Changes according to reviews (with Olivier)

Triangulation/doc/Triangulation/CGAL/Delaunay_triangulation.h

@@ -23,7 +23,7 @@ structure. `TriangulationDataStructure` must be a model of the concept
 be defined by specifying only the first parameter, or by using the
 tag `CGAL::Default` as
 the second parameter. In both cases, `TriangulationDataStructure` defaults to
-`Triangulation_data_structure<Maximal_dimension<TriangulationTraits::Point_d>::type, Triangulation_vertex<TriangulationTraits>, Triangulation_full_cell<TriangulationTraits>>`.
+`Triangulation_data_structure<TriangulationTraits::Dimension, Triangulation_vertex<TriangulationTraits>, Triangulation_full_cell<TriangulationTraits>>`.
 
 The class `Delaunay_triangulation<DelaunayTriangulationTraits, TriangulationDataStructure>` inherits all the types
 defined in the base class `Triangulation<DelaunayTriangulationTraits, TriangulationDataStructure>`. Additionally, it

Triangulation/doc/Triangulation/CGAL/Triangulation.h

@@ -22,7 +22,7 @@ structure. `TriangulationDataStructure` must be a model of the concept
 be defined by specifying only the first parameter, or by using the
 tag `CGAL::Default` as
 the second parameter. In both cases, `TriangulationDataStructure` defaults to
-`Triangulation_data_structure<Maximal_dimension<TriangulationTraits::Point_d>::type, Triangulation_vertex<TriangulationTraits>, Triangulation_full_cell<TriangulationTraits>>`.
+`Triangulation_data_structure<TriangulationTraits::Dimension, Triangulation_vertex<TriangulationTraits>, Triangulation_full_cell<TriangulationTraits>>`.
 
 Input/Output
 --------------

Triangulation/doc/Triangulation/CGAL/Triangulation_ds_full_cell.h

@@ -73,9 +73,7 @@ The `is_valid` method is only minimally defined in the
 precisely here, for the model `Triangulation_ds_full_cell`.
 
 \cgalAdvanced Implements the validity checks required by the concept 
-`TriangulationDSFullCell`. In addition, it is checked that there is no 
-`NULL` handle to vertices in the middle of non-`NULL` ones, that is, 
-that the internal memory layout is not corrupted. 
+`TriangulationDSFullCell`.
 */ 
 bool is_valid(bool verbose=false) const; 
 

Triangulation/doc/Triangulation/CGAL/Triangulation_full_cell.h

@@ -60,10 +60,8 @@ typedef Data Data;
 
 /*! 
 Sets the maximum possible dimension of the cell to `dmax`. 
-The parameter `t` is passed to the `Data` constructor. 
 */ 
-template< typename T> Triangulation_full_cell(int dmax, const T 
-& t); 
+template< typename T> Triangulation_full_cell(int dmax); 
 
 /// @} 
 

Triangulation/doc/Triangulation/Concepts/TriangulationDSFace.h

@@ -63,10 +63,10 @@ Triangulation_face(Full_cell_handle c);
 
 /*!
 Setup the `Face` knowing
-the maximal dimension `ad`. Sets the `Face`'s full cell to the
+the maximal dimension `md`. Sets the `Face`'s full cell to the
 default-constructed one.
 */
-Triangulation_face(const int ad);
+Triangulation_face(const int md);
 
 /// @}
 

Triangulation/doc/Triangulation/Concepts/TriangulationDataStructure.h

@@ -267,7 +267,7 @@ full cells are also good.
 
 The argument `tp` is a predicate, i.e.\ a function or a functor providing 
 `operator()`, that takes as argument a `Facet`
-whose defining `Full_cell` is good.
+whose `Full_cell` is good.
 The predicate must return `true`
 if the traversal of that `Facet` leads to a good full cell.
 
@@ -330,8 +330,7 @@ Returns a handle to the `i`-th `Vertex` of the `Full_cell` `c`.
 Vertex_handle vertex(Full_cell_handle c, const int i) const;
 
 /*!
-Returns the index of the vertex mirror of the `i`-th vertex of `c`.
-Equivalently, returns the index of `c` as a neighbor of its `i`-th neighbor.
+Returns the index of `c` as a neighbor of its `i`-th neighbor.
 \pre \f$0 \leq i \leq \f$`tds`.`current_dimension`()
 
 and `c!=Full_cell_handle()`.
@@ -339,8 +338,7 @@ and `c!=Full_cell_handle()`.
 int mirror_index(Full_cell_handle c, int i) const;
 
 /*!
-Returns the vertex mirror of the `i`-th vertex of `c`.
-Equivalently, returns the vertex of the `i`-th neighbor of `c`
+Returns the vertex of the `i`-th neighbor of `c`
 that is not vertex of `c`.
 \pre \f$0 \leq i \leq \f$`tds`.`current_dimension`()
 
@@ -472,7 +470,7 @@ does not, with `f=(c,i)`.
 \f$ H\f$ the union of full cells in \f$ C\f$ is simply connected and its
 boundary \f$ \partial H\f$ is a
 combinatorial triangulation of the sphere \f$ \mathcal S^{d-1}\f$.
-All vertices of the triangulation are on \f$ \partial H\f$.
+All vertices of cells of \f$ C\f$ are on \f$ \partial H\f$.
 
 \cgalFigureBegin{triangulationfiginserthole,insert-in-hole.png}
 Insertion in a hole, \f$ d=2\f$
@@ -504,9 +502,9 @@ full cell is such that, if `f` was a full cell of maximal dimension in the
 initial complex, then `(f,v)`, in this order, is the corresponding full cell
 in the updated triangulation. A handle to `v` is returned
 (see Figure \cgalFigureRef{triangulationfiginsertincreasedim}).
-\pre `tds`.
+\pre
 If the current dimension is -2 (empty triangulation), then `star`
-has to be omitted, otherwise
+can be omitted (it is ignored), otherwise
 the current dimension must be strictly less than the maximal dimension
 and `star` must be a vertex of `tds`.
 
