diff --git a/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_2.tex b/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_2.tex
index 86a6eaefceb..c1c6ebc5e49 100755
--- a/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_2.tex
+++ b/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_2.tex
@@ -38,6 +38,7 @@ for example \ccc{CGAL::Cartesian<double>} or \ccc{CGAL::Simple_cartesian<CGAL::G
 
 \ccTypedef {Kernel::Point_2 Point_d;}{Point type.}
 \ccTypedef {Kernel::Iso_rectangle_2 Iso_box_d;}{Iso box type.}
+\ccTypedef {Kernel::Sphere_2 Sphere_d;}{Sphere type.}
 
 \ccTypedef {Kernel::Cartesian_const_iterator_2 Cartesian_const_iterator_d;}{An iterator over the Cartesian coordinates.}
 
@@ -49,6 +50,15 @@ has as argument a \ccc{Point_d} and an \ccc{int}.}
 \ccTypedef {Kernel::Construct_iso_rectangle_2 Construct_iso_box_d;}{Functor with operator to construct 
 the iso box from two points.}
 
+\ccTypedef {Kernel::Construct_center_2 Construct_center_d;}{Functor with operator to construct 
+the center of an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Compute_squared_radius_2 Construct_squared_radius_d;}{Functor with operator to compute 
+the squared radius of a an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Construct_vertex_2 Construct_vertex_d;}{Functor with operator to construct 
+the vertices with index $0$ and $3$ of an object of type \ccc{Iso_box_d}.}
+
 \ccSeeAlso
 
 \ccc{Search_traits_3<Kernel>}\\
diff --git a/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_3.tex b/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_3.tex
index 1d9ca6c8bc2..fca86d23c4a 100755
--- a/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_3.tex
+++ b/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/Kd_tree_traits_point_3.tex
@@ -37,7 +37,8 @@ for example \ccc{CGAL::Cartesian<double>} or \ccc{CGAL::Simple_cartesian<CGAL::G
 \ccTypedef{Kernel::FT FT;}{Number type.}
 
 \ccTypedef {Kernel::Point_3 Point_d;}{Point type.}
-\ccTypedef {Kernel::Iso_rectangle_2 Iso_box_d;}{Iso box type.}
+\ccTypedef {Kernel::Iso_cuboid_3 Iso_box_d;}{Iso box type.}
+\ccTypedef {Kernel::Sphere_3 Sphere_d;}{Sphere type.}
 
 \ccTypedef {Kernel::Cartesian_const_iterator_3 Cartesian_const_iterator_d;}{An iterator over the Cartesian
 	coordinates.}
@@ -51,6 +52,15 @@ has as argument a \ccc{Point_d} and an \ccc{int}.}
 \ccTypedef {Kernel::Construct_iso_cuboid_3 Construct_iso_box_d;}{Functor with operator to construct 
 the iso box from two points.}
 
+\ccTypedef {Kernel::Construct_center_3 Construct_center_d;}{Functor with operator to construct 
+the center of an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Compute_squared_radius_3 Construct_squared_radius_d;}{Functor with operator to compute 
+the squared radius of a an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Construct_vertex_3 Construct_vertex_d;}{Functor with operator to construct 
+the vertices with index $0$ and $7$ of an object of type \ccc{Iso_box_d}.}
+
 \ccSeeAlso
 
 \ccc{Search_traits_2<Kernel>}\\
diff --git a/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/SpatialPoint.tex b/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/SpatialPoint.tex
index d44bfab70a7..3e3c5c32d3b 100755
--- a/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/SpatialPoint.tex
+++ b/Packages/Spatial_searching/doc_tex/Spatial_searching_ref/SpatialPoint.tex
@@ -27,6 +27,7 @@ specialized for the point type.
 \ccTypes
 \ccNestedType{Point_d}{Point type.}
 \ccNestedType{Iso_box_d}{Iso box type.}
+\ccNestedType{Sphere_d}{Sphere type.}
 
 \ccNestedType{FT}{The number type of the \ccHtmlNoLinksFrom{Cartesian} coordinates of type \ccc{Point_d}.}
 
