{
+      Tp_ tp(this->kernel());
+      return result_type(a,tp(a,b));
+    }
+  };
+}
+CGAL_KD_DEFAULT_TYPE(Line_tag,(CGAL::Line<K>),(Point_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Line_tag>,(CartesianDKernelFunctors::Construct_line<K>),(Line_tag,Point_tag,Vector_tag),(Translated_point_tag));
+
+} // namespace CGAL
+
+#endif // CGAL_KERNELD_TYPES_LINE_H

NewKernel_d/include/CGAL/Kernel_d/Types/Ray.h

@@ -0,0 +1,47 @@
+#ifndef CGAL_KERNELD_TYPES_RAY_H
+#define CGAL_KERNELD_TYPES_RAY_H
+#include <utility>
+#include <CGAL/functor_tags.h>
+#include <CGAL/Kernel/mpl.h>
+namespace CGAL {
+template <class R_> class Ray {
+	typedef typename Get_type<R_, FT_tag>::type FT_;
+	typedef typename Get_type<R_, Point_tag>::type	Point_;
+	typedef typename Get_type<R_, Vector_tag>::type	Vector_;
+	typedef std::pair<Point_,Vector_> Data_;
+	Data_ data;
+	public:
+	Ray(){}
+	Ray(Point_ const&a, Vector_ const&b): data(a,b) {}
+	Point_ source()const{
+	  return data.first;
+	}
+	// FIXME: return a R_::Direction?
+	Vector_ direction()const{
+	  return data.second;
+	}
+};
+namespace CartesianDKernelFunctors {
+  template <class R_> struct Construct_ray : Store_kernel<R_> {
+    CGAL_FUNCTOR_INIT_STORE(Construct_ray)
+    typedef typename Get_type<R_, Ray_tag>::type	result_type;
+    typedef typename Get_type<R_, Point_tag>::type	Point;
+    typedef typename Get_type<R_, Vector_tag>::type	Vector;
+    typedef typename Get_functor<R_, Difference_of_points_tag>::type Dp_;
+    //typedef typename Get_functor<R_, Translated_point_tag>::type Tp_;
+    //typedef typename Get_functor<R_, Scaled_vector_tag>::type Sv_;
+    result_type operator()(Point const&a, Vector const&b)const{
+      return result_type(a,b);
+    }
+    result_type operator()(Point const&a, typename First_if_different<Point,Vector>::Type const&b)const{
+      Dp_ dp(this->kernel());
+      return result_type(a,dp(b,a));
+    }
+  };
+}
+CGAL_KD_DEFAULT_TYPE(Ray_tag,(CGAL::Ray<K>),(Point_tag,Vector_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Ray_tag>,(CartesianDKernelFunctors::Construct_ray<K>),(Point_tag,Ray_tag,Vector_tag),(Difference_of_points_tag));
+
+} // namespace CGAL
+
+#endif // CGAL_KERNELD_TYPES_RAY_H

NewKernel_d/include/CGAL/Kernel_d/Types/Segment.h

@@ -0,0 +1,96 @@
+#ifndef CGAL_KERNELD_SEGMENTD_H
+#define CGAL_KERNELD_SEGMENTD_H
+#include <utility>
+#include <CGAL/functor_tags.h>
+namespace CGAL {
+template <class R_> class Segment {
+	typedef typename Get_type<R_, FT_tag>::type FT_;
+	typedef typename Get_type<R_, Point_tag>::type	Point_;
+	//typedef typename R_::Vector Vector_;
+	//typedef typename Get_functor<R_, Construct_ttag<Vector_tag> >::type Cv_;
+//	typedef typename R_::Squared_distance Csd_;
+	typedef std::pair<Point_,Point_> Data_;
+	Data_ data;
+	public:
+	//typedef Segmentd<R_> Segment;
+#ifdef CGAL_CXX0X
+	//FIXME: don't forward directly, piecewise_constuct should call the point construction functor (I guess? or is it unnecessary?)
+	template<class...U,class=typename std::enable_if<!std::is_same<std::tuple<typename std::decay<U>::type...>,std::tuple<Segment>>::value>::type>
+	Segment(U&&...u):data(std::forward<U>(u)...){}
+#else
+	Segment(){}
+	Segment(Point_ const&a, Point_ const&b): data(a,b) {}
+	//template<class A,class T1,class T2>
+	  //Segment(A const&,T1 const&t1,T2 const&t2)
+#endif
+	Point_ source()const{return data.first;}
+	Point_ target()const{return data.second;}
+	Point_ operator[](int i)const{
+		if((i%2)==0)
+			return source();
+		else
+			return target();
+	}
+	Segment opposite()const{
+		return Segment(target(),source());
+	}
+	//Vector_ vector()const{
+	//	return Cv_()(data.first,data.second);
+	//}
+//	FT_ squared_length()const{
+//		return Csd_()(data.first,data.second);
+//	}
+};
+
+namespace CartesianDKernelFunctors {
+
+template<class R_> struct Construct_segment {
+	CGAL_FUNCTOR_INIT_IGNORE(Construct_segment)
+	typedef R_ R;
+	typedef typename Get_type<R_, Point_tag>::type	Point;
+	typedef typename Get_type<R_, Segment_tag>::type	Segment;
+	typedef typename Get_functor<R_, Construct_ttag<Point_tag> >::type CP;
+	typedef Segment result_type;
+	result_type operator()(Point const&a, Point const&b)const{
+		return result_type(a,b);
+	}
+	// T should only be std::piecewise_construct_t, but we shouldn't fail if it doesn't exist.
+	template<class T,class U,class V>
+	result_type operator()(CGAL_FORWARDABLE(T),CGAL_FORWARDABLE(U) u,CGAL_FORWARDABLE(V) v)const{
+		CP cp(this->kernel());
+		result_type r = {{
+			call_on_tuple_elements<Point>(cp, CGAL_FORWARD(U,u)),
+			call_on_tuple_elements<Point>(cp, CGAL_FORWARD(V,v)) }};
+		return r;
+	}
+};
+
+// This should be part of Construct_point, according to Kernel_23 conventions
+template<class R_> struct Segment_extremity {
+	CGAL_FUNCTOR_INIT_IGNORE(Segment_extremity)
+	typedef R_ R;
+	typedef typename Get_type<R_, Point_tag>::type	Point;
+	typedef typename Get_type<R_, Segment_tag>::type	Segment;
+	typedef Point result_type;
+	result_type operator()(Segment const&s, int i)const{
+		if(i==0) return s.source();
+		CGAL_assertion(i==1);
+		return s.target();
+	}
+#ifdef CGAL_CXX0X
+	result_type operator()(Segment &&s, int i)const{
+		if(i==0) return std::move(s.source());
+		CGAL_assertion(i==1);
+		return std::move(s.target());
+	}
+#endif
+};
+} // CartesianDKernelFunctors
+
+CGAL_KD_DEFAULT_TYPE(Segment_tag,(CGAL::Segment<K>),(Point_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Segment_tag>,(CartesianDKernelFunctors::Construct_segment<K>),(Segment_tag,Point_tag),(Construct_ttag<Point_tag>));
+CGAL_KD_DEFAULT_FUNCTOR(Segment_extremity_tag,(CartesianDKernelFunctors::Segment_extremity<K>),(Segment_tag,Point_tag),());
+
+} // namespace CGAL
+
+#endif // CGAL_KERNELD_SEGMENTD_H

NewKernel_d/include/CGAL/Kernel_d/Types/Sphere.h

@@ -0,0 +1,90 @@
+#ifndef CGAL_KD_TYPE_SPHERE_H
+#define CGAL_KD_TYPE_SPHERE_H
+#include <CGAL/store_kernel.h>
+#include <boost/iterator/counting_iterator.hpp>
+namespace CGAL {
+template <class R_> class Sphere {
+	typedef typename Get_type<R_, FT_tag>::type FT_;
+	typedef typename Get_type<R_, Point_tag>::type	Point_;
+	Point_ c_;
+	FT_ r2_;
+
+	public:
+	Sphere(Point_ const&p, FT_ const&r2): c_(p), r2_(r2) {}
+	// TODO: Add a piecewise constructor?
+
+	Point_ const& center()const{return c_;}
+	FT_ const& squared_radius()const{return r2_;}
+};
+namespace CartesianDKernelFunctors {
+template <class R_> struct Construct_sphere : Store_kernel<R_> {
+  CGAL_FUNCTOR_INIT_STORE(Construct_sphere)
+  typedef typename Get_type<R_, Sphere_tag>::type	result_type;
+  typedef typename Get_type<R_, Point_tag>::type	Point;
+  typedef typename Get_type<R_, FT_tag>::type FT;
+  typedef typename R_::LA LA;
+  result_type operator()(Point const&a, FT const&b)const{
+    return result_type(a,b);
+  }
+  template <class Iter>
+  result_type operator()(Iter f, Iter e)const{
+    throw "not implemented yet!";
+  }
+};
+template <class R_> struct Center_of_sphere {
+  CGAL_FUNCTOR_INIT_IGNORE(Center_of_sphere)
+  typedef typename Get_type<R_, Sphere_tag>::type	Sphere;
+  typedef typename Get_type<R_, Point_tag>::type const&	result_type;
+  result_type operator()(Sphere const&s)const{
+    return s.center();
+  }
+};
+template <class R_> struct Squared_radius {
+  CGAL_FUNCTOR_INIT_IGNORE(Squared_radius)
+  typedef typename Get_type<R_, Sphere_tag>::type	Sphere;
+  typedef typename Get_type<R_, FT_tag>::type const&	result_type;
+  // TODO: Is_exact?
+  result_type operator()(Sphere const&s)const{
+    return s.squared_radius();
+  }
+};
+// FIXME: Move it to the generic functors, using the two above and conditional to the existence of sqrt(FT)
+template<class R_> struct Point_of_sphere : private Store_kernel<R_> {
+  CGAL_FUNCTOR_INIT_STORE(Point_of_sphere)
+  typedef R_ R;
+  typedef typename Get_type<R, FT_tag>::type FT;
+  typedef typename Get_type<R, RT_tag>::type RT;
+  typedef typename Get_type<R, Point_tag>::type Point;
+  typedef typename Get_type<R, Sphere_tag>::type Sphere;
+  typedef typename Get_functor<R, Construct_ttag<Point_tag> >::type CP;
+  typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+  typedef typename Get_functor<R, Point_dimension_tag>::type PD;
+  typedef Point result_type;
+  typedef Sphere first_argument_type;
+  typedef int second_argument_type;
+  struct Trans : std::binary_function<FT,FT,int> {
+    FT const& r_; int idx; bool sgn;
+    Trans (int n, FT const& r, bool b) : r_(r), idx(n), sgn(b) {}
+    FT operator()(FT const&x, int i)const{
+      return (i == idx) ? sgn ? x + r_ : x - r_ : x;
+    }
+  };
+  result_type operator()(Sphere const&s, int i)const{
+    CI ci(this->kernel());
+    PD pd(this->kernel());
+    typedef boost::counting_iterator<int,std::random_access_iterator_tag> Count;
+    Point const&c = s.center();
+    int d=pd(c);
+    bool last = (i == d);
+    Trans t(last ? 0 : i, sqrt(s.radius()), !last);
+    return CP(this->kernel())(make_transforming_pair_iterator(ci(c,Begin_tag()),Count(0),t),make_transforming_pair_iterator(ci(c,End_tag()),Count(d+1),t));
+  }
+};
+}
+CGAL_KD_DEFAULT_TYPE(Sphere_tag,(CGAL::Sphere<K>),(Point_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Sphere_tag>,(CartesianDKernelFunctors::Construct_sphere<K>),(Sphere_tag,Point_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Center_of_sphere_tag,(CartesianDKernelFunctors::Center_of_sphere<K>),(Sphere_tag,Point_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Squared_radius_tag,(CartesianDKernelFunctors::Squared_radius<K>),(Sphere_tag),());
+CGAL_KD_DEFAULT_FUNCTOR(Point_of_sphere_tag,(CartesianDKernelFunctors::Point_of_sphere<K>),(Sphere_tag,Point_tag),(Construct_ttag<Point_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+} // namespace CGAL
+#endif

NewKernel_d/include/CGAL/Kernel_d/Wrapper/Cartesian_wrap.h

@@ -0,0 +1,262 @@
+#ifndef CGAL_KERNEL_D_CARTESIAN_WRAP_H
+#define CGAL_KERNEL_D_CARTESIAN_WRAP_H
+
+#include <CGAL/basic.h>
+#include <CGAL/is_iterator.h>
+
+#include <CGAL/Kernel_d/Wrapper/Point_d.h>
+#include <CGAL/Kernel_d/Wrapper/Vector_d.h>
+#include <CGAL/Kernel_d/Wrapper/Segment_d.h>
+#include <CGAL/Kernel_d/Wrapper/Sphere_d.h>
+
+#include <CGAL/Kernel_d/Wrapper/Ref_count_obj.h>
+
+#include <boost/mpl/or.hpp>
+#include <boost/mpl/contains.hpp>
+#include <boost/mpl/vector.hpp>
+
+//TODO: do we want to store the kernel ref in the Object wrappers? It would allow for additions and operator[] and things like that to work, but objects would still need to be created by functors.
+
+namespace CGAL {
+namespace internal {
+BOOST_MPL_HAS_XXX_TRAIT_DEF(Is_wrapper)
+template<class T,bool=has_Is_wrapper<T>::value> struct Is_wrapper {
+	enum { value=false };
+	typedef Tag_false type;
+};
+template<class T> struct Is_wrapper<T,true> {
+	typedef typename T::Is_wrapper type;
+	enum { value=type::value };
+};
+
+template<class T,bool=is_iterator<T>::value> struct Is_wrapper_iterator {
+	enum { value=false };
+	typedef Tag_false type;
+};
+template<class T> struct Is_wrapper_iterator<T,true> :
+	Is_wrapper<typename std::iterator_traits<T>::value_type>
+{ };
+
+struct Forward_rep {
+//TODO: make a good C++0X version with perfect forwarding
+//#ifdef CGAL_CXX0X
+//template <class T,class=typename std::enable_if<!Is_wrapper<typename std::decay<T>::type>::value&&!Is_wrapper_iterator<typename std::decay<T>::type>::value>::type>
+//T&& operator()(typename std::remove_reference<T>::type&& t) const {return static_cast<T&&>(t);};
+//template <class T,class=typename std::enable_if<!Is_wrapper<typename std::decay<T>::type>::value&&!Is_wrapper_iterator<typename std::decay<T>::type>::value>::type>
+//T&& operator()(typename std::remove_reference<T>::type& t) const {return static_cast<T&&>(t);};
+//
+//template <class T,class=typename std::enable_if<Is_wrapper<typename std::decay<T>::type>::value>::type>
+//typename Type_copy_cvref<T,typename std::decay<T>::type::Rep>::type&&
+//operator()(T&& t) const {
+//	return static_cast<typename Type_copy_cvref<T,typename std::decay<T>::type::Rep>::type&&>(t.rep());
+//};
+//
+//template <class T,class=typename std::enable_if<Is_wrapper_iterator<typename std::decay<T>::type>::value>::type>
+//transforming_iterator<Forward_rep,typename std::decay<T>::type>
+//operator()(T&& t) const {
+//	return make_transforming_iterator(std::forward<T>(t),Forward_rep());
+//};
+//#else
+template <class T,bool=Is_wrapper<T>::value,bool=Is_wrapper_iterator<T>::value> struct result_;
+template <class T> struct result_<T,false,false>{typedef T const& type;};
+template <class T> struct result_<T,true,false>{typedef typename decay<T>::type::Rep const& type;};
+template <class T> struct result_<T,false,true>{typedef transforming_iterator<Forward_rep,typename decay<T>::type> type;};
+template<class> struct result;
+template<class T> struct result<Forward_rep(T)> : result_<T> {};
+
+template <class T> typename boost::disable_if<boost::mpl::or_<Is_wrapper<T>,Is_wrapper_iterator<T> >,T>::type const& operator()(T const& t) const {return t;}
+
+template <class T> typename boost::enable_if<Is_wrapper<T>,T>::type::Rep const& operator()(T const& t) const {return t.rep();}
+
+template <class T> transforming_iterator<Forward_rep,typename boost::enable_if<Is_wrapper_iterator<T>,T>::type> operator()(T const& t) const {return make_transforming_iterator(t,Forward_rep());}
+//#endif
+};
+}
+
+template <class B, class K, class T, bool = Provides_type<B, T>::value>
+struct Map_wrapping_type : Get_type<B, T> {};
+#define CGAL_REGISTER_OBJECT_WRAPPER(X) \
+  template <class B, class K> \
+  struct Map_wrapping_type <B, K, X##_tag, true> { \
+    typedef X##_d<K> type; \
+  }
+CGAL_REGISTER_OBJECT_WRAPPER(Point);
+CGAL_REGISTER_OBJECT_WRAPPER(Vector);
+CGAL_REGISTER_OBJECT_WRAPPER(Segment);
+CGAL_REGISTER_OBJECT_WRAPPER(Sphere);
+#undef CGAL_REGISTER_OBJECT_WRAPPER
+
+// Note: this tends to be an all or nothing thing currently, wrapping
+// only some types breaks, probably because we don't check whether the
+// return type is indeed wrapped.
+template < typename Base_ , typename Derived_ = Default >
+struct Cartesian_wrap : public Base_
+{
+    CGAL_CONSTEXPR Cartesian_wrap(){}
+    CGAL_CONSTEXPR Cartesian_wrap(int d):Base_(d){}
+    typedef Base_ Kernel_base;
+    typedef Cartesian_wrap Self;
+    typedef typename Default::Get<Derived_, Self>::type Derived;
+    // FIXME: The list doesn't belong here.
+    typedef boost::mpl::vector<Point_tag,Segment_tag,Sphere_tag,Vector_tag> Wrapped_list;
+
+    template <class T>
+    struct Type : Map_wrapping_type<Base_, Derived, T> {};
+
+    //Translate the arguments
+    template <class T, class D = void,
+      class=typename Get_functor_category<Derived,T>::type,
+      bool=Provides_functor<Kernel_base, T>::value,
+      bool=boost::mpl::contains<Wrapped_list,typename map_result_tag<T>::type>::type::value>
+    struct Functor {
+	    typedef typename Get_functor<Kernel_base, T>::type B;
+	    struct type {
+		    B b;
+		    type(){}
+		    type(Self const&k):b(k){}
+		    typedef typename B::result_type result_type;
+#ifdef CGAL_CXX0X
+		    template<class...U> result_type operator()(U&&...u)const{
+			    return b(internal::Forward_rep()(u)...);
+		    }
+#else
+#define VAR(Z,N,_) internal::Forward_rep()(u##N)
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class U)> result_type \
+		    operator()(BOOST_PP_ENUM_BINARY_PARAMS(N,U,const&u))const{ \
+			    return b(BOOST_PP_ENUM(N,VAR,)); \
+		    }
+		    BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+#undef VAR
+#endif
+	    };
+    };
+
+    // Preserve the difference between Null_functor and nothing.
+    template <class T, class D, class C, bool b>
+    struct Functor <T, D, C, false, b>
+      : Get_functor <Kernel_base, T> {};
+
+    //Translate both the arguments and the result
+    //TODO: Check Is_wrapper instead of relying on map_result_tag?
+    template<class T,class D> struct Functor<T,D,Construct_tag,true,true> {
+	    typedef typename Get_functor<Kernel_base, T>::type B;
+	    struct type {
+		    B b;
+		    type(){}
+		    type(Self const&k):b(k){}
+		    typedef typename map_result_tag<T>::type result_tag;
+		    // FIXME: Self or Derived?
+		    typedef typename Get_type<Self,result_tag>::type result_type;
+#ifdef CGAL_CXX0X
+		    template<class...U> result_type operator()(U&&...u)const{
+			    return result_type(Eval_functor(),b,internal::Forward_rep()(u)...);
+		    }
+#else
+#define VAR(Z,N,_) internal::Forward_rep()(u##N)
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class U)> result_type \
+		    operator()(BOOST_PP_ENUM_BINARY_PARAMS(N,U,const&u))const{ \
+			    return result_type(Eval_functor(),b,BOOST_PP_ENUM(N,VAR,)); \
+		    }
+		    BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+#undef VAR
+#endif
+	    };
+    };
+
+};
+
+template < typename Base_ >
+struct Cartesian_refcount : public Base_
+{
+    CGAL_CONSTEXPR Cartesian_refcount(){}
+    CGAL_CONSTEXPR Cartesian_refcount(int d):Base_(d){}
+    typedef Base_ Kernel_base;
+    typedef Cartesian_refcount Self;
+
+    // FIXME: Use object_list, or a list passed as argument, or anything
+    // automatic.
+    template <class T, class=void> struct Type : Get_type<Base_, T> {};
+#define CGAL_Kernel_obj(X,Y) \
+    template <class D> struct Type<X##_tag, D> { typedef Ref_count_obj<Cartesian_refcount, X##_tag> type; };
+
+    CGAL_Kernel_obj(Point,point)
+    CGAL_Kernel_obj(Vector,vector)
+#undef CGAL_Kernel_obj
+
+    template<class T> struct Dispatch {
+	    //typedef typename map_functor_type<T>::type f_t;
+	    typedef typename map_result_tag<T>::type r_t;
+	    enum {
+		    is_nul = boost::is_same<typename Get_functor<Kernel_base, T>::type,Null_functor>::value,
+		    ret_rcobj = boost::is_same<r_t,Point_tag>::value || boost::is_same<r_t,Vector_tag>::value
+	    };
+    };
+
+    //Translate the arguments
+    template<class T,class D=void,bool=Dispatch<T>::is_nul,bool=Dispatch<T>::ret_rcobj> struct Functor {
+	    typedef typename Get_functor<Kernel_base, T>::type B;
+	    struct type {
+		    B b;
+		    type(){}
+		    type(Self const&k):b(k){}
+		    typedef typename B::result_type result_type;
+#ifdef CGAL_CXX0X
+		    template<class...U> result_type operator()(U&&...u)const{
+			    return b(internal::Forward_rep()(u)...);
+		    }
+#else
+		    result_type operator()()const{
+			    return b();
+		    }
+#define VAR(Z,N,_) internal::Forward_rep()(u##N)
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class U)> result_type \
+		    operator()(BOOST_PP_ENUM_BINARY_PARAMS(N,U,const&u))const{ \
+			    return b(BOOST_PP_ENUM(N,VAR,)); \
+		    }
+		    BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+#undef VAR
+#endif
+	    };
+    };
+
+    //Translate both the arguments and the result
+    template<class T,class D,bool b> struct Functor<T,D,true,b> {
+	    typedef Null_functor type;
+    };
+
+    template<class T,class D> struct Functor<T,D,false,true> {
+	    typedef typename Get_functor<Kernel_base, T>::type B;
+	    struct type {
+		    B b;
+		    type(){}
+		    type(Self const&k):b(k){}
+		    typedef typename map_result_tag<T>::type result_tag;
+		    typedef typename Get_type<Self,result_tag>::type result_type;
+#ifdef CGAL_CXX0X
+		    template<class...U> result_type operator()(U&&...u)const{
+			    return result_type(Eval_functor(),b,internal::Forward_rep()(u)...);
+		    }
+#else
+		    result_type operator()()const{
+			     return result_type(Eval_functor(),b);
+		    }
+#define VAR(Z,N,_) internal::Forward_rep()(u##N)
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class U)> result_type \
+		    operator()(BOOST_PP_ENUM_BINARY_PARAMS(N,U,const&u))const{ \
+			    return result_type(Eval_functor(),b,BOOST_PP_ENUM(N,VAR,)); \
+		    }
+		    BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+#undef VAR
+#endif
+	    };
+    };
+
+};
+
+} //namespace CGAL
+
+#endif // CGAL_KERNEL_D_CARTESIAN_WRAP_H

