math::operators Namespace Reference

Mathematical operators. More...

Functions
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator+ (const matrix< T, N, M > &a, const matrix< T, N, M > &b) noexcept
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator/ (const matrix< T, N, M > &a, const matrix< T, N, M > &b) noexcept
	Divides a matrix by a matrix. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator/ (const matrix< T, N, M > &a, T b) noexcept
	Divides a matrix by a scalar. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator/ (T a, const matrix< T, N, M > &b) noexcept
	Divides a scalar by a matrix. More...
template<class T , std::size_t N, std::size_t M, std::size_t P>
constexpr matrix< T, P, M >	operator* (const matrix< T, N, M > &a, const matrix< T, P, N > &b) noexcept
	Multiplies two matrices. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >::column_vector_type	operator* (const matrix< T, N, M > &a, const typename matrix< T, N, M >::row_vector_type &b) noexcept
	Calculates the product of a matrix and a row vector. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >::row_vector_type	operator* (const typename matrix< T, N, M >::column_vector_type &a, const matrix< T, N, M > &b) noexcept
	Calculates the product of a column vector and a matrix. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator- (const matrix< T, N, M > &a, const matrix< T, N, M > &b) noexcept
	Subtracts a matrix from another matrix. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator- (const matrix< T, N, M > &a, T b) noexcept
	Subtracts a scalar from matrix. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator- (T a, const matrix< T, N, M > &b) noexcept
	Subtracts a matrix from a scalar. More...
template<class T >
constexpr quaternion< T >	operator+ (const quaternion< T > &a, const quaternion< T > &b) noexcept
template<class T >
constexpr quaternion< T >	operator/ (const quaternion< T > &a, const quaternion< T > &b) noexcept
	Divides a quaternion by another quaternion. More...
template<class T >
constexpr quaternion< T >	operator/ (const quaternion< T > &a, T b) noexcept
	Divides a quaternion by a scalar. More...
template<class T >
constexpr quaternion< T >	operator/ (T a, const quaternion< T > &b) noexcept
	Divides a scalar by a quaternion. More...
template<class T >
constexpr quaternion< T >	operator* (const quaternion< T > &a, const quaternion< T > &b) noexcept
	Multiplies two quaternions. More...
template<class T >
constexpr vec3< T >	operator* (const quaternion< T > &q, const vec3< T > &v) noexcept
	Rotates a vector by a unit quaternion. More...
template<class T >
constexpr vec3< T >	operator* (const vec3< T > &v, const quaternion< T > &q) noexcept
	Rotates a vector by the inverse of a unit quaternion. More...
template<class T >
constexpr quaternion< T >	operator- (const quaternion< T > &a, const quaternion< T > &b) noexcept
	Subtracts a quaternion from another quaternion. More...
template<class T >
constexpr quaternion< T >	operator- (const quaternion< T > &q) noexcept
	Negates a quaternion. More...
template<class T >
math::transform< T >	operator* (const math::transform< T > &x, const math::transform< T > &y)
	Combines two transforms. More...
template<class T >
constexpr math::vec3< T >	operator* (const math::transform< T > &t, const math::vec3< T > &v) noexcept
template<class T >
constexpr math::vec3< T >	operator* (const math::vec3< T > &v, const math::transform< T > &t) noexcept
template<class T >
math::transform< T > &	operator*= (math::transform< T > &x, const math::transform< T > &y)
	Combines two transforms and stores the result in the first transform. More...
template<class T , std::size_t N>
constexpr vector< T, N >	operator+ (const vector< T, N > &x, const vector< T, N > &y) noexcept
template<class T , std::size_t N>
constexpr vector< T, N >	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 >	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 >	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 >	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 >	operator- (const vector< T, N > &x) noexcept
	Negates a vector. More...
template<class T , std::size_t N>
constexpr vector< T, N >	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 >	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 >	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	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	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, std::size_t M>
constexpr matrix< T, N, M >	operator+ (const matrix< T, N, M > &a, T b) noexcept
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator+ (T a, const matrix< T, N, M > &b) noexcept
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator* (const matrix< T, N, M > &a, T b) noexcept
