%% =============================================================================
%% The CGAL Reference Manual
%% Chapter: STL Extensions - The Reference Part
%% -----------------------------------------------------------------------------
%% file  : doc_tex/support/STL_Extension/STL_Extension_ref/stl_extension.tex
%% author: Michael Hoffmann, Lutz Kettner 
%% -----------------------------------------------------------------------------
%% $CGAL_Chapter: STL_Extension $
%% $Id$
%% $Date$
%% =============================================================================

%% +=========================================================================+

%% +---------------------------------------------+
\begin{ccRefFunction}{predecessor}
  \label{sectionPredecessor}
  \label{sectionGenericFunctions}

  \ccDefinition The function \ccRefName\ returns the previous iterator,
  i.e. the result of \ccc{operator--} on a bidirectional iterator.
  
  \ccInclude{CGAL/algorithm.h}
  
  \ccThree{BidirectionalIterator}{predecessor}{}
  \ccFunction{template <class BidirectionalIterator>
              BidirectionalIterator predecessor(BidirectionalIterator it);}
    {returns \ccc{--it}.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::successor}
\end{ccRefFunction}

%% +---------------------------------------------+
\begin{ccRefFunction}{successor}
  \label{sectionSuccessor}

  \ccDefinition The function \ccRefName\ returns the next iterator, i.e.
  the result of \ccc{operator++} on a forward iterator.
  
  \ccInclude{CGAL/algorithm.h}
  
  \ccThree{ForwardIterator}{successor}{}
  \ccFunction{template <class ForwardIterator>
              ForwardIterator successor(ForwardIterator it);}
    {returns \ccc{++it}.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::predecessor}
\end{ccRefFunction}

%% +---------------------------------------------+
\begin{ccRefFunction}{copy_n}
  \label{sectionCopyN}

  \ccDefinition The function \ccRefName\ copies $n$ items from an
  input iterator to an output iterator which is useful for possibly
  infinite
  sequences of random geometric objects.\footnote{%
    The \stl\ release June 13, 1997, from SGI contains an equivalent
    function, but it is not part of the ISO standard.}
  
  \ccInclude{CGAL/algorithm.h}
  
  \ccThree{OutputIterator}{copy_n}{}
  \ccFunction{template <class InputIterator, class Size, class
    OutputIterator> OutputIterator copy_n(InputIterator first, Size n,
    OutputIterator result);}{copies the first $n$ items from
    \ccc{first} to \ccc{result}. Returns the value of \ccc{result}
    after inserting the $n$ items.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Counting_iterator<Iterator, Value>}
\end{ccRefFunction}

%% +---------------------------------------------+
\begin{ccRefFunction}{min_max_element}
  \label{sectionMinmaxelement}
  
  \ccDefinition The function \ccRefName\ computes the minimal and the
  maximal element of a range. It is modeled after the STL functions
  \ccc{min_element} and \ccc{max_element}. The advantage of
  \ccc{min_max_element} compared to calling both STL functions is that
  one only iterates once over the sequence. This is more efficient
  especially for large and/or complex sequences.

  \ccInclude{CGAL/algorithm.h}
  
  \ccFunction{template < class ForwardIterator > std::pair<
    ForwardIterator, ForwardIterator > min_max_element(ForwardIterator
    first, ForwardIterator last);}{returns a pair of iterators where
    the first component refers to the minimal and the second component
    refers to the maximal element in the range [\ccc{first},
    \ccc{last}). The ordering is defined by \ccc{operator<} on the
    value type of \ccc{ForwardIterator}.}
  
  \ccFunction{template < class ForwardIterator, class CompareMin,
    class CompareMax > std::pair< ForwardIterator, ForwardIterator >
    min_max_element(ForwardIterator first, ForwardIterator last,
    CompareMin comp_min, CompareMax comp_max);}{returns a pair of
    iterators where the first component refers to the minimal and the
    second component refers to the maximal element in the range
    [\ccc{first}, \ccc{last}). \ccRequire
    \ccc{CompareMin} and \ccc{CompareMax} are adaptable binary
    function objects:
    \ccc{VT}~$\times$~\ccc{VT}~$\rightarrow$~\ccc{bool} where \ccc{VT}
    is the value type of \ccc{ForwardIterator}.}
  
  \ccExample The following example program computes the minimal and
  maximal element of the sequence $(3,\,6,\,5)$. Hence the output is
  \ccc{min = 3, max = 6}.
  
  \ccIncludeExampleCode{STL_Extension/min_max_element_example_noheader.cpp}

\end{ccRefFunction}

%% Michael: I commented these, as I think they should be replaced by combining 
%% Filter_iterator with std::min/max_element().
%%
%% %% +---------------------------------------------+
%% \begin{ccRefFunction}{min_element_if}
%%   \label{sectionMinElementIf}
  
%%   \ccDefinition The function \ccRefName\ computes the minimum among
%%   the elements of a range which satisfy a certain predicate. It is
%%   modeled after the STL function \ccc{min_element}.

%%   \ccInclude{CGAL/algorithm.h}
  
%%   \ccFunction{template < class ForwardIterator, class Predicate >
%%     ForwardIterator min_element_if(ForwardIterator first,
%%     ForwardIterator last, Predicate pred);}{returns an iterator
%%     referring to the minimal element among those satifying the
%%     predicate \ccc{pred} in the range [\ccc{first}, \ccc{last}). The
%%     ordering is defined by the \ccc{operator<} on \ccc{VT} where
%%     \ccc{VT} is the value type of \ccc{ForwardIterator}.
%%     \ccRequire \ccc{pred} is an unary function
%%     object: \ccc{VT}~$\rightarrow$~\ccc{bool}.}
  
%%   \ccFunction{template < class ForwardIterator, class Compare, class
%%     Predicate > ForwardIterator min_element_if(ForwardIterator first,
%%     ForwardIterator last, Compare comp, Predicate pred);} {return an
%%     iterator referring to the minimal element among those satifying
%%     the predicate \ccc{pred} in the range [\ccc{first}, \ccc{last}).
%%     The ordering is defined by \ccc{comp}.
%%     \ccRequire \ccc{comp} is a binary function
%%     object: \ccc{VT}~$\times$~\ccc{VT}~$\rightarrow$~\ccc{bool} where
%%     \ccc{VT} is the value type of \ccc{ForwardIterator}. \ccc{pred} is
%%     an unary function object: \ccc{VT}~$\rightarrow$~\ccc{bool}.}
  
%%   \ccSeeAlso
%%   \ccRefIdfierPage{CGAL::max_element_if}\\
%%   \ccRefIdfierPage{CGAL::min_max_element}

%%   \ccExample The following example program computes the minimal odd
%%   element of the sequence $(3,\,5,\,2)$. Hence the output is
%%   \ccc{min_odd = 3}.
  
