#include <Arr_geodesic_arc_on_sphere_traits_2.h>

Inheritance diagram for Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >:

Classes
class	Approximate_2
class	Are_mergeable_2
class	Clockwise_in_between_2
class	Compare_endpoints_xy_2
class	Compare_x_2
class	Compare_x_near_boundary_2
class	Compare_x_on_boundary_2
class	Compare_xy_2
class	Compare_y_at_x_2
class	Compare_y_at_x_left_2
class	Compare_y_at_x_right_2
class	Compare_y_near_boundary_2
class	Compare_y_on_boundary_2
class	Construct_max_vertex_2
class	Construct_min_vertex_2
class	Construct_opposite_2
class	Construct_x_monotone_curve_2
class	Equal_2
class	Intersect_2
class	Is_on_x_identification_2
class	Is_on_y_identification_2
class	Is_vertical_2
class	Make_x_monotone_2
class	Merge_2
class	Parameter_space_in_x_2
class	Parameter_space_in_y_2
class	Split_2
Public Types
typedef T_Kernel	Kernel
typedef Tag_true	Has_left_category
typedef Tag_true	Has_merge_category
typedef Arr_identified_side_tag	Arr_left_side_tag
typedef Arr_contracted_side_tag	Arr_bottom_side_tag
typedef Arr_contracted_side_tag	Arr_top_side_tag
typedef Arr_identified_side_tag	Arr_right_side_tag
typedef Arr_extended_direction_3 < Kernel >	Point_2
typedef Arr_x_monotone_geodesic_arc_on_sphere_3 < Kernel >	X_monotone_curve_2
typedef Arr_geodesic_arc_on_sphere_3 < Kernel >	Curve_2
typedef unsigned int	Multiplicity
Public Member Functions
	Arr_geodesic_arc_on_sphere_traits_2 ()
Comparison_result	compare_y (const Direction_3 &d1, const Direction_3 &d2) const
Comparison_result	compare_x (const Direction_2 &d1, const Direction_2 &d2) const
Comparison_result	compare_x (const Direction_3 &d1, const Direction_3 &d2) const
Comparison_result	compare_xy (const Direction_3 &d1, const Direction_3 &d2) const
Basic functor definitions
Compare_x_2	compare_x_2_object () const
Compare_xy_2	compare_xy_2_object () const
Construct_min_vertex_2	construct_min_vertex_2_object () const
Construct_max_vertex_2	construct_max_vertex_2_object () const
Is_vertical_2	is_vertical_2_object () const
Compare_y_at_x_2	compare_y_at_x_2_object () const
Compare_y_at_x_left_2	compare_y_at_x_left_2_object () const
Compare_y_at_x_right_2	compare_y_at_x_right_2_object () const
Equal_2	equal_2_object () const
Functor definitions to handle boundaries
Parameter_space_in_x_2	parameter_space_in_x_2_object () const
Parameter_space_in_y_2	parameter_space_in_y_2_object () const
Compare_x_near_boundary_2	compare_x_near_boundary_2_object () const
Compare_y_near_boundary_2	compare_y_near_boundary_2_object () const
Is_on_x_identification_2	is_on_x_identification_2_object () const
Is_on_y_identification_2	is_on_y_identification_2_object () const
Compare_x_on_boundary_2	compare_x_on_boundary_2_object () const
Compare_y_on_boundary_2	compare_y_on_boundary_2_object () const
Functor definitions for supporting intersections.
Make_x_monotone_2	make_x_monotone_2_object () const
Split_2	split_2_object () const
Clockwise_in_between_2	clockwise_in_between_2_object () const
Intersect_2	intersect_2_object () const
Are_mergeable_2	are_mergeable_2_object () const
Merge_2	merge_2_object () const
Functor definitions for the Boolean set-operation traits.
Compare_endpoints_xy_2	compare_endpoints_xy_2_object () const
Construct_opposite_2	construct_opposite_2_object () const
Protected Types
typedef Kernel::FT	FT
typedef Kernel::Direction_3	Direction_3
typedef Kernel::Vector_3	Vector_3
typedef Kernel::Direction_2	Direction_2
typedef Kernel::Vector_2	Vector_2
typedef Direction_2(*	Project )(const Direction_3 &d)
Protected Member Functions
Oriented_side	oriented_side (const Direction_3 &normal, const Direction_3 dir) const
bool	has_on (const Direction_3 &normal, const Direction_3 &dir) const
Static Protected Member Functions
static const Direction_3 &	pos_pole ()
static const Direction_3 &	neg_pole ()
static const Direction_2 &	identification_xy ()
static const Direction_3 &	identification_normal ()
static const Direction_2 &	neg_x_2 ()
static const Direction_2 &	neg_y_2 ()
static Sign	x_sign (Direction_3 d)
static Sign	y_sign (Direction_3 d)
static Sign	z_sign (Direction_3 d)
static Direction_2	project_xy (const Direction_3 &d)
static Direction_2	project_yz (const Direction_3 &d)
static Direction_2	project_xz (const Direction_3 &d)
static Orientation	orientation (const Direction_2 &d1, const Direction_2 &d2)
Friends
class	Arr_x_monotone_geodesic_arc_on_sphere_3< T_Kernel >
class	Arr_geodesic_arc_on_sphere_3< T_Kernel >
class	Arr_extended_direction_3< T_Kernel >
Functor definitions for the landmarks point-location strategy.
typedef double	Approximate_number_type
Approximate_2	approximate_2_object () const
Construct_x_monotone_curve_2	construct_x_monotone_curve_2_object () const

