gf::Vector< T, N > Struct Template Reference

General purpose math vector. More...

#include <gf/Vector.h>

Public Member Functions
	Vector ()=default
	Default constructor. More...
constexpr	Vector (ZeroType) noexcept
	Constructor that zero the vector out. More...
	Vector (T val) noexcept
	Constructor that fills the vector with a value. More...
	Vector (const T *array)
	Constructor that takes an array. More...
	Vector (std::initializer_list< T > list) noexcept
	Constructor that takes an initializer list. More...
	Vector (const Vector &other)=default
	Default copy constructor. More...
template<typename U >
	Vector (const Vector< U, N > &other) noexcept
	Converting copy constructor. More...
Vector &	operator= (const Vector &other)=default
	Default copy assignment. More...
constexpr T	operator[] (std::size_t i) const
	Access to the \( i \)-th coordinate. More...
constexpr T &	operator[] (std::size_t i)
	Access to the \( i \)-th coordinate. More...
T *	begin ()
	Iterator.to the first element. More...
T *	end ()
	Iterator to the element after the last one. More...
const T *	begin () const
	Iterator.to the first element (const version). More...
const T *	end () const
	Iterator on the element after the last one (const version). More...
const T *	cbegin () const
	Iterator.on the first element (const version). More...
const T *	cend () const
	Iterator on the element after the last one (const version). More...
constexpr void	zero () noexcept
	Zero out the vector. More...

Public Attributes
T	data [N]
	The internal representation of the vector. More...

