\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 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

  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.