	Multiplies a matrix by a scalar. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	operator* (T a, const matrix< T, N, M > &b) noexcept
	Multiplies a matrix by a scalar. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M > &	operator+= (matrix< T, N, M > &a, const matrix< T, N, M > &b) noexcept
	Adds two values and stores the result in the first value. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M > &	operator+= (matrix< T, N, M > &a, T b) noexcept
	Adds two values and stores the result in the first value. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M > &	operator-= (matrix< T, N, M > &a, const matrix< T, N, M > &b) 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, std::size_t M>
constexpr matrix< T, N, M > &	operator-= (matrix< T, N, M > &a, T b) 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 matrix< T, N, N > &	operator*= (matrix< T, N, N > &a, const matrix< T, N, N > &b) noexcept
	Multiplies two values and stores the result in the first value. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M > &	operator*= (matrix< T, N, M > &a, T b) noexcept
	Multiplies two values and stores the result in the first value. More...
template<class T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M > &	operator/= (matrix< T, N, M > &a, const matrix< T, N, M > &b) 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, std::size_t M>
constexpr matrix< T, N, M > &	operator/= (matrix< T, N, M > &a, T b) noexcept
	Divides the first value by the second value and stores the result in the first value. More...
template<class T >
constexpr quaternion< T >	operator+ (const quaternion< T > &a, T b) noexcept
template<class T >
constexpr quaternion< T >	operator+ (T a, const quaternion< T > &b) noexcept
template<class T >
constexpr quaternion< T >	operator* (const quaternion< T > &a, T b) noexcept
	Multiplies a quaternion by a scalar. More...
template<class T >
constexpr quaternion< T >	operator* (T a, const quaternion< T > &b) noexcept
	Multiplies a quaternion by a scalar. More...
template<class T >
constexpr quaternion< T >	operator- (const quaternion< T > &a, T b) noexcept
	Subtracts a quaternion and a scalar. More...
template<class T >
constexpr quaternion< T >	operator- (T a, const quaternion< T > &b) noexcept
	Subtracts a quaternion and a scalar. More...
template<class T >
constexpr quaternion< T > &	operator+= (quaternion< T > &a, const quaternion< T > &b) noexcept
	Adds two values and stores the result in the first value. More...
template<class T >
constexpr quaternion< T > &	operator+= (quaternion< T > &a, T b) noexcept
	Adds two values and stores the result in the first value. More...
template<class T >
constexpr quaternion< T > &	operator-= (quaternion< T > &a, const quaternion< T > &b) noexcept
	Subtracts the first value by the second value and stores the result in the first value. More...
template<class T >
constexpr quaternion< T > &	operator-= (quaternion< T > &a, T b) noexcept
	Subtracts the first value by the second value and stores the result in the first value. More...
template<class T >
constexpr quaternion< T > &	operator*= (quaternion< T > &a, const quaternion< T > &b) noexcept
	Multiplies two values and stores the result in the first value. More...
template<class T >
constexpr quaternion< T > &	operator*= (quaternion< T > &a, T b) noexcept
	Multiplies two values and stores the result in the first value. More...
template<class T >
constexpr quaternion< T > &	operator/= (quaternion< T > &a, const quaternion< T > &b) noexcept
	Divides the first value by the second value and stores the result in the first value. More...
template<class T >
constexpr quaternion< T > &	operator/= (quaternion< T > &a, T b) 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 >	operator+ (const vector< T, N > &x, T y) noexcept
template<class T , std::size_t N>
constexpr vector< T, N >	operator+ (T x, const vector< T, N > &y) noexcept
template<class T , std::size_t N>
constexpr vector< T, N >	operator* (const vector< T, N > &x, T y) noexcept
	Multiplies two values. More...
template<class T , std::size_t N>
constexpr vector< T, N >	operator* (T x, const vector< T, N > &y) noexcept
	Multiplies two values. More...
template<class T , std::size_t N>
constexpr vector< T, N > &	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 > &	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 > &	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 > &	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 > &	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 > &	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 > &	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 > &	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...