Related Functions
(Note that these are not member functions.)
template<typename T , std::size_t N>
void	swap (Vector< T, N > &lhs, Vector< T, N > &rhs) noexcept
	Swap two vectors. More...
template<typename ... Types>
constexpr auto	vec (Types... values) -> Vector< std::common_type_t< Types... >, sizeof...(Types)>
	Universal vector factory. More...
template<typename T , std::size_t N>
constexpr bool	operator== (Vector< T, N > lhs, Vector< T, N > rhs)
	Equality operator between two vectors. More...
template<typename T , std::size_t N>
constexpr bool	operator!= (Vector< T, N > lhs, Vector< T, N > rhs)
	Inequality operator between two vectors. More...
template<typename T , std::size_t N>
constexpr Vector< T, N >	operator- (Vector< T, N > val)
	Component-wise unary minus. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< std::common_type_t< T, U >, N >	operator+ (Vector< T, N > lhs, Vector< U, N > rhs)
	Component-wise addition. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator+= (Vector< T, N > &lhs, Vector< U, N > rhs)
	Component-wise addition and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator+ (Vector< T, N > lhs, U rhs)
	Right scalar addition. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator+= (Vector< T, N > &lhs, U rhs)
	Right scalar addition and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator+ (T lhs, Vector< U, N > rhs)
	Left scalar addition. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< std::common_type_t< T, U >, N >	operator- (Vector< T, N > lhs, Vector< U, N > rhs)
	Component-wise substraction. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator-= (Vector< T, N > &lhs, Vector< U, N > rhs)
	Component-wise substraction and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator- (Vector< T, N > lhs, U rhs)
	Right scalar substraction. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator-= (Vector< T, N > &lhs, U rhs)
	Right scalar substraction and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator- (T lhs, Vector< U, N > rhs)
	Left scalar substraction. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< std::common_type_t< T, U >, N >	operator* (Vector< T, N > lhs, Vector< U, N > rhs)
	Component-wise multiplication. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator*= (Vector< T, N > &lhs, Vector< U, N > rhs)
	Component-wise multiplication and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator* (Vector< T, N > lhs, U rhs)
	Right scalar multiplication. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator*= (Vector< T, N > &lhs, U rhs)
	Right scalar multiplication and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator* (T lhs, Vector< U, N > rhs)
	Left scalar multiplication. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< std::common_type_t< T, U >, N >	operator/ (Vector< T, N > lhs, Vector< U, N > rhs)
	Component-wise division. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator/= (Vector< T, N > &lhs, Vector< U, N > rhs)
	Component-wise division and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator/ (Vector< T, N > lhs, U rhs)
	Right scalar division. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N > &	operator/= (Vector< T, N > &lhs, U rhs)
	Right scalar division and assignment. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>
constexpr Vector< std::common_type_t< T, U >, N >	operator/ (T lhs, Vector< U, N > rhs)
	Left scalar division. More...
template<std::size_t N>
constexpr Vector< bool, N >	operator|| (Vector< bool, N > lhs, Vector< bool, N > rhs)
	Component-wise logical or operator. More...
template<std::size_t N>
constexpr Vector< bool, N >	operator&& (Vector< bool, N > lhs, Vector< bool, N > rhs)
	Component-wise logical and operator. More...
template<typename T , std::size_t N>
constexpr T	dot (Vector< T, N > lhs, Vector< T, N > rhs)
	Scalar product. More...
template<typename T , std::size_t N>
constexpr Vector< T, N >	min (Vector< T, N > lhs, Vector< T, N > rhs)
	Component-wise minimum. More...
template<typename T , std::size_t N>
constexpr Vector< T, N >	max (Vector< T, N > lhs, Vector< T, N > rhs)
	Component-wise maximum. More...
template<typename T , std::size_t N>
Vector< T, N >	abs (Vector< T, N > val)
	Component-wise absolute value. More...
template<typename T , std::size_t N>
constexpr Vector< int, N >	sign (Vector< T, N > val)
	Component-wise sign value. More...
template<typename T , std::size_t N>
constexpr Vector< bool, N >	equals (Vector< T, N > lhs, Vector< T, N > rhs)
	Component-wise equality operator. More...
template<typename T , std::size_t N>
constexpr Vector< bool, N >	lessThan (Vector< T, N > lhs, Vector< T, N > rhs)
	Component-wise comparison operator. More...
template<typename T , std::size_t N>
constexpr Vector< bool, N >	greaterThan (Vector< T, N > lhs, Vector< T, N > rhs)
	Component-wise comparison operator. More...
template<typename T , std::size_t N>
constexpr Vector< T, N >	select (Vector< bool, N > cond, Vector< T, N > lhs, Vector< T, N > rhs)
	Component-wise selection operator. More...
template<typename T , std::size_t N>
constexpr Vector< T, N >	clamp (Vector< T, N > val, Vector< T, N > lo, Vector< T, N > hi)
	Component-wise clamp function. More...
template<typename T , std::size_t N>
constexpr Vector< T, N >	clamp (Vector< T, N > val, T lo, T hi)
	Component-wise clamp function. More...
template<typename T , typename U , std::size_t N>
constexpr Vector< T, N >	lerp (Vector< T, N > lhs, Vector< T, N > rhs, U t)
	Component-wise lerp function. More...
template<typename T , std::size_t N>
T	manhattanLength (Vector< T, N > vec)
	Manhattan length of a vector. More...
template<typename T , std::size_t N>
constexpr T	squareLength (Vector< T, N > vec)
	Square Euclidean length of a vector. More...
template<typename T , std::size_t N>
T	euclideanLength (Vector< T, N > vec)
	Euclidean length of a vector. More...
template<typename T , std::size_t N>
T	chebyshevLength (Vector< T, N > vec)
	Chebyshev length of a vector. More...
template<typename T , std::size_t N>
T	naturalLength (Vector< T, N > vec)
	Natural length of a vector. More...
template<typename T , std::size_t N>
T	manhattanDistance (Vector< T, N > lhs, Vector< T, N > rhs)
	Manhattan distance between two vectors. More...
template<typename T , std::size_t N>
constexpr T	squareDistance (Vector< T, N > lhs, Vector< T, N > rhs)
	Square Euclidean distance between two vectors. More...
template<typename T , std::size_t N>
T	euclideanDistance (Vector< T, N > lhs, Vector< T, N > rhs)
	Euclidean distance between two vectors. More...
template<typename T , std::size_t N>
T	chebyshevDistance (Vector< T, N > lhs, Vector< T, N > rhs)
	Chebyshev distance between two vectors. More...
template<typename T , std::size_t N>
T	naturalDistance (Vector< T, N > lhs, Vector< T, N > rhs)
	Natural distance between two vectors. More...
template<typename T , std::size_t N>
Vector< T, N >	normalize (Vector< T, N > vec)
	Normalize a vector. More...
template<typename T >
constexpr Vector< T, 2 >	projx (Vector< T, 2 > vec)
	Project the vector on the x axis. More...
template<typename T >
constexpr Vector< T, 2 >	projy (Vector< T, 2 > vec)
	Project the vector on the y axis. More...
template<typename T >
constexpr Vector< T, 2 >	dirx (T length)
	Create a vector in the x direction. More...
template<typename T >
constexpr Vector< T, 2 >	diry (T length)
	Create a vector in the y direction. More...
template<typename T >
Vector< T, 2 >	unit (T angle)
	Unit vector in a specified direction. More...
template<typename T >
float	angle (Vector< T, 2 > vec)
	Angle of a vector relative to the x-axis. More...
template<typename T >
constexpr Vector< T, 2 >	perp (Vector< T, 2 > vec)
	Perpendicular vector. More...
template<typename T >
constexpr Vector< T, 2 >	vectorTripleProduct (Vector< T, 2 > a, Vector< T, 2 > b, Vector< T, 2 > c)
	Regular vector triple product. More...
template<typename T >
constexpr Vector< T, 2 >	inverseVectorTripleProduct (Vector< T, 2 > a, Vector< T, 2 > b, Vector< T, 2 > c)
	Inverse vector triple product. More...
template<typename T >
constexpr T	cross (Vector< T, 2 > lhs, Vector< T, 2 > rhs)
	Cross product for 2D vectors. More...
template<typename T >
constexpr Vector< T, 3 >	cross (Vector< T, 3 > lhs, Vector< T, 3 > rhs)
	Cross product for 3D vectors. More...
template<typename T >
float	angleTo (Vector< T, 2 > lhs, Vector< T, 2 > rhs)
	Angle between two vectors. More...
template<typename T >
constexpr Vector< T, 2 >	projectOnto (Vector< T, 2 > vec, Vector< T, 2 > axis)
	Projection of a vector onto an axis. More...
template<typename Archive , typename T , std::size_t N>
Archive &	operator| (Archive &ar, Vector< T, N > &vec)
	Serialize and deserialize a vector. More...

