mirror of https://github.com/CGAL/cgal
75 lines
2.3 KiB
TeX
75 lines
2.3 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: is_simple_2.tex
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% +------------------------------------------------------------------------+
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% | 21.06.2001 Author
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% | Package: Polygon
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% |
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\RCSdef{\RCSissimpleRev}{$Revision$}
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\RCSdefDate{\RCSissimpleDate}{$Date$}
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% |
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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\begin{ccRefFunction}{is_simple_2}
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[function]{} %% add further index entries
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\ccDefinition
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The function \ccRefName\ computes if a polygon is simple, that is, does not
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self-intersect.
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\ccInclude{CGAL/Polygon_2_algorithms.h}
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\ccGlobalFunction{
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template <class ForwardIterator, class Traits>
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inline bool is_simple_2(ForwardIterator first, ForwardIterator last,
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Traits traits);
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}
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{
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A polygon is called simple if the edges do not intersect, except consecutive
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edge in their common vertex. This function checks if the polygon defined by the
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range \ccc{first} \ldots\ \ccc{last} is simple.
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}
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\ccHeading{Requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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PolygonTraits\_2\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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\begin{itemize}
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\item \ccc{Point_2}
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\item \ccc{Less_xy_2}
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\item \ccc{Orientation_2}
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\item \ccc{less_xy_2}
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\item \ccc{orientation_2}
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\end{itemize}
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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\end{enumerate}
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\ccImplementation
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The simplicity test is implemented by means of a plane sweep algorithm.
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The algorithm is quite robust when used with inexact number types.
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The running time is O(n log n), where n is the number of vertices of the
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polygon.
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\ccSeeAlso
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\ccRefIdfierPage{PolygonTraits_2} \\
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\ccRefIdfierPage{CGAL::Polygon_2<PolygonTraits_2, Container>} \\
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%% \ccIncludeExampleCode{examples/Polygon/is_simple_2_prog.C}
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\end{ccRefFunction}
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% +------------------------------------------------------------------------+
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%%RefPage: end of main body, begin of footer
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% EOF
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% +------------------------------------------------------------------------+
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