NewKernel_d/include/CGAL/Kernel_d/Wrapper/Point_d.h

@@ -0,0 +1,248 @@
+#ifndef CGAL_WRAPPER_POINT_D_H
+#define CGAL_WRAPPER_POINT_D_H
+
+#include <CGAL/Origin.h>
+#include <CGAL/Kernel/mpl.h>
+#include <CGAL/representation_tags.h>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits.hpp>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
+#ifndef CGAL_CXX0X
+#include <boost/preprocessor/repetition.hpp>
+#endif
+#include <boost/utility/result_of.hpp>
+
+namespace CGAL {
+
+template <class R_>
+class Point_d : public Get_type<typename R_::Kernel_base, Point_tag>::type
+		// Deriving won't work if the point is just a __m256d.
+		// Test boost/std::is_class for instance
+{
+  typedef typename Get_type<R_, RT_tag>::type		RT_;
+  typedef typename Get_type<R_, FT_tag>::type		FT_;
+  typedef typename R_::Kernel_base		Kbase;
+  typedef typename Get_type<R_, Vector_tag>::type	Vector_;
+  typedef typename Get_functor<Kbase, Construct_ttag<Point_tag> >::type CPBase;
+  typedef typename Get_functor<Kbase, Compute_point_cartesian_coordinate_tag>::type CCBase;
+
+  typedef Point_d                            Self;
+  BOOST_STATIC_ASSERT((boost::is_same<Self, typename Get_type<R_, Point_tag>::type>::value));
+
+public:
+
+  typedef Tag_true Is_wrapper;
+  typedef typename R_::Default_ambient_dimension Ambient_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
+
+  //typedef typename R_::Point_cartesian_const_iterator Cartesian_const_iterator;
+  typedef typename Get_type<Kbase, Point_tag>::type      Rep;
+
+  const Rep& rep() const
+  {
+    return *this;
+  }
+
+  Rep& rep()
+  {
+    return *this;
+  }
+
+  typedef          R_                       R;
+
+#ifdef CGAL_CXX0X
+  template<class...U,class=typename std::enable_if<!std::is_same<std::tuple<typename std::decay<U>::type...>,std::tuple<Point_d> >::value>::type> explicit Point_d(U&&...u)
+	  : Rep(CPBase()(std::forward<U>(u)...)){}
+
+//  // called from Construct_point_d
+//  template<class...U> explicit Point_d(Eval_functor&&,U&&...u)
+//	  : Rep(Eval_functor(), std::forward<U>(u)...){}
+  template<class F,class...U> explicit Point_d(Eval_functor&&,F&&f,U&&...u)
+	  : Rep(std::forward<F>(f)(std::forward<U>(u)...)){}
+
+#if 0
+  // the new standard may make this necessary
+  Point_d(Point_d const&)=default;
+  Point_d(Point_d &);//=default;
+  Point_d(Point_d &&)=default;
+#endif
+
+  // try not to use these
+  Point_d(Rep const& v) : Rep(v) {}
+  Point_d(Rep& v) : Rep(static_cast<Rep const&>(v)) {}
+  Point_d(Rep&& v) : Rep(std::move(v)) {}
+
+  // this one should be implicit
+  Point_d(Origin const& v)
+    : Rep(CPBase()(v)) {}
+  Point_d(Origin& v)
+    : Rep(CPBase()(v)) {}
+  Point_d(Origin&& v)
+    : Rep(CPBase()(std::move(v))) {}
+
+#else
+
+  Point_d() : Rep(CPBase()()) {}
+
+  Point_d(Rep const& v) : Rep(v) {} // try not to use it
+
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  explicit Point_d(BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(CPBase()( \
+	BOOST_PP_ENUM_PARAMS(N,t))) {} \
+  \
+  template<class F,BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Point_d(Eval_functor,F const& f,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(f(BOOST_PP_ENUM_PARAMS(N,t))) {}
+  /*
+  template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Point_d(Eval_functor,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(Eval_functor(), BOOST_PP_ENUM_PARAMS(N,t)) {}
+  */
+
+  BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+ 
+  // this one should be implicit
+  Point_d(Origin const& o)
+    : Rep(CPBase()(o)) {}
+
+#endif
+
+  typename boost::result_of<CCBase(Rep,int)>::type cartesian(int i)const{
+	  return CCBase()(rep(),i);
+  }
+
+
+  /*
+  Direction_d direction() const
+  {
+    return R().construct_direction_d_object()(*this);
+  }
+
+  Vector_d transform(const Aff_transformation_d &t) const
+  {
+    return t.transform(*this);
+  }
+
+  Vector_d operator/(const RT& c) const
+  {
+   return R().construct_divided_vector_d_object()(*this,c);
+  }
+
+  Vector_d operator/(const typename First_if_different<FT_,RT>::Type & c) const
+  {
+   return R().construct_divided_vector_d_object()(*this,c);
+  }
+
+  typename Qualified_result_of<typename R::Compute_x_3, Vector_3>::type
+  x() const
+  {
+    return R().compute_x_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_y_3, Vector_3>::type
+  y() const
+  {
+    return R().compute_y_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_z_3, Vector_3>::type
+  z() const
+  {
+    return R().compute_z_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hx_3, Vector_3>::type
+  hx() const
+  {
+    return R().compute_hx_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hy_3, Vector_3>::type
+  hy() const
+  {
+    return R().compute_hy_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hz_3, Vector_3>::type
+  hz() const
+  {
+    return R().compute_hz_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hw_3, Vector_3>::type
+  hw() const
+  {
+    return R().compute_hw_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_x_3, Vector_3>::type
+  cartesian(int i) const
+  {
+    CGAL_kernel_precondition( (i == 0) || (i == 1) || (i == 2) );
+    if (i==0) return x();
+    if (i==1) return y();
+    return z();
+  }
+
+  typename Qualified_result_of<typename R::Compute_hw_3, Vector_3>::type
+  homogeneous(int i) const
+  {
+    CGAL_kernel_precondition( (i >= 0) || (i <= 3) );
+    if (i==0) return hx();
+    if (i==1) return hy();
+    if (i==2) return hz();
+    return hw();
+  }
+
+  int dimension() const // bad idea?
+  {
+      return rep.dimension();
+  }
+
+  typename Qualified_result_of<typename R::Compute_x_3, Vector_3>::type
+  operator[](int i) const
+  {
+      return cartesian(i);
+  }
+
+  Cartesian_const_iterator cartesian_begin() const
+  {
+    return typename R::Construct_cartesian_const_iterator_3()(*this);
+  }
+
+  Cartesian_const_iterator cartesian_end() const
+  {
+    return typename R::Construct_cartesian_const_iterator_3()(*this,3);
+  }
+
+  typename Qualified_result_of<typename R::Compute_squared_length_3, Vector_3>::type
+  squared_length() const
+  {
+    return R().compute_squared_length_3_object()(*this);
+  }
+*/
+};
+#if 0
+template <class R_> Point_d<R_>::Point_d(Point_d &)=default;
+#endif
+
+//TODO: IO
+
+//template <class R_>
+//Vector_d<R_> operator+(const Vector_d<R_>& v,const Vector_d<R_>& w) const
+//{
+//	return typename R::template Construct<Sum_of_vectors_tag>::type()(v,w);
+//}
+//
+//template <class R_>
+//Vector_d<R_> operator-(const Vector_d<R_>& v,const Vector_d<R_>& w) const
+//{
+//	return typename R::template Construct<Difference_of_vectors_tag>::type()(v,w);
+//}
+
+} //namespace CGAL
+
+#endif // CGAL_WRAPPER_POINT_D_H

NewKernel_d/include/CGAL/Kernel_d/Wrapper/Ref_count_obj.h

@@ -0,0 +1,101 @@
+#ifndef CGAL_WRAPPER_REF_COUNT_OBJ_H
+#define CGAL_WRAPPER_REF_COUNT_OBJ_H
+
+#include <CGAL/Origin.h>
+#include <CGAL/Handle_for.h>
+#include <CGAL/Kernel/mpl.h>
+#include <CGAL/representation_tags.h>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits.hpp>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
+#ifndef CGAL_CXX0X
+#include <boost/preprocessor/repetition.hpp>
+#endif
+#include <boost/utility/result_of.hpp>
+
+// no need for a fancy interface here, people can use the Point_d wrapper on
+// top.
+
+namespace CGAL {
+
+template <class R_, class Tag_>
+class Ref_count_obj
+{
+  typedef typename R_::Kernel_base	Kbase;
+  typedef typename Get_functor<Kbase, Construct_ttag<Tag_> >::type CBase;
+
+  typedef Ref_count_obj			Self;
+  BOOST_STATIC_ASSERT((boost::is_same<Self, typename Get_type<R_, Tag_>::type>::value));
+
+public:
+  typedef R_ R;
+
+  typedef Tag_true Is_wrapper;
+  typedef typename R_::Default_ambient_dimension Ambient_dimension;
+  //typedef Dimension_tag<0>  Feature_dimension;
+
+  typedef typename Get_type<Kbase, Tag_>::type	Rep;
+  typedef Handle_for<Rep> Data;
+
+private:
+  Data data;
+public:
+
+  const Rep& rep() const
+  {
+    return CGAL::get(data);
+  }
+
+#ifdef CGAL_CXX0X
+  template<class...U,class=typename std::enable_if<!std::is_same<std::tuple<typename std::decay<U>::type...>,std::tuple<Ref_count_obj> >::value>::type> explicit Ref_count_obj(U&&...u)
+	  : data(Eval_functor(),CBase(),std::forward<U>(u)...){}
+
+  template<class F,class...U> explicit Ref_count_obj(Eval_functor&&,F&&f,U&&...u)
+	  : data(Eval_functor(),std::forward<F>(f),std::forward<U>(u)...){}
+
+  // try not to use these
+  Ref_count_obj(Rep const& v) : data(v) {}
+  Ref_count_obj(Rep& v) : data(static_cast<Rep const&>(v)) {}
+  Ref_count_obj(Rep&& v) : data(std::move(v)) {}
+
+  // Do we really need this for point?
+//  // this one should be implicit
+//  Ref_count_obj(Origin const& v)
+//    : data(Eval_functor(),CBase(),v) {}
+//  Ref_count_obj(Origin& v)
+//    : data(Eval_functor(),CBase(),v) {}
+//  Ref_count_obj(Origin&& v)
+//    : data(Eval_functor(),CBase(),std::move(v)) {}
+
+#else
+
+  Ref_count_obj() : data(Eval_functor(),CBase()) {}
+
+  Ref_count_obj(Rep const& v) : data(v) {} // try not to use it
+
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  explicit Ref_count_obj(BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : data(Eval_functor(),CBase(),BOOST_PP_ENUM_PARAMS(N,t)) {} \
+  \
+  template<class F,BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Ref_count_obj(Eval_functor,F const& f,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : data(Eval_functor(),f,BOOST_PP_ENUM_PARAMS(N,t)) {}
+
+  BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+  template<class F>
+  Ref_count_obj(Eval_functor,F const& f)
+  : data(Eval_functor(),f) {}
+
+//  // this one should be implicit
+//  Ref_count_obj(Origin const& o)
+//    : data(Eval_functor(),CBase(),o) {}
+
+#endif
+
+};
+
+} //namespace CGAL
+
+#endif

NewKernel_d/include/CGAL/Kernel_d/Wrapper/Segment_d.h

@@ -0,0 +1,112 @@
+#ifndef CGAL_WRAPPER_SEGMENT_D_H
+#define CGAL_WRAPPER_SEGMENT_D_H
+
+#include <CGAL/Origin.h>
+#include <CGAL/Kernel/mpl.h>
+#include <CGAL/representation_tags.h>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits.hpp>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
+#ifndef CGAL_CXX0X
+#include <boost/preprocessor/repetition.hpp>
+#endif
+#include <boost/utility/result_of.hpp>
+
+namespace CGAL {
+
+template <class R_>
+class Segment_d : public Get_type<typename R_::Kernel_base, Segment_tag>::type
+{
+  typedef typename Get_type<R_, RT_tag>::type		RT_;
+  typedef typename Get_type<R_, FT_tag>::type		FT_;
+  typedef typename R_::Kernel_base			Kbase;
+  typedef typename Get_type<R_, Point_tag>::type	Point_;
+  typedef typename Get_functor<Kbase, Construct_ttag<Point_tag> >::type CPBase;
+  typedef typename Get_functor<Kbase, Construct_ttag<Segment_tag> >::type CSBase;
+  typedef typename Get_functor<Kbase, Segment_extremity_tag>::type CSEBase;
+
+  typedef Segment_d                            Self;
+  BOOST_STATIC_ASSERT((boost::is_same<Self, typename Get_type<R_, Segment_tag>::type>::value));
+
+public:
+
+  typedef Tag_true Is_wrapper;
+  typedef typename R_::Default_ambient_dimension Ambient_dimension;
+  typedef Dimension_tag<1>  Feature_dimension;
+
+  typedef typename Get_type<Kbase, Segment_tag>::type	Rep;
+
+  const Rep& rep() const
+  {
+    return *this;
+  }
+
+  Rep& rep()
+  {
+    return *this;
+  }
+
+  typedef          R_                       R;
+
+#ifdef CGAL_CXX0X
+  template<class...U,class=typename std::enable_if<!std::is_same<std::tuple<typename std::decay<U>::type...>,std::tuple<Segment_d> >::value>::type> explicit Segment_d(U&&...u)
+	  : Rep(CSBase()(std::forward<U>(u)...)){}
+
+//  // called from Construct_point_d
+//  template<class...U> explicit Point_d(Eval_functor&&,U&&...u)
+//	  : Rep(Eval_functor(), std::forward<U>(u)...){}
+  template<class F,class...U> explicit Segment_d(Eval_functor&&,F&&f,U&&...u)
+	  : Rep(std::forward<F>(f)(std::forward<U>(u)...)){}
+
+#if 0
+  // the new standard may make this necessary
+  Point_d(Point_d const&)=default;
+  Point_d(Point_d &);//=default;
+  Point_d(Point_d &&)=default;
+#endif
+
+  // try not to use these
+  Segment_d(Rep const& v) : Rep(v) {}
+  Segment_d(Rep& v) : Rep(static_cast<Rep const&>(v)) {}
+  Segment_d(Rep&& v) : Rep(std::move(v)) {}
+
+#else
+
+  Segment_d() : Rep(CSBase()()) {}
+
+  Segment_d(Rep const& v) : Rep(v) {} // try not to use it
+
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  explicit Segment_d(BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(CSBase()( \
+	BOOST_PP_ENUM_PARAMS(N,t))) {} \
+  \
+  template<class F,BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Segment_d(Eval_functor,F const& f,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(f(BOOST_PP_ENUM_PARAMS(N,t))) {}
+  /*
+  template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Point_d(Eval_functor,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(Eval_functor(), BOOST_PP_ENUM_PARAMS(N,t)) {}
+  */
+
+  BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+ 
+#endif
+
+	  //TODO: if CSEBase returns a reference to a base point, cast it to a
+	  //reference to a wrapper point. Ugly but should be safe.
+	  Point_ source()const{
+		  return Point_(Eval_functor(),CSEBase(),rep(),0);
+	  }
+	  Point_ target()const{
+		  return Point_(Eval_functor(),CSEBase(),rep(),1);
+	  }
+
+};
+
+} //namespace CGAL
+
+#endif // CGAL_WRAPPER_SEGMENT_D_H

NewKernel_d/include/CGAL/Kernel_d/Wrapper/Sphere_d.h

@@ -0,0 +1,109 @@
+#ifndef CGAL_WRAPPER_SPHERE_D_H
+#define CGAL_WRAPPER_SPHERE_D_H
+
+#include <CGAL/representation_tags.h>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits.hpp>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
+#ifndef CGAL_CXX0X
+#include <boost/preprocessor/repetition.hpp>
+#endif
+#include <boost/utility/result_of.hpp>
+
+namespace CGAL {
+
+template <class R_>
+class Sphere_d : public Get_type<typename R_::Kernel_base, Sphere_tag>::type
+{
+  typedef typename Get_type<R_, FT_tag>::type		FT_;
+  typedef typename R_::Kernel_base		Kbase;
+  typedef typename Get_type<R_, Point_tag>::type	Point_;
+  typedef typename Get_functor<Kbase, Construct_ttag<Sphere_tag> >::type	CSBase;
+  typedef typename Get_functor<Kbase, Center_of_sphere_tag>::type		COSBase;
+  typedef typename Get_functor<Kbase, Squared_radius_tag>::type			SRBase;
+
+  typedef Sphere_d                            Self;
+  BOOST_STATIC_ASSERT((boost::is_same<Self, typename Get_type<R_, Sphere_tag>::type>::value));
+
+public:
+
+  typedef Tag_true Is_wrapper;
+  typedef typename R_::Default_ambient_dimension Ambient_dimension;
+  typedef typename Increment_dimension<Ambient_dimension,-1>::type Feature_dimension;
+
+  typedef typename Get_type<Kbase, Sphere_tag>::type	Rep;
+
+  const Rep& rep() const
+  {
+    return *this;
+  }
+
+  Rep& rep()
+  {
+    return *this;
+  }
+
+  typedef          R_                       R;
+
+#ifdef CGAL_CXX0X
+  template<class...U,class=typename std::enable_if<!std::is_same<std::tuple<typename std::decay<U>::type...>,std::tuple<Sphere_d> >::value>::type> explicit Sphere_d(U&&...u)
+	  : Rep(CSBase()(std::forward<U>(u)...)){}
+
+//  // called from Construct_point_d
+//  template<class...U> explicit Point_d(Eval_functor&&,U&&...u)
+//	  : Rep(Eval_functor(), std::forward<U>(u)...){}
+  template<class F,class...U> explicit Sphere_d(Eval_functor&&,F&&f,U&&...u)
+	  : Rep(std::forward<F>(f)(std::forward<U>(u)...)){}
+
+#if 0
+  // the new standard may make this necessary
+  Point_d(Point_d const&)=default;
+  Point_d(Point_d &);//=default;
+  Point_d(Point_d &&)=default;
+#endif
+
+  // try not to use these
+  Sphere_d(Rep const& v) : Rep(v) {}
+  Sphere_d(Rep& v) : Rep(static_cast<Rep const&>(v)) {}
+  Sphere_d(Rep&& v) : Rep(std::move(v)) {}
+
+#else
+
+  Sphere_d() : Rep(CSBase()()) {}
+
+  Sphere_d(Rep const& v) : Rep(v) {} // try not to use it
+
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  explicit Sphere_d(BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(CSBase()( \
+	BOOST_PP_ENUM_PARAMS(N,t))) {} \
+  \
+  template<class F,BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Sphere_d(Eval_functor,F const& f,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(f(BOOST_PP_ENUM_PARAMS(N,t))) {}
+  /*
+  template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Point_d(Eval_functor,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(Eval_functor(), BOOST_PP_ENUM_PARAMS(N,t)) {}
+  */
+
+  BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+ 
+#endif
+
+    //TODO: if COSBase returns a reference to a base point, cast it to a
+    //reference to a wrapper point. Ugly but should be safe.
+    Point_ center()const{
+      return Point_(Eval_functor(),COSBase(),rep());
+    }
+  FT_ squared_radius()const{
+    return SRBase()(rep());
+  }
+
+};
+
+} //namespace CGAL
+
+#endif // CGAL_WRAPPER_SPHERE_D_H

NewKernel_d/include/CGAL/Kernel_d/Wrapper/Vector_d.h

@@ -0,0 +1,250 @@
+#ifndef CGAL_WRAPPER_VECTOR_D_H
+#define CGAL_WRAPPER_VECTOR_D_H
+
+#include <CGAL/Origin.h>
+#include <CGAL/Kernel/mpl.h>
+#include <CGAL/representation_tags.h>
+#include <boost/static_assert.hpp>
+#include <boost/type_traits.hpp>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/Dimension.h>
+#ifndef CGAL_CXX0X
+#include <boost/preprocessor/repetition.hpp>
+#endif
+#include <boost/utility/result_of.hpp>
+
+namespace CGAL {
+
+template <class R_>
+class Vector_d : public Get_type<typename R_::Kernel_base, Vector_tag>::type
+{
+  typedef typename Get_type<R_, RT_tag>::type		RT_;
+  typedef typename Get_type<R_, FT_tag>::type		FT_;
+  typedef typename R_::Kernel_base           Kbase;
+  typedef typename Get_type<R_, Point_tag>::type	Point_;
+  typedef typename Get_functor<Kbase, Construct_ttag<Vector_tag> >::type CVBase;
+  typedef typename Get_functor<Kbase, Compute_vector_cartesian_coordinate_tag>::type CCBase;
+
+  typedef Vector_d                            Self;
+  BOOST_STATIC_ASSERT((boost::is_same<Self, typename Get_type<R_, Vector_tag>::type>::value));
+
+public:
+
+  typedef Tag_true Is_wrapper;
+  typedef typename R_::Default_ambient_dimension Ambient_dimension;
+  typedef Dimension_tag<0>  Feature_dimension;
+
+  //typedef typename R_::Vector_cartesian_const_iterator Cartesian_const_iterator;
+  typedef typename Get_type<Kbase, Vector_tag>::type	Rep;
+
+  const Rep& rep() const
+  {
+    return *this;
+  }
+
+  Rep& rep()
+  {
+    return *this;
+  }
+
+  typedef          R_                       R;
+
+#ifdef CGAL_CXX0X
+  template<class...U,class=typename std::enable_if<!std::is_same<std::tuple<typename std::decay<U>::type...>,std::tuple<Vector_d> >::value>::type> explicit Vector_d(U&&...u)
+	  : Rep(CVBase()(std::forward<U>(u)...)){}
+
+//  // called from Construct_vector_d
+//  template<class...U> explicit Vector_d(Eval_functor&&,U&&...u)
+//	  : Rep(Eval_functor(), std::forward<U>(u)...){}
+  template<class F,class...U> explicit Vector_d(Eval_functor&&,F&&f,U&&...u)
+	  : Rep(std::forward<F>(f)(std::forward<U>(u)...)){}
+
+#if 0
+  // the new standard may make this necessary
+  Vector_d(Vector_d const&)=default;
+  Vector_d(Vector_d &);//=default;
+  Vector_d(Vector_d &&)=default;
+#endif
+
+  // try not to use these
+  Vector_d(Rep const& v) : Rep(v) {}
+  Vector_d(Rep& v) : Rep(static_cast<Rep const&>(v)) {}
+  Vector_d(Rep&& v) : Rep(std::move(v)) {}
+
+  // this one should be implicit
+  Vector_d(Null_vector const& v)
+    : Rep(CVBase()(v)) {}
+  Vector_d(Null_vector& v)
+    : Rep(CVBase()(v)) {}
+  Vector_d(Null_vector&& v)
+    : Rep(CVBase()(std::move(v))) {}
+
+#else
+
+  Vector_d() : Rep(CVBase()()) {}
+
+  Vector_d(Rep const& v) : Rep(v) {} // try not to use it
+
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  explicit Vector_d(BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(CVBase()( \
+	BOOST_PP_ENUM_PARAMS(N,t))) {} \
+  \
+  template<class F,BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Vector_d(Eval_functor,F const& f,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(f(BOOST_PP_ENUM_PARAMS(N,t))) {}
+  /*
+  template<BOOST_PP_ENUM_PARAMS(N,class T)> \
+  Vector_d(Eval_functor,BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t)) \
+  : Rep(Eval_functor(), BOOST_PP_ENUM_PARAMS(N,t)) {}
+  */
+
+  BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+ 
+  // this one should be implicit
+  Vector_d(Null_vector const& v)
+    : Rep(CVBase()(v)) {}
+
+#endif
+
+  typename boost::result_of<CCBase(Rep,int)>::type cartesian(int i)const{
+	  return CCBase()(rep(),i);
+  }
+
+  Vector_d operator-() const
+  {
+    return typename Get_functor<R, Opposite_vector_tag>::type()(*this);
+  }
+
+  /*
+  Direction_d direction() const
+  {
+    return R().construct_direction_d_object()(*this);
+  }
+
+  Vector_d transform(const Aff_transformation_d &t) const
+  {
+    return t.transform(*this);
+  }
+
+  Vector_d operator/(const RT& c) const
+  {
+   return R().construct_divided_vector_d_object()(*this,c);
+  }
+
+  Vector_d operator/(const typename First_if_different<FT_,RT>::Type & c) const
+  {
+   return R().construct_divided_vector_d_object()(*this,c);
+  }
+
+  typename Qualified_result_of<typename R::Compute_x_3, Vector_3>::type
+  x() const
+  {
+    return R().compute_x_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_y_3, Vector_3>::type
+  y() const
+  {
+    return R().compute_y_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_z_3, Vector_3>::type
+  z() const
+  {
+    return R().compute_z_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hx_3, Vector_3>::type
+  hx() const
+  {
+    return R().compute_hx_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hy_3, Vector_3>::type
+  hy() const
+  {
+    return R().compute_hy_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hz_3, Vector_3>::type
+  hz() const
+  {
+    return R().compute_hz_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_hw_3, Vector_3>::type
+  hw() const
+  {
+    return R().compute_hw_3_object()(*this);
+  }
+
+  typename Qualified_result_of<typename R::Compute_x_3, Vector_3>::type
+  cartesian(int i) const
+  {
+    CGAL_kernel_precondition( (i == 0) || (i == 1) || (i == 2) );
+    if (i==0) return x();
+    if (i==1) return y();
+    return z();
+  }
+
+  typename Qualified_result_of<typename R::Compute_hw_3, Vector_3>::type
+  homogeneous(int i) const
+  {
+    CGAL_kernel_precondition( (i >= 0) || (i <= 3) );
+    if (i==0) return hx();
+    if (i==1) return hy();
+    if (i==2) return hz();
+    return hw();
+  }
+
+  int dimension() const // bad idea?
+  {
+      return rep.dimension();
+  }
+
+  typename Qualified_result_of<typename R::Compute_x_3, Vector_3>::type
+  operator[](int i) const
+  {
+      return cartesian(i);
+  }
+
+  Cartesian_const_iterator cartesian_begin() const
+  {
+    return typename R::Construct_cartesian_const_iterator_3()(*this);
+  }
+
+  Cartesian_const_iterator cartesian_end() const
+  {
+    return typename R::Construct_cartesian_const_iterator_3()(*this,3);
+  }
+
+  typename Qualified_result_of<typename R::Compute_squared_length_3, Vector_3>::type
+  squared_length() const
+  {
+    return R().compute_squared_length_3_object()(*this);
+  }
+*/
+};
+#if 0
+template <class R_> Vector_d<R_>::Vector_d(Vector_d &)=default;
+#endif
+
+//TODO: IO
+
+template <class R_>
+Vector_d<R_> operator+(const Vector_d<R_>& v,const Vector_d<R_>& w)
+{
+	return typename Get_functor<R_, Sum_of_vectors_tag>::type()(v,w);
+}
+
+template <class R_>
+Vector_d<R_> operator-(const Vector_d<R_>& v,const Vector_d<R_>& w)
+{
+	return typename Get_functor<R_, Difference_of_vectors_tag>::type()(v,w);
+}
+
+} //namespace CGAL
+
+#endif // CGAL_WRAPPER_VECTOR_D_H

