implementing the reviews

.gitattributes

@@ -4227,10 +4227,10 @@ Triangulation/doc_tex/Triangulation_ref/Delaunay_triangulation.tex -text
 Triangulation/doc_tex/Triangulation_ref/RegularTriangulation.tex -text
 Triangulation/doc_tex/Triangulation_ref/RegularTriangulationTraits.tex -text
 Triangulation/doc_tex/Triangulation_ref/Triangulation.tex -text
+Triangulation/doc_tex/Triangulation_ref/TriangulationDSFace.tex -text
 Triangulation/doc_tex/Triangulation_ref/TriangulationDSFullCell.tex -text
 Triangulation/doc_tex/Triangulation_ref/TriangulationDSVertex.tex -text
 Triangulation/doc_tex/Triangulation_ref/TriangulationDataStructure.tex -text
-Triangulation/doc_tex/Triangulation_ref/TriangulationFace.tex -text
 Triangulation/doc_tex/Triangulation_ref/TriangulationFullCell.tex -text
 Triangulation/doc_tex/Triangulation_ref/TriangulationTraits.tex -text
 Triangulation/doc_tex/Triangulation_ref/TriangulationVertex.tex -text

Triangulation/TODO

@@ -20,6 +20,12 @@ check all is_valid function, precise in the doc what they are doing.
 
 small feature with iterator "all tuples"
 
+make the code and doc agree on Flat_* stuff  (orientation in a flat)
+
+iterator on points in concept TriangulationVertex should be removed to keep requirements minimal
+
+
+
 
 
 

Triangulation/doc_tex/Triangulation_ref/DelaunayTriangulationTraits.tex

@@ -5,8 +5,9 @@
 
 The concept \ccRefName\ describes the various types and functions that a class
 has to provide as the first parameter (\ccc{DCTraits}) to the class template
-\ccc{Delaunay_triangulation<DelaunayTriangulationTraits, TriangulationDataStructure>}. It brings the geometric ingredient to
+\ccc{Delaunay_triangulation<DelaunayTriangulationTraits, TriangulationDataStructure>}. It brings the geometric ingredients to
-the definition of a Delaunay complex, while the combinatorial ingredient is
+the definition of a Delaunay complex, while the combinatorial
+ingredients are
 brought by the second template parameter, \ccc{TriangulationDataStructure}.
 
 \ccRefines
@@ -15,6 +16,8 @@ brought by the second template parameter, \ccc{TriangulationDataStructure}.
 
 \ccTypes
 
+\ccTwo{DelaunayTriangulationTraits ::}{}
+
 %\ccNestedType{Point_d}{This nested type is defined in the ``parent'' concept
 %\ccc{TriangulationTraits}.}
 
@@ -35,7 +38,7 @@ to its bounded side.
 \ccPrecond
  \ccc{std::distance(start,end)=D+1}, where 
 \ccc{Point_dimension_d(*it)} is $D$ for all \ccc{it} in
-\ccc{[start,end)}. \ccc{Point_dimension_d(p)} is also $D$
+\ccc{[start,end)}. \ccc{Point_dimension_d(p)} is also $D$.
  The points in range
 \ccc{[start,end)} must be affinely independent, i.e., the simplex must
 not be flat.}
@@ -58,7 +61,7 @@ to its bounded side.
 The points in range \ccc{[start,end)} and \ccc{p} are supposed to belong to the lower dimensional flat
  whose orientation is given by \ccc{orient}.
 \ccPrecond 
- \ccc{std::distance(start,end)=k} where $k$ is the number of
+ \ccc{std::distance(start,end)=k+1} where $k$ is the number of
 points used to construct \ccc{orient}.
 \ccc{Point_dimension_d(*it)} is $D$ for all \ccc{it} in
 \ccc{[start,end)}. \ccc{Point_dimension_d(p)} is also $D$.
@@ -85,6 +88,9 @@ not be flat.
 \ccConstructor{DelaunayTriangulationTraits();}{The default constructor.}
 
 \ccOperations
+\ccThree{In_flat_side_of_oriented_sphere_d}{in_flat_side_of_oriented_sphere_d_object()
+    const;}{}
+
 
 The following methods permit access to the traits class's predicates:
 
@@ -95,20 +101,16 @@ The following methods permit access to the traits class's predicates:
 const;}
 {}
 
-%%%%%%% unused !
-%\ccGlue
-%\ccMethod{ Center_of_sphere_d center_of_sphere_d_object()
-%const;}%
-%{}
 
 \ccHasModels
 
 \ccc{CGAL::Cartesian_d<FT, Dim, LA>},\\
 \ccc{CGAL::Simple_cartesian_d<FT, Dim, LA>},\\
-\ccc{CGAL::Filtered_kernel_d} (recommended)
+\ccc{CGAL::New_kernel_d} (recommended when available)
 
 \ccSeeAlso
 
-\ccc{TriangulationTraits}
+\ccc{TriangulationTraits}\\
+\ccc{DelaunayTriangulation}
 
