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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_caching_polyline_traits_2.h>
CGAL::Arr_polycurve_traits_2< SegmentTraits_2 >.
The traits class Arr_caching_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.
This traits class template serves as an alternative to the more general traits class template Arr_polyline_traits_2<SubcurveTraits_2>, which handles polylines as well. Use this alternative when you need to construct many polylines and every polyline comprises many points. Typically (depending on the substituted Kernel) the geometric objects that compose the polylines (e.g., points) are reference counted, which implies that a copy of a single point amounts to copying a small piece of data (a handle). However, when a polyline is constructed, split, or subdivided into \(x\)-monotone pieces, a large number of points might be copied, which yields with a costly operation. This traits class template uses an internal type to represent polylines, which in turn uses an internal type to represent lines and points that compose polylines. Polylines in the internal representation share the geometric data; thus, only one copy of the geometric objects that compose several polylines reside in memory. Only a shallow copy is performed to carry out each one of the operations above.
CAUTION: If you construct polylines using this traits class template and then insert the polylines into an arrangement, for instance, you must retain the polyline in memory as long as the arrangement is in memory.
| Kernel | a type that represents a geometric kernel. The number type used by the substituted kernel 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. |
| Range | a type that represents a valid range of points. |
A polyline that comprises \(n > 0\) segments has \( n+1 \) points, and they are represented as objects of type Kernel::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.
Arr_polyline_traits_2<SubcurveTraits_2> Classes | |
| class | Construct_curve_2 |
| Construction functor of a polyline. More... | |
| class | Construct_x_monotone_curve_2 |
| Construction functor of a \(x\)-monotone polyline. More... | |
Types | |
| typedef Kernel::Point_2 | Point_2 |
| typedef unspecified_type | X_monotone_curve_2 |
| typedef unspecified_type | Curve_2 |
Accessing Functor Objects | |
| Construct_curve_2 | construct_curve_2_object () const |
| Construct_x_monotone_curve_2 | construct_x_monotone_curve_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