vector.hpp File Reference

#include <algorithm>
#include <cstddef>
#include <cstring>
#include <cmath>
#include <concepts>
#include <format>
#include <iterator>
#include <limits>
#include <type_traits>
#include <utility>

Go to the source code of this file.

Classes
struct	math::vector< T, N >
	n-dimensional vector. More...
struct	std::tuple_size< math::vector< T, N > >
	Provides access to the number of elements in a math::vector as a compile-time constant expression. More...
struct	std::tuple_element< I, math::vector< T, N > >
	Provides compile-time indexed access to the type of the elements in a math::vector using a tuple-like interface. More...
struct	std::formatter< math::vector< T, N > >
	Specialization of std::formatter for math::vector. More...

Namespaces
	math
	Mathematical functions and data types.
	math::vector_types
	Vector types.
	math::types
	Linear algebra data types.
	math::operators
	Mathematical operators.

Typedefs
template<class T >
using	math::vector_types::vec2 = vector< T, 2 >
	2-dimensional vector. More...
template<class T >
using	math::vector_types::vec3 = vector< T, 3 >
	3-dimensional vector. More...
template<class T >
using	math::vector_types::vec4 = vector< T, 4 >
	4-dimensional vector. More...
template<std::size_t N>
using	math::vector_types::bvec = vector< bool, N >
	n-dimensional vector of Boolean values. More...
using	math::vector_types::bvec2 = bvec< 2 >
	n-dimensional vector of Boolean values. More...
using	math::vector_types::bvec3 = bvec< 3 >
	n-dimensional vector of Boolean values. More...
using	math::vector_types::bvec4 = bvec< 4 >
	n-dimensional vector of Boolean values. More...
template<std::size_t N>
using	math::vector_types::ivec = vector< int, N >
	n-dimensional vector of signed integers. More...
using	math::vector_types::ivec2 = ivec< 2 >
	n-dimensional vector of signed integers. More...
using	math::vector_types::ivec3 = ivec< 3 >
	n-dimensional vector of signed integers. More...
using	math::vector_types::ivec4 = ivec< 4 >
	n-dimensional vector of signed integers. More...
template<std::size_t N>
using	math::vector_types::uvec = vector< unsigned int, N >
	n-dimensional vector of unsigned integers. More...
using	math::vector_types::uvec2 = uvec< 2 >
	n-dimensional vector of unsigned integers. More...
using	math::vector_types::uvec3 = uvec< 3 >
	n-dimensional vector of unsigned integers. More...
using	math::vector_types::uvec4 = uvec< 4 >
	n-dimensional vector of unsigned integers. More...
template<std::size_t N>
using	math::vector_types::fvec = vector< float, N >
	n-dimensional vector of single-precision floating-point numbers. More...
using	math::vector_types::fvec2 = fvec< 2 >
	n-dimensional vector of single-precision floating-point numbers. More...
using	math::vector_types::fvec3 = fvec< 3 >
	n-dimensional vector of single-precision floating-point numbers. More...
using	math::vector_types::fvec4 = fvec< 4 >
	n-dimensional vector of single-precision floating-point numbers. More...
template<std::size_t N>
using	math::vector_types::dvec = vector< double, N >
	n-dimensional vector of double-precision floating-point numbers. More...
using	math::vector_types::dvec2 = dvec< 2 >
	n-dimensional vector of double-precision floating-point numbers. More...
using	math::vector_types::dvec3 = dvec< 3 >
	n-dimensional vector of double-precision floating-point numbers. More...
using	math::vector_types::dvec4 = dvec< 4 >
	n-dimensional vector of double-precision floating-point numbers. More...

