#include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>

Definition

The X_monotone_curve_2 class nested within the traits is used to represent an \(x\)-monotone geodesic arc on the a sphere centered at the origin.

The pre-image of an \(x\)-monotone geodesic arc does not intersect the identified left and right sides of the boundary of the parameter space.

Is Model Of:

Assignable

DefaultConstructible

CopyConstructible

Types
typedef Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::Point_2	Point_2

Creation
	X_monotone_curve_2 (const Point_2 &source, const Point_2 &target, const Direction_3 &normal, bool is_vertical, bool is_directed_right, bool is_full=false, bool is_degenerate=false, bool is_empty=false)
	Constructs an \(x\)-monotone geodesic arc. More...

	X_monotone_curve_2 (const Point_2 &source, const Point_2 &target, const Direction_3 &normal)
	Construct an \(x\)-monotone geodesic arc. More...

	X_monotone_curve_2 (const Point_2 &point, const Direction_3 &normal)
	Construct a full great-circle. More...

Operations
void	set_source (const Point_2 &source)
	Sets the source endpoint. More...

void	set_target (const Point_2 &target)
	Sets the target endpoint. More...

void	set_normal (const Direction_3 &normal)
	Sets the normal of the underlying plane. More...

void	set_is_vertical (bool flag)
	Sets the flag that indicates whether the arc is vertical. More...

void	set_is_directed_right (bool flag)
	Sets the flag that indicates whether the direction of the arc pre-image in the parameter space is from left to right. More...

void	set_is_full (bool flag)
	Sets the flag that indicates whether the arc is a full great circle. More...

void	set_is_degenerate (bool flag)
	Sets the flag that indicates whether the arc degenerates to a point. More...

void	set_is_empty (bool flag)
	Sets the flag that indicates whether the arc is empty. More...

const Point_2 &	source () const
	Obtains the source point.

const Point_2 &	target () const
	Obtains the target point.

const Direction_3 &	normal () const
	Obtains the normal to the containing plane.

const Point_2 &	left () const
	Obtains the (lexicographically) left endpoint direction.

const Point_2 &	right () const
	Obtains the (lexicographically) right endpoint.

bool	is_vertical () const
	Determines whether the arc is vertical.

bool	is_directed_right () const
	Determines whether the arc is directed lexicographically from left to right.

bool	is_full () const
	Determines whether the arc is a great circle.

bool	is_degenerate () const
	Determines whether the arc is degenerate.

bool	is_empty () const
	Determines whether the arc is empty. More...

bool	is_meridian () const
	Determines whether the arc is a meridian.

Constructor & Destructor Documentation

◆ X_monotone_curve_2() [1/3]

template<typename Kernel , typename X , typename Y >

CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::X_monotone_curve_2	(	const Point_2 &	source,
		const Point_2 &	target,
		const Direction_3 &	normal,
		bool	is_vertical,
		bool	is_directed_right,
		bool	is_full = `false`,
		bool	is_degenerate = `false`,
		bool	is_empty = `false`
	)

Constructs an \(x\)-monotone geodesic arc.

Parameters

[in]	source	the source point of the arc.
[in]	target	the target point of the arc.
[in]	normal	the normal of the plane that contains the arc.
[in]	is_vertical	is the arc vertical ?
[in]	is_directed_right	is the arc directed from left to right?
[in]	is_full	is the arc a full great circle?
[in]	is_degenerate	is the arc degenerate (single point)?
[in]	is_empty	is the arc empty?

Precondition: Both endpoints lie on the given plane.

◆ X_monotone_curve_2() [2/3]

template<typename Kernel , typename X , typename Y >

CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::X_monotone_curve_2	(	const Point_2 &	source,
		const Point_2 &	target,
		const Direction_3 &	normal
	)

Construct an \(x\)-monotone geodesic arc.

Parameters

[in]	normal	the normal of the plane containing the arc.
[in]	source	the source-point direction.
[in]	target	the target-point direction.

Precondition: Both endpoints lie on the given plane.

◆ X_monotone_curve_2() [3/3]

template<typename Kernel , typename X , typename Y >

CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::X_monotone_curve_2	(	const Point_2 &	point,
		const Direction_3 &	normal
	)

Construct a full great-circle.

Parameters

[in]	point	the endpoint of the full great-circle.
[in]	normal	the normal of the plane containing the arc.

Precondition: the point lies on the given plane.; the point pre-image lies on the identified left and right sides of the boundary of the parameter space.

Member Function Documentation

◆ is_empty()

template<typename Kernel , typename X , typename Y >

bool CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::is_empty ( ) const

Determines whether the arc is empty.

◆ set_is_degenerate()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_is_degenerate ( bool flag )

Sets the flag that indicates whether the arc degenerates to a point.

Parameters

[in] flag indicates whether the arc degenerates to a point.

◆ set_is_directed_right()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_is_directed_right ( bool flag )

Sets the flag that indicates whether the direction of the arc pre-image in the parameter space is from left to right.

Parameters

flag	indicates whether the arc pre-image in the parameter space is from left to right.

◆ set_is_empty()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_is_empty ( bool flag )

Sets the flag that indicates whether the arc is empty.

Parameters

[in] flag indicates whether the arc is empty.

◆ set_is_full()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_is_full ( bool flag )

Sets the flag that indicates whether the arc is a full great circle.

Parameters

[in] flag indicates whether the arc is a full great circle.

◆ set_is_vertical()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_is_vertical ( bool flag )

Sets the flag that indicates whether the arc is vertical.

Parameters

[in] flag indicates whether the arc pre-image in the parameter space is vertical.

◆ set_normal()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_normal ( const Direction_3 & normal )

Sets the normal of the underlying plane.

Parameters

[in] normal the updated normal of the underlying plane.

◆ set_source()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_source ( const Point_2 & source )

Sets the source endpoint.

Parameters

[in] source the updated source endpoint.

◆ set_target()

template<typename Kernel , typename X , typename Y >

void CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2::set_target ( const Point_2 & target )

Sets the target endpoint.

Parameters

[in] target the updated target endpoint.

Definition

Types

Creation

Operations

Constructor & Destructor Documentation

◆ X_monotone_curve_2() [1/3]

◆ X_monotone_curve_2() [2/3]

◆ X_monotone_curve_2() [3/3]

Member Function Documentation

◆ is_empty()

◆ set_is_degenerate()

◆ set_is_directed_right()

◆ set_is_empty()

◆ set_is_full()

◆ set_is_vertical()

◆ set_normal()

◆ set_source()

◆ set_target()