fcppt.math.dim

Description

A class representing static n-dimensional dimensions.

Motivation Converting from and to vectors Header files

Motivation

Conceptually, a dimension is very similar to an fcppt::math::vector::object. However, it is often useful to distinguish the two on the type level. For example, there are operations that apply to vectors (like the dot product) that make no sense in the context of a dimension. Conversely, there are operations like "take the area of the dimension" that make no sense for vectors. Also, the lower-dimensional getters for vector (x(),y(),z(),w()) have different names than the lower-dimensional getters for dim (w(),h(),d()).

Converting from and to vectors

To convert a dimension to a vector, use fcppt::math::dim::to_vector:

using dim3 = fcppt::math::dim::static_<int, 3>;
 
using vector3 = fcppt::math::vector::static_<int, 3>;
 
void f()
{
  dim3 const d{1, 2, 3};
 
  vector3 const v(fcppt::math::dim::to_vector(d));
 
  std::cout << v << '\n';
}

Conversely, use fcppt::math::vector::to_dim to convert a vector to a dim:

void g()
{
  vector3 const v{1, 2, 3};
 
  dim3 const d(fcppt::math::vector::to_dim(v));
 
  std::cout << d << '\n';
}

Header files

Header file	Description
object_fwd.hpp	Contains fcppt::math::dim::object's declaration.
object_decl.hpp	Contains fcppt::math::dim::object's definition.
object_impl.hpp	Contains the definition of fcppt::math::dim::object's member functions.
object.hpp	Includes object_fwd.hpp, object_decl.hpp and object_impl.hpp.
arithmetic.hpp	Contains symmetric and scalar arithmetic operators.
comparison.hpp	Contains all comparison operators.
input.hpp	Contains operator>>.
output.hpp	Contains operator<<.

Classes
struct	fcppt::math::dim::has_dim< Dim, Size >
	Metafunction to check the dimension of a static dim. More...
struct	fcppt::math::dim::is_dim< T >
	Metafunction to test if a type is a dim type. More...
class	fcppt::math::dim::object< T, N, S >
	A class representing a static n-dimensional dimension. More...

Typedefs
template<typename T , fcppt::math::size_type N>
using	fcppt::math::dim::static_ = fcppt::math::dim::object<T, N, fcppt::math::detail::static_storage<T, N>>
	Typedef helper for static dimsSee the introduction to fcppt::math::vector::object for more information on static dims (and on this class).

