#include <Arr_geodesic_arc_on_sphere_traits_2.h>

Inheritance diagram for Arr_geodesic_arc_on_sphere_3< T_Kernel >:

Collaboration diagram for Arr_geodesic_arc_on_sphere_3< T_Kernel >:

Public Member Functions
	Arr_geodesic_arc_on_sphere_3 ()
	Arr_geodesic_arc_on_sphere_3 (const Arr_geodesic_arc_on_sphere_3 &other)
	Arr_geodesic_arc_on_sphere_3 (const Arr_extended_direction_3 &src, const Arr_extended_direction_3 &trg, const Direction_3 &normal, bool is_x_monotone, bool is_vertical, bool is_directed_right, bool is_full=false, bool is_degenerate=false, bool is_empty=false)
	Arr_geodesic_arc_on_sphere_3 (const Arr_extended_direction_3 &source, const Arr_extended_direction_3 &target)
	Arr_geodesic_arc_on_sphere_3 (const Arr_extended_direction_3 &source, const Arr_extended_direction_3 &target, const Direction_3 &normal)
	Arr_geodesic_arc_on_sphere_3 (const Direction_3 &normal)
bool	is_x_monotone () const
void	set_is_x_monotone (bool flag)
Protected Types
typedef T_Kernel	Kernel
typedef Arr_x_monotone_geodesic_arc_on_sphere_3 < Kernel >	Base
typedef Base::Plane_3	Plane_3
typedef Base::Direction_3	Direction_3
typedef Base::Direction_2	Direction_2
typedef CGAL::Arr_extended_direction_3 < Kernel >	Arr_extended_direction_3
Protected Attributes
bool	m_is_x_monotone

Detailed Description

template<typename T_Kernel>
class Arr_geodesic_arc_on_sphere_3< T_Kernel >

A representation of a general great circular arc embedded on a sphere, used by the Arr_geodesic_arc_on_sphere_traits_2 traits-class An arc is uniqely represented by a plane p, and two endpoints the source s and the target t, which lie in the plane p. The points of the arc are the locus of points visited when moving from the source s toward the target t on the plane p in counterclockwise direction along the circle defined by s and t.

Member Typedef Documentation

template<typename T_Kernel >

typedef CGAL::Arr_extended_direction_3<Kernel> Arr_geodesic_arc_on_sphere_3< T_Kernel >::Arr_extended_direction_3 [protected]

Reimplemented from Arr_x_monotone_geodesic_arc_on_sphere_3< T_Kernel >.

template<typename T_Kernel >

typedef Arr_x_monotone_geodesic_arc_on_sphere_3<Kernel> Arr_geodesic_arc_on_sphere_3< T_Kernel >::Base [protected]

template<typename T_Kernel >

typedef Base::Direction_2 Arr_geodesic_arc_on_sphere_3< T_Kernel >::Direction_2 [protected]

Reimplemented from Arr_x_monotone_geodesic_arc_on_sphere_3< T_Kernel >.

template<typename T_Kernel >

typedef Base::Direction_3 Arr_geodesic_arc_on_sphere_3< T_Kernel >::Direction_3 [protected]

Reimplemented from Arr_x_monotone_geodesic_arc_on_sphere_3< T_Kernel >.

template<typename T_Kernel >

typedef T_Kernel Arr_geodesic_arc_on_sphere_3< T_Kernel >::Kernel [protected]

Reimplemented from Arr_x_monotone_geodesic_arc_on_sphere_3< T_Kernel >.

template<typename T_Kernel >

typedef Base::Plane_3 Arr_geodesic_arc_on_sphere_3< T_Kernel >::Plane_3 [protected]

Reimplemented from Arr_x_monotone_geodesic_arc_on_sphere_3< T_Kernel >.

Constructor & Destructor Documentation

template<typename T_Kernel >

Arr_geodesic_arc_on_sphere_3< T_Kernel >::Arr_geodesic_arc_on_sphere_3 ( ) [inline]

Default constructor - constructs an empty arc

template<typename T_Kernel >

Arr_geodesic_arc_on_sphere_3< T_Kernel >::Arr_geodesic_arc_on_sphere_3 ( const Arr_geodesic_arc_on_sphere_3< T_Kernel > & other ) [inline]

Copy constructor

Parameters:

other the other arc

template<typename T_Kernel >

Arr_geodesic_arc_on_sphere_3< T_Kernel >::Arr_geodesic_arc_on_sphere_3	(	const Arr_extended_direction_3 &	src,
		const Arr_extended_direction_3 &	trg,
		const Direction_3 &	normal,
		bool	is_x_monotone,
		bool	is_vertical,
		bool	is_directed_right,
		bool	is_full = `false`,
		bool	is_degenerate = `false`,
		bool	is_empty = `false`
	)		`[inline]`

Constructor

Parameters:

src	the source point of the arc
trg	the target point of the arc
normal	the normal to the plane that contains the arc
is_x_monotone	is arc x-monotone ?
is_vertical	is the arc vertical ?
is_directed_right	is the arc directed from left to right?
is_full	is the arc a full (great) circle?
is_degenerate	is the arc degenerate (single point)?

Precondition:: plane contains the origin; plane contains src; plane contains trg

Here is the call graph for this function:

template<typename T_Kernel >

Arr_geodesic_arc_on_sphere_3< T_Kernel >::Arr_geodesic_arc_on_sphere_3	(	const Arr_extended_direction_3 &	source,
		const Arr_extended_direction_3 &	target
	)		`[inline]`

Construct a spherical_arc from two endpoint directions. It is assumed that the arc is the one with the smaller angle among the two. 1. Find out whether the arc is x-monotone. 2. If it is x-monotone, 2.1 Find out whether it is vertical, and 2.2 whether the target is larger than the source (directed right). The arc is vertical, iff 1. one of its endpoint direction pierces a pole, or 2. the projections onto the xy-plane coincide.

Parameters:

source	the source point.
target	the target point.

Precondition:: the source and target cannot be equal.; the source and target cannot be the opoosite of each other.

Here is the call graph for this function:

template<typename T_Kernel >

Arr_geodesic_arc_on_sphere_3< T_Kernel >::Arr_geodesic_arc_on_sphere_3	(	const Arr_extended_direction_3 &	source,
		const Arr_extended_direction_3 &	target,
		const Direction_3 &	normal
	)		`[inline]`