@@ -629,6 +627,9 @@ neighbors as its number of facets (`current_dimension()+1`).
 vertices with each of its neighbor.
 </UL>
 
+When `verbose` is set to `true`, messages are printed to give
+a precise indication on the kind of invalidity encountered.
+
 Returns `true` if all the tests pass, `false` if any test fails. See
 the documentation for the models of this concept to see the additionnal (if
 any) validity checks that they implement.

Triangulation/doc/Triangulation/PackageDescription.txt

@@ -19,8 +19,8 @@
 \cgalPkgShortInfoEnd
 \cgalPkgDescriptionEnd
 
-A triangulation is a pure simplicial complex which is connected and has no
-singularities. Its faces are such that two of them either do not
+A triangulation is a pure manifold simplicial complex which is connected and has no
+boundaries. Its faces are such that two of them either do not
 intersect or share a common face.
 
 The basic triangulation class of \cgal is primarily designed to

Triangulation/doc/Triangulation/Triangulation.txt

@@ -41,6 +41,12 @@ In the sequel, we will call these maximal simplices <I>full cells</I>.
 A <I>face</I> of a simplex is a subset of it.
 A <I>proper face</I> of a simplex is a strict subset of it.
 
+\cgalModifBegin
+A complex has <i>no boundaries</i> if any proper face of a simplex is also a 
+proper face of another simplex. A pure complex is <i>manifold</i> if all faces
+of dimension \f$ d-1 \f$ are proper faces of exactly two simplices.
+\cgalModifEnd
+
 If the vertices are embedded into Euclidean space \f$ \R^d\f$, we deal with
 <I>finite simplicial complexes</I> which have slightly different simplices
 and additional requirements:
@@ -56,8 +62,8 @@ entry</A> for more about simplicial complexes.
 
 ## What's in this package? ##
 
-This \cgal package deals with pure simplicial complexes which are connected 
-and have no singularities, which
+This \cgal package deals with pure manifold simplicial complexes which are connected 
+and have no boundaries, which
 we will simply call in the sequel <I>triangulations</I>. It provides three main classes
 for creating and manipulating triangulations.
 
@@ -65,9 +71,12 @@ The class `CGAL::Triangulation_data_structure<Dimensionality, TriangulationDSVer
 class are not embedded in Euclidean space but are only of combinatorial
 nature.
 
-The class `CGAL::Triangulation<TriangulationTraits, TriangulationDataStructure>` embeds an abstract
-triangulation in Euclidean space, thus forming a geometric
-triangulation. Methods are
+\cgalModifBegin 
+The class `CGAL::Triangulation<TriangulationTraits, TriangulationDataStructure>` 
+describes an embedded triangulation that has as vertices a given set of points
+and which fills the convex hull of these points.
+\cgalModifEnd
+Methods are
 provided for the insertion of points in the triangulation, the
 traversal of various elements of the triangulation, as well as the localization of a
 query point inside the triangulation.
@@ -332,6 +341,10 @@ The template parameter `TriangulationTraits` must be a model of the concept
 `TriangulationTraits` which provides the geometric `Point` type as well
 as various geometric predicates used by the `Triangulation` class.
 
+\cgalModifBegin
+The dimension of the predicates provided by `TriangulationTraits` must match
+the dimension of the `TriangulationDataStructure`.
+\cgalModifEnd
 
 \cgalModifBegin
 The template parameter `TriangulationDataStructure` must be a model of the concept
@@ -451,6 +464,8 @@ triangulation, and sorts the points with spatial sort to insert a
 set of points. Thus the theoretical complexity are
 \f$ O(n\log n)\f$ for inserting \f$ n\f$ random points and \f$ O(n^{\frac{1}{d}})\f$
 for inserting one point in a triangulation of \f$ n\f$ random points.
+In the worst case, the expected complexity is 
+\f$ O(n^{\lceil\frac{d}{2}\rceil}+n\log n)\f$.
 
 The actual timing are the following:
 

Triangulation/examples/Triangulation/triangulation.cpp

@@ -28,7 +28,9 @@ int main()
     // collect faces of dimension 1 (edges) incident to the infinite vertex
     std::cout << "There are " << edges.size() 
 	      << " vertices on the convex hull." << std::endl;
-#include "triangulation1.cpp"    
-#include "triangulation2.cpp"    
+
+#include "triangulation1.cpp" // See below
+#include "triangulation2.cpp"
+
     return 0;
 }

Triangulation/include/CGAL/Triangulation_data_structure.h

@@ -1140,10 +1140,6 @@ Triangulation_data_structure<Dim, Vb, Fcb>
         CGAL_precondition( Vertex_handle() != star );
         CGAL_expensive_precondition(is_vertex(star));
     }
-    else
-    {
-        CGAL_precondition( Vertex_handle() == star );
-    }
 
     set_current_dimension(prev_cur_dim + 1);
     Vertex_handle v = new_vertex();

Triangulation/include/CGAL/Triangulation_full_cell.h

@@ -57,14 +57,10 @@ public:
         typedef typename Base::template Rebind_TDS<TDS2>::Other TDSFullCell2;
         typedef Triangulation_full_cell<TriangulationTraits, Data_, TDSFullCell2> Other;
     };
-
+ 
     Triangulation_full_cell(const int d)
         : Base(d), data_() {}
 
-    template< typename T >
-    Triangulation_full_cell(const int d, const T & t)
-        : Base(d), data_(t) {}
-
     Triangulation_full_cell(const Self & s)
         : Base(s), data_(s.data_)  {}