Detailed Description

Mathematical operators.

Function Documentation

operator!=()

template<class T , std::size_t N>

constexpr bool math::operators::operator!= ( const vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Tests two vector for inequality.

Parameters

x	First value.
y	Second value.

Returns

false if the vectors are identical, true otherwise.

Definition at line 1830 of file vector.hpp.

operator*() [1/16]

template<class T >

constexpr math::vec3<T> math::operators::operator* ( const math::transform< T > &  t, const math::vec3< T > &  v  )

inlineconstexprnoexcept

Definition at line 194 of file transform.hpp.

operator*() [2/16]

template<class T >

math::transform<T> math::operators::operator* ( const math::transform< T > &  x, const math::transform< T > &  y  )

inline

Combines two transforms.

Parameters

x	First transform.
y	Second transform.

Returns

Product of the two transforms.

Definition at line 187 of file transform.hpp.

operator*() [3/16]

template<class T >

constexpr math::vec3<T> math::operators::operator* ( const math::vec3< T > &  v, const math::transform< T > &  t  )

inlineconstexprnoexcept

Definition at line 201 of file transform.hpp.

operator*() [4/16]

template<class T , std::size_t N, std::size_t M, std::size_t P>

constexpr matrix<T, P, M> math::operators::operator* ( const matrix< T, N, M > &  a, const matrix< T, P, N > &  b  )

inlineconstexprnoexcept

Multiplies two matrices.

Template Parameters

T	Matrix element type.
N	Number of columns in matrix a, and rows in matrix b.
M	Number of rows in matrix a.
P	Number of columns in matrix b.

Parameters

a	First matrix.
b	Second matrix.

Returns

Product of a * b.

Definition at line 1289 of file math/matrix.hpp.

operator*() [5/16]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>::column_vector_type math::operators::operator* ( const matrix< T, N, M > &  a, const typename matrix< T, N, M >::row_vector_type &  b  )

inlineconstexprnoexcept

Calculates the product of a matrix and a row vector.

Parameters

a	Matrix.
b	Row vector

Returns

Product of the matrix and the row vector.

Definition at line 1310 of file math/matrix.hpp.

operator*() [6/16]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator* ( const matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Multiplies a matrix by a scalar.

Parameters

a	Matrix.
b	Scalar.

Returns

Product of the matrix and the scalar.

Definition at line 1297 of file math/matrix.hpp.

operator*() [7/16]

template<class T >

constexpr quaternion<T> math::operators::operator* ( const quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Multiplies two quaternions.

Parameters

a	First quaternion.
b	Second quaternion.

Returns

Product of the two quaternions.

Definition at line 903 of file quaternion.hpp.

operator*() [8/16]

template<class T >

constexpr quaternion<T> math::operators::operator* ( const quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Multiplies a quaternion by a scalar.

Parameters

a	First value.
b	Second value.

Returns

Product of the quaternion and scalar.

Definition at line 911 of file quaternion.hpp.

operator*() [9/16]

template<class T >

constexpr vec3<T> math::operators::operator* ( const quaternion< T > &  q, const vec3< T > &  v  )

inlineconstexprnoexcept

Rotates a vector by a unit quaternion.

Parameters

q	Unit quaternion.
v	Vector to rotate.

Returns

Rotated vector.

Warning

q must be a unit quaternion.

See also

https://fgiesen.wordpress.com/2019/02/09/rotating-a-single-vector-using-a-quaternion/

Definition at line 924 of file quaternion.hpp.

operator*() [10/16]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>::row_vector_type math::operators::operator* ( const typename matrix< T, N, M >::column_vector_type &  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Calculates the product of a column vector and a matrix.

Parameters

a	Column vector.
b	Matrix.

Returns

Product of the column vector and the matrix.

Definition at line 1317 of file math/matrix.hpp.

operator*() [11/16]

template<class T >

constexpr vec3<T> math::operators::operator* ( const vec3< T > &  v, const quaternion< T > &  q  )

inlineconstexprnoexcept

Rotates a vector by the inverse of a unit quaternion.