Detailed Description

template<typename T_Kernel>
class Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >

A traits class-template for constructing and maintaining arcs of great circles embedded on spheres. It is parameterized from a (linear) geometry kernel, which it also derives from

Member Typedef Documentation

template<typename T_Kernel >

typedef double Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Approximate_number_type

template<typename T_Kernel >

typedef Arr_contracted_side_tag Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Arr_bottom_side_tag

template<typename T_Kernel >

typedef Arr_identified_side_tag Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Arr_left_side_tag

template<typename T_Kernel >

typedef Arr_identified_side_tag Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Arr_right_side_tag

template<typename T_Kernel >

typedef Arr_contracted_side_tag Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Arr_top_side_tag

template<typename T_Kernel >

typedef Arr_geodesic_arc_on_sphere_3<Kernel> Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Curve_2

template<typename T_Kernel >

typedef Kernel::Direction_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Direction_2 [protected]

template<typename T_Kernel >

typedef Kernel::Direction_3 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Direction_3 [protected]

template<typename T_Kernel >

typedef Kernel::FT Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::FT [protected]

template<typename T_Kernel >

typedef Tag_true Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Has_left_category

template<typename T_Kernel >

typedef Tag_true Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Has_merge_category

template<typename T_Kernel >

typedef T_Kernel Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Kernel

Reimplemented in Arr_polyhedral_sgm_traits< T_Kernel >.

template<typename T_Kernel >

typedef unsigned int Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Multiplicity

template<typename T_Kernel >

typedef Arr_extended_direction_3<Kernel> Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Point_2

Reimplemented in Arr_geodesic_arc_on_sphere_partition_traits_2< T_Kernel, Container_P >.

template<typename T_Kernel >

typedef Direction_2(* Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Project)(const Direction_3 &d) [protected]

template<typename T_Kernel >

typedef Kernel::Vector_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Vector_2 [protected]

template<typename T_Kernel >

typedef Kernel::Vector_3 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Vector_3 [protected]

Reimplemented in Arr_polyhedral_sgm_traits< T_Kernel >.

template<typename T_Kernel >

typedef Arr_x_monotone_geodesic_arc_on_sphere_3<Kernel> Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::X_monotone_curve_2

Constructor & Destructor Documentation

template<typename T_Kernel >

Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::Arr_geodesic_arc_on_sphere_traits_2 ( ) [inline]

Default constructor

Member Function Documentation

template<typename T_Kernel >

Approximate_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::approximate_2_object ( ) const [inline]

Obtain an Approximate_2 function object

template<typename T_Kernel >

Are_mergeable_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::are_mergeable_2_object ( ) const [inline]

Obtain an Are_mergeable_2 function object

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template<typename T_Kernel >

Clockwise_in_between_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::clockwise_in_between_2_object ( ) const [inline]

Obtain a Clockwise_in_between function object

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template<typename T_Kernel >

Compare_endpoints_xy_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_endpoints_xy_2_object ( ) const [inline]

Obtain a Compare_endpoints_xy_2 function object

template<typename T_Kernel >

Comparison_result Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_x	(	const Direction_2 &	d1,
		const Direction_2 &	d2
	)		const `[inline]`

Compare two directions contained in the xy plane by u.

Parameters:

d1	the first direction.
d2	the second direction.

Returns:: SMALLER - u(d1) < u(d2); EQUAL - u(d1) = u(d2); LARGER - u(d1) > u(d2).

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template<typename T_Kernel >

Comparison_result Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_x	(	const Direction_3 &	d1,
		const Direction_3 &	d2
	)		const `[inline]`

Compare two endpoint directions by u.

Parameters:

d1	the first enpoint direction.
d2	the second endpoint direction.

Returns:: SMALLER - u(d1) < u(d2); EQUAL - u(d1) = u(d2); LARGER - u(d1) > u(d2).

