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

General purpose math vector. More...

#include <gf/Vector.h>

Public Member Functions
	Vector ()=default
	Default constructor. More...
	Vector (T val)
	Constructor that fills the vector with a value. More...
	Vector (T *array)
	Constructor that takes an array. More...
	Vector (std::initializer_list< T > list)
	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)
	Converting copy constructor. More...
Vector &	operator= (const Vector &other)=default
	Default copy assignment. More...
T	operator[] (std::size_t i) const
	Access to the \( i \)-th coordinate. More...
T &	operator[] (std::size_t i)
	Access to the \( i \)-th coordinate. More...
T *	begin (void)
	Iterator.to the first element. More...
T *	end (void)
	Iterator to the element after the last one. More...
T const *	begin (void) const
	Iterator.to the first element (const version). More...
T const *	end (void) const
	Iterator on the element after the last one (const version). More...
T const *	cbegin (void) const
	Iterator.on the first element (const version). More...
T const *	cend (void) const
	Iterator on the element after the last one (const version). 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>
bool	operator== (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Equality operator between two vectors. More...
template<typename T , std::size_t N>
bool	operator!= (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Inequality operator between two vectors. More...
template<typename T , std::size_t N>
Vector< T, N >	operator- (const Vector< T, N > &val)
	Component-wise unary minus. More...
template<typename T , typename U , std::size_t N>
Vector< typename std::common_type< T, U >::type, N >	operator+ (const Vector< T, N > &lhs, const Vector< U, N > &rhs)
	Component-wise addition. More...
template<typename T , typename U , std::size_t N>
Vector< T, N > &	operator+= (Vector< T, N > &lhs, const 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>
Vector< typename std::common_type< T, U >::type, N >	operator+ (const Vector< T, N > &lhs, U rhs)
	Right scalar addition. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>
Vector< typename std::common_type< T, U >::type, N >	operator+ (T lhs, const Vector< U, N > &rhs)
	Left scalar addition. More...
template<typename T , typename U , std::size_t N>
Vector< typename std::common_type< T, U >::type, N >	operator- (const Vector< T, N > &lhs, const Vector< U, N > &rhs)
	Component-wise substraction. More...
template<typename T , typename U , std::size_t N>
Vector< T, N > &	operator-= (Vector< T, N > &lhs, const 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>
Vector< typename std::common_type< T, U >::type, N >	operator- (const Vector< T, N > &lhs, U rhs)
	Right scalar substraction. More...
template<typename T , typename U , std::size_t N, typename E = typename std::enable_if<std::is_arithmetic<T>::value, T>::type>
Vector< typename std::common_type< T, U >::type, N >	operator- (T lhs, const Vector< U, N > &rhs)
	Left scalar substraction. More...
template<typename T , typename U , std::size_t N>
Vector< typename std::common_type< T, U >::type, N >	operator* (const Vector< T, N > &lhs, const Vector< U, N > &rhs)
	Component-wise multiplication. More...
template<typename T , typename U , std::size_t N>
Vector< T, N > &	operator*= (Vector< T, N > &lhs, const 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>
Vector< typename std::common_type< T, U >::type, N >	operator* (const Vector< T, N > &lhs, U rhs)
	Right scalar multiplication. More...
template<typename T , typename U , std::size_t N>
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>
Vector< typename std::common_type< T, U >::type, N >	operator* (T lhs, const Vector< U, N > &rhs)
	Left scalar multiplication. More...
template<typename T , typename U , std::size_t N>
Vector< typename std::common_type< T, U >::type, N >	operator/ (const Vector< T, N > &lhs, const Vector< U, N > &rhs)
	Component-wise division. More...
template<typename T , typename U , std::size_t N>
Vector< T, N > &	operator/= (Vector< T, N > &lhs, const 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>
Vector< typename std::common_type< T, U >::type, N >	operator/ (const Vector< T, N > &lhs, U rhs)
	Right scalar division. More...
template<typename T , typename U , std::size_t N>
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>
Vector< typename std::common_type< T, U >::type, N >	operator/ (T lhs, const Vector< U, N > &rhs)
	Left scalar division. More...
template<std::size_t N>
Vector< bool, N >	operator|| (const Vector< bool, N > &lhs, const Vector< bool, N > &rhs)
	Component-wise logical or operator. More...
template<std::size_t N>
Vector< bool, N >	operator&& (const Vector< bool, N > &lhs, const Vector< bool, N > &rhs)
	Component-wise logical and operator. More...
template<typename T , std::size_t N>
T	dot (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Scalar product. More...
template<typename T , std::size_t N>
Vector< T, N >	min (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Component-wise minimum. More...
template<typename T , std::size_t N>
Vector< T, N >	max (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Component-wise maximum. More...
template<typename T , std::size_t N>
Vector< T, N >	abs (const Vector< T, N > &val)
	Component-wise absolute value. More...
template<typename T , std::size_t N>
Vector< bool, N >	equals (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Component-wise equality operator. More...
template<typename T , std::size_t N>
Vector< bool, N >	lessThan (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Component-wise comparison operator. More...
template<typename T , std::size_t N>
Vector< bool, N >	greaterThan (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Component-wise comparison operator. More...
template<typename T , std::size_t N>
Vector< T, N >	select (const Vector< bool, N > &cond, const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Component-wise selection operator. More...
template<typename T , std::size_t N>
Vector< T, N >	clamp (const Vector< T, N > &val, const Vector< T, N > &lo, const Vector< T, N > &hi)
	Component-wise clamp function. More...
template<typename T , std::size_t N>
Vector< T, N >	clamp (const Vector< T, N > &val, T lo, T hi)
	Component-wise clamp function. More...
template<typename T , typename U , std::size_t N>
Vector< typename std::common_type< T, U >::type, N >	lerp (const Vector< T, N > &lhs, const Vector< T, N > &rhs, U t)
	Component-wise lerp function. More...
template<typename T , std::size_t N>
T	manhattanLength (const Vector< T, N > &vec)
	Manhattan length of a vector. More...
template<typename T , std::size_t N>
T	squareLength (const Vector< T, N > &vec)
	Square Euclidean length of a vector. More...
template<typename T , std::size_t N>
T	euclideanLength (const Vector< T, N > &vec)
	Euclidean length of a vector. More...
template<typename T , std::size_t N>
T	chebyshevLength (const Vector< T, N > &vec)
	Chebyshev length of a vector. More...
template<typename T , std::size_t N>
T	manhattanDistance (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Manhattan distance between two vectors. More...
template<typename T , std::size_t N>
T	squareDistance (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Square Euclidean distance between two vectors. More...
template<typename T , std::size_t N>
T	euclideanDistance (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Euclidean distance between two vectors. More...
template<typename T , std::size_t N>
T	chebyshevDistance (const Vector< T, N > &lhs, const Vector< T, N > &rhs)
	Chebyshev distance between two vectors. More...
template<typename T , std::size_t N>
Vector< T, N >	normalize (const Vector< T, N > &vec)
	Normalize a vector. More...
template<typename T >
Vector< T, 2 >	unit (T angle)
	Unit vector in a specified direction. More...
template<typename T >
constexpr Vector< T, 2 >	perp (const Vector< T, 2 > &vec)
	Perpendicular vector. More...
template<typename T >
constexpr Vector< T, 3 >	cross (const Vector< T, 3 > &lhs, const Vector< T, 3 > &rhs)
	Cross product. 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

