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@ -29,7 +29,7 @@ Currently, the \ccc{Polygon_2} class is a nice wrapper around the algorithms,
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but little more. Especially, computed values are not cached.
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but little more. Especially, computed values are not cached.
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That is, when the \ccc{is_simple()} member function is called twice or more,
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That is, when the \ccc{is_simple()} member function is called twice or more,
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the result is computed each time anew. It is possible to set a preprocessor flag
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the result is computed each time anew. It is possible to set a preprocessor flag
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to alter this behaviour. In the future, caching will become the default.
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to alter this behavior. In the future, caching will become the default.
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\section{Example}
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\section{Example}
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@ -19,7 +19,7 @@
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\ccDefinition
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\ccDefinition
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The class \ccRefName\ implements polygons.
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The class \ccRefName\ implements polygons.
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The \ccRefName\ is parameterised by a traits class and a container class.
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The \ccRefName\ is parameterized by a traits class and a container class.
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The latter can be any class that fulfills the requirements for an STL container.
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The latter can be any class that fulfills the requirements for an STL container.
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It defaults to the vector class.
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It defaults to the vector class.
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@ -199,7 +199,7 @@ circulators and iterators that allow to traverse the vertices and edges.
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{ Returns the bottommost vertex of the polygon \ccStyle{p} with the smallest
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{ Returns the bottommost vertex of the polygon \ccStyle{p} with the smallest
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\ccStyle{x}-coordinate. }
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\ccStyle{x}-coordinate. }
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For convenience we provide the following boolean functions:
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For convenience we provide the following Boolean functions:
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\ccThree{Segment_2}{}{\hspace*{10cm}}
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\ccThree{Segment_2}{}{\hspace*{10cm}}
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\ccMethod{bool is_counterclockwise_oriented() const;}
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\ccMethod{bool is_counterclockwise_oriented() const;}
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@ -41,7 +41,7 @@ returns the area instead of taking it as a parameter.
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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Only the following members of this traits class are used:
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\begin{itemize}
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\begin{itemize}
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\item \ccc{Compute_area_2} : Computes the signed area of the
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\item \ccc{Compute_area_2} : Computes the signed area of the
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@ -34,7 +34,7 @@ Returns the bounding box of the range \ccStyle{[first,last)}.
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%\ccIndexSubitem[C]{bbox_2}{requirements}
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%\ccIndexSubitem[C]{bbox_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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In fact, only the members \ccc{Construct_bbox_2} and
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In fact, only the members \ccc{Construct_bbox_2} and
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\ccc{construct_bbox_2_object} are used.
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\ccc{construct_bbox_2_object} are used.
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\item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_2},
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\item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_2},
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@ -36,7 +36,7 @@ with the smallest \ccStyle{x}-coordinate is taken.
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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In fact, only the members \ccc{Less_yx_2} and
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In fact, only the members \ccc{Less_yx_2} and
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\ccc{less_yx_2_object} are used.
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\ccc{less_yx_2_object} are used.
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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@ -42,7 +42,7 @@ According to the definition points in the bounded region are inside the polygon.
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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Only the following members of this traits class are used:
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\begin{itemize}
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\begin{itemize}
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\item \ccc{Compare_x_2}
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\item \ccc{Compare_x_2}
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@ -33,7 +33,7 @@ const Traits& traits); }
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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Only the following members of this traits class are used:
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\begin{itemize}
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\begin{itemize}
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\item \ccc{Less_xy_2}
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\item \ccc{Less_xy_2}
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@ -39,7 +39,7 @@ range \ccc{first} \ldots\ \ccc{last} is simple.
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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Only the following members of this traits class are used:
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\begin{itemize}
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\begin{itemize}
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\item \ccc{Point_2}
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\item \ccc{Point_2}
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@ -36,7 +36,7 @@ with the smallest \ccStyle{y}-coordinate is taken.
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\ccIndexSubitem[C]{left_vertex_2}{requirements}
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\ccIndexSubitem[C]{left_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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In fact, only the members \ccc{Less_xy_2} and
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In fact, only the members \ccc{Less_xy_2} and
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\ccc{less_xy_2_object} are used.
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\ccc{less_xy_2_object} are used.
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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@ -36,7 +36,7 @@ Orientation orientation_2(ForwardIterator first, ForwardIterator last,
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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Only the following members of this traits class are used:
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\begin{itemize}
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\begin{itemize}
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\item \ccc{Less_xy_2}
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\item \ccc{Less_xy_2}
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@ -35,7 +35,7 @@ Oriented_side oriented_side_2(ForwardIterator first, ForwardIterator last,
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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Only the following members of this traits class are used:
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\begin{itemize}
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\begin{itemize}
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\item \ccc{Less_xy_2}
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\item \ccc{Less_xy_2}
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@ -38,7 +38,7 @@ clockwise polygons. If the polygon is not simple, the area is not well defined.
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\ccIndexSubitem[C]{bottom_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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Only the following members of this traits class are used:
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Only the following members of this traits class are used:
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\begin{itemize}
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\begin{itemize}
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\item \ccc{Compute_area_2} : Computes the signed area of the
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\item \ccc{Compute_area_2} : Computes the signed area of the
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@ -36,7 +36,7 @@ with the largest \ccStyle{y}-coordinate is taken.
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\ccIndexSubitem[C]{right_vertex_2}{requirements}
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\ccIndexSubitem[C]{right_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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In fact, only the members \ccc{Less_xy_2} and
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In fact, only the members \ccc{Less_xy_2} and
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\ccc{less_xy_2_object} are used.
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\ccc{less_xy_2_object} are used.
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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@ -36,7 +36,7 @@ with the largest \ccStyle{x}-coordinate is taken.
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\ccIndexSubitem[C]{top_vertex_2}{requirements}
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\ccIndexSubitem[C]{top_vertex_2}{requirements}
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\begin{enumerate}
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\begin{enumerate}
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\item \ccc{Traits} is a model of the concept
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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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\ccc{PolygonTraits_2}\ccIndexMainItem[c]{PolygonTraits_2}.
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In fact, only the members \ccc{Less_yx_2} and
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In fact, only the members \ccc{Less_yx_2} and
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\ccc{less_yx_2_object} are used.
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\ccc{less_yx_2_object} are used.
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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\item \ccc{ForwardIterator::value_type} should be \ccc{Traits::Point_2},
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