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A model of this concept must define nested Point_2 and X_monotone_curve_2 types, which represent planar points and continuous x-monotone curves (a vertical segment is also considered to be weakly x-monotone), respectively. The x-monotone curves are assumed to be pairwise disjoint in their interiors, so they do not intersect except at their endpoints.
The X_monotone_curve_2 curves of an arrangement are confined to an iso-rectangular area called the parameter space. The iso-rectangule can be unbounded, open, or closed. The set of predicates provided by a model the concept ArrangementBasicTraits_2 is sufficient for constructing arrangements of x-monotone curves that do not reach or approach the boundary of the parameter space. The nature of the input curves, whether they are expected to reach or approach the left, right, bottom, or top side of the boundary of the parameter space, are conveyed through the definition of four additional nested types, namely Left_side_category, Right_side_category, Bottom_side_category, and Top_side_category. Each such type must be convertible to the type Arr_oblivious_side_tag.
| ArrangementBasicTraits_2::Point_2 | |
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models the concept ArrTraits::Point_2.
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| ArrangementBasicTraits_2::X_monotone_curve_2 | |
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models the concept ArrTraits::XMonotoneCurve_2.
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| ArrangementBasicTraits_2::Has_left_category | |
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indicates whether the nested functor Compare_at_x_left_2 is
provided.
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| ArrangementBasicTraits_2::Left_side_category | |
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Must be convertible to Arr_oblivious_side_tag.
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| ArrangementBasicTraits_2::Bottom_side_category | |
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Must be convertible to Arr_oblivious_side_tag.
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| ArrangementBasicTraits_2::Top_side_category | |
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Must be convertible to Arr_oblivious_side_tag.
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| ArrangementBasicTraits_2::Right_side_category | |
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Must be convertible to Arr_oblivious_side_tag.
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| ArrangementBasicTraits_2::Compare_x_2 | |
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models the concept ArrTraits::CompareX_2.
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| ArrangementBasicTraits_2::Compare_xy_2 | |
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models the concept ArrTraits::CompareXy_2.
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| ArrangementBasicTraits_2::Construct_min_vertex_2 | |
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models the concept ArrTraits::ConstructMinVertex_2.
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| ArrangementBasicTraits_2::Construct_max_vertex_2 | |
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models the concept ArrTraits::ConstructMaxVertex_2.
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| ArrangementBasicTraits_2::Is_vertical_2 | |
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models the concept ArrTraits::IsVertical_2.
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| ArrangementBasicTraits_2::Compare_y_at_x_2 | |
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models the concept ArrTraits::CompareYAtX_2.
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| ArrangementBasicTraits_2::Compare_y_at_x_left_2 | |
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models the concept ArrTraits::CompareYAtXLeft_2.
Required only if the Has_left_category category is convertible to
Tag_true.
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| ArrangementBasicTraits_2::Compare_y_at_x_right_2 | |
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models the concept ArrTraits::CompareYAtXRight_2.
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| ArrangementBasicTraits_2::Equal_2 | |
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models the concept ArrTraits::Equal_2.
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| Compare_x_2 | traits.compare_x_2_object () const | |
| Compare_xy_2 | traits.compare_xy_2_object () const | |
| Construct_min_vertex_2 | traits.construct_min_vertex_2_object () const | |
| Construct_max_vertex_2 | traits.construct_max_vertex_2_object () const | |
| Is_vertical_2 | traits.is_vertical_2_object () const | |
| Compare_y_at_x_2 | traits.compare_y_at_x_2_object () const | |
| Compare_y_at_x_left_2 | traits.compare_y_at_x_left_2_object () const | |
| Compare_y_at_x_right_2 | traits.compare_y_at_x_right_2_object () const | |
| Equal_2 | traits.equal_2_object () const | |