%%   \ccIncludeExampleCode{STL_Extension_ref/min_element_if_example_noheader.cpp}

%% \end{ccRefFunction}

%% %% +---------------------------------------------+
%% \begin{ccRefFunction}{max_element_if}
  
%%   \ccDefinition The function \ccRefName\ computes the maximum among
%%   the elements of a range which satisfy a certain predicate. It is
%%   modeled after the STL function \ccc{max_element}.

%%   \ccInclude{CGAL/algorithm.h}
  
%%   \ccFunction{template < class ForwardIterator, class Predicate >
%%     ForwardIterator max_element_if(ForwardIterator first,
%%     ForwardIterator last, Predicate pred);}{returns an iterator
%%     referring to the maximal element among those satifying the
%%     predicate \ccc{pred} in the range [\ccc{first}, \ccc{last}). The
%%     ordering is defined by the \ccc{operator<} on \ccc{VT} where
%%     \ccc{VT} is the value type of \ccc{ForwardIterator}.
%%     \ccRequire \ccc{pred} is an unary function
%%     object: \ccc{VT}~$\rightarrow$~\ccc{bool}.}
  
%%   \ccFunction{template < class ForwardIterator, class Compare, class
%%     Predicate > ForwardIterator max_element_if(ForwardIterator first,
%%     ForwardIterator last, Compare comp, Predicate pred);} {return an
%%     iterator referring to the maximal element among those satifying
%%     the predicate \ccc{pred} in the range [\ccc{first}, \ccc{last}).
%%     The ordering is defined by \ccc{comp}.
%%     \ccRequire \ccc{comp} is a binary function
%%     object: \ccc{VT}~$\times$~\ccc{VT}~$\rightarrow$~\ccc{bool} where
%%     \ccc{VT} is the value type of \ccc{ForwardIterator}. \ccc{pred} is
%%     an unary function object: \ccc{VT}~$\rightarrow$~\ccc{bool}.}

%%   \ccSeeAlso
%%   \ccRefIdfierPage{CGAL::min_element_if}\\
%%   \ccRefIdfierPage{CGAL::min_max_element}

%% \end{ccRefFunction}

%% +=========================================================================+

\begin{ccRefClass}{Emptyset_iterator}
  \label{sectionEmptysetIterator}

  \ccCreationVariable{i}
  
  \ccDefinition The class \ccClassName\ defines an
  \ccc{OutputIterator} that ignores everything written to it. One can
  think of it as being connected to \texttt{/dev/null}.

  \ccInclude{CGAL/iterator.h}

  \ccIsModel
  \ccc{OutputIterator}
  
  \ccCreation

  \ccTwo{Emptyset_iterator()}{}
  
  \ccConstructor{Emptyset_iterator();}{default constructor.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Oneset_iterator}\\
  \ccRefIdfierPage{CGAL::Const_oneset_iterator}

\end{ccRefClass}

\begin{ccRefClass}{Oneset_iterator<T>}
  \label{sectionOnesetIterator}

  \ccCreationVariable{i}
  
  \ccDefinition The class \ccClassTemplateName\ defines an
  \ccc{BidirectionalIterator} that always refers to one specific
  object of type \ccc{T}.  Internally, \ccClassTemplateName\ stores a
  pointer to the referred object.
  
  \ccInclude{CGAL/iterator.h}

  \ccIsModel
  \ccc{BidirectionalIterator}
  
  \ccCreation

  \ccTwo{Oneset_iterator(T& t);}{}
  
  \ccTagFullDeclarations\ccConstructor{Oneset_iterator(T& t);}{creates
    an iterator referring to \ccc{t}.}\ccTagDefaults
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Emptyset_iterator}\\
  \ccRefIdfierPage{CGAL::Const_oneset_iterator}

\end{ccRefClass}

\begin{ccRefClass}{Const_oneset_iterator<T>}
  \label{sectionConst_onesetIterator}

  \ccCreationVariable{i}
  
  \ccDefinition The class \ccClassTemplateName\ defines an
  \ccc{RandomAccessIterator} that always refers to a copy of a
  specific object of type \ccc{T}.
  
  \ccInclude{CGAL/iterator.h}

  \ccIsModel
  \ccc{RandomAccessIterator}
  
  \ccCreation

  \ccTwo{Const_oneset_iterator(const T& t);}{}
  
  \ccTagFullDeclarations\ccConstructor{Const_oneset_iterator(T&
    t);}{creates an iterator that always refers to some copy of
    \ccc{t}.  The copy is constructed by invoking \ccc{T}'s copy
    constructor and remains constant during $i$'s
    lifetime.}\ccTagDefaults
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Emptyset_iterator}\\
  \ccRefIdfierPage{CGAL::Oneset_iterator}

\end{ccRefClass}

%% +--------------------------------------------------------+
\begin{ccRefClass}{Counting_iterator<Iterator, Value>}
  \label{sectionCountingIterator}

  \ccCreationVariable{i}
  
  \ccDefinition The iterator adaptor \ccClassTemplateName\ adds a
  counter to the internal iterator of type \ccc{Iterator} and defines
  equality of two instances in terms of this counter. It can be used
  to create finite sequences of possibly infinite sequences of values
  from input iterators.

  \ccInclude{CGAL/iterator.h}

  \ccIsModel
  \ccc{InputIterator}
  
  \ccRequirements \ccc{Iterator} is a model for
  \ccc{InputIterator}.

  \ccCreation

  \ccTwo{Identity<Value>MMMMMM}{}
  
  \ccConstructor{Counting_iterator( std::size_t n = 0);}{initializes
    the internal counter to $n$ and \ccVar\ has a singular value.}
  
  \ccConstructor{Counting_iterator( Iterator j, std::size_t n = 0);}{
    initializes the internal counter to $n$ and \ccVar\ to $j$.}

  \ccSeeAlso
  \ccRefIdfierPage{CGAL::copy_n}

\end{ccRefClass}

%% +--------------------------------------------------------+
\begin{ccRefClass}{Insert_iterator<Container>}
  \label{sectionInsertIterator}

  \ccCreationVariable{i}
  
  \ccDefinition The output iterator \ccClassTemplateName\ is similar
  to \ccc{std::insert_iterator}, but differs in that it calls the
  \ccc{insert()} function of the container without the iterator
  additional argument.

  \ccInclude{CGAL/iterator.h}

  \ccIsModel
  \ccc{OutputIterator}
  
  \ccRequirements \ccc{Container} provides a member function
  \ccc{insert(const Container::const_reference&)}.

