CGAL 4.7 - 2D Arrangements: Traits Concepts

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 2D Arrangements

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## Concepts

concept | ArrangementApproximateTraits_2
| The concept `ArrangementApproximateTraits_2` refines the basic traits concept `ArrangementBasicTraits_2`. A model of this concept is able to approximate a point. More...
concept | ArrangementBasicTraits_2

The concept `ArrangementBasicTraits_2` defines the minimal set of geometric predicates needed for the construction and maintenance of objects of the class `Arrangement_2`, as well as performing simple queries (such as point-location queries) on such arrangements. More...

concept | ArrangementConstructXMonotoneCurveTraits_2
| The concept `ArrangementConstructXMonotoneCurveTraits_2` refines the basic traits concept `ArrangementBasicTraits_2`. A model of this concept is able to construct an \( x\)-monotone curve from two points. More...
concept | ArrangementLandmarkTraits_2

The concept `ArrangementLandmarkTraits_2` refines the traits concepts `ArrangementApproximateTraits_2` and `ArrangementConstructXMonotoneCurveTraits_2`. The type of an arrangement associated with the landmark point-location strategy (see `CGAL::Arr_landmarks_point_location`) must be an instance of the `CGAL::Arrangement_2<Traits,Dcel>` class template, where the Traits parameter is substituted with a model of this concept. More...

concept | ArrangementOpenBoundaryTraits_2

Several predicates are required to handle \( x\)-monotone curves that approach infinity and thus approach the boundary of the parameter space. These predicates are sufficient to handle not only curves embedded in an unbounded parameter space, but also curves embedded in a bounded parameter space with open boundaries. Models of the concept `ArrangementOpenBoundaryTraits_2` handle curves that approach the boundary of a parameter space. This concept refines the concept `ArrangementBasicTraits_2`. The arrangement template instantiated with a traits class that models this concept can handle \( x\)-monotone curves that are unbounded in any direction. The concept `ArrangementOpenBoundaryTraits_2`, nontheless, also supports planar \( x\)-monotone curves that reach the boundary of an open yet bounded parameter space. More...

concept | ArrangementTraits_2

The concept `ArrangementTraits_2` allows the construction of arrangement of general planar curves. Models of this concept are used by the free `CGAL::insert()` functions of the arrangement package and by the `CGAL::Arrangement_with_history_2` class. More...

concept | ArrangementXMonotoneTraits_2

The concept `ArrangementXMonotoneTraits_2` refines the basic arrangement-traits concept. A model of this concept is able to handle \( x\)-monotone curves that intersect in their interior (and points that coincide with curve interiors). This is necessary for constructing arrangements of sets of intersecting \( x\)-monotone curves. More...

concept | OverlayTraits
| A model for the `OverlayTraits` should be able to operate on records (namely, vertices, halfedges and faces) of two input Dcel classes, named `Dcel_A` and `Dcel_B`, and construct the records of an output Dcel class, referred to as `Dcel_R`. More...