\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.2 - 2D Arrangements
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Concepts

conceptArrangementBasicTraits_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...
 
conceptArrangementLandmarkTraits_2
 The concept ArrangementLandmarkTraits_2 refines the general traits concept by adding operations needed for the landmarks point-location strategy, namely - approximating points and connecting points with a simple \( x\)-monotone curve. More...
 
conceptArrangementOpenBoundaryTraits_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...
 
conceptArrangementTraits_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...
 
conceptArrangementXMonotoneTraits_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...
 
conceptOverlayTraits
 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...