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@ -30,7 +30,7 @@ CGAL_BEGIN_NAMESPACE
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// same as |convex_hull_2(first,last,result)|.
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// {\sc traits}: operates on |Traits::Point_2| using |Traits::Less_xy_2|,
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// |Traits::Less_yx_2|, and |Traits::Left_turn_2|.
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// |Traits::Less_yx_2|, |Traits::Equal_2| and |Traits::Left_turn_2|.
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template <class ForwardIterator, class OutputIterator, class Traits>
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OutputIterator
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ch_akl_toussaint(ForwardIterator first, ForwardIterator last,
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@ -30,7 +30,7 @@ CGAL_BEGIN_NAMESPACE
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// same as |convex_hull_2(first,last,result)|. {\sc traits}:
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// uses |Traits::Point_2|, |Traits::Less_signed_distance_to_line_2|,
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// |Traits::Left_turn_2|, and |Traits::Less_xy_2|.
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// |Traits::Left_turn_2|,, |Traits::Equal_2| and |Traits::Less_xy_2|.
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template <class InputIterator, class OutputIterator, class Traits>
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OutputIterator
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ch_bykat(InputIterator first, InputIterator last,
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@ -30,7 +30,7 @@ CGAL_BEGIN_NAMESPACE
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// same as |convex_hull_2(first,last,result)|. {\sc traits}: uses
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// |Traits::Point_2|, |Traits::Less_signed_distance_to_line_2|,
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// |Traits::Left_turn_2|, and |Traits::Less_xy_2|.
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// |Traits::Left_turn_2|, |Traits::Equal_2| and |Traits::Less_xy_2|.
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template <class InputIterator, class OutputIterator, class Traits>
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OutputIterator
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ch_eddy(InputIterator first, InputIterator last,
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@ -36,7 +36,7 @@ CGAL_BEGIN_NAMESPACE
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// {\it Precondition:} The points in [|first|,|last|) are sorted with respect
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// to $pq$ and the range [|first|,|last|) contains at least two different
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// points.
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// {\sc traits}: uses |Traits::Left_turn_2| operating on the
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// {\sc traits}: uses |Traits::Left_turn_2| and |Traits::Equal_2| operating on the
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// point type |Traits::Point_2|.
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template <class BidirectionalIterator, class OutputIterator, class Traits>
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OutputIterator
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@ -37,7 +37,7 @@ CGAL_BEGIN_NAMESPACE
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// {\it Precondition:} |start_p| and |stop_p| are extreme points with respect
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// to the points in the range [|first|,|last|) and |stop_p| is an element of
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// range [|first|,|last|).
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// {\sc traits}: uses |Traits::Point_2| $\equiv$ |Point|, and
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// {\sc traits}: uses |Traits::Point_2| $\equiv$ |Point|, |Traits::Equal_2| and
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// |Traits::Less_rotate_ccw_2|.
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template <class ForwardIterator, class OutputIterator,
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class Point, class Traits>
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@ -62,7 +62,7 @@ ch_jarvis_march(ForwardIterator first, ForwardIterator last,
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// same as |convex_hull_2(first,last,result)|.
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// {\sc traits}: uses |Traits::Point_2|, |Traits::Less_rotate_ccw_2|, and
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// {\sc traits}: uses |Traits::Point_2|, |Traits::Less_rotate_ccw_2|, |Traits::Equal_2| and
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// |Traits::Less_xy_2|.
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template <class ForwardIterator, class OutputIterator, class Traits>
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OutputIterator
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@ -111,7 +111,7 @@ convex_hull_points_2(ForwardIterator first, ForwardIterator last,
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// {\it Preconditions:}
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// [|first|,|last|) does not contain |result|.
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// {\sc traits}: operates on |Traits::Point_2| using |Traits::Less_xy_2|,
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// |Traits::Less_yx_2|, and |Traits::Left_turn_2|.
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// |Traits::Equal_2|, |Traits::Less_yx_2|, and |Traits::Left_turn_2|.
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template <class InputIterator, class OutputIterator, class Traits>
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inline
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OutputIterator
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@ -140,7 +140,7 @@ convex_hull_2(ForwardIterator first, ForwardIterator last,
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// {\it Preconditions:}
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// [|first|,|last|) does not contain |result|.
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// {\sc traits}: operates on |Traits::Point_2| using |Traits::Less_xy_2|
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// and |Traits::Left_turn_2|.
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// |Traits::Equal_2| and |Traits::Left_turn_2|.
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template <class InputIterator, class OutputIterator, class Traits>
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inline
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OutputIterator
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@ -171,8 +171,8 @@ lower_hull_points_2(ForwardIterator first, ForwardIterator last,
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// not included.
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// {\it Preconditions:}
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// [|first|,|last|) does not contain |result|.
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// {\sc traits}: operates on |Traits::Point_2| using |Traits::Less_xy_2|
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// and |Traits::Left_turn_2|.
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// {\sc traits}: operates on |Traits::Point_2| using |Traits::Less_xy_2|,
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// |Traits::Equal_2| and |Traits::Left_turn_2|.
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template <class InputIterator, class OutputIterator, class Traits>
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inline
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OutputIterator
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@ -31,7 +31,7 @@ CGAL_BEGIN_NAMESPACE
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// returns true, if the point elements in [|first|,|last|) form a
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// counterclockwise oriented strongly convex polygon. Strongly means,
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// there are no three collinear points.
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// {\sc traits}: uses |Traits::Left_turn_2| and |Traits::Less_xy_2|.
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// {\sc traits}: uses |Traits::Left_turn_2|, |Traits::Equal_2| and |Traits::Less_xy_2|.
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template <class ForwardIterator, class Traits>
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bool
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is_ccw_strongly_convex_2( ForwardIterator first, ForwardIterator last,
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@ -55,7 +55,7 @@ is_ccw_strongly_convex_2( ForwardIterator first, ForwardIterator last )
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// returns true, if the point elements in [|first|,|last|) form a
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// clockwise oriented strongly convex polygon. Strongly means, there are
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// no three collinear points.
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// {\sc traits}: uses |Traits::Left_turn_2| and |Traits::Less_xy_2|.
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// {\sc traits}: uses |Traits::Left_turn_2|, |Traits::Equal_2| and |Traits::Less_xy_2|.
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template <class ForwardIterator, class Traits>
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bool
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is_cw_strongly_convex_2( ForwardIterator first, ForwardIterator last,
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