Description

A class representing axis-aligned rectangles, boxes, hypercubes, ...

Overview

A box is defined by two n-dimensional points. For example, a rectangle has a dimension of 2. The two points give a minimum bound and a non-inclusive maximum bound. More precisely, let a box be given by p = (x_1,...,x_n) and q = (y_1,...,y_n). A point r = (z_1,...,z_n) is inside the box if for all 1 <= i <= n it holds that x_i <= z_i < y_i. This representation makes it easy to specify empty boxes: For example, a rectangle defined by (1,2), (1,2) is empty.

Constructors and getters

A box can be constructed in two ways:

A minimum point and a non-inclusive maximum point:

using box2i = fcppt::math::box::object<unsigned, 2>;

box2i const box{box2i::min_t{box2i::vector{1U, 2U}}, box2i::max_t{box2i::vector{2U, 3U}}};
A minimum point and a size:

box2i const box2{box2i::vector{1U, 2U}, box2i::dim{1U, 1U}};

There are getters and setters for both representations as well:

std::cout << box.pos() << ", " << box.max() << '\n';

std::cout << box.pos() << ", " << box.size() << '\n';

Header files

Header file	Description
`object_fwd.hpp`	Contains fcppt::math::box::object's declaration.
`object_decl.hpp`	Contains fcppt::math::box::object's definition.
`object_impl.hpp`	Contains the definition of fcppt::math::box::object's member functions.
`object.hpp`	Includes `object_fwd.hpp`, `object_decl.hpp` and `object_impl.hpp`.
`comparison.hpp`	Contains all comparison operators.
`output.hpp`	Contains `operator<<`.

Classes
struct	fcppt::math::box::has_dim< Box, Dim >
	Metafunction to check the dimension of a box. More...

struct	fcppt::math::box::is_box< T >
	Metafunction to test if a type is a box type. More...

class	fcppt::math::box::object< T, N >
	A class representing axis aligned boxes, cubes, hypercubes, ... More...

Typedefs
template<typename T >
using	fcppt::math::box::rect = fcppt::math::box::object< T, 2 >
	Typedefs a two dimensional box (a rect)

Functions
template<typename T , fcppt::math::size_type N>
fcppt::math::box::object< T, N >::vector	fcppt::math::box::center (fcppt::math::box::object< T, N > const &_box)
	Returns the center of the box.

template<typename T , fcppt::math::size_type N>
bool	fcppt::math::box::operator== (fcppt::math::box::object< T, N > const &_a, fcppt::math::box::object< T, N > const &_b)
	Compare two boxes componentwise using `value_type`'s `operator==`

template<typename T , fcppt::math::size_type N>
bool	fcppt::math::box::operator!= (fcppt::math::box::object< T, N > const &_a, fcppt::math::box::object< T, N > const &_b)
	Compare two boxes componentwise using `value_type`'s `operator!=`

template<typename T , fcppt::math::size_type N>
bool	fcppt::math::box::operator< (fcppt::math::box::object< T, N > const &_a, fcppt::math::box::object< T, N > const &_b)
	Compare two boxes lexicographically.

template<typename T , fcppt::math::size_type N>
bool	fcppt::math::box::componentwise_equal (fcppt::math::box::object< T, N > const &_v1, fcppt::math::box::object< T, N > const &_v2, T const _epsilon)
	Compare two boxes component-wise using an epsilon.

template<typename T , fcppt::math::size_type N>
bool	fcppt::math::box::contains (fcppt::math::box::object< T, N > const &_outer, fcppt::math::box::object< T, N > const &_inner)
	Test if one box is completely inside another box.

template<typename T , typename S , fcppt::math::size_type N>
bool	fcppt::math::box::contains_point (fcppt::math::box::object< T, N > const &_box, fcppt::math::vector::object< T, N, S > const &_point)
	Test if a box contains a point.

template<typename T , fcppt::math::size_type N>
fcppt::array::object< fcppt::math::vector::static_< T, N >, fcppt::math::power_of_2< std::size_t >(N)>	fcppt::math::box::corner_points (fcppt::math::box::object< T, N > const &_box)
	Returns the 2^N corner points (vertices) of the given box.