Functions
template<typename T , fcppt::math::size_type N, typename S >
fcppt::math::dim::static_< FCPPT_MATH_DETAIL_UNARY_TYPE(T, -), N >	fcppt::math::dim::operator- (fcppt::math::dim::object< T, N, S > const &_left)
	Negates a dim.
template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >
fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L,+, R), N >	fcppt::math::dim::operator+ (fcppt::math::dim::object< L, N, S1 > const &_left, fcppt::math::dim::object< R, N, S2 > const &_right)
	Adds a dim to a dim.
template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >
fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, -, R), N >	fcppt::math::dim::operator- (fcppt::math::dim::object< L, N, S1 > const &_left, fcppt::math::dim::object< R, N, S2 > const &_right)
	Subtracts a dim from a dim.
template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >
fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, *, R), N >	fcppt::math::dim::operator* (fcppt::math::dim::object< L, N, S1 > const &_left, fcppt::math::dim::object< R, N, S2 > const &_right)
	Multiplies a dim by a dim.
template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >
fcppt::optional::object< fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L,/, R), N > >	fcppt::math::dim::operator/ (fcppt::math::dim::object< L, N, S1 > const &_left, fcppt::math::dim::object< R, N, S2 > const &_right)
	Divides a dim by a dim.
template<typename L , typename R , fcppt::math::size_type N, typename S >
fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, *, R), N >	fcppt::math::dim::operator* (fcppt::math::dim::object< L, N, S > const &_left, R const &_right)
	Multiplies a dim by a scalar on the right.
template<typename L , typename R , fcppt::math::size_type N, typename S >
fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, *, R), N >	fcppt::math::dim::operator* (L const &_left, fcppt::math::dim::object< R, N, S > const &_right)
	Multiplies a dim by a scalar on the left.
template<typename L , typename R , fcppt::math::size_type N, typename S >
fcppt::optional::object< fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L,/, R), N > >	fcppt::math::dim::operator/ (fcppt::math::dim::object< L, N, S > const &_left, R const &_right)
	Divides a dim by a scalar.
template<fcppt::math::size_type Index, typename Dim >
fcppt::container::to_reference_type< std::remove_reference_t< Dim > >	fcppt::math::dim::at (Dim &_value)
	Access an element using a compile-time constant.
template<typename T1 , typename T2 , fcppt::math::size_type N, typename S1 , typename S2 , typename Function >
fcppt::math::dim::static_< std::invoke_result_t< Function, T1, T2 >, N >	fcppt::math::dim::binary_map (fcppt::math::dim::object< T1, N, S1 > const &_left, fcppt::math::dim::object< T2, N, S2 > const &_right, Function const &_function)
	Maps over two dims.
template<typename T , fcppt::math::size_type N, typename S1 , typename S2 >
bool	fcppt::math::dim::operator== (fcppt::math::dim::object< T, N, S1 > const &_v1, fcppt::math::dim::object< T, N, S2 > const &_v2)
	Compares two dims for equality.
template<typename T , fcppt::math::size_type N, typename S1 , typename S2 >
bool	fcppt::math::dim::operator!= (fcppt::math::dim::object< T, N, S1 > const &_v1, fcppt::math::dim::object< T, N, S2 > const &_v2)
	Compares two dims for disequality.
template<typename T , fcppt::math::size_type N, typename S1 , typename S2 >
bool	fcppt::math::dim::componentwise_equal (fcppt::math::dim::object< T, N, S1 > const &_v1, fcppt::math::dim::object< T, N, S2 > const &_v2, T const _epsilon)
	Compares two dims for equality using an epsilon.
template<typename T , fcppt::math::size_type N, typename S >
T	fcppt::math::dim::contents (fcppt::math::dim::object< T, N, S > const &_dim)
	Returns the area/volume of the dimension.
template<typename Dim >
Dim	fcppt::math::dim::fill (fcppt::type_traits::value_type< Dim > const &_value)
	Constructs a static dim with all components set to a given value.
template<typename Dim , typename Function >
Dim	fcppt::math::dim::init (Function const &_function)
	Initializes a dim.
template<typename T , fcppt::math::size_type N, typename S , typename Ch , typename Traits >
std::basic_istream< Ch, Traits > &	fcppt::math::dim::operator>> (std::basic_istream< Ch, Traits > &_stream, fcppt::math::dim::object< T, N, S > &_dim)
	Reads a dim from s, expecting it in the format.
template<typename T , fcppt::math::size_type N, typename S >
bool	fcppt::math::dim::is_quadratic (fcppt::math::dim::object< T, N, S > const &_dim)
	Checks if all elements of the dim are the same.
template<typename T , fcppt::math::size_type N, typename S , typename Function >
fcppt::math::dim::static_< std::invoke_result_t< Function, T >, N >	fcppt::math::dim::map (fcppt::math::dim::object< T, N, S > const &_value, Function const &_function)
	Maps over the elements of a dim.
template<typename Dest , typename T , fcppt::math::size_type N, typename S >
Dest	fcppt::math::dim::narrow_cast (fcppt::math::dim::object< T, N, S > const &_src)
	Shortens a dim to a smaller dimension.
template<typename Dim >
fcppt::math::dim::static_< fcppt::type_traits::value_type< Dim >, Dim::static_size::value >	fcppt::math::dim::null ()
	Returns the null dim.
template<typename T , fcppt::math::size_type N, typename S , typename Ch , typename Traits >
std::basic_ostream< Ch, Traits > &	fcppt::math::dim::operator<< (std::basic_ostream< Ch, Traits > &_stream, fcppt::math::dim::object< T, N, S > const &_dim)
	Outputs a dim to s, in the format.
template<typename T , fcppt::math::size_type N, typename S >
fcppt::math::dim::static_< T, N+1U >	fcppt::math::dim::push_back (fcppt::math::dim::object< T, N, S > const &_dim, T const &_value)
	Pushes an element to the back of a dim.
template<typename T , fcppt::math::size_type N, typename S >
fcppt::optional::object< fcppt::math::dim::static_< T, N > >	fcppt::math::dim::sequence (fcppt::math::dim::object< fcppt::optional::object< T >, N, S > const &_value)
	Sequence for a dim.
template<typename Dest , typename Conv , typename T , fcppt::math::size_type N, typename S >
Dest	fcppt::math::dim::structure_cast (fcppt::math::dim::object< T, N, S > const &_src)
	Converts a dim into a different dim of the same dimension.
template<typename T , fcppt::math::size_type N, typename S >
fcppt::math::dim::static_< std::make_signed_t< T >, N >	fcppt::math::dim::to_signed (fcppt::math::dim::object< T, N, S > const &_src)
	Converts a dim into a corresponding signed dim.
template<typename T , fcppt::math::size_type N, typename S >
fcppt::math::dim::static_< std::make_unsigned_t< T >, N >	fcppt::math::dim::to_unsigned (fcppt::math::dim::object< T, N, S > const &_src)
	Converts a dim into a corresponding unsigned dim.
template<typename T , fcppt::math::size_type N, typename S >
fcppt::math::vector::static_< T, N >	fcppt::math::dim::to_vector (fcppt::math::dim::object< T, N, S > const &_src)
	Converts a dim into a corresponding vector.

