#include <Utils.h>

Public Member Functions
void	dot (const std::array< T, 3 > &v1, const std::array< T, 3 > &v2, T &out)

void	dot (const std::array< std::complex< T >, 3 > &cv1, const std::array< std::complex< T >, 3 > &cv2, std::complex< T > &out)

void	dot (const std::array< std::complex< T >, 3 > &cv1, const std::array< T, 3 > &v2, std::complex< T > &out)

void	dot (const std::array< T, 3 > &v1, const std::array< std::complex< T >, 3 > &cv2, std::complex< T > &out)

void	ext (const std::array< T, 3 > &v1, const std::array< T, 3 > &v2, std::array< T, 3 > &out)

void	ext (const std::array< std::complex< T >, 3 > &cv1, const std::array< std::complex< T >, 3 > &cv2, std::array< std::complex< T >, 3 > &out)

void	ext (const std::array< std::complex< T >, 3 > &cv1, const std::array< T, 3 > &v2, std::array< std::complex< T >, 3 > &out)

void	ext (const std::array< T, 3 > &v1, const std::array< std::complex< T >, 3 > &cv2, std::array< std::complex< T >, 3 > &out)

void	abs (const std::array< T, 3 > &v, T &out)

void	diff (const std::array< T, 3 > &v1, const std::array< T, 3 > &v2, std::array< T, 3 > &out)

void	diff (const std::array< std::complex< T >, 3 > &cv1, const std::array< std::complex< T >, 3 > &cv2, std::array< std::complex< T >, 3 > &out)

void	normalize (const std::array< T, 3 > &v, std::array< T, 3 > &out)

void	add (const std::array< T, 3 > &v1, const std::array< T, 3 > &v2, std::array< T, 3 > &out)

void	s_mult (const std::array< T, 3 > &v, const T &s, std::array< T, 3 > &out)

void	s_mult (const std::array< std::complex< T >, 3 > &cv, const std::complex< T > &cs, std::array< std::complex< T >, 3 > &out)

void	s_mult (const std::array< T, 3 > &v, const std::complex< T > &cs, std::array< std::complex< T >, 3 > &out)

void	s_mult (const std::array< std::complex< T >, 3 > &cv, const T &s, std::array< std::complex< T >, 3 > &out)

void	conj (const std::array< std::complex< T >, 3 > &cv, std::array< std::complex< T >, 3 > &out)

void	snell (const std::array< T, 3 > &vin, const std::array< T, 3 > &normal, std::array< T, 3 > &out)

void	snell_t (const std::array< T, 3 > &vin, const std::array< T, 3 > &normal, T mu, std::array< T, 3 > &out)

void	dyad (const std::array< T, 3 > &v1, const std::array< T, 3 > &v2, std::array< std::array< T, 3 >, 3 > &out)

void	matDiff (const std::array< std::array< T, 3 >, 3 > &m1, const std::array< std::array< T, 3 >, 3 > &m2, std::array< std::array< T, 3 >, 3 > &out)

void	matVec (const std::array< std::array< T, 3 >, 3 > &m1, const std::array< T, 3 > &v1, std::array< T, 3 > &out)

void	matVec (const std::array< std::array< T, 3 >, 3 > &m1, const std::array< std::complex< T >, 3 > &cv1, std::array< std::complex< T >, 3 > &out)

void	matVec4 (const T *m1, const std::array< T, 3 > &v1, std::array< T, 3 > &out, bool vec=false)

void	invmatVec4 (const T *m1, const std::array< T, 3 > &v1, std::array< T, 3 > &out, bool vec=false)

void	matRot (const std::array< T, 3 > &rot, const std::array< T, 3 > &v1, const std::array< T, 3 > &cRot, std::array< T, 3 > &out)

Detailed Description

template<typename T>
class Utils< T >

Class for basic 3D linear algebra functions.

Note that no function returns. All values are stored inside a variable which is passed by reference to the function.

Member Function Documentation

◆ abs()

template<typename T >

void Utils< T >::abs	(	const std::array< T, 3 > &	v,
		T &	out
	)

inline

Absolute value.

Calculate absolute value of real valued vector of size 3.

Parameters

v	Array of 3 double/float.
out	Scalar double/float.