NewKernel_d/include/CGAL/Kernel_d/function_objects_cartesian.h

@@ -0,0 +1,796 @@
+#ifndef CGAL_KERNEL_D_FUNCTION_OBJECTS_CARTESIAN_H
+#define CGAL_KERNEL_D_FUNCTION_OBJECTS_CARTESIAN_H
+
+#include <CGAL/marcutils.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/Uncertain.h>
+#include <CGAL/store_kernel.h>
+#include <CGAL/is_iterator.h>
+#include <CGAL/number_utils.h>
+#include <CGAL/Kernel/Return_base_tag.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/transforming_pair_iterator.h>
+#include <CGAL/functor_tags.h>
+#include <CGAL/functor_properties.h>
+#include <CGAL/predicates/sign_of_determinant.h>
+#include <functional>
+#ifdef CGAL_CXX0X
+#include <initializer_list>
+#endif
+
+namespace CGAL {
+namespace CartesianDKernelFunctors {
+namespace internal {
+template<class,int> struct Dimension_at_most { enum { value = false }; };
+template<int a,int b> struct Dimension_at_most<Dimension_tag<a>,b> {
+	enum { value = (a <= b) };
+};
+}
+
+template<class R_,class D_=typename R_::Default_ambient_dimension,bool=internal::Dimension_at_most<D_,6>::value> struct Orientation_of_points : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Orientation_of_points)
+	typedef R_ R;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename R::LA::Square_matrix Matrix;
+
+	template<class Iter>
+	result_type operator()(Iter f, Iter e)const{
+		typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+		typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+		Point const& p0=*f++;
+		int d=pd(p0);
+		Matrix m(d,d);
+		for(int i=0;f!=e;++f,++i) {
+			Point const& p=*f;
+		for(int j=0;j<d;++j){
+			m(i,j)=c(p,j)-c(p0,j);
+			// should we cache the coordinates of p0 in case they are computed?
+		}
+		}
+		return R::LA::sign_of_determinant(CGAL_MOVE(m));
+	}
+
+#ifdef CGAL_CXX0X
+	// Since the dimension is at least 2, there are at least 3 points and no ambiguity with iterators.
+	// template <class...U,class=typename std::enable_if<std::is_same<Dimension_tag<sizeof...(U)-1>,typename R::Default_ambient_dimension>::value>::type>
+	template <class...U,class=typename std::enable_if<(sizeof...(U)>=3)>::type>
+	result_type operator()(U&&...u) const {
+		return operator()({std::forward<U>(u)...});
+	}
+
+	template <class P>
+	result_type operator()(std::initializer_list<P> l) const {
+		return operator()(l.begin(),l.end());
+	}
+#else
+	//should we make it template to avoid instantiation for wrong dim?
+	//or iterate outside the class?
+#define VAR(Z,J,I) m(I,J)=c(p##I,J)-c(x,J);
+#define VAR2(Z,I,N) BOOST_PP_REPEAT(N,VAR,I)
+#define CODE(Z,N,_) \
+	result_type operator()(Point const&x, BOOST_PP_ENUM_PARAMS(N,Point const&p)) const { \
+		typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel()); \
+		Matrix m(N,N); \
+		BOOST_PP_REPEAT(N,VAR2,N) \
+		return R::LA::sign_of_determinant(CGAL_MOVE(m)); \
+	}
+
+BOOST_PP_REPEAT_FROM_TO(7, 10, CODE, _ )
+	// No need to do it for <=6, since that uses a different code path
+#undef CODE
+#undef VAR2
+#undef VAR
+#endif
+};
+
+#ifdef CGAL_CXX0X
+template<class R_,int d> struct Orientation_of_points<R_,Dimension_tag<d>,true> : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Orientation_of_points)
+	typedef R_ R;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	template<class>struct Help;
+	template<int...I>struct Help<Indices<I...> > {
+		template<class C,class P,class T> result_type operator()(C const&c,P const&x,T&&t)const{
+			return sign_of_determinant(c(std::get<I/d>(t),I%d)-c(x,I%d)...);
+		}
+	};
+	template<class P0,class...P> result_type operator()(P0 const&x,P&&...p)const{
+		static_assert(d==sizeof...(P),"Wrong number of arguments");
+		typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+		return Help<typename N_increasing_indices<d*d>::type>()(c,x,std::forward_as_tuple(std::forward<P>(p)...));
+	}
+
+
+	template<int N,class Iter,class...U> result_type help2(Dimension_tag<N>, Iter f, Iter const&e, U&&...u)const{
+		auto const&p=*f;
+		return help2(Dimension_tag<N-1>(),++f,e,std::forward<U>(u)...,p);
+	}
+	template<class Iter,class...U> result_type help2(Dimension_tag<0>, Iter CGAL_assertion_code(f), Iter const& CGAL_assertion_code(e), U&&...u)const{
+		CGAL_assertion(f==e);
+		return operator()(std::forward<U>(u)...);
+	}
+	template<class Iter>
+	result_type operator()(Iter f, Iter e)const{
+		return help2(Dimension_tag<d+1>(),f,e);
+	}
+};
+#else
+#define VAR(Z,J,I) c(p##I,J)-x##J
+#define VAR2(Z,I,N) BOOST_PP_ENUM(N,VAR,I)
+#define VAR3(Z,N,_) Point const&p##N=*++f;
+#define VAR4(Z,N,_) RT const&x##N=c(x,N);
+#define CODE(Z,N,_) \
+template<class R_> struct Orientation_of_points<R_,Dimension_tag<N>,true> : private Store_kernel<R_> { \
+	CGAL_FUNCTOR_INIT_STORE(Orientation_of_points) \
+	typedef R_ R; \
+	typedef typename Get_type<R, RT_tag>::type RT; \
+	typedef typename Get_type<R, Point_tag>::type Point; \
+	typedef typename Get_type<R, Orientation_tag>::type result_type; \
+	result_type operator()(Point const&x, BOOST_PP_ENUM_PARAMS(N,Point const&p)) const { \
+		typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel()); \
+		BOOST_PP_REPEAT(N,VAR4,) \
+		return sign_of_determinant(BOOST_PP_ENUM(N,VAR2,N)); \
+	} \
+	template<class Iter> \
+	result_type operator()(Iter f, Iter CGAL_assertion_code(e))const{ \
+		Point const&x=*f; \
+		BOOST_PP_REPEAT(N,VAR3,) \
+		CGAL_assertion(++f==e); \
+		return operator()(x,BOOST_PP_ENUM_PARAMS(N,p)); \
+	} \
+};
+
+	BOOST_PP_REPEAT_FROM_TO(2, 7, CODE, _ )
+#undef CODE
+#undef VAR2
+#undef VAR
+
+#endif
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Orientation_of_points_tag,(CartesianDKernelFunctors::Orientation_of_points<K>),(Point_tag),(Point_dimension_tag,Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Orientation_of_vectors : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Orientation_of_vectors)
+	typedef R_ R;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename R::LA::Square_matrix Matrix;
+
+	template<class Iter>
+	result_type operator()(Iter f, Iter e)const{
+		typename Get_functor<R, Compute_vector_cartesian_coordinate_tag>::type c(this->kernel());
+		typename Get_functor<R, Point_dimension_tag>::type vd(this->kernel());
+		// FIXME: Uh? Using it on a vector ?!
+		Vector const& v0=*f;
+		int d=vd(v0);
+		Matrix m(d,d);
+		for(int j=0;j<d;++j){
+			m(0,j)=c(v0,j);
+		}
+		for(int i=1;++f!=e;++i) {
+			Vector const& v=*f;
+		for(int j=0;j<d;++j){
+			m(i,j)=c(v,j);
+		}
+		}
+		return R::LA::sign_of_determinant(CGAL_MOVE(m));
+	}
+
+#ifdef CGAL_CXX0X
+	template <class...U,class=typename std::enable_if<(sizeof...(U)>=3)>::type>
+	result_type operator()(U&&...u) const {
+		return operator()({std::forward<U>(u)...});
+	}
+
+	template <class V>
+	result_type operator()(std::initializer_list<V> l) const {
+		return operator()(l.begin(),l.end());
+	}
+#else
+	//TODO
+#endif
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Orientation_of_vectors_tag,(CartesianDKernelFunctors::Orientation_of_vectors<K>),(Vector_tag),(Point_dimension_tag,Compute_vector_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+#if 0
+template<class R_,bool=boost::is_same<typename R_::Point,typename R_::Vector>::value> struct Orientation : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Orientation)
+	typedef R_ R;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename Get_functor<R, Orientation_of_points_tag>::type OP;
+	typedef typename Get_functor<R, Orientation_of_vectors_tag>::type OV;
+
+	//FIXME!!!
+	//when Point and Vector are distinct types, the dispatch should be made
+	//in a way that doesn't instantiate a conversion from Point to Vector
+	template<class Iter>
+	result_type operator()(Iter const&f, Iter const& e)const{
+		typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+		typename std::iterator_traits<Iter>::difference_type d=std::distance(f,e);
+		int dim=pd(*f); // BAD
+		if(d==dim) return OV(this->kernel())(f,e);
+		CGAL_assertion(d==dim+1);
+		return OP(this->kernel())(f,e);
+	}
+	//TODO: version that takes objects directly instead of iterators
+};
+
+template<class R_> struct Orientation<R_,false> : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Orientation)
+	typedef R_ R;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Orientation_tag>::type result_type;
+	typedef typename Get_functor<R, Orientation_of_points_tag>::type OP;
+	typedef typename Get_functor<R, Orientation_of_vectors_tag>::type OV;
+	typedef typename R::LA::Square_matrix Matrix;
+
+	//FIXME!!!
+	//when Point and Vector are distinct types, the dispatch should be made
+	//in a way that doesn't instantiate a conversion from Point to Vector
+	template<class Iter>
+	typename boost::enable_if<is_iterator_to<Iter,Point>,result_type>::type
+	operator()(Iter const&f, Iter const& e)const{
+		return OP(this->kernel())(f,e);
+	}
+	template<class Iter>
+	typename boost::enable_if<is_iterator_to<Iter,Vector>,result_type>::type
+	operator()(Iter const&f, Iter const& e)const{
+		return OV(this->kernel())(f,e);
+	}
+	//TODO: version that takes objects directly instead of iterators
+};
+#endif
+
+template<class R_> struct Side_of_oriented_sphere : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Side_of_oriented_sphere)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Oriented_side_tag>::type result_type;
+	typedef typename Increment_dimension<typename R::Default_ambient_dimension>::type D1;
+	typedef typename Increment_dimension<typename R::Max_ambient_dimension>::type D2;
+	typedef typename R::LA::template Rebind_dimension<D1,D2>::Other LA;
+	typedef typename LA::Square_matrix Matrix;
+
+	template<class Iter>
+	result_type operator()(Iter f, Iter const& e)const{
+	  Point const& p0=*f++; // *--e ?
+	  return this->operator()(f,e,p0);
+	}
+
+	template<class Iter>
+	result_type operator()(Iter f, Iter const& e, Point const& p0) const {
+	  typedef typename Get_functor<R, Squared_distance_to_origin_tag>::type Sqdo;
+	  typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
+	  typename Get_functor<R, Point_dimension_tag>::type pd(this->kernel());
+
+	  int d=pd(p0);
+	  Matrix m(d+1,d+1);
+	  if(CGAL::Is_stored<Sqdo>::value) {
+	    Sqdo sqdo(this->kernel());
+	    for(int i=0;f!=e;++f,++i) {
+	      Point const& p=*f;
+	      for(int j=0;j<d;++j){
+		RT const& x=c(p,j);
+		m(i,j)=x-c(p0,j);
+	      }
+	      m(i,d) = sqdo(p) - sqdo(p0);
+	    }
+	  } else {
+	    for(int i=0;f!=e;++f,++i) {
+	      Point const& p=*f;
+	      m(i,d) = 0;
+	      for(int j=0;j<d;++j){
+		RT const& x=c(p,j);
+		m(i,j)=x-c(p0,j);
+		m(i,d)+=CGAL::square(m(i,j));
+	      }
+	    }
+	  }
+	  if(d%2)
+	    return -LA::sign_of_determinant(CGAL_MOVE(m));
+	  else
+	    return LA::sign_of_determinant(CGAL_MOVE(m));
+	}
+
+#ifdef CGAL_CXX0X
+	template <class...U,class=typename std::enable_if<(sizeof...(U)>=4)>::type>
+	result_type operator()(U&&...u) const {
+		return operator()({std::forward<U>(u)...});
+	}
+
+	template <class P>
+	result_type operator()(std::initializer_list<P> l) const {
+		return operator()(l.begin(),l.end());
+	}
+#else
+	//TODO
+#endif
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Side_of_oriented_sphere_tag,(CartesianDKernelFunctors::Side_of_oriented_sphere<K>),(Point_tag),(Point_dimension_tag,Squared_distance_to_origin_tag,Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Point_to_vector : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Point_to_vector)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+	typedef Vector result_type;
+	typedef Point argument_type;
+	result_type operator()(argument_type const&v)const{
+		CI ci(this->kernel());
+		return CV(this->kernel())(ci(v,Begin_tag(),ci(v,End_tag())));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Point_to_vector_tag,(CartesianDKernelFunctors::Point_to_vector<K>),(Point_tag,Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Vector_to_point : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Vector_to_point)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_functor<R, Construct_ttag<Point_tag> >::type CV;
+	typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+	typedef Point result_type;
+	typedef Vector argument_type;
+	result_type operator()(argument_type const&v)const{
+		CI ci(this->kernel());
+		return CV(this->kernel())(ci(v,Begin_tag(),ci(v,End_tag())));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Vector_to_point_tag,(CartesianDKernelFunctors::Vector_to_point<K>),(Point_tag,Vector_tag),(Construct_ttag<Point_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Opposite_vector : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Opposite_vector)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+	typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+	typedef Vector result_type;
+	typedef Vector argument_type;
+	result_type operator()(Vector const&v)const{
+		CI ci(this->kernel());
+		return CV(this->kernel())(make_transforming_iterator(ci(v,Begin_tag()),std::negate<RT>()),make_transforming_iterator(ci(v,End_tag()),std::negate<RT>()));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Opposite_vector_tag,(CartesianDKernelFunctors::Opposite_vector<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Scaled_vector : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Scaled_vector)
+	typedef R_ R;
+	typedef typename Get_type<R, FT_tag>::type FT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+	typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+	typedef Vector result_type;
+	typedef Vector first_argument_type;
+	typedef FT second_argument_type;
+	result_type operator()(Vector const&v,FT const& s)const{
+		CI ci(this->kernel());
+		return CV(this->kernel())(make_transforming_iterator(ci(v,Begin_tag()),Scale<FT>(s)),make_transforming_iterator(ci(v,End_tag()),Scale<FT>(s)));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Scaled_vector_tag,(CartesianDKernelFunctors::Scaled_vector<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Sum_of_vectors : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Sum_of_vectors)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+	typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+	typedef Vector result_type;
+	typedef Vector first_argument_type;
+	typedef Vector second_argument_type;
+	result_type operator()(Vector const&a, Vector const&b)const{
+		CI ci(this->kernel());
+		return CV(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),std::plus<RT>()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),std::plus<RT>()));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Sum_of_vectors_tag,(CartesianDKernelFunctors::Sum_of_vectors<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Difference_of_vectors : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Difference_of_vectors)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+	typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+	typedef Vector result_type;
+	typedef Vector first_argument_type;
+	typedef Vector second_argument_type;
+	result_type operator()(Vector const&a, Vector const&b)const{
+		CI ci(this->kernel());
+		return CV(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),std::minus<RT>()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),std::minus<RT>()));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Difference_of_vectors_tag,(CartesianDKernelFunctors::Difference_of_vectors<K>),(Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Translated_point : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Translated_point)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_functor<R, Construct_ttag<Point_tag> >::type CP;
+	typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CVI;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CPI;
+	typedef Point  result_type;
+	typedef Point  first_argument_type;
+	typedef Vector second_argument_type;
+	result_type operator()(Point const&a, Vector const&b)const{
+		CVI cvi(this->kernel());
+		CPI cpi(this->kernel());
+		return CP(this->kernel())(make_transforming_pair_iterator(cpi(a,Begin_tag()),cvi(b,Begin_tag()),std::plus<RT>()),make_transforming_pair_iterator(cpi(a,End_tag()),cvi(b,End_tag()),std::plus<RT>()));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Translated_point_tag,(CartesianDKernelFunctors::Translated_point<K>),(Point_tag, Vector_tag),(Construct_ttag<Point_tag>, Construct_ttag<Vector_cartesian_const_iterator_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Difference_of_points : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Difference_of_points)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_functor<R, Construct_ttag<Vector_tag> >::type CV;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+	typedef Vector result_type;
+	typedef Point first_argument_type;
+	typedef Point second_argument_type;
+	result_type operator()(Point const&a, Point const&b)const{
+		CI ci(this->kernel());
+		return CV(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),std::minus<RT>()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),std::minus<RT>()));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Difference_of_points_tag,(CartesianDKernelFunctors::Difference_of_points<K>),(Point_tag, Vector_tag),(Construct_ttag<Vector_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Midpoint : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Midpoint)
+	typedef R_ R;
+	typedef typename Get_type<R, FT_tag>::type FT;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_functor<R, Construct_ttag<Point_tag> >::type CP;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+	typedef Point result_type;
+	typedef Point first_argument_type;
+	typedef Point second_argument_type;
+	// There is a division, but it will be cast to RT afterwards anyway, so maybe we could use RT.
+	struct Average : std::binary_function<FT,FT,RT> {
+		FT operator()(FT const&a, RT const&b)const{
+			return (a+b)/2;
+		}
+	};
+	result_type operator()(Point const&a, Point const&b)const{
+		CI ci(this->kernel());
+		//Divide<FT,int> half(2);
+		//return CP(this->kernel())(make_transforming_iterator(make_transforming_pair_iterator(ci.begin(a),ci.begin(b),std::plus<FT>()),half),make_transforming_iterator(make_transforming_pair_iterator(ci.end(a),ci.end(b),std::plus<FT>()),half));
+		return CP(this->kernel())(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),Average()),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),Average()));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Midpoint_tag,(CartesianDKernelFunctors::Midpoint<K>),(Point_tag),(Construct_ttag<Point_tag>, Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Squared_length : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Squared_length)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Vector_tag>::type Vector;
+	typedef typename Get_functor<R, Construct_ttag<Vector_cartesian_const_iterator_tag> >::type CI;
+	typedef RT result_type;
+	typedef Vector argument_type;
+	result_type operator()(Vector const&a)const{
+		CI ci(this->kernel());
+		typename Algebraic_structure_traits<RT>::Square f;
+		// TODO: avoid this RT(0)+...
+		return std::accumulate(make_transforming_iterator(ci(a,Begin_tag()),f),make_transforming_iterator(ci(a,End_tag()),f),RT(0));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Squared_length_tag,(CartesianDKernelFunctors::Squared_length<K>),(Vector_tag),(Construct_ttag<Vector_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Squared_distance_to_origin : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Squared_distance_to_origin)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+	typedef RT result_type;
+	typedef Point argument_type;
+	result_type operator()(Point const&a)const{
+		CI ci(this->kernel());
+		typename Algebraic_structure_traits<RT>::Square f;
+		// TODO: avoid this RT(0)+...
+		return std::accumulate(make_transforming_iterator(ci(a,Begin_tag()),f),make_transforming_iterator(ci(a,End_tag()),f),RT(0));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Squared_distance_to_origin_tag,(CartesianDKernelFunctors::Squared_distance_to_origin<K>),(Point_tag),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Squared_distance : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Squared_distance)
+	typedef R_ R;
+	typedef typename Get_type<R, RT_tag>::type RT;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+	typedef RT result_type;
+	typedef Point first_argument_type;
+	typedef Point second_argument_type;
+	struct Sq_diff : std::binary_function<RT,RT,RT> {
+		RT operator()(RT const&a, RT const&b)const{
+			return CGAL::square(a-b);
+		}
+	};
+	result_type operator()(Point const&a, Point const&b)const{
+		CI ci(this->kernel());
+		Sq_diff f;
+		// TODO: avoid this RT(0)+...
+		return std::accumulate(make_transforming_pair_iterator(ci(a,Begin_tag()),ci(b,Begin_tag()),f),make_transforming_pair_iterator(ci(a,End_tag()),ci(b,End_tag()),f),RT(0));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Squared_distance_tag,(CartesianDKernelFunctors::Squared_distance<K>),(Point_tag),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Compare_distance : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Compare_distance)
+	typedef R_ R;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_functor<R, Squared_distance_tag>::type CSD;
+	typedef typename Get_type<R, Comparison_result_tag>::type result_type;
+	typedef Point first_argument_type;
+	typedef Point second_argument_type;
+	typedef Point third_argument_type; // why am I doing this already?
+	typedef Point fourth_argument_type;
+	result_type operator()(Point const&a, Point const&b, Point const&c)const{
+		CSD csd(this->kernel());
+		return CGAL_NTS compare(csd(a,b),csd(a,c));
+	}
+	result_type operator()(Point const&a, Point const&b, Point const&c, Point const&d)const{
+		CSD csd(this->kernel());
+		return CGAL_NTS compare(csd(a,b),csd(c,d));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Compare_distance_tag,(CartesianDKernelFunctors::Compare_distance<K>),(Point_tag),(Squared_distance_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Less_point_cartesian_coordinate : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Less_point_cartesian_coordinate)
+	typedef R_ R;
+	typedef typename Get_type<R, Bool_tag>::type result_type;
+	typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type Cc;
+	// TODO: This is_exact thing should be reengineered.
+	// the goal is to have a way to tell: don't filter this
+	typedef typename CGAL::Is_exact<Cc> Is_exact;
+
+	template<class V,class W,class I>
+	result_type operator()(V const&a, W const&b, I i)const{
+		Cc c(this->kernel());
+		return c(a,i)<c(b,i);
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Less_point_cartesian_coordinate_tag,(CartesianDKernelFunctors::Less_point_cartesian_coordinate<K>),(),(Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Compare_point_cartesian_coordinate : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Compare_point_cartesian_coordinate)
+	typedef R_ R;
+	typedef typename Get_type<R, Comparison_result_tag>::type result_type;
+	typedef typename Get_functor<R, Compute_point_cartesian_coordinate_tag>::type Cc;
+	// TODO: This is_exact thing should be reengineered.
+	// the goal is to have a way to tell: don't filter this
+	typedef typename CGAL::Is_exact<Cc> Is_exact;
+
+	template<class V,class W,class I>
+	result_type operator()(V const&a, W const&b, I i)const{
+		Cc c(this->kernel());
+		return CGAL_NTS compare(c(a,i),c(b,i));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Compare_point_cartesian_coordinate_tag,(CartesianDKernelFunctors::Compare_point_cartesian_coordinate<K>),(),(Compute_point_cartesian_coordinate_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Compare_lexicographically : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Compare_lexicographically)
+	typedef R_ R;
+	typedef typename Get_type<R, Comparison_result_tag>::type result_type;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+	// TODO: This is_exact thing should be reengineered.
+	// the goal is to have a way to tell: don't filter this
+	typedef typename CGAL::Is_exact<CI> Is_exact;
+
+	template<class V,class W>
+	result_type operator()(V const&a, W const&b)const{
+		CI c(this->kernel());
+#ifdef CGAL_CXX0X
+		auto
+#else
+		typename CI::result_type
+#endif
+		a_begin=c(a,Begin_tag()),
+		b_begin=c(b,Begin_tag()),
+		a_end=c(a,End_tag());
+		result_type res;
+		// can't we do slightly better for Uncertain<*> ?
+		// after res=...; if(is_uncertain(res))return indeterminate<result_type>();
+		do res=CGAL_NTS compare(*a_begin++,*b_begin++);
+		while(a_begin!=a_end && res==EQUAL);
+		return res;
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Compare_lexicographically_tag,(CartesianDKernelFunctors::Compare_lexicographically<K>),(),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Less_lexicographically : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Less_lexicographically)
+	typedef R_ R;
+	typedef typename Get_type<R, Bool_tag>::type result_type;
+	typedef typename Get_functor<R, Compare_lexicographically_tag>::type CL;
+	typedef typename CGAL::Is_exact<CL> Is_exact;
+
+	template <class V, class W>
+	result_type operator() (V const&a, W const&b) const {
+		CL c (this->kernel());
+		return c(a,b) < 0;
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Less_lexicographically_tag,(CartesianDKernelFunctors::Less_lexicographically<K>),(),(Compare_lexicographically_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Less_or_equal_lexicographically : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Less_or_equal_lexicographically)
+	typedef R_ R;
+	typedef typename Get_type<R, Bool_tag>::type result_type;
+	typedef typename Get_functor<R, Compare_lexicographically_tag>::type CL;
+	typedef typename CGAL::Is_exact<CL> Is_exact;
+
+	template <class V, class W>
+	result_type operator() (V const&a, W const&b) const {
+		CL c (this->kernel());
+		return c(a,b) <= 0;
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Less_or_equal_lexicographically_tag,(CartesianDKernelFunctors::Less_or_equal_lexicographically<K>),(),(Compare_lexicographically_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Equal_points : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Equal_points)
+	typedef R_ R;
+	typedef typename Get_type<R, Bool_tag>::type result_type;
+	typedef typename Get_functor<R, Construct_ttag<Point_cartesian_const_iterator_tag> >::type CI;
+	// TODO: This is_exact thing should be reengineered.
+	// the goal is to have a way to tell: don't filter this
+	typedef typename CGAL::Is_exact<CI> Is_exact;
+
+	template<class V,class W>
+	result_type operator()(V const&a, W const&b)const{
+		CI c(this->kernel());
+#ifdef CGAL_CXX0X
+		auto
+#else
+		typename CI::result_type
+#endif
+		a_begin=c(a,Begin_tag()),
+		b_begin=c(b,Begin_tag()),
+		a_end=c(a,End_tag());
+		result_type res = true;
+		// Is using CGAL::possibly for Uncertain really an optimization?
+		do res = res & (*a_begin++ == *b_begin++);
+		while(a_begin!=a_end && possibly(res));
+		return res;
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Equal_points_tag,(CartesianDKernelFunctors::Equal_points<K>),(),(Construct_ttag<Point_cartesian_const_iterator_tag>));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Oriented_side : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Oriented_side)
+	typedef R_ R;
+	typedef typename Get_type<R, Oriented_side_tag>::type result_type;
+	typedef typename Get_type<R, Point_tag>::type Point;
+	typedef typename Get_type<R, Hyperplane_tag>::type Hyperplane;
+	typedef typename Get_type<R, Sphere_tag>::type Sphere;
+	typedef typename Get_functor<R, Value_at_tag>::type VA;
+	typedef typename Get_functor<R, Hyperplane_translation_tag>::type HT;
+	typedef typename Get_functor<R, Squared_distance_tag>::type SD;
+	typedef typename Get_functor<R, Squared_radius_tag>::type SR;
+	typedef typename Get_functor<R, Center_of_sphere_tag>::type CS;
+
+	result_type operator()(Hyperplane const&h, Point const&p)const{
+		HT ht(this->kernel());
+		VA va(this->kernel());
+		return CGAL::compare(va(h,p),ht(h));
+	}
+	result_type operator()(Sphere const&s, Point const&p)const{
+		SD sd(this->kernel());
+		SR sr(this->kernel());
+		CS cs(this->kernel());
+		return CGAL::compare(sd(cs(s),p),sr(s));
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Oriented_side_tag,(CartesianDKernelFunctors::Oriented_side<K>),(Point_tag,Sphere_tag,Hyperplane_tag),(Value_at_tag,Hyperplane_translation_tag,Squared_distance_tag,Squared_radius_tag,Center_of_sphere_tag));
+
+namespace CartesianDKernelFunctors {
+template<class R_> struct Has_on_positive_side : private Store_kernel<R_> {
+	CGAL_FUNCTOR_INIT_STORE(Has_on_positive_side)
+	typedef R_ R;
+	typedef typename Get_type<R, Bool_tag>::type result_type;
+	typedef typename Get_functor<R, Oriented_side_tag>::type OS;
+
+	template <class Obj, class Pt>
+	result_type operator()(Obj const&o, Pt const&p)const{
+		OS os(this->kernel());
+		return os(o,p) == ON_POSITIVE_SIDE;
+	}
+};
+}
+
+CGAL_KD_DEFAULT_FUNCTOR(Has_on_positive_side_tag,(CartesianDKernelFunctors::Has_on_positive_side<K>),(),(Oriented_side_tag));
+
+}
+#include <CGAL/Kernel_d/Coaffine.h>
+#endif // CGAL_KERNEL_D_FUNCTION_OBJECTS_CARTESIAN_H

