## CGAL::Width_default_traits_3<K>

### Definition

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

#include <CGAL/Width_default_traits_3.h>

### Requirements

The template parameter K is a model for Kernel

### Is Model for the Concept

WidthTraits_3

### Types

typedef typename K::Point_3
| Point_3;
typedef typename K::Plane_3
| Plane_3;
typedef typename K::Vector_3
| Vector_3;
typedef typename K::RT
| RT;
typedef Convex_hull_traits_3<K>
| ChullTraits;

### Creation

Width_default_traits_3<K> traits;
| default constructor.

### Operations

RT | traits.get_hx ( Point_3 p)
|  | returns the homogeneous x-coordinate of point p.
RT | traits.get_hy ( Point_3 p)
|  | returns the homogeneous y-coordinate of point p.
RT | traits.get_hz ( Point_3 p)
|  | returns the homogeneous z-coordinate of point p.
RT | traits.get_hw ( Point_3 p)
|  | returns the homogenizing coordinate of point p.

void

traits.get_point_coordinates ( | Point_3 p, RT& px, RT& py, RT& pz, RT& ph)

|  | returns all homogeneous coordinates of point p at once.
RT | traits.get_a ( Plane_3 f)
|  | returns the first coefficient of plane f.
RT | traits.get_b ( Plane_3 f)
|  | returns the second coefficient of plane f.
RT | traits.get_c ( Plane_3 f)
|  | returns the third coefficient of plane f.
RT | traits.get_d ( Plane_3 f)
|  | returns the fourth coefficient of plane f.

void

traits.get_plane_coefficients ( | Plane_3 f, RT& a, RT& b, RT& c, RT& d)

|  | returns all four plane coefficients of f at once.
Point_3 | traits.make_point ( RT hx, RT hy, RT hz, RT hw)
|  | returns a point of type Point_3 with homogeneous coordinates hx, hy, hz and hw.
Plane_3 | traits.make_plane ( RT a, RT b, RT c, RT d)
|  | returns a plane of type Plane_3 whose coefficients are a, b, c and d.
Vector | traits.make_vector ( RT a, RT b, RT c)
|  | returns a vector of type Vector_3 with the four coefficients a, b, c and 1.

### See Also

CGAL::Width_3<Traits>
WidthTraits_3