#include <algorithm>
#include <array>
#include <cmath>
#include <cstddef>
#include <cstdint>
#include <initializer_list>
#include <string>
#include <type_traits>
#include <vector>

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Classes
class	svector::Vector< D, T >
	A base vector representation. More...

class	svector::Vector2D
	A simple 2D vector representation. More...

class	svector::Vector3D
	A simple 3D vector representation. More...

Typedefs
typedef Vector< 2 >	svector::Vec2_
	An alias to Vector<2>.

typedef Vector< 3 >	svector::Vec3_
	An alias to Vector<3>.

Enumerations
enum	svector::AngleDir { svector::ALPHA , svector::BETA , svector::GAMMA }
	Angle enumerator. More...

Functions
template<std::size_t D, typename T >
Vector< D, T >	svector::makeVector (std::array< T, D > array)
	Creates a vector from an std::array. More...

template<std::size_t D, typename T >
Vector< D, T >	svector::makeVector (std::vector< T > vector)
	Creates a vector from a std::vetor. More...

template<std::size_t D, typename T >
Vector< D, T >	svector::makeVector (const std::initializer_list< T > args)
	Creates a vector from an initializer list. More...

double	svector::x (const Vector2D &v)
	Gets the x-component of a 2D vector. More...

void	svector::x (Vector2D &v, const double xValue)
	Sets the x-component of a 2D vector. More...

double	svector::x (const Vector3D &v)
	Gets the x-component of a 3D vector. More...

void	svector::x (Vector3D &v, const double xValue)
	Sets the x-component of a 3D vector. More...

double	svector::y (const Vector2D &v)
	Gets the y-component of a 2D vector. More...

void	svector::y (Vector2D &v, const double yValue)
	Sets the y-component of a 2D vector. More...

double	svector::y (const Vector3D &v)
	Gets the y-component of a 3D vector. More...

void	svector::y (Vector3D &v, const double yValue)
	Sets the y-component of a 3D vector. More...

double	svector::z (const Vector3D &v)
	Gets the z-component of a 3D vector. More...

void	svector::z (Vector3D &v, const double zValue)
	Sets the z-component of a 3D vector. More...

template<typename T , std::size_t D>
T	svector::dot (const Vector< D, T > &lhs, const Vector< D, T > &rhs)
	Calculates the dot product of two vectors. More...

template<typename T , std::size_t D>
T	svector::magn (const Vector< D, T > &v)
	Gets the magnitude of the vector. More...

template<typename T , std::size_t D>
Vector< D, T >	svector::normalize (const Vector< D, T > &v)
	Normalizes a vector. More...

template<typename T , std::size_t D>
bool	svector::isZero (const Vector< D, T > &v)
	Determines whether a vector is a zero vector. More...

double	svector::angle (const Vector2D &v)
	Gets the angle of a 2D vector in radians. More...

Vector2D	svector::rotate (const Vector2D &v, const double ang)
	Rotates a 2D vector by a certain angle. More...

Vector3D	svector::cross (const Vector3D &lhs, const Vector3D &rhs)
	Cross product of two vectors. More...

double	svector::alpha (const Vector3D &v)
	Gets α angle. More...

double	svector::beta (const Vector3D &v)
	Gets β angle. More...

double	svector::gamma (const Vector3D &v)
	Gets γ angle. More...

Vector3D	svector::rotateAlpha (const Vector3D &v, const double &ang)
	Rotates around x-axis. More...

Vector3D	svector::rotateBeta (const Vector3D &v, const double &ang)
	Rotates around y-axis. More...

Vector3D	svector::rotateGamma (const Vector3D &v, const double &ang)
	Rotates around z-axis. More...

template<typename T , std::size_t D>
Vector< D, T >	svector::operator+ (const Vector< D, T > &lhs, const Vector< D, T > &rhs)
	Vector addition. More...

template<typename T , std::size_t D>
Vector< D, T >	svector::operator- (const Vector< D, T > &lhs, const Vector< D, T > &rhs)
	Vector subtraction. More...

template<typename T , typename T2 , std::size_t D>
Vector< D, T >	svector::operator* (const Vector< D, T > &lhs, const T2 rhs)
	Scalar multiplication. More...

template<typename T , typename T2 , std::size_t D>
Vector< D, T >	svector::operator/ (const Vector< D, T > &lhs, const T2 rhs)
	Scalar division. More...

template<typename T , std::size_t D>
bool	svector::operator== (const Vector< D, T > &lhs, const Vector< D, T > &rhs)
	Compares equality of two vectors. More...

template<typename T , std::size_t D>
bool	svector::operator!= (const Vector< D, T > &lhs, const Vector< D, T > &rhs)
	Compares inequality of two vectors. More...