  \ccCreation

  \ccTwo{Identity<Value>MMMMMM}{}
  
  \ccConstructor{Insert_iterator( Container &c );}{initializes
    the internal container reference to $c$.}

  There is also a global function similar to \ccc{std::inserter}:

  \ccFunction{template < class Container >
              Insert_iterator<Container>
              inserter(Container &x);}
  { Constructs \ccc{Insert_iterator<Container>(x)}. }
  
\end{ccRefClass}

%% +--------------------------------------------------------+
\begin{ccRefClass}{N_step_adaptor<I,int N>}
  \ccCreationVariable{i}
  
  \ccDefinition The adaptor \ccRefName\ changes the step width of the
  iterator or circulator class \ccStyle{I} to $N$. It is itself an
  iterator or circulator respectively. The behavior is undefined if
  the adaptor is used on a range [$i,j$) where $j-i$ is not a multiple
  of $n$.
  
  \ccInclude{CGAL/iterator.h}
  
  \ccCreation
  \ccTwo{N_step_adaptor<I,int N> i( I j);;M}{}
  
  \ccConstructor{N_step_adaptor(const I& j);}{down cast.}
  
\end{ccRefClass}

\begin{ccRefClass}{Filter_iterator<Iterator, Predicate>}
  \label{sectionFilterIterator}

  \ccCreationVariable{i}
  
  \ccDefinition The iterator adaptor \ccClassTemplateName\ acts as a
  filter on a given range. Whenever the iterator is in-- or
  decremented, it ignores all iterators for which the given
  \ccc{Predicate} is true. The iterator category is the same as for
  \ccc{Iterator}.

  Note: Boost also provides the same functionality via the
  \ccc{boost::filter_iterator} class.  Unfortunately, the semantics
  chosen for accepting or rejecting elements based on the predicate's
  result are opposite as the semantic chosen here. What is more, the
  argument of the predicate is different: the predicate used with
  \ccc{boost::filter_iterator} must take the value type of the iterator, as
  argument, and not the iterator itself.

  \ccInclude{CGAL/iterator.h}
  
  \ccRequirements
  \begin{itemize}
  \item \ccc{Iterator} is a model for \ccc{ForwardIterator}.
  \item \ccc{Predicate} is a functor: \ccc{Iterator} $\rightarrow$
    \ccc{bool}.
  \end{itemize}

  \ccCreation

  %%\ccTwo{Identity<Value>MMMMMM}{}
  
  \ccConstructor{Filter_iterator();}{}
  
  \ccConstructor{Filter_iterator(Iterator e, Predicate p, Iterator c = e);}
   {creates an iterator which filters values according to \ccc{p}.
    Initializes by taking the first valid iterator (according to \ccc{p}),
    starting at \ccc{c}, and stopping at \ccc{e} if none is found.}

  There is also a global function to help the use of \ccClassTemplateName{}:

  \ccFunction{template < class Iterator, class Predicate >
    inline Filter_iterator< Iterator, Predicate >
    filter_iterator(Iterator e, const Predicate& p, Iterator c = e);}
  { Constructs \ccc{Filter_iterator<Iterator, Predicate>(e, p, c)}. }
\end{ccRefClass}

%% +---------------------------------------------+

\begin{ccRefClass}{Join_input_iterator_1<Iterator, Creator>}
  \label{sectionJoinInputIterator}
  
  \ccDefinition The class \ccRefName\ joins an iterator and a creator
  function object. The result is again an iterator (of the same
  iterator category type as the original iterator) that reads an object
  from the stream and applies a creator function object to that
  object.

  \ccInclude{CGAL/iterator.h}
  
  \ccIsModel \ccc{InputIterator}

  \ccTypes
  \ccNestedType{value_type}{typedef to \ccc{Creator::result_type}.}
  
  \ccCreation\ccCreationVariable{join}
  
  \ccConstructor{Join_input_iterator_1( Iterator i, const Creator&
    creator);} {creates a join iterator from the given iterator $i$
    and the functor \ccc{creator}. Applies \ccc{creator} to each item
    read from $i$.}

  \ccConstructor{Join_input_iterator_1( Iterator i);} {creates a join
    iterator from the given iterator $i$ and a default constructed
    instance of \ccc{Creator}. The latter instance is applied to each
    item read from $i$.}

  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Creator_1<Arg, Result>}
\end{ccRefClass}


%%  +--------------------------------------------------------+
\begin{ccRefClass}{Inverse_index<IC>}
  
  \ccDefinition The class \ccClassTemplateName\ constructs an inverse
  index for a given range [$i,j$) of two iterators or circulators of
  type \ccc{IC}.  The first element $I$ in the range [$i,j$) has the
  index 0.  Consecutive elements are numbered incrementally. The
  inverse index provides a query for a given iterator or circulator
  $k$ to retrieve its index number. {\em Precondition:}\/ The iterator
  or circulator must be either of the random access category or the
  dereference operator must return stable and distinguishable
  addresses for the values, e.g.~proxies or non-modifiable iterator
  with opaque values will not work.

  \ccInclude{CGAL/iterator.h}

  \ccCreation\ccCreationVariable{inverse}
  
  \ccTwo{Inverse_index< IC,> inverse( IC i, IC j);;}{}
  \ccConstructor{Inverse_index();}{invalid index.}
  
  \ccGlue\ccConstructor{Inverse_index( const IC& i);}{empty inverse
    index initialized to start at $i$.}
  
  \ccGlue\ccConstructor{Inverse_index( const IC& i, const IC& j);}
  {inverse index initialized with range [$i,j$).}

  \ccOperations
  \ccThree{std::size_t}{inverse.find( const T* p);}{}
  
  \ccMethod{std::size_t operator[]( const IC& k);}{returns inverse
    index of $k$. \ccPrecond $k$ has been stored in the inverse
    index.}
  
  \ccMethod{void push_back( const IC& k);}{adds $k$ at the end of the
    indices.}

  \ccImplementation
  
  For random access iterators or circulators, it is done in constant
  time by subtracting $i$. For other iterator categories, an \stl\ 
  \ccc{map} is used, which results in a $\log j-i$ query time. The
  comparisons are done using the operator \ccc{operator<} on pointers.

  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Random_access_adaptor<IC>}\\
  \ccRefIdfierPage{CGAL::Random_access_value_adaptor<IC,T>}

\end{ccRefClass}

%% +--------------------------------------------------------+
\begin{ccRefClass}{Random_access_adaptor<IC>}
  
  \ccDefinition The class \ccClassTemplateName\ provides a random
  access for data structures. Either the data structure supports
  random access iterators or circulators where this class maps
  function calls to the iterator or circulator, or a \stl\ 
  \ccc{std::vector} is used to provide the random access. The iterator
  or circulator of the data structure are of type \ccc{IC}.