Parameters

v	Vector to rotate.
q	Unit quaternion.

Returns

Rotated vector.

Warning

q must be a unit quaternion.

Definition at line 931 of file quaternion.hpp.

operator*() [12/16]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator* ( const vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Multiplies two values.

Parameters

x	First value.
y	Second value.

Returns

Product of the two values.

Definition at line 1661 of file vector.hpp.

operator*() [13/16]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator* ( const vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Multiplies two values.

Parameters

x	First value.
y	Second value.

Returns

Product of the two values.

Definition at line 1669 of file vector.hpp.

operator*() [14/16]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator* ( T  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Multiplies a matrix by a scalar.

Parameters

a	Matrix.
b	Scalar.

Returns

Product of the matrix and the scalar.

Definition at line 1302 of file math/matrix.hpp.

operator*() [15/16]

template<class T >

constexpr quaternion<T> math::operators::operator* ( T  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Multiplies a quaternion by a scalar.

Parameters

a	First value.
b	Second value.

Returns

Product of the quaternion and scalar.

Definition at line 916 of file quaternion.hpp.

operator*() [16/16]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator* ( T  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Multiplies two values.

Parameters

x	First value.
y	Second value.

Returns

Product of the two values.

Definition at line 1674 of file vector.hpp.

operator*=() [1/7]

template<class T >

math::transform<T>& math::operators::operator*= ( math::transform< T > &  x, const math::transform< T > &  y  )

inline

Combines two transforms and stores the result in the first transform.

Parameters

x	First transform.
y	Second transform.

Returns

Reference to the first transform.

Definition at line 215 of file transform.hpp.

operator*=() [2/7]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>& math::operators::operator*= ( matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Multiplies two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1400 of file math/matrix.hpp.

operator*=() [3/7]

template<class T , std::size_t N>

constexpr matrix<T, N, N>& math::operators::operator*= ( matrix< T, N, N > &  a, const matrix< T, N, N > &  b  )

inlineconstexprnoexcept

Multiplies two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1395 of file math/matrix.hpp.

operator*=() [4/7]

template<class T >

constexpr quaternion<T>& math::operators::operator*= ( quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Multiplies two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1016 of file quaternion.hpp.

operator*=() [5/7]

template<class T >

constexpr quaternion<T>& math::operators::operator*= ( quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Multiplies two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1021 of file quaternion.hpp.

operator*=() [6/7]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator*= ( vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Multiplies two values and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1760 of file vector.hpp.

operator*=() [7/7]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator*= ( vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Multiplies two values and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1765 of file vector.hpp.

operator+() [1/9]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator+ ( const matrix< T, N, M > &  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Definition at line 1247 of file math/matrix.hpp.

operator+() [2/9]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator+ ( const matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Definition at line 1255 of file math/matrix.hpp.

operator+() [3/9]

template<class T >

constexpr quaternion<T> math::operators::operator+ ( const quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Definition at line 861 of file quaternion.hpp.

operator+() [4/9]

template<class T >

constexpr quaternion<T> math::operators::operator+ ( const quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Definition at line 869 of file quaternion.hpp.

operator+() [5/9]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator+ ( const vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Definition at line 1619 of file vector.hpp.

operator+() [6/9]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator+ ( const vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Definition at line 1627 of file vector.hpp.

operator+() [7/9]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator+ ( T  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Definition at line 1260 of file math/matrix.hpp.

operator+() [8/9]

template<class T >

constexpr quaternion<T> math::operators::operator+ ( T  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Definition at line 874 of file quaternion.hpp.

operator+() [9/9]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator+ ( T  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Definition at line 1632 of file vector.hpp.

operator+=() [1/6]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>& math::operators::operator+= ( matrix< T, N, M > &  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Adds two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1353 of file math/matrix.hpp.

operator+=() [2/6]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>& math::operators::operator+= ( matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Adds two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1358 of file math/matrix.hpp.

operator+=() [3/6]

template<class T >

constexpr quaternion<T>& math::operators::operator+= ( quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Adds two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 974 of file quaternion.hpp.

operator+=() [4/6]

template<class T >

constexpr quaternion<T>& math::operators::operator+= ( quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Adds two values and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 979 of file quaternion.hpp.

operator+=() [5/6]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator+= ( vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Adds two values and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1718 of file vector.hpp.

operator+=() [6/6]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator+= ( vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Adds two values and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1723 of file vector.hpp.

operator-() [1/11]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator- ( const matrix< T, N, M > &  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Subtracts a matrix from another matrix.