Enumeration Type Documentation

◆ AngleDir

enum svector::AngleDir

Angle enumerator.

An enum representing the angle to use for a 3D vector.

This is only used in svector::Vector3D::angle() and svector::Vector3D::rotate().

Enumerator
ALPHA	Angle between positive x-axis and vector.
BETA	Angle between positive y-axis and vector.
GAMMA	Angle between positive z-axis and vector.

Function Documentation

◆ alpha()

double svector::alpha ( const Vector3D & v )

inline

Gets α angle.

α is the angle between the vector and the x-axis.

Note: This method will result in undefined behavior if the vector is a zero vector (if the magnitude equals zero).

Parameters

v	A 3D vector.

Returns: α

◆ angle()

double svector::angle ( const Vector2D & v )

inline

Gets the angle of a 2D vector in radians.

The angle will be in the range (-π, π].

Parameters

v	A 2D vector.

Returns: angle of the vector.

◆ beta()

double svector::beta ( const Vector3D & v )

inline

Gets β angle.

β is the angle between the vector and the y-axis.

Note: This method will result in undefined behavior if the vector is a zero vector (if the magnitude equals zero).

Parameters

v	A 3D vector.

Returns: β

◆ cross()

Vector3D svector::cross	(	const Vector3D &	lhs,
		const Vector3D &	rhs
	)

inline

Cross product of two vectors.

Parameters

lhs	The first vector.
rhs	The second vector, crossed with the first vector.

Returns: The cross product of the two vectors.

◆ dot()

template<typename T , std::size_t D>

T svector::dot	(	const Vector< D, T > &	lhs,
		const Vector< D, T > &	rhs
	)

inline

Calculates the dot product of two vectors.

Note: The dimensions of the two vectors must be the same.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

lhs	First vector.
rhs	Second vector.

Returns: The dot product of lhs and rhs.

◆ gamma()

double svector::gamma ( const Vector3D & v )

inline

Gets γ angle.

γ is the angle between the vector and the z-axis.

Note: This method will result in undefined behavior if the vector is a zero vector (if the magnitude equals zero).

Parameters

v	A 3D vector.

Returns: γ

◆ isZero()

template<typename T , std::size_t D>

bool svector::isZero ( const Vector< D, T > & v )

inline

Determines whether a vector is a zero vector.

Template Parameters

D	The number of dimensions.
T	Vector type.

Returns: Whether the given vector is a zero vector.

◆ magn()

template<typename T , std::size_t D>

T svector::magn ( const Vector< D, T > & v )

inline

Gets the magnitude of the vector.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

v	The vector to get magnitude of.

Returns: magnitude of vector.

◆ makeVector() [1/3]

template<std::size_t D, typename T >

Vector<D, T> svector::makeVector ( const std::initializer_list< T > args )

Creates a vector from an initializer list.

The initializer list should represent the components of the vector in each dimension. If the size of the initializer list is greater than the number of dimensions given, then the vector only initializes with the first D elements in the list, where D is the number of dimensions. If the size of the initializer list is less than the number of dimensions given, then the vector fills the rest of the dimensions with the value 0.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

args	the initializer list.

Returns: A vector whose dimensions reflect the elements in the initializer list.

◆ makeVector() [2/3]

template<std::size_t D, typename T >

Vector<D, T> svector::makeVector ( std::array< T, D > array )

Creates a vector from an std::array.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

array An array.

Returns: A vector whose dimensions reflect the elements in the array.

◆ makeVector() [3/3]

template<std::size_t D, typename T >

Vector<D, T> svector::makeVector ( std::vector< T > vector )

Creates a vector from a std::vetor.

If the given std::vector has fewer elements than the specified dimensions, then this function will fill up the first elements of the vector with those in the given std::vector. The rest of the elements would be 0.