NewKernel_d/include/CGAL/Kernel_d/interface_macros.h

@@ -0,0 +1,133 @@
+#ifndef CGAL_Kernel_pred
+#  define CGAL_Kernel_pred(X, Y)
+#endif
+
+#ifndef CGAL_Kernel_comp
+#  define CGAL_Kernel_comp(X, Y)
+#endif
+#ifndef CGAL_Kernel_comp1
+#  define CGAL_Kernel_comp1(X, Y) CGAL_Kernel_comp(X, Y)
+#endif
+#ifndef CGAL_Kernel_comp2
+#  define CGAL_Kernel_comp2(X, Y) CGAL_Kernel_comp(X, Y)
+#endif
+
+#ifndef CGAL_Kernel_cons
+#  define CGAL_Kernel_cons(X, Y)
+#endif
+#ifndef CGAL_Kernel_cons1
+#  define CGAL_Kernel_cons1(X, Y) CGAL_Kernel_cons(X, Y)
+#endif
+#ifndef CGAL_Kernel_cons2
+#  define CGAL_Kernel_cons2(X, Y) CGAL_Kernel_cons(X, Y)
+#endif
+
+#ifndef CGAL_Kernel_obj
+#  define CGAL_Kernel_obj(X,Y)
+#endif
+#ifndef CGAL_Kernel_obj1
+#  define CGAL_Kernel_obj1(X,Y) CGAL_Kernel_obj(X,Y)
+#endif
+#ifndef CGAL_Kernel_obj2
+#  define CGAL_Kernel_obj2(X,Y) CGAL_Kernel_obj(X,Y)
+#endif
+#ifndef CGAL_Kernel_obj3
+#  define CGAL_Kernel_obj3(X,Y) CGAL_Kernel_obj2(X,Y)
+#endif
+
+//CGAL_Kernel_obj1(Vector,vector)
+//CGAL_Kernel_obj1(Point,point)
+CGAL_Kernel_obj2(Segment,segment)
+//CGAL_Kernel_obj2(Sphere,sphere)
+//CGAL_Kernel_obj3(Line,line)
+//CGAL_Kernel_obj3(Ray,ray)
+//CGAL_Kernel_obj3(Hyperplane,hyperplane)
+//CGAL_Kernel_obj3(Aff_transformation,aff_transformation)
+//CGAL_Kernel_obj3(Iso_box,iso_box)
+
+//CGAL_Kernel_cons1(Construct_point_cartesian_const_iterator,
+//		  construct_point_cartesian_const_iterator_object)
+//CGAL_Kernel_cons1(Construct_vector_cartesian_const_iterator,
+//		  construct_vector_cartesian_const_iterator_object)
+//CGAL_Kernel_cons2(Sum_of_vectors,
+//		  sum_of_vectors_object)
+//CGAL_Kernel_cons2(Difference_of_vectors,
+//		  difference_of_vectors_object)
+//CGAL_Kernel_cons2(Translated_point,
+//		  translated_point_object)
+//CGAL_Kernel_cons2(Opposite_vector,
+//		  opposite_vector_object)
+//CGAL_Kernel_cons2(Scaled_vector,
+//		  scaled_vector_object)
+//CGAL_Kernel_cons2(Difference_of_points,
+//		  difference_of_points_object)
+//CGAL_Kernel_cons2(Vector_to_point,
+//		  vector_to_point_object)
+//CGAL_Kernel_cons2(Point_to_vector,
+//		  point_to_vector_object)
+//CGAL_Kernel_cons2(Midpoint,
+//		  midpoint_object)
+//CGAL_Kernel_cons2(Orthogonal_vector,
+//		  orthogonal_vector_object)
+//CGAL_Kernel_cons2(Hyperplane_translation,
+//		  hyperplane_translation_object)
+//CGAL_Kernel_cons2(Construct_segment,
+//		  construct_segment_object)
+CGAL_Kernel_cons2(Segment_extremity,
+		  segment_extremity_object)
+
+//CGAL_Kernel_comp1(Compute_point_cartesian_coordinate,
+//		  compute_point_cartesian_coordinate_object)
+//CGAL_Kernel_comp1(Compute_vector_cartesian_coordinate,
+//		  compute_vector_cartesian_coordinate_object)
+//CGAL_Kernel_comp2(Squared_length,
+//		  squared_length_object)
+//CGAL_Kernel_comp2(Squared_distance,
+//		  squared_distance_object)
+//CGAL_Kernel_comp2(Squared_distance_to_origin,
+//		  squared_distance_to_origin_object)
+
+#if 0
+CGAL_Kernel_pred(Orientation,
+		 orientation_object)
+#endif
+//CGAL_Kernel_pred(Orientation_of_points,
+//		 orientation_of_points_object)
+//CGAL_Kernel_pred(Orientation_of_vectors,
+//		 orientation_of_vectors_object)
+//CGAL_Kernel_pred(Side_of_oriented_sphere,
+//		 side_of_oriented_sphere_object)
+//CGAL_Kernel_pred(Less_point_cartesian_coordinate,
+//		 less_point_cartesian_coordinate_object)
+//CGAL_Kernel_pred(Compare_point_cartesian_coordinate,
+//		 compare_point_cartesian_coordinate_object)
+//CGAL_Kernel_pred(Compare_distance,
+//		 compare_distance_object)
+//CGAL_Kernel_pred(Compare_lexicographically,
+//		 compare_lexicographically_object)
+//CGAL_Kernel_pred(Less_lexicographically,
+//		 less_lexicographically_object)
+//CGAL_Kernel_pred(Equal_points,
+//		 equal_points_object)
+//CGAL_Kernel_pred(Less_or_equal_lexicographically,
+//		 less_or_equal_lexicographically_object)
+//CGAL_Kernel_pred(Contained_in_affine_hull,
+//		 contained_in_affine_hull_object)
+//CGAL_Kernel_pred(In_flat_orientation,
+//		 in_flat_orientation_object)
+//CGAL_Kernel_pred(In_flat_side_of_oriented_sphere,
+//		 in_flat_side_of_oriented_sphere_object)
+//CGAL_Kernel_pred(Construct_flat_orientation,
+//		 construct_flat_orientation_object)
+
+#undef CGAL_Kernel_pred
+#undef CGAL_Kernel_comp
+#undef CGAL_Kernel_comp1
+#undef CGAL_Kernel_comp2
+#undef CGAL_Kernel_cons
+#undef CGAL_Kernel_cons1
+#undef CGAL_Kernel_cons2
+#undef CGAL_Kernel_obj
+#undef CGAL_Kernel_obj1
+#undef CGAL_Kernel_obj2
+#undef CGAL_Kernel_obj3

NewKernel_d/include/CGAL/LA_eigen/LA.h

@@ -0,0 +1,121 @@
+#ifndef CGAL_LA_EIGEN_H
+#define CGAL_LA_EIGEN_H
+
+#ifndef CGAL_EIGEN3_ENABLED
+#error Requires Eigen
+#endif
+#include <boost/type_traits/is_arithmetic.hpp>
+#include <boost/utility/enable_if.hpp>
+#include <CGAL/Dimension.h>
+#include <Eigen/Dense>
+#include <CGAL/LA_eigen/constructors.h>
+#include <CGAL/iterator_from_indices.h>
+
+namespace CGAL {
+
+//FIXME: where could we use Matrix_base instead of Matrix?
+// Dim_ real dimension
+// Max_dim_ upper bound on the dimension
+template<class NT_,class Dim_,class Max_dim_=Dim_> struct LA_eigen {
+	typedef NT_ NT;
+	typedef Dim_ Dimension;
+	typedef Max_dim_ Max_dimension;
+	enum { dimension = Eigen_dimension<Dimension>::value };
+	enum { max_dimension = Eigen_dimension<Max_dimension>::value };
+	template< class D2, class D3=D2 >
+	struct Rebind_dimension {
+	  typedef LA_eigen< NT, D2, D3 > Other;
+	};
+	template<class,class=void> struct Property : boost::false_type {};
+	template<class D> struct Property<Has_vector_plus_minus_tag,D> : boost::true_type {};
+	template<class D> struct Property<Has_vector_scalar_ops_tag,D> : boost::true_type {};
+	template<class D> struct Property<Has_dot_product_tag,D> : boost::true_type {};
+
+	typedef Eigen::Matrix<NT,Eigen_dimension<Dim_>::value,1,Eigen::ColMajor|Eigen::AutoAlign,Eigen_dimension<Max_dim_>::value,1> Vector;
+	typedef Eigen::Matrix<NT,Eigen::Dynamic,1> Dynamic_vector;
+	typedef Construct_eigen<Vector> Construct_vector;
+
+#if (EIGEN_WORLD_VERSION>=3)
+	typedef NT const* Vector_const_iterator;
+#else
+	typedef Iterator_from_indices<const type,const NT
+#ifndef CGAL_CXX0X
+	  ,NT
+#endif
+	  > Vector_const_iterator;
+#endif
+
+	template<class Vec_>static Vector_const_iterator vector_begin(Vec_ const&a){
+#if (EIGEN_WORLD_VERSION>=3)
+	  return &a[0];
+#else
+	  return Vector_const_iterator(a,0);
+#endif
+	}
+
+	template<class Vec_>static Vector_const_iterator vector_end(Vec_ const&a){
+#if (EIGEN_WORLD_VERSION>=3)
+	  return &a[0]+a.size();
+#else
+	  return Vector_const_iterator(a,a.size());
+#endif
+	}
+
+	typedef Eigen::Matrix<NT,dimension,dimension,Eigen::ColMajor|Eigen::AutoAlign,max_dimension,max_dimension> Square_matrix;
+	typedef Eigen::Matrix<NT,dimension,Eigen::Dynamic,Eigen::ColMajor|Eigen::AutoAlign,max_dimension,Eigen::Dynamic> Dynamic_matrix;
+		//TODO: don't pass on the values of Max_* for an expensive NT
+                // typedef ... Constructor
+                // typedef ... Accessor
+#if 0
+	private:
+	template <class T> class Canonicalize_vector {
+		typedef typename Dimension_eigen<T::SizeAtCompileTime>::type S1;
+		typedef typename Dimension_eigen<T::MaxSizeAtCompileTime>::type S2;
+		public:
+		typedef typename Vector<S1,S2>::type type;
+	};
+	public:
+#endif
+
+	template<class Vec_>static int size_of_vector(Vec_ const&v){
+		return v.size();
+	}
+
+	template<class Vec_>static NT dot_product(Vec_ const&a,Vec_ const&b){
+		return a.dot(b);
+	}
+
+	template<class Mat_> static NT determinant(Mat_ const&m,bool=false){
+		return m.determinant();
+	}
+
+	template<class Mat_> static typename
+	Same_uncertainty_nt<CGAL::Sign, NT>::type
+	sign_of_determinant(Mat_ const&m,bool=false)
+	{
+		return CGAL::sign(m.determinant());
+	}
+
+	template<class Vec1,class Vec2> static Vector homogeneous_add(Vec1 const&a,Vec2 const&b){
+		//TODO: use compile-time size when available
+		int d=a.size();
+		Vector v(d);
+		v << b[d-1]*a.topRows(d-1)+a[d-1]*b.topRows(d-1), a[d-1]*b[d-1];
+		return v;
+	}
+
+	template<class Vec1,class Vec2> static Vector homogeneous_sub(Vec1 const&a,Vec2 const&b){
+		int d=a.size();
+		Vector v(d);
+		v << b[d-1]*a.topRows(d-1)-a[d-1]*b.topRows(d-1), a[d-1]*b[d-1];
+		return v;
+	}
+
+	template<class Vec1,class Vec2> static std::pair<NT,NT> homogeneous_dot_product(Vec1 const&a,Vec2 const&b){
+		int d=a.size();
+		return make_pair(a.topRows(d-1).dot(b.topRows(d-1)), a[d-1]*b[d-1]);
+	}
+
+};
+}
+#endif

NewKernel_d/include/CGAL/LA_eigen/constructors.h

@@ -0,0 +1,133 @@
+#ifndef ecs_h
+#define ecs_h
+
+#ifndef CGAL_EIGEN3_ENABLED
+#error Requires Eigen
+#endif
+#include <boost/type_traits/is_arithmetic.hpp>
+#include <boost/utility/enable_if.hpp>
+#include <CGAL/Dimension.h>
+#include <Eigen/Dense>
+#include <CGAL/iterator_from_indices.h>
+#include <CGAL/marcutils.h>
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/preprocessor/repetition/enum.hpp>
+#include <boost/preprocessor/repetition/enum_params.hpp>
+
+namespace CGAL {
+  template <class Vector_> struct Construct_eigen {
+    typedef Vector_ result_type;
+    typedef typename Vector_::Scalar NT;
+
+    private:
+    static void check_dim(int d){
+      int m = result_type::MaxSizeAtCompileTime;
+      CGAL_assertion((m == Eigen::Dynamic) || (d <= m));
+      // could omit the first check since they use a big value for Dynamic.
+    }
+    public:
+
+    struct Dimension {
+      // Initialize with NaN if possible?
+      result_type operator()(int d) const {
+	check_dim(d);
+	return result_type(d);
+      }
+    };
+
+    struct Iterator {
+      template<typename Iter>
+	result_type operator()(int d,Iter const& f,Iter const& e) const {
+	  check_dim(d);
+	  CGAL_assertion(d==std::distance(f,e));
+	  result_type a(d);
+	  // TODO: check the right way to do this
+	  std::copy(f,e,&a[0]);
+	  return a;
+	}
+    };
+
+#if 0
+    struct Iterator_add_one {
+      template<typename Iter>
+	result_type operator()(int d,Iter const& f,Iter const& e) const {
+	  check_dim(d);
+	  CGAL_assertion(d==std::distance(f,e)+1);
+	  result_type a(d);
+	  std::copy(f,e,&a[0]);
+	  a[d-1]=1;
+	  return a;
+	}
+    };
+#endif
+
+    struct Iterator_and_last {
+      template<typename Iter,typename T>
+	result_type operator()(int d,Iter const& f,Iter const& e,CGAL_FORWARDABLE(T) t) const {
+	  check_dim(d);
+	  CGAL_assertion(d==std::distance(f,e)+1);
+	  result_type a(d);
+	  std::copy(f,e,&a[0]);
+	  a[d-1]=CGAL_FORWARD(T,t);
+	  return a;
+	}
+    };
+
+#ifdef CGAL_CXX0X
+    struct Initializer_list {
+      // Fix T==NT?
+      template<class T>
+	result_type operator()(std::initializer_list<T> l) const {
+	  return Iterator()(l.size(),l.begin(),l.end());
+	}
+    };
+#endif
+
+    struct Values {
+#ifdef CGAL_CXX0X
+      // TODO avoid going through Initializer_list which may cause extra copies. Possibly use forward_as_tuple.
+      template<class...U>
+	result_type operator()(U&&...u) const {
+	  check_dim(sizeof...(U)); // TODO: use static_assert
+	  return Initializer_list()({forward_safe<NT,U>(u)...});
+	}
+#else
+
+#define CODE(Z,N,_) result_type operator()(BOOST_PP_ENUM_PARAMS(N,NT const& t)) const { \
+  check_dim(N); \
+  result_type a(N); \
+  a << BOOST_PP_ENUM_PARAMS(N,t); \
+  return a; \
+}
+BOOST_PP_REPEAT_FROM_TO(1, 11, CODE, _ )
+#undef CODE
+
+#endif
+  };
+
+struct Values_divide {
+#ifdef CGAL_CXX0X
+  template<class H,class...U>
+    result_type operator()(H const&h,U&&...u) const {
+      check_dim(sizeof...(U)); // TODO: use static_assert
+      return Initializer_list()({Rational_traits<NT>().make_rational(std::forward<U>(u),h)...});
+    }
+#else
+
+#define VAR(Z,N,_) ( Rational_traits<NT>().make_rational( t##N ,h) )
+#define CODE(Z,N,_) template <class H> result_type \
+  operator()(H const&h, BOOST_PP_ENUM_PARAMS(N,NT const& t)) const { \
+    check_dim(N); \
+    result_type a(N); \
+    a << BOOST_PP_ENUM(N,VAR,); \
+    return a; \
+  }
+  BOOST_PP_REPEAT_FROM_TO(1, 11, CODE, _ )
+#undef CODE
+#undef VAR
+
+#endif
+};
+};
+}
+#endif

NewKernel_d/include/CGAL/Vector/array.h

@@ -0,0 +1,146 @@
+#ifndef CGAL_VECTOR_ARRAY_H
+#define CGAL_VECTOR_ARRAY_H
+#include <boost/type_traits/is_arithmetic.hpp>
+#include <boost/utility/enable_if.hpp>
+#include <CGAL/Dimension.h>
+#include <CGAL/marcutils.h>
+#include <CGAL/array.h>
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/preprocessor/repetition/enum.hpp>
+
+#include <CGAL/Vector/determinant_of_points_from_vectors.h>
+#include <CGAL/Vector/determinant_of_vectors_small_dim.h>
+#include <CGAL/Vector/determinant_of_iterator_to_points_from_iterator_to_vectors.h>
+#include <CGAL/Vector/determinant_of_iterator_to_points_from_points.h>
+#include <CGAL/Vector/determinant_of_iterator_to_vectors_from_vectors.h>
+
+
+
+namespace CGAL {
+
+// May not be safe to use with dim!=max_dim.
+// In that case, we should store the real dim next to the array.
+template<class NT_,class Dim_,class Max_dim_=Dim_> struct Array_vector {
+        typedef NT_ NT;
+	typedef Dim_ Dimension;
+	typedef Max_dim_ Max_dimension;
+	template< class D2, class D3=D2 >
+	struct Rebind_dimension {
+	  typedef Array_vector< NT, D2, D3 > Other;
+	};
+	template<class> struct Property : boost::false_type {};
+
+	static const unsigned d_=Max_dim_::value;
+	CGAL_static_assertion(d_ != (unsigned)UNKNOWN_DIMENSION);
+
+	typedef cpp0x::array<NT,d_> Vector;
+	struct Construct_vector {
+		struct Dimension {
+			// Initialize with NaN if possible?
+			Vector operator()(unsigned d) const {
+				CGAL_assertion(d<=d_);
+				return Vector();
+			}
+		};
+
+		struct Iterator {
+			template<typename Iter>
+				Vector operator()(unsigned CGAL_assertion_code(d),Iter const& f,Iter const& e) const {
+					CGAL_assertion(d==std::distance(f,e));
+					CGAL_assertion(d<=d_);
+					//TODO: optimize for forward iterators
+					Vector a;
+					std::copy(f,e,a.begin());
+					return a;
+				}
+		};
+
+#if 0
+		struct Iterator_add_one {
+			template<typename Iter>
+				Vector operator()(unsigned d,Iter const& f,Iter const& e) const {
+					CGAL_assertion(d==std::distance(f,e)+1);
+					CGAL_assertion(d<=d_);
+					//TODO: optimize
+					Vector a;
+					std::copy(f,e,a.begin());
+					a.back()=1;
+					return a;
+				}
+		};
+#endif
+
+		struct Iterator_and_last {
+			template<typename Iter,typename T>
+				Vector operator()(unsigned d,Iter const& f,Iter const& e,CGAL_FORWARDABLE(T) t) const {
+					CGAL_assertion(d==std::distance(f,e)+1);
+					CGAL_assertion(d<=d_);
+					//TODO: optimize for forward iterators
+					Vector a;
+					std::copy(f,e,a.begin());
+					a.back()=CGAL_FORWARD(T,t);
+					return a;
+				}
+		};
+
+		struct Values {
+#ifdef CGAL_CXX0X
+			template<class...U>
+				Vector operator()(U&&...u) const {
+					static_assert(sizeof...(U)<=d_,"too many arguments");
+					Vector a={{forward_safe<NT,U>(u)...}};
+					return a;
+				}
+#else
+
+#define CODE(Z,N,_) Vector operator()(BOOST_PP_ENUM_PARAMS(N,NT const& t)) const { \
+	CGAL_assertion(N<=d_); \
+	Vector a={{BOOST_PP_ENUM_PARAMS(N,t)}}; \
+	return a; \
+}
+BOOST_PP_REPEAT_FROM_TO(1, 11, CODE, _ )
+#undef CODE
+
+#endif
+		};
+
+		struct Values_divide {
+#ifdef CGAL_CXX0X
+			template<class H,class...U>
+				Vector operator()(H const& h,U&&...u) const {
+					static_assert(sizeof...(U)<=d_,"too many arguments");
+					Vector a={{Rational_traits<NT>().make_rational(std::forward<U>(u),h)...}};
+					return a;
+				}
+#else
+
+#define VAR(Z,N,_) Rational_traits<NT>().make_rational( t##N , h)
+#define CODE(Z,N,_) template <class H> Vector \
+			operator()(H const&h, BOOST_PP_ENUM_PARAMS(N,NT const& t)) const { \
+				CGAL_assertion(N<=d_); \
+				Vector a={{BOOST_PP_ENUM(N,VAR,_)}}; \
+				return a; \
+			}
+			BOOST_PP_REPEAT_FROM_TO(1, 11, CODE, _ )
+#undef CODE
+#undef VAR
+
+#endif
+		};
+	};
+
+	typedef NT const* Vector_const_iterator;
+	static Vector_const_iterator vector_begin(Vector const&a){
+		return &a[0];
+	}
+	static Vector_const_iterator vector_end(Vector const&a){
+		return &a[0]+d_; // Don't know the real size
+	}
+	static unsigned size_of_vector(Vector const&){
+		return d_; // Don't know the real size
+	}
+
+};
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/avx4.h