template<typename T , fcppt::math::size_type N>
fcppt::math::vector::static_< T, N >	fcppt::math::box::distance (fcppt::math::box::object< T, N > const &_box1, fcppt::math::box::object< T, N > const &_box2)
	Calculates the interval distance between all box dimensions.

template<typename T , fcppt::math::size_type N>
fcppt::math::box::object< T, N >	fcppt::math::box::extend_bounding_box (fcppt::math::box::object< T, N > const _box, typename fcppt::math::box::object< T, N >::vector const _pos)
	Extend a box to fit a point in it.

template<typename T , fcppt::math::size_type N>
fcppt::math::box::object< T, N >	fcppt::math::box::extend_bounding_box (fcppt::math::box::object< T, N > const &_box1, fcppt::math::box::object< T, N > const &_box2)
	Take the bounding box of two boxes.

template<typename Box , typename Function >
Box	fcppt::math::box::init_dim (Function const &_function)
	Initializes a box from pairs of positions and sizes.

template<typename Box , typename Function >
Box	fcppt::math::box::init_max (Function const &_function)
	Initializes a box from pairs of min and max positions.

template<typename T , fcppt::math::size_type N>
fcppt::math::box::object< T, N >	fcppt::math::box::intersection (fcppt::math::box::object< T, N > const &_a, fcppt::math::box::object< T, N > const &_b)
	Calculates the intersection of two boxes (which is, again, a box)

template<typename T , fcppt::math::size_type N>
bool	fcppt::math::box::intersects (fcppt::math::box::object< T, N > const &_a, fcppt::math::box::object< T, N > const &_b)
	Tests if two boxes intersect.

template<fcppt::math::size_type Index, typename T , fcppt::math::size_type N>
fcppt::tuple::object< T, T >	fcppt::math::box::interval (fcppt::math::box::object< T, N > const &_box)
	Creates an interval from a box.

template<typename Box >
Box	fcppt::math::box::null ()
	Returns the null box.

template<typename T , fcppt::math::size_type N, typename Ch , typename Traits >
std::basic_ostream< Ch, Traits > &	fcppt::math::box::operator<< (std::basic_ostream< Ch, Traits > &_stream, fcppt::math::box::object< T, N > const &_box)
	Outputs a box to a basic_ostream.

template<typename T , fcppt::math::size_type N>
fcppt::math::box::object< T, N >	fcppt::math::box::shrink (fcppt::math::box::object< T, N > const &_box, typename fcppt::math::box::object< T, N >::vector const &_absolute_values)
	Shrink a box towards its center using an absolute value.

template<typename T , fcppt::math::size_type N>
fcppt::math::box::object< T, N >	fcppt::math::box::stretch_absolute (fcppt::math::box::object< T, N > const &_box, typename fcppt::math::box::object< T, N >::vector const &_absolute_values)
	Stretch a box around its center using an absolute value.

template<typename T , fcppt::math::size_type N>
fcppt::math::box::object< T, N >	fcppt::math::box::stretch_relative (fcppt::math::box::object< T, N > const &_box, typename fcppt::math::box::object< T, N >::vector const &_factors)
	Stretch a box around its center by a given factor.

template<typename Dest , typename Conv , typename T , fcppt::math::size_type N>
Dest	fcppt::math::box::structure_cast (fcppt::math::box::object< T, N > const &_src)
	Converts a box into a different box of the same dimension using Conv.

Typedef Documentation

◆ rect

template<typename T >

using fcppt::math::box::rect = typedef fcppt::math::box::object<T, 2>

Typedefs a two dimensional box (a rect)

Template Parameters

T	The box's `value_type`

Function Documentation

◆ center()

template<typename T , fcppt::math::size_type N>

fcppt::math::box::object< T, N >::vector fcppt::math::box::center ( fcppt::math::box::object< T, N > const & _box )

Returns the center of the box.