  \ccInclude{CGAL/iterator.h}

  \ccTypes

  \ccNestedType{size_type}{size type of the \stl\ \ccc{std::vector}.}

  \ccCreation\ccCreationVariable{random_access}

  \ccTwo{Random_access_adaptor< IC> random_access;}{}
  \ccConstructor{Random_access_adaptor();}{invalid index.}
  
  \ccConstructor{Random_access_adaptor( const IC& i);} {empty random
    access index initialized to start at $i$.}
  
  \ccConstructor{Random_access_adaptor( const IC& i, const IC& j);}
  {random access index initialized to the range [$i,j$).}
  
  \ccThree{Dist}{random_access.push_back( IC k);}{} \ccMethod{void
    reserve( size_type r);}{reserve $r$ entries, if a
    \ccc{std::vector} is used internally.}
  
  \ccOperations
  
  \ccMethod{IC operator[]( size_type n);}{returns iterator or
    circulator to the $n$-th item.  \ccPrecond $n <$ number of items
    in \ccVar.}
  
  \ccMethod{void push_back( const IC& k);}{adds $k$ at the end of the
    indices.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Inverse_index<IC>}\\
  \ccRefIdfierPage{CGAL::Random_access_value_adaptor<IC,T>}

\end{ccRefClass}


%% +--------------------------------------------------------+
\begin{ccRefClass}{Random_access_value_adaptor<IC,T>}
  
  \ccDefinition The class \ccClassTemplateName\ provides a random
  access for data structures. It is derived from
  \ccc{Random_access_adaptor<IC>}. Instead of returning iterators from
  the \ccc{operator[]} methods, it returns the dereferenced value of
  the iterator.  The iterator or circulator of the data structure are
  of type \ccc{IC}. Their value type is $T$.

  \ccInclude{CGAL/iterator.h}

  \ccOperations
  
  Creation and operations see \ccc{Random_access_adaptor<IC>}, with
  the exception of:
  
  \ccCreationVariable{random_access}

  \ccThree{Dist}{random_access.push_back( IC k);}{}
  
  \ccMethod{T& operator[]( size_type n);}{returns a reference to the
    $n$-th item.  \ccPrecond $n <$ number of items in \ccVar.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Inverse_index<IC>}\\
  \ccRefIdfierPage{CGAL::Random_access_adaptor<IC>}

\end{ccRefClass}

%% +=========================================================================+

\begin{ccRefFunction}{compare_to_less}
  \ccDefinition The function \ccRefName\ is used to change a functor
  returning a \ccc{Comparison_result} to one which returns a bool.
  The returned functor will return \ccc{true} iff the original one
  returns \ccc{SMALLER}.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccThree{typename Compare_to_less< F >::Type}{compare_to_less}{}
  
  \ccFunction{template < class F > Compare_to_less< F >
    compare_to_less(const F& f);}{returns a functor equivalent to
    \ccc{f}, but which returns a bool instead of a
    \ccc{Comparison_result}.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::Compare_to_less<F>}
  
\end{ccRefFunction}

\begin{ccRefClass}{Compare_to_less<F>}
  \ccDefinition The class \ccRefName\ is used to convert a functor which
  returns a \ccc{Comparison_result} to a predicate (returning bool) : it
  will return true iff the return value of \ccc{F} is \ccc{SMALLER}.
  The class is used in conjunction with the \ccc{compare_to_less}
  function; see there for an explanation on how exactly the functors
  are combined.

  \ccInclude{CGAL/function_objects.h}
  
  \ccTypes
  \ccNestedType{Type}{type of the composed functor.}
  
  \ccSeeAlso
  \ccRefIdfierPage{CGAL::compare_to_less}
  
\end{ccRefClass}

%% +=========================================================================+

\begin{ccRefFunctionObjectConcept}{Projection_object}
  \label{sectionProjectionFunctionObjects}
  
  \ccDefinition The concept \ccRefName\ is modeled after the STL
  concept \ccc{UnaryFunction}, but takes also care of (const)
  references.
  
  \ccTagFullDeclarations
  \ccNestedType{argument_type}{argument type.}
  \ccNestedType{result_type}{result type.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Projection_object();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  \ccMethod{result_type& operator()(argument_type &) const;}{}
  \ccGlue
  \ccMethod{const result_type& operator()(const argument_type &) const;}{}
  \ccTagDefaults

  \ccHasModels
  \ccRefIdfierPage{CGAL::Identity<Value>}\\
  \ccRefIdfierPage{CGAL::Dereference<Value>}\\
  \ccRefIdfierPage{CGAL::Get_address<Value>}\\
  \ccRefIdfierPage{CGAL::Cast_function_object<Arg, Result>}\\
  \ccRefIdfierPage{CGAL::Project_vertex<Node>}\\
  \ccRefIdfierPage{CGAL::Project_facet<Node>}\\
  \ccRefIdfierPage{CGAL::Project_point<Node>}\\
  \ccRefIdfierPage{CGAL::Project_normal<Node>}\\
  \ccRefIdfierPage{CGAL::Project_plane<Node>}\\
  \ccRefIdfierPage{CGAL::Project_next<Node>}\\
  \ccRefIdfierPage{CGAL::Project_prev<Node>}\\
  \ccRefIdfierPage{CGAL::Project_next_opposite<Node>}\\
  \ccRefIdfierPage{CGAL::Project_opposite_prev<Node>}
  
\end{ccRefFunctionObjectConcept}

\begin{ccRefFunctionObjectClass}{Identity<Value>}
  \ccDefinition The class \ccRefName\ represents the identity function
  on \ccc{Value}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Value}.}
  \ccNestedType{result_type}{typedef to \ccc{Value}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Identity();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& x) const;}{returns
    \ccc{x}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    x) const;}{returns \ccc{x}.}  \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Dereference<Value>}
  \ccDefinition The class \ccRefName\ dereferences a pointer
  (\ccc{operator*}).
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Value*}.}
  \ccNestedType{result_type}{typedef to \ccc{Value}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Dereference();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& x) const;}{returns
    \ccc{*x}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    x) const;}{returns \ccc{*x}.} \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Get_address<Value>}
  \ccDefinition The class \ccRefName\ gets the address of an lvalue
  (\ccc{operator&}).
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Value}.}
  \ccNestedType{result_type}{typedef to \ccc{Value*}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Get_address();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& x) const;}{returns
    \ccc{&x}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    x) const;}{returns \ccc{&x}.} \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Cast_function_object<Arg, Result>}
  \ccDefinition The class \ccRefName\ applies a C-style type cast to
  its argument.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Arg}.}
  \ccNestedType{result_type}{typedef to \ccc{Result}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Cast_function_object();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& x) const;}{returns
    \ccc{(Result)x}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    x) const;}{returns \ccc{(Result)x}.} \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_vertex<Node>}
  \ccDefinition The class \ccRefName\ calls the member function
  \ccc{vertex()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node}.}
  \ccNestedType{result_type}{typedef to \ccc{Node::Vertex}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_vertex();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n.vertex()}.}
  
