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CGAL 5.3 - 2D Arrangements
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CGAL 5.3 - 2D Arrangements
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#include <CGAL/Arr_polyline_traits_2.h>
CGAL::Arr_polycurve_traits_2< SegmentTraits_2 >.
The traits class Arr_polyline_traits_2 handles piecewise linear curves, commonly referred to as polylines.
Each polyline is a chain of segments, where each two neighboring segments in the chain share a common endpoint; that is, the polyline is continuous. Furthermore, the target of the \(i\)th segement of a polyline has to coincide with the source of the \(i+1\)st segment; that is, the polyline has to be well-oriented. Note that it is possible to construct general polylines that are neither continuous nor well-oriented, as it is impossible to enforce this precondition (using the set of predicates required by the relevant concepts, see below). However, such polylines cannot be used for the actual computation of arrangements. The traits class template exploits the functionality of the SegmentTraits_2 template-parameter to handle the segments that compose the polyline curves.
The type substituting the template parameter SegmentTraits_2 when the template Arr_polyline_traits_2 is instantiated must be a model of the concepts
ArrangementTraits_2,ArrangementDirectionalXMonotoneTraits_2,ArrangementConstructXMonotoneCurveTraits_2.If, in addition, the GeometryTraits_2 models the concept ArrangementApproximateTraits_2 then Arr_polycurve_traits_2 models this concept as well. The same holds for the concept ArrangementOpenBoundaryTraits_2. If no type is provided, then Arr_segment_traits_2 (instantiated with Exact_predicates_exact_constructions_kernel as the kernel) is used. Otherwise, Arr_Bezier_curve_traits_2<RatKernel, AlgKernel, NtTraits>, Arr_circle_segment_traits_2<Kernel>, Arr_conic_traits_2<RatKernel, AlgKernel, NtTraits> Arr_linear_traits_2<Kernel> Arr_non_caching_segment_traits_2<Kernel>, Arr_segment_traits_2<Kernel>, or any other model of the concepts above can be used.
The number type used by the injected segment traits should support exact rational arithmetic (that is, the number type should support the arithmetic operations \( +\), \( -\), \( \times\) and \( \div\) carried out without loss of precision), in order to avoid robustness problems, although other inexact number types could be used at the user's own risk.
A polyline that comprises \(n > 0\) segments has \( n+1 \) points, and they are represented as objects of type SegmentTraits_2::Point_2. Since the notion of a vertex is reserved to 0-dimensional elements of an arrangement, we use, in this context, the notion of points in order to refer to the vertices of a polyline. For example, an arrangement induced by a single non-self intersecting polyline has exactly two vertices regardless of the number of points. Finally, the types Segment_2 and X_monotone_segment_2 nested in Arr_polyline_traits_2 are nothing but SegmentTraits_2::Curve_2 and SegmentTraits_2::X_monotone_curve_2, respectively.
A note on Backwards compatibility
In CGAL version 4.2 (and earlier) any object of the X_monotone_curve_2 type nested in Arr_polyline_traits_2 maintained a direction invariant; namely, its vertices were ordered in an ascending lexicographical \((xy)\)-order. This restriction is no longer imposed and X_monotone_curve_2 can be now directed either from right-to-left or left-to-right. If you wish to maintain a left-to-right orientations of the \(x\)-monotone polylines, set the macro CGAL_ALWAYS_LEFT_TO_RIGHT to 1 before any CGAL header is included.
ArrangementDirectionalXMonotoneTraits_2
ArrangementConstructXMonotoneCurveTraits_2
ArrangementApproximateTraits_2 (if the type that substitutes the template parameter SegmentTraits_2 models the concept as well)
Arr_polycurve_traits_2<SubcurveTraits_2> Arr_Bezier_curve_traits_2<RatKernel, AlgKernel, NtTraits> Arr_circle_segment_traits_2<Kernel> Arr_conic_traits_2<RatKernel, AlgKernel, NtTraits> Arr_linear_traits_2<Kernel> Arr_non_caching_segment_traits_2<Kernel> Arr_segment_traits_2<Kernel> CGAL_ALWAYS_LEFT_TO_RIGHT Classes | |
| class | Construct_curve_2 |
| Construction functor of a general (not necessarily \(x\)-monotone) polyline. More... | |
| class | Construct_x_monotone_curve_2 |
| Construction functor of \(x\)-monotone polyline. More... | |
| class | Push_back_2 |
| Functor to augment a polyline by either adding a vertex or a segment at the back. More... | |
| class | Push_front_2 |
| Functor to augment a polyline by either adding a vertex or a segment at the front. More... | |
Types | |
| typedef SegmentTraits_2 | Segment_traits_2 |
| typedef SegmentTraits_2::Point_2 | Point_2 |
| typedef SegmentTraits_2::Curve_2 | Segment_2 |
| typedef SegmentTraits_2::X_monotone_curve_2 | X_monotone_segment_2 |
Accessing Functor Objects | |
| Construct_curve_2 | construct_curve_2_object () const |
| Construct_x_monotone_curve_2 | construct_x_monotone_curve_2_object () const |
| Push_back_2 | push_back_2_object () const |
| Push_front_2 | push_front_2_object () const |
Additional Inherited Members | |
 Public Types inherited from CGAL::Arr_polycurve_traits_2< SegmentTraits_2 > | |
| typedef SegmentTraits_2 ::Point_2 | Point_2 |
| typedef SegmentTraits_2 ::Curve_2 | Subcurve_2 |
| typedef SegmentTraits_2 ::X_monotone_curve_2 | X_monotone_subcurve_2 |
| Public Member Functions inherited from CGAL::Arr_polycurve_traits_2< SegmentTraits_2 > | |
| Construct_curve_2 | construct_curve_2_object () const |
| Construct_x_monotone_curve_2 | construct_x_monotone_curve_2_object () const |
| Number_of_points_2 | number_of_points_2_object () const |
| Push_back_2 | push_back_2_object () const |
| Push_front_2 | push_front_2_object () const |
| Make_x_monotone_2 | make_x_monotone_2_object () const |
1.8.13