#include <SO3_Algebra.hpp>

Inheritance diagram for SO3::Algebra< T_SCALAR_TYPE >:

Collaboration diagram for SO3::Algebra< T_SCALAR_TYPE >:

Public Member Functions
	Algebra (const Eigen::Matrix< T_SCALAR_TYPE, 3, 1 > &v)

	Algebra (const T_SCALAR_TYPE a, const T_SCALAR_TYPE b, const T_SCALAR_TYPE c)

Algebra< T_SCALAR_TYPE >	inverse () const

void	operator+= (const Algebra< T_SCALAR_TYPE > &g)

void	*operator=** (T_SCALAR_TYPE s)

Algebra< T_SCALAR_TYPE >	bracket (const Algebra< T_SCALAR_TYPE > &g) const

Algebra< T_SCALAR_TYPE >	Ad (const Group< T_SCALAR_TYPE > &g) const

Algebra< T_SCALAR_TYPE >	Ad_star (const Group< T_SCALAR_TYPE > &g) const

Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	operator* (const Eigen::Matrix< T_SCALAR_TYPE, 3, 1 > &vec) const

Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	v () const

void	v (const Eigen::AngleAxis< T_SCALAR_TYPE > &aa)

void	v (const Eigen::Matrix< T_SCALAR_TYPE, 3, 1 > &vec)

T_SCALAR_TYPE const &	operator[] (size_t index) const

T_SCALAR_TYPE &	operator[] (size_t index)

void	normalize ()

Algebra< T_SCALAR_TYPE >	normalized () const

T_SCALAR_TYPE	norm () const

T_SCALAR_TYPE	angle () const

Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	axis () const

Group< T_SCALAR_TYPE >	exp () const

Eigen::Matrix< T_SCALAR_TYPE, 3, 3 >	partialExp (const unsigned int i) const

Algebra< T_SCALAR_TYPE >	computeDExpRInv (const Algebra< T_SCALAR_TYPE > &y, unsigned int order_p=0) const

Group< T_SCALAR_TYPE >	cay () const

Eigen::Matrix< T_SCALAR_TYPE, 3, 3 >	dCayRInv () const

Algebra< T_SCALAR_TYPE >	dCayRInv (const Algebra< T_SCALAR_TYPE > &g) const

Eigen::AngleAxis< T_SCALAR_TYPE >	toAngleAxis () const

Eigen::Matrix< T_SCALAR_TYPE, 3, 3 >	toRotationMatrix () const

Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	toVector () const

NOXVector< 3 >	toNOXVector () const

Public Member Functions inherited from LieAlgebraBase< Algebra< T_SCALAR_TYPE >, Group< T_SCALAR_TYPE >, 3, T_SCALAR_TYPE >
Algebra< T_SCALAR_TYPE >	inverse () const

void	inverted ()

void	operator+= (const Algebra< T_SCALAR_TYPE > &g)

Algebra< T_SCALAR_TYPE >	operator+ (const Algebra< T_SCALAR_TYPE > &g) const

Algebra< T_SCALAR_TYPE >	operator- (const Algebra< T_SCALAR_TYPE > &g) const

void	operator*= (T_SCALAR_TYPE s)

Algebra< T_SCALAR_TYPE >	operator* (const T_SCALAR_TYPE &s) const

Algebra< T_SCALAR_TYPE >	bracket (const Algebra< T_SCALAR_TYPE > &g) const

Algebra< T_SCALAR_TYPE >	Ad (const Group< T_SCALAR_TYPE > &g) const

Algebra< T_SCALAR_TYPE >	Ad_star (const Group< T_SCALAR_TYPE > &g) const

T_SCALAR_TYPE	norm () const

Group< T_SCALAR_TYPE >	exp () const

NOXVector< T_DOF >	toNOXVector () const

Public Member Functions inherited from CRTP< Algebra< T_SCALAR_TYPE > >
Algebra< T_SCALAR_TYPE > &	underlying ()

Algebra< T_SCALAR_TYPE > const &	underlying () const

Static Public Member Functions
static Algebra< T_SCALAR_TYPE >	Identity ()

static Algebra< T_SCALAR_TYPE >	cay_inv (const Group< T_SCALAR_TYPE > &g)

static Algebra< T_SCALAR_TYPE >	fromRotationMatrix (const Eigen::Matrix< T_SCALAR_TYPE, 3, 3 > &m)

static Eigen::Matrix< T_SCALAR_TYPE, 3, 3 >	GeneratorMatrix (int const i)

static Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	GeneratorVector (int const i)

static Algebra< T_SCALAR_TYPE >	Generator (int const i)

static Algebra< T_SCALAR_TYPE >	Zero ()