  \ccGlue \ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n.vertex()}.}  \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_facet<Node>}
  \ccDefinition The class \ccRefName\ calls the member function
  \ccc{facet()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node}.}
  \ccNestedType{result_type}{typedef to \ccc{Node::Facet}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_facet();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n.facet()}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n.facet()}.} \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_point<Node>}
  \ccDefinition The class \ccRefName\ calls the member function
  \ccc{point()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node}.}
  \ccNestedType{result_type}{typedef to \ccc{Node::Point}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_point();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n.point()}.}
  
  \ccGlue \ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n.point()}.} \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_normal<Node>}
  \ccDefinition The class \ccRefName\ calls the member function
  \ccc{normal()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node}.}
  \ccNestedType{result_type}{typedef to \ccc{Node::Normal}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_normal();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n.normal()}.}
  
  \ccGlue \ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n.normal()}.}  \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_plane<Node>}
  \ccDefinition The class \ccRefName\ calls the member function
  \ccc{plane()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node}.}
  \ccNestedType{result_type}{typedef to \ccc{Node::Plane}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_plane();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n.plane()}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n.plane()}.}  \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_next<Node>}
  \ccDefinition The class \ccRefName\ calls the member function
  \ccc{next()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node*}.}
  \ccNestedType{result_type}{typedef to \ccc{Node*}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_next();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n->next()}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n->next()}.}  \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_prev<Node>}
  \ccDefinition The class \ccRefName\ calls the member function
  \ccc{prev()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node*}.}
  \ccNestedType{result_type}{typedef to \ccc{Node*}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_prev();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n->prev()}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n->prev()}.}  \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_next_opposite<Node>}
  \ccDefinition The class \ccRefName\ calls the member functions
  \ccc{next()->opposite()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node*}.}
  \ccNestedType{result_type}{typedef to \ccc{Node*}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_next_opposite();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n->next()->opposite()}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n->next()->opposite()}.}  \ccTagDefaults

\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Project_opposite_prev<Node>}
  \ccDefinition The class \ccRefName\ calls the member functions
  \ccc{opposite()->prev()} on an instance of type \ccc{Node}.
  
  \ccInclude{CGAL/function_objects.h}

  \ccIsModel
  \ccRefConceptPage{Projection_object}

  \ccTagFullDeclarations
  \ccNestedType{argument_type}{typedef to \ccc{Node*}.}
  \ccNestedType{result_type}{typedef to \ccc{Node*}.}
  \ccCreationVariable{o}
  \ccCreation
  \ccConstructor{Project_opposite_prev();}{default constructor.}
  \ccOperations
  \ccThree{const result_type&;;}{A}{}
  
  \ccMethod{result_type& operator()(argument_type& n) const;}{returns
    \ccc{n->opposite()->prev()}.}
  
  \ccGlue\ccMethod{const result_type& operator()(const argument_type&
    n) const;}{returns \ccc{n->opposite()->prev()}.}
  \ccTagDefaults

\end{ccRefFunctionObjectClass}

%% +--------------------------------------------------------+

\begin{ccRefFunctionObjectClass}{Creator_1<Arg, Result>}
  \label{sectionCreatorFunctionObjects}
  
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from one argument.
  
  \ccInclude{CGAL/function_objects.h}

  \ccHeading{Requirements} \ccc{Arg} is convertible to \ccc{Result}.
  
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of argument.}
  \ccNestedType{result_type}{type of object to create.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a) const;}{returns
    \ccc{result_type(a)}.}

  \ccTagDefaults
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_2<Arg1, Arg2, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from two arguments.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a corresponding
  constructor.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument1_type}{type of first argument.}
  \ccNestedType{argument2_type}{type of second argument.}
  \ccNestedType{result_type}{type of object to create.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type1 a1, argument_type2
    a2) const;}{returns \ccc{result_type(a1, a2)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_3<Arg1, Arg2, Arg3, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from three arguments.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a corresponding
  constructor.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument1_type}{type of first argument.}
  \ccNestedType{argument2_type}{type of second argument.}
  \ccNestedType{argument3_type}{type of third argument.}
  \ccNestedType{result_type}{type of object to create.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type1 a1, argument_type2
    a2, argument_type3 a3) const;}{returns \ccc{result_type(a1, a2,
      a3)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_4<Arg1, Arg2, Arg3, Arg4, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from four arguments.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a corresponding
  constructor.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument1_type}{type of first argument.}
  \ccNestedType{argument2_type}{type of second argument.}
  \ccNestedType{argument3_type}{type of third argument.}
  \ccNestedType{argument4_type}{type of 4th argument.}
  \ccNestedType{result_type}{type of object to create.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type1 a1, argument_type2
    a2, argument_type3 a3, argument_type4 a4) const;}{returns
    \ccc{result_type(a1, a2, a3, a4)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_5<Arg1, Arg2, Arg3, Arg4, Arg5, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from five arguments.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a corresponding
  constructor.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument1_type}{type of first argument.}
  \ccNestedType{argument2_type}{type of second argument.}
  \ccNestedType{argument3_type}{type of third argument.}
  \ccNestedType{argument4_type}{type of 4th argument.}
  \ccNestedType{argument5_type}{type of 5th argument.}
  \ccNestedType{result_type}{type of object to create.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type1 a1, argument_type2
    a2, argument_type3 a3, argument_type4 a4, argument_type5 a5)
    const;}{returns \ccc{result_type(a1, a2, a3, a4, a5)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_2<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from two arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from two
  \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2)
    const;}{returns \ccc{result_type(a1, a2)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_3<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from three arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from
  three \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2,
    argument_type a3) const;}{returns \ccc{result_type(a1, a2, a3)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_4<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from four arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from
  four \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2,
    argument_type a3, argument_type a4) const;}{returns
    \ccc{result_type(a1, a2, a3, a4)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_5<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from five arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from
  five \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2,
    argument_type a3, argument_type a4, argument_type a5)
    const;}{returns \ccc{result_type(a1, a2, a3, a4, a5)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_6<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from six arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from six
  \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2,
    argument_type a3, argument_type a4, argument_type a5,
    argument_type a6) const;}{returns \ccc{result_type(a1, a2, a3, a4,
      a5, a6)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_7<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from seven arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from
  seven \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2,
    argument_type a3, argument_type a4, argument_type a5,
    argument_type a6, argument_type a7) const;}{returns
    \ccc{result_type(a1, a2, a3, a4, a5, a6, a7)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_8<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from eight arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from
  eight \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2,
    argument_type a3, argument_type a4, argument_type a5,
    argument_type a6, argument_type a7, argument_type a8)
    const;}{returns \ccc{result_type(a1, a2, a3, a4, a5, a6, a7,
      a8)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_9<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from nine arguments of the same type.
  