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.

template<typename T, std::size_t N>

gf::Vector< T, N >::Vector ( T  val )

inlineexplicit

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

template<typename T, std::size_t N>

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

template<typename T, std::size_t N>

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

inline

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.

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

template<typename T, std::size_t N>

template<typename U >

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

inline

Converting copy constructor.

Parameters

other

The vector to copy from

Member Function Documentation

template<typename T, std::size_t N>

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

inline

Iterator.to the first element.

Returns

A pointer to the first element.

template<typename T, std::size_t N>

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

inline

Iterator.to the first element (const version).

Returns

A pointer on the first const element.

template<typename T, std::size_t N>

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

inline

Iterator.on the first element (const version).

Returns

A pointer on the first const element.

template<typename T, std::size_t N>

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

template<typename T, std::size_t N>

T* gf::Vector< T, N >::end ( void  )

inline

Iterator to the element after the last one.

Returns

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

template<typename T, std::size_t N>

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

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.

template<typename T, std::size_t N>

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

inline

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

template<typename T, std::size_t N>

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

inline

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

Friends And Related Function Documentation

template<typename T , std::size_t N>

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

related

Component-wise absolute value.

template<typename T , std::size_t N>

T chebyshevDistance ( const Vector< T, N > &  lhs, const 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()

template<typename T , std::size_t N>

T chebyshevLength ( const Vector< T, N > &  vec )

related

Chebyshev length of a vector.

The Chebyshev length \( l \) of a vector \( (u_1, \ldots, u_N) \) is:

\[ l = \max_{i = 1}^{N} |u_i| \]

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()

template<typename T , std::size_t N>

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

related

Component-wise clamp function.

Relative to two other vectors.

template<typename T , std::size_t N>

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

related

Component-wise clamp function.

Relative to two values.

template<typename T >

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

related

Cross product.

Parameters

lhs	A first vector
rhs	A second vector

Returns

The cross product of the two vectors

template<typename T , std::size_t N>

T dot ( const Vector< T, N > &  lhs, const Vector< T, N > &  rhs  )

related

Scalar product.

template<typename T , std::size_t N>

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

related

Component-wise equality operator.

template<typename T , std::size_t N>

T euclideanDistance ( const Vector< T, N > &  lhs, const 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()

template<typename T , std::size_t N>

T euclideanLength ( const Vector< T, N > &  vec )

related

Euclidean length of a vector.

The Euclidean length \( l \) of a vector \( (u_1, \ldots, u_N) \) is:

\[ l = \sqrt{\sum_{i = 1}^{N} u_i^2} \]

The Euclidean length is also called the 2-norm.