◆ add()

template<typename T >

void Utils< T >::add	(	const std::array< T, 3 > &	v1,
		const std::array< T, 3 > &	v2,
		std::array< T, 3 > &	out
	)

inline

Vector addition.

Add two real valued vectors of size 3 element-wise.

Parameters

v1	Array of 3 double/float.
v2	Array of 3 double/float.
out	Array of 3 complex double/float.

◆ conj()

template<typename T >

void Utils< T >::conj	(	const std::array< std::complex< T >, 3 > &	cv,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Conjugate.

Conjugate complex valued vector of size 3.

Parameters

cv	Array of 3 complex double/float.
out	Array of 3 complex double/float.

◆ diff() [1/2]

template<typename T >

void Utils< T >::diff	(	const std::array< std::complex< T >, 3 > &	cv1,
		const std::array< std::complex< T >, 3 > &	cv2,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Component-wise vector difference.

Subtract two complex valued vectors of size 3, element-wise.

Parameters

cv1	Array of 3 complex double/float.
cv2	Array of 3 complex double/float.
out	Array of 3 complex double/float.

◆ diff() [2/2]

template<typename T >

void Utils< T >::diff	(	const std::array< T, 3 > &	v1,
		const std::array< T, 3 > &	v2,
		std::array< T, 3 > &	out
	)

inline

Component-wise vector difference.

Subtract two real valued vectors of size 3, element-wise.

Parameters

v1	Array of 3 double/float.
v2	Array of 3 double/float.
out	Array of 3 double/float.

◆ dot() [1/4]

template<typename T >

void Utils< T >::dot	(	const std::array< std::complex< T >, 3 > &	cv1,
		const std::array< std::complex< T >, 3 > &	cv2,
		std::complex< T > &	out
	)

inline

Dot product.

Take the dot (inner) product of two complex valued double/float arrays of size 3.

Parameters

cv1	Array of 3 complex double/float.
cv2	Array of 3 complex double/float.
out	Scalar complex double/float.

◆ dot() [2/4]

template<typename T >

void Utils< T >::dot	(	const std::array< std::complex< T >, 3 > &	cv1,
		const std::array< T, 3 > &	v2,
		std::complex< T > &	out
	)

inline

Dot product.

Take the dot (inner) product of one complex valued and one real valued double/float array of size 3.

Parameters

cv1	Array of 3 complex double/float.
v2	Array of 3 double/float.
out	Scalar complex double/float.

◆ dot() [3/4]

template<typename T >

void Utils< T >::dot	(	const std::array< T, 3 > &	v1,
		const std::array< std::complex< T >, 3 > &	cv2,
		std::complex< T > &	out
	)

inline

Dot product.

Take the dot (inner) product of one real valued and one complex valued double/float array of size 3.

Parameters

v1	Array of 3 double/float.
cv2	Array of 3 complex double/float.
out	Scalar complex double/float.

◆ dot() [4/4]

template<typename T >

void Utils< T >::dot	(	const std::array< T, 3 > &	v1,
		const std::array< T, 3 > &	v2,
		T &	out
	)

inline

Dot product.

Take the dot (inner) product of two real valued arrays of size 3.

Parameters

v1	Array of 3 double/float.
v2	Array of 3 double/float.
out	Scalar double/float.

◆ dyad()

template<typename T >

void Utils< T >::dyad	(	const std::array< T, 3 > &	v1,
		const std::array< T, 3 > &	v2,
		std::array< std::array< T, 3 >, 3 > &	out
	)

inline

Dyadic product.

Calculate dyadic product between two real valued double/float vectors of size 3.

Parameters

v1	Array of 3 double/float.
v2	Array of 3 double/float.
out	Array of 3 double/float, nested inside array of size 3.

◆ ext() [1/4]

template<typename T >

void Utils< T >::ext	(	const std::array< std::complex< T >, 3 > &	cv1,
		const std::array< std::complex< T >, 3 > &	cv2,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Cross product.

Take the cross (outer) product of two complex valued double/float arrays of size 3.

Parameters

cv1	Array of 3 complex double/float.
cv2	Array of 3 complex double/float.
out	Array of 3 complex double/float.

