#include <so3.h>
Public Member Functions | |
SO3 () | |
template<int S, typename P, typename A> | |
SO3 (const Vector< S, P, A > &v) | |
template<int R, int C, typename P, typename A> | |
SO3 (const Matrix< R, C, P, A > &rhs) | |
template<int S1, int S2, typename P1, typename P2, typename A1, typename A2> | |
SO3 (const Vector< S1, P1, A1 > &a, const Vector< S2, P2, A2 > &b) | |
template<int R, int C, typename P, typename A> | |
SO3 & | operator= (const Matrix< R, C, P, A > &rhs) |
void | coerce () |
Vector< 3, Precision > | ln () const |
SO3 | inverse () const |
SO3 & | operator *= (const SO3 &rhs) |
SO3 | operator * (const SO3 &rhs) const |
const Matrix< 3, 3, Precision > & | get_matrix () const |
template<int S, typename A> | |
Vector< 3, Precision > | adjoint (Vector< 3, Precision, A > vect) const |
Static Public Member Functions | |
template<int S, typename A> | |
static SO3 | exp (const Vector< S, Precision, A > &vect) |
static Matrix< 3, 3, Precision > | generator (int i) |
template<typename Base> | |
static Vector< 3, Precision > | generator_field (int i, const Vector< 3, Precision, Base > &pos) |
Friends | |
std::istream & | o (std::istream &is, SO3< Precision > &rhs) |
std::istream & | o (std::istream &is, SE3< Precision > &rhs) |
Related Functions | |
(Note that these are not member functions.) | |
template<typename Precision> | |
std::ostream & | operator<< (std::ostream &os, const SO3< Precision > &rhs) |
template<typename Precision> | |
std::istream & | operator>> (std::istream &is, SO3< Precision > &rhs) |
template<int S, typename P, typename PV, typename A> | |
Vector< 3, typename Internal::MultiplyType < P, PV >::type > | operator * (const SO3< P > &lhs, const Vector< S, PV, A > &rhs) |
template<int S, typename P, typename PV, typename A> | |
Vector< 3, typename Internal::MultiplyType < PV, P >::type > | operator * (const Vector< S, PV, A > &lhs, const SO3< P > &rhs) |
template<int R, int C, typename P, typename PM, typename A> | |
Matrix< 3, C, typename Internal::MultiplyType < P, PM >::type > | operator * (const SO3< P > &lhs, const Matrix< R, C, PM, A > &rhs) |
template<int R, int C, typename P, typename PM, typename A> | |
Matrix< R, 3, typename Internal::MultiplyType < PM, P >::type > | operator * (const Matrix< R, C, PM, A > &lhs, const SO3< P > &rhs) |
Classes | |
struct | Invert |
Three-dimensional rotation matrices are members of the Special Orthogonal Lie group SO3. This group can be parameterised three numbers (a vector in the space of the Lie Algebra). In this class, the three parameters are the finite rotation vector, i.e. a three-dimensional vector whose direction is the axis of rotation and whose length is the angle of rotation in radians. Exponentiating this vector gives the matrix, and the logarithm of the matrix gives this vector.
Default constructor. Initialises the matrix to the identity (no rotation).
SO3& TooN::SO3< Precision >::operator= | ( | const Matrix< R, C, P, A > & | rhs | ) |
Assigment operator from a general matrix.
This also calls coerce() to make sure that the matrix is a valid rotation matrix.
void TooN::SO3< Precision >::coerce | ( | ) |
Modifies the matrix to make sure it is a valid rotation matrix.
SO3< Precision > TooN::SO3< Precision >::exp | ( | const Vector< S, Precision, VA > & | vect | ) | [static] |
Exponentiate a vector in the Lie algebra to generate a new SO3.
See the Detailed Description for details of this vector.
Take the logarithm of the matrix, generating the corresponding vector in the Lie Algebra.
See the Detailed Description for details of this vector.
Returns the inverse of this matrix (=the transpose, so this is a fast operation).
SO3& TooN::SO3< Precision >::operator *= | ( | const SO3< Precision > & | rhs | ) |
Right-multiply by another rotation matrix.
SO3 TooN::SO3< Precision >::operator * | ( | const SO3< Precision > & | rhs | ) | const |
Right-multiply by another rotation matrix.