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

CGAL 4.8 - Intersecting Sequences of dD Iso-oriented Boxes

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CGAL::Box_intersection_d::Box_with_handle_d< NT, D, Handle, IdPolicy > Class Template Reference
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`#include <CGAL/Box_intersection_d/Box_with_handle_d.h>`

## Definition

`Box_with_handle_d` is a generic iso-oriented bounding box in dimension \( D\) that stores additionally a handle to some underlying geometric object.

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.

Template Parameters

  NT | number type for the box boundaries, needs to be a model of the `Assignable` and the `LessThanComparable` concept.
  D | the dimension of the box.
  Handle | Handle concept, e.g., a pointer, an iterator, or a circulator.
  IdPolicy | specifies how the `id`-number will be provided. Can be one of the following types, where `ID_FROM_HANDLE` is the default for this parameter: `ID_NONE`: no `id`-number is provided. Can be useful to have this class as a base class for different implementations 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 `CGAL::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 `CGAL::box_self_intersection_d()` algorithm creates copies of the boxes that would not have identical `id`-numbers. `ID_FROM_HANDLE`: casts the address of the value of the handle into a `std::ptrdiff_t` to create the `id`-number. Works in many conceivable settings, e.g., it works with boxes copied by value or by pointer, and the self intersection test. It will not work if there is no one-to-one mapping between boxes and the geometry that is referred to with the handles, i.e., this `id`-number scheme fails if a geometric object creates several boxes with the same handle value. Note that this option is not available for the `CGAL::Box_intersection_d::Box_d` type that does not store a handle.

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_traits_d<BoxHandle>`
  `BoxIntersectionTraits_d`

Examples:
  Box_intersection_d/triangle_self_intersect.cpp, and Box_intersection_d/triangle_self_intersect_pointers.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_with_handle_d ()
| Default constructor. More...
| Box_with_handle_d (bool complete, Handle h)
| initializes to the complete or the empty space. More...
| Box_with_handle_d (NT lo[D], NT hi[D], Handle h)
| initializes the box intervals to [`lo[i]`,`hi[i]`], \( 0 \leq i < D\) and sets the handle to \( h\). More...
| Box_with_handle_d (const Bbox_2 &bbox, Handle h)
| constructs from bbox and sets the handle to \( h\), exists iff \( D=2\) and `NT` \( \equiv\)`double`.
| Box_with_handle_d (const Bbox_3 &bbox, Handle h)
| constructs from bbox and sets the handle to \( h\), exists iff \( D=3\) and `NT` \( \equiv\)`double`.

## 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`.

## Access Functions
Handle | handle () const
| returns the handle stored in `box`.
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`, \( 0 \leq\)`d` \( < D\).
NT | max_coord (int d) const
| returns the upper boundary in dimension `d`, \( 0 \leq\)`d` \( < D\).
const Bbox_2 & | bbox () const
| returns the bounding box iff \( D=2\) and `NT` \( \equiv\)`double`.
const Bbox_3 & | bbox () const
| returns the bounding box iff \( D=3\) and `NT` \( \equiv\)`double`.
static int | dimension ()
| returns \( D\), the dimension of the box.

## Member Typedef Documentation

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

typedef unspecified_type CGAL::Box_intersection_d::Box_with_handle_d< NT, D, Handle, 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 Handle , typename IdPolicy >

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

Default constructor.

No particular initialization.

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

CGAL::Box_intersection_d::Box_with_handle_d< NT, D, Handle, IdPolicy >::Box_with_handle_d | ( | bool | complete,
|  | Handle | h
| ) |  |

initializes to the complete or the empty space.

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

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

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

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

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

## Member Function Documentation

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

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

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

Does not exist if `ID_NONE` has been chosen for the `IdPolicy`.

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

void CGAL::Box_intersection_d::Box_with_handle_d< NT, D, Handle, 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.