Detailed Description

template<typename T, std::size_t N>
struct gf::Vector< T, N >

General purpose math vector.

gf::Vector is a class that represents an element of a N-dimensional space. It is used throughout the library for different purposes.

The template parameter T is the type of coordinates. . It can be any type that supports arithmetic operations (+, -, *, /) and relational operators (==, !=, <, >).

Several specializations are defined for common use cases:

• For dimension 2: gf::Vector<T, 2>
• For dimension 3: gf::Vector<T, 3>
• For dimension 4: gf::Vector<T, 4>

This class was designed according to the article On Vector Math Libraries by Nathan Reed.

Constructor & Destructor Documentation

Vector() [1/7]

template<typename T , std::size_t N>

gf::Vector< T, N >::Vector ( )

default

Default constructor.

This constructor is defaulted so that this type is trivial.

Vector() [2/7]

template<typename T , std::size_t N>

constexpr gf::Vector< T, N >::Vector ( ZeroType  )

inlineconstexprnoexcept

Constructor that zero the vector out.

Vector() [3/7]

template<typename T , std::size_t N>

gf::Vector< T, N >::Vector ( T  val )

inlineexplicitnoexcept

Constructor that fills the vector with a value.

This constructor takes a value and fills the entire vector with this value. Care must be taken when calling this constructor:

gf::Vector<int, 5> vecOK(42); // OK, vector is filled with 42
gf::Vector<int, 5> vecKO{42}; // KO, vector is initialized with a 42 in the first coordinate

Parameters

val	The value to fill the vector with

Vector() [4/7]

template<typename T , std::size_t N>

gf::Vector< T, N >::Vector ( const T *  array )

inlineexplicit

Constructor that takes an array.

