The class Segment_Delaunay_graph_filtered_traits_2
provides a model for the SegmentDelaunayGraphTraits_2
concept.
The class Segment_Delaunay_graph_filtered_traits_2
uses the filtering technique [1] to achieve traits for the Segment_Delaunay_graph_2<Gt,DS>
class with efficient and exact predicates given an exact kernel EK
and a filtering kernel FK
. The geometric constructions associated provided by this class are equivalent to those provided by the traits class Segment_Delaunay_graph_traits_2<CK,CM>
, which means that they may be inexact depending on the choice of the CK
kernel.
This class has six template parameters. The first, third and fifth template parameters must be a models of the Kernel
concept. The parameter CK
is the construction kernel and it is the kernel that will be used for constructions. The parameter FK
is the filtering kernel; this kernel will be used for performing the arithmetic filtering for the predicates involved in the computation of the segment Delaunay graph. Finally, the parameter EK
is the exact kernel; this kernel will be used for computing the predicates if the filtering kernel fails to produce an answer.
The second, fourth and sixth template parameters correspond to how predicates are evaluated. There are two predefined possible values for these parameters, namely Field_with_sqrt_tag
and Field_tag
. The first one must be used when the number type used in the representation supports the exact evaluation of signs of expressions involving all four basic operations and square roots, whereas the second one requires that only field operations are exact. Finally, in order to get exact constructions CM
must be set to Field_with_sqrt_tag
and the number type in CK
must support operations involing divisions and square roots (as well as the other three basic operations of course). The way the predicates are evaluated is discussed in [2] and [3] (the geometric filtering part).
The default values for the template parameters are as follows: CM = Field_with_sqrt_tag
(it is assumed that Cartesian<double>
or Simple_cartesian<double>
will be the entry for the template parameter CK
), EM = Field_tag
, FK = Simple_cartesian<Interval_nt<false> >
, FM = Field_with_sqrt_tag
. If the Gmp package is installed with CGAL, the template parameter EK
has the default value: EK = Simple_cartesian<Gmpq>
, otherwise its default value is EK = Simple_cartesian<Quotient<MP_Float> >
.
- Is Model Of:
SegmentDelaunayGraphTraits_2
DefaultConstructible
CopyConstructible
Assignable
- See also
Kernel
-
SegmentDelaunayGraphTraits_2
-
CGAL::Field_tag
-
CGAL::Field_with_sqrt_tag
-
CGAL::Segment_Delaunay_graph_2<Gt,DS>
-
CGAL::Segment_Delaunay_graph_hierarchy_2<Gt,STag,DS>
-
CGAL::Segment_Delaunay_graph_traits_2<K,MTag>
-
CGAL::Segment_Delaunay_graph_traits_without_intersections_2<K,MTag>
-
CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>
- Examples:
- Segment_Delaunay_graph_2/sdg-count-sites.cpp, Segment_Delaunay_graph_2/sdg-filtered-traits.cpp, Segment_Delaunay_graph_2/sdg-info-set.cpp, and Segment_Delaunay_graph_2/sdg-red-blue-info.cpp.