◆ ext() [2/4]

template<typename T >

void Utils< T >::ext	(	const std::array< std::complex< T >, 3 > &	cv1,
		const std::array< T, 3 > &	v2,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Cross product.

Take the cross (outer) product of one complex valued and one real valued double/float array of size 3.

Parameters

cv1	Array of 3 complex double/float.
v2	Array of 3 double/float.
out	Array of 3 complex double/float.

◆ ext() [3/4]

template<typename T >

void Utils< T >::ext	(	const std::array< T, 3 > &	v1,
		const std::array< std::complex< T >, 3 > &	cv2,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Cross product.

Take the cross (outer) product of one real valued and one complex valued double/float array of size 3.

Parameters

v1	Array of 3 double/float.
cv2	Array of 3 complex double/float.
out	Array of 3 complex double/float.

◆ ext() [4/4]

template<typename T >

void Utils< T >::ext	(	const std::array< T, 3 > &	v1,
		const std::array< T, 3 > &	v2,
		std::array< T, 3 > &	out
	)

inline

Cross product.

Take the cross (outer) product of two real valued double/float arrays of size 3.

Parameters

v1	Array of 3 double/float.
v2	Array of 3 double/float.
out	Array of 3 double/float.

◆ invmatVec4()

template<typename T >

void Utils< T >::invmatVec4	(	const T *	m1,
		const std::array< T, 3 > &	v1,
		std::array< T, 3 > &	out,
		bool	vec = `false`
	)

inline

Inverse matrix-vector product.

Multiply the inverse of a real valued 4x4 matrix by a real valued size 3 vector to generate a new size 3 vector. This function is only used for multiplying 3D vectors by a 4D transformation matrix.

Parameters

m1	Array of 4 double/float, nested inside array of size 4.
v1	Array of 3 double/float.
out	Array of 3 double/float.
vec	Whether or not to transform v1 as a point or a vector.

◆ matDiff()

template<typename T >

void Utils< T >::matDiff	(	const std::array< std::array< T, 3 >, 3 > &	m1,
		const std::array< std::array< T, 3 >, 3 > &	m2,
		std::array< std::array< T, 3 >, 3 > &	out
	)

inline

Matrix difference, element wise.

Subtract two 3x3 matrices, element wise.

Parameters

m1	Array of 3 double/float, nested inside array of size 3.
m2	Array of 3 double/float, nested inside array of size 3.
out	Array of 3 double/float, nested inside array of size 3.

◆ matRot()

template<typename T >

void Utils< T >::matRot	(	const std::array< T, 3 > &	rot,
		const std::array< T, 3 > &	v1,
		const std::array< T, 3 > &	cRot,
		std::array< T, 3 > &	out
	)

inline

Manual vector rotation.

Rotate a real valued size 3 vector without defining a transformation matrix.

Parameters

rot	Array of 3 double/float, containing rotation angles.
v1	Array of 3 double/float.
cRot	Array of 3, center of rotation.
out	Array of 3 double/float.

◆ matVec() [1/2]

template<typename T >

void Utils< T >::matVec	(	const std::array< std::array< T, 3 >, 3 > &	m1,
		const std::array< std::complex< T >, 3 > &	cv1,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Matrix-vector product.

Multiply a real valued 3x3 matrix and a complex valued size 3 vector to generate a new complex valued size 3 vector.

Parameters

m1	Array of 3 double/float, nested inside array of size 3.
cv1	Array of 3 complex double/float.
out	Array of 3 complex double/float.

◆ matVec() [2/2]

template<typename T >

void Utils< T >::matVec	(	const std::array< std::array< T, 3 >, 3 > &	m1,
		const std::array< T, 3 > &	v1,
		std::array< T, 3 > &	out
	)

inline

Matrix-vector product.

Multiply a real valued 3x3 matrix and a real valued size 3 vector to generate a new real valued size 3 vector.

Parameters

m1	Array of 3 double/float, nested inside array of size 3.
v1	Array of 3 double/float.
out	Array of 3 double/float.

◆ matVec4()

template<typename T >

void Utils< T >::matVec4	(	const T *	m1,
		const std::array< T, 3 > &	v1,
		std::array< T, 3 > &	out,
		bool	vec = `false`
	)

inline

Matrix-vector product.