This constructor can ease conversion from other math libraries. The array must contain enough data for N dimensions.

float array[5] = { 1.0f, -1.0f, 0.5f, -2.0f, 0.0f };
gf::Vector<float, 5> vec(array);

Parameters

array

An array with the values of the vector

Vector() [5/7]

template<typename T , std::size_t N>

gf::Vector< T, N >::Vector ( std::initializer_list< T >  list )

inlinenoexcept

Constructor that takes an initializer list.

This constructor allows to use an initializer list to define the coordinates of the vector.

gf::Vector<bool, 5> vec1{ true, true, false, true, false };
gf::Vector<bool, 5> vec2 = { false, true, true, false, true };

Parameters

list	An initializer list.

Vector() [6/7]

template<typename T , std::size_t N>

gf::Vector< T, N >::Vector ( const Vector< T, N > &  other )

default

Default copy constructor.

This constructor is defaulted so that this type is trivial.

Parameters

other

The vector to copy from

Vector() [7/7]

template<typename T , std::size_t N>

template<typename U >

gf::Vector< T, N >::Vector ( const Vector< U, N > &  other )

inlinenoexcept

Converting copy constructor.

Parameters

other

The vector to copy from

Member Function Documentation

begin() [1/2]

template<typename T , std::size_t N>

T * gf::Vector< T, N >::begin ( )

inline

Iterator.to the first element.

Returns

A pointer to the first element.

begin() [2/2]

template<typename T , std::size_t N>

const T * gf::Vector< T, N >::begin ( ) const

inline

Iterator.to the first element (const version).

Returns

A pointer on the first const element.

cbegin()

template<typename T , std::size_t N>

const T * gf::Vector< T, N >::cbegin ( ) const

inline

Iterator.on the first element (const version).

Returns

A pointer on the first const element.

cend()

template<typename T , std::size_t N>

const T * gf::Vector< T, N >::cend ( ) const

inline

Iterator on the element after the last one (const version).

Returns

An invalid pointer that is the adress after the last const element.

end() [1/2]

template<typename T , std::size_t N>

T * gf::Vector< T, N >::end ( )

inline

Iterator to the element after the last one.

Returns

An invalid pointer that is the adress after the last element.

end() [2/2]

template<typename T , std::size_t N>

const T * gf::Vector< T, N >::end ( ) const

inline

Iterator on the element after the last one (const version).

Returns

An invalid pointer that is the adress after the last const element.

operator=()

template<typename T , std::size_t N>

Vector & gf::Vector< T, N >::operator= ( const Vector< T, N > &  other )

default

Default copy assignment.

This operator is defaulted so that this type is trivial.

operator[]() [1/2]

template<typename T , std::size_t N>

constexpr T & gf::Vector< T, N >::operator[] ( std::size_t  i )

inlineconstexpr

Access to the \( i \)-th coordinate.

gf::Vector<int, 5> vec;
vec[0] = vec[1] = vec[2] = vec[3] = vec[4] = 0;

Parameters

i	the coordinate number

Returns

The \( i \)-th coordinate of the vector

operator[]() [2/2]

template<typename T , std::size_t N>

constexpr T gf::Vector< T, N >::operator[] ( std::size_t  i ) const

inlineconstexpr

Access to the \( i \)-th coordinate.

gf::Vector<int, 5> vec = { 1, 3, 5, 7, 9 };
std::printf("%i", vec[1]); // prints 3

Parameters

i	the coordinate number

Returns

The \( i \)-th coordinate of the vector

zero()

template<typename T , std::size_t N>

constexpr void gf::Vector< T, N >::zero ( )

inlineconstexprnoexcept

Zero out the vector.