Precondition:: d1 does not coincide with any pole.; d2 does not coincide with any pole.

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template<typename T_Kernel >

Compare_x_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_x_2_object ( ) const [inline]

Obtain a Compare_x_2 function object

Reimplemented in Arr_geodesic_arc_on_sphere_partition_traits_2< T_Kernel, Container_P >.

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template<typename T_Kernel >

Compare_x_near_boundary_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_x_near_boundary_2_object ( ) const [inline]

Obtain a Compare_x_near_boundary_2 function object

template<typename T_Kernel >

Compare_x_on_boundary_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_x_on_boundary_2_object ( ) const [inline]

Obtain a Compare_x_on_boundary_2 function object

template<typename T_Kernel >

Comparison_result Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_xy	(	const Direction_3 &	d1,
		const Direction_3 &	d2
	)		const `[inline]`

Compare two endpoint directions lexigoraphically: by u, then by v.

Parameters:

d1	the first enpoint direction.
d2	the second endpoint direction.

Returns:: SMALLER - u(d1) < u(d2); SMALLER - u(d1) = u(d2) and v(d1) < v(d2); EQUAL - u(d1) = u(d2) and v(d1) = v(d2); LARGER - u(d1) = u(d2) and v(d1) > v(d2); LARGER - u(d1) > u(d2).

Precondition:: d1 does not lie on the discontinuity arc.; d2 does not lie on the discontinuity arc.

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template<typename T_Kernel >

Compare_xy_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_xy_2_object ( ) const [inline]

Obtain a Compare_xy_2 function object

template<typename T_Kernel >

Comparison_result Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_y	(	const Direction_3 &	d1,
		const Direction_3 &	d2
	)		const `[inline]`

Compare two endpoint directions by v.

Parameters:

d1	the first enpoint direction.
d2	the second endpoint direction.

Returns:: SMALLER - v(d1) < v(d2); EQUAL - v(d1) = v(d2); LARGER - v(d1) > v(d2).

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template<typename T_Kernel >

Compare_y_at_x_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_y_at_x_2_object ( ) const [inline]

Obtain a Compare_y_at_x_2 function object

template<typename T_Kernel >

Compare_y_at_x_left_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_y_at_x_left_2_object ( ) const [inline]

Obtain a Compare_y_at_x_left_2 function object

template<typename T_Kernel >

Compare_y_at_x_right_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_y_at_x_right_2_object ( ) const [inline]

Obtain a Compare_y_at_x_right_2 function object

template<typename T_Kernel >

Compare_y_near_boundary_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_y_near_boundary_2_object ( ) const [inline]

Obtain a Compare_y_near_boundary_2 function object

template<typename T_Kernel >

Compare_y_on_boundary_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::compare_y_on_boundary_2_object ( ) const [inline]

Obtain a Compare_y_on_boundary_2 function object

template<typename T_Kernel >

Construct_max_vertex_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::construct_max_vertex_2_object ( ) const [inline]

Obtain a Construct_max_vertex_2 function object

template<typename T_Kernel >

Construct_min_vertex_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::construct_min_vertex_2_object ( ) const [inline]

Obtain a Construct_min_vertex_2 function object

template<typename T_Kernel >

Construct_opposite_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::construct_opposite_2_object ( ) const [inline]

Obtain a Construct_opposite_2 function object

template<typename T_Kernel >

Construct_x_monotone_curve_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::construct_x_monotone_curve_2_object ( ) const [inline]

Obtain a Construct_x_monotone_curve_2 function object

template<typename T_Kernel >

Equal_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::equal_2_object ( ) const [inline]

Obtain an Equal_2 function object

template<typename T_Kernel >

bool Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::has_on	(	const Direction_3 &	normal,
		const Direction_3 &	dir
	)		const `[inline, protected]`

Determined whether a direction is contained in a plane given by its normal

Parameters:

normal	the direction of the 3D plane.
dir	the 3D direction.

Returns:: true if dir is contained in plane; false otherwise.

Precondition:: the plane contains the origin.

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template<typename T_Kernel >

static const Direction_3& Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::identification_normal ( ) [inline, static, protected]

Obtain the normal of the plane that contains the identification arc. By default, it is the vector directed along the positive y axis (y = infinity).

Returns:: the normal of the plane that contains the identification arc.

template<typename T_Kernel >

static const Direction_2& Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::identification_xy ( ) [inline, static, protected]

Obtain the intersection of the identification arc and the xy plane. By default, it is the vector directed along the negative x axis (x = -infinity).

Returns:: the intersection of the identification arc and the xy plane.