 \end{ccRefConcept}

Triangulation/doc_tex/Triangulation_ref/Triangulation.tex

@@ -50,7 +50,7 @@ is used.}
 \ccTypedef{typedef TriangulationDataStructure::Facet Facet;}{}
 \ccGlue
 \ccTypedef{typedef TriangulationDataStructure::Face Face;}%
-{A model of the concept \ccc{TriangulationFace}.}
+{A model of the concept \ccc{TriangulationDSFace}.}
 
 The vertices and full cells of triangulations are accessed through handles,
 iterators and circulators. A handle is a model of the \ccc{Handle} concept,
@@ -458,7 +458,7 @@ defined by the infinite full cell \ccc{c} must contain \ccc{p}.}
 
 \ccHeading{Validity check}
 
-\ccMethod{bool is_valid(bool verbose = true, int level = 0) const;}
+\ccMethod{bool is_valid(bool verbose = true) const;}
 {Partially checks whether \ccVar\ is a triangulation. This function returns
 \ccc{true} if the combinatorial triangulation data structure's \ccc{is_valid()}
 test returns \ccc{true} and if some geometric tests are passed with success.
@@ -469,7 +469,7 @@ For each finite full cell, it is checked that its orientation is
 positive.}
 
 \ccMethod{bool are_incident_full_cells_valid(Vertex_const_handle v, bool
-verbose = true, int level = 0) const;} {Returns \ccc{true} if and only if all
+verbose = true) const;} {Returns \ccc{true} if and only if all
 finite full cells incident to \ccc{v} have positive orientation.}
 
 \ccHeading{Input/Output}

Triangulation/doc_tex/Triangulation_ref/TriangulationDSFace.tex

@@ -1,8 +1,8 @@
-\begin{ccRefConcept}{TriangulationFace}
+\begin{ccRefConcept}{TriangulationDSFace}
 
 \ccDefinition
 
-A \ccRefName\ simply describes a \ccc{k}-face \ccc{f} in a triangulation.
+A \ccRefName\ describes a \ccc{k}-face \ccc{f} in a triangulation.
 It gives access to a handle to a full cell \ccc{c} containing the face
 \ccc{f} in its boundary, as well as the indices of the vertices of \ccc{f} in
 \ccc{c}. It must hold that \ccc{f} is a {\em proper} face of full cell
@@ -12,11 +12,11 @@ the dimension of \ccc{c}.
 \ccTypes
 
 \ccNestedType{Full_cell_handle}{Must be the same as the nested type
-\ccc{TriangulationDataStructure::Full_cell_handle} of the \ccc{TriangulationDataStructure} in which the \ccc{TriangulationFace} is
+\ccc{TriangulationDataStructure::Full_cell_handle} of the \ccc{TriangulationDataStructure} in which the \ccc{TriangulationDSFace} is
 defined/used.}
 
 \ccNestedType{Vertex_handle}{Must be the same as the nested type
-\ccc{TriangulationDataStructure::Vertex_handle} of the \ccc{TriangulationDataStructure} in which the \ccc{TriangulationFace} is
+\ccc{TriangulationDataStructure::Vertex_handle} of the \ccc{TriangulationDataStructure} in which the \ccc{TriangulationDSFace} is
 defined/used.}
 
 \ccHasModels
@@ -32,8 +32,10 @@ dimension of the full cells) must be known by the constructors of a \ccRefName.
 \ccConstructor{Triangulation_face(Triangulation_face g);}{Copy constructor.}
 
 \ccConstructor{Triangulation_face(Full_cell_handle c);}{Sets the \ccc{Face}'s
-full cell to \ccc{c}. \ccPrecond \ccc{c} must be a handle to an existing
+full cell to \ccc{c} and the ambient dimension to 
-full cell (not the default-constructed \ccc{Full_cell_handle()}).}
+\ccc{c.ambient_dimension()}.
+\ccPrecond \ccc{c!=Full_cell_handle()}
+}
 
 \ccConstructor{Triangulation_face(const int ad);}{Setup the \ccc{Face} knowing
 the ambient dimension \ccc{ad}. Sets the \ccc{Face}'s full cell to the
@@ -44,32 +46,37 @@ default-constructed one.}
 \ccMethod{Full_cell_handle full_cell() const;}{Returns a handle to a cell that
 has the face in its boundary.}
 
-\ccMethod{int feature_dimension() const;}{Returns the dimension of the face
+\ccMethod{int face_dimension() const;}{Returns the dimension of the face
 (one less than the number of vertices).}
 
 \ccMethod{int index(int i) const;}{Returns the index of the \ccc{i}-th vertex
-of the face in the cell \ccVar.\ccc{full_cell()}. \ccPrecond $0\leq i\leq$\ccVar.\ccc{feature_dimension()}.}
+of the face in the cell \ccVar.\ccc{full_cell()}. \ccPrecond $0\leq i\leq$\ccVar.\ccc{face_dimension()}.}
 