Friends And Related Function Documentation

abs()

template<typename T , std::size_t N>

Vector< T, N > abs ( Vector< T, N >  val )

related

Component-wise absolute value.

angle()

template<typename T >

float angle ( Vector< T, 2 >  vec )

related

Angle of a vector relative to the x-axis.

Parameters

vec	The vector

Returns

The angle of the vector

angleTo()

template<typename T >

float angleTo ( Vector< T, 2 >  lhs, Vector< T, 2 >  rhs  )

related

Angle between two vectors.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The signed angle between the two vectors

chebyshevDistance()

template<typename T , std::size_t N>

T chebyshevDistance ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Chebyshev distance between two vectors.

The Chebyshev distance between two vectors is the Chebyshev length of the difference of the two vectors.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The Chebyshev distance between the two vectors

See also

chebyshevLength()

chebyshevLength()

template<typename T , std::size_t N>

T chebyshevLength ( Vector< T, N >  vec )

related

Chebyshev length of a vector.

The Chebyshev length \( \|\mathbf{u}\|_{\infty} \) of a vector \( \mathbf{u} = (u_1, \ldots, u_N) \) is:

\[ \|u\|_{\infty} = \max_{i = 1}^{N} |u_i| \]

The Chebyshev length is also called the infinity norm or maximum norm.

Parameters

vec

A vector.

Returns

The Chebyshev length of the vector

See also

chebyshevDistance()

clamp() [1/2]

template<typename T , std::size_t N>

constexpr Vector< T, N > clamp ( Vector< T, N >  val, T  lo, T  hi  )

related

Component-wise clamp function.

Relative to two values.

clamp() [2/2]

template<typename T , std::size_t N>

constexpr Vector< T, N > clamp ( Vector< T, N >  val, Vector< T, N >  lo, Vector< T, N >  hi  )

related

Component-wise clamp function.

Relative to two other vectors.

cross() [1/2]

template<typename T >

constexpr T cross ( Vector< T, 2 >  lhs, Vector< T, 2 >  rhs  )

related

Cross product for 2D vectors.

The cross product of 2D vectors is not really a cross product, it is the magnitude of the vector resulting from a 3D cross product of 2D vectors with \( z = 0 \). The cross product \( \mathbf{a} \times \mathbf{b} \) of the vectors \( \mathbf{a} \) and \( \mathbf{b} \) is:

\[ \mathbf{a} \times \mathbf{b} = \mathbf{a}^{\perp} \cdot \mathbf{b} \]

The 2D cross product is also known as the perp dot product or wedge product.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The cross product of the two vectors

cross() [2/2]

template<typename T >

constexpr Vector< T, 3 > cross ( Vector< T, 3 >  lhs, Vector< T, 3 >  rhs  )

related

Cross product for 3D vectors.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The cross product of the two vectors

dirx()

template<typename T >

constexpr Vector< T, 2 > dirx ( T  length )

related

Create a vector in the x direction.

Parameters

length

The length of the vector

Returns

A vector in the x direction

diry()

template<typename T >

constexpr Vector< T, 2 > diry ( T  length )

related

Create a vector in the y direction.

Parameters

length

The length of the vector

Returns

A vector in the y direction

dot()

template<typename T , std::size_t N>

constexpr T dot ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Scalar product.

The scalar product or dot product of two vectors \( \mathbf{a} = (a_1, \ldots, a_N) \) and \( \mathbf{b} = (b_1, \ldots, b_N) \) is:

\[ \mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^{N} a_i b_i = a_1 b_1 + \ldots + a_N b_N \]

equals()

template<typename T , std::size_t N>

constexpr Vector< bool, N > equals ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Component-wise equality operator.

euclideanDistance()

template<typename T , std::size_t N>

T euclideanDistance ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Euclidean distance between two vectors.

The Euclidean distance between two vectors is the Euclidean length of the difference of the two vectors.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The Euclidean distance between the two vectors

See also

euclideanLength()

euclideanLength()

template<typename T , std::size_t N>

T euclideanLength ( Vector< T, N >  vec )

related

Euclidean length of a vector.