Parameters

vec

A vector.

Returns

The Euclidean length of the vector

See also

euclideanDistance()

template<typename T , std::size_t N>

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

related

Component-wise comparison operator.

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

Vector< typename std::common_type< T, U >::type, N > lerp ( const Vector< T, N > &  lhs, const Vector< T, N > &  rhs, U  t  )

related

Component-wise lerp function.

template<typename T , std::size_t N>

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

related

Component-wise comparison operator.

template<typename T , std::size_t N>

T manhattanDistance ( const Vector< T, N > &  lhs, const 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()

template<typename T , std::size_t N>

T manhattanLength ( const Vector< T, N > &  vec )

related

Manhattan length of a vector.

The Manhattan length \( l \) of a vector \( (u_1, \ldots, u_N) \) is:

\[ l = \sum_{i = 1}^{N} |u_i| \]

The Manhattan length is also called the 1-norm.

Parameters

vec

A vector.

Returns

The Manhattan length of the vector

See also

manhattanDistance()

template<typename T , std::size_t N>

Vector< T, N > max ( const Vector< T, N > &  lhs, const Vector< T, N > &  rhs  )

related

Component-wise maximum.

template<typename T , std::size_t N>

Vector< T, N > min ( const Vector< T, N > &  lhs, const Vector< T, N > &  rhs  )

related

Component-wise minimum.

template<typename T , std::size_t N>

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

related

Normalize a vector.

The normalized vector of \( v \) is a vector in the same direction but with a (euclidean) length of 1. A normalized vector is also called a unit vector.

Parameters

vec

A vector

Returns

A normalized vector

template<typename T , std::size_t N>

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

related

Inequality operator between two vectors.

template<std::size_t N>

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

related

Component-wise logical and operator.

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

Vector< typename std::common_type< T, U >::type, N > operator* ( const Vector< T, N > &  lhs, const Vector< U, N > &  rhs  )

related

Component-wise multiplication.

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

Vector< typename std::common_type< T, U >::type, N > operator* ( const Vector< T, N > &  lhs, U  rhs  )

related

Right scalar multiplication.

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

Vector< typename std::common_type< T, U >::type, N > operator* ( T  lhs, const Vector< U, N > &  rhs  )

related

Left scalar multiplication.

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

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

related

Component-wise multiplication and assignment.

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

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

related

Right scalar multiplication and assignment.

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

Vector< typename std::common_type< T, U >::type, N > operator+ ( const Vector< T, N > &  lhs, const Vector< U, N > &  rhs  )

related

Component-wise addition.

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

Vector< typename std::common_type< T, U >::type, N > operator+ ( const Vector< T, N > &  lhs, U  rhs  )

related

Right scalar addition.

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

Vector< typename std::common_type< T, U >::type, N > operator+ ( T  lhs, const Vector< U, N > &  rhs  )

related

Left scalar addition.

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

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

related

Component-wise addition and assignment.

template<typename T , std::size_t N>

Vector< T, N > operator- ( const Vector< T, N > &  val )

related

Component-wise unary minus.

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

Vector< typename std::common_type< T, U >::type, N > operator- ( const Vector< T, N > &  lhs, const Vector< U, N > &  rhs  )

related

Component-wise substraction.

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

Vector< typename std::common_type< T, U >::type, N > operator- ( const Vector< T, N > &  lhs, U  rhs  )

related

Right scalar substraction.

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

Vector< typename std::common_type< T, U >::type, N > operator- ( T  lhs, const Vector< U, N > &  rhs  )

related

Left scalar substraction.

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

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

related

Component-wise substraction and assignment.

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

Vector< typename std::common_type< T, U >::type, N > operator/ ( const Vector< T, N > &  lhs, const Vector< U, N > &  rhs  )

related

Component-wise division.

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

Vector< typename std::common_type< T, U >::type, N > operator/ ( const Vector< T, N > &  lhs, U  rhs  )

related

Right scalar division.

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

Vector< typename std::common_type< T, U >::type, N > operator/ ( T  lhs, const Vector< U, N > &  rhs  )

related

Left scalar division.

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

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

related

Component-wise division and assignment.

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

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

related

Right scalar division and assignment.

template<typename T , std::size_t N>

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

related

Equality operator between two vectors.

template<std::size_t N>

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

related

Component-wise logical or operator.

template<typename T >

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

related

Perpendicular vector.

Parameters

vec

A vector

Returns

A perpendicular vector

template<typename T , std::size_t N>

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

related

Component-wise selection operator.

template<typename T , std::size_t N>

T squareDistance ( const Vector< T, N > &  lhs, const 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()

template<typename T , std::size_t N>

T squareLength ( const Vector< T, N > &  vec )

related

Square Euclidean length of a vector.

The square Euclidean length \( l \) of a vector \( (u_1, \ldots, u_N) \) is:

\[ l = \sum_{i = 1}^{N} u_i^2 \]

Parameters

vec

A vector.

Returns

The square Euclidean length of the vector

See also

euclideanLength(), squareDistance()

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

Member Data Documentation

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.