@@ -39,7 +40,14 @@ first and the past-the-end iterator for the \ccHtmlNoLinksFrom{Cartesian} coordi
 
 \ccNestedType{Construct_iso_box_d}{Functor with operator to construct the iso box from two points.}
 
-\ccCreationVariable{p}  %% choose variable name
+\ccNestedType {Construct_center_d;}{Functor with operator to construct 
+the center of an object of type \ccc{Sphere_d}.}
+
+\ccNestedType {Construct_squared_radius_d;}{Functor with operator to compute 
+the squared radius of a an object of type \ccc{Sphere_d}.}
+
+\ccNestedType {Construct_vertex_d;}{Functor with operator to construct 
+the vertices with index $0$ and $2^d-1$ of an object of type \ccc{Iso_box_d}.}
 
 
 
diff --git a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_2.tex b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_2.tex
index 86a6eaefceb..c1c6ebc5e49 100755
--- a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_2.tex
+++ b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_2.tex
@@ -38,6 +38,7 @@ for example \ccc{CGAL::Cartesian<double>} or \ccc{CGAL::Simple_cartesian<CGAL::G
 
 \ccTypedef {Kernel::Point_2 Point_d;}{Point type.}
 \ccTypedef {Kernel::Iso_rectangle_2 Iso_box_d;}{Iso box type.}
+\ccTypedef {Kernel::Sphere_2 Sphere_d;}{Sphere type.}
 
 \ccTypedef {Kernel::Cartesian_const_iterator_2 Cartesian_const_iterator_d;}{An iterator over the Cartesian coordinates.}
 
@@ -49,6 +50,15 @@ has as argument a \ccc{Point_d} and an \ccc{int}.}
 \ccTypedef {Kernel::Construct_iso_rectangle_2 Construct_iso_box_d;}{Functor with operator to construct 
 the iso box from two points.}
 
+\ccTypedef {Kernel::Construct_center_2 Construct_center_d;}{Functor with operator to construct 
+the center of an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Compute_squared_radius_2 Construct_squared_radius_d;}{Functor with operator to compute 
+the squared radius of a an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Construct_vertex_2 Construct_vertex_d;}{Functor with operator to construct 
+the vertices with index $0$ and $3$ of an object of type \ccc{Iso_box_d}.}
+
 \ccSeeAlso
 
 \ccc{Search_traits_3<Kernel>}\\
diff --git a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_3.tex b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_3.tex
index 1d9ca6c8bc2..fca86d23c4a 100755
--- a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_3.tex
+++ b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/Kd_tree_traits_point_3.tex
@@ -37,7 +37,8 @@ for example \ccc{CGAL::Cartesian<double>} or \ccc{CGAL::Simple_cartesian<CGAL::G
 \ccTypedef{Kernel::FT FT;}{Number type.}
 
 \ccTypedef {Kernel::Point_3 Point_d;}{Point type.}
-\ccTypedef {Kernel::Iso_rectangle_2 Iso_box_d;}{Iso box type.}
+\ccTypedef {Kernel::Iso_cuboid_3 Iso_box_d;}{Iso box type.}
+\ccTypedef {Kernel::Sphere_3 Sphere_d;}{Sphere type.}
 
 \ccTypedef {Kernel::Cartesian_const_iterator_3 Cartesian_const_iterator_d;}{An iterator over the Cartesian
 	coordinates.}
@@ -51,6 +52,15 @@ has as argument a \ccc{Point_d} and an \ccc{int}.}
 \ccTypedef {Kernel::Construct_iso_cuboid_3 Construct_iso_box_d;}{Functor with operator to construct 
 the iso box from two points.}
 
+\ccTypedef {Kernel::Construct_center_3 Construct_center_d;}{Functor with operator to construct 
+the center of an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Compute_squared_radius_3 Construct_squared_radius_d;}{Functor with operator to compute 
+the squared radius of a an object of type \ccc{Sphere_d}.}
+
+\ccTypedef {Kernel::Construct_vertex_3 Construct_vertex_d;}{Functor with operator to construct 
+the vertices with index $0$ and $7$ of an object of type \ccc{Iso_box_d}.}
+
 \ccSeeAlso
 
