CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2 Class Reference

#include <CGAL/Arr_conic_traits_2.h>

Definition

template<typename RatKernel, typename AlgKernel, typename NtTraits>
class CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2

The Curve_2 class nested within the conic-arc traits can represent arbitrary conic arcs and support their construction in various ways.

The copy and default constructor as well as the assignment operator are provided for conic arcs. In addition, an operator<< for the curves is defined for standard output streams.

Creation
	Curve_2 ()
	constructs an empty (invalid) arc.

Access Functions
bool	is_valid () const
	indicates whether a is a valid conic arc.
bool	is_x_monotone () const
	determines whether the arc is \(x\)-monotone, namely each vertical line intersects it at most once.
bool	is_y_monotone () const
	determines whether the arc is \(y\)-monotone, namely each horizontal line intersects it at most once.
bool	is_full_conic () const
	indicates whether the arc represents a full conic curve (en ellipse or a circle).
The six following methods return the coefficients of the supported conic, after their conversion to integer number (represented by the Integer type of the NtTraits class):
const NtTraits::Integer &	r () const
	returns the coefficient of \(x^2\).
const NtTraits::Integer &	s () const
	returns the coefficient of \(t^2\).
const NtTraits::Integer &	t () const
	returns the coefficient of \(x y\).
const NtTraits::Integer &	u () const
	returns the coefficient of \(x\).
const NtTraits::Integer &	v () const
	returns the coefficient of \(y\).
const NtTraits::Integer &	w () const
	returns the free coefficient.
const Point_2 &	source () const
	returns the source point of the arc.
const Point_2 &	target () const
	returns the target point of the arc.
Orientation	orientation () const
	returns the orientation of the arc.

Operations
void	set_source (const Point_2 &ps)
	sets a new source point for the conic arc.
void	set_target (const Point_2 &pt)
	sets a new target point for the conic arc.

Member Function Documentation

is_valid()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

bool CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::is_valid

(

)

const

indicates whether a is a valid conic arc.

As the precondition to some of the constructor listed above are quite complicated, their violation does not cause the program to abort. Instead, the constructed arc is invalid (a defaultly constructed arc is also invalid). It is however recommended to check that a constructed arc is valid before inserting it to an arrangement.

is_x_monotone()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

bool CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::is_x_monotone

(

)

const

determines whether the arc is \(x\)-monotone, namely each vertical line intersects it at most once.

A vertical line segment is also considered (weakly) \(x\)-monotone.

is_y_monotone()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

bool CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::is_y_monotone

(

)

const

determines whether the arc is \(y\)-monotone, namely each horizontal line intersects it at most once.

A horizontal line segment is also considered (weakly) \(x\)-monotone.

set_source()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

void CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::set_source

(

const Point_2 &

ps

)

sets a new source point for the conic arc.

Precondition

ps lies on the supporting conic of a.

set_target()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

void CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::set_target

(

const Point_2 &

pt

)

sets a new target point for the conic arc.

Precondition

pt lies on the supporting conic of a.

source()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

const Point_2 & CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::source

(

)

const

returns the source point of the arc.

Precondition

a is not a full conic curve.

target()

template<typename RatKernel , typename AlgKernel , typename NtTraits >

const Point_2 & CGAL::Arr_conic_traits_2< RatKernel, AlgKernel, NtTraits >::Curve_2::target

(

)

const

returns the target point of the arc.

Precondition

a is not a full conic curve.