CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::Construct_x_monotone_curve_2 Class Reference

#include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>

Definition

template<typename Kernel, typename X, typename Y>
class CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::Construct_x_monotone_curve_2

Construction functor of \(x\)-monotone geodesic arcs.

Is Model Of:

Assignable

CopyConstructible

AdaptableUnaryFunction

AdaptableBinaryFunction

AdaptableTernaryFunction

Types
typedef Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::Point_2	Point_2
typedef Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::X_monotone_curve_2	result_type
typedef Kernel::Direction_3	Direction_3
typedef Direction_3	argument_type
typedef Point_2	first_argument_type
typedef Point_2	second_argument_type
typedef Direction_3	third_argument_type

Operations
X_monotone_curve_2	operator() (const Point_2 &p, const Point_2 &q)
	Construct the minor geodesic arc from two endpoints. More...
X_monotone_curve_2	operator() (const Direction_3 &normal)
	Construct a full great circle from a normal to a plane. More...
X_monotone_curve_2	operator() (const Point_2 &p, const Point_2 &q, const Direction_3 &normal)
	Construct a geodesic arc from two endpoints contained in a plane. More...

Member Function Documentation

operator()() [1/3]

template<typename Kernel , typename X , typename Y >

X_monotone_curve_2 CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::Construct_x_monotone_curve_2::operator()	(	const Point_2 &	p,
		const Point_2 &	q
	)

Construct the minor geodesic arc from two endpoints.

The minor arc is the one with the smaller angle among the two geodesic arcs with the given endpoints.

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

   [in]	p	the first endpoint.
   [in]	q	the second endpoint.

   Precondition

   p and q must not coincide.

   p and q cannot be antipodal.

operator()() [2/3]

template<typename Kernel , typename X , typename Y >

X_monotone_curve_2 CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::Construct_x_monotone_curve_2::operator()

(

const Direction_3 &

normal

)

Construct a full great circle from a normal to a plane.

Parameters

normal

the normal to the plane containing the great circle.

Precondition

the plane is not vertical.

operator()() [3/3]

template<typename Kernel , typename X , typename Y >

X_monotone_curve_2 CGAL::Arr_geodesic_arc_on_sphere_traits_2< Kernel, X, Y >::Construct_x_monotone_curve_2::operator()	(	const Point_2 &	p,
		const Point_2 &	q,
		const Direction_3 &	normal
	)

Construct a geodesic arc from two endpoints contained in a plane.

Parameters

[in]	p	the first endpoint.
[in]	q	the second endpoint.
[in]	normal	the normal to the plane containing the arc.

Precondition

Both endpoint lie on the given plane.

Both endpoint lie on the given plane.