The Euclidean length \( \|\mathbf{u}\|_2 \) of a vector \( \mathbf{u} = (u_1, \ldots, u_N) \) is:

\[ \|\mathbf{u}\|_2 = \sqrt{\sum_{i = 1}^{N} u_i^2} \]

The Euclidean length is also called the 2-norm.

Parameters

vec

A vector.

Returns

The Euclidean length of the vector

See also

euclideanDistance()

greaterThan()

template<typename T , std::size_t N>

constexpr Vector< bool, N > greaterThan ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Component-wise comparison operator.

inverseVectorTripleProduct()

template<typename T >

constexpr Vector< T, 2 > inverseVectorTripleProduct ( Vector< T, 2 >  a, Vector< T, 2 >  b, Vector< T, 2 >  c  )

related

Inverse vector triple product.

The inverse vector triple product of vectors \( \mathbf{a} \), \( \mathbf{b} \) and \( \mathbf{c} \) is:

\[ (\mathbf{a} \times \mathbf{b}) \times \mathbf{c} = -\mathbf{c} \times (\mathbf{a} \times \mathbf{b}) = -(\mathbf{c} \cdot \mathbf{b}) \mathbf{a} + (\mathbf{c} \cdot \mathbf{a}) \mathbf{b} \]

See also

vectorTripleProduct()

lerp()

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > lerp ( Vector< T, N >  lhs, Vector< T, N >  rhs, U  t  )

related

Component-wise lerp function.

lessThan()

template<typename T , std::size_t N>

constexpr Vector< bool, N > lessThan ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Component-wise comparison operator.

manhattanDistance()

template<typename T , std::size_t N>

T manhattanDistance ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Manhattan distance between two vectors.

The Manhattan distance between two vectors is the Manhattan length of the difference of the two vectors.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The Manhattan distance between the two vectors

See also

manhattanLength()

manhattanLength()

template<typename T , std::size_t N>

T manhattanLength ( Vector< T, N >  vec )

related

Manhattan length of a vector.

The Manhattan length \( \|\mathbf{u}\|_1 \) of a vector \( \mathbf{u} = (u_1, \ldots, u_N) \) is:

\[ \|\mathbf{u}\|_1 = \sum_{i = 1}^{N} |u_i| \]

The Manhattan length is also called the 1-norm.

Parameters

vec

A vector.

Returns

The Manhattan length of the vector

See also

manhattanDistance()

max()

template<typename T , std::size_t N>

constexpr Vector< T, N > max ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Component-wise maximum.

min()

template<typename T , std::size_t N>

constexpr Vector< T, N > min ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Component-wise minimum.

naturalDistance()

template<typename T , std::size_t N>

T naturalDistance ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Natural distance between two vectors.

The natural distance between two vectors is the natural length of the difference of the two vectors.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The natural distance between the two vectors

See also

naturalLength()

naturalLength()

template<typename T , std::size_t N>

T naturalLength ( Vector< T, N >  vec )

related

Natural length of a vector.

The natural length \( L \) of a vector: \( \mathbf{u} = (u_1, \ldots, u_N) \) is:

\[ L = \|\mathbf{u}\|_1 + \|\mathbf{u}\|_2^2 = \sum_{i = 1}^{N} |u_i| + \sum_{i = 1}^{N} u_i^2 \]

It's the sum of the Manhattan length and the square length.

Parameters

vec

A vector.

Returns

The natural length of the vector

See also

naturalDistance()

normalize()

template<typename T , std::size_t N>

Vector< T, N > normalize ( Vector< T, N >  vec )

related

Normalize a vector.

The normalized vector of \( \mathbf{u} \) is a vector in the same direction but with a (euclidean) length of 1:

\[ \frac{\mathbf{u}}{\|\mathbf{u}\|_2} \]

A normalized vector is also called a unit vector.