 \ccMethod{Vertex_handle vertex(int i) const;}{Returns a handle to the
 \ccc{i}-th \ccc{Vertex} of the face in the cell \ccVar.\ccc{full_cell()}.
-\ccPrecond $0\leq i\leq$\ccVar.\ccc{feature_dimension()}.}
+\ccPrecond $0\leq i\leq$\ccVar.\ccc{face_dimension()}.}
 
 \ccHeading{Update functions}
 
-\ccMethod{void clear();}{Sets the facet to the empty set.}
+\ccMethod{void clear();}{Sets the facet to the empty set. Ambient
+  dimension remains unchanged.}
 
 \ccMethod{void set_full_cell(Full_cell_handle c);}{Sets the cell of the face to
-\ccc{c}. \ccPrecond \ccc{c} must not be the default-constructed
+\ccc{c}. 
-\ccc{Full_cell_handle}.}
+\ccPrecond \ccc{c!=Full_cell_handle()}
+}
 
 \ccMethod{void set_index(int i, int j);}{Sets the index of the \ccc{i}-th
-vertex of the face.
+vertex of the face to be the \ccc{j}-th vertex of the full cell.
-\ccPrecond $0\leq i<$\ccVar.\ccc{full_cell()->ambient_dimension()}.
+\ccPrecond $0\leq i\leq$\ccVar.\ccc{full_cell()->face_dimension()}.
 \ccPrecond $0\leq j\leq$\ccVar.\ccc{full_cell()->ambient_dimension()}.}
 
 \ccSeeAlso
 
-\ccc{TriangulationDataStructure}, \\
+
-\ccc{Triangulation_face<TriangulationDataStructure>}.
+\ccc{TriangulationDataStructure::FullCell} \\
+\ccc{TriangulationDataStructure::Vertex} \\
+\ccc{TriangulationDataStructure}\\
+\ccc{Triangulation}
 
 \end{ccRefConcept}

Triangulation/doc_tex/Triangulation_ref/TriangulationDSFullCell.tex

@@ -5,15 +5,13 @@
 The concept \ccRefName\ describes what a full cell is in a model of the concept
 \ccc{TriangulationDataStructure}. It sets requirements of combinatorial nature
 only, as geometry is not concerned here.
-In the context of triangulation, the term full cell refer to a face of
+In the context of triangulation, the term full cell refers to a face of
 \emph{maximal} dimension. This maximality characteristic is emphasized by using
 the adjective {\em full}.
 
 A \ccRefName\ is responsible for storing handles to the vertices of a
 full cell as well as handles to its neighbors.
 
-This concept is a \emph{sub-concept} of the \ccc{TriangulationDataStructure}
-concept.
 
 \ccHasModels
 
@@ -22,6 +20,10 @@ concept.
 
 \ccTypes
 
+\ccThree{Full_cell_handle}{v. set_full_cell(Full_cell_handle c);}{}
+\ccThreeToTwo
+
+
 \ccNestedType{Vertex_handle}%{}
 %\ccGlue\ccNestedType{Vertex_const_handle}
 {A handle to a vertex. It must be the same as the
@@ -37,11 +39,26 @@ the vertices of the full cell.}
 nested type \ccc{TriangulationDataStructure::Full_cell_handle} of the \ccc{TriangulationDataStructure} in which the
 \ccc{TriangulationDSFullCell} is defined/used.}
 
-\ccTypedef{typedef TriangulationDataStructure::Full_cell_data TDS_data;}{}
+\ccThree{Full_cell_handle}{TriangulationDataStructure::Full_cell_data TDS_data}{}
+\ccThreeToTwo
+
+\ccTypedef{typedef TriangulationDataStructure::Full_cell_data
+  TDS_data;}{A data member of this type has to be stored and accessible through
+  access function below.}
+
+
+\ccThree{Full_cell_handle}{v. set_full_cell(Full_cell_handle c);}{}
+\ccThreeToTwo
+
+\ccNestedType{
+  template <typename TDS2>
+  Rebind_TDS}
+{This nested template class has to define a type \ccc{Other} which is the
+{\it rebound} vertex, that is, the one whose \ccc{Triangulation_data_structure}
+will be the actually used one.  The \ccc{Other} type will be the real base
+class of \ccc{Triangulation_data_structure::Full_cell}.}
+
 
-\ccNestedType{template<typename TDS2> Rebind_TDS}{This nested template
-class must define a nested type \ccc{Other} which is the rebound full cell
-class template, that is: \ccc{Other == TriangulationDSFullCell<TDS2>}.}
 
 \ccCreation	
 \ccCreationVariable{c}
@@ -86,7 +103,7 @@ returned integer is not negative, it holds that \ccVar.%
 \ccPrecond $0\leq i\leq$\ccc{ambient_dimension()}.}
 
