CGAL::Width_default_traits_3< K > Class Template Reference

#include <CGAL/Width_default_traits_3.h>

Definition

template<typename K>
class CGAL::Width_default_traits_3< K >

The class Width_default_traits_3 is a traits class for Width_3<Traits> using the three-dimensional CGAL kernel.

Template Parameters

K	must be a model for Kernel.

Is model of

WidthTraits_3

See also

CGAL::Width_3<Traits>

WidthTraits_3

Examples

Polytope_distance_d/width_simplex.cpp.

Types
typedef K::Point_3	Point_3
typedef K::Plane_3	Plane_3
typedef K::Vector_3	Vector_3
typedef K::RT	RT
typedef Convex_hull_traits_3< K >	ChullTraits

Creation
	Width_default_traits_3 ()
	default constructor.

Operations
RT	get_hx (const Point_3 &p) const
	returns the homogeneous \( x\)-coordinate of point \( p\).
RT	get_hy (const Point_3 &p) const
	returns the homogeneous \( y\)-coordinate of point \( p\).
RT	get_hz (const Point_3 &p) const
	returns the homogeneous \( z\)-coordinate of point \( p\).
RT	get_hw (const Point_3 &p) const
	returns the homogenizing coordinate of point \( p\).
void	get_point_coordinates (const Point_3 &p, RT &px, RT &py, RT &pz, RT &ph) const
	returns all homogeneous coordinates of point \( p\) at once.
RT	get_a (const Plane_3 &f) const
	returns the first coefficient of plane \( f\).
RT	get_b (const Plane_3 &f) const
	returns the second coefficient of plane \( f\).
RT	get_c (const Plane_3 &f) const
	returns the third coefficient of plane \( f\).
RT	get_d (const Plane_3 &f) const
	returns the fourth coefficient of plane \( f\).
void	get_plane_coefficients (const Plane_3 &f, RT &a, RT &b, RT &c, RT &d) const
	returns all four plane coefficients of \( f\) at once.
Point_3	make_point (const RT &hx, const RT &hy, const RT &hz, const RT &hw) const
	returns a point of type Point_3 with homogeneous coordinates \( hx\), \( hy\), \( hz\) and \( hw\).
Plane_3	make_plane (const RT &a, const RT &b, const RT &c, const RT &d) const
	returns a plane of type Plane_3 whose coefficients are \( a\), \( b\), \( c\) and \( d\).
Vector	make_vector (const RT &a, const RT &b, const RT &c) const
	returns a vector of type Vector_3 with the four coefficients \( a\), \( b\), \( c\) and 1.

Member Typedef Documentation

ChullTraits

template<typename K >

typedef Convex_hull_traits_3<K> CGAL::Width_default_traits_3< K >::ChullTraits

Plane_3

template<typename K >

typedef K::Plane_3 CGAL::Width_default_traits_3< K >::Plane_3

Point_3

template<typename K >

typedef K::Point_3 CGAL::Width_default_traits_3< K >::Point_3

RT

template<typename K >

typedef K::RT CGAL::Width_default_traits_3< K >::RT

Vector_3

template<typename K >

typedef K::Vector_3 CGAL::Width_default_traits_3< K >::Vector_3

Constructor & Destructor Documentation

Width_default_traits_3()

template<typename K >

CGAL::Width_default_traits_3< K >::Width_default_traits_3

(

)

default constructor.

Member Function Documentation

get_a()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_a

(

const Plane_3 &

f

)

const

returns the first coefficient of plane \( f\).

get_b()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_b

(

const Plane_3 &

f

)

const

returns the second coefficient of plane \( f\).

get_c()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_c

(

const Plane_3 &

f

)

const

returns the third coefficient of plane \( f\).

get_d()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_d

(

const Plane_3 &

f

)

const

returns the fourth coefficient of plane \( f\).

get_hw()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_hw

(

const Point_3 &

p

)

const

returns the homogenizing coordinate of point \( p\).

get_hx()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_hx

(

const Point_3 &

p

)

const

returns the homogeneous \( x\)-coordinate of point \( p\).

get_hy()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_hy

(

const Point_3 &

p

)

const

returns the homogeneous \( y\)-coordinate of point \( p\).

get_hz()

template<typename K >

RT CGAL::Width_default_traits_3< K >::get_hz

(

const Point_3 &

p

)

const

returns the homogeneous \( z\)-coordinate of point \( p\).

get_plane_coefficients()

template<typename K >

void CGAL::Width_default_traits_3< K >::get_plane_coefficients	(	const Plane_3 &	f,
		RT &	a,
		RT &	b,
		RT &	c,
		RT &	d
	)		const

returns all four plane coefficients of \( f\) at once.

get_point_coordinates()

template<typename K >

void CGAL::Width_default_traits_3< K >::get_point_coordinates	(	const Point_3 &	p,
		RT &	px,
		RT &	py,
		RT &	pz,
		RT &	ph
	)		const

returns all homogeneous coordinates of point \( p\) at once.

make_plane()

template<typename K >

Plane_3 CGAL::Width_default_traits_3< K >::make_plane	(	const RT &	a,
		const RT &	b,
		const RT &	c,
		const RT &	d
	)		const

returns a plane of type Plane_3 whose coefficients are \( a\), \( b\), \( c\) and \( d\).

make_point()

template<typename K >

Point_3 CGAL::Width_default_traits_3< K >::make_point	(	const RT &	hx,
		const RT &	hy,
		const RT &	hz,
		const RT &	hw
	)		const

returns a point of type Point_3 with homogeneous coordinates \( hx\), \( hy\), \( hz\) and \( hw\).

make_vector()

template<typename K >

Vector CGAL::Width_default_traits_3< K >::make_vector	(	const RT &	a,
		const RT &	b,
		const RT &	c
	)		const

returns a vector of type Vector_3 with the four coefficients \( a\), \( b\), \( c\) and 1.