If the given std::vector has more elements than the specified dimensions, then the resulting vector would ignore the numbers in those dimensions.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

vector A std::vector.

Returns: A vector whose dimensions reflect the elements in the std::vector.

◆ normalize()

template<typename T , std::size_t D>

Vector<D, T> svector::normalize ( const Vector< D, T > & v )

inline

Normalizes a vector.

Finds the unit vector with the same direction angle as the current vector.

Note: This method will result in undefined behavior if the vector is a zero vector (if the magnitude equals zero).

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

v	The vector to normalize.

Returns: Normalized vector.

◆ operator!=()

template<typename T , std::size_t D>

bool svector::operator!=	(	const Vector< D, T > &	lhs,
		const Vector< D, T > &	rhs
	)

inline

Compares inequality of two vectors.

Note: This method is only used if SVECTOR_USE_CLASS_OPERATORS is not defined. Otherwise, the operators in svector::Vector are used.; The dimensions of the two vectors must be the same.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

lhs	The first vector.
rhs	The second vector.

Returns: A boolean representing whether the two vectors do not compare equal.

◆ operator*()

template<typename T , typename T2 , std::size_t D>

Vector<D, T> svector::operator*	(	const Vector< D, T > &	lhs,
		const T2	rhs
	)

inline

Scalar multiplication.

Performs scalar multiplication and returns a new vector representing the product.

Note: This method is only used if SVECTOR_USE_CLASS_OPERATORS is not defined. Otherwise, the operators in svector::Vector are used.

Template Parameters

D	The number of dimensions.
T	Vector type.
T2	Scalar multiplication type.

Parameters

lhs	The first vector.
rhs	The second vector.

Returns: A new vector representing the scalar product.

◆ operator+()

template<typename T , std::size_t D>

Vector<D, T> svector::operator+	(	const Vector< D, T > &	lhs,
		const Vector< D, T > &	rhs
	)

inline

Vector addition.

Performs vector addition and returns a new vector representing the sum of the two vectors.

Note: This method is only used if SVECTOR_USE_CLASS_OPERATORS is not defined. Otherwise, the operators in svector::Vector are used.; The dimensions of the two vectors must be the same.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

lhs	The first vector.
rhs	The second vector.

Returns: A new vector representing the vector sum.

◆ operator-()

template<typename T , std::size_t D>

Vector<D, T> svector::operator-	(	const Vector< D, T > &	lhs,
		const Vector< D, T > &	rhs
	)

inline

Vector subtraction.

Performs vector subtraction and returns a new vector representing the difference of the two vectors.

Note: This method is only used if SVECTOR_USE_CLASS_OPERATORS is not defined. Otherwise, the operators in svector::Vector are used.; The dimensions of the two vectors must be the same.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

lhs	The first vector.
rhs	The second vector.

Returns: A new vector representing the vector sum.

◆ operator/()

template<typename T , typename T2 , std::size_t D>

Vector<D, T> svector::operator/	(	const Vector< D, T > &	lhs,
		const T2	rhs
	)

inline

Scalar division.

Performs scalar division and returns a new vector representing the quotient.

Note: This method is only used if SVECTOR_USE_CLASS_OPERATORS is not defined. Otherwise, the operators in svector::Vector are used.

Template Parameters

D	The number of dimensions.
T	Vector type.
T2	Scalar division type.

Parameters

lhs	The first vector.
rhs	The second vector.

Returns: A new vector representing the scalar product.

◆ operator==()

template<typename T , std::size_t D>

bool svector::operator==	(	const Vector< D, T > &	lhs,
		const Vector< D, T > &	rhs
	)

inline

Compares equality of two vectors.

Note: This method is only used if SVECTOR_USE_CLASS_OPERATORS is not defined. Otherwise, the operators in svector::Vector are used.; The dimensions of the two vectors must be the same.

Template Parameters

D	The number of dimensions.
T	Vector type.

Parameters

lhs	The first vector.
rhs	The second vector.

Returns: A boolean representing whether the two vectors compare equal.

◆ rotate()

Vector2D svector::rotate	(	const Vector2D &	v,
		const double	ang
	)

inline

Rotates a 2D vector by a certain angle.