  \ccInclude{CGAL/function_objects.h}
  
  \ccRequirements \ccc{Result} defines a constructor from
  nine \ccc{Arg} arguments.
  
  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}
  
  \ccMethod{result_type operator()(argument_type a1, argument_type a2,
    argument_type a3, argument_type a4, argument_type a5,
    argument_type a6, argument_type a7, argument_type a8,
    argument_type a9) const;}{returns \ccc{result_type(a1, a2, a3, a4,
      a5, a6, a7, a8, a9)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}

\begin{ccRefFunctionObjectClass}{Creator_uniform_d<Arg, Result>}
  \ccDefinition The concept \ccRefName\ defines types and operations
  for creating objects from two arguments of the same type.

  \ccInclude{CGAL/function_objects.h}

  \ccRequirements \ccc{Result} defines a constructor from three arguments: 
  one \ccc{d} dimension and two \ccc{Arg} arguments.

  \def\ccLongParamLayout{\ccTrue}
  \ccTagFullDeclarations\ccCreationVariable{c}
  \ccNestedType{argument_type}{type of arguments; typedef to
    \ccc{Arg}.}
  \ccNestedType{result_type}{type of object to create; typedef to
    \ccc{Result}.}
  \ccThree{result_type;;}{operator()(argument_type a) const;;}{}

  \ccMethod{result_type operator()(argument_type a1, argument_type a2)
    const;}{returns \ccc{result_type(d, a1, a2)}.}

  \ccTagDefaults\def\ccLongParamLayout{\ccFalse}
\end{ccRefFunctionObjectClass}


%% +--------------------------------------------------------+

\begin{ccRefClass}{Twotuple<T>}
  
  \ccDefinition The \ccRefName\ class stores a homogeneous (same type) pair
  of objects of type \ccc{T}.  A \ccRefName\ is much like a container, in that
  it "owns" its elements. It is not actually a model of container, though,
  because it does not support the standard methods (such as iterators) for
  accessing the elements of a container.

  This class is DEPRECATED, and will be removed in some future CGAL release.
  Please use \ccc{boost::array} instead.

  \ccInclude{CGAL/Twotuple.h}
  
  \ccRequirements \ccc{T} must be \ccc{Assignable}.

  %\ccSetThreeColumns{T*}{next_link ;}{}
  \ccThree{result_type;;}{operator()(argument a) ;;}{}

  \ccTypes
  \ccTypedef{typedef T value_type;}{}

  \ccHeading{Variables}
  \ccVariable{T e0;}{first element}
  \ccGlue
  \ccVariable{T e1;}{second element}

  \ccCreation
  \ccCreationVariable{t}
  
  \ccConstructor{Twotuple();}{introduces a \ccRefName\ using the default
    constructor of the elements.}
  
  \ccConstructor{Twotuple(T x, T y);}{constructs a \ccRefName\ such
    that \ccc{e0} is constructed from \ccc{x} and \ccc{e1} is
    constructed from \ccc{y}.}
  
\end{ccRefClass}

%% +--------------------------------------------------------+

\begin{ccRefClass}{Threetuple<T>}
  
  \ccDefinition The \ccRefName\ class stores a homogeneous (same type) triple
  of objects of type \ccc{T}.  A \ccRefName\ is much like a container, in that
  it "owns" its elements. It is not actually a model of container, though,
  because it does not support the standard methods (such as iterators) for
  accessing the elements of a container.

  This class is DEPRECATED, and will be removed in some future CGAL release.
  Please use \ccc{boost::array} instead.

  \ccInclude{CGAL/Threetuple.h}
  
  \ccRequirements \ccc{T} must be \ccc{Assignable}.

  %\ccSetThreeColumns{T*}{next_link ;}{}
  \ccThree{result_type;;}{operator()(argument a) ;;}{}

  \ccTypes
  \ccTypedef{typedef T value_type;}{}

  \ccHeading{Variables}
  \ccVariable{T e0;}{first element}
  \ccGlue
  \ccVariable{T e1;}{second element}
  \ccGlue
  \ccVariable{T e2;}{third element}

  \ccCreation
  \ccCreationVariable{t}
  
  \ccConstructor{Threetuple();}{introduces a \ccRefName\ using the default
    constructor of the elements.}
  
  \ccConstructor{Threetuple(T x, T y, T z);}{constructs a \ccRefName\ such
    that \ccc{e0} is constructed from \ccc{x}, \ccc{e1} is
    constructed from \ccc{y} and \ccc{e2} is constructed from \ccc{z}.}
  
\end{ccRefClass}

%% +--------------------------------------------------------+

\begin{ccRefClass}{Fourtuple<T>}
  
  \ccDefinition The \ccRefName\ class stores a homogeneous (same type)
  fourtuple of objects of type \ccc{T}.  A \ccRefName\ is much like a
  container, in that it "owns" its elements. It is not actually a model of
  container, though, because it does not support the standard methods (such as
  iterators) for accessing the elements of a container.

  This class is DEPRECATED, and will be removed in some future CGAL release.
  Please use \ccc{boost::array} instead.

  \ccInclude{CGAL/Fourtuple.h}
  
  \ccRequirements \ccc{T} must be \ccc{Assignable}.

  %\ccSetThreeColumns{T*}{next_link ;}{}
  \ccThree{result_type;;}{operator()(argument a) ;;}{}

  \ccTypes
  \ccTypedef{typedef T value_type;}{}

  \ccHeading{Variables}
  \ccVariable{T e0;}{first element}
  \ccGlue
  \ccVariable{T e1;}{second element}
  \ccGlue
  \ccVariable{T e2;}{third element}
  \ccGlue
  \ccVariable{T e3;}{fourth element}

  \ccCreation
  \ccCreationVariable{t}
  
  \ccConstructor{Fourtuple();}{introduces a \ccRefName\ using the default
    constructor of the elements.}
  
  \ccConstructor{Fourtuple(T x, T y, T z, T t);}{constructs a \ccRefName\ such
    that \ccc{e0} is constructed from \ccc{x}, \ccc{e1} from \ccc{y},
    \ccc{e2} from \ccc{z} and \ccc{e3} from \ccc{t}.}
  
\end{ccRefClass}

%% +--------------------------------------------------------+

\begin{ccRefClass}{Sixtuple<T>}
  
  \ccDefinition The \ccRefName\ class stores a homogeneous (same type)
  sixtuple of objects of type \ccc{T}.  A \ccRefName\ is much like a
  container, in that it "owns" its elements. It is not actually a model of
  container, though, because it does not support the standard methods (such as
  iterators) for accessing the elements of a container.

  This class is DEPRECATED, and will be removed in some future CGAL release.
  Please use \ccc{boost::array} instead.

