#include <CGAL/Iso_cuboid_3.h>

Definition

template<typename Kernel>
class CGAL::Iso_cuboid_3< Kernel >

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`.

	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`.

	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`).

	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`.

Point_3< Kernel >	operator[] (int i) const
	returns `vertex(i)`, as indicated in the figure below:

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`.

Kernel::FT	max_coord (int i) const
	returns `i`-th Cartesian coordinate of the largest vertex of `c`.

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`.

Constructor & Destructor Documentation

◆ Iso_cuboid_3() [1/5]

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.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ Iso_cuboid_3() [2/5]

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().

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ Iso_cuboid_3() [3/5]

template<typename Kernel >

CGAL::Iso_cuboid_3< Kernel >::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.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ Iso_cuboid_3() [4/5]

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 != 0.

◆ Iso_cuboid_3() [5/5]

template<typename Kernel >

CGAL::Iso_cuboid_3< Kernel >::Iso_cuboid_3 ( const Bbox_3 & bbox )

If Kernel::RT is constructible from double, introduces an iso-oriented cuboid from bbox.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Member Function Documentation

◆ bbox()

template<typename Kernel >

Bbox_3 CGAL::Iso_cuboid_3< Kernel >::bbox ( ) const

returns a bounding box containing c.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ max()

template<typename Kernel >

Point_3< Kernel > CGAL::Iso_cuboid_3< Kernel >::max ( ) const

returns the largest vertex of c (= vertex(7)).

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ 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 <= i <= 2.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ min()

template<typename Kernel >

Point_3< Kernel > CGAL::Iso_cuboid_3< Kernel >::min ( ) const

returns the smallest vertex of c (= vertex(0)).

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ 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 <= i <= 2.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ 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:

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ 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.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ xmax()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::xmax ( ) const

returns largest Cartesian $x$ -coordinate in c.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ xmin()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::xmin ( ) const

returns smallest Cartesian $x$ -coordinate in c.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ ymax()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::ymax ( ) const

returns largest Cartesian $y$ -coordinate in c.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ ymin()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::ymin ( ) const

returns smallest Cartesian $y$ -coordinate in c.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ zmax()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::zmax ( ) const

returns largest Cartesian $z$ -coordinate in c.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

◆ zmin()

template<typename Kernel >

Kernel::FT CGAL::Iso_cuboid_3< Kernel >::zmin ( ) const

returns smallest Cartesian $z$ -coordinate in c.

Exactness: This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Definition

Creation

Operations

Predicates

Miscellaneous

Constructor & Destructor Documentation

◆ Iso_cuboid_3() [1/5]

◆ Iso_cuboid_3() [2/5]

◆ Iso_cuboid_3() [3/5]

◆ Iso_cuboid_3() [4/5]

◆ Iso_cuboid_3() [5/5]

Member Function Documentation

◆ bbox()

◆ max()

◆ max_coord()

◆ min()

◆ min_coord()

◆ operator[]()

◆ transform()

◆ vertex()

◆ xmax()

◆ xmin()

◆ ymax()

◆ ymin()

◆ zmax()

◆ zmin()