CGAL 4.7 - Optimal Distances
CGAL::Width_default_traits_3< K > Class Template 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
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.