@@ -0,0 +1,194 @@
+#ifndef CGAL_VECTOR_AVX4_H
+#define CGAL_VECTOR_AVX4_H
+
+#if !defined __AVX__ || (__GNUC__ * 100 + __GNUC_MINOR__ < 408)
+#error Requires AVX and gcc 4.8+
+#endif
+#include <x86intrin.h>
+
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/enum.h> // CGAL::Sign
+#include <CGAL/number_utils.h> // CGAL::sign
+
+
+
+namespace CGAL {
+
+  struct Avx_vector_4 {
+    typedef double NT;
+    typedef Dimension_tag<4> Dimension;
+    typedef Dimension_tag<4> Max_dimension;
+    // No Rebind_dimension, this is a building block
+    template<class,bool=true> struct Property : boost::false_type {};
+    template<bool b> struct Property<Has_vector_plus_minus_tag,b>
+      : boost::true_type {};
+    /* MAYBE?
+       template<bool b> struct Property<Has_vector_scalar_ops_tag,b>
+       : boost::true_type {};
+       */
+    template<bool b> struct Property<Has_determinant_of_vectors_tag,b>
+      : boost::true_type {};
+    template<bool b> struct Property<Has_dot_product_tag,b>
+      : boost::true_type {};
+    template<bool b> struct Property<Has_determinant_of_vectors_omit_last_tag,b>
+      : boost::true_type {};
+
+    typedef __m256d Vector;
+    struct Construct_vector {
+      struct Dimension {
+	// Initialize with NaN?
+	Vector operator()(unsigned d) const {
+	  CGAL_assertion(d==4);
+	  return Vector();
+	}
+      };
+
+      struct Iterator {
+	template<typename Iter>
+	  Vector operator()(unsigned d,Iter const& f,Iter const& e) const {
+	    CGAL_assertion(d==4);
+	    double x0 = *f;
+	    double x1 = *++f;
+	    double x2 = *++f;
+	    double x3 = *++f;
+	    CGAL_assertion(++f==e);
+	    Vector a = { x0, x1, x2, x3 };
+	    return a;
+	  }
+      };
+
+      struct Iterator_and_last {
+	template<typename Iter,typename T>
+	  Vector operator()(unsigned d,Iter const& f,Iter const& e,double t) const {
+	    CGAL_assertion(d==4);
+	    double x0 = *f;
+	    double x1 = *++f;
+	    double x2 = *++f;
+	    CGAL_assertion(++f==e);
+	    Vector a = { x0, x1, x2, t };
+	    return a;
+	  }
+      };
+
+      struct Values {
+	  Vector operator()(double a,double b,double c,double d) const {
+	    Vector r = { a, b, c, d };
+	    return r;
+	  }
+      };
+
+      struct Values_divide {
+	Vector operator()(double h,double a,double b,double c,double d) const {
+	  // {a,b,c,d}/{h,h,h,h} should be roughly the same
+	  Vector r = { a/h, b/h, c/h, d/h };
+	  return r;
+	}
+      };
+    };
+
+    public:
+    typedef double const* Vector_const_iterator;
+    static inline Vector_const_iterator vector_begin(Vector const&a){
+      return (Vector_const_iterator)(&a);
+    }
+    static inline Vector_const_iterator vector_end(Vector const&a){
+      return (Vector_const_iterator)(&a)+4;
+    }
+    static inline unsigned size_of_vector(Vector){
+      return 4;
+    }
+    static inline double dot_product(__m256d x, __m256d y){
+      __m256d p=x*y;
+      __m256d z=_mm256_hadd_pd(p,p);
+      return z[0]+z[2];
+    }
+    private:
+    static inline __m256d avx_sym(__m256d x){
+#if 0
+      return __builtin_shuffle(x,(__m256i){2,3,0,1});
+#else
+      return _mm256_permute2f128_pd(x,x,1);
+#endif
+    }
+    static inline __m256d avx_left(__m256d x){
+#if 0
+      return __builtin_shuffle(x,(__m256i){1,2,3,0});
+#else
+#ifdef __AVX2__
+      return _mm256_permute4x64_pd(x,1+2*4+3*16+0*64);
+#else
+      __m256d s = _mm256_permute2f128_pd(x,x,1);
+      return _mm256_shuffle_pd(x,s,5);
+#endif
+#endif
+    }
+    static inline __m256d avx_right(__m256d x){
+#if 0
+      return __builtin_shuffle(x,(__m256i){3,0,1,2});
+#else
+#ifdef __AVX2__
+      return _mm256_permute4x64_pd(x,3+0*4+1*16+2*64);
+#else
+      __m256d s = _mm256_permute2f128_pd(x,x,1);
+      return _mm256_shuffle_pd(s,x,5);
+#endif
+#endif
+    }
+    static inline double avx_altprod(__m256d x, __m256d y){
+      __m256d p=x*y;
+      __m256d z=_mm256_hsub_pd(p,p);
+      return z[0]+z[2];
+    }
+    public:
+    static double
+      determinant_of_vectors(Vector a, Vector b, Vector c, Vector d) {
+      __m256d x=a*avx_left(b)-avx_left(a)*b;
+      __m256d yy=a*avx_sym(b);
+      __m256d y=yy-avx_sym(yy);
+      __m256d z0=x*avx_sym(c);
+      __m256d z1=avx_left(x)*c;
+      __m256d z2=y*avx_left(c);
+      __m256d z=z0+z1-z2;
+      return avx_altprod(z,avx_right(d));
+    }
+    static CGAL::Sign
+      sign_of_determinant_of_vectors(Vector a, Vector b, Vector c, Vector d) {
+      return CGAL::sign(determinant_of_vectors(a,b,c,d));
+    }
+
+    private:
+    static inline __m256d avx3_right(__m256d x){
+#if 0
+      return __builtin_shuffle(x,(__m256i){2,0,1,3}); // can replace 3 with anything
+#else
+#ifdef __AVX2__
+      return _mm256_permute4x64_pd(x,2+0*4+1*16+3*64);
+#else
+      __m256d s = _mm256_permute2f128_pd(x,x,1);
+      return _mm256_shuffle_pd(s,x,12);
+#endif
+#endif
+    }
+    public:
+    static inline double dot_product_omit_last(__m256d x, __m256d y){
+      __m256d p=x*y;
+      __m128d q=_mm256_extractf128_pd(p,0);
+      double z=_mm_hadd_pd(q,q)[0];
+      return z+p[2];
+    }
+    // Note: without AVX2, is it faster than the scalar computation?
+    static double
+      determinant_of_vectors_omit_last(Vector a, Vector b, Vector c) {
+      __m256d x=a*avx3_right(b)-avx3_right(a)*b;
+      return dot_product_omit_last(c,avx3_right(x));
+    }
+    static CGAL::Sign
+      sign_of_determinant_of_vectors_omit_last(Vector a, Vector b, Vector c) {
+      return CGAL::sign(determinant_of_vectors_omit_last(a,b,c));
+    }
+
+  };
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/determinant_of_iterator_to_points_from_iterator_to_vectors.h

@@ -0,0 +1,57 @@
+#ifndef CGAL_VECTOR_DET_ITER_PTS_ITER_VEC_H
+#define CGAL_VECTOR_DET_ITER_PTS_ITER_VEC_H
+#include <functional>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+
+namespace CGAL {
+
+template <class LA, class Dim_=typename LA::Dimension,
+	 class Max_dim_=typename LA::Max_dimension,
+	 bool = LA::template Property<Has_determinant_of_iterator_to_points_tag>::value,
+	 bool = LA::template Property<Has_determinant_of_iterator_to_vectors_tag>::value>
+struct Add_determinant_of_iterator_to_points_from_iterator_to_vectors : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_iterator_to_vectors<LA2> Other;
+    };
+};
+
+template <class LA, class Dim_,class Max_dim_>
+struct Add_determinant_of_iterator_to_points_from_iterator_to_vectors
+<LA, Dim_, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_iterator_to_vectors<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_points_tag, D> :
+    boost::true_type {};
+
+  // TODO: use std::minus, std::bind, etc
+  template<class T> struct Minus_fixed {
+    T const& a;
+    Minus_fixed(T const&a_):a(a_){}
+    T operator()(T const&b)const{return b-a;}
+  };
+  template<class Iter>
+  static NT determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Minus_fixed<Vector> f(a);
+    return LA::determinant_of_iterator_to_vectors(make_transforming_iterator(first,f),make_transforming_iterator(end,f));
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Minus_fixed<Vector> f(a);
+    return LA::sign_of_determinant_of_iterator_to_vectors(make_transforming_iterator(first,f),make_transforming_iterator(end,f));
+  }
+};
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/determinant_of_iterator_to_points_from_points.h

@@ -0,0 +1,192 @@
+#ifndef CGAL_VECTOR_DET_ITER_PTS_PTS_H
+#define CGAL_VECTOR_DET_ITER_PTS_PTS_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+
+namespace CGAL {
+
+template <class LA, class Dim_=typename LA::Dimension,
+	 class Max_dim_=typename LA::Max_dimension,
+	 bool = LA::template Property<Has_determinant_of_iterator_to_points_tag>::value,
+	 bool = LA::template Property<Has_determinant_of_points_tag>::value>
+struct Add_determinant_of_iterator_to_points_from_points : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_points<LA2> Other;
+    };
+};
+
+//FIXME: Use variadics and boost so it works in any dimension.
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_points_from_points
+<LA, Dimension_tag<2>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_points<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_points_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_points(a,b,c);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_points(a,b,c);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_points_from_points
+<LA, Dimension_tag<3>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_points<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_points_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_points(a,b,c,d);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_points(a,b,c,d);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_points_from_points
+<LA, Dimension_tag<4>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_points<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_points_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_points(a,b,c,d,e);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_points(a,b,c,d,e);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_points_from_points
+<LA, Dimension_tag<5>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_points<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_points_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; ++first;
+    Vector const&f=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_points(a,b,c,d,e,f);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; ++first;
+    Vector const&f=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_points(a,b,c,d,e,f);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_points_from_points
+<LA, Dimension_tag<6>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_points_from_points<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_points_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; ++first;
+    Vector const&f=*first; ++first;
+    Vector const&g=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_points(a,b,c,d,e,f,g);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_points(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; ++first;
+    Vector const&f=*first; ++first;
+    Vector const&g=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_points(a,b,c,d,e,f,g);
+  }
+};
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/determinant_of_iterator_to_vectors_from_vectors.h

@@ -0,0 +1,182 @@
+#ifndef CGAL_VECTOR_DET_ITER_VEC_VEC_H
+#define CGAL_VECTOR_DET_ITER_VEC_VEC_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+
+namespace CGAL {
+
+template <class LA, class Dim_=typename LA::Dimension,
+	 class Max_dim_=typename LA::Max_dimension,
+	 bool = LA::template Property<Has_determinant_of_iterator_to_vectors_tag>::value,
+	 bool = LA::template Property<Has_determinant_of_vectors_tag>::value>
+struct Add_determinant_of_iterator_to_vectors_from_vectors : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_vectors_from_vectors<LA2> Other;
+    };
+};
+
+//FIXME: Use variadics and boost so it works in any dimension.
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_vectors_from_vectors
+<LA, Dimension_tag<2>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_vectors_from_vectors<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_vectors_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_vectors(a,b);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_vectors(a,b);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_vectors_from_vectors
+<LA, Dimension_tag<3>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_vectors_from_vectors<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_vectors_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_vectors(a,b,c);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_vectors(a,b,c);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_vectors_from_vectors
+<LA, Dimension_tag<4>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_vectors_from_vectors<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_vectors_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_vectors(a,b,c,d);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_vectors(a,b,c,d);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_vectors_from_vectors
+<LA, Dimension_tag<5>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_vectors_from_vectors<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_vectors_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_vectors(a,b,c,d,e);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_vectors(a,b,c,d,e);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_iterator_to_vectors_from_vectors
+<LA, Dimension_tag<6>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_iterator_to_vectors_from_vectors<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_iterator_to_vectors_tag, D> :
+    boost::true_type {};
+
+  template<class Iter>
+  static NT determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; ++first;
+    Vector const&f=*first; CGAL_assertion(++first==end);
+    return LA::determinant_of_vectors(a,b,c,d,e,f);
+  }
+  template<class Iter>
+  static Sign sign_of_determinant_of_iterator_to_vectors(Iter const&first, Iter const&end){
+    Vector const&a=*first; ++first;
+    Vector const&b=*first; ++first;
+    Vector const&c=*first; ++first;
+    Vector const&d=*first; ++first;
+    Vector const&e=*first; ++first;
+    Vector const&f=*first; CGAL_assertion(++first==end);
+    return LA::sign_of_determinant_of_vectors(a,b,c,d,e,f);
+  }
+};
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/determinant_of_points_from_vectors.h

@@ -0,0 +1,145 @@
+#ifndef CGAL_VECTOR_DETPTS_H
+#define CGAL_VECTOR_DETPTS_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+
+namespace CGAL {
+
+template <class LA, class Dim_=typename LA::Dimension,
+	 class Max_dim_=typename LA::Max_dimension,
+	 bool = LA::template Property<Has_determinant_of_points_tag>::value,
+	 bool = LA::template Property<Has_determinant_of_vectors_tag>::value
+	   && LA::template Property<Has_vector_plus_minus_tag>::value>
+struct Add_determinant_of_points_from_vectors_and_minus : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_points_from_vectors_and_minus<LA2> Other;
+    };
+};
+
+//FIXME: Use variadics and boost so it works in any dimension.
+template <class LA, class Max_dim_>
+struct Add_determinant_of_points_from_vectors_and_minus
+<LA, Dimension_tag<2>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_points_from_vectors_and_minus<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_points_tag, D> :
+    boost::true_type {};
+
+  static NT determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c){
+    return LA::determinant_of_vectors(b-a,c-a);
+  }
+  static Sign sign_of_determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c){
+    return LA::sign_of_determinant_of_vectors(b-a,c-a);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_points_from_vectors_and_minus
+<LA, Dimension_tag<3>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_points_from_vectors_and_minus<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_points_tag, D> :
+    boost::true_type {};
+
+  static NT determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return LA::determinant_of_vectors(b-a,c-a,d-a);
+  }
+  static Sign sign_of_determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return LA::sign_of_determinant_of_vectors(b-a,c-a,d-a);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_points_from_vectors_and_minus
+<LA, Dimension_tag<4>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_points_from_vectors_and_minus<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_points_tag, D> :
+    boost::true_type {};
+
+  static NT determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e){
+    return LA::determinant_of_vectors(b-a,c-a,d-a,e-a);
+  }
+  static Sign sign_of_determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e){
+    return LA::sign_of_determinant_of_vectors(b-a,c-a,d-a,e-a);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_points_from_vectors_and_minus
+<LA, Dimension_tag<5>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_points_from_vectors_and_minus<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_points_tag, D> :
+    boost::true_type {};
+
+  static NT determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
+    return LA::determinant_of_vectors(b-a,c-a,d-a,e-a,f-a);
+  }
+  static Sign sign_of_determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
+    return LA::sign_of_determinant_of_vectors(b-a,c-a,d-a,e-a,f-a);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_points_from_vectors_and_minus
+<LA, Dimension_tag<6>, Max_dim_, false, true> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_points_from_vectors_and_minus<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_points_tag, D> :
+    boost::true_type {};
+
+  static NT determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f,
+      Vector const&g){
+    return LA::determinant_of_vectors(b-a,c-a,d-a,e-a,f-a,g-a);
+  }
+  static Sign sign_of_determinant_of_points(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f,
+      Vector const&g){
+    return LA::sign_of_determinant_of_vectors(b-a,c-a,d-a,e-a,f-a,g-a);
+  }
+};
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/determinant_of_vectors_small_dim.h

@@ -0,0 +1,39 @@
+#ifndef CGAL_VECTOR_DETVEC_SMALL_H
+#define CGAL_VECTOR_DETVEC_SMALL_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/determinant_of_vectors.h>
+
+#define CGAL_ALLOWED_INCLUSION 1
+
+#define CGAL_CLASS Add_determinant_of_vectors_small_dim
+#define CGAL_TAG Has_determinant_of_vectors_tag
+#define CGAL_FUNC determinant_of_vectors
+#define CGAL_SIGN_FUNC sign_of_determinant_of_vectors
+#define CGAL_SHIFT 0
+
+#include <CGAL/Vector/determinant_of_vectors_small_dim_internal.h>
+
+#undef CGAL_CLASS
+#undef CGAL_TAG
+#undef CGAL_FUNC
+#undef CGAL_SIGN_FUNC
+#undef CGAL_SHIFT
+
+#define CGAL_CLASS Add_determinant_of_vectors_omit_last_small_dim
+#define CGAL_TAG Has_determinant_of_vectors_omit_last_tag
+#define CGAL_FUNC determinant_of_vectors_omit_last
+#define CGAL_SIGN_FUNC sign_of_determinant_of_vectors_omit_last
+#define CGAL_SHIFT 1
+
+#include <CGAL/Vector/determinant_of_vectors_small_dim_internal.h>
+
+#undef CGAL_CLASS
+#undef CGAL_TAG
+#undef CGAL_FUNC
+#undef CGAL_SIGN_FUNC
+#undef CGAL_SHIFT
+
+#undef CGAL_ALLOWED_INCLUSION
+
+#endif

NewKernel_d/include/CGAL/Vector/determinant_of_vectors_small_dim_internal.h

@@ -0,0 +1,145 @@
+#ifndef CGAL_ALLOWED_INCLUSION
+#error Must not include this header directly
+#endif
+#if !defined(CGAL_TAG) \
+  || ! defined(CGAL_CLASS) \
+  || ! defined(CGAL_FUNC) \
+  || ! defined(CGAL_SIGN_FUNC) \
+  || ! defined(CGAL_SHIFT)
+
+#error Forgot one macro
+#endif
+
+namespace CGAL {
+
+template <class LA, class Dim_=typename LA::Dimension,
+	 class Max_dim_=typename LA::Max_dimension,
+	 bool=LA::template Property<CGAL_TAG>::value>
+struct CGAL_CLASS : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef CGAL_CLASS<LA2> Other;
+    };
+};
+
+template <class LA, class Max_dim_>
+struct CGAL_CLASS
+<LA, Dimension_tag<2+CGAL_SHIFT>, Max_dim_, false> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef CGAL_CLASS<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<CGAL_TAG, D> :
+    boost::true_type {};
+
+  static NT CGAL_FUNC(Vector const&a, Vector const&b){
+    return CGAL::determinant_of_vectors<NT>(a,b);
+  }
+  template <class V1, class V2>
+  static Sign CGAL_SIGN_FUNC(V1 const&a, V2 const&b){
+    return CGAL::sign_of_determinant_of_vectors<NT>(a,b);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct CGAL_CLASS
+<LA, Dimension_tag<3+CGAL_SHIFT>, Max_dim_, false> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef CGAL_CLASS<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<CGAL_TAG, D> :
+    boost::true_type {};
+
+  static NT CGAL_FUNC(Vector const&a, Vector const&b,
+      Vector const&c){
+    return CGAL::determinant_of_vectors<NT>(a,b,c);
+  }
+  static Sign CGAL_SIGN_FUNC(Vector const&a, Vector const&b,
+      Vector const&c){
+    return CGAL::sign_of_determinant_of_vectors<NT>(a,b,c);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct CGAL_CLASS
+<LA, Dimension_tag<4+CGAL_SHIFT>, Max_dim_, false> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef CGAL_CLASS<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<CGAL_TAG, D> :
+    boost::true_type {};
+
+  static NT CGAL_FUNC(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return CGAL::determinant_of_vectors<NT>(a,b,c,d);
+  }
+  static Sign CGAL_SIGN_FUNC(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return CGAL::sign_of_determinant_of_vectors<NT>(a,b,c,d);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct CGAL_CLASS
+<LA, Dimension_tag<5+CGAL_SHIFT>, Max_dim_, false> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef CGAL_CLASS<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<CGAL_TAG, D> :
+    boost::true_type {};
+
+  static NT CGAL_FUNC(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e){
+    return CGAL::determinant_of_vectors<NT>(a,b,c,d,e);
+  }
+  static Sign CGAL_SIGN_FUNC(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e){
+    return CGAL::sign_of_determinant_of_vectors<NT>(a,b,c,d,e);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct CGAL_CLASS
+<LA, Dimension_tag<6+CGAL_SHIFT>, Max_dim_, false> : LA {
+  using typename LA::NT;
+  using typename LA::Vector;
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef CGAL_CLASS<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<CGAL_TAG, D> :
+    boost::true_type {};
+
+  static NT CGAL_FUNC(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
+    return CGAL::determinant_of_vectors<NT>(a,b,c,d,e,f);
+  }
+  static Sign CGAL_SIGN_FUNC(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
+    return CGAL::sign_of_determinant_of_vectors<NT>(a,b,c,d,e,f);
+  }
+};
+
+}

NewKernel_d/include/CGAL/Vector/sse2.h

@@ -0,0 +1,126 @@
+#ifndef CGAL_VECTOR_SSE2_H
+#define CGAL_VECTOR_SSE2_H
+
+// Check what needs adapting for clang, intel and microsoft
+#if !defined __SSE2__ || (__GNUC__ * 100 + __GNUC_MINOR__ < 408)
+#error Requires SSE2 and gcc 4.8+
+#endif
+#include <x86intrin.h> // FIXME: other platforms call it differently
+
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/enum.h> // CGAL::Sign
+#include <CGAL/number_utils.h> // CGAL::sign
+
+
+
+namespace CGAL {
+
+  struct Sse_vector_2 {
+    typedef double NT;
+    typedef Dimension_tag<2> Dimension;
+    typedef Dimension_tag<2> Max_dimension;
+    // No Rebind_dimension, this is a building block
+    template<class,bool=true> struct Property : boost::false_type {};
+    template<bool b> struct Property<Has_vector_plus_minus_tag,b>
+      : boost::true_type {};
+    /* MAYBE?
+       template<bool b> struct Property<Has_vector_scalar_ops_tag,b>
+       : boost::true_type {};
+       */
+    template<bool b> struct Property<Has_determinant_of_vectors_tag,b>
+      : boost::true_type {};
+    template<bool b> struct Property<Has_dot_product_tag,b>
+      : boost::true_type {};
+
+    typedef __m128d Vector;
+    struct Construct_vector {
+      struct Dimension {
+	// Initialize with NaN?
+	Vector operator()(unsigned d) const {
+	  CGAL_assertion(d==2);
+	  return Vector();
+	}
+      };
+
+      struct Iterator {
+	template<typename Iter>
+	  Vector operator()(unsigned d,Iter const& f,Iter const& e) const {
+	    CGAL_assertion(d==2);
+	    double x0 = *f;
+	    double x1 = *++f;
+	    CGAL_assertion(++f==e);
+	    Vector a = { x0, x1 };
+	    return a;
+	  }
+      };
+
+      struct Iterator_and_last {
+	template<typename Iter,typename T>
+	  Vector operator()(unsigned d,Iter const& f,Iter const& e,double t) const {
+	    CGAL_assertion(d==2);
+	    Vector a = { *f, t };
+	    CGAL_assertion(++f==e);
+	    return a;
+	  }
+      };
+
+      struct Values {
+	  Vector operator()(double a,double b) const {
+	    Vector r = { a, b };
+	    return r;
+	  }
+      };
+
+      struct Values_divide {
+	Vector operator()(double h,double a,double b) const {
+	  // {a,b}/{h,h} is probably slower
+	  Vector r = { a/h, b/h };
+	  return r;
+	}
+      };
+    };
+
+    typedef double const* Vector_const_iterator;
+    static inline Vector_const_iterator vector_begin(Vector const&a){
+      return (Vector_const_iterator)(&a);
+    }
+    static inline Vector_const_iterator vector_end(Vector const&a){
+      return (Vector_const_iterator)(&a)+2;
+    }
+    static inline unsigned size_of_vector(Vector){
+      return 2;
+    }
+    public:
+
+    static double determinant_of_vectors(Vector a, Vector b) {
+      __m128d c = _mm_shuffle_pd (b, b, 1); // b1, b0
+      __m128d d = a * c; // a0*b1, a1*b0
+#ifdef __SSE3__
+      __m128d e = _mm_hsub_pd (d, d);
+      return e[0];
+#else
+      return d[0]-d[1];
+#endif
+    }
+    static CGAL::Sign sign_of_determinant_of_vectors(Vector a, Vector b) {
+      return CGAL::sign(determinant_of_vectors(a,b));
+    }
+
+    static double dot_product(Vector a,Vector b){
+#ifdef __SSE4_1__
+      return _mm_dp_pd (a, b, 1+16+32)[0];
+#else
+      __m128d p = a * b;
+#if defined __SSE3__
+      __m128d s = _mm_hadd_pd (p, p);
+      return s[0];
+#else
+      return p[0]+p[1];
+#endif
+#endif
+    };
+  };
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/v2int.h

@@ -0,0 +1,162 @@
+#ifndef CGAL_VECTOR_2INT_H
+#define CGAL_VECTOR_2INT_H
+
+#include <stdint.h>
+#include <cmath>
+#include <CGAL/array.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/enum.h>
+#include <CGAL/number_utils.h>
+#include <CGAL/NT_converter.h>
+#include <CGAL/transforming_iterator.h>
+#include <CGAL/determinant_of_vectors.h>
+#include <CGAL/functor_tags.h>
+
+
+// What are the pros and cons of having NT be int vs double?
+
+namespace CGAL {
+  struct Vector_2_int_prop1 {
+    typedef double NT; // try lying a bit
+    typedef int32_t NT1; // what is really stored
+    typedef int32_t NT1b; // slightly longer
+    typedef int_fast64_t NT2; // longer type for computations
+    typedef int_fast64_t NT2b; // slightly longer
+    bool check_limits(int32_t x){return std::abs(x)<(1<<30);}
+    // TODO: find nice bounds
+  };
+#ifdef __SIZEOF_INT128__
+  struct Vector_2_int_prop2 {
+    typedef double NT;
+    typedef int32_t NT1;
+    typedef int_fast64_t NT1b;
+    typedef int_fast64_t NT2;
+    typedef __int128 NT2b;
+    bool check_limits(int32_t){return true;}
+    // take a template/int64_t input and still check the limits?
+  };
+  struct Vector_2_int_prop3 {
+    typedef long double NT;
+    typedef int64_t NT1;
+    typedef int64_t NT1b;
+    typedef __int128 NT2;
+    typedef __int128 NT2b;
+    enum { has_limit=true };
+    bool check_limits(int32_t x){return std::abs(x)<(1L<<62);}
+    // TODO: find nice bounds
+  };
+#endif
+
+  template<class Prop=Vector_2_int_prop1>
+  struct Vector_2_int : Prop {
+    using typename Prop::NT;
+    using typename Prop::NT1;
+    using typename Prop::NT1b;
+    using typename Prop::NT2;
+    using typename Prop::NT2b;
+    using Prop::check_limits;
+
+    typedef Dimension_tag<2> Dimension;
+    typedef Dimension_tag<2> Max_dimension;
+    // No Rebind_dimension, this is a building block
+    template<class,bool=true> struct Property : boost::false_type {};
+    //template<bool b> struct Property<Has_vector_plus_minus_tag,b>
+    //  : boost::true_type {};
+    template<bool b> struct Property<Has_determinant_of_vectors_tag,b>
+      : boost::true_type {};
+    //template<bool b> struct Property<Has_determinant_of_points_tag,b>
+    //  : boost::true_type {};
+    // Advertise somehow that the sign_of_determinant* are exact?
+
+    typedef cpp0x::array<NT1,2> Vector;
+    struct Construct_vector {
+      struct Dimension {
+	Vector operator()(unsigned d) const {
+	  CGAL_assertion(d==2);
+	  return Vector();
+	}
+      };
+
+      // TODO (for all constructors): check that input fits in NT1...
+      struct Iterator {
+	template<typename Iter>
+	  Vector operator()(unsigned d,Iter const& f,Iter const& e) const {
+	    CGAL_assertion(d==2);
+	    NT1 x0 = *f;
+	    NT1 x1 = *++f;
+	    CGAL_assertion (++f == e);
+	    CGAL_assertion (check_limits(x0) && check_limits(x1));
+	    Vector a = { x0, x1 };
+	    return a;
+	  }
+      };
+
+      struct Iterator_and_last {
+	template<typename Iter,typename T>
+	  Vector operator()(unsigned d,Iter const& f,Iter const& e,double t) const {
+	    CGAL_assertion(d==2);
+	    NT1 x = *f;
+	    CGAL_assertion (++f == e);
+	    CGAL_assertion (check_limits(x) && check_limits(t));
+	    Vector a = { x, t };
+	    return a;
+	  }
+      };
+
+      struct Values {
+	  Vector operator()(NT1 a,NT1 b) const {
+	    CGAL_assertion (check_limits(a) && check_limits(b));
+	    Vector r = { a, b };
+	    return r;
+	  }
+      };
+
+      /*
+	 // Maybe safer not to provide it
+      struct Values_divide {
+	Vector operator()(double h,double a,double b) const {
+	  Vector r = { a/h, b/h };
+	  return r;
+	}
+      };
+      */
+    };
+
+    // Since we lie about NT, be consistent about it
+    typedef transforming_iterator<NT_converter<NT1,NT>,NT1 const*> Vector_const_iterator;
+    static inline Vector_const_iterator vector_begin(Vector const&a){
+      return Vector_const_iterator(a.begin());
+    }
+    static inline Vector_const_iterator vector_end(Vector const&a){
+      return Vector_const_iterator(a.end());
+    }
+    static inline unsigned size_of_vector(Vector){
+      return 2;
+    }
+
+    // for unsigned NT1, check what changes to do.
+    // return NT or NT2?
+    static NT determinant_of_vectors(Vector a, Vector b) {
+      return CGAL::determinant_of_vectors<NT2>(a,b);
+    }
+    static CGAL::Sign sign_of_determinant_of_vectors(Vector a, Vector b) {
+      return CGAL::sign_of_determinant_of_vectors<NT2>(a,b);
+    }
+
+    static NT determinant_of_points(Vector a, Vector b, Vector c) {
+      // could be faster to convert to NT directly
+      NT1b a0=a[0];    NT1b a1=a[1];
+      NT1b x0=b[0]-a0; NT1b x1=b[1]-a1;
+      NT1b y0=c[0]-a0; NT1b y1=c[1]-a1;
+      return CGAL::determinant<NT>(x0,x1,y0,y1);
+    }
+    static CGAL::Sign sign_of_determinant_of_points(Vector a, Vector b, Vector c) {
+      NT1b a0=a[0];    NT1b a1=a[1];
+      NT1b x0=b[0]-a0; NT1b x1=b[1]-a1;
+      NT2b y0=c[0]-a0; NT2b y1=c[1]-a1;
+      return CGAL::compare(x0*y1,x1*y0);
+    }
+  };
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/vector.h

