 Reference documentation for deal.II version GIT c1ddcf411d 2023-11-30 16:30:02+00:00
BoundingBox< spacedim, Number > Class Template Reference

#include <deal.II/base/bounding_box.h>

Inheritance diagram for BoundingBox< spacedim, Number >: [legend]

## Public Member Functions

BoundingBox ()=default

BoundingBox (const BoundingBox< spacedim, Number > &box)=default

BoundingBox< spacedim, Number > & operator= (const BoundingBox< spacedim, Number > &t)=default

BoundingBox (const Point< spacedim, Number > &point)

BoundingBox (const std::pair< Point< spacedim, Number >, Point< spacedim, Number >> &boundary_points)

template<class Container >
BoundingBox (const Container &points)

std::pair< Point< spacedim, Number >, Point< spacedim, Number > > & get_boundary_points ()

const std::pair< Point< spacedim, Number >, Point< spacedim, Number > > & get_boundary_points () const

bool operator== (const BoundingBox< spacedim, Number > &box) const

bool operator!= (const BoundingBox< spacedim, Number > &box) const

bool has_overlap_with (const BoundingBox< spacedim, Number > &other_bbox, const double tolerance=std::numeric_limits< Number >::epsilon()) const

NeighborType get_neighbor_type (const BoundingBox< spacedim, Number > &other_bbox, const double tolerance=std::numeric_limits< Number >::epsilon()) const

void merge_with (const BoundingBox< spacedim, Number > &other_bbox)

bool point_inside (const Point< spacedim, Number > &p, const double tolerance=std::numeric_limits< Number >::epsilon()) const

void extend (const Number amount)

BoundingBox< spacedim, Number > create_extended (const Number amount) const

BoundingBox< spacedim, Number > create_extended_relative (const Number relative_amount) const

double volume () const

Point< spacedim, Number > center () const

Number side_length (const unsigned int direction) const

Number lower_bound (const unsigned int direction) const

Number upper_bound (const unsigned int direction) const

BoundingBox< 1, Number > bounds (const unsigned int direction) const

Point< spacedim, Number > vertex (const unsigned int index) const

BoundingBox< spacedim, Number > child (const unsigned int index) const

BoundingBox< spacedim - 1, Number > cross_section (const unsigned int direction) const

Point< spacedim, Number > real_to_unit (const Point< spacedim, Number > &point) const

Point< spacedim, Number > unit_to_real (const Point< spacedim, Number > &point) const

Number signed_distance (const Point< spacedim, Number > &point, const unsigned int direction) const

Number signed_distance (const Point< spacedim, Number > &point) const

template<class Archive >
void serialize (Archive &ar, const unsigned int version)

## Private Attributes

std::pair< Point< spacedim, Number >, Point< spacedim, Number > > boundary_points

## Related Functions

(Note that these are not member functions.)

template<int dim, typename Number = double>
BoundingBox< dim, Number > create_unit_bounding_box ()

template<int dim>
int coordinate_to_one_dim_higher (const int locked_coordinate, const int coordinate_in_dim)

## Detailed Description

### template<int spacedim, typename Number = double> class BoundingBox< spacedim, Number >

A class that represents a box of arbitrary dimension spacedim and with sides parallel to the coordinate axes, that is, a region

$[x_0^L, x_0^U] \times ... \times [x_{spacedim-1}^L, x_{spacedim-1}^U],$

where $$(x_0^L , ..., x_{spacedim-1}^L)$$ and $$(x_0^U , ..., x_{spacedim-1}^U)$$ denote the two vertices (bottom left and top right) which are used to represent the box. The quantities $$x_k^L$$ and $$x_k^U$$ denote the "lower" and "upper" bounds of values that are within the box for each coordinate direction $$k$$.

Geometrically, a bounding box is thus:

• 1d: a segment (represented by its vertices in the proper order)
• 2d: a rectangle (represented by the vertices V at bottom left, top right)
.--------V
| |
V--------.
static const char V
• 3d: a cuboid (in which case the two vertices V follow the convention and are not owned by the same face)
.------V
/ /|
.------. |
| | /
| |/
V------.

