CGAL::Iso_cuboid_3< Kernel > Class Template Reference

#include <CGAL/Iso_cuboid_3.h>

Definition

An object c of the data type Iso_cuboid_3 is a cuboid in the Euclidean space $\E^3$ with edges parallel to the $x$, $y$ and $z$ axis of the coordinate system.

Although they are represented in a canonical form by only two vertices, namely the lexicographically smallest and largest vertex with respect to Cartesian $xyz$ coordinates, we provide functions for "accessing" the other vertices as well.

Iso-oriented cuboids and bounding boxes are quite similar. The difference however is that bounding boxes have always double coordinates, whereas the coordinate type of an iso-oriented cuboid is chosen by the user.

Is Model Of:

Kernel::IsoCuboid_3

Hashable if Kernel is a cartesian kernel and if Kernel::FT is Hashable

Creation
	Iso_cuboid_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q)
	introduces an iso-oriented cuboid c with diagonal opposite vertices p and q. More...
	Iso_cuboid_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q, int)
	introduces an iso-oriented cuboid c with diagonal opposite vertices p and q. More...
	Iso_cuboid_3 (const Point_3< Kernel > &left, const Point_3< Kernel > &right, const Point_3< Kernel > &bottom, const Point_3< Kernel > &top, const Point_3< Kernel > &far, const Point_3< Kernel > &close)
	introduces an iso-oriented cuboid c whose minimal $x$ coordinate is the one of left, the maximal $x$ coordinate is the one of right, the minimal $y$ coordinate is the one of bottom, the maximal $y$ coordinate is the one of top, the minimal $z$ coordinate is the one of far, the maximal $z$ coordinate is the one of close.
	Iso_cuboid_3 (const Kernel::RT &min_hx, const Kernel::RT &min_hy, const Kernel::RT &min_hz, const Kernel::RT &max_hx, const Kernel::RT &max_hy, const Kernel::RT &max_hz, const Kernel::RT &hw=RT(1))
	introduces an iso-oriented cuboid c with diagonal opposite vertices (min_hx/hw, min_hy/hw, min_hz/hw) and (max_hx/hw, max_hy/hw, max_hz/hw). More...
	Iso_cuboid_3 (const Bbox_3 &bbox)
	If Kernel::RT is constructible from double, introduces an iso-oriented cuboid from bbox.

Operations
bool	operator== (const Iso_cuboid_3< Kernel > &c2) const
	Test for equality: two iso-oriented cuboid are equal, iff their lower left and their upper right vertices are equal.
bool	operator!= (const Iso_cuboid_3< Kernel > &c2) const
	Test for inequality.
Point_3< Kernel >	vertex (int i) const
	returns the i'th vertex modulo 8 of c. More...
Point_3< Kernel >	operator[] (int i) const
	returns vertex(i), as indicated in the figure below: More...
Point_3< Kernel >	min () const
	returns the smallest vertex of c (= vertex(0)).
Point_3< Kernel >	max () const
	returns the largest vertex of c (= vertex(7)).
Kernel::FT	xmin () const
	returns smallest Cartesian $x$-coordinate in c.
Kernel::FT	ymin () const
	returns smallest Cartesian $y$-coordinate in c.
Kernel::FT	zmin () const
	returns smallest Cartesian $z$-coordinate in c.
Kernel::FT	xmax () const
	returns largest Cartesian $x$-coordinate in c.
Kernel::FT	ymax () const
	returns largest Cartesian $y$-coordinate in c.
Kernel::FT	zmax () const
	returns largest Cartesian $z$-coordinate in c.
Kernel::FT	min_coord (int i) const
	returns i-th Cartesian coordinate of the smallest vertex of c. More...
Kernel::FT	max_coord (int i) const
	returns i-th Cartesian coordinate of the largest vertex of c. More...

Predicates
bool	is_degenerate () const
	c is degenerate, if all vertices are coplanar.
Bounded_side	bounded_side (const Point_3< Kernel > &p) const
	returns either ON_UNBOUNDED_SIDE, ON_BOUNDED_SIDE, or the constant ON_BOUNDARY, depending on where point p is.
bool	has_on_boundary (const Point_3< Kernel > &p) const
bool	has_on_bounded_side (const Point_3< Kernel > &p) const
bool	has_on_unbounded_side (const Point_3< Kernel > &p) const

Miscellaneous
Kernel::FT	volume () const
	returns the volume of c.
Bbox_3	bbox () const
	returns a bounding box containing c.
Iso_cuboid_3< Kernel >	transform (const Aff_transformation_3< Kernel > &t) const
	returns the iso-oriented cuboid obtained by applying t on the smallest and the largest of c. More...

Constructor & Destructor Documentation

Iso_cuboid_3() [1/3]

template<typename Kernel >

CGAL::Iso_cuboid_3< Kernel >::Iso_cuboid_3	(	const Point_3< Kernel > &	p,
		const Point_3< Kernel > &	q
	)

introduces an iso-oriented cuboid c with diagonal opposite vertices p and q.

Note that the object is brought in the canonical form.

Iso_cuboid_3() [2/3]

template<typename Kernel >

CGAL::Iso_cuboid_3< Kernel >::Iso_cuboid_3	(	const Point_3< Kernel > &	p,
		const Point_3< Kernel > &	q,
		int
	)

introduces an iso-oriented cuboid c with diagonal opposite vertices p and q.

The int argument value is only used to distinguish the two overloaded functions.

Precondition

p.x()<=q.x(), p.y()<=q.y()and p.z()<=q.z().

Iso_cuboid_3() [3/3]

template<typename Kernel >

CGAL::Iso_cuboid_3< Kernel >::Iso_cuboid_3	(	const Kernel::RT &	min_hx,
		const Kernel::RT &	min_hy,
		const Kernel::RT &	min_hz,
		const Kernel::RT &	max_hx,
		const Kernel::RT &	max_hy,
		const Kernel::RT &	max_hz,
		const Kernel::RT &	hw = RT(1)
	)

introduces an iso-oriented cuboid c with diagonal opposite vertices (min_hx/hw, min_hy/hw, min_hz/hw) and (max_hx/hw, max_hy/hw, max_hz/hw).

Precondition

hw $\neq$ 0.

Member Function Documentation

max_coord()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::max_coord

(

int

i

)

const

returns i-th Cartesian coordinate of the largest vertex of c.

Precondition

$0 \leq i \leq2$.

min_coord()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::min_coord

(

int

i

)

const

returns i-th Cartesian coordinate of the smallest vertex of c.

Precondition

$0 \leq i \leq2$.

operator[]()

template<typename Kernel >

Point_3<Kernel> CGAL::Iso_cuboid_3< Kernel >::operator[]

(

int

i

)

const

returns vertex(i), as indicated in the figure below:

transform()

template<typename Kernel >

Iso_cuboid_3<Kernel> CGAL::Iso_cuboid_3< Kernel >::transform

(

const Aff_transformation_3< Kernel > &

t

)

const

returns the iso-oriented cuboid obtained by applying t on the smallest and the largest of c.

Precondition

The angle at a rotation must be a multiple of $\pi/2$, otherwise the resulting cuboid does not have the same size. Note that rotating about an arbitrary angle can even result in a degenerate iso-oriented cuboid.

vertex()

template<typename Kernel >

Point_3<Kernel> CGAL::Iso_cuboid_3< Kernel >::vertex

(

int

i

)

const

returns the i'th vertex modulo 8 of c.

starting with the lower left vertex.