@@ -0,0 +1,148 @@
+#ifndef CGAL_VECTOR_VECTOR_H
+#define CGAL_VECTOR_VECTOR_H
+#include <boost/type_traits/is_arithmetic.hpp>
+#include <boost/utility/enable_if.hpp>
+#include <CGAL/Dimension.h>
+#include <CGAL/marcutils.h>
+#include <vector>
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/preprocessor/repetition/enum.hpp>
+namespace CGAL {
+
+//Derive from a class that doesn't depend on Dim, or still use Dim for checking?
+template<class NT_,class Dim_,class Max_dim_=Dim_> struct Vector_vector {
+        typedef NT_ NT;
+	typedef Dim_ Dimension;
+	typedef Max_dim_ Max_dimension;
+	typedef std::vector<NT> Vector;
+        template< class D2, class D3=D2 >
+        struct Rebind_dimension {
+	  typedef Vector_vector< NT, D2, D3 > Other;
+        };
+        template<class> struct Property : boost::false_type {};
+
+	struct Construct_vector {
+		struct Dimension {
+			Vector operator()(int d) const {
+				return Vector(d);
+			}
+		};
+
+		struct Iterator {
+			template<typename Iter>
+				Vector operator()(int d,Iter const& f,Iter const& e) const {
+					CGAL_assertion(d==std::distance(f,e));
+					return Vector(f,e);
+				}
+		};
+
+		// unneeded thanks to Iterator_and_last?
+#if 0
+		struct Iterator_add_one {
+			template<typename Iter>
+				Vector operator()(int d,Iter const& f,Iter const& e) const {
+					CGAL_assertion(d==std::distance(f,e)+1);
+					Vector a;
+					a.reserve(d+1);
+					a.insert(a.end(),f,e);
+					a.push_back(1);
+					return a;
+				}
+		};
+#endif
+
+		struct Iterator_and_last {
+			template<typename Iter,typename T>
+				Vector operator()(int d,Iter const& f,Iter const& e,CGAL_FORWARDABLE(T) t) const {
+					CGAL_assertion(d==std::distance(f,e)+1);
+					Vector a;
+					a.reserve(d+1);
+					a.insert(a.end(),f,e);
+					a.push_back(CGAL_FORWARD(T,t));
+					return a;
+				}
+		};
+
+		// useless, use a transform_iterator?
+#if 0
+		struct Iterator_and_last_divide {
+			template<typename Iter,typename T>
+				Vector operator()(int d,Iter f,Iter const& e,T const&t) const {
+					CGAL_assertion(d==std::distance(f,e)+1);
+					Vector a;
+					a.reserve(d+1);
+					for(;f!=e;++f){
+						a.push_back(*f/t);
+					}
+					return a;
+				}
+		};
+#endif
+
+		struct Values {
+#ifdef CGAL_CXX0X
+			template<class...U>
+				Vector operator()(U&&...u) const {
+					//TODO: check the right number of {}, g++ accepts one and two
+					Vector a={forward_safe<NT,U>(u)...};
+					return a;
+				}
+#else
+
+#define VAR(Z,N,_) a.push_back(t##N);
+#define CODE(Z,N,_) Vector operator()(BOOST_PP_ENUM_PARAMS(N,NT const& t)) const { \
+	Vector a; \
+	a.reserve(N); \
+	BOOST_PP_REPEAT(N,VAR,) \
+	return a; \
+}
+BOOST_PP_REPEAT_FROM_TO(1, 11, CODE, _ )
+#undef CODE
+#undef VAR
+
+#endif
+		};
+
+		struct Values_divide {
+#ifdef CGAL_CXX0X
+			template<class H,class...U>
+				Vector operator()(H const&h,U&&...u) const {
+					//TODO: do we want to cast at some point?
+					//e.g. to avoid 1/2 in integers
+					// ==> use Rational_traits<NT>().make_rational(x,y) ?
+					Vector a={Rational_traits<NT>().make_rational(std::forward<U>(u),h)...};
+					return a;
+				}
+#else
+
+#define VAR(Z,N,_) a.push_back(Rational_traits<NT>().make_rational( t##N ,h));
+#define CODE(Z,N,_) template<class H> Vector \
+			operator()(H const&h, BOOST_PP_ENUM_PARAMS(N,NT const& t)) const { \
+				Vector a; \
+				a.reserve(N); \
+				BOOST_PP_REPEAT(N,VAR,) \
+				return a; \
+			}
+			BOOST_PP_REPEAT_FROM_TO(1, 11, CODE, _ )
+#undef CODE
+#undef VAR
+
+#endif
+		};
+	};
+	typedef typename Vector::const_iterator Vector_const_iterator;
+	static Vector_const_iterator vector_begin(Vector const&a){
+		return a.begin();
+	}
+	static Vector_const_iterator vector_end(Vector const&a){
+		return a.end();
+	}
+	static int size_of_vector(Vector const&a){
+		return a.size();
+	}
+};
+
+
+}
+#endif
+

NewKernel_d/include/CGAL/argument_swaps.h

@@ -0,0 +1,69 @@
+#ifndef CGAL_ARGUMENT_SWAPS_H
+#define CGAL_ARGUMENT_SWAPS_H
+
+#include <CGAL/config.h>
+#include <utility>
+
+#ifndef CGAL_CXX0X
+#include <boost/preprocessor/repetition.hpp>
+#include <boost/utility/result_of.hpp>
+#endif
+
+namespace CGAL {
+
+#ifdef CGAL_CXX0X
+
+namespace internal {
+
+template<int,class...> struct Apply_to_last_then_rest_;
+
+template<int d,class F,class T,class... U>
+struct Apply_to_last_then_rest_<d,F,T,U...> {
+	typedef typename Apply_to_last_then_rest_<d-1,F,U...,T>::result_type result_type;
+	inline result_type operator()(F&&f,T&&t,U&&...u)const{
+		return Apply_to_last_then_rest_<d-1,F,U...,T>()(
+				std::forward<F>(f),
+				std::forward<U>(u)...,
+				std::forward<T>(t));
+	}
+};
+
+template<class F,class T,class... U>
+struct Apply_to_last_then_rest_<0,F,T,U...> {
+	typedef decltype(std::declval<F>()(std::declval<T>(), std::declval<U>()...)) result_type;
+	inline result_type operator()(F&&f,T&&t,U&&...u)const{
+	return std::forward<F>(f)(std::forward<T>(t), std::forward<U>(u)...);
+	}
+};
+
+} // namespace internal
+
+
+struct Apply_to_last_then_rest {
+	template<class F,class T,class...U> inline
+	typename internal::Apply_to_last_then_rest_<sizeof...(U),F,T,U...>::result_type
+	operator()(F&&f,T&&t,U&&...u)const{
+	return internal::Apply_to_last_then_rest_<sizeof...(U),F,T,U...>()(
+			std::forward<F>(f),
+			std::forward<T>(t),
+			std::forward<U>(u)...);
+	}
+};
+
+#else // CGAL_CXX0X
+
+struct Apply_to_last_then_rest {
+#define CODE(Z,N,_) template<class F,class T,BOOST_PP_ENUM_PARAMS(N,class T)> \
+	typename boost::result_of<F(T,BOOST_PP_ENUM_PARAMS(N,T))>::type \
+	operator()(F const&f, BOOST_PP_ENUM_BINARY_PARAMS(N,T,const&t), T const&t) const { \
+		return f(t,BOOST_PP_ENUM_PARAMS(N,t)); \
+	}
+	BOOST_PP_REPEAT_FROM_TO(1,11,CODE,_)
+#undef CODE
+};
+
+#endif // CGAL_CXX0X
+
+} // namespace CGAL
+
+#endif // CGAL_ARGUMENT_SWAPS_H

NewKernel_d/include/CGAL/determinant_of_vectors.h

@@ -0,0 +1,98 @@
+#ifndef CGAL_DETVEC_H
+#define CGAL_DETVEC_H
+#include <CGAL/determinant.h>
+#include <CGAL/predicates/sign_of_determinant.h>
+
+namespace CGAL {
+  // TODO: determine whether it is better to pass them by lines or columns.
+
+  template <class NT, class Vector> inline
+  NT determinant_of_vectors(Vector const&a, Vector const&b){
+    return determinant<NT>(a[0],a[1],b[0],b[1]);
+  }
+  template <class NT, class Vector> inline
+  typename Sgn<NT>::result_type
+  sign_of_determinant_of_vectors(Vector const&a, Vector const&b){
+    return sign_of_determinant<NT>(a[0],a[1],b[0],b[1]);
+  }
+
+  template <class NT, class Vector>
+  NT determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c){
+    return determinant<NT>(a[0],a[1],a[2],b[0],b[1],b[2],c[0],c[1],c[2]);
+  }
+  template <class NT, class Vector>
+  typename Sgn<NT>::result_type
+  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c){
+    return sign_of_determinant<NT>(a[0],a[1],a[2],b[0],b[1],b[2],c[0],c[1],c[2]);
+  }
+
+  template <class NT, class Vector>
+  NT determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return determinant<NT>(
+	a[0],a[1],a[2],a[3],
+	b[0],b[1],b[2],b[3],
+	c[0],c[1],c[2],c[3],
+	d[0],d[1],d[2],d[3]);
+  }
+  template <class NT, class Vector>
+  typename Sgn<NT>::result_type
+  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return sign_of_determinant<NT>(
+	a[0],a[1],a[2],a[3],
+	b[0],b[1],b[2],b[3],
+	c[0],c[1],c[2],c[3],
+	d[0],d[1],d[2],d[3]);
+  }
+
+  template <class NT, class Vector>
+  NT determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e){
+    return determinant<NT>(
+	a[0],a[1],a[2],a[3],a[4],
+	b[0],b[1],b[2],b[3],b[4],
+	c[0],c[1],c[2],c[3],c[4],
+	d[0],d[1],d[2],d[3],d[4],
+	e[0],e[1],e[2],e[3],e[4]);
+  }
+  template <class NT, class Vector>
+  typename Sgn<NT>::result_type
+  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e){
+    return sign_of_determinant<NT>(
+	a[0],a[1],a[2],a[3],a[4],
+	b[0],b[1],b[2],b[3],b[4],
+	c[0],c[1],c[2],c[3],c[4],
+	d[0],d[1],d[2],d[3],d[4],
+	e[0],e[1],e[2],e[3],e[4]);
+  }
+
+  template <class NT, class Vector>
+  NT determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
+    return determinant<NT>(
+	a[0],a[1],a[2],a[3],a[4],a[5],
+	b[0],b[1],b[2],b[3],b[4],b[5],
+	c[0],c[1],c[2],c[3],c[4],c[5],
+	d[0],d[1],d[2],d[3],d[4],d[5],
+	e[0],e[1],e[2],e[3],e[4],e[5],
+	f[0],f[1],f[2],f[3],f[4],f[5]);
+  }
+  template <class NT, class Vector>
+  typename Sgn<NT>::result_type
+  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
+    return sign_of_determinant<NT>(
+	a[0],a[1],a[2],a[3],a[4],a[5],
+	b[0],b[1],b[2],b[3],b[4],b[5],
+	c[0],c[1],c[2],c[3],c[4],c[5],
+	d[0],d[1],d[2],d[3],d[4],d[5],
+	e[0],e[1],e[2],e[3],e[4],e[5],
+	f[0],f[1],f[2],f[3],f[4],f[5]);
+  }
+
+}
+#endif

NewKernel_d/include/CGAL/functor_properties.h

@@ -0,0 +1,21 @@
+#ifndef CGAL_EXACTNESS_H
+#define CGAL_EXACTNESS_H
+#include <boost/mpl/has_xxx.hpp>
+#include <CGAL/tags.h>
+namespace CGAL {
+
+#define CGAL_STRAWBERRY(Is_pretty) \
+  namespace internal { \
+    BOOST_MPL_HAS_XXX_TRAIT_DEF(Is_pretty) \
+  } \
+  template<class T,bool=internal::has_##Is_pretty<T>::value> \
+  struct Is_pretty : boost::false_type {}; \
+  template<class T> \
+  struct Is_pretty<T,true> : T::Is_pretty {}
+
+CGAL_STRAWBERRY(Is_exact);
+CGAL_STRAWBERRY(Is_fast);
+CGAL_STRAWBERRY(Is_stored);
+#undef CGAL_STRAWBERRY
+}
+#endif // CGAL_EXACTNESS_H

NewKernel_d/include/CGAL/functor_tags.h

@@ -0,0 +1,310 @@
+#ifndef CGAL_FUNCTOR_TAGS_H
+#define CGAL_FUNCTOR_TAGS_H
+#include <CGAL/tags.h> // for Null_tag
+#include <CGAL/marcutils.h>
+#include <boost/mpl/has_xxx.hpp>
+#include <boost/mpl/not.hpp>
+#include <boost/type_traits/is_same.hpp>
+#include <boost/mpl/vector.hpp>
+#include <boost/mpl/empty.hpp>
+#include <boost/mpl/front.hpp>
+#include <boost/mpl/pop_front.hpp>
+namespace CGAL {
+
+  // Find a better place for this later
+
+  template <class K, class T, class=void> struct Get_type
+    : K::template Type<T> {};
+  template <class K, class F, class O=void, class=void> struct Get_functor
+    : K::template Functor<F, O> {};
+#ifdef CGAL_CXX0X
+  template <class K, class T> using Type = typename Get_type<K, T>::type;
+  template <class K, class T> using Functor = typename Get_functor<K, T>::type;
+#endif
+
+  class Null_type {~Null_type();}; // no such object should be created
+
+	// To construct iterators
+	struct Begin_tag {};
+	struct End_tag {};
+
+	// Functor category
+	struct Predicate_tag {};
+	struct Construct_tag {};
+	struct Construct_iterator_tag {};
+	struct Compute_tag {};
+	struct Misc_tag {};
+
+	struct No_filter_tag {};
+
+	template<class>struct Construct_ttag {};
+	template<class>struct Convert_ttag {};
+
+	template <class K, class F, class=void, class=void> struct Get_functor_category { typedef Misc_tag type; };
+	template<class Tg, class Obj, class Base> struct Typedef_tag_type;
+	//template<class Kernel, class Tg> struct Read_tag_type {};
+
+	template<class Kernel, class Tg>
+	struct Provides_type
+	  : Has_type_different_from<Get_type<Kernel, Tg>, Null_type> {};
+
+	template<class Kernel, class Tg, class O=void>
+	struct Provides_functor
+	  : Has_type_different_from<Get_functor<Kernel, Tg, O>, Null_functor> {};
+
+	template<class K, class List, bool=boost::mpl::empty<List>::type::value>
+	struct Provides_functors : boost::mpl::and_ <
+				   Provides_functor<K, typename boost::mpl::front<List>::type>,
+				   Provides_functors<K, typename boost::mpl::pop_front<List>::type> > {};
+	template<class K, class List>
+	struct Provides_functors<K, List, true> : boost::true_type {};
+
+	template<class K, class List, bool=boost::mpl::empty<List>::type::value>
+	struct Provides_types : boost::mpl::and_ <
+				   Provides_type<K, typename boost::mpl::front<List>::type>,
+				   Provides_types<K, typename boost::mpl::pop_front<List>::type> > {};
+	template<class K, class List>
+	struct Provides_types<K, List, true> : boost::true_type {};
+
+	namespace internal { BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(has_Type,template Type<Null_tag>,false) }
+	template<class Kernel, class Tg,
+	  bool = internal::has_Type<Kernel>::value /* false */>
+	struct Provides_type_i : boost::false_type {};
+	template<class Kernel, class Tg>
+	struct Provides_type_i <Kernel, Tg, true>
+	  : Has_type_different_from<typename Kernel::template Type<Tg>, Null_type> {};
+
+	namespace internal { BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(has_Functor,template Functor<Null_tag>,false) }
+	template<class Kernel, class Tg, class O=void,
+	  bool = internal::has_Functor<Kernel>::value /* false */>
+	struct Provides_functor_i : boost::false_type {};
+	template<class Kernel, class Tg, class O>
+	struct Provides_functor_i <Kernel, Tg, O, true>
+	  : Has_type_different_from<typename Kernel::template Functor<Tg, O>, Null_functor> {};
+
+	// TODO: Refine this a bit.
+	template <class K, class T, class D=void,
+		  //bool=Provides_functor<K,T>::value,
+		  //bool=Provides_functor_i<K,T>::value,
+		  bool=internal::has_Functor<K>::value>
+	struct Inherit_functor : K::template Functor<T> {};
+	template <class K, class T, class D>
+	struct Inherit_functor <K, T, D, false> {};
+
+	template <class K, class T, bool=internal::has_Type<K>::value>
+	struct Inherit_type : K::template Type<T> {};
+	template <class K, class T>
+	struct Inherit_type <K, T, false> {};
+
+	struct Number_tag {};
+	struct Discrete_tag {};
+	struct Object_tag {};
+	template <class K, class T, class=void> struct Get_type_category {
+	  // The lazy kernel uses it too eagerly,
+	  // so it currently needs a default.
+	  typedef Null_tag type;
+	};
+
+#define DECL_OBJ_(X,Y) \
+  template<class Obj,class Base> \
+  struct Typedef_tag_type<X##_tag, Obj, Base> : Base { typedef Obj X; }; \
+  template<class K, class D> \
+  struct Get_type_category <K, X##_tag, D> { typedef Y##_tag type; }
+#define DECL_OBJ(X,Y) struct X##_tag {}; \
+  DECL_OBJ_(X,Y)
+
+  //namespace has_object { BOOST_MPL_HAS_XXX_TRAIT_DEF(X) }
+  //template<class Kernel>
+  //struct Provides_tag_type<Kernel, X##_tag> : has_object::has_##X<Kernel> {};
+  //template<class Kernel>
+  //struct Read_tag_type<Kernel, X##_tag> { typedef typename Kernel::X type; }
+
+	// Not exactly objects, but the extras can't hurt.
+	DECL_OBJ(FT, Number);
+	DECL_OBJ(RT, Number);
+
+	DECL_OBJ(Bool, Discrete); // Boolean_tag is already taken, and is a template :-(
+	DECL_OBJ(Comparison_result, Discrete);
+	DECL_OBJ(Sign, Discrete);
+	DECL_OBJ(Orientation, Discrete); // Note: duplicate with the functor tag!
+	DECL_OBJ(Oriented_side, Discrete);
+	DECL_OBJ(Bounded_side, Discrete);
+	DECL_OBJ(Angle, Discrete);
+	DECL_OBJ(Flat_orientation, Discrete);
+
+	DECL_OBJ(Vector, Object);
+	DECL_OBJ(Point, Object);
+	DECL_OBJ(Segment, Object);
+	DECL_OBJ(Sphere, Object);
+	DECL_OBJ(Line, Object);
+	DECL_OBJ(Direction, Object);
+	DECL_OBJ(Hyperplane, Object);
+	DECL_OBJ(Ray, Object);
+	DECL_OBJ(Iso_box, Object);
+	DECL_OBJ(Bbox, Object);
+	DECL_OBJ(Aff_transformation, Object);
+#undef DECL_OBJ_
+#undef DECL_OBJ
+
+	CGAL_KD_DEFAULT_TYPE(RT_tag,(typename Get_type<K, FT_tag>::type),(),());
+	CGAL_KD_DEFAULT_TYPE(FT_tag,(CGAL::Quotient<typename Get_type<K, RT_tag>::type>),(),());
+
+#define SMURF2(A,B) CGAL_KD_DEFAULT_TYPE(A##_tag,(typename Same_uncertainty_nt<B, typename Get_type<K,RT_tag>::type>::type),(RT_tag),())
+#define SMURF1(A) SMURF2(A,CGAL::A)
+	SMURF2(Bool, bool);
+	SMURF1(Sign);
+	SMURF1(Comparison_result);
+	SMURF1(Orientation);
+	SMURF1(Oriented_side);
+	SMURF1(Bounded_side);
+	SMURF1(Angle);
+#undef SMURF1
+#undef SMURF2
+
+	// TODO: replace with Get_type_category
+	template<class> struct is_NT_tag { enum { value = false }; };
+	template<> struct is_NT_tag<FT_tag> { enum { value = true }; };
+	template<> struct is_NT_tag<RT_tag> { enum { value = true }; };
+
+	template<class> struct iterator_tag_traits {
+	  enum { is_iterator = false, has_nth_element = false };
+	  typedef Null_tag value_tag;
+	};
+
+#define DECL_COMPUTE(X) struct X##_tag {}; \
+	template<class A,class B,class C>struct Get_functor_category<A,X##_tag,B,C>{typedef Compute_tag type;}
+	DECL_COMPUTE(Compute_point_cartesian_coordinate);
+	DECL_COMPUTE(Compute_vector_cartesian_coordinate);
+	DECL_COMPUTE(Compute_homogeneous_coordinate);
+	DECL_COMPUTE(Squared_distance);
+	DECL_COMPUTE(Squared_distance_to_origin);
+	DECL_COMPUTE(Squared_length);
+	DECL_COMPUTE(Squared_radius);
+	DECL_COMPUTE(Scalar_product);
+	DECL_COMPUTE(Hyperplane_translation);
+	DECL_COMPUTE(Value_at);
+#undef DECL_COMPUTE
+
+#define DECL_ITER_OBJ(X,Y,Z,C) struct X##_tag {}; \
+  template<>struct iterator_tag_traits<X##_tag> { \
+    enum { is_iterator = true, has_nth_element = true }; \
+    typedef Y##_tag value_tag; \
+    typedef Z##_tag nth_element; \
+    typedef C##_tag container; \
+  }; \
+  template<class Obj,class Base> \
+  struct Typedef_tag_type<X##_tag, Obj, Base> : Base { typedef Obj X; }
+
+  //namespace has_object { BOOST_MPL_HAS_XXX_TRAIT_DEF(X) }
+  //template<class Kernel>
+  //struct Provides_tag_type<Kernel, X##_tag> : has_object::has_##X<Kernel> {};
+  //template<class Kernel>
+  //struct Read_tag_type<Kernel, X##_tag> { typedef typename Kernel::X type; }
+
+	DECL_ITER_OBJ(Vector_cartesian_const_iterator, FT, Compute_vector_cartesian_coordinate, Vector);
+	DECL_ITER_OBJ(Point_cartesian_const_iterator, FT, Compute_point_cartesian_coordinate, Point);
+#undef DECL_ITER_OBJ
+
+	template<class>struct map_result_tag{typedef Null_type type;};
+	template<class T>struct map_result_tag<Construct_ttag<T> >{typedef T type;};
+
+	template<class A,class T,class B,class C>struct Get_functor_category<A,Construct_ttag<T>,B,C> :
+	  BOOSTD conditional<iterator_tag_traits<T>::is_iterator,
+		 Construct_iterator_tag,
+		 Construct_tag> {};
+
+	// Really?
+	template<class A,class T,class B,class C>struct Get_functor_category<A,Convert_ttag<T>,B,C>{typedef Misc_tag type;};
+
+#define DECL_CONSTRUCT(X,Y) struct X##_tag {}; \
+	template<>struct map_result_tag<X##_tag>{typedef Y##_tag type;}; \
+	template<class A,class B,class C>struct Get_functor_category<A,X##_tag,B,C>{typedef Construct_tag type;}
+	DECL_CONSTRUCT(Midpoint,Point);
+	DECL_CONSTRUCT(Center_of_sphere,Point);
+	DECL_CONSTRUCT(Point_of_sphere,Point);
+	DECL_CONSTRUCT(Segment_extremity,Point);
+	DECL_CONSTRUCT(Sum_of_vectors,Vector);
+	DECL_CONSTRUCT(Difference_of_vectors,Vector);
+	DECL_CONSTRUCT(Opposite_vector,Vector);
+	DECL_CONSTRUCT(Scaled_vector,Vector);
+	DECL_CONSTRUCT(Orthogonal_vector,Vector);
+	DECL_CONSTRUCT(Difference_of_points,Vector);
+	DECL_CONSTRUCT(Translated_point,Point);
+	DECL_CONSTRUCT(Point_to_vector,Vector);
+	DECL_CONSTRUCT(Vector_to_point,Point);
+#undef DECL_CONSTRUCT
+#if 0
+#define DECL_ITER_CONSTRUCT(X,Y) struct X##_tag {}; \
+	template<>struct map_result_tag<X##_tag>{typedef Y##_tag type;}; \
+	template<>struct map_functor_type<X##_tag>{typedef Construct_iterator_tag type;}
+	DECL_ITER_CONSTRUCT(Construct_point_cartesian_const_iterator,Point_cartesian_const_iterator);
+	DECL_ITER_CONSTRUCT(Construct_vector_cartesian_const_iterator,Vector_cartesian_const_iterator);
+#undef DECL_ITER_CONSTRUCT
+#endif
+
+	//FIXME: choose a convention: prefix with Predicate_ ?
+#define DECL_PREDICATE_(X) \
+	template<class A,class B,class C>struct Get_functor_category<A,X##_tag,B,C>{typedef Predicate_tag type;}
+#define DECL_PREDICATE(X) struct X##_tag {}; \
+	DECL_PREDICATE_(X)
+	DECL_PREDICATE(Less_point_cartesian_coordinate);
+	DECL_PREDICATE(Compare_point_cartesian_coordinate);
+	DECL_PREDICATE(Compare_distance);
+	DECL_PREDICATE(Compare_lexicographically);
+	DECL_PREDICATE(Less_lexicographically);
+	DECL_PREDICATE(Less_or_equal_lexicographically);
+	DECL_PREDICATE(Equal_points);
+	DECL_PREDICATE(Has_on_positive_side);
+	DECL_PREDICATE_(Orientation); // duplicate with the type
+	DECL_PREDICATE_(Oriented_side); // duplicate with the type
+	DECL_PREDICATE(Orientation_of_points);
+	DECL_PREDICATE(Orientation_of_vectors);
+	DECL_PREDICATE(Side_of_oriented_sphere);
+	DECL_PREDICATE(Contained_in_affine_hull);
+	DECL_PREDICATE(In_flat_orientation);
+	DECL_PREDICATE(In_flat_side_of_oriented_sphere);
+	DECL_PREDICATE(Construct_flat_orientation); // Making it a predicate is a questionable choice, it should be possible to let it be a construction for some implementations. Not sure how to do that... TODO
+#undef DECL_PREDICATE
+
+#define DECL_MISC(X) struct X##_tag {}; \
+	template<class A,class B,class C>struct Get_functor_category<A,X##_tag,B,C>{typedef Misc_tag type;}
+	//TODO: split into _begin and _end ?
+	//DECL_MISC(Construct_point_cartesian_const_iterator);
+	//DECL_MISC(Construct_vector_cartesian_const_iterator);
+	DECL_MISC(Point_dimension);
+	DECL_MISC(Vector_dimension);
+#undef DECL_MISC
+
+
+	// Properties for LA
+	struct Has_extra_dimension_tag {};
+	struct Has_vector_plus_minus_tag {};
+	struct Has_vector_scalar_ops_tag {};
+	struct Has_dot_product_tag {};
+	struct Has_determinant_of_vectors_tag {};
+	struct Has_determinant_of_points_tag {};
+	struct Has_determinant_of_iterator_to_vectors_tag {};
+	struct Has_determinant_of_iterator_to_points_tag {};
+	struct Has_determinant_of_vectors_omit_last_tag {};
+	struct Stores_squared_norm_tag {};
+
+	template<class> struct Preserved_by_non_linear_extra_coordinate
+	  : boost::false_type {};
+	template<> struct Preserved_by_non_linear_extra_coordinate
+	  <Has_extra_dimension_tag> : boost::true_type {};
+	template<> struct Preserved_by_non_linear_extra_coordinate
+	  <Has_determinant_of_vectors_tag> : boost::true_type {};
+	template<> struct Preserved_by_non_linear_extra_coordinate
+	  <Has_determinant_of_points_tag> : boost::true_type {};
+	template<> struct Preserved_by_non_linear_extra_coordinate
+	  <Has_determinant_of_iterator_to_vectors_tag> : boost::true_type {};
+	template<> struct Preserved_by_non_linear_extra_coordinate
+	  <Has_determinant_of_iterator_to_points_tag> : boost::true_type {};
+	template<> struct Preserved_by_non_linear_extra_coordinate
+	  <Has_determinant_of_vectors_omit_last_tag> : boost::true_type {};
+
+	// Kernel properties
+	struct Point_stores_squared_distance_to_origin_tag {};
+
+}
+#endif // CGAL_FUNCTOR_TAGS_H