Functions
template<class T , std::size_t N>
constexpr vector< T, N >	math::abs (const vector< T, N > &x)
	Returns the absolute values of each element. More...
template<std::size_t N>
constexpr bool	math::all (const vector< bool, N > &x) noexcept
	Checks if all elements of a boolean vector are true. More...
template<std::floating_point T, std::size_t N>
T	math::angle (const vector< T, N > &from, const vector< T, N > &to)
	Calculates the angle between two direction vectors. More...
template<std::size_t N>
constexpr bool	math::any (const vector< bool, N > &x) noexcept
	Checks if any elements of a boolean vector are true. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::ceil (const vector< T, N > &x)
	Performs an element-wise ceil operation. More...
template<std::floating_point T, std::size_t N>
vector< T, N >	math::clamp_length (const vector< T, N > &x, T max_length)
	Clamps the length of a vector. More...
template<class T >
constexpr vector< T, 3 >	math::cross (const vector< T, 3 > &x, const vector< T, 3 > &y) noexcept
	Calculates the cross product of two vectors. More...
template<std::floating_point T, std::size_t N>
T	math::distance (const vector< T, N > &p0, const vector< T, N > &p1)
	Calculates the distance between two points. More...
template<class T , std::size_t N>
constexpr T	math::dot (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Calculates the dot product of two vectors. More...
template<class T , std::size_t N>
constexpr vector< bool, N >	math::equal (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Compares two vectors for equality. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::floor (const vector< T, N > &x)
	Performs a element-wise floor operation. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::fract (const vector< T, N > &x)
	Returns a vector containing the fractional part of each element. More...
template<class T , std::size_t N>
constexpr vector< bool, N >	math::greater_than (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Performs a element-wise greater-than comparison of two vectors. More...
template<class T , std::size_t N>
constexpr vector< bool, N >	math::greater_than_equal (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Performs a element-wise greater-than or equal-to comparison of two vectors. More...
template<std::floating_point T, std::size_t N>
T	math::inv_length (const vector< T, N > &x)
	Calculates the inverse length of a vector. More...
template<std::floating_point T, std::size_t N>
T	math::length (const vector< T, N > &x)
	Calculates the length of a vector. More...
template<class T , std::size_t N>
constexpr vector< bool, N >	math::less_than (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Performs a element-wise less-than comparison of two vectors. More...
template<class T , std::size_t N>
constexpr vector< bool, N >	math::less_than_equal (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Performs a element-wise less-than or equal-to comparison of two vectors. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::max (const vector< T, N > &x, const vector< T, N > &y)
	Returns a vector containing the maximum elements of two vectors. More...
template<class T , std::size_t N>
constexpr T	math::max (const vector< T, N > &x)
	Returns the value of the greatest element in a vector. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::min (const vector< T, N > &x, const vector< T, N > &y)
	Returns a vector containing the minimum elements of two vectors. More...
template<class T , std::size_t N>
constexpr T	math::min (const vector< T, N > &x)
	Returns the value of the smallest element in a vector. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::negate (const vector< T, N > &x) noexcept
	Negates a vector. More...
template<std::floating_point T, std::size_t N>
vector< T, N >	math::normalize (const vector< T, N > &x)
	Calculates the unit vector in the same direction as the original vector. More...
template<class T , std::size_t N>
constexpr vector< bool, N >	math::logical_not (const vector< T, N > &x) noexcept
	Logically inverts a boolean vector. More...
template<class T , std::size_t N>
constexpr vector< bool, N >	math::not_equal (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Compares two vectors for inequality. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::round (const vector< T, N > &x)
	Performs a element-wise round operation. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::sign (const vector< T, N > &x)
	Returns a vector containing the signs of each element. More...
template<std::floating_point T>
T	math::signed_angle (const vector< T, 3 > &x, const vector< T, 3 > &y, const vector< T, 3 > &n)
	Calculates the signed angle between two direction vectors about axis. More...
template<class T , std::size_t N>
constexpr T	math::sqr_distance (const vector< T, N > &p0, const vector< T, N > &p1) noexcept
	Calculates the square distance between two points. More...
template<class T , std::size_t N>
constexpr T	math::sqr_length (const vector< T, N > &x) noexcept
	Calculates the square length of a vector. More...
template<std::floating_point T, std::size_t N>
vector< T, N >	math::sqrt (const vector< T, N > &x)
	Takes the square root of each element. More...
template<class T , std::size_t N>
constexpr T	math::sum (const vector< T, N > &x) noexcept
	Calculates the sum of all elements in a vector. More...
template<std::size_t... Indices, class T , std::size_t N>
constexpr vector< T, sizeof...(Indices)>	math::swizzle (const vector< T, N > &x) noexcept
	Makes an m-dimensional vector by rearranging and/or duplicating elements of an n-dimensional vector. More...
template<class T >
constexpr T	math::triple (const vector< T, 3 > &x, const vector< T, 3 > &y, const vector< T, 3 > &z) noexcept
	Calculates the triple product of three vectors. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::trunc (const vector< T, N > &x)
	Performs a element-wise trunc operation. More...
template<std::floating_point T, std::size_t N>
vector< T, N >	math::sqrt (const vector< T, N > &x, const vector< T, N > &y)
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator+ (const vector< T, N > &x, const vector< T, N > &y) noexcept
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator/ (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Divides a vector by a value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator/ (const vector< T, N > &x, T y) noexcept