 \ccMethod{int index(Full_cell_handle n) const;}{Returns the index \ccc{i}
-of the neighbor \ccc{n} such that \ccVar\ccc{.neighbor(i)==n}. \ccPrecond \ccc{n}
+such that \ccVar\ccc{.neighbor(i)==n}. \ccPrecond \ccc{n}
 must be a neighbor of \ccVar.}
 \ccGlue
 \ccMethod{int index(Vertex_handle v) const;}{Returns the index \ccc{i} of
@@ -112,6 +129,7 @@ i,$\ccc{cur_dim}$\leq$\ccc{ambient_dimension()}.}
 
 
 \ccHeading{Update functions} % - - - - - - - - - - - - - - - - - UPDATES
+\ccThree{ostream&}{c. set_mirror_index(const int i, const int index)}{}
 
 \ccMethod{void set_vertex(const int i, Vertex_handle v);}{Sets the $i$-th
 vertex of the full cell. 
@@ -153,13 +171,18 @@ if the full cell \ccc{n} is a neighbor of the full cell \ccVar. Returns
 a neighbor of \ccVar\ if the full cell \ccc{n} is a neighbor of the full cell
 \ccVar. Returns \ccc{false} otherwise.}
 
+
+\begin{ccDebug}
 \ccHeading{Validity check}
 
-\ccMethod{bool is_valid(bool verbose=false, int level=0) const;}{Performs any
+\ccMethod{bool is_valid(bool verbose=false) const;}{Performs any
-desired test on a full cell. \emph{E.g.}, checks that for each existing vertex,
+desired test on a full cell. \emph{E.g.}, checks that for each
-there is an existing neighbor.}
+existing neighbor \ccc{n}, \ccVar\ and \ccc{n} share relevant vertices
+and  \ccVar\ is the relevant neighbor of \ccc{n}.
+}
+\end{ccDebug}
 
-% \ccHeading{Memory management}
+\ccHeading{Memory management}
 
 % \ccMethod{void*   for_compact_container() const;}{}
 % \ccGlue\ccMethod{void* & for_compact_container();}{}
@@ -170,21 +193,33 @@ there is an existing neighbor.}
 % \ccc{Compact_container} to store their vertices and full cells. See the
 % documentation of \ccc{Compact_container} for the exact requirements.
 
+\ccMethod{void * for_compact_container() const;}{}
+\ccGlue
+\ccMethod{void * & for_compact_container();}{}
+{ These member functions are required by \ccc{Triangulation_data_structure}
+  because it uses \ccc{Compact_container} to store its cells.  See the
+  documentation of \ccc{Compact_container} for the exact requirements.}
+
+
 \ccHeading{Input/Output}
+These operators can be used directly and are called by the I/O
+operator of class \ccc{TriangulationDataStructure}.
 
 \ccFunction{template<class TriangulationDataStructure> istream& operator>>(istream & is,
         Triangulation_ds_full_cell<TriangulationDataStructure> & c);}
-{Reads (possible) non-combinatorial information about a full cell from the stream \ccc{is}
+{Reads (possibly) non-combinatorial information about a full cell from the stream \ccc{is}
 into \ccc{c}.}
 
 \ccFunction{template<class TriangulationDataStructure> ostream& operator<<(ostream & os, const
         Triangulation_ds_full_cell<TriangulationDataStructure> & c);}
-{Writes (possible) non-combinatorial information about full cell \ccc{c} to the stream
+{Writes (possibly) non-combinatorial information about full cell \ccc{c} to the stream
     \ccc{os}.}
 
 \ccSeeAlso
 
 \ccc{TriangulationDSVertex}\\
-\ccc{TriangulationDataStructure}
+\ccc{TriangulationDSFace}\\
+\ccc{TriangulationDataStructure}\\
+\ccc{Triangulation}
 
 \end{ccRefConcept}

Triangulation/doc_tex/Triangulation_ref/TriangulationDSVertex.tex

@@ -5,10 +5,9 @@
 The concept \ccRefName\ describes what a vertex is in a model of the concept
 \ccc{TriangulationDataStructure}. It sets requirements of combinatorial nature
 only, as geometry is not concerned here. In particular, we only require that
-the vertex hold a handle to a full cell incident to it in the triangulation.
+the vertex holds a handle to a full cell incident to it in the triangulation.
+
 
-This concept is a \emph{sub-concept} of the \ccc{TriangulationDataStructure}
-concept.
 
 \ccHasModels
 
@@ -16,14 +15,21 @@ concept.
 \ccc{CGAL::Triangulation_vertex<TriangulationTraits, Data, TriangulationDSVertex>}
 
 \ccTypes
+\ccThree{Full_cell_handle}{v. set_full_cell(Full_cell_handle c);}{}
+\ccThreeToTwo
 
 \ccNestedType{Full_cell_handle}{A handle to a cell. It must be the same as the
 nested type \ccc{TriangulationDataStructure::Full_cell_handle} of the \ccc{TriangulationDataStructure} in which the
 \ccc{TriangulationDSVertex} is defined/used.}
 
