nc::rotations Namespace Reference

Data Structures
class	DCM
	Factory methods for generating direction cosine matrices and vectors. More...
class	Quaternion
	Holds a unit quaternion. More...

Functions
template<typename dtype >
NdArray< double >	rodriguesRotation (const NdArray< dtype > &k, double theta, const NdArray< dtype > &v)
Vec3	rodriguesRotation (const Vec3 &k, double theta, const Vec3 &v) noexcept
template<typename dtype >
NdArray< double >	wahbasProblem (const NdArray< dtype > &wk, const NdArray< dtype > &vk)
template<typename dtype >
NdArray< double >	wahbasProblem (const NdArray< dtype > &wk, const NdArray< dtype > &vk, const NdArray< dtype > &ak)

Function Documentation

rodriguesRotation() [1/2]

template<typename dtype >

NdArray< double > nc::rotations::rodriguesRotation	(	const NdArray< dtype > &	k,
		double	theta,
		const NdArray< dtype > &	v
	)

Performs Rodriques' rotation formula https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

Parameters

k	the axis to rotate around
theta	the angle in radians to rotate
v	the vector to rotate

Returns

NdArray<double>

rodriguesRotation() [2/2]

Vec3 nc::rotations::rodriguesRotation ( const Vec3 &  k, double  theta, const Vec3 &  v  )

inlinenoexcept

Performs Rodriques' rotation formula https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

Parameters

k	the axis to rotate around
theta	the angle in radians to rotate
v	the vector to rotate

Returns

Vec3

wahbasProblem() [1/2]

template<typename dtype >

NdArray< double > nc::rotations::wahbasProblem	(	const NdArray< dtype > &	wk,
		const NdArray< dtype > &	vk
	)

Finds a rotation matrix (special orthogonal matrix) between two coordinate systems from a set of (weighted) vector observations. Solutions to Wahba's problem are often used in satellite attitude determination utilising sensors such as magnetometers and multi-antenna GPS receivers https://en.wikipedia.org/wiki/Wahba%27s_problem

Parameters

wk	k-th 3-vector measurement in the reference frame
vk	corresponding k-th 3-vector measurement in the body frame

Returns

NdArray rotation matrix

wahbasProblem() [2/2]

template<typename dtype >

NdArray< double > nc::rotations::wahbasProblem	(	const NdArray< dtype > &	wk,
		const NdArray< dtype > &	vk,
		const NdArray< dtype > &	ak
	)

Finds a rotation matrix (special orthogonal matrix) between two coordinate systems from a set of (weighted) vector observations. Solutions to Wahba's problem are often used in satellite attitude determination utilising sensors such as magnetometers and multi-antenna GPS receivers https://en.wikipedia.org/wiki/Wahba%27s_problem

Parameters

wk	k-th 3-vector measurement in the reference frame (n x 3 matrix)
vk	corresponding k-th 3-vector measurement in the body frame (n x 3 matrix)
ak	set of weights for each observation (1 x n or n x 1 matrix)

Returns

NdArray rotation matrix