Parameters

a	First matrix.
b	Second matrix.

Returns

Difference between the two matrices.

Definition at line 1324 of file math/matrix.hpp.

operator-() [2/11]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator- ( const matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Subtracts a scalar from matrix.

Parameters

a	Matrix.
b	Scalar.

Returns

Difference between the matrix and scalar.

Definition at line 1331 of file math/matrix.hpp.

operator-() [3/11]

template<class T >

constexpr quaternion<T> math::operators::operator- ( const quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Subtracts a quaternion from another quaternion.

Parameters

a	First quaternion.
b	Second quaternion.

Returns

Difference between the quaternions.

Definition at line 938 of file quaternion.hpp.

operator-() [4/11]

template<class T >

constexpr quaternion<T> math::operators::operator- ( const quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Subtracts a quaternion and a scalar.

Parameters

a	First value.
b	Second second.

Returns

Difference between the quaternion and scalar.

Definition at line 946 of file quaternion.hpp.

operator-() [5/11]

template<class T >

constexpr quaternion<T> math::operators::operator- ( const quaternion< T > &  q )

inlineconstexprnoexcept

Negates a quaternion.

Parameters

q	Quaternion to negate.

Returns

Negated quaternion.

Definition at line 959 of file quaternion.hpp.

operator-() [6/11]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator- ( const vector< T, N > &  x )

inlineconstexprnoexcept

Negates a vector.

Parameters

x	Vector to negate.

Returns

Negated vector.

Definition at line 1682 of file vector.hpp.

operator-() [7/11]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator- ( const vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Subtracts a value by another value.

Parameters

x	First value.
y	Second value.

Returns

Difference between the two values.

Definition at line 1689 of file vector.hpp.

operator-() [8/11]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator- ( const vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Subtracts a value by another value.

Parameters

x	First value.
y	Second value.

Returns

Difference between the two values.

Definition at line 1696 of file vector.hpp.

operator-() [9/11]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator- ( T  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Subtracts a matrix from a scalar.

Parameters

a	Scalar.
b	Matrix.

Returns

Difference between the scalar and matrix.

Definition at line 1338 of file math/matrix.hpp.

operator-() [10/11]

template<class T >

constexpr quaternion<T> math::operators::operator- ( T  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Subtracts a quaternion and a scalar.

Parameters

a	First value.
b	Second second.

Returns

Difference between the quaternion and scalar.

Definition at line 951 of file quaternion.hpp.

operator-() [11/11]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator- ( T  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Subtracts a value by another value.

Parameters

x	First value.
y	Second value.

Returns

Difference between the two values.

Definition at line 1703 of file vector.hpp.

operator-=() [1/6]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>& math::operators::operator-= ( matrix< T, N, M > &  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Subtracts the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1374 of file math/matrix.hpp.

operator-=() [2/6]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>& math::operators::operator-= ( matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Subtracts the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1379 of file math/matrix.hpp.

operator-=() [3/6]

template<class T >

constexpr quaternion<T>& math::operators::operator-= ( quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Subtracts the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 995 of file quaternion.hpp.

operator-=() [4/6]

template<class T >

constexpr quaternion<T>& math::operators::operator-= ( quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Subtracts the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1000 of file quaternion.hpp.

operator-=() [5/6]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator-= ( vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Subtracts the first value by the second value and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1739 of file vector.hpp.

operator-=() [6/6]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator-= ( vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Subtracts the first value by the second value and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1744 of file vector.hpp.

operator/() [1/9]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator/ ( const matrix< T, N, M > &  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Divides a matrix by a matrix.

