SO3::Group< T_SCALAR_TYPE > Class Template Reference

#include <SO3_Group.hpp>

Inheritance diagram for SO3::Group< T_SCALAR_TYPE >:

Collaboration diagram for SO3::Group< T_SCALAR_TYPE >:

Public Member Functions
	Group (const Group< T_SCALAR_TYPE > &g)
	Group (const Eigen::Quaternion< T_SCALAR_TYPE > &q_)
	Group (const T_SCALAR_TYPE &w, const T_SCALAR_TYPE &x, const T_SCALAR_TYPE &y, const T_SCALAR_TYPE &z)
	Group (const T_SCALAR_TYPE *data)
template<class Derived >
	Group (const Eigen::QuaternionBase< Derived > &other)
	Group (const Eigen::AngleAxis< T_SCALAR_TYPE > &aa)
template<typename Derived >
	Group (const Eigen::MatrixBase< Derived > &other)
template<class OtherScalar , int OtherOptions>
	Group (const Eigen::Quaternion< OtherScalar, OtherOptions > &other)
Eigen::Quaternion< T_SCALAR_TYPE >	q () const
void	q (const Eigen::Quaternion< T_SCALAR_TYPE > &q_)
void	q (const T_SCALAR_TYPE &w, const T_SCALAR_TYPE &x, const T_SCALAR_TYPE &y, const T_SCALAR_TYPE &z)
void	q (const T_SCALAR_TYPE *data)
template<class Derived >
void	q (const Eigen::QuaternionBase< Derived > &other)
void	q (const Eigen::AngleAxis< T_SCALAR_TYPE > &aa)
template<typename Derived >
void	q (const Eigen::MatrixBase< Derived > &other)
template<class OtherScalar , int OtherOptions>
void	q (const Eigen::Quaternion< OtherScalar, OtherOptions > &other)
Group< T_SCALAR_TYPE >	inverse () const
void	operator*= (Group< T_SCALAR_TYPE > const &g)
Group< T_SCALAR_TYPE >	operator* (Group< T_SCALAR_TYPE > const &g) const
Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	transformVector (const Eigen::Matrix< T_SCALAR_TYPE, 3, 1 > &v) const
Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	operator* (Eigen::Matrix< T_SCALAR_TYPE, 3, 1 > const &v) const
Eigen::Matrix< T_SCALAR_TYPE, 3, 3 >	toRotationMatrix () const
Eigen::Matrix< T_SCALAR_TYPE, 3, 3 >	toAxisAngle () const
Eigen::Matrix< T_SCALAR_TYPE, 3, 1 >	toVector () const
bool	isApprox (Group< T_SCALAR_TYPE > const &g) const
Public Member Functions inherited from LieGroupBase< Group< T_SCALAR_TYPE >, 3 >
Group< T_SCALAR_TYPE >	inverse () const
void	inverted ()
void	operator*= (Group< T_SCALAR_TYPE > const &g)
NOXVector< T_DOF >	toNOXVector () const
Public Member Functions inherited from CRTP< Group< T_SCALAR_TYPE > >
Group< T_SCALAR_TYPE > &	underlying ()
Group< T_SCALAR_TYPE > const &	underlying () const

Static Public Member Functions
static Group< T_SCALAR_TYPE >	Identity ()
Static Public Member Functions inherited from LieGroupBase< Group< T_SCALAR_TYPE >, 3 >
static Group< T_SCALAR_TYPE >	Identity ()
static const unsigned int	dof ()

Protected Attributes
Eigen::Quaternion< T_SCALAR_TYPE >	m_q

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

Detailed Description

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

Class for Lie group \(SO(3)\) implementation.

Template Parameters

T_SCALAR_TYPE

Floating point type used for internal representation of coefficients.

Member Function Documentation

Identity()

template<typename T_SCALAR_TYPE>

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

inlinestatic

Returns

the element representing the group identity for operation *.

inverse()

template<typename T_SCALAR_TYPE>

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

inline

Returns

the group inverse of *this.

operator*() [1/2]

template<typename T_SCALAR_TYPE>

Group<T_SCALAR_TYPE> SO3::Group< T_SCALAR_TYPE >::operator* ( Group< T_SCALAR_TYPE > const &  g ) const

inline

Implements the group operation on \(SO(3)\). The * operator has been chosen instead of the + operator since the usual matrix and quaternion representations of rotations are groups defined with a natural mutliplication operation.

Returns

the group addition of *this and g.

operator*() [2/2]

template<typename T_SCALAR_TYPE>

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

inline

Implements the product of the matrix representation of the rotation *this and the voctor v.

Returns

the transformation of the \(\mathbb R^3\) vector v by the rotation represented by *this.

q()

template<typename T_SCALAR_TYPE>

Eigen::Quaternion<T_SCALAR_TYPE> SO3::Group< T_SCALAR_TYPE >::q ( ) const

inline

Returns

the quaternion representation of the rotation.

toAxisAngle()

template<typename T_SCALAR_TYPE>

Eigen::Matrix<T_SCALAR_TYPE,3,3> SO3::Group< T_SCALAR_TYPE >::toAxisAngle ( ) const

inline

Returns

the axis-angle representation of the rotation.

toRotationMatrix()

template<typename T_SCALAR_TYPE>

Eigen::Matrix<T_SCALAR_TYPE,3,3> SO3::Group< T_SCALAR_TYPE >::toRotationMatrix ( ) const

inline

Returns

the 3 by 3 matrix representation of the rotation.

toVector()

template<typename T_SCALAR_TYPE>

Eigen::Matrix<T_SCALAR_TYPE,3,1> SO3::Group< T_SCALAR_TYPE >::toVector ( ) const

inline

Returns

the vector representation of the rotation, that is the vector \(\vec v\) such that the rotation of any given vector \(\vec u\) is the result of \(vec v\wedge\vec u\).

transformVector()

template<typename T_SCALAR_TYPE>

Eigen::Matrix<T_SCALAR_TYPE,3,1> SO3::Group< T_SCALAR_TYPE >::transformVector ( const Eigen::Matrix< T_SCALAR_TYPE, 3, 1 > &  v ) const

inline

Returns

the transformation of the \(\mathbb R^3\) vector v by the rotation represented by *this.

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

• Geomi/src/Common/SO3_Group.hpp