## CGAL::Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>

### Definition

The class Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM> provides a model for the ApolloniusGraphTraits_2 concept.

The class Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM> uses the filtering technique [BBP01] to achieve traits for the Apollonius_graph_2<Gt,Agds> 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 Apollonius_graph_traits_2<CK,CM>, which means that they may be inexact.

This class has six template parameters. 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 Method_tag, namely CGAL::Sqrt_field_tag and CGAL::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 one requires the exact evaluation of signs of ring-type expressions, i.e., expressions involving only additions, subtractions and multiplications. The way the predicates are evaluated is discussed in [KE02, KE03].

The default values for the template parameters are as follows: CM = CGAL::Ring_tag, EK = CGAL::Simple_cartesian<CGAL::MP_Float>, EM = CM, FK = CGAL::Simple_cartesian<CGAL::Interval_nt<false> >, FM = CM.

#include <CGAL/Apollonius_graph_filtered_traits_2.h>

### Is Model for the Concept

ApolloniusGraphTraits_2

### Creation

Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM> traits;
| Default constructor.
Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM> traits ( other);
| Copy constructor.

Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>
| traits = other | Assignment operator.

### See Also

Kernel
ApolloniusGraphTraits_2
CGAL::Ring_tag
CGAL::Sqrt_field_tag
CGAL::Apollonius_graph_2<Gt,Agds>
CGAL::Apollonius_graph_traits_2<K,Method_tag>