Parameters

a	First matrix.
b	Second matrix.

Returns

Result of the division.

Definition at line 1268 of file math/matrix.hpp.

operator/() [2/9]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator/ ( const matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Divides a matrix by a scalar.

Parameters

a	Matrix.
b	Scalar.

Returns

Result of the division.

Definition at line 1275 of file math/matrix.hpp.

operator/() [3/9]

template<class T >

constexpr quaternion<T> math::operators::operator/ ( const quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Divides a quaternion by another quaternion.

Parameters

a	First value.
b	Second value.

Returns

Result of the division.

Definition at line 882 of file quaternion.hpp.

operator/() [4/9]

template<class T >

constexpr quaternion<T> math::operators::operator/ ( const quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Divides a quaternion by a scalar.

Parameters

a	Quaternion.
b	Scalar.

Returns

Result of the division.

Definition at line 889 of file quaternion.hpp.

operator/() [5/9]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator/ ( const vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Divides a vector by a value.

Parameters

x	First value.
y	Second value.

Returns

Result of the division.

Definition at line 1640 of file vector.hpp.

operator/() [6/9]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator/ ( const vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Divides a vector by a value.

Parameters

x	First value.
y	Second value.

Returns

Result of the division.

Definition at line 1647 of file vector.hpp.

operator/() [7/9]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M> math::operators::operator/ ( T  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Divides a scalar by a matrix.

Parameters

a	Scalar.
b	Matrix.

Returns

Result of the division.

Definition at line 1282 of file math/matrix.hpp.

operator/() [8/9]

template<class T >

constexpr quaternion<T> math::operators::operator/ ( T  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Divides a scalar by a quaternion.

Parameters

a	Scalar.
b	Quaternion.

Returns

Result of the division.

Definition at line 896 of file quaternion.hpp.

operator/() [9/9]

template<class T , std::size_t N>

constexpr vector<T, N> math::operators::operator/ ( T  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Divides a vector by a value.

Parameters

x	First value.
y	Second value.

Returns

Result of the division.

Definition at line 1654 of file vector.hpp.

operator/=() [1/6]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>& math::operators::operator/= ( matrix< T, N, M > &  a, const matrix< T, N, M > &  b  )

inlineconstexprnoexcept

Divides the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1416 of file math/matrix.hpp.

operator/=() [2/6]

template<class T , std::size_t N, std::size_t M>

constexpr matrix<T, N, M>& math::operators::operator/= ( matrix< T, N, M > &  a, T  b  )

inlineconstexprnoexcept

Divides the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1421 of file math/matrix.hpp.

operator/=() [3/6]

template<class T >

constexpr quaternion<T>& math::operators::operator/= ( quaternion< T > &  a, const quaternion< T > &  b  )

inlineconstexprnoexcept

Divides the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1037 of file quaternion.hpp.

operator/=() [4/6]

template<class T >

constexpr quaternion<T>& math::operators::operator/= ( quaternion< T > &  a, T  b  )

inlineconstexprnoexcept

Divides the first value by the second value and stores the result in the first value.

Parameters

a	First value.
b	Second value.

Returns

Reference to the first value.

Definition at line 1042 of file quaternion.hpp.

operator/=() [5/6]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator/= ( vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Divides the first value by the second value and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1781 of file vector.hpp.

operator/=() [6/6]

template<class T , std::size_t N>

constexpr vector<T, N>& math::operators::operator/= ( vector< T, N > &  x, T  y  )

inlineconstexprnoexcept

Divides the first value by the second value and stores the result in the first value.

Parameters

x	First value.
y	Second value.

Returns

Reference to the first value.

Definition at line 1786 of file vector.hpp.

operator==()

template<class T , std::size_t N>

constexpr bool math::operators::operator== ( const vector< T, N > &  x, const vector< T, N > &  y  )

inlineconstexprnoexcept

Tests two vector for equality.

Parameters

x	First value.
y	Second value.

Returns

true if the vectors are identical, false otherwise.

Definition at line 1801 of file vector.hpp.