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template<typename T_Kernel >

Intersect_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::intersect_2_object ( ) const [inline]

Obtain an Intersect_2 function object

template<typename T_Kernel >

Is_on_x_identification_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::is_on_x_identification_2_object ( ) const [inline]

Obtain a Is_on_x_identification_2 function object

template<typename T_Kernel >

Is_on_y_identification_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::is_on_y_identification_2_object ( ) const [inline]

Obtain a Is_on_y_identification_2 function object

template<typename T_Kernel >

Is_vertical_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::is_vertical_2_object ( ) const [inline]

Obtain an Is_vertical_2 function object

template<typename T_Kernel >

Make_x_monotone_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::make_x_monotone_2_object ( ) const [inline]

Obtain a Make_x_monotone_2 function object

template<typename T_Kernel >

Merge_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::merge_2_object ( ) const [inline]

Obtain a Merge_2 function object

template<typename T_Kernel >

static const Direction_3& Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::neg_pole ( ) [inline, static, protected]

Obtain the negative (south) pole

Returns:: the negative (south) pole

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template<typename T_Kernel >

static const Direction_2& Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::neg_x_2 ( ) [inline, static, protected]

Obtain the 2D direction directed along the negative x axis

Returns:: the direction directed at x = -infinity

template<typename T_Kernel >

static const Direction_2& Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::neg_y_2 ( ) [inline, static, protected]

Obtain the 2D direction directed along the negative y axis

Returns:: the direction directed at y = -infinity

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template<typename T_Kernel >

static Orientation Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::orientation	(	const Direction_2 &	d1,
		const Direction_2 &	d2
	)		`[inline, static, protected]`

Compute the orientation of two directions.

Parameters:

d1	the first direction.
d2	the second direction.

Returns:: the relative orientation of d1 and d2.

template<typename T_Kernel >

Oriented_side Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::oriented_side	(	const Direction_3 &	normal,
		const Direction_3	dir
	)		const `[inline, protected]`

Compare the relative position of a direction and a plane given by its normal.

Parameters:

normal	the direction of the plane.
dir	the direction.

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template<typename T_Kernel >

Parameter_space_in_x_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::parameter_space_in_x_2_object ( ) const [inline]

Obtain a Parameter_space_in_x_2 function object

template<typename T_Kernel >

Parameter_space_in_y_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::parameter_space_in_y_2_object ( ) const [inline]

Obtain a Parameter_space_in_y_2 function object

template<typename T_Kernel >

static const Direction_3& Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::pos_pole ( ) [inline, static, protected]

Obtain the possitive (north) pole

Returns:: the possitive (north) pole

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template<typename T_Kernel >

static Direction_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::project_xy ( const Direction_3 & d ) [inline, static, protected]

Project a 3D direction onto the xy-plane

Parameters:

d	the 3D direction

Returns:: the projection onto the xy-plane

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template<typename T_Kernel >

static Direction_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::project_xz ( const Direction_3 & d ) [inline, static, protected]

Project a 3D direction onto the zx-plane

Parameters:

d	the 3D direction

Returns:: the projection onto the xz-plane

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template<typename T_Kernel >

static Direction_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::project_yz ( const Direction_3 & d ) [inline, static, protected]

Project a 3D direction onto the yz-plane

Parameters:

d	the 3D direction

Returns:: the projection onto the yz-plane

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template<typename T_Kernel >

Split_2 Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::split_2_object ( ) const [inline]

Obtain a Split_2 function object

template<typename T_Kernel >

static Sign Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::x_sign ( Direction_3 d ) [inline, static, protected]

Obtain the sign of the x-coordinate of a direction in space

Parameters:

d	the direction in space

Returns:: the sign of the x-coordinate of d

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template<typename T_Kernel >

static Sign Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::y_sign ( Direction_3 d ) [inline, static, protected]

Obtain the sign of the y-coordinate of a direction in space

Parameters:

d	the direction in space

Returns:: the sign of the y-coordinate of d

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template<typename T_Kernel >

static Sign Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >::z_sign ( Direction_3 d ) [inline, static, protected]

Obtain the sign of the z-coordinate of a direction in space

Parameters:

d	the direction in space

Returns:: the sign of the z-coordinate of d

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Friends And Related Function Documentation

template<typename T_Kernel >

friend class Arr_extended_direction_3< T_Kernel > [friend]

template<typename T_Kernel >

friend class Arr_geodesic_arc_on_sphere_3< T_Kernel > [friend]

template<typename T_Kernel >

friend class Arr_x_monotone_geodesic_arc_on_sphere_3< T_Kernel > [friend]

The documentation for this class was generated from the following file:

SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h

Classes

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Static Protected Member Functions

Friends

Functor definitions for the landmarks point-location strategy.

Detailed Description

template<typename T_Kernel> class Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename T_Kernel>
class Arr_geodesic_arc_on_sphere_traits_2< T_Kernel >