-\ccNestedType{template<typename TDS2> Rebind_TDS}{This nested template
+\ccNestedType{
-class must define a nested type \ccc{Other} which is the rebound vertex
+  template <typename TDS2>
-class template, that is: \ccc{Other == TriangulationDSVertex<TDS2>}.}
+  Rebind_TDS}
+{This nested template class has to define a type \ccc{Other} which is the
+{\it rebound} vertex, that is, the one whose \ccc{Triangulation_data_structure}
+will be the actually used one.  The \ccc{Other} type will be the real base
+class of \ccc{Triangulation_data_structure::Vertex}.}
+
 
 \ccCreation	
 \ccCreationVariable{v}
@@ -36,6 +42,7 @@ full cell to \ccc{c}. \ccPrecond \ccc{c} must not be the default-constructed
 \ccc{Full_cell_handle}.}
 
 \ccOperations
+\ccThree{Full_cell_handle}{v. set_full_cell(Full_cell_handle c);}{}
 
 \ccMethod{void set_full_cell(Full_cell_handle c);}{Set \ccc{c} as the vertex's
 incident full cell. \ccPrecond \ccc{c} must not be the default-constructed
@@ -44,13 +51,14 @@ incident full cell. \ccPrecond \ccc{c} must not be the default-constructed
 \ccMethod{Full_cell_handle full_cell() const;}{Returns a handle to a
   full cell incident to the vertex.}
 
+\begin{ccDebug}
 \ccHeading{Validity check}
 
-\ccMethod{bool is_valid(bool verbose=false, int level=0) const;}{Performs any
+\ccMethod{bool is_valid(bool verbose=false) const;}{Performs any
-desired test on a vertex. Al least, checks that the pointer to an incident
+desired test on a vertex. Should check if the incident full cell
-full cell is not the default constructed handle ({i.e.}, is not
+actually contains the vertex.
-\ccc{NULL}). The parameter \ccc{level} is not used, but can be used in derived
+}
-classes.}
+\end{ccDebug}
 
 % \ccHeading{Memory management}
 
@@ -64,21 +72,35 @@ classes.}
 % full cells. See the documentation of \ccc{Compact_container} for the exact
 % requirements.
 
+\ccHeading{Memory management}
+
+\ccMethod{void * for_compact_container() const;}{}
+\ccGlue
+\ccMethod{void * & for_compact_container();}{}
+{ These member functions are required by \ccc{Triangulation_data_structure}
+  because it uses \ccc{Compact_container} to store its cells.  See the
+  documentation of \ccc{Compact_container} for the exact requirements.}
+
 \ccHeading{Input/Output}
 
+These operators can be used directly and are called by the I/O
+operator of class \ccc{TriangulationDataStructure}.
+
 \ccFunction{template<class TriangulationDataStructure> istream& operator>>(istream & is,
         Triangulation_ds_vertex<TriangulationDataStructure> & v);}
-{Reads (possible) non-combinatorial information about a vertex from the stream \ccc{is}
+{Reads (possibly) non-combinatorial information about a vertex from the stream \ccc{is}
 into \ccc{v}.}
 
 \ccFunction{template<class TriangulationDataStructure> ostream& operator<<(ostream & os, const
         Triangulation_ds_vertex<TriangulationDataStructure> & v);}
-{Writes (possible) non-combinatorial information about vertex \ccc{v} to the stream
+{Writes (possibly) non-combinatorial information about vertex \ccc{v} to the stream
     \ccc{os}.}
 
 \ccSeeAlso
 
 \ccc{TriangulationDSFullCell}\\
-\ccc{TriangulationDataStructure}
+\ccc{TriangulationDSFace}\\
+\ccc{TriangulationDataStructure}\\
+\ccc{Triangulation}
 
 \end{ccRefConcept}

Triangulation/doc_tex/Triangulation_ref/TriangulationDataStructure.tex

@@ -81,7 +81,7 @@ full cell \ccc{c} opposite to its \ccc{i}-th vertex.
 \ccThreeToTwo
 
 \ccNestedType{Face}
-{A model of the concept \ccc{TriangulationFace}.}
+{A model of the concept \ccc{TriangulationDSFace}.}
 
 Vertices and full cells are manipulated via \emph{handles}. Handles support the
 usual two dereference operators \ccc{operator*} and \ccc{operator->}.
@@ -599,13 +599,15 @@ The information stored in the \ccc{iostream} is:
 The indices of vertices and full cells correspond to the order in the
 file, the user cannot control it.
 The classes \ccc{Vertex} and
-\ccc{Full_cell} has to provide the relevant I/O operators
+\ccc{Full_cell} have to provide the relevant I/O operators
 (possibly empty).
 
 
 \ccSeeAlso
 
 \ccc{TriangulationDSVertex}\\
-\ccc{TriangulationDSFullCell}
+\ccc{TriangulationDSFullCell}\\
+\ccc{TriangulationDSFace}\\
+\ccc{Triangulation}
 
 \end{ccRefConcept}

Triangulation/doc_tex/Triangulation_ref/TriangulationFullCell.tex

@@ -13,8 +13,9 @@ represent a full cell.
 We only list below the additional specific requirements of \ccRefName.
 