Bounding boxes are, for example, useful in parallel distributed meshes to give a general description of the owners of each portion of the mesh. More generally, bounding boxes are often used to roughly describe a region of space in which an object is contained; if a candidate point is not within the bounding box (a test that is cheap to execute), then it is not necessary to perform an expensive test whether the candidate point is in fact inside the object itself. Bounding boxes are therefore often used as a first, cheap rejection test before more detailed checks. As such, bounding boxes serve many of the same purposes as the convex hull, for which it is also relatively straightforward to compute whether a point is inside or outside, though not quite as cheap as for the bounding box.

Taking the cross section of a BoundingBox<spacedim> orthogonal to a given direction gives a box in one dimension lower: BoundingBox<spacedim - 1>. In 3d, the 2 coordinates of the cross section of BoundingBox<3> can be ordered in 2 different ways. That is, if we take the cross section orthogonal to the y direction we could either order a 3d-coordinate into a 2d-coordinate as $$(x,z)$$ or as $$(z,x)$$. This class uses the second convention, corresponding to the coordinates being ordered cyclicly $$x \rightarrow y \rightarrow z \rightarrow x \rightarrow ...$$ To be precise, if we take a cross section:

Orthogonal to Cross section coordinates ordered as
x (y, z)
y (z, x)
z (x, y)

This is according to the convention set by the function coordinate_to_one_dim_higher.

Definition at line 136 of file bounding_box.h.

## ◆ BoundingBox() [1/5]

template<int spacedim, typename Number = double>
 BoundingBox< spacedim, Number >::BoundingBox ( )
default

Standard constructor. Creates an object that corresponds to an empty box, i.e. a degenerate box with both points being the origin.

## ◆ BoundingBox() [2/5]

template<int spacedim, typename Number = double>
 BoundingBox< spacedim, Number >::BoundingBox ( const BoundingBox< spacedim, Number > & box )
default

Standard copy constructor operator.

## ◆ BoundingBox() [3/5]

template<int spacedim, typename Number = double>
 BoundingBox< spacedim, Number >::BoundingBox ( const Point< spacedim, Number > & point )

Standard constructor for an empty box around a point point.

## ◆ BoundingBox() [4/5]

template<int spacedim, typename Number = double>
 BoundingBox< spacedim, Number >::BoundingBox ( const std::pair< Point< spacedim, Number >, Point< spacedim, Number >> & boundary_points )

Standard constructor for non-empty boxes: it uses a pair of points which describe the box: one for the bottom and one for the top corner.

## ◆ BoundingBox() [5/5]

template<int spacedim, typename Number = double>
template<class Container >
 BoundingBox< spacedim, Number >::BoundingBox ( const Container & points )

Construct the bounding box that encloses all the points in the given container.

The constructor supports any Container that provides begin() and end() iterators to Point<spacedim, Number> elements.

## ◆ operator=()

template<int spacedim, typename Number = double>
 BoundingBox& BoundingBox< spacedim, Number >::operator= ( const BoundingBox< spacedim, Number > & t )
default

Standard copy assignment operator.

## ◆ get_boundary_points() [1/2]

template<int spacedim, typename Number = double>
 std::pair, Point >& BoundingBox< spacedim, Number >::get_boundary_points ( )

Return a reference to the boundary_points

## ◆ get_boundary_points() [2/2]

template<int spacedim, typename Number = double>
 const std::pair, Point >& BoundingBox< spacedim, Number >::get_boundary_points ( ) const

Return a const reference to the boundary_points

## ◆ operator==()

template<int spacedim, typename Number = double>
 bool BoundingBox< spacedim, Number >::operator== ( const BoundingBox< spacedim, Number > & box ) const

Test for equality.

## ◆ operator!=()

template<int spacedim, typename Number = double>
 bool BoundingBox< spacedim, Number >::operator!= ( const BoundingBox< spacedim, Number > & box ) const

Test for inequality.

## ◆ has_overlap_with()

template<int spacedim, typename Number >
 bool BoundingBox< spacedim, Number >::has_overlap_with ( const BoundingBox< spacedim, Number > & other_bbox, const double tolerance = std::numeric_limits::epsilon() ) const

Check if the current object and other_bbox are neighbors, i.e. if the boxes have dimension spacedim, check if their intersection is non empty.

Definition at line 62 of file bounding_box.cc.

## ◆ get_neighbor_type()

template<int spacedim, typename Number >
 NeighborType BoundingBox< spacedim, Number >::get_neighbor_type ( const BoundingBox< spacedim, Number > & other_bbox, const double tolerance = std::numeric_limits::epsilon() ) const

Check which NeighborType other_bbox is to the current object.

