This concept defines the requirements for traits classes of Width_3<Traits>.
 
The point type. The (in)equality tests must be
available. Access to the point coordinates is done via the get_.()
functions. Constructing a point is done with the make_point( )
operation.
 
 
The plane type. Access to the coefficients of the
plane is made via the get_.() functions. Constructing a plane is
done with the make_plane() operation.
 
 
The vector type. There is no need to access the
coefficients of a vector; only constructing is required and is done with
the make_vector operation.
 
 
The traits class for using the convex hull
algorithm. It must be a model of the concept ConvexHullTraits_3.
This class is used only if the width is computed from a set
of points.
 
 
Ring type numbers. Internally all numbers are treated as
ring type numbers, i.e., neither $$/operator nor $$sqrt(.) nor other
inexact operations are used. But because the algorithm does not use any
divisions, but multiplication instead, the numbers can get really big.
Therefore it is recommended to use a ring type number, that provides
values of arbitrary length. Furthermore it is assumed that the underlying
number type of Point_3, Plane_3 and Vector_3 equals
RT.

Notes: If you want to compute the width of a polyhedron then you have to make sure that the point type in the traits class and the point type in the polyhedron class are the same! The same holds for Traits::Plane_3 and Polyhedron::Plane_3.
Only a default constructor is required.


 
returns the homogeneous $$xcoordinate of point $$p.  

 
returns the homogeneous $$ycoordinate of point $$p.  

 
returns the homogeneous $$zcoordinate of point $$p.  

 
returns the homogenizing coordinate of point $$p.  

 
returns all homogeneous coordinates of point $$p at once.  

 
returns the first coefficient of plane $$f.  

 
returns the second coefficient of plane $$f.  

 
returns the third coefficient of plane $$f.  

 
returns the fourth coefficient of plane $$f.  

 
returns all four plane coefficients of $$f at once.  

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

 
returns a plane of type Plane_3 with coefficients $$a, $$b, $$c and $$d.  

 
returns a vector of type Vector_3 with the four homogeneous coefficients $$a, $$b, $$c and 1. 
CGAL::Width_default_traits_3<K>
CGAL::Width_3<Traits>