 Compared to \ccc{TriangulationDSFullCell}, the main difference is the addition of
-methods to access and iterate over the position of the full cell's vertices as
+methods to access and iterate over the position of the full cell's
-well as a method for constructing the center of the full cell's circumsphere.
+vertices.
+% as well as a method for constructing the center of the full cell's circumsphere.
 
 \ccHasModels
 
@@ -34,6 +35,8 @@ full cell.}
 \ccCreationVariable{c}
 
 \ccOperations
+These operators can be used directly and are called by the I/O
+operator of class \ccc{Triangulation}.
 
 \ccMethod{Point_const_iterator points_begin() const;}
 {Returns an iterator pointing to the first point of the full cell.}
@@ -41,8 +44,20 @@ full cell.}
 \ccMethod{Point_const_iterator points_end() const;}
 {Returns an iterator pointing beyond the last point of the full cell.}
 
-\ccMethod{Point circumcenter() const;}{Returns the center of the sphere
+\ccHeading{Input/Output}
-circumscribing the full cell.}
+
+These operators can be used directly and are called by the I/O
+operator of class \ccc{Triangulation}.
+
+\ccFunction{istream & operator>>(istream & is, TriangulationFullCell & c);}%
+{Inputs additional  information stored in the full cell.}
+
+\ccFunction{ostream & operator<<(ostream & os, const TriangulationFullCell & c);}%
+{Outputs additional  information stored in the full cell.}
+
+
+%\ccMethod{Point circumcenter() const;}{Returns the center of the sphere
+%circumscribing the full cell.}
 
 \ccSeeAlso
 

Triangulation/doc_tex/Triangulation_ref/TriangulationTraits.tex

@@ -10,24 +10,26 @@ the second template parameter, \ccc{TriangulationDataStructure}.
 
 Inserting a range of points in a triangulation is optimized using
 spatial sorting, thus besides the requirements below, 
-a class provided as \ccc{TriangulationTraits} should also satisfies the concept 
+a class provided as \ccc{TriangulationTraits} should also satisfy the concept 
 \ccc{SpatialSortingTraits_d}.
 
 \ccRefines
 \ccc{SpatialSortingTraits_d}
 
-{If range of points are inserted, the
+{If a range of points is inserted, the
-  traits must refine \ccc{SpatialSortingTraits_d}, this is not needed
+  traits must refine \ccc{SpatialSortingTraits_d}, This is not needed
   if the points are inserted one by one.}
 
 \ccTypes
 
+\ccTwo{TriangulationTraits ::Compare_lexicographically_d}{}
+
 \ccNestedType{Point_d}%
 {A type representing a point in Euclidean space.}
 
 
 \ccNestedType{Point_dimension_d}%
-       {Functor object type returning the dimension of a  \ccc{Point_d}.
+       {Functor  returning the dimension of a  \ccc{Point_d}.
        Must provide 
         \ccc{int operator()(Point_d p)}  returning the dimension of $p$. 
        }
@@ -35,7 +37,7 @@ a class provided as \ccc{TriangulationTraits} should also satisfies the concept
 \ccNestedType{Orientation_d}{A predicate object that must provide the
 templated operator\\\ccc{template<typename ForwardIterator> Orientation
 operator()(ForwardIterator start, ForwardIterator end)}.\\The operator returns
-\ccc{POSITIVE}, \ccc{NEGATIVE} or \ccc{COPLANAR}  depending on
+\ccc{CGAL::POSITIVE}, \ccc{CGAL::NEGATIVE} or \ccc{CGAL::COPLANAR}  depending on
 the orientation of the simplex defined by the points in the range \ccc{[start,
 end)}.
  \ccPrecond \ccc{std::distance(start,end)=D+1}, where 
@@ -52,24 +54,37 @@ in the range.
 \ccPrecond  The $k$ points in the range
 must be affinely independent. 
 \ccc{Point_dimension_d(*it)} is $D$ for all \ccc{it} in
-\ccc{[start,end)}.
+\ccc{[start,end)}, for some $D$.
 $2\leq k\leq D$.
 }
 
+
+In the $D$-dimensional oriented space, a $k-1$ dimensional subspace (flat)
+define by $k$ points can be oriented in two different ways.
+Choosing the orientation of any simplex defined by $k$ points fix the
+orientation of all other simplices. To be able to orient lower
+dimensional flats, we use the following classes:
+
+
 \ccNestedType{Flat_orientation_d}{
   A type representing an orientation of an affine subspace of
-  dimension $k$ strictly smaller than the ambiant dimension.
+  dimension $k$ strictly smaller than the ambient dimension.
 }
 
