Definition

This concept defines the requirements for traits classes of Width_3<Traits>.

Operations

Whatever the coordinates of the points are, it is required for the width-algorithm to have access to the homogeneous representation of points.

Has Models:: CGAL::Width_default_traits_3

See also: CGAL::Width_3<Traits>

Related Functions
(Note that these are not member functions.)
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` with coefficients \( a\), \( b\), \( c\) and \( d\).

Vector_3	make_vector (const RT &a, const RT &b, const RT &c) const
	returns a vector of type `Vector_3` with the four homogeneous coefficients \( a\), \( b\), \( c\) and 1.

Types
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`.
typedef unspecified_type	Point_3
	The point type. More...

typedef unspecified_type	Plane_3
	The plane type. More...

typedef unspecified_type	Vector_3
	The vector type. More...

typedef unspecified_type	ChullTraits
	The traits class for using the convex hull algorithm. More...

typedef unspecified_type	RT
	Ring type numbers. More...

Creation
Only a default constructor is required.
	WidthTraits_3 ()

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.

Member Typedef Documentation

◆ ChullTraits

typedef unspecified_type WidthTraits_3::ChullTraits

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.

◆ Plane_3

typedef unspecified_type WidthTraits_3::Plane_3

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.

◆ Point_3

typedef unspecified_type WidthTraits_3::Point_3

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.

◆ RT

typedef unspecified_type WidthTraits_3::RT

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.

◆ Vector_3

typedef unspecified_type WidthTraits_3::Vector_3

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.