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% | Reference manual page: is_simple_2.tex
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% | 21.06.2001   Author
% | Package: Polygon
% | 
\RCSdef{\RCSissimpleRev}{$Id$}
\RCSdefDate{\RCSissimpleDate}{$Date$}
% |
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\begin{ccRefFunction}{is_simple_2} 

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

\ccDefinition
  
The function \ccRefName\ computes if a polygon is simple, that is, if the edges 
do not intersect, except consecutive edges in their common vertex.

\ccInclude{CGAL/Polygon_2_algorithms.h}

\ccGlobalFunction{
template <class ForwardIterator, class Traits>
inline bool is_simple_2(ForwardIterator first, ForwardIterator last,
                      Traits traits);
}
{
Checks if the polygon defined by the
iterator range \ccc{first} \ldots\ \ccc{last} is simple.
}


\ccHeading{Requirements}
\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
\begin{enumerate}
    \item \ccc{Traits} is a model of the concept 
	  \ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
	  Only the following members of this traits class are used:
          \begin{itemize}
            \item \ccc{Point_2}
            \item \ccc{Less_xy_2}
            \item \ccc{Orientation_2}
            \item \ccc{less_xy_2_object()}
            \item \ccc{orientation_2_object()}
          \end{itemize}
    \item The value type of \ccc{ForwardIterator} must be \ccc{Traits::Point_2},
\end{enumerate}

\ccImplementation

The simplicity test is implemented by means of a plane sweep algorithm.
The algorithm is quite robust when used with inexact number types.
The running time is O(n log n), where n is the number of vertices of the
polygon.

\ccSeeAlso

\ccRefIdfierPage{PolygonTraits_2} \\
\ccRefIdfierPage{CGAL::Polygon_2<PolygonTraits_2, Container>} \\

%% \ccIncludeExampleCode{Polygon/is_simple_2_prog.cpp}

\end{ccRefFunction}

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