Definition at line 80 of file bounding_box.cc.

## ◆ merge_with()

template<int spacedim, typename Number >
 void BoundingBox< spacedim, Number >::merge_with ( const BoundingBox< spacedim, Number > & other_bbox )

Enlarge the current object so that it contains other_bbox . If the current object already contains other_bbox then it is not changed by this function.

Definition at line 46 of file bounding_box.cc.

## ◆ point_inside()

template<int spacedim, typename Number >
 bool BoundingBox< spacedim, Number >::point_inside ( const Point< spacedim, Number > & p, const double tolerance = std::numeric_limits::epsilon() ) const

Return true if the point is inside the Bounding Box, false otherwise. The parameter tolerance is a factor by which the bounding box is enlarged relative to the dimensions of the bounding box in order to determine in a numerically robust way whether the point is inside.

Definition at line 26 of file bounding_box.cc.

## ◆ extend()

template<int spacedim, typename Number = double>
 void BoundingBox< spacedim, Number >::extend ( const Number amount )

Increase (or decrease) the size of the bounding box by the given amount. After calling this method, the lower left corner of the bounding box will have each coordinate decreased by amount, and the upper right corner of the bounding box will have each coordinate increased by amount.

If you call this method with a negative number, and one of the axes of the original bounding box is smaller than amount/2, the method will trigger an assertion.

## ◆ create_extended()

template<int spacedim, typename Number = double>
 BoundingBox BoundingBox< spacedim, Number >::create_extended ( const Number amount ) const

The same as above with the difference that a new BoundingBox instance is created without changing the current object.

## ◆ create_extended_relative()

template<int spacedim, typename Number = double>
 BoundingBox BoundingBox< spacedim, Number >::create_extended_relative ( const Number relative_amount ) const

Increase (or decrease) each side of the bounding box by the given relative_amount.

After calling this method, the lower left corner of the bounding box will have each coordinate decreased by relative_amount * side_length(direction), and the upper right corner of the bounding box will have each coordinate increased by relative_amount * side_length(direction).

If you call this method with a negative number, and one of the axes of the original bounding box is smaller than relative_amount * side_length(direction) / 2, the method will trigger an assertion.

## ◆ volume()

template<int spacedim, typename Number >
 double BoundingBox< spacedim, Number >::volume

Compute the volume (i.e. the dim-dimensional measure) of the BoundingBox.

Definition at line 160 of file bounding_box.cc.

## ◆ center()

template<int spacedim, typename Number >
 Point< spacedim, Number > BoundingBox< spacedim, Number >::center

Returns the point in the center of the box.

Definition at line 194 of file bounding_box.cc.

## ◆ side_length()

template<int spacedim, typename Number >
 Number BoundingBox< spacedim, Number >::side_length ( const unsigned int direction ) const

Returns the side length of the box in direction.

Definition at line 222 of file bounding_box.cc.

## ◆ lower_bound()

template<int spacedim, typename Number >
 Number BoundingBox< spacedim, Number >::lower_bound ( const unsigned int direction ) const

Return the lower bound of the box in direction.

Definition at line 172 of file bounding_box.cc.

## ◆ upper_bound()

template<int spacedim, typename Number >
 Number BoundingBox< spacedim, Number >::upper_bound ( const unsigned int direction ) const

Return the upper bound of the box in direction.

Definition at line 183 of file bounding_box.cc.

## ◆ bounds()

template<int spacedim, typename Number >
 BoundingBox< 1, Number > BoundingBox< spacedim, Number >::bounds ( const unsigned int direction ) const

Return the bounds of the box in direction, as a one-dimensional box.

Definition at line 207 of file bounding_box.cc.

## ◆ vertex()

template<int spacedim, typename Number >
 Point< spacedim, Number > BoundingBox< spacedim, Number >::vertex ( const unsigned int index ) const

Returns the indexth vertex of the box. Vertex is meant in the same way as for a cell, so that index $$\in [0, 2^{\text{dim}} - 1]$$.

Definition at line 233 of file bounding_box.cc.

## ◆ child()

template<int spacedim, typename Number >
 BoundingBox< spacedim, Number > BoundingBox< spacedim, Number >::child ( const unsigned int index ) const

Returns the indexth child of the box. Child is meant in the same way as for a cell.