Parameters

vec

A vector

Returns

A normalized vector

operator!=()

template<typename T , std::size_t N>

constexpr bool operator!= ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Inequality operator between two vectors.

operator&&()

template<std::size_t N>

constexpr Vector< bool, N > operator&& ( Vector< bool, N >  lhs, Vector< bool, N >  rhs  )

related

Component-wise logical and operator.

operator*() [1/3]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator* ( T  lhs, Vector< U, N >  rhs  )

related

Left scalar multiplication.

operator*() [2/3]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator* ( Vector< T, N >  lhs, U  rhs  )

related

Right scalar multiplication.

operator*() [3/3]

template<typename T , typename U , std::size_t N>

constexpr Vector< std::common_type_t< T, U >, N > operator* ( Vector< T, N >  lhs, Vector< U, N >  rhs  )

related

Component-wise multiplication.

operator*=() [1/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator*= ( Vector< T, N > &  lhs, U  rhs  )

related

Right scalar multiplication and assignment.

operator*=() [2/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator*= ( Vector< T, N > &  lhs, Vector< U, N >  rhs  )

related

Component-wise multiplication and assignment.

operator+() [1/3]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator+ ( T  lhs, Vector< U, N >  rhs  )

related

Left scalar addition.

operator+() [2/3]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator+ ( Vector< T, N >  lhs, U  rhs  )

related

Right scalar addition.

operator+() [3/3]

template<typename T , typename U , std::size_t N>

constexpr Vector< std::common_type_t< T, U >, N > operator+ ( Vector< T, N >  lhs, Vector< U, N >  rhs  )

related

Component-wise addition.

operator+=() [1/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator+= ( Vector< T, N > &  lhs, U  rhs  )

related

Right scalar addition and assignment.

operator+=() [2/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator+= ( Vector< T, N > &  lhs, Vector< U, N >  rhs  )

related

Component-wise addition and assignment.

operator-() [1/4]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator- ( T  lhs, Vector< U, N >  rhs  )

related

Left scalar substraction.

operator-() [2/4]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator- ( Vector< T, N >  lhs, U  rhs  )

related

Right scalar substraction.

operator-() [3/4]

template<typename T , typename U , std::size_t N>

constexpr Vector< std::common_type_t< T, U >, N > operator- ( Vector< T, N >  lhs, Vector< U, N >  rhs  )

related

Component-wise substraction.

operator-() [4/4]

template<typename T , std::size_t N>

constexpr Vector< T, N > operator- ( Vector< T, N >  val )

related

Component-wise unary minus.

operator-=() [1/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator-= ( Vector< T, N > &  lhs, U  rhs  )

related

Right scalar substraction and assignment.

operator-=() [2/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator-= ( Vector< T, N > &  lhs, Vector< U, N >  rhs  )

related

Component-wise substraction and assignment.

operator/() [1/3]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator/ ( T  lhs, Vector< U, N >  rhs  )

related

Left scalar division.

operator/() [2/3]

template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<U>::value, U>::type>

constexpr Vector< std::common_type_t< T, U >, N > operator/ ( Vector< T, N >  lhs, U  rhs  )

related

Right scalar division.

operator/() [3/3]

template<typename T , typename U , std::size_t N>

constexpr Vector< std::common_type_t< T, U >, N > operator/ ( Vector< T, N >  lhs, Vector< U, N >  rhs  )

related

Component-wise division.

operator/=() [1/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator/= ( Vector< T, N > &  lhs, U  rhs  )

related

Right scalar division and assignment.

operator/=() [2/2]

template<typename T , typename U , std::size_t N>

constexpr Vector< T, N > & operator/= ( Vector< T, N > &  lhs, Vector< U, N >  rhs  )

related

Component-wise division and assignment.

operator==()

template<typename T , std::size_t N>

constexpr bool operator== ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Equality operator between two vectors.

operator|()

template<typename Archive , typename T , std::size_t N>

Archive & operator| ( Archive &  ar, Vector< T, N > &  vec  )

related

Serialize and deserialize a vector.

