WidthTraits

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WidthTraits_3

Definition

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

Types

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.
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.
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.
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.
WidthTraits_3::RT
	Ring type numbers. Internally all numbers are treated as ring type numbers, i.e., neither /-operator nor √. 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.

Creation

Only a default constructor is required.

WidthTraits_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.

RT	get_hx ( Point_3 p) const	returns the homogeneous x-coordinate of point p.
RT	get_hy ( Point_3 p) const	returns the homogeneous y-coordinate of point p.
RT	get_hz ( Point_3 p) const	returns the homogeneous z-coordinate of point p.
RT	get_hw ( Point_3 p) const	returns the homogenizing coordinate of point p.
void	get_point_coordinates ( Point_3 p, RT& px, RT& py, RT& pz, RT& ph) const
		returns all homogeneous coordinates of point p at once.

RT	get_a ( Plane_3 f) const	returns the first coefficient of plane f.
RT	get_b ( Plane_3 f) const	returns the second coefficient of plane f.
RT	get_c ( Plane_3 f) const	returns the third coefficient of plane f.
RT	get_d ( Plane_3 f) const	returns the fourth coefficient of plane f.
void	get_plane_coefficients ( 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 ( RT hx, RT hy, RT hz, RT hw) const
		returns a point of type Point_3 with homogeneous coordinates hx, hy, hz and hw.
Plane_3	make_plane ( RT a, RT b, RT c, RT d) const
		returns a plane of type Plane_3 with coefficients a, b, c and d.
Vector_3	make_vector ( RT a, RT b, RT c) const
		returns a vector of type Vector_3 with the four homogeneous coefficients a, b, c and 1.

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