\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.7 - Optimal Distances
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CGAL::Width_default_traits_3< K > Class Template Reference
Optimal Distances Reference

#include <CGAL/Width_default_traits_3.h>

Definition

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

Template Parameters
Kmust 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. More...
 

Operations

RT get_hx (const Point_3 &p) const
 returns the homogeneous \( x\)-coordinate of point \( p\). More...
 
RT get_hy (const Point_3 &p) const
 returns the homogeneous \( y\)-coordinate of point \( p\). More...
 
RT get_hz (const Point_3 &p) const
 returns the homogeneous \( z\)-coordinate of point \( p\). More...
 
RT get_hw (const Point_3 &p) const
 returns the homogenizing coordinate of point \( p\). More...
 
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. More...
 
RT get_a (const Plane_3 &f) const
 returns the first coefficient of plane \( f\). More...
 
RT get_b (const Plane_3 &f) const
 returns the second coefficient of plane \( f\). More...
 
RT get_c (const Plane_3 &f) const
 returns the third coefficient of plane \( f\). More...
 
RT get_d (const Plane_3 &f) const
 returns the fourth coefficient of plane \( f\). More...
 
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. More...
 
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 \( hw\). More...
 
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 \( d\). More...
 
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. More...
 

Member Typedef Documentation

template<typename K >
typedef Convex_hull_traits_3<K> CGAL::Width_default_traits_3< K >::ChullTraits
template<typename K >
typedef K::Plane_3 CGAL::Width_default_traits_3< K >::Plane_3
template<typename K >
typedef K::Point_3 CGAL::Width_default_traits_3< K >::Point_3
template<typename K >
typedef K::RT CGAL::Width_default_traits_3< K >::RT
template<typename K >
typedef K::Vector_3 CGAL::Width_default_traits_3< K >::Vector_3

Constructor & Destructor Documentation

template<typename K >
CGAL::Width_default_traits_3< K >::Width_default_traits_3 ( )

default constructor.

Member Function Documentation

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_a ( const Plane_3 &  f) const

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

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_b ( const Plane_3 &  f) const

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

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_c ( const Plane_3 &  f) const

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

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_d ( const Plane_3 &  f) const

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

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_hw ( const Point_3 &  p) const

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

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_hx ( const Point_3 &  p) const

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

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_hy ( const Point_3 &  p) const

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

template<typename K >
RT CGAL::Width_default_traits_3< K >::get_hz ( const Point_3 &  p) const

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

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.

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.

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 \( d\).

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 \( hw\).

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.