Typedef Documentation

static_

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

using fcppt::math::dim::static_ = fcppt::math::dim::object<T, N, fcppt::math::detail::static_storage<T, N>>

Typedef helper for static dimsSee the introduction to fcppt::math::vector::object for more information on static dims (and on this class).

Function Documentation

at()

template<fcppt::math::size_type Index, typename Dim >

fcppt::container::to_reference_type< std::remove_reference_t< Dim > > fcppt::math::dim::at ( Dim & _value )

inline

Access an element using a compile-time constant.

Template Parameters

Dim	Must be an fcppt::math::dim::object.

binary_map()

template<typename T1 , typename T2 , fcppt::math::size_type N, typename S1 , typename S2 , typename Function >

fcppt::math::dim::static_< std::invoke_result_t< Function, T1, T2 >, N > fcppt::math::dim::binary_map ( fcppt::math::dim::object< T1, N, S1 > const & _left, fcppt::math::dim::object< T2, N, S2 > const & _right, Function const & _function )

inline

Maps over two dims.

componentwise_equal()

template<typename T , fcppt::math::size_type N, typename S1 , typename S2 >

bool fcppt::math::dim::componentwise_equal ( fcppt::math::dim::object< T, N, S1 > const & _v1, fcppt::math::dim::object< T, N, S2 > const & _v2, T const _epsilon )

inline

Compares two dims for equality using an epsilon.

contents()

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

T fcppt::math::dim::contents

(

fcppt::math::dim::object< T, N, S > const &

_dim

)

Returns the area/volume of the dimension.

This is equal to the product of all components of the dimension.

fill()

template<typename Dim >

Dim fcppt::math::dim::fill

(

fcppt::type_traits::value_type< Dim > const &

_value

)

Constructs a static dim with all components set to a given value.

Template Parameters

Dim	Must be a dim

Parameters

_value

The value to fill the dim with

init()

template<typename Dim , typename Function >

Dim fcppt::math::dim::init ( Function const & _function )

inline

Initializes a dim.

Calls _function for every index of the dim.

Template Parameters

Dim	Must be a dim
Function	Must be a function of type Dim::value_type (Dim::size_type)

is_quadratic()

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

bool fcppt::math::dim::is_quadratic

(

fcppt::math::dim::object< T, N, S > const &

_dim

)

Checks if all elements of the dim are the same.

Parameters

_dim	The dimension to check

map()

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

fcppt::math::dim::static_< std::invoke_result_t< Function, T >, N > fcppt::math::dim::map ( fcppt::math::dim::object< T, N, S > const & _value, Function const & _function )

inline

Maps over the elements of a dim.

narrow_cast()

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

Dest fcppt::math::dim::narrow_cast ( fcppt::math::dim::object< T, N, S > const & _src )

inline

Shortens a dim to a smaller dimension.

null()

template<typename Dim >

fcppt::math::dim::static_< fcppt::type_traits::value_type< Dim >, Dim::static_size::value > fcppt::math::dim::null

(

)

Returns the null dim.

operator!=()

template<typename T , fcppt::math::size_type N, typename S1 , typename S2 >

bool fcppt::math::dim::operator!= ( fcppt::math::dim::object< T, N, S1 > const & _v1, fcppt::math::dim::object< T, N, S2 > const & _v2 )

inline

Compares two dims for disequality.

operator*() [1/3]

template<typename L , typename R , fcppt::math::size_type N, typename S >

fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, *, R), N > fcppt::math::dim::operator* ( fcppt::math::dim::object< L, N, S > const & _left, R const & _right )

inline

Multiplies a dim by a scalar on the right.

operator*() [2/3]

template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >

fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, *, R), N > fcppt::math::dim::operator* ( fcppt::math::dim::object< L, N, S1 > const & _left, fcppt::math::dim::object< R, N, S2 > const & _right )

inline

Multiplies a dim by a dim.