 
 \ccNestedType{Construct_flat_orientation_d}{
    A construction object that must 
 provide the templated operator\\\ccc{template<typename ForwardIterator> Flat_orientation_d
-operator()(ForwardIterator start, ForwardIterator end)}.\\The operator
+operator()(ForwardIterator start, ForwardIterator end)}.\\
-return an orientation of the flat spanned by the points in
+The flat spanned by the points in
-the range \ccc{R=[start, end)}. \ccPrecond The $k$ points in the range
+the range \ccc{R=[start, end)}  can be oriented in two different ways,
+the operator
+returns an object that allow to orient that flat so that \ccc{R=[start, end)}
+defines a positive simplex.
+ \ccPrecond The $k$ points in the range
 must be affinely independent. 
-\ccc{Point_dimension_d(*it)} is $D$ for all \ccc{it} in \ccc{R}.
+\ccc{Point_dimension_d(*it)} is $D$ for all \ccc{it} in \ccc{R} for
+some $D$.
 $2\leq k\leq D$.
 }
 
@@ -80,7 +95,7 @@ templated operator\\\ccc{template<typename ForwardIterator> Orientation
 operator()(Flat_orientation_d orient,ForwardIterator start,
 ForwardIterator end)}.\\
 The operator returns
-\ccc{POSITIVE}, \ccc{NEGATIVE} or \ccc{COPLANAR}  depending on
+\ccc{CGAL::POSITIVE}, \ccc{CGAL::NEGATIVE} or \ccc{CGAL::COPLANAR}  depending on
 the orientation of the simplex defined by the points in the range \ccc{[start,
 end)}.
 The points are supposed to belong to the lower dimensional flat
@@ -89,7 +104,8 @@ The points are supposed to belong to the lower dimensional flat
 points
 used to construct \ccc{orient}.
 \ccc{Point_dimension_d(*it)} is $D$ for all \ccc{it} in
-\ccc{[start,end)}.
+\ccc{[start,end)} where  $D$ is the dimension of the points used to
+construct \ccc{orient}.
 $2\leq k\leq D$.
 }
 
@@ -116,6 +132,7 @@ the same and \ccc{LARGER} otherwise.}
 \ccConstructor{TriangulationTraits();}{The default constructor.}
 
 \ccOperations
+\ccThree{Construct_flat_orientation_d}{construct_flat_orientation_d_object() const}{}
 
 The following methods permit access to the traits class's predicates:
 
@@ -149,6 +166,7 @@ const;}%
 \ccSeeAlso
 
 \ccc{DelaunayTriangulationTraits}
+\ccc{Triangulation}
 
 
 \end{ccRefConcept}

Triangulation/doc_tex/Triangulation_ref/TriangulationVertex.tex

@@ -13,13 +13,15 @@ represent a vertex.
 We only list below the additional specific requirements of \ccRefName.
 
 Compared to \ccc{TriangulationDSVertex}, the main difference is the addition of
-an embedding of the vertex into a geometric point.
+an association of the vertex into a geometric point.
 
 \ccHasModels
 
 \ccc{CGAL::Triangulation_vertex<TriangulationTraits, Data, TriangulationDSVertex>}
 
 \ccTypes
+\ccThree{TriangulationVertex}{v(Full_cell_handle c, const Point & p);}{}
+\ccThreeToTwo
 
 \ccNestedType{Point}{The type of the point stored in the vertex. It must be
 the same as the point type \ccc{TriangulationTraits::Point} (or its refined
@@ -48,6 +50,9 @@ concepts) when the \ccc{TriangulationVertex} is used in the class
 
 \ccHeading{Input/Output}
 
+These operators can be used directly and are called by the I/O
+operator of class \ccc{Triangulation}.
+
 \ccFunction{istream & operator>>(istream & is, TriangulationVertex & v);}%
 {Inputs the non-combinatorial information given by the vertex, {i.e.},
 the point and other possible information.}

Triangulation/doc_tex/Triangulation_ref/Triangulation_data_structure.tex

@@ -21,8 +21,9 @@ constructor (see \ccc{TriangulationDataStructure}).\end{itemize}
 
 \ccc{TriangulationDSVertex} is the class to be used as the base \ccc{Vertex} type in the
 triangulation data structure. It must be a model of the concept
-\ccc{TriangulationDSVertex}. The class template \ccRefName\ accepts that no
+\ccc{TriangulationDSVertex}. The class template \ccRefName\ can be
-second parameter be specified. It also accepts the tag \ccc{CGAL::Default} as
+defined by specifying 
+ only the first parameter. It also accepts the tag \ccc{CGAL::Default} as
 second parameter. In both cases, \ccc{TriangulationDSVertex} defaults to
 \ccc{CGAL::Triangulation_ds_vertex<>}.
 