NewKernel_d/include/CGAL/iterator_from_indices.h

@@ -0,0 +1,56 @@
+#ifndef CGAL_ITERATOR_FROM_INDICES_H
+#define CGAL_ITERATOR_FROM_INDICES_H
+#include <boost/iterator/iterator_facade.hpp>
+namespace CGAL {
+template <class Ref_>
+struct Default_coordinate_access {
+	typedef Ref_ result_type;
+	template<class T> Ref_ operator()(T const& t, int i)const{
+		return t[i];
+	}
+};
+
+//TODO: default type for Value_: typename same_cv<Container_,typename remove_cv<Container_>::type::value_type>::type
+template <class Container_, class Value_, class Ref_=
+#ifdef CGAL_CXX0X
+	decltype(std::declval<Container_>()[0])
+#else
+	Value_&
+#endif
+	, class Coord_access = Default_coordinate_access<Ref_>
+	>
+class Iterator_from_indices
+: public boost::iterator_facade<Iterator_from_indices<Container_,Value_,Ref_,Coord_access>,
+	Value_, std::bidirectional_iterator_tag, Ref_>
+{
+	friend class boost::iterator_core_access;
+	//FIXME: use int to save space
+	//FIXME: use a signed type
+	typedef std::size_t index_t;
+	Container_* cont;
+	index_t index;
+	Coord_access ca;
+	void increment(){ ++index; }
+	void decrement(){ --index; }
+	void advance(std::ptrdiff_t n){ index+=n; }
+	ptrdiff_t distance_to(Iterator_from_indices const& other)const{
+		return static_cast<ptrdiff_t>(other.index)
+			-static_cast<ptrdiff_t>(index);
+	}
+	bool equal(Iterator_from_indices const& other)const{
+		return index==other.index;
+	}
+	Ref_ dereference()const{
+		//FIXME: use the functor properly
+		//Uh, and what did I mean by that?
+		return ca(*cont,index);
+	}
+	public:
+	Iterator_from_indices(Container_& cont_,std::size_t n)
+		: cont(&cont_), index(n) {}
+	template<class T>
+	Iterator_from_indices(Container_& cont_,std::size_t n,T const&t)
+		: cont(&cont_), index(n), ca(t) {}
+};
+}
+#endif // CGAL_ITERATOR_FROM_INDICES_H

NewKernel_d/include/CGAL/marcutils.h

@@ -0,0 +1,266 @@
+#ifndef marcutils
+#define marcutils
+
+#ifdef CGAL_CXX0X
+#include <type_traits>
+#include <utility>
+#define CGAL_FORWARDABLE(T) T&&
+#define CGAL_FORWARD(T,t) std::forward<T>(t)
+#define CGAL_MOVE(t) std::move(t)
+#define CGAL_CONSTEXPR constexpr
+#else
+#define CGAL_FORWARDABLE(T) T const&
+#define CGAL_FORWARD(T,t) t
+#define CGAL_MOVE(t) t
+#define CGAL_CONSTEXPR
+#endif
+#include <boost/utility/enable_if.hpp>
+#include <boost/preprocessor/repetition.hpp>
+#include <CGAL/Rational_traits.h>
+#include <CGAL/tuple.h>
+#include <boost/mpl/has_xxx.hpp>
+#include <boost/mpl/not.hpp>
+#include <boost/type_traits.hpp>
+
+#ifdef CGAL_CXX0X
+#define BOOSTD std::
+#else
+#define BOOSTD boost::
+#endif
+
+namespace CGAL {
+namespace internal {
+	BOOST_MPL_HAS_XXX_TRAIT_DEF(type)
+}
+
+template <class T, class No, bool=internal::has_type<T>::value /*false*/>
+struct Has_type_different_from : boost::false_type {};
+template <class T, class No>
+struct Has_type_different_from <T, No, true>
+: boost::mpl::not_<boost::is_same<typename T::type, No> > {};
+
+
+	template <class T> struct Wrap_type { typedef T type; };
+
+	// tell a function f(a,b,c) that its real argument is a(b,c)
+	struct Eval_functor {};
+
+	// forget the first argument. Useful to make something dependant
+	// (and thus usable in SFINAE), although that's not a great design.
+	template<class A,class B> struct Second_arg {
+		typedef B type; 
+	};      
+
+	// like std::forward, except for basic types where it does a cast, to
+	// avoid issues with narrowing conversions
+#ifdef CGAL_CXX0X
+	template<class T,class U,class V> inline
+		typename std::conditional<std::is_arithmetic<T>::value&&std::is_arithmetic<typename std::remove_reference<U>::type>::value,T,U&&>::type
+	       	forward_safe(V&& u) { return std::forward<U>(u); }
+#else
+	template<class T,class U> inline U const& forward_safe(U const& u) {
+		return u;
+	}
+#endif
+
+#ifdef CGAL_CXX0X
+	template<class...> struct Constructible_from_each;
+	template<class To,class From1,class...From> struct Constructible_from_each<To,From1,From...>{
+		enum { value=std::is_convertible<From1,To>::value&&Constructible_from_each<To,From...>::value };
+	};
+	template<class To> struct Constructible_from_each<To>{
+		enum { value=true };
+	};
+#else
+// currently only used in C++0X code
+#endif
+
+	template<class T> struct Scale {
+		T const& scale;
+		Scale(T const& t):scale(t){}
+		template<class FT>
+#ifdef CGAL_CXX0X
+		auto operator()(FT&& x)const->decltype(scale*std::forward<FT>(x))
+#else
+		FT operator()(FT const& x)const
+#endif
+		{
+			return scale*CGAL_FORWARD(FT,x);
+		}
+	};
+	template<class NT,class T> struct Divide {
+#if !defined(CGAL_CXX0X) || !defined(BOOST_RESULT_OF_USE_DECLTYPE)
+		// requires boost > 1.44
+		// shouldn't be needed with C++0X
+		//template<class> struct result;
+		//template<class FT> struct result<Divide(FT)> {
+		//	typedef FT type;
+		//};
+		typedef NT result_type;
+#endif
+		T const& scale;
+		Divide(T const& t):scale(t){}
+		template<class FT>
+#ifdef CGAL_CXX0X
+		//FIXME: gcc complains for Gmpq
+		//auto operator()(FT&& x)const->decltype(Rational_traits<NT>().make_rational(std::forward<FT>(x),scale))
+		NT operator()(FT&& x)const
+#else
+		NT operator()(FT const& x)const
+#endif
+		{
+			return Rational_traits<NT>().
+				make_rational(CGAL_FORWARD(FT,x),scale);
+		}
+	};
+
+	template <class NT> struct has_cheap_constructor : boost::is_arithmetic<NT>{};
+	template <bool p> struct has_cheap_constructor<Interval_nt<p> > {
+		        enum { value=true };
+	};
+
+	// like std::multiplies but allows mixing types
+	// in C++0x in doesn't need to be a template
+	template < class Ret >
+	struct multiplies {
+		template<class A,class B>
+#ifdef CGAL_CXX0X
+		auto operator()(A&&a,B&&b)const->decltype(std::forward<A>(a)*std::forward<B>(b))
+#else
+		Ret operator()(A const& a, B const& b)const
+#endif
+		{
+			return CGAL_FORWARD(A,a)*CGAL_FORWARD(B,b);
+		}
+	};
+	template < class Ret >
+	struct division {
+		template<class A,class B>
+#ifdef CGAL_CXX0X
+		auto operator()(A&&a,B&&b)const->decltype(std::forward<A>(a)/std::forward<B>(b))
+#else
+		Ret operator()(A const& a, B const& b)const
+#endif
+		{
+			return CGAL_FORWARD(A,a)/CGAL_FORWARD(B,b);
+		}
+	};
+
+#ifdef CGAL_CXX0X
+	using std::decay;
+#else
+	template<class T> struct decay : boost::remove_cv<typename boost::decay<T>::type> {};
+#endif
+
+	template<class T,class U> struct Type_copy_ref { typedef U type; };
+	template<class T,class U> struct Type_copy_ref<T&,U> { typedef U& type; };
+#ifdef CGAL_CXX0X
+	template<class T,class U> struct Type_copy_ref<T&&,U> { typedef U&& type; };
+#endif
+	template<class T,class U> struct Type_copy_cv { typedef U type; };
+	template<class T,class U> struct Type_copy_cv<T const,U> { typedef U const type; };
+	template<class T,class U> struct Type_copy_cv<T volatile,U> { typedef U volatile type; };
+	template<class T,class U> struct Type_copy_cv<T const volatile,U> { typedef U const volatile type; };
+
+	template<class T,class U> struct Type_copy_cvref :
+		Type_copy_ref<T,typename Type_copy_cv<typename boost::remove_reference<T>::type,U>::type> {};
+
+	struct Dereference_functor {
+		template<class> struct result{};
+		template<class It> struct result<Dereference_functor(It)> {
+			typedef typename std::iterator_traits<It>::reference type;
+		};
+		template<class It> typename result<Dereference_functor(It)>::type
+			operator()(It const&i)const{
+				return *i;
+			}
+	};
+
+#ifdef CGAL_CXX0X
+	template<int...> struct Indices{};
+	template<class> struct Next_increasing_indices;
+	template<int...I> struct Next_increasing_indices<Indices<I...> > {
+		typedef Indices<I...,sizeof...(I)> type;
+	};
+	template<int N> struct N_increasing_indices {
+		typedef typename Next_increasing_indices<typename N_increasing_indices<N-1>::type>::type type;
+	};
+	template<> struct N_increasing_indices<0> { typedef Indices<> type; };
+	namespace internal {
+	template<class F,class...U,int...I> inline typename std::result_of<F&&(U...)>::type
+	do_call_on_tuple_elements(F&&f, std::tuple<U...>&&t, Indices<I...>&&) {
+		return f(std::get<I>(std::move(t))...);
+	}
+	} // internal
+	template<class/*result type, ignored*/,class F,class...U>
+	inline typename std::result_of<F&&(U...)>::type
+	call_on_tuple_elements(F&&f, std::tuple<U...>&&t) {
+		return internal::do_call_on_tuple_elements(std::forward<F>(f),std::move(t),
+				typename N_increasing_indices<sizeof...(U)>::type());
+	}
+#else
+#define VAR(Z,N,_) cpp0x::get<N>(t)
+#define CODE(Z,N,_) template<class Res, class F BOOST_PP_COMMA_IF(N) BOOST_PP_ENUM_PARAMS(N,class U)> \
+	inline Res call_on_tuple_elements(F const&f, \
+			cpp0x::tuple<BOOST_PP_ENUM_PARAMS(N,U)> const&t) { \
+		return f(BOOST_PP_ENUM(N,VAR,)); \
+	}
+BOOST_PP_REPEAT_FROM_TO(0, 8, CODE, _ )
+#undef CODE
+#undef VAR
+#endif
+
+	template<class A> struct Factory {
+	  typedef A result_type;
+#ifdef CGAL_CXX0X
+	  template<class...U> result_type operator()(U&&...u)const{
+	    return A(std::forward<U>(u)...);
+	  }
+#else
+	  result_type operator()()const{
+	    return A();
+	  }
+#define CODE(Z,N,_) template<BOOST_PP_ENUM_PARAMS(N,class U)> \
+	  result_type operator()(BOOST_PP_ENUM_BINARY_PARAMS(N,U,const&u))const{ \
+	    return A(BOOST_PP_ENUM_PARAMS(N,u)); \
+	  }
+BOOST_PP_REPEAT_FROM_TO(1, 8, CODE, _ )
+#undef CODE
+#endif
+	};
+}
+
+// TODO: make a Cartesian-only variant
+// WARNING: do not use the Req* parameters too much, they can cause circular instanciations and are only useful for dispatching.
+#define CGAL_STRIP_PAREN_(...) __VA_ARGS__
+#define CGAL_STRIP_PAREN(...) CGAL_STRIP_PAREN_ __VA_ARGS__
+// What to do with O? pass it down to other functors or drop it?
+#define CGAL_KD_DEFAULT_FUNCTOR(Tg,Name,ReqTyp,ReqFun) \
+    template <class K, class O> \
+    struct Get_functor<K, Tg, O, \
+      typename boost::mpl::if_c< \
+        Provides_functor_i<K, Tg, O>::value \
+        || !Provides_types<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqTyp> >::value \
+        || !Provides_functors<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqFun> >::value \
+      , int, void>::type> \
+    { \
+      typedef CGAL_STRIP_PAREN_ Name type; \
+      typedef K Bound_kernel; \
+    }
+
+// Not used yet, may need some changes.
+#define CGAL_KD_DEFAULT_TYPE(Tg,Name,ReqTyp,ReqFun) \
+    template <class K> \
+    struct Get_type<K, Tg, \
+      typename boost::mpl::if_c< \
+        Provides_type_i<K, Tg>::value \
+        || !Provides_types<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqTyp> >::value \
+        || !Provides_functors<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqFun> >::value \
+      , int, void>::type> \
+    { \
+      typedef CGAL_STRIP_PAREN_ Name type; \
+      typedef K Bound_kernel; \
+    }
+
+
+#endif

NewKernel_d/include/CGAL/static_int.h

@@ -0,0 +1,42 @@
+#ifndef CGAL_STATIC_INT_H
+#define CGAL_STATIC_INT_H
+#include <CGAL/constant.h>
+
+namespace CGAL {
+template <class NT> struct static_zero {
+	operator NT() const { return constant<NT,0>(); }
+};
+template <class NT> struct static_one {
+	operator NT() const { return constant<NT,1>(); }
+};
+
+template <class NT> static_zero<NT> operator-(static_zero<NT>) { return static_zero<NT>(); }
+
+template <class NT> NT operator+(NT const& x, static_zero<NT>) { return x; }
+template <class NT> NT operator+(static_zero<NT>, NT const& x) { return x; }
+template <class NT> static_zero<NT> operator+(static_zero<NT>, static_zero<NT>) { return static_zero<NT>(); }
+template <class NT> static_one<NT> operator+(static_zero<NT>, static_one<NT>) { return static_one<NT>(); }
+template <class NT> static_one<NT> operator+(static_one<NT>, static_zero<NT>) { return static_one<NT>(); }
+
+template <class NT> NT operator-(NT const& x, static_zero<NT>) { return x; }
+template <class NT> NT operator-(static_zero<NT>, NT const& x) { return -x; }
+template <class NT> static_zero<NT> operator-(static_zero<NT>, static_zero<NT>) { return static_zero<NT>(); }
+template <class NT> static_zero<NT> operator-(static_one<NT>, static_one<NT>) { return static_zero<NT>(); }
+template <class NT> static_one<NT> operator-(static_one<NT>, static_zero<NT>) { return static_one<NT>(); }
+
+template <class NT> NT operator*(NT const& x, static_one<NT>) { return x; }
+template <class NT> NT operator*(static_one<NT>, NT const& x) { return x; }
+template <class NT> static_zero<NT> operator*(NT const&, static_zero<NT>) { return static_zero<NT>(); }
+template <class NT> static_zero<NT> operator*(static_zero<NT>, NT const&) { return static_zero<NT>(); }
+template <class NT> static_zero<NT> operator*(static_zero<NT>, static_zero<NT>) { return static_zero<NT>(); }
+template <class NT> static_one<NT> operator*(static_one<NT>, static_one<NT>) { return static_one<NT>(); }
+template <class NT> static_zero<NT> operator*(static_zero<NT>, static_one<NT>) { return static_zero<NT>(); }
+template <class NT> static_zero<NT> operator*(static_one<NT>, static_zero<NT>) { return static_zero<NT>(); }
+
+template <class NT> NT operator/(NT const& x, static_one<NT>) { return x; }
+template <class NT> static_zero<NT> operator/(static_zero<NT>, NT const&) { return static_zero<NT>(); }
+template <class NT> static_zero<NT> operator/(static_zero<NT>, static_one<NT>) { return static_zero<NT>(); }
+template <class NT> static_one<NT> operator/(static_one<NT>, static_one<NT>) { return static_one<NT>(); }
+
+}
+#endif // CGAL_STATIC_INT_H

NewKernel_d/include/CGAL/store_kernel.h

@@ -0,0 +1,81 @@
+#ifndef CGAL_STORE_KERNEL_H
+#define CGAL_STORE_KERNEL_H
+
+#include <CGAL/assertions.h>
+#include <boost/type_traits/is_empty.hpp>
+
+namespace CGAL {
+namespace internal {
+BOOST_MPL_HAS_XXX_TRAIT_DEF(Do_not_store_kernel)
+template<class T,bool=has_Do_not_store_kernel<T>::value> struct Do_not_store_kernel {
+	enum { value=false };
+	typedef Tag_false type;
+};
+template<class T> struct Do_not_store_kernel<T,true> {
+	typedef typename T::Do_not_store_kernel type;
+	enum { value=type::value };
+};
+}
+
+template<class R_,bool=boost::is_empty<R_>::value||internal::Do_not_store_kernel<R_>::value>
+struct Store_kernel {
+	Store_kernel(){}
+	Store_kernel(R_ const&){}
+	enum { kernel_is_stored = false };
+	R_ kernel()const{return R_();}
+	typedef R_ reference_type;
+	void set_kernel(R_ const&){}
+};
+template<class R_>
+struct Store_kernel<R_,false> {
+	Store_kernel():rp(0){
+		CGAL_warning_msg(true,"I should know my kernel");
+	}
+	Store_kernel(R_ const& r):rp(&r){}
+	enum { kernel_is_stored = true };
+	R_ const& kernel()const{
+		CGAL_warning_msg(rp!=0,"I should know my kernel");
+		return *rp;
+	}
+	typedef R_ const& reference_type;
+	void set_kernel(R_ const&r){rp=&r;}
+	private:
+	R_ const* rp;
+};
+
+//For a second kernel. TODO: find something more elegant
+template<class R_,bool=boost::is_empty<R_>::value||internal::Do_not_store_kernel<R_>::value>
+struct Store_kernel2 {
+	Store_kernel2(){}
+	Store_kernel2(R_ const&){}
+	enum { kernel2_is_stored = false };
+	R_ kernel2()const{return R_();}
+	typedef R_ reference2_type;
+	void set_kernel2(R_ const&){}
+};
+template<class R_>
+struct Store_kernel2<R_,false> {
+	Store_kernel2(){
+		//CGAL_warning_msg(true,"I should know my kernel");
+	}
+	Store_kernel2(R_ const& r):rp(&r){}
+	enum { kernel2_is_stored = true };
+	R_ const& kernel2()const{
+		CGAL_warning_msg(rp==0,"I should know my kernel");
+		return *rp;
+	}
+	typedef R_ const& reference2_type;
+	void set_kernel2(R_ const&r){rp=&r;}
+	private:
+	R_ const* rp;
+};
+}
+#define CGAL_BASE_INIT(X,Y) \
+	X():Y(){} \
+	X(R_ const&r):Y(r){}
+#define CGAL_FUNCTOR_INIT_STORE(X) CGAL_BASE_INIT(X,Store_kernel<R_>)
+#define CGAL_FUNCTOR_INIT_IGNORE(X) \
+	X(){} \
+	X(R_ const&){}
+
+#endif // CGAL_STORE_KERNEL_H

NewKernel_d/include/CGAL/transforming_iterator.h

@@ -0,0 +1,92 @@
+#ifndef CGAL_TRANSFORMING_ITERATOR_H
+#define CGAL_TRANSFORMING_ITERATOR_H
+#include <boost/iterator/iterator_adaptor.hpp>
+#include <boost/utility/result_of.hpp>
+#include <boost/type_traits/is_empty.hpp>
+#include <CGAL/Default.h>
+#include <utility>
+
+// Inspired by the boost version, but more compact and
+// without any iterator_category games.
+
+namespace CGAL {
+namespace internal {
+
+// non-empty case
+template<class T,bool=boost::is_empty<T>::value> struct Functor_as_base {
+	Functor_as_base(){}
+	Functor_as_base(T const& t):f(t){}
+	//template<class T2> Functor_as_base(Functor_as_base<T2> const&g):f(g.functor()){}
+	T const& functor()const{return f;}
+	T &      functor()     {return f;}
+	private:
+		T f;
+};
+
+// empty case
+template<class T> struct Functor_as_base<T,true> : public T {
+	Functor_as_base(){}
+	Functor_as_base(T const& t):T(t){}
+	//template<class T2> Functor_as_base(Functor_as_base<T2> const&g):T(g.functor()){}
+	T const& functor()const{return *this;}
+	T &      functor()     {return *this;}
+};
+
+template <typename Derived, typename F, typename Iter, typename Ref, typename Val>
+class transforming_iterator_helper
+{
+	typedef typename Default::Get<Ref,
+#ifndef CGAL_CFG_NO_CPP0X_DECLTYPE
+		decltype(std::declval<F>()(std::declval<typename std::iterator_traits<Iter>::reference>()))
+#else
+		typename boost::result_of<F(typename std::iterator_traits<Iter>::value_type)>::type
+	// should be reference instead of value_type
+#endif
+			>::type reference;
+
+	typedef typename Default::Get<Val,typename boost::remove_cv<typename boost::remove_reference<reference>::type>::type>::type value_type;
+
+	public:
+	typedef boost::iterator_adaptor<
+		Derived,
+		Iter,
+		value_type,
+		typename std::iterator_traits<Iter>::iterator_category,
+		reference
+			> type;
+};
+}
+
+template <typename F, typename Iter, typename Ref=Default, typename Val=Default>
+class transforming_iterator
+: public internal::transforming_iterator_helper<transforming_iterator<F,Iter,Ref,Val>,F,Iter,Ref,Val>::type,
+private internal::Functor_as_base<F>
+{
+	friend class boost::iterator_core_access;
+	typedef typename internal::transforming_iterator_helper<transforming_iterator,F,Iter,Ref,Val>::type Base;
+	typedef internal::Functor_as_base<F> Functor_base;
+	typename Base::reference dereference()const{
+		return functor()(*this->base_reference());
+	}
+	public:
+	using Functor_base::functor;
+	transforming_iterator(){}
+	explicit transforming_iterator(Iter i,F const& f=F())
+		:Base(i),Functor_base(f){}
+	template<class F2,class I2,class R2,class V2>
+	transforming_iterator(
+		transforming_iterator<F2,I2,R2,V2> const&i,
+		typename boost::enable_if_convertible<I2, Iter>::type* = 0,
+		typename boost::enable_if_convertible<F2, F>::type* = 0)
+		: Base(i.base()),Functor_base(i.functor()) {}
+
+};
+
+template <typename F, typename Iter> inline
+transforming_iterator<F,Iter> make_transforming_iterator(Iter i, F const&f=F()) {
+	return transforming_iterator<F,Iter>(i,f);
+}
+
+}
+
+#endif // CGAL_TRANSFORMING_ITERATOR_H