The angle should be given in radians. The vector rotates counterclockwise when the angle is positive and clockwise when the angle is negative.

Parameters

v	A 2D vector.
ang	the angle to rotate the vector, in radians.

Returns: a new, rotated vector.

◆ rotateAlpha()

Vector3D svector::rotateAlpha	(	const Vector3D &	v,
		const double &	ang
	)

inline

Rotates around x-axis.

Uses the basic gimbal-like 3D rotation matrices for rotation.

Parameters

v	A 3D vector.
ang	The angle to rotate the vector, in radians.

Returns: A new, rotated vector.

◆ rotateBeta()

Vector3D svector::rotateBeta	(	const Vector3D &	v,
		const double &	ang
	)

inline

Rotates around y-axis.

Uses the basic gimbal-like 3D rotation matrices for rotation.

Parameters

v	A 3D vector.
ang	The angle to rotate the vector, in radians.

Returns: A new, rotated vector.

◆ rotateGamma()

Vector3D svector::rotateGamma	(	const Vector3D &	v,
		const double &	ang
	)

inline

Rotates around z-axis.

Uses the basic gimbal-like 3D rotation matrices for rotation.

Parameters

v	A 3D vector.
ang	The angle to rotate the vector, in radians.

Returns: A new, rotated vector.

◆ x() [1/4]

double svector::x ( const Vector2D & v )

inline

Gets the x-component of a 2D vector.

Parameters

v	A 2D Vector.

Returns: x-component of the vector.

◆ x() [2/4]

double svector::x ( const Vector3D & v )

inline

Gets the x-component of a 3D vector.

Parameters

v	A 3D Vector.

Returns: x-component of the vector.

◆ x() [3/4]

void svector::x	(	Vector2D &	v,
		const double	xValue
	)

inline

Sets the x-component of a 2D vector.

Parameters

v	A 2D Vector.
xValue	The x-value to set to the vector.

◆ x() [4/4]

void svector::x	(	Vector3D &	v,
		const double	xValue
	)

inline

Sets the x-component of a 3D vector.

Parameters

v	A 3D Vector.
xValue	The x-value to set to the vector.

◆ y() [1/4]

double svector::y ( const Vector2D & v )

inline

Gets the y-component of a 2D vector.

Parameters

v	A 2D Vector.

Returns: y-component of the vector.

◆ y() [2/4]

double svector::y ( const Vector3D & v )

inline

Gets the y-component of a 3D vector.

Parameters

v	A 3D Vector.

Returns: y-component of the vector.

◆ y() [3/4]

void svector::y	(	Vector2D &	v,
		const double	yValue
	)

inline

Sets the y-component of a 2D vector.

Parameters

v	A 2D Vector.
yValue	The y-value to set to the vector.

◆ y() [4/4]

void svector::y	(	Vector3D &	v,
		const double	yValue
	)

inline

Sets the y-component of a 3D vector.

Parameters

v	A 3D Vector.
yValue	The y value to set to the vector.

◆ z() [1/2]

double svector::z ( const Vector3D & v )

inline

Gets the z-component of a 3D vector.

Parameters

v	A 3D Vector.

Returns: z-component of the vector.

◆ z() [2/2]

void svector::z	(	Vector3D &	v,
		const double	zValue
	)

inline

Sets the z-component of a 3D vector.

Parameters

v	A 3D Vector.
zValue	The z value to set to the vector.

Classes

Typedefs

Enumerations

Functions

Enumeration Type Documentation

◆ AngleDir

Function Documentation

◆ alpha()

◆ angle()

◆ beta()

◆ cross()

◆ dot()

◆ gamma()

◆ isZero()

◆ magn()

◆ makeVector() [1/3]

◆ makeVector() [2/3]

◆ makeVector() [3/3]

◆ normalize()

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator/()

◆ operator==()

◆ rotate()

◆ rotateAlpha()

◆ rotateBeta()

◆ rotateGamma()

◆ x() [1/4]

◆ x() [2/4]

◆ x() [3/4]

◆ x() [4/4]

◆ y() [1/4]

◆ y() [2/4]

◆ y() [3/4]

◆ y() [4/4]

◆ z() [1/2]

◆ z() [2/2]