Static Public Member Functions inherited from LieAlgebraBase< Algebra< T_SCALAR_TYPE >, Group< T_SCALAR_TYPE >, 3, T_SCALAR_TYPE >
static Algebra< T_SCALAR_TYPE >	Zero ()

static Algebra< T_SCALAR_TYPE >	static_bracket (const Algebra< T_SCALAR_TYPE > &g1, const Algebra< T_SCALAR_TYPE > &g2)

static Algebra< T_SCALAR_TYPE >	static_Ad (const Algebra< T_SCALAR_TYPE > &a, const Group< T_SCALAR_TYPE > &g)

static Algebra< T_SCALAR_TYPE >	static_Ad_star (const Group< T_SCALAR_TYPE > &g, const Algebra< T_SCALAR_TYPE > &a)

static Group< T_SCALAR_TYPE >	exp (const Algebra< T_SCALAR_TYPE > &g)

static const unsigned int	dof ()

Protected Attributes
Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	m_v

Additional Inherited Members
Static Public Attributes inherited from LieAlgebraBase< Algebra< T_SCALAR_TYPE >, Group< T_SCALAR_TYPE >, 3, T_SCALAR_TYPE >
static const unsigned int	DOF

Detailed Description

template<typename T_SCALAR_TYPE>
class SO3::Algebra< T_SCALAR_TYPE >

Class Lie algebra \(\mathfrak{so}(3)\) implementation.

Template Parameters

T	Floating point type used for internal representation of coefficients.

Member Function Documentation

◆ bracket()

template<typename T_SCALAR_TYPE>

Algebra<T_SCALAR_TYPE> SO3::Algebra< T_SCALAR_TYPE >::bracket ( const Algebra< T_SCALAR_TYPE > & g ) const

inline

Implements the non-commutative Lie bracket operation \([a,b]\) where \(a\) is *this and \(b\) is g.

Returns: the bracket operation between *this and g.

◆ cay()

template<typename T_SCALAR_TYPE>

Group<T_SCALAR_TYPE> SO3::Algebra< T_SCALAR_TYPE >::cay ( ) const

inline

Implements the Cayley map \(cay:\mathfrak{so}(3)\rightarrow SO(3)\) evalutated at *this.

Returns: the Lie::SO3::Group<T> implementation of the Lie group \(SO(3)\) element that represents the image of *this by the Cayley map.

◆ exp()

template<typename T_SCALAR_TYPE>

Group<T_SCALAR_TYPE> SO3::Algebra< T_SCALAR_TYPE >::exp ( ) const

inline

Implements the exponential map \(\exp:\mathfrak{so}(3)\rightarrow SO(3)\) evalutated at *this.

Returns: the Lie::SO3::Group<T> implementation of the Lie group \(SO(3)\) element that represents the exponential of *this.

◆ GeneratorMatrix()

template<typename T_SCALAR_TYPE>

static Eigen::Matrix<T_SCALAR_TYPE,3,3> SO3::Algebra< T_SCALAR_TYPE >::GeneratorMatrix ( int const i )

inlinestatic

Implements the three generators of the skew matrix representation of \(\mathfrak{so}(3)\). Those generators are repsectively

\[ \widehat J_0=\begin{pmatrix}0&0&0\\0&0&-1\\0&1&0\end{pmatrix},\quad \widehat J_1=\begin{pmatrix}0&0&1\\0&0&0\\-1&0&0\end{pmatrix},\quad \widehat J_2=\begin{pmatrix}0&-1&0\\1&0&0\\0&0&0\end{pmatrix} \]

and define the isomorphism between 3 by 3 skew matrices and size 3 vectors

\[ \widehat\omega = \omega\cdot\left(\widehat J_0,\widehat J_1,\widehat J_2\right)^T. \]

Returns: the i-th generator matrix.

◆ Identity()

template<typename T_SCALAR_TYPE>

static Algebra<T_SCALAR_TYPE> SO3::Algebra< T_SCALAR_TYPE >::Identity ( )

inlinestatic

Returns: the element representing the group identity for operation +.

◆ inverse()

template<typename T_SCALAR_TYPE>

Algebra<T_SCALAR_TYPE> SO3::Algebra< T_SCALAR_TYPE >::inverse ( ) const

inline

Returns: the group inverse of *this.

◆ operator*()

template<typename T_SCALAR_TYPE>

Eigen::Matrix<T_SCALAR_TYPE,3,1> SO3::Algebra< T_SCALAR_TYPE >::operator* ( const Eigen::Matrix< T_SCALAR_TYPE, 3, 1 > & vec ) const

inline

Transforms the size 3 vector vec by the algebra element represented by *this. With a skew matrix representation, it implements the operation \(\widehat\omega v\); with a vector reprentation it implements \(\omega\wedge v\).

Returns: the result of the action of *this on vec.

◆ toAngleAxis()

template<typename T_SCALAR_TYPE>

Eigen::AngleAxis<T_SCALAR_TYPE> SO3::Algebra< T_SCALAR_TYPE >::toAngleAxis ( ) const

inline

Returns: the axis-angle representation of *this.

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

Geomi/src/Common/SO3_Algebra.hpp

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

template<typename T_SCALAR_TYPE> class SO3::Algebra< T_SCALAR_TYPE >

Member Function Documentation

◆ bracket()

◆ cay()

◆ exp()

◆ GeneratorMatrix()

◆ Identity()

◆ inverse()

◆ operator*()

◆ toAngleAxis()

template<typename T_SCALAR_TYPE>
class SO3::Algebra< T_SCALAR_TYPE >