Parameters

ar	The archive
vec	The vector to serialize

See also

gf::Serialize, gf::Deserialiser

operator||()

template<std::size_t N>

constexpr Vector< bool, N > operator|| ( Vector< bool, N >  lhs, Vector< bool, N >  rhs  )

related

Component-wise logical or operator.

perp()

template<typename T >

constexpr Vector< T, 2 > perp ( Vector< T, 2 >  vec )

related

Perpendicular vector.

The perpendicular vector \( \mathbf{u}^{\perp} \) of vector \( \mathbf{u} = (x, y) \) is:

\[ \mathbf{u}^{\perp} = (-y, x) \]

Parameters

vec

A vector

Returns

A perpendicular vector

projectOnto()

template<typename T >

constexpr Vector< T, 2 > projectOnto ( Vector< T, 2 >  vec, Vector< T, 2 >  axis  )

related

Projection of a vector onto an axis.

Parameters

vec	The vector to project
axis	The vector being projected onto

Returns

The projection of vec onto axis

projx()

template<typename T >

constexpr Vector< T, 2 > projx ( Vector< T, 2 >  vec )

related

Project the vector on the x axis.

Parameters

vec

A vector

Returns

The projection of the vector on the x axis

projy()

template<typename T >

constexpr Vector< T, 2 > projy ( Vector< T, 2 >  vec )

related

Project the vector on the y axis.

Parameters

vec

A vector

Returns

The projection of the vector on the y axis

select()

template<typename T , std::size_t N>

constexpr Vector< T, N > select ( Vector< bool, N >  cond, Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Component-wise selection operator.

sign()

template<typename T , std::size_t N>

constexpr Vector< int, N > sign ( Vector< T, N >  val )

related

Component-wise sign value.

squareDistance()

template<typename T , std::size_t N>

constexpr T squareDistance ( Vector< T, N >  lhs, Vector< T, N >  rhs  )

related

Square Euclidean distance between two vectors.

The square Euclidean distance between two vectors is the square Euclidean length of the difference of the two vectors.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The square Euclidean distance between the two vectors

See also

squareLength(), euclideanDistance()

squareLength()

template<typename T , std::size_t N>

constexpr T squareLength ( Vector< T, N >  vec )

related

Square Euclidean length of a vector.

The square Euclidean length \( \|\mathbf{u}\|_2^2 \) of a vector \( \mathbf{u} = (u_1, \ldots, u_N) \) is:

\[ \|\mathbf{u}\|_2^2 = \sum_{i = 1}^{N} u_i^2 \]

Parameters

vec

A vector.

Returns

The square Euclidean length of the vector

See also

euclideanLength(), squareDistance()

swap()

template<typename T , std::size_t N>

void swap ( Vector< T, N > &  lhs, Vector< T, N > &  rhs  )

related

Swap two vectors.

unit()

template<typename T >

Vector< T, 2 > unit ( T  angle )

related

Unit vector in a specified direction.

Parameters

angle

The angle of the direction

Returns

A unit vector

vec()

template<typename ... Types>

constexpr auto vec ( Types...  values ) -> Vector<std::common_type_t<Types...>, sizeof...(Types)>

related

Universal vector factory.

Parameters

values

The values for the vector

Returns

A vector with a deduced type and initialized with the values provided

vectorTripleProduct()

template<typename T >

constexpr Vector< T, 2 > vectorTripleProduct ( Vector< T, 2 >  a, Vector< T, 2 >  b, Vector< T, 2 >  c  )

related

Regular vector triple product.

The regular vector triple product of vectors \( \mathbf{a} \), \( \mathbf{b} \) and \( \mathbf{c} \) is:

\[ \mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = (\mathbf{a} \cdot \mathbf{c}) \mathbf{b} - (\mathbf{a} \cdot \mathbf{b}) \mathbf{c} \]

See also

inverseVectorTripleProduct()

Member Data Documentation

data

template<typename T , std::size_t N>

T gf::Vector< T, N >::data[N]

The internal representation of the vector.

A vector is represented with an array of N values of type T. It can be accessed directly, like an array or like a pointer, which can ease interoperability with other libraries.