take into account Mariette's comments (still doc only for the moment)

Alpha_shapes_3/doc_tex/Alpha_shapes_3_ref/Alpha_shape_3.tex

@@ -45,31 +45,24 @@
 
 %----------------------------------------------------------------------
 
-\begin{ccRefClass} {Alpha_shape_3<Dt,Atag>}
+\begin{ccRefClass} {Alpha_shape_3<Dt,ExactAlphaComparisonTag>}
 
 \ccDefinition
 
 The class \ccClassTemplateName\ represents the family of
 alpha shapes of points in the 3D space for {\em all} real
 $\alpha$. It maintains an  underlying triangulation 
-of the class \ccc{Dt} which
-represents connectivity and order among its faces. Each
-$k$-dimensional face of the \ccc{Dt} is associated with
-an interval that specifies for which values of $\alpha$ the face
-belongs to the alpha shape. 
-%
-The second template parameter \ccc{Atag} indicates whether the comparison
-of alpha-values needs to be exact or not. Possible values are \ccc{CGAL::Tag_false}
-(the default) and \ccc{CGAL::Tag_true}. The purpose of this tag is to provide
-a robust implementation in the case a traits class with exact predicates but inexact 
-constructions is used for the triangulation. It is by default not activated as 
-it induces a small overhead and does not make sense if used together with a traits
-class with exact constructions.
+of the class \ccc{Dt}. Each k-dimensional face of Dt is associated with an
+interval that specifies for which values of alpha the face belongs to the alpha shape.
+The second template parameter \ccc{ExactAlphaComparisonTag} is a tag that, when set to
+\ccc{CGAL::Tag_true}, triggers exact comparisons between alpha values. This is useful
+when the Delaunay triangulation is instantiated with an exact predicates inexact constructions
+kernel. By default the \ccc{ExactAlphaComparisonTag} is set to \ccc{CGAL::Tag_false} as it induces a small
+overhead and does not make sense if used together with a traits class with exact constructions.
 
 Note that this class is at the same time used for {\em basic} and
 for {\em weighted} Alpha Shapes\ccIndexMainItem[C]{Weighted_alpha_shapes_3}.
 
-
 \ccInclude{CGAL/Alpha_shape_3.h}
 
 \ccInheritsFrom
@@ -90,12 +83,18 @@ it has to derive from a triangulation traits class.
 For example \ccc{Dt::Point} is a Point class. 
 
 \ccNestedType{FT}{the number type of alpha values. \\
-In case \ccc{Atag} is \ccc{CGAL::Tag_false}, it is {Gt::FT}.\\
-In the case \ccc{Atag} is \ccc{CGAL::Tag_true}, it is a number type allowing filtered exact comparisons.
-It provides functions \ccc{FT::Approximate_nt approx() const} and \ccc{FT::Exact_nt exact() const}
-where \ccc{FT::Approximate_nt} and \ccc{FT::Exact_nt} are an interval number type and an exact field number type
-respectively. It must be noted that an object of type \ccc{FT} is valid as long as the alpha shapes that creates
-it is valid and has not been cleared.
+In case \ccc{ExactAlphaComparisonTag} is \ccc{CGAL::Tag_false}, it is {Gt::FT}.\\
+In case \ccc{ExactAlphaComparisonTag} is \ccc{CGAL::Tag_true}, it is a number type
+allowing filtered exact comparisons (that is, interval arithmetic is first used before
+resorting to exact arithmetic).\\
+Access to the interval containing the exact value is provided through the function
+\ccc{FT::Approximate_nt approx() const} where \ccc{FT::Approximate_nt} is \ccc{Interval_nt<Protected>}
+with \ccc{Protected=true}.\\
+Access to the exact value is provided through the function 
+\ccc{FT::Exact_nt exact() const} where \ccc{FT::Exact_nt} depends on the configuration of CGAL 
+(it is \ccc{CGAL::Gmpq} if \ccc{gmp} is available and \ccc{CGAL::Quotient<CGAL::MP_Float>} otherwise).\\
+It must be noted that an object of type \ccc{FT} is valid as long as the alpha shapes class that creates
+it is valid and has not been modified.
 }
 
 \ccNestedType{size_type}{The size type.}
@@ -387,7 +386,7 @@ is an internal format.
 \ccInclude{CGAL/IO/io.h}
 
 \ccFunction{ostream& operator<<(ostream& os,
-                  const Alpha_shape_3<Dt,Atag>& A);}
+                  const Alpha_shape_3<Dt,ExactAlphaComparisonTag>& A);}
 {Inserts the alpha shape \ccVar\ for the current alpha value into the stream \ccc{os}.
 \ccPrecond The insert operator must be defined for \ccc{Point}.}
 
@@ -396,7 +395,7 @@ is an internal format.
 \ccInclude{CGAL/IO/alpha_shape_geomview_ostream_3.h}
 
 \ccFunction{Geomview_stream& operator<<(Geomview_stream& W,
-                         	const Alpha_shape_3<Dt,Atag>& A);}
+                         	const Alpha_shape_3<Dt,ExactAlphaComparisonTag>& A);}
 {Inserts the alpha shape \ccVar\ for the current alpha value into the Geomview stream \ccc{W}.
 \ccPrecond The insert operator must be defined for \ccc{GT::Point} and \ccc{GT::Triangle}.}
 

Alpha_shapes_3/doc_tex/Alpha_shapes_3_ref/intro.tex

@@ -133,7 +133,7 @@ of the alpha complex where singular faces are removed.
 
 \subsection*{Classes}
 \ccRefIdfierPage{CGAL::Alpha_status<NT>} \\
-\ccRefIdfierPage{CGAL::Alpha_shape_3<Dt,Atag>}\\
+\ccRefIdfierPage{CGAL::Alpha_shape_3<Dt,ExactAlphaComparisonTag>}\\
 \ccRefIdfierPage{CGAL::Alpha_shape_vertex_base_3<Traits,Vb>}\\
 \ccRefIdfierPage{CGAL::Alpha_shape_cell_base_3<Traits,Fb>}