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% | Reference manual page: ConstrainedTriangulationTraits_2.tex
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% | 05.02.2002   Mariette Yvinec
% | Package: Triangulation_2
% | 
\RCSdef{\RCSConstrainedTriangulationTraitsRev}{$Id$}
\RCSdefDate{\RCSConstrainedTriangulationTraitsDate}{$Date$}
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\begin{ccRefConcept}{ConstrainedTriangulationTraits_2}

%% \ccHtmlCrossLink{}     %% add further rules for cross referencing links
%% \ccHtmlIndexC[concept]{} %% add further index entries

\ccDefinition
  
The concept \ccRefName\ defines the requirements for the geometric
traits class of a constrained triangulation
( \ccc{Constrained_Triangulation_2<Traits,Tds,Itag>})
that supports intersections of input constraints (i. e.
when the template parameter \ccc{Itag} is instantiated
by one of the tag classes \ccc{Exact_intersections_tag} or
\ccc{Exact_predicates_tag}). This concept refines the concept
\ccc{TriangulationTraits_2}, adding requirements for function objects
to compute the intersection points of two constraints.
When \ccc{Exact_predicates_tag} is used, the 
traits class is
also required to provide  additional types
to compute the squared distance between a point and a line


\ccRefines
\ccc{TriangulationTraits_2} 


\ccTypes

\ccNestedType{Intersect_2}{A function object whose operator()
computes the intersection of two segments : \\
\ccc{Object_2 operator()(Segment_2 s1, Segment_2 s2);}
Returns the intersection of \ccc{s1} and \ccc{s2}.}

When the constrained triangulation is instantiated with 
the intersection tag \ccc{Exact_predicates_tag},
the used algorithm needs to be able to compare some
distances between points and lines and the following
types are further required.
\ccNestedType{RT}{A number type supporting the comparison operator
\ccc{<}.}
\ccNestedType{Line_2}{The line type.}
\ccGlue
\ccNestedType{Construct_line_2} {A function object whose operator()
constructs a line from two points : \\
\ccc{Line_2 operator()(Point_2 p1, Point_2 p2)}.}
\ccGlue
\ccNestedType{Compute_squared_distance_2}{A function object with an
operator() designed to compute the squared distance between
a line  and a point : 
\ccc{RT operator()(Point_2 p1, Line_2);} Return the squared distance
between \ccc{p} and \ccc{l}.}


\ccCreationVariable{traits}  %% choose variable name

\ccHeading{Access to constructor object}
\ccMethod{Intersect_2  intersect_2_object();}{}
\ccMethod{Construct_line_2 construct_line_2_object();}{required when
the intersection tag is \ccc{Exact_predicates_tag}.}
\ccMethod{Compute_squared_distance_2
compute_squared_distance_2_object();}
{required when
the intersection tag is \ccc{Exact_predicates_tag}.}


\ccHasModels
The kernels of \cgal\ are models for this traits class.



\ccSeeAlso
\ccc{TriangulationTraits_2} \\
\ccc{ConstrainedDelaunayTriangulationTraits_2} \\
\ccc{CGAL:Constrained_Triangulation_2<Traits,Tds,Itag>}

%\ccExample

%A short example program.
%Instead of a short program fragment, a full running program can be
%included using the 
%\verb|\ccIncludeExampleCode{Package/ConstrainedTriangulationPlusTraits_2_prog.cpp}| 
%macro. The program example would be part of the source code distribution and
%also part of the automatic test suite.

%\begin{ccExampleCode}
%void your_example_code() {
%}
%\end{ccExampleCode}

%% \ccIncludeExampleCode{Package/ConstrainedTriangulationPlusTraits_2_prog.cpp}

\end{ccRefConcept}

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