  \ccInclude{CGAL/Sixtuple.h}
  
  \ccRequirements \ccc{T} must be \ccc{Assignable}.

  %\ccSetThreeColumns{T*}{next_link ;}{}
  \ccThree{result_type;;}{operator()(argument a) ;;}{}

  \ccTypes
  \ccTypedef{typedef T value_type;}{}

  \ccHeading{Variables}
  \ccVariable{T e0;}{first element}
  \ccGlue
  \ccVariable{T e1;}{second element}
  \ccGlue
  \ccVariable{T e2;}{third element}
  \ccGlue
  \ccVariable{T e3;}{fourth element}
  \ccGlue
  \ccVariable{T e4;}{fifth element}
  \ccGlue
  \ccVariable{T e5;}{sixth element}

  \ccCreation
  \ccCreationVariable{t}
  
  \ccConstructor{Sixtuple();}{introduces a \ccRefName\ using the default
    constructor of the elements.}
  
  \ccConstructor{Sixtuple(T x, T y, T z, T t, T u, T v);}{constructs a
    \ccRefName\ such that \ccc{e0} is constructed from \ccc{x}, \ccc{e1} from
    \ccc{y}, \ccc{e2} from \ccc{z}, \ccc{e3} from \ccc{t}, \ccc{e4} from
    \ccc{u} and \ccc{e5} from \ccc{v}.}
  
\end{ccRefClass}

%% +--------------------------------------------------------+

\begin{ccRefClass}{Triple<T1, T2, T3>}
  
  \ccDefinition The Triple class is an extension of \ccc{std::pair}.
  \ccRefName\ is a heterogeneous triple: it holds one object of type
  \ccc{T1}, one of type \ccc{T2}, and one of type \ccc{T3}.  A
  \ccRefName\ is much like a container, in that it "owns" its
  elements. It is not actually a model of container, though, because
  it does not support the standard methods (such as iterators) for
  accessing the elements of a container.

  This class is NOT RECOMMENDED anymore.  We recommend that you use
  \ccc{boost::tuple} or \ccc{boost::array} instead for new uses.

  \ccInclude{CGAL/utility.h}
  
  \ccRequirements \ccc{T1}, \ccc{T2} and \ccc{T3} must be \ccc{Assignable}.
  Additional operations have additional requirements.

  %\ccSetThreeColumns{T*}{next_link ;}{}
  \ccThree{result_type;;}{operator()(argument a) ;;}{}

  \ccTypes
  \ccTypedef{typedef T1 first_type;}{}
  \ccGlue
  \ccTypedef{typedef T2 second_type;}{}
  \ccGlue
  \ccTypedef{typedef T3 third_type;}{}

  \ccHeading{Variables}
  \ccVariable{T1 first;}{first element.  Please access it using \ccc{get<0>()}.}
  \ccGlue
  \ccVariable{T2 second;}{second element.  Please access it using \ccc{get<1>()}.}
  \ccGlue
  \ccVariable{T3 third;}{third element.  Please access it using \ccc{get<2>()}.}

  \ccCreation
  \ccCreationVariable{t}
  
  \ccConstructor{Triple();}{introduces a triple using the default
    constructor of the three elements.}
  
  \ccConstructor{Triple(T1 x, T2 y, T3 z);}{constructs a triple such
    that \ccc{first} is constructed from \ccc{x}, \ccc{second} is
    constructed from \ccc{y}, and \ccc{third} is constructed from
    \ccc{z}.}
  
  \ccConstructor{template <class U, class V, class W> Triple(U u, V v,
    W w);} {constructs a triple such that \ccc{first} is constructed
    from \ccc{u}, \ccc{second} is constructed from \ccc{v}, and
    \ccc{third} is constructed from \ccc{w}. \ccRequire Proper
    conversion operators exist from \ccc{U} to \ccc{T1}, \ccc{V} to
    \ccc{T2}, and \ccc{W} to \ccc{T3}.}

  \ccMemberFunction{template <int i> T get();}
    {Gives access to \ccc{first}, \ccc{second} or \ccc{third} whenever
     \ccc{i} is 0, 1 or 2, via a, potentially const, reference.
     Note: \ccc{T} stands for \ccc{T1}, \ccc{T2} or \ccc{T3} depending
     on \ccc{i}.}

  \ccFunction{template <class T1, class T2, class T3> bool
    operator<(Triple<T1, T2, T3> x, Triple<T1, T2, T3> y);} {The
    comparison operator. It uses lexicographic comparison: the return
    value is true if the first element of \ccc{x} is less than the
    first element of \ccc{y}, and false if the first element of
    \ccc{y} is less than the first element of \ccc{x}. If neither of
    these is the case, then it returns true if the second element of
    \ccc{x} is less than the second element of \ccc{y}, and false if
    the second element of \ccc{y} is less than the second element of
    \ccc{x}.  If neither of these is the case, then it returns the
    result of comparing the third elements of \ccc{x} and \ccc{y}.
    This operator may only be used if \ccc{T1}, \ccc{T2} and \ccc{T3}
    define the comparison operator.}

  \ccFunction{template <class T1, class T2, class T3> bool
    operator==(Triple<T1, T2, T3> x, Triple<T1, T2, T3> y);} {The
    equality operator. The return value is true if and only the first
    elements of \ccc{x} and \ccc{y} are equal, the second elements of
    \ccc{x} and \ccc{y} are equal, and the third elements of \ccc{x}
    and \ccc{y} are equal.  This operator may only be used if
    \ccc{T1}, \ccc{T2} and \ccc{T3} define the equality operator.}
  
  \ccFunction{template <class T1, class T2, class T3> Triple<T1, T2,
    T3> make_triple(T1 x, T2 y, T3 z);} {Equivalent to
    \ccStyle{Triple<T1, T2, T3>(x, y, z)}.}
  
  \ccFunction{template <class T1, class T2, class T3> Triple<T1, T2,
    T3> make_tuple(T1 x, T2 y, T3 z);} {Equivalent to
    \ccStyle{Triple<T1, T2, T3>(x, y, z)}.}

\end{ccRefClass}

%% +--------------------------------------------------------+

\begin{ccRefClass}{Quadruple<T1, T2, T3, T4>}
  
  \ccDefinition The Quadruple class is an extension of
  \ccc{std::pair}.  \ccRefName\ is a heterogeneous quadruple: it holds
  one object of type \ccc{T1}, one of type \ccc{T2}, one of type
  \ccc{T3}, and one of type \ccc{T4}.  A \ccRefName\ is much like a
  container, in that it ``owns'' its elements. It is not actually a
  model of container, though, because it does not support the standard
  methods (such as iterators) for accessing the elements of a
  container.

  This class is NOT RECOMMENDED anymore.  We recommend that you use
  \ccc{boost::tuple} or \ccc{boost::array} instead for new uses.