 \ccc{Search_traits_2<Kernel>}\\
diff --git a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/SpatialPoint.tex b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/SpatialPoint.tex
index d44bfab70a7..3e3c5c32d3b 100755
--- a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/SpatialPoint.tex
+++ b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching_ref/SpatialPoint.tex
@@ -27,6 +27,7 @@ specialized for the point type.
 \ccTypes
 \ccNestedType{Point_d}{Point type.}
 \ccNestedType{Iso_box_d}{Iso box type.}
+\ccNestedType{Sphere_d}{Sphere type.}
 
 \ccNestedType{FT}{The number type of the \ccHtmlNoLinksFrom{Cartesian} coordinates of type \ccc{Point_d}.}
 
@@ -39,7 +40,14 @@ first and the past-the-end iterator for the \ccHtmlNoLinksFrom{Cartesian} coordi
 
 \ccNestedType{Construct_iso_box_d}{Functor with operator to construct the iso box from two points.}
 
-\ccCreationVariable{p}  %% choose variable name
+\ccNestedType {Construct_center_d;}{Functor with operator to construct 
+the center of an object of type \ccc{Sphere_d}.}
+
+\ccNestedType {Construct_squared_radius_d;}{Functor with operator to compute 
+the squared radius of a an object of type \ccc{Sphere_d}.}
+
+\ccNestedType {Construct_vertex_d;}{Functor with operator to construct 
+the vertices with index $0$ and $2^d-1$ of an object of type \ccc{Iso_box_d}.}
 
 
 
diff --git a/Packages/Spatial_searching/include/CGAL/Fuzzy_iso_box.h b/Packages/Spatial_searching/include/CGAL/Fuzzy_iso_box.h
index ad0c171a5c2..3fc5483083a 100644
--- a/Packages/Spatial_searching/include/CGAL/Fuzzy_iso_box.h
+++ b/Packages/Spatial_searching/include/CGAL/Fuzzy_iso_box.h
@@ -37,10 +37,14 @@ namespace CGAL {
     typedef typename SearchTraits::Point_d Point_d;
     typedef typename SearchTraits::Iso_box_d Iso_box_d;
     typedef typename SearchTraits::FT FT;
-    
+    typedef typename SearchTraits::Construct_vertex_d Construct_vertex_d;
+    typedef typename SearchTraits::Cartesian_const_iterator_d Cartesian_const_iterator_d;
+    typedef typename SearchTraits::Construct_cartesian_const_iterator_d Construct_cartesian_const_iterator_d;
+
     private:
 
-    Iso_box_d box;
+    Point_d min, max;
+    Cartesian_const_iterator_d min_begin, max_begin;
     FT eps;
     unsigned int dim;
 
@@ -53,36 +57,46 @@ namespace CGAL {
 	Fuzzy_iso_box(const Point_d& p, const Point_d& q, FT epsilon=FT(0)) 
 	  : eps(epsilon)
         {
-	  typename SearchTraits::Construct_cartesian_const_iterator_d construct_it;
-	  typename SearchTraits::Cartesian_const_iterator_d begin = construct_it(p),
+	  Construct_cartesian_const_iterator_d construct_it;
+	  Cartesian_const_iterator_d begin = construct_it(p),
 	    end = construct_it(p,1);
 	  dim = end - begin;
-	  box = SearchTraits::Construct_iso_box_d()(p,q);
+
+	  Iso_box_d box = SearchTraits::Construct_iso_box_d()(p,q);
+	  Construct_vertex_d construct_vertex_d;
+	  min = construct_vertex_d(box, 0);
+	  max = construct_vertex_d(box, (1<<dim)-1);
+	  min_begin = construct_it(min);
+	  max_begin = construct_it(max);
+	  
 	}
 