NewKernel_d/include/CGAL/transforming_pair_iterator.h

@@ -0,0 +1,107 @@
+#ifndef CGAL_TRANSFORMING_PAIR_ITERATOR_H
+#define CGAL_TRANSFORMING_PAIR_ITERATOR_H
+// Should be a combination of transform_iterator and zip_iterator,
+// but boost's iterator_category games are a pain.
+
+#include <CGAL/transforming_iterator.h>
+#include <boost/type_traits/is_convertible.hpp>
+#include <boost/static_assert.hpp>
+
+
+
+namespace CGAL {
+namespace internal {
+template <class Cat1, class Cat2, bool=boost::is_convertible<Cat1,Cat2>::value>
+struct Min_category {
+	BOOST_STATIC_ASSERT((boost::is_convertible<Cat2,Cat1>::value));
+	typedef Cat1 type;
+};
+
+template <class Cat1, class Cat2>
+struct Min_category<Cat1,Cat2,true> {
+	typedef Cat2 type;
+};
+
+
+template <typename Derived, typename F, typename It1, typename It2, typename Ref, typename Val>
+class transforming_pair_iterator_helper
+{
+	typedef typename Min_category<
+		typename std::iterator_traits<It1>::iterator_category,
+		typename std::iterator_traits<It1>::iterator_category>
+			::type iterator_category;
+
+	typedef typename Default::Get<Ref,
+#ifndef CGAL_CFG_NO_CPP0X_DECLTYPE
+		decltype(std::declval<F>()(std::declval<typename std::iterator_traits<It1>::reference>(),std::declval<typename std::iterator_traits<It2>::reference>()))
+#else
+		typename boost::result_of<F(typename std::iterator_traits<It1>::value_type,typename std::iterator_traits<It2>::value_type)>::type
+	// should be reference instead of value_type
+#endif
+			>::type reference;
+
+	typedef typename Default::Get<Val,typename boost::remove_cv<typename boost::remove_reference<reference>::type>::type>::type value_type;
+
+	public:
+	typedef boost::iterator_facade<
+		Derived,
+		value_type,
+		iterator_category,
+		reference
+	// expect ptrdiff_t is good enough for difference
+			> type;
+};
+}
+
+template <typename F, typename It1, typename It2, typename Ref=Default, typename Val=Default>
+class transforming_pair_iterator
+: public internal::transforming_pair_iterator_helper<transforming_pair_iterator<F,It1,It2,Ref,Val>,F,It1,It2,Ref,Val>::type,
+private internal::Functor_as_base<F>
+{
+	It1 iter1; It2 iter2;
+	friend class boost::iterator_core_access;
+	typedef typename internal::transforming_pair_iterator_helper<transforming_pair_iterator,F,It1,It2,Ref,Val>::type Base;
+	typedef internal::Functor_as_base<F> Functor_base;
+	typename Base::reference dereference()const{
+		return functor()(*iter1,*iter2);
+	}
+	bool equal(transforming_pair_iterator const&i)const{
+		bool b=(iter1==i.iter1);
+		CGAL_assertion(b==(iter2==i.iter2));
+		//FIXME: or do we want only one driving iterator
+		return b;
+	}
+	void increment(){ ++iter1; ++iter2; }
+	void decrement(){ --iter1; --iter2; }
+	void advance(std::ptrdiff_t n){
+		std::advance(iter1,n);
+		std::advance(iter2,n);
+	}
+	std::ptrdiff_t distance_to(transforming_pair_iterator const&i)const{
+		std::ptrdiff_t dist=std::distance(iter1,i.iter1);
+		CGAL_assertion(dist==std::distance(iter2,i.iter2));
+		return dist;
+	}
+	public:
+	using Functor_base::functor;
+	transforming_pair_iterator(){}
+	explicit transforming_pair_iterator(It1 i1,It2 i2,F const& f=F())
+		:Functor_base(f),iter1(i1),iter2(i2){}
+	template<class F2,class J1,class J2,class R2,class V2>
+	transforming_pair_iterator(
+		transforming_pair_iterator<F2,J1,J2,R2,V2> const&i,
+		typename boost::enable_if_convertible<J1, It1>::type* = 0,
+		typename boost::enable_if_convertible<J2, It2>::type* = 0,
+		typename boost::enable_if_convertible<F2, F>::type* = 0)
+		: Functor_base(i.functor()),iter1(i.iter1),iter2(i.iter2) {}
+
+};
+
+template <typename F, typename It1, typename It2> inline
+transforming_pair_iterator<F,It1,It2> make_transforming_pair_iterator(It1 i1, It2 i2, F const&f=F()) {
+	return transforming_pair_iterator<F,It1,It2>(i1,i2,f);
+}
+
+}
+
+#endif // CGAL_TRANSFORMING_PAIR_ITERATOR_H

NewKernel_d/include/CGAL/typeset.h

@@ -0,0 +1,97 @@
+#ifndef CGAL_TYPESET_H
+#define CGAL_TYPESET_H
+#ifdef CGAL_CXX0X
+#include <type_traits>
+#else
+#include <boost/type_traits.hpp>
+#endif
+
+// Sometimes using tuple just to list types is overkill (takes forever to
+// instantiate).
+
+namespace CGAL {
+#ifdef CGAL_CXX0X
+  template<class...> struct typeset;
+  template<class H,class...U> struct typeset<H,U...> {
+    typedef H head;
+    typedef typeset<U...> tail;
+    typedef typeset type;
+    template<class X> using contains = typename
+      std::conditional<
+        std::is_same<H,X>::value,
+        std::true_type,
+        typename tail::template contains<X>
+      >::type;
+    template<class X> using add = typename
+      std::conditional<
+        contains<X>::value,
+        typeset<H,U...>,
+	typeset<H,U...,X>
+      >::type;
+  };
+  template<> struct typeset<> {
+    typedef typeset type;
+    template<class X> using contains = std::false_type;
+    template<class X> using add = typeset<X>;
+  };
+#else
+  template<class,class> struct typeset;
+  template<class H=void, class T=typename
+    boost::mpl::if_<boost::is_same<H,void>, void, typeset<void, void> >::type >
+  struct typeset {
+    typedef typeset type;
+    typedef H head;
+    typedef T tail;
+    template<class X> struct contains :
+      boost::mpl::if_<boost::is_same<H,X>,boost::true_type,typename tail::template contains<X> >::type
+    {};
+    template<class X,class=void> struct add;
+      //boost::mpl::if_<boost::is_same<H,X>,typeset,typeset<X,typeset> >::type
+  };
+  template<> struct typeset<> {
+    typedef typeset type;
+    template<class X> struct contains : boost::false_type {};
+    template<class X> struct add : typeset<X> {};
+  };
+
+  template<class H,class T>
+    template<class X,class>
+    struct typeset<H,T>::add : typeset<H,typename T::template add<X>::type> {};
+  template<class H,class T>
+    template<class V>
+    struct typeset<H,T>::add<H,V> : typeset<H,T> {};
+#endif
+
+  template<class T1, class T2> struct typeset_union_ :
+    typeset_union_<typename T1::template add<typename T2::head>::type, typename T2::tail>
+  {};
+  template<class T> struct typeset_union_ <T, typeset<> > : T {};
+
+  template<class T1, class T2>
+    struct typeset_intersection_ {
+      typedef typename T1::head H;
+      typedef typename typeset_intersection_<typename T1::tail,T2>::type U;
+      typedef typename
+#ifdef CGAL_CXX0X
+	std::conditional<T2::template contains<H>::value,
+#else
+	boost::mpl::if_<typename T2::template contains<H>,
+#endif
+	typename U::template add<H>::type, U>::type type;
+    };
+  template<class T>
+    struct typeset_intersection_<typeset<>,T> : typeset<> {};
+
+#ifdef CGAL_CXX0X
+  template<class T1, class T2>
+    using typeset_union = typename typeset_union_<T1,T2>::type;
+  template<class T1, class T2>
+    using typeset_intersection = typename typeset_intersection_<T1,T2>::type;
+#else
+  template<class T1, class T2>
+    struct typeset_union : typeset_union_<T1,T2>::type {};
+  template<class T1, class T2>
+    struct typeset_intersection : typeset_intersection_<T1,T2>::type {};
+#endif
+}
+#endif

NewKernel_d/package_info/Kernel_d/description.txt

@@ -0,0 +1 @@
+d-dimensional Geometry Kernel

NewKernel_d/package_info/Kernel_d/maintainer

@@ -0,0 +1 @@
+Marc Glisse <marc.glisse@inria.fr>

NewKernel_d/test/NewKernel_d/Makefile

@@ -0,0 +1,15 @@
+all: normal cxx0x
+
+CGAL_INC = -I../../../Algebraic_foundations/include -I../../../STL_Extension/include -I../../../Number_types/include -I../../../Kernel_23/include -DCGAL_DISABLE_ROUNDING_MATH_CHECK
+
+EIGEN_INC = `pkg-config --cflags eigen3|sed -e 's/-I/-isystem/g'` -DCGAL_EIGEN3_ENABLED
+
+normal:
+	g++ test.cpp -O2 -lCGAL -lboost_thread -frounding-math -Wall -Wextra -I. -lmpfr -lgmp -I../../include ${EIGEN_INC} ${CGAL_INC} -DCGAL_CFG_NO_CPP0X_COPY_N -DCGAL_CFG_NO_CPP0X_NEXT_PREV
+	./a.out
+
+cxx0x:
+	g++ -std=c++0x -O2 test.cpp -lCGAL -lboost_thread -frounding-math -Wall -Wextra -I. -lmpfr -lgmp -DCGAL_CXX0X -I../../include ${EIGEN_INC} ${CGAL_INC} -o b.out
+	./b.out
+
+#-DBOOST_RESULT_OF_USE_DECLTYPE 

NewKernel_d/test/NewKernel_d/test.cpp

@@ -0,0 +1,266 @@
+//#define BOOST_RESULT_OF_USE_DECLTYPE 1
+#include <CGAL/Epick_d.h>
+#include <typeinfo>
+#include <CGAL/Kernel_d/Cartesian_base.h>
+#include <CGAL/Kernel_d/Cartesian_static_filters.h>
+#include <CGAL/Kernel_d/Cartesian_filter_NT.h>
+#include <CGAL/Kernel_d/Cartesian_filter_K.h>
+#include <CGAL/Kernel_d/Lazy_cartesian.h>
+#include <CGAL/Kernel_d/Wrapper/Cartesian_wrap.h>
+#include <CGAL/Kernel_d/Kernel_d_interface.h>
+#include <CGAL/Gmpq.h>
+#include <CGAL/Interval_nt.h>
+#include <iostream>
+
+template<class>void marc_use(){}
+#define USE_TYPE(T) marc_use<T>()
+
+//typedef CGAL::Cartesian_base_d<double,CGAL::Dimension_tag<2> > K0;
+//typedef CGAL::Cartesian_base_d<CGAL::Interval_nt_advanced,CGAL::Dimension_tag<2> > KA;
+struct KA : CGAL::Cartesian_static_filters<CGAL::Dimension_tag<2>, CGAL::Cartesian_base_d<CGAL::Interval_nt_advanced,CGAL::Dimension_tag<2>, KA>, KA> {};
+typedef CGAL::Cartesian_base_d<CGAL::Gmpq,CGAL::Dimension_tag<2> > KE;
+
+struct RC: public
+CGAL::Cartesian_static_filters<CGAL::Dimension_tag<2>, // Yes, it is silly to put it there.
+ CGAL::Cartesian_refcount<
+  CGAL::Cartesian_LA_base_d<double,CGAL::Dimension_tag<2> >
+ >, RC
+>
+{
+	RC(){}
+	RC(int){}
+};
+
+struct K0 : RC {};
+
+
+#if 0
+typedef K0 K2;
+#elif 0
+typedef CGAL::Cartesian_filter_NT<K0> K2;
+#elif 0
+typedef CGAL::Cartesian_filter_K<K0,KA,KE> K2;
+#elif 1
+typedef CGAL::Lazy_cartesian<KE,KA,CGAL::KernelD_converter<KE,KA> > K2;
+#endif
+
+#if 0
+typedef K2 KK;
+#elif 1
+typedef CGAL::Cartesian_wrap<K2> KK;
+#elif 1
+typedef CGAL::Cartesian_wrap<K2> K3;
+typedef CGAL::Cartesian_wrap<K3> KK;
+#endif
+
+#if 1
+#define Kinit(f) =k.f()
+#else
+#define Kinit(f)
+#endif
+
+template<class Ker>
+void test2(){
+  typedef Ker K1;
+  typedef typename K1::Point_d P;
+  typedef typename K1::Cartesian_const_iterator_d CI;
+  typedef typename K1::Vector_d V;
+  typedef typename K1::Segment_d S;
+  typedef typename K1::Flat_orientation_d FO;
+
+  //typedef K1::Construct_point CP;
+  typedef typename K1::Construct_point_d CP;
+  typedef typename K1::Construct_vector_d CV;
+  typedef typename K1::Construct_segment_d CS;
+  typedef typename CGAL::Get_functor<K1, CGAL::Segment_extremity_tag>::type CSE;
+  typedef typename K1::Construct_cartesian_const_iterator_d CCI;
+  typedef typename K1::Orientation_d PO;
+  typedef typename K1::Side_of_oriented_sphere_d SOS;
+  typedef typename K1::Compute_coordinate_d CC;
+  typedef typename K1::Construct_flat_orientation_d CFO;
+  typedef typename K1::In_flat_orientation_d IFO;
+  typedef typename K1::In_flat_side_of_oriented_sphere_d IFSOS;
+  typedef typename K1::Contained_in_affine_hull_d CAH;
+  typedef typename K1::Compare_lexicographically_d CL;
+
+  USE_TYPE(V);
+  USE_TYPE(CV);
+  USE_TYPE(FO);
+  USE_TYPE(CL);
+  Ker k
+#if 0
+    (2)
+#endif
+    ;
+  CP cp Kinit(construct_point_d_object);
+  CCI ci Kinit(construct_cartesian_const_iterator_d_object);
+  CC cc Kinit(compute_coordinate_d_object);
+  PO po Kinit(orientation_d_object);
+  CS cs Kinit(construct_segment_d_object);
+  CSE cse (k);
+  SOS sos Kinit(side_of_oriented_sphere_d_object);
+  CFO cfo Kinit(construct_flat_orientation_d_object);
+  IFO ifo Kinit(in_flat_orientation_d_object);
+  IFSOS ifsos Kinit(in_flat_side_of_oriented_sphere_d_object);
+  CAH cah Kinit(contained_in_affine_hull_d_object);
+  P a=cp(3,4);
+  P b=cp(5,6,7);
+  int rr[]={3,5,2};
+  int* r=rr;
+  P c=cp(r,r+2);
+  P d=cp(r,r+3,CGAL::Homogeneous_tag());
+  S s=cs(c,d);
+  std::cout << cc(a,1) << std::endl;
+  std::cout << cc(b,1) << std::endl;
+  std::cout << cc(cse(s,0),1) << std::endl;
+  std::cout << cc(cse(s,1),1) << std::endl;
+  for(CI i=ci(a);i!=ci(a,0);++i)
+    std::cout << *i << ' ';
+  std::cout << '\n';
+  P tab[]={a,b,c,d};
+  std::cout << po (&tab[0],tab+3) << std::endl;
+  std::cout << sos(&tab[0],tab+4) << std::endl;
+  P x1=cp(0,1);
+  P x2=cp(-1,-1);
+  P x3=cp(1,-1);
+  P x4=cp(0,0);
+  P x5=cp(0,-1);
+  P tab2[]={x1,x2,x3,x4};
+  assert(po(tab2+0,tab2+3)==CGAL::COUNTERCLOCKWISE);
+  assert(sos(tab2+0,tab2+3,x4)==CGAL::ON_POSITIVE_SIDE);
+#if 0
+  // Doesn't compile with Lazy yet.
+  FO fo=cfo(tab2+1,tab2+3);
+  assert(ifo(fo,tab2+1,tab2+3)==CGAL::POSITIVE);
+  assert(ifsos(fo,tab2+1,tab2+3,x5)==CGAL::ON_POSITIVE_SIDE);
+#endif
+}
+
+template<class CP> struct Construct_point3_helper {
+  CP const& cp;
+  Construct_point3_helper(CP const& x) : cp(x) {}
+  template<class T1,class T2,class T3>
+  typename CP::result_type operator()(T1 const&t1, T2 const&t2, T3 const&t3)const{
+    double tab[]={(double)t1,(double)t2,(double)t3};
+    return cp(tab+0,tab+3);
+  }
+  template<class T1,class T2,class T3,class T4>
+  typename CP::result_type operator()(T1 const&t1, T2 const&t2, T3 const&t3, T4 const&t4)const{
+    double tab[]={(double)t1,(double)t2,(double)t3};
+    return cp(tab+0,tab+3,t4);
+  }
+};
+
+template<class Ker>
+void test3(){
+  typedef Ker K1;
+  typedef typename K1::Point_d P;
+  typedef typename K1::Cartesian_const_iterator_d CI;
+  typedef typename K1::Vector_d V;
+  typedef typename K1::Segment_d S;
+  typedef typename K1::Flat_orientation_d FO;
+
+  //typedef K1::Construct_point CP;
+  typedef typename K1::Construct_point_d CP_;
+  typedef typename K1::Construct_vector_d CV;
+  typedef typename K1::Construct_segment_d CS;
+  typedef typename CGAL::Get_functor<K1, CGAL::Segment_extremity_tag>::type CSE;
+  typedef typename K1::Construct_cartesian_const_iterator_d CCI;
+  typedef typename K1::Orientation_d PO;
+  typedef typename K1::Side_of_oriented_sphere_d SOS;
+  typedef typename K1::Compute_coordinate_d CC;
+  typedef typename K1::Construct_flat_orientation_d CFO;
+  typedef typename K1::In_flat_orientation_d IFO;
+  typedef typename K1::In_flat_side_of_oriented_sphere_d IFSOS;
+  typedef typename K1::Contained_in_affine_hull_d CAH;
+  typedef typename K1::Compare_lexicographically_d CL;
+
+  USE_TYPE(V);
+  USE_TYPE(CV);
+  USE_TYPE(FO);
+  Ker k
+#if 1
+    (3)
+#endif
+    ;
+  CP_ cp_ Kinit(construct_point_d_object);
+  typename boost::conditional<boost::is_same<typename Ker::Default_ambient_dimension,CGAL::Dynamic_dimension_tag>::value,Construct_point3_helper<CP_>,CP_>::type cp(cp_);
+  CCI ci Kinit(construct_cartesian_const_iterator_d_object);
+  CC cc Kinit(compute_coordinate_d_object);
+  CL cl Kinit(compare_lexicographically_d_object);
+  PO po Kinit(orientation_d_object);
+  CS cs Kinit(construct_segment_d_object);
+  CSE cse (k);
+  SOS sos Kinit(side_of_oriented_sphere_d_object);
+  CFO cfo Kinit(construct_flat_orientation_d_object);
+  IFO ifo Kinit(in_flat_orientation_d_object);
+  IFSOS ifsos Kinit(in_flat_side_of_oriented_sphere_d_object);
+  CAH cah Kinit(contained_in_affine_hull_d_object);
+  P a=cp(2,3,4);
+  P b=cp(5,6,7,8);
+  int rr[]={3,5,2,3};
+  int* r=rr;
+  P c=cp_(3,r,r+3);
+  P d=cp_(r,r+4,CGAL::Homogeneous_tag());
+  S s=cs(c,d);
+  std::cout << cc(a,1) << std::endl;
+  std::cout << cc(b,2) << std::endl;
+  std::cout << cc(cse(s,0),1) << std::endl;
+  std::cout << cc(cse(s,1),2) << std::endl;
+  for(CI i=ci(a);i!=ci(a,0);++i)
+    std::cout << *i << ' ';
+  std::cout << '\n';
+  P e=cp(-2,3,0);
+  P tab[]={a,b,c,d,e};
+  std::cout << po (&tab[0],tab+4) << std::endl;
+  std::cout << sos(&tab[0],tab+5) << std::endl;
+  FO fo=cfo(&tab[0],tab+3);
+  std::cout << fo;
+  P x[]={cp(2,2,3),cp(2,2,0),cp(1,2,1)};
+  FO fo2=cfo(&x[0],x+3);
+  std::cout << fo2;
+  P y[]={cp(0,2,4),cp(3,1,2),cp(3,3,6),cp(0,4,8)};
+  FO fo3=cfo(&y[0],y+3);
+  assert(fo3.rest.size()==1 && fo3.rest[0]!=3);
+  std::cout << fo3;
+  CGAL::Orientation base=ifo(fo3,&y[0],y+3);
+  assert(ifo(fo3,y+1,y+4)==base);
+  P yy[]={y[1],y[3],y[0],y[2]};
+  assert(ifo(fo3,yy+0,yy+3)==base);
+  assert(ifo(fo3,yy+1,yy+4)==base);
+  std::cout << ifsos(fo3,y+0,y+3,y[3]) << ' ';
+  std::cout << ifsos(fo3,y+1,y+4,y[0]) << ' ';
+  std::cout << ifsos(fo3,yy+0,yy+3,yy[3]) << ' ';
+  std::cout << ifsos(fo3,yy+1,yy+4,yy[0]) << '\n';
+  P buf[]={cp(100,900,0),y[0],y[1],y[2],y[3]};
+  std::cout << sos(buf+0,buf+5) << ' ';
+  buf[1]=y[1];buf[2]=y[2];buf[3]=y[3];buf[4]=y[0];
+  std::cout << sos(buf+0,buf+5) << ' ';
+  buf[1]=yy[0];buf[2]=yy[1];buf[3]=yy[2];buf[4]=yy[3];
+  std::cout << sos(buf+0,buf+5) << ' ';
+  buf[1]=yy[1];buf[2]=yy[2];buf[3]=yy[3];buf[4]=yy[0];
+  std::cout << sos(buf+0,buf+5) << '\n';
+  assert(cah(y+0,y+3,y[3]));
+  assert(!cah(y+0,y+3,buf[0]));
+  assert(cl(a,a)==CGAL::EQUAL);
+  assert(cl(a,b)==CGAL::LARGER);
+  P x1=cp(0,1,-1);
+  P x2=cp(-1,-1,-1);
+  P x3=cp(1,-1,-1);
+  P x4=cp(0,0,1);
+  P x5=cp(0,0,0);
+  P x6=cp(0,0,-1);
+  P tab2[]={x1,x2,x3,x4,x5};
+  assert(po(tab2+0,tab2+4)==CGAL::POSITIVE);
+  assert(sos(tab2+0,tab2+4,x5)==CGAL::ON_POSITIVE_SIDE);
+  FO fo4=cfo(tab2+0,tab2+3);
+  assert(ifo(fo4,tab2+0,tab2+3)==CGAL::POSITIVE);
+  assert(ifsos(fo4,tab2+0,tab2+3,x6)==CGAL::ON_POSITIVE_SIDE);
+}
+
+int main(){
+  test2<CGAL::Kernel_d_interface<KK> >();
+  test2<CGAL::Epick_d<CGAL::Dimension_tag<2> > >();
+  test3<CGAL::Epick_d<CGAL::Dimension_tag<3> > >();
+  test3<CGAL::Epick_d<CGAL::Dynamic_dimension_tag> >();
+}

Number_types/include/CGAL/long_long.h

@@ -88,6 +88,50 @@ template <> class Real_embeddable_traits< unsigned long long >
     };
 };
 
+#ifdef __SIZEOF_INT128__
+// __int128
+template<> class Algebraic_structure_traits< __int128 >
+  : public Algebraic_structure_traits_base< __int128,
+                                            Euclidean_ring_tag > {
+
+  public:
+    typedef Tag_true            Is_exact;
+    typedef Tag_false           Is_numerical_sensitive;
+
+    typedef INTERN_AST::Div_per_operator< Type >  Div;
+    typedef INTERN_AST::Mod_per_operator< Type >  Mod;
+
+};
+
+template <> class Real_embeddable_traits< __int128 >
+  : public INTERN_RET::Real_embeddable_traits_base< __int128 , CGAL::Tag_true > {
+  public:
+
+    class To_interval
+      : public std::unary_function< Type, std::pair< double, double > > {
+      public:
+        std::pair<double, double> operator()( const Type& x ) const {
+	  return (Interval_nt<>((double)x)+Interval_nt<>::smallest()).pair();
+        }
+    };
+};
+
+// unsigned __int128
+template <> class Real_embeddable_traits< unsigned __int128 >
+  : public INTERN_RET::Real_embeddable_traits_base< unsigned __int128 , CGAL::Tag_true > {
+  public:
+
+    class To_interval
+      : public std::unary_function< Type, std::pair< double, double > > {
+      public:
+        std::pair<double, double> operator()( const Type& x ) const {
+	  return (Interval_nt<>((double)x)+Interval_nt<>::smallest()).pair();
+        }
+    };
+};
+#endif
+
+
 } //namespace CGAL
 
 #include <CGAL/Interval_nt.h>

STL_Extension/include/CGAL/is_iterator.h

@@ -68,6 +68,13 @@ template <class T> struct is_iterator :
 template <class T,class Tag> struct is_iterator_type :
 	internal::is_iterator_type_<typename boost::remove_cv<typename boost::remove_reference<T>::type>::type,Tag> {};
 
+template <class T,class U,bool=is_iterator<T>::value> struct is_iterator_to {
+          enum { value=false };
+};
+template <class T,class U> struct is_iterator_to<T,U,true> :
+        boost::is_convertible<typename std::iterator_traits<T>::value_type,U>
+{ };
+
 }
 
 #endif // CGAL_IS_ITERATOR_H