Template Parameters

N	The box's dimension
T	The box's `value_type`

Note that this might not calculate the box's "real" center, since the calculation is performed using T, which might be integral.

◆ componentwise_equal()

template<typename T , fcppt::math::size_type N>

bool fcppt::math::box::componentwise_equal	(	fcppt::math::box::object< T, N > const &	_v1,
		fcppt::math::box::object< T, N > const &	_v2,
		T const	_epsilon
	)

inline

Compare two boxes component-wise using an epsilon.

Componentwise in this context means: Compare the positions and the sizes component-wise. For each component of the position and the size, check if the components differ by more than the specified epsilon. If so, return false.

◆ contains()

template<typename T , fcppt::math::size_type N>

bool fcppt::math::box::contains	(	fcppt::math::box::object< T, N > const &	_outer,
		fcppt::math::box::object< T, N > const &	_inner
	)

inline

Test if one box is completely inside another box.

Parameters

_outer	The outer (larger) box
_inner	The inner (smaller) box

◆ contains_point()

template<typename T , typename S , fcppt::math::size_type N>

bool fcppt::math::box::contains_point	(	fcppt::math::box::object< T, N > const &	_box,
		fcppt::math::vector::object< T, N, S > const &	_point
	)

inline

Test if a box contains a point.

◆ corner_points()

template<typename T , fcppt::math::size_type N>

fcppt::array::object< fcppt::math::vector::static_< T, N >, fcppt::math::power_of_2< std::size_t >(N)> fcppt::math::box::corner_points ( fcppt::math::box::object< T, N > const & _box )

Returns the 2^N corner points (vertices) of the given box.

◆ distance()

template<typename T , fcppt::math::size_type N>

fcppt::math::vector::static_< T, N > fcppt::math::box::distance	(	fcppt::math::box::object< T, N > const &	_box1,
		fcppt::math::box::object< T, N > const &	_box2
	)

Calculates the interval distance between all box dimensions.

◆ extend_bounding_box() [1/2]

template<typename T , fcppt::math::size_type N>

fcppt::math::box::object< T, N > fcppt::math::box::extend_bounding_box	(	fcppt::math::box::object< T, N > const &	_box1,
		fcppt::math::box::object< T, N > const &	_box2
	)

Take the bounding box of two boxes.

◆ extend_bounding_box() [2/2]

template<typename T , fcppt::math::size_type N>

fcppt::math::box::object< T, N > fcppt::math::box::extend_bounding_box	(	fcppt::math::box::object< T, N > const	_box,
		typename fcppt::math::box::object< T, N >::vector const	_pos
	)

Extend a box to fit a point in it.

The result will either be the same box (if the point is contained in the box) or a box that's just big enough to hold the given point.

◆ init_dim()

template<typename Box , typename Function >

Box fcppt::math::box::init_dim ( Function const & _function )

inline

Initializes a box from pairs of positions and sizes.

Initializes an object of type Box by calling _function for every index. The result _function must be a tuple where the first element is the position and the second element is the size.

Template Parameters

Box	Must be a box
Function	A (polymorphic) function of type `fcppt::tuple::object<Box::value_type, Box::value_type> (Index)`

◆ init_max()

template<typename Box , typename Function >

Box fcppt::math::box::init_max ( Function const & _function )

inline

Initializes a box from pairs of min and max positions.

Initializes an object of type Box by calling _function for every index. The result _function must be a fcppt::tuple::object where the first element is the min position and the second element is the max position.

Template Parameters

Box	Must be a box
Function	A (polymorphic) function of type `fcppt::tuple::object<Box::value_type,Box::value_type> (Index)`

◆ intersection()

template<typename T , fcppt::math::size_type N>

fcppt::math::box::object< T, N > fcppt::math::box::intersection	(	fcppt::math::box::object< T, N > const &	_a,
		fcppt::math::box::object< T, N > const &	_b
	)

Calculates the intersection of two boxes (which is, again, a box)

If there is no intersection, the null box will be returned.

