#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()