Multiply a real valued 4x4 matrix and a real valued size 3 vector to generate a new real valued size 3 vector. This function is only used for multiplying 3D vectors by a 4D transformation matrix.

Parameters

m1	Array of 4 double/float, nested inside array of size 4.
v1	Array of 3 double/float.
out	Array of 3 double/float.
vec	Whether or not to transform v1 as a point or a vector.

◆ normalize()

template<typename T >

void Utils< T >::normalize	(	const std::array< T, 3 > &	v,
		std::array< T, 3 > &	out
	)

inline

Normalize vector.

Normalize real valued vector of size 3.

Parameters

v	Array of 3 double/float.
out	Array of 3 double/float.

◆ s_mult() [1/4]

template<typename T >

void Utils< T >::s_mult	(	const std::array< std::complex< T >, 3 > &	cv,
		const std::complex< T > &	cs,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Scalar multiplication.

Multiply complex valued vector of size 3 by complex scalar, element-wise.

Parameters

cv	Array of 3 complex double/float.
cs	Scalar complex double/float.
out	Array of 3 complex double/float.

◆ s_mult() [2/4]

template<typename T >

void Utils< T >::s_mult	(	const std::array< std::complex< T >, 3 > &	cv,
		const T &	s,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Scalar multiplication.

Multiply complex valued vector of size 3 by real scalar, element-wise.

Parameters

cv	Array of 3 complex double/float.
s	Scalar double/float.
out	Array of 3 complex double/float.

◆ s_mult() [3/4]

template<typename T >

void Utils< T >::s_mult	(	const std::array< T, 3 > &	v,
		const std::complex< T > &	cs,
		std::array< std::complex< T >, 3 > &	out
	)

inline

Scalar multiplication.

Multiply real valued vector of size 3 by complex scalar, element-wise.

Parameters

v	Array of 3 double/float.
cs	Scalar complex double/float.
out	Array of 3 complex double/float.

◆ s_mult() [4/4]

template<typename T >

void Utils< T >::s_mult	(	const std::array< T, 3 > &	v,
		const T &	s,
		std::array< T, 3 > &	out
	)

inline

Scalar multiplication.

Multiply real valued vector of size 3 by real scalar, element-wise.

Parameters

v	Array of 3 double/float.
s	Scalar double/float.
out	Array of 3 double/float.

◆ snell()

template<typename T >

void Utils< T >::snell	(	const std::array< T, 3 > &	vin,
		const std::array< T, 3 > &	normal,
		std::array< T, 3 > &	out
	)

inline

Snell's law for reflection.

Calculate reflected direction vector from incoming direction and normal vector.

Parameters

vin	Array of 3 double/float, incoming direction vector.
normal	Array of 3 double/float, normal vector of surface.
out	Array of 3 double/float.

◆ snell_t()

template<typename T >

void Utils< T >::snell_t	(	const std::array< T, 3 > &	vin,
		const std::array< T, 3 > &	normal,
		T	mu,
		std::array< T, 3 > &	out
	)

inline

Snell's law refraction.

Calculate refracted direction vector from incoming direction and normal vector.

Parameters

vin	Array of 3 double/float, incoming direction vector.
normal	Array of 3 double/float, normal vector of surface.
mu	Ratio of n1 to n2.
out	Array of 3 double/float.

The documentation for this class was generated from the following file:

src/include/Utils.h

Public Member Functions

Detailed Description

template<typename T> class Utils< T >

Member Function Documentation

◆ abs()

◆ add()

◆ conj()

◆ diff() [1/2]

◆ diff() [2/2]

◆ dot() [1/4]

◆ dot() [2/4]

◆ dot() [3/4]

◆ dot() [4/4]

◆ dyad()

◆ ext() [1/4]

◆ ext() [2/4]

◆ ext() [3/4]

◆ ext() [4/4]

◆ invmatVec4()

◆ matDiff()

◆ matRot()

◆ matVec() [1/2]

◆ matVec() [2/2]

◆ matVec4()

◆ normalize()

◆ s_mult() [1/4]

◆ s_mult() [2/4]

◆ s_mult() [3/4]

◆ s_mult() [4/4]

◆ snell()

◆ snell_t()

template<typename T>
class Utils< T >