◆ intersects()

template<typename T , fcppt::math::size_type N>

bool fcppt::math::box::intersects	(	fcppt::math::box::object< T, N > const &	_a,
		fcppt::math::box::object< T, N > const &	_b
	)

inline

Tests if two boxes intersect.

◆ interval()

template<fcppt::math::size_type Index, typename T , fcppt::math::size_type N>

fcppt::tuple::object< T, T > fcppt::math::box::interval ( fcppt::math::box::object< T, N > const & _box )

inline

Creates an interval from a box.

◆ null()

template<typename Box >

Box fcppt::math::box::null ( )

inline

Returns the null box.

◆ operator!=()

template<typename T , fcppt::math::size_type N>

bool fcppt::math::box::operator!=	(	fcppt::math::box::object< T, N > const &	_a,
		fcppt::math::box::object< T, N > const &	_b
	)

inline

Compare two boxes componentwise using value_type's operator!=

◆ operator<()

template<typename T , fcppt::math::size_type N>

bool fcppt::math::box::operator<	(	fcppt::math::box::object< T, N > const &	_a,
		fcppt::math::box::object< T, N > const &	_b
	)

inline

Compare two boxes lexicographically.

◆ operator<<()

template<typename T , fcppt::math::size_type N, typename Ch , typename Traits >

std::basic_ostream< Ch, Traits > & fcppt::math::box::operator<<	(	std::basic_ostream< Ch, Traits > &	_stream,
		fcppt::math::box::object< T, N > const &	_box
	)

Outputs a box to a basic_ostream.

Template Parameters

N	The box's dimension
T	The box's `value_type`

The format will be

(position,size)

◆ operator==()

template<typename T , fcppt::math::size_type N>

bool fcppt::math::box::operator==	(	fcppt::math::box::object< T, N > const &	_a,
		fcppt::math::box::object< T, N > const &	_b
	)

inline

Compare two boxes componentwise using value_type's operator==

◆ shrink()

template<typename T , fcppt::math::size_type N>

fcppt::math::box::object< T, N > fcppt::math::box::shrink	(	fcppt::math::box::object< T, N > const &	_box,
		typename fcppt::math::box::object< T, N >::vector const &	_absolute_values
	)

Shrink a box towards its center using an absolute value.

◆ stretch_absolute()

template<typename T , fcppt::math::size_type N>

fcppt::math::box::object< T, N > fcppt::math::box::stretch_absolute	(	fcppt::math::box::object< T, N > const &	_box,
		typename fcppt::math::box::object< T, N >::vector const &	_absolute_values
	)

Stretch a box around its center using an absolute value.

◆ stretch_relative()

template<typename T , fcppt::math::size_type N>

fcppt::math::box::object< T, N > fcppt::math::box::stretch_relative	(	fcppt::math::box::object< T, N > const &	_box,
		typename fcppt::math::box::object< T, N >::vector const &	_factors
	)

Stretch a box around its center by a given factor.

◆ structure_cast()

template<typename Dest , typename Conv , typename T , fcppt::math::size_type N>

Dest fcppt::math::box::structure_cast ( fcppt::math::box::object< T, N > const & _src )

Converts a box into a different box of the same dimension using Conv.

Template Parameters

T	The original box's `value_type`
Dest	The destination box's `value_type`
N	The box's dimension

	4.4.1
Freundlich's C++ toolkit

Description

Overview

Constructors and getters

Header files

Classes

Typedefs

Functions

Typedef Documentation

◆ rect

Function Documentation

◆ center()

◆ componentwise_equal()

◆ contains()

◆ contains_point()

◆ corner_points()

◆ distance()

◆ extend_bounding_box() [1/2]

◆ extend_bounding_box() [2/2]

◆ init_dim()

◆ init_max()

◆ intersection()

◆ intersects()

◆ interval()

◆ null()

◆ operator!=()

◆ operator<()

◆ operator<<()

◆ operator==()

◆ shrink()

◆ stretch_absolute()

◆ stretch_relative()

◆ structure_cast()