  \ccInclude{CGAL/utility.h}
  
  \ccRequirements \ccc{T1}, \ccc{T2}, \ccc{T3} and \ccc{T4} must be
  \ccc{Assignable}. Additional operations have additional requirements.

  %\ccSetThreeColumns{T*}{next_link ;}{}
  \ccThree{result_type;;}{operator()(argument a) ;;}{}

  \ccTypes
  \ccTypedef{typedef T1 first_type;}{}
  \ccGlue
  \ccTypedef{typedef T2 second_type;}{}
  \ccGlue
  \ccTypedef{typedef T3 third_type;}{}
  \ccGlue
  \ccTypedef{typedef T4 fourth_type;}{}

  \ccHeading{Variables}
  \ccVariable{T1 first;}{first element.  Please access it using \ccc{get<0>()}.}
  \ccGlue
  \ccVariable{T2 second;}{second element.  Please access it using \ccc{get<1>()}.}
  \ccGlue
  \ccVariable{T3 third;}{third element.  Please access it using \ccc{get<2>()}.}
  \ccGlue
  \ccVariable{T4 fourth;}{fourth element.  Please access it using \ccc{get<3>()}.}

  \ccCreation
  \ccCreationVariable{t}
  
  \ccConstructor{Quadruple();} {introduces a quadruple using the
    default constructor of the four elements.}
  
  \ccConstructor{Quadruple(T1 x, T2 y, T3 z, T4 w);} {constructs a
    quadruple such that \ccc{first} is constructed from \ccc{x},
    \ccc{second} is constructed from \ccc{y}, \ccc{third} is
    constructed from \ccc{z}, and \ccc{fourth} is constructed from
    \ccc{w}.}
  
  \ccConstructor{template <class U, class V, class W, class X>
    Quadruple(U u, V v, W w, X x);} {constructs a quadruple such that
    \ccc{first} is constructed from \ccc{u}, \ccc{second} is
    constructed from \ccc{v}, \ccc{third} is constructed from \ccc{w},
    and \ccc{fourth} is constructed from \ccc{x}. \ccRequire Proper
    conversion operators exist from \ccc{U} to \ccc{T1}, \ccc{V} to
    \ccc{T2}, \ccc{W} to \ccc{T3}, and \ccc{X} to \ccc{T4}.  }

  \ccMemberFunction{template <int i> T get();}
    {Gives access to \ccc{first}, \ccc{second}, \ccc{third} or \ccc{fourth}
     whenever \ccc{i} is 0, 1, 2 or 3, via a, potentially const, reference.
     Note: \ccc{T} stands for \ccc{T1}, \ccc{T2}, \ccc{T3} or \ccc{T4}
     depending on \ccc{i}.}
   
  \ccFunction{template <class T1, class T2, class T3, class T4> bool
    operator<(Quadruple<T1, T2, T3, T4> x, Quadruple<T1, T2, T3, T4>
    y);} {The comparison operator. It uses lexicographic comparison:
    the return value is true if the first element of \ccc{x} is less
    than the first element of \ccc{y}, and false if the first element
    of \ccc{y} is less than the first element of \ccc{x}. If neither
    of these is the case, then it returns true if the second element
    of \ccc{x} is less than the second element of \ccc{y}, and false
    if the second element of \ccc{y} is less than the second element
    of \ccc{x}. If neither of these is the case, then it returns true
    if the third element of \ccc{x} is less than the third element of
    \ccc{y}, and false if the third element of \ccc{y} is less than
    the third element of \ccc{x}.  If neither of these is the case,
    then it returns the result of comparing the fourth elements of
    \ccc{x} and \ccc{y}. This operator may only be used if \ccc{T1},
    \ccc{T2}, \ccc{T3}, and \ccc{T4} define the comparison operator.}
  
  \ccFunction{template <class T1, class T2, class T3, class T4> bool
    operator==(Quadruple<T1, T2, T3, T4> x, Quadruple<T1, T2, T3, T4>
    y);} {The equality operator. The return value is true if and only
    the first elements of \ccc{x} and \ccc{y} are equal, the second
    elements of \ccc{x} and \ccc{y} are equal, the third elements of
    \ccc{x} and \ccc{y} are equal, and the fourth elements of \ccc{x}
    and \ccc{y} are equal.  This operator may only be used if
    \ccc{T1}, \ccc{T2}, \ccc{T3}, and \ccc{T4} define the equality
    operator.}
  
  \ccFunction{template <class T1, class T2, class T3, class T4>
    Quadruple<T1, T2, T3, T4> make_quadruple(T1 x, T2 y, T3 z, T4 w);}
  {Equivalent to \ccStyle{Quadruple<T1, T2, T3, T4>(x, y, z, w)}.}
  
  \ccFunction{template <class T1, class T2, class T3, class T4>
    Quadruple<T1, T2, T3, T4> make_tuple(T1 x, T2 y, T3 z, T4 w);}
  {Equivalent to \ccStyle{Quadruple<T1, T2, T3, T4>(x, y, z, w)}.}

\end{ccRefClass}

%% +=========================================================================+

\begin{ccRefClass}{Boolean_tag<bool value>}

\ccDefinition

Depending on \ccc{bool value} the class \ccRefName\ indicates that
something is \ccc{true} or \ccc{false} respectively.

\ccInclude{CGAL/tags.h}

\ccConstants

\ccVariable{static const bool value;}{}

\ccSeeAlso
\ccRefIdfierPage{CGAL::Tag_true} \\
\ccRefIdfierPage{CGAL::Tag_false}

\end{ccRefClass}


\begin{ccRefClass}{Tag_true}

\ccDefinition

The typedef \ccRefName\ is \ccc{Boolean_tag<true>}.
It is used to indicate, for example,
that a certain feature is available in a class.

\ccInclude{CGAL/tags.h}

\ccVariable{static const bool value;}{ is \ccc{true} }

\ccSeeAlso
\ccRefIdfierPage{CGAL::Boolean_tag<bool value>} \\
\ccRefIdfierPage{CGAL::Tag_false}

\end{ccRefClass}


\begin{ccRefClass}{Tag_false}

\ccDefinition

The typedef \ccRefName\ is \ccc{Boolean_tag<false>}.
It is used to indicate, for example,
that a certain feature is not available in a class.

\ccInclude{CGAL/tags.h}

\ccVariable{static const bool value;}{ is \ccc{false} }

\ccSeeAlso
\ccRefIdfierPage{CGAL::Boolean_tag<bool value>} \\
\ccRefIdfierPage{CGAL::Tag_true}

\end{ccRefClass}

\input{STL_Extension_ref/Null_functor.tex}
\input{STL_Extension_ref/Null_tag.tex}

%% +--------------------------------------------------------+
\ccParDims

%% EOF