Definition at line 251 of file bounding_box.cc.

## ◆ cross_section()

template<int spacedim, typename Number >
 BoundingBox< spacedim - 1, Number > BoundingBox< spacedim, Number >::cross_section ( const unsigned int direction ) const

Returns the cross section of the box orthogonal to direction. This is a box in one dimension lower.

Note
Calling this method in 1d will result in an exception since BoundingBox<0> is not implemented.

Definition at line 287 of file bounding_box.cc.

## ◆ real_to_unit()

template<int spacedim, typename Number >
 Point< spacedim, Number > BoundingBox< spacedim, Number >::real_to_unit ( const Point< spacedim, Number > & point ) const

Apply the affine transformation that transforms this BoundingBox to a unit BoundingBox object.

If $$B$$ is this bounding box, and $$\hat{B}$$ is the unit bounding box, compute the affine mapping that satisfies $$G(B) = \hat{B}$$ and apply it to point.

Definition at line 312 of file bounding_box.cc.

## ◆ unit_to_real()

template<int spacedim, typename Number >
 Point< spacedim, Number > BoundingBox< spacedim, Number >::unit_to_real ( const Point< spacedim, Number > & point ) const

Apply the affine transformation that transforms the unit BoundingBox object to this object.

If $$B$$ is this bounding box, and $$\hat{B}$$ is the unit bounding box, compute the affine mapping that satisfies $$F(\hat{B}) = B$$ and apply it to point.

Definition at line 327 of file bounding_box.cc.

## ◆ signed_distance() [1/2]

template<int spacedim, typename Number >
 Number BoundingBox< spacedim, Number >::signed_distance ( const Point< spacedim, Number > & point, const unsigned int direction ) const

Returns the signed distance from a point orthogonal to the bounds of the box in direction. The signed distance is negative for points inside the interval described by the bounds of the rectangle in the respective direction, zero for points on the interval boundary and positive for points outside.

Definition at line 341 of file bounding_box.cc.

## ◆ signed_distance() [2/2]

template<int spacedim, typename Number >
 Number BoundingBox< spacedim, Number >::signed_distance ( const Point< spacedim, Number > & point ) const

Returns the signed distance from a point to the bounds of the box. The signed distance is negative for points inside the rectangle, zero for points on the rectangle and positive for points outside the rectangle.

Definition at line 360 of file bounding_box.cc.

## ◆ serialize()

template<int spacedim, typename Number = double>
template<class Archive >
 void BoundingBox< spacedim, Number >::serialize ( Archive & ar, const unsigned int version )

Write or read the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

## ◆ create_unit_bounding_box()

template<int dim, typename Number = double>
 BoundingBox< dim, Number > create_unit_bounding_box ( )
related

Returns the unit box $$[0,1]^\text{dim}$$.

Definition at line 396 of file bounding_box.cc.

## ◆ coordinate_to_one_dim_higher()

template<int dim>
 int coordinate_to_one_dim_higher ( const int locked_coordinate, const int coordinate_in_dim )
related

This function defines a convention for how coordinates in dim dimensions should translate to the coordinates in dim + 1 dimensions, when one of the coordinates in dim + 1 dimensions is locked to a given value.

The convention is the following: Starting from the locked coordinate we store the lower dimensional coordinates consecutively and wrap around when going over the dimension. This relationship is, in 2d,

locked in 2D 1d coordinate 2d coordinate
x0 (a) (x0, a)
x1 (a) (a , x1)

and, in 3d,

locked in 3D 2d coordinates 3d coordinates
x0 (a, b) (x0, a, b)
x1 (a, b) ( b, x1, a)
x2 (a, b) ( a, b, x2)

Given a locked coordinate, this function maps a coordinate index in dim dimension to a coordinate index in dim + 1 dimensions.

Parameters
 locked_coordinate should be in the range [0, dim+1). coordinate_in_dim should be in the range [0, dim).
Returns
A coordinate index in the range [0, dim+1)

Definition at line 461 of file bounding_box.h.

## ◆ boundary_points

template<int spacedim, typename Number = double>
 std::pair, Point > BoundingBox< spacedim, Number >::boundary_points
private

Definition at line 385 of file bounding_box.h.

The documentation for this class was generated from the following files: