\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Intersecting Sequences of dD Iso-oriented Boxes

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CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy > Class Template Reference
Classes

`#include <CGAL/Box_intersection_d/Box_d.h>`

## Definition

`Box_d` is a generic iso-oriented bounding box in dimension \( D\).

It provides in each dimension an interval with lower and upper endpoints represented with the number type `NT`. This class is designed to work smoothly with the algorithms for intersecting sequences of iso-oriented boxes. For degeneracy handling, the boxes need to provide a unique `id`-number. The policy parameter `IdPolicy` offers several choices. The template parameters have to comply with the following requirements:

- `NT`: number type for the box boundaries, needs to be a model of the `Assignable` and the `LessThanComparable` concept.
- `int D`: the dimension of the box.
- `IdPolicy`: specifies how the `id`-number will be provided. Can be one of the following types, where `ID_EXPLICIT` is the default for this parameter:
  - `ID_NONE`: no `id`-number is provided. Can be useful if `Box_d` is used as a base class for a different implementation of `id`-numbers than the ones provided here.
  - `ID_EXPLICIT`: the `id`-number is stored explicitly in the box and automatically created and assigned at construction time of the box. Note that copying a box (copy-constructor and assignment) does not create a new `id`-number but keeps the old one, which is the behavior needed by the `box_self_intersection_d()` algorithm. This is therefore the safe default implementation.
  - `ID_FROM_BOX_ADDRESS`: casts the address of the box into a `std::ptrdiff_t` to create the `id`-number. Works fine if the intersection algorithms work effectively with pointers to boxes, but not in the case where the algorithms work with box values, because the algorithms modify the order of the boxes, and the `box_self_intersection_d()` algorithm creates copies of the boxes that would not have identical `id`-numbers.

Is Model Of:
  `BoxIntersectionBox_d`

See Also
  `CGAL::box_intersection_d()`
  `CGAL::box_self_intersection_d()`
  `CGAL::box_intersection_all_pairs_d()`
  `CGAL::box_self_intersection_all_pairs_d()`
  `CGAL::Box_intersection_d::Box_with_handle_d<NT, int D, Handle, IdPolicy>`
  `CGAL::Box_intersection_d::Box_traits_d<BoxHandle>`
  `BoxIntersectionTraits_d`

Examples:
  Box_intersection_d/box_grid.cpp, Box_intersection_d/minimal.cpp, and Box_intersection_d/minimal_self.cpp.

## Types
typedef unspecified_type | NT
| number type to represent the box boundaries. More...
typedef std::size_t | ID
| type for the box `id`-number.

## Creation
| Box_d ()
| Default constructor. More...
| Box_d (bool complete)
| Constructor initialized to the complete or the empty space. More...
| Box_d (NT lo[D], NT hi[D])
| initializes the box intervals to [`lo[i]`,`hi[i]`], \( 0 \leq i < D\). More...
| Box_d (const Bbox_2 &bbox)
| constructs from `bbox`. More...
| Box_d (const Bbox_3 &bbox)
| constructs from `bbox`. More...

## Modifiers
void | init (bool complete=false)
| initializes to the complete or the empty space. More...
void | extend (NT point[D])
| extend `box` to contain the old `box` and `point`.
static int | dimension ()
| returns \( D\), the dimension of the box.

## Access Functions
std::size_t | id ()
| returns a unique box id, see the `IdPolicy` template parameter above for the different choices. More...
NT | min_coord (int d) const
| returns the lower boundary in dimension `d` More...
NT | max_coord (int d) const
| returns the upper boundary in dimension `d` More...
const Bbox_2 & | bbox () const
| returns the bounding box Requirements: \( D=2\) and `NT` \( \equiv\)`double`
const Bbox_3 & | bbox () const
| returns the bounding box Requirements: \( D=3\) and `NT` \( \equiv\)`double`
void | extend (NT p[N])
| extends `box` to the smallest box that additionally contains the point represented by coordinates in `p`.
void | extend (std::pair< NT, NT > p[N])
| extends `box` to the smallest box that additionally contains the point represented by coordinate intervals in `p`.

## Member Typedef Documentation

template<typename NT , typename int D, typename IdPolicy >

typedef unspecified_type CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::NT

number type to represent the box boundaries.

Allowed are the built-in types `int`, `unsigned int`, `float`, and `double`.

## Constructor & Destructor Documentation

template<typename NT , typename int D, typename IdPolicy >

CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::Box_d | ( | ) |  |

Default constructor.

No particular initialization.

template<typename NT , typename int D, typename IdPolicy >

CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::Box_d | ( | bool | complete) |  |

Constructor initialized to the complete or the empty space.

If empty, all interval starting(end) points will be set to positive(negative) infinity.

template<typename NT , typename int D, typename IdPolicy >

CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::Box_d | ( | NT | lo[D],
|  | NT | hi[D]
| ) |  |

initializes the box intervals to [`lo[i]`,`hi[i]`], \( 0 \leq i < D\).

Precondition
  `lo[i]` \( <\) `hi[i]` for \( 0 \leq i < D\).

template<typename NT , typename int D, typename IdPolicy >

CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::Box_d | ( | const Bbox_2 & | bbox) |  |

constructs from `bbox`.

Requirements: \( D=2\) and `NT` \( \equiv\)`double`.

template<typename NT , typename int D, typename IdPolicy >

CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::Box_d | ( | const Bbox_3 & | bbox) |  |

constructs from `bbox`.

Requirements: \( D=3\) and `NT` \( \equiv\)`double`.

## Member Function Documentation

template<typename NT , typename int D, typename IdPolicy >

std::size_t CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::id | ( | ) |  |

returns a unique box id, see the `IdPolicy` template parameter above for the different choices.

Template Parameters

  <tt>IdPolicy</tt> | \( \neq\)`ID_NONE`

template<typename NT , typename int D, typename IdPolicy >

void CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::init | ( | bool | complete = `false`) |  |

initializes to the complete or the empty space.

If empty, all interval starting(end) points will be set to positive(negative) infinity.

template<typename NT , typename int D, typename IdPolicy >

NT CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::max_coord | ( | int | d) |  | const

returns the upper boundary in dimension `d`

Precondition
  \( 0 \leq\)`d` \( < D\).

template<typename NT , typename int D, typename IdPolicy >

NT CGAL::Box_intersection_d::Box_d< NT, D, IdPolicy >::min_coord | ( | int | d) |  | const

returns the lower boundary in dimension `d`

Precondition
  \( 0 \leq\)`d` \( < D\).