Untested LA experiment.

NewKernel_d/include/CGAL/Vector/array.h

@@ -13,6 +13,8 @@ namespace CGAL {
 // 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;

NewKernel_d/include/CGAL/Vector/determinant_of_points.h

@@ -0,0 +1,90 @@
+#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_=LA::Dimension, class Max_dim_=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_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_vectors_small_dim<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 {
+  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 {
+  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 {
+  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);
+  }
+};
+
+//TODO: Go up to 6. First check that it won't be done differently eventually.
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/determinant_of_vectors_small_dim.h

@@ -0,0 +1,97 @@
+#ifndef CGAL_VECTOR_DETVEC_SMALL_H
+#define CGAL_VECTOR_DETVEC_SMALL_H
+#include <CGAL/functor_tags.h>
+#include <CGAL/Dimension.h>
+#include <CGAL/determinant.h>
+#include <CGAL/predicates/sign_of_determinant.h>
+
+namespace CGAL {
+
+template <class LA, class Dim_=LA::Dimension, class Max_dim_=LA::Max_dimension,
+	 bool=LA::template Property<Has_determinant_of_vectors_tag>::value>
+struct Add_determinant_of_vectors_small_dim : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_vectors_small_dim<LA2> Other;
+    };
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_vectors_small_dim
+<LA, Dimension_tag<2>, Max_dim_, false> : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_vectors_small_dim<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_vectors_tag, D> :
+    boost::true_type {};
+
+  template <class V1, class V2>
+  static NT determinant_of_vectors(V1 const&a, V2 const&b){
+    return determinant(a[0],a[1],b[0],b[1]);
+  }
+  template <class V1, class V2>
+  static Sign sign_of_determinant_of_vectors(V1 const&a, V2 const&b){
+    return sign_of_determinant(a[0],a[1],b[0],b[1]);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_vectors_small_dim
+<LA, Dimension_tag<3>, Max_dim_, false> : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_vectors_small_dim<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_vectors_tag, D> :
+    boost::true_type {};
+
+  static NT determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c){
+    return determinant(a[0],a[1],a[2],b[0],b[1],b[2],c[0],c[1],c[2]);
+  }
+  static Sign sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c){
+    return sign_of_determinant(a[0],a[1],a[2],b[0],b[1],b[2],c[0],c[1],c[2]);
+  }
+};
+
+template <class LA, class Max_dim_>
+struct Add_determinant_of_vectors_small_dim
+<LA, Dimension_tag<4>, Max_dim_, false> : LA {
+  template< class D2, class D3=D2 >
+    struct Rebind_dimension {
+      typedef typename LA::template Rebind_dimension<D2,D3> LA2;
+      typedef Add_determinant_of_vectors_small_dim<LA2> Other;
+    };
+  template<class P,class=void> struct Property : LA::template Property<P> {};
+  template<class D> struct Property<Has_determinant_of_vectors_tag, D> :
+    boost::true_type {};
+
+  static NT determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return determinant(
+	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]);
+  }
+  static Sign sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
+      Vector const&c, Vector const&d){
+    return sign_of_determinant(
+	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]);
+  }
+};
+
+//TODO: Go up to 6. First check that it won't be done differently eventually.
+
+}
+#endif

NewKernel_d/include/CGAL/Vector/vector.h

@@ -12,6 +12,8 @@ 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 {