         	
         bool contains(const Point_d& p) const {	
-	  typename SearchTraits::Construct_cartesian_const_iterator_d construct_it;
-	  typename SearchTraits::Cartesian_const_iterator_d pit = construct_it(p); 
-		for (unsigned int i = 0; i < dim; ++i, ++pit) {
-			if ( ((*pit) < box.min()[i]) || ((*pit) >= box.max()[i]) ) return false;
+	  Construct_cartesian_const_iterator_d construct_it;
+	  Cartesian_const_iterator_d pit = construct_it(p);
+	  Cartesian_const_iterator_d minit= min_begin, maxit = max_begin; 
+		for (unsigned int i = 0; i < dim; ++i, ++pit, ++minit, ++maxit) {
+			if ( ((*pit) < (*minit)) || ((*pit) >= (*maxit)) ) return false;
 		}
 		return true; 
         }
 
-	bool inner_range_intersects(const Kd_tree_rectangle<SearchTraits>& rectangle) const {   
- 		for (unsigned int i = 0; i < dim; ++i) {
-        		if ( (box.max()[i]-eps < rectangle.min_coord(i)) 
-			|| (box.min()[i]+eps >= rectangle.max_coord(i)) ) return false;
+	bool inner_range_intersects(const Kd_tree_rectangle<SearchTraits>& rectangle) const { 
+	  Cartesian_const_iterator_d minit= min_begin, maxit = max_begin;   
+ 		for (unsigned int i = 0; i < dim; ++i, ++minit, ++maxit) {
+        		if ( ((*maxit)-eps < rectangle.min_coord(i)) 
+			|| ((*minit)+eps >= rectangle.max_coord(i)) ) return false;
     		}
     		return true;                                     
 	}
 
 
-	bool outer_range_is_contained_by(const Kd_tree_rectangle<SearchTraits>& rectangle) const { 
-    		for (unsigned int i = 0; i < dim; ++i) {
-        		if (  (box.max()[i]+eps < rectangle.max_coord(i) ) 
-			|| (box.min()[i]-eps >= rectangle.min_coord(i)) ) return false;
+	bool outer_range_is_contained_by(const Kd_tree_rectangle<SearchTraits>& rectangle) const {  
+	  Cartesian_const_iterator_d minit= min_begin, maxit = max_begin;   
+    		for (unsigned int i = 0; i < dim; ++i, ++minit, ++maxit) {
+        		if (  ((*maxit)+eps < rectangle.max_coord(i) ) 
+			|| ((*minit)-eps >= rectangle.min_coord(i)) ) return false;
     		}
     		return true;
   	} 
diff --git a/Packages/Spatial_searching/include/CGAL/Search_traits_2.h b/Packages/Spatial_searching/include/CGAL/Search_traits_2.h
index f806da73e89..d58ecc8d221 100644
--- a/Packages/Spatial_searching/include/CGAL/Search_traits_2.h
+++ b/Packages/Spatial_searching/include/CGAL/Search_traits_2.h
@@ -39,6 +39,7 @@ namespace CGAL {
     typedef typename K::Cartesian_const_iterator_2 Cartesian_const_iterator_d;
     typedef typename K::Construct_cartesian_const_iterator_2 Construct_cartesian_const_iterator_d;
 
+    typedef typename K::Construct_vertex_2 Construct_vertex_d;
     typedef typename K::Construct_center_2 Construct_center_d;
     typedef typename K::Compute_squared_radius_2 Compute_squared_radius_d;
 
diff --git a/Packages/Spatial_searching/include/CGAL/Search_traits_3.h b/Packages/Spatial_searching/include/CGAL/Search_traits_3.h
index eede75580e1..67b7b81b0cf 100644
--- a/Packages/Spatial_searching/include/CGAL/Search_traits_3.h
+++ b/Packages/Spatial_searching/include/CGAL/Search_traits_3.h
@@ -41,6 +41,7 @@ namespace CGAL {
     typedef typename K::Sphere_3 Sphere_d;
     typedef typename K::Construct_iso_cuboid_3 Construct_iso_box_d;
 
+    typedef typename K::Construct_vertex_3 Construct_vertex_d;
     typedef typename K::Construct_center_3 Construct_center_d;
     typedef typename K::Compute_squared_radius_3 Compute_squared_radius_d;
     typedef typename K::FT FT;