	Divides a vector by a value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator/ (T x, const vector< T, N > &y) noexcept
	Divides a vector by a value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator* (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Multiplies two values. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator- (const vector< T, N > &x) noexcept
	Negates a vector. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator- (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Subtracts a value by another value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator- (const vector< T, N > &x, T y) noexcept
	Subtracts a value by another value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator- (T x, const vector< T, N > &y) noexcept
	Subtracts a value by another value. More...
template<class T , std::size_t N>
constexpr bool	math::operators::operator== (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Tests two vector for equality. More...
template<class T , std::size_t N>
constexpr bool	math::operators::operator!= (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Tests two vector for inequality. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::add (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Adds two values. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::add (const vector< T, N > &x, T y) noexcept
	Adds two values. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::clamp (const vector< T, N > &x, const vector< T, N > &min, const vector< T, N > &max)
	Clamps the values of a vector's elements. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::clamp (const vector< T, N > &x, T min, T max)
	Clamps the values of a vector's elements. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::div (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Divides a vector by a value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::div (const vector< T, N > &x, T y) noexcept
	Divides a vector by a value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::div (T x, const vector< T, N > &y) noexcept
	Divides a vector by a value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::fma (const vector< T, N > &x, const vector< T, N > &y, const vector< T, N > &z)
	Performs a multiply-add operation. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::fma (const vector< T, N > &x, T y, T z)
	Performs a multiply-add operation. More...
template<std::size_t I, class T , std::size_t N>
constexpr T &	math::get (math::vector< T, N > &v) noexcept
	Extracts the Ith element from a vector. More...
template<std::size_t I, class T , std::size_t N>
constexpr T &&	math::get (math::vector< T, N > &&v) noexcept
	Extracts the Ith element from a vector. More...
template<std::size_t I, class T , std::size_t N>
constexpr const T &	math::get (const math::vector< T, N > &v) noexcept
	Extracts the Ith element from a vector. More...
template<std::size_t I, class T , std::size_t N>
constexpr const T &&	math::get (const math::vector< T, N > &&v) noexcept
	Extracts the Ith element from a vector. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::mod (const vector< T, N > &x, const vector< T, N > &y)
	Calculates the element-wise remainder of the division operation x / y. More...
template<std::floating_point T, std::size_t N>
constexpr vector< T, N >	math::mod (const vector< T, N > &x, T y)
	Calculates the element-wise remainder of the division operation x / y. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::mul (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Multiplies two values. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::mul (const vector< T, N > &x, T y) noexcept
	Multiplies two values. More...
template<std::floating_point T, std::size_t N>
vector< T, N >	math::pow (const vector< T, N > &x, const vector< T, N > &y)
	Raises each element to a power. More...
template<std::floating_point T, std::size_t N>
vector< T, N >	math::pow (const vector< T, N > &x, T y)
	Raises each element to a power. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::sub (const vector< T, N > &x, const vector< T, N > &y) noexcept
	Subtracts a value by another value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::sub (const vector< T, N > &x, T y) noexcept
	Subtracts a value by another value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::sub (T x, const vector< T, N > &y) noexcept
	Subtracts a value by another value. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator+ (const vector< T, N > &x, T y) noexcept
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator+ (T x, const vector< T, N > &y) noexcept
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator* (const vector< T, N > &x, T y) noexcept
	Multiplies two values. More...
template<class T , std::size_t N>
constexpr vector< T, N >	math::operators::operator* (T x, const vector< T, N > &y) noexcept
	Multiplies two values. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator+= (vector< T, N > &x, const vector< T, N > &y) noexcept
	Adds two values and stores the result in the first value. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator+= (vector< T, N > &x, T y) noexcept
	Adds two values and stores the result in the first value. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator-= (vector< T, N > &x, const vector< T, N > &y) noexcept
	Subtracts the first value by the second value and stores the result in the first value. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator-= (vector< T, N > &x, T y) noexcept
	Subtracts the first value by the second value and stores the result in the first value. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator*= (vector< T, N > &x, const vector< T, N > &y) noexcept
	Multiplies two values and stores the result in the first value. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator*= (vector< T, N > &x, T y) noexcept
	Multiplies two values and stores the result in the first value. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator/= (vector< T, N > &x, const vector< T, N > &y) noexcept
	Divides the first value by the second value and stores the result in the first value. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	math::operators::operator/= (vector< T, N > &x, T y) noexcept
	Divides the first value by the second value and stores the result in the first value. More...