@@ -63,10 +64,16 @@ full cells, during modifications of the triangulation data structure.}
         Vertex_handle v, Facet f, OutputIterator new_full_cells);}
 {A set \ccc{C} of full cells satisfying the same condition as in method
 \ccRefName\ccc{::insert_in_hole()} is assumed to be marked. This
-method creates new full cells from \ccc{Vertex} v to the boundary of \ccc{C}.
+method creates new full cells from vertex \ccc{v} to the boundary of \ccc{C}.
 The boundary is recognized by checking the mark of the full cells.
 This method is used by \ccRefName\ccc{::insert_in_hole()}.}
 
 \end{ccAdvanced}
 
+\ccSeeAlso
+
+\ccc{Triangulation_ds_vertex}\\
+\ccc{Triangulation_ds_full_cell}\\
+\ccc{Triangulation}
+
 \end{ccRefClass}

Triangulation/doc_tex/Triangulation_ref/Triangulation_face.tex

@@ -2,7 +2,7 @@
 
 \ccDefinition
 
-A \ccRefName\ is a model of the concept \ccc{TriangulationFace}.
+A \ccRefName\ is a model of the concept \ccc{TriangulationDSFace}.
 
 \ccParameters
 
@@ -17,11 +17,11 @@ types\begin{itemize}
 
 \ccIsModel
 
-\ccc{TriangulationFace}.
+\ccc{TriangulationDSFace}.
 
 \ccSeeAlso
 
-\ccc{TriangulationFace},\\
+\ccc{TriangulationDSFace},\\
 \ccc{TriangulationDataStructure}.
 
 \end{ccRefClass}

Triangulation/doc_tex/Triangulation_ref/intro.tex

@@ -54,7 +54,7 @@ following concepts:
 
 \ccRefConceptPage{TriangulationDSVertex}\\
 \ccRefConceptPage{TriangulationDSFullCell}\\
-\ccRefConceptPage{TriangulationFace}
+\ccRefConceptPage{TriangulationDSFace}
 
 \subsubsection*{(Geometric) triangulations}
 

Triangulation/doc_tex/Triangulation_ref/main.tex

@@ -11,7 +11,7 @@
 
 \input{Triangulation_ref/TriangulationDSVertex.tex}
 \input{Triangulation_ref/TriangulationDSFullCell.tex}
-\input{Triangulation_ref/TriangulationFace.tex}
+\input{Triangulation_ref/TriangulationDSFace.tex}
 
 \input{Triangulation_ref/TriangulationTraits.tex}
 \input{Triangulation_ref/DelaunayTriangulationTraits.tex}

Triangulation/include/CGAL/Triangulation.h

@@ -399,7 +399,7 @@ public:
         if( is_infinite(s) )
         {
 	  Vertex_handle v;
-	  for( int i(0); i<= f.feature_dimension(); ++i)
+	  for( int i(0); i<= f.face_dimension(); ++i)
             if ( is_infinite( f.vertex(i) )) return true;
 	}
         return false;

Triangulation/include/CGAL/Triangulation_data_structure.h

@@ -524,7 +524,7 @@ public:
                                             const Face & f)
         : f_(f), tds_(tds)
         {
-            dim_ = f.feature_dimension();
+            dim_ = f.face_dimension();
         }
         bool operator()(const Facet & facet) const
         {
@@ -549,7 +549,7 @@ public:
                                             const Face & f)
         : f_(f), tds_(tds)
         {
-            dim_ = f.feature_dimension();
+            dim_ = f.face_dimension();
         }
         bool operator()(const Facet & facet) const
         {
@@ -780,7 +780,7 @@ typename Triangulation_data_structure<Dim, Vb, Fcb>::Vertex_handle
 Triangulation_data_structure<Dim, Vb, Fcb>
 ::collapse_face(const Face & f) /* Concept */
 {
-    const int fd = f.feature_dimension();
+    const int fd = f.face_dimension();
     CGAL_precondition( (1 <= fd ) && (fd < current_dimension()));
     std::vector<Full_cell_handle> simps;
     // save the Face's vertices:

Triangulation/include/CGAL/Triangulation_face.h

@@ -38,14 +38,14 @@ protected:
 
 public:
     explicit Triangulation_face(Full_cell_handle s) /* Concept */
-    : full_cell_(s), indices_(s->ambient_dimension()+1) // FIXME: +2 to allow for arbitrary dimensioned Face
+    : full_cell_(s), indices_(s->ambient_dimension()+2) 
     {
         CGAL_assertion( Full_cell_handle() != s );
         clear();
     }
 
     explicit Triangulation_face(const int ambient_dim) /* Concept */
-    : full_cell_(), indices_(ambient_dim+1) // FIXME: +2 to allow for arbitrary dimensioned Face
+    : full_cell_(), indices_(ambient_dim+2) 
     {
         clear();
     }
@@ -54,7 +54,7 @@ public:
     : full_cell_(f.full_cell_), indices_(f.indices_)
     {}
 
-    int feature_dimension() const /* Concept */
+    int face_dimension() const /* Concept */
     {
         int i(0);
         while( -1 != indices_[i] ) ++i;
@@ -68,7 +68,7 @@ public:
 
     int index(const int i) const /* Concept */
     {
-        CGAL_precondition( (0 <= i) && (i <= feature_dimension()) );
+        CGAL_precondition( (0 <= i) && (i <= face_dimension()) );
         return indices_[i];
     }