CGAL 4.12 - 2D Segment Delaunay Graphs
CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2< CK, CM, EK, EM, FK, FM > Struct Template Reference

#include <CGAL/Segment_Delaunay_graph_filtered_traits_2.h>

## Definition

The class Segment_Delaunay_graph_filtered_traits_without_intersections_2 provides a model for the SegmentDelaunayGraphTraits_2 concept.

The class Segment_Delaunay_graph_filtered_traits_without_intersections_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_without_intersections_2<CK,CM>, which means that they may be inexact, depending on the choice of the CK kernel.

This class has six template parameters.

Template Parameters
 CK is the construction kernel and it is the kernel that will be used for constructions. CM must be Field_with_sqrt_tag or Field_tag 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. FM must be Field_with_sqrt_tag or Field_tag EK is the exact kernel; this kernel will be used for computing the predicates if the filtering kernel fails to produce an answer. EM must be Field_with_sqrt_tag or Field_tag

The first, third and fifth template parameters must be a models of the Kernel concept. 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 Euclidean_ring_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 requires the exact evaluation of signs of ring-type expressions, i.e., expressions involving only additions, subtractions and multiplications. 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 [4] (the geometric filtering part).

The default values for the template parameters are as follows:

• CM = CGAL::Field_with_sqrt_tag (it is assumed that Cartesian<double> or Simple_cartesian<double> will be the entry for the template parameter CK),
• EM = CGAL::Euclidean_ring_tag,
• FK = CGAL::Simple_cartesian<CGAL::Interval_nt<false> >,
• FM = CGAL::Field_with_sqrt_tag.
• If the Gmp package is installed with CGAL, the template parameter EK has the default value: EK = CGAL::Simple_cartesian<CGAL::Gmpq>, otherwise its default value is EK = CGAL::Simple_cartesian<CGAL::MP_Float>.
Is Model Of:

SegmentDelaunayGraphTraits_2

DefaultConstructible

CopyConstructible

Assignable

Kernel
SegmentDelaunayGraphTraits_2
CGAL::Euclidean_ring_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_2<CK,CM,EK,EM,FK,FM>
Examples:
Segment_Delaunay_graph_2/sdg-fast-sp-polygon.cpp, and Segment_Delaunay_graph_2/sdg-fast-sp.cpp.

## Types

In addition to the types required by the SegmentDelaunayGraphTraits_2 concept the class Segment_Delaunay_graph_filtered_traits_without_intersections_2 defines the following types:

typedef CGAL::Tag_false Intersections_tag

typedef CK Kernel

typedef CK Construction_kernel

typedef FK Filtering_kernel

typedef EK Exact_kernel

typedef CM Method_tag

typedef CM Construction_traits_method_tag

typedef FM Filtering_traits_method_tag

typedef EM Exact_traits_method_tag

typedef unspecified_type Construction_traits
A type for the segment Delaunay graph traits, where the kernel is CK.

typedef unspecified_type Filtering_traits
A type for the segment Delaunay graph traits, where the kernel is FK.

typedef unspecified_type Exact_traits
A type for the segment Delaunay graph traits, where the kernel is EK.