operator*() [3/3]

template<typename L , typename R , fcppt::math::size_type N, typename S >

fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, *, R), N > fcppt::math::dim::operator* ( L const & _left, fcppt::math::dim::object< R, N, S > const & _right )

inline

Multiplies a dim by a scalar on the left.

operator+()

template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >

fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L,+, R), N > fcppt::math::dim::operator+ ( fcppt::math::dim::object< L, N, S1 > const & _left, fcppt::math::dim::object< R, N, S2 > const & _right )

inline

Adds a dim to a dim.

operator-() [1/2]

template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >

fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L, -, R), N > fcppt::math::dim::operator- ( fcppt::math::dim::object< L, N, S1 > const & _left, fcppt::math::dim::object< R, N, S2 > const & _right )

inline

Subtracts a dim from a dim.

operator-() [2/2]

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

fcppt::math::dim::static_< FCPPT_MATH_DETAIL_UNARY_TYPE(T, -), N > fcppt::math::dim::operator- ( fcppt::math::dim::object< T, N, S > const & _left )

inline

Negates a dim.

operator/() [1/2]

template<typename L , typename R , fcppt::math::size_type N, typename S >

fcppt::optional::object< fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L,/, R), N > > fcppt::math::dim::operator/ ( fcppt::math::dim::object< L, N, S > const & _left, R const & _right )

inline

Divides a dim by a scalar.

operator/() [2/2]

template<typename L , typename R , fcppt::math::size_type N, typename S1 , typename S2 >

fcppt::optional::object< fcppt::math::dim::static_< FCPPT_MATH_DETAIL_BINARY_TYPE(L,/, R), N > > fcppt::math::dim::operator/ ( fcppt::math::dim::object< L, N, S1 > const & _left, fcppt::math::dim::object< R, N, S2 > const & _right )

inline

Divides a dim by a dim.

operator<<()

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

std::basic_ostream< Ch, Traits > & fcppt::math::dim::operator<< ( std::basic_ostream< Ch, Traits > & _stream, fcppt::math::dim::object< T, N, S > const & _dim )

inline

Outputs a dim to s, in the format.

(a_1,a_2,...)

where a_i are the dim's components.

operator==()

template<typename T , fcppt::math::size_type N, typename S1 , typename S2 >

bool fcppt::math::dim::operator== ( fcppt::math::dim::object< T, N, S1 > const & _v1, fcppt::math::dim::object< T, N, S2 > const & _v2 )

inline

Compares two dims for equality.

operator>>()

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

std::basic_istream< Ch, Traits > & fcppt::math::dim::operator>> ( std::basic_istream< Ch, Traits > & _stream, fcppt::math::dim::object< T, N, S > & _dim )

inline

Reads a dim from s, expecting it in the format.

(a_1,a_2,...)

where a_i are the components

push_back()

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

fcppt::math::dim::static_< T, N+1U > fcppt::math::dim::push_back ( fcppt::math::dim::object< T, N, S > const & _dim, T const & _value )

inline

Pushes an element to the back of a dim.

sequence()

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

fcppt::optional::object< fcppt::math::dim::static_< T, N > > fcppt::math::dim::sequence ( fcppt::math::dim::object< fcppt::optional::object< T >, N, S > const & _value )

inline

Sequence for a dim.

Uses fcppt::optional::sequence.

structure_cast()

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

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

inline

Converts a dim into a different dim of the same dimension.

Template Parameters

Dest	The destination dim type (not its value type!)
Conv	the converter to use for each element
N	The source dim's dimension
T	The source dim's value_type
S	The source dim's storage type

Parameters

_src	The dim to cast

See the introduction to fcppt::math::vector::object for more information on this function (and dim/vector in general).

to_signed()

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

fcppt::math::dim::static_< std::make_signed_t< T >, N > fcppt::math::dim::to_signed ( fcppt::math::dim::object< T, N, S > const & _src )

inline

Converts a dim into a corresponding signed dim.

to_unsigned()

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

fcppt::math::dim::static_< std::make_unsigned_t< T >, N > fcppt::math::dim::to_unsigned ( fcppt::math::dim::object< T, N, S > const & _src )

inline

Converts a dim into a corresponding unsigned dim.

to_vector()

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

fcppt::math::vector::static_< T, N > fcppt::math::dim::to_vector ( fcppt::math::dim::object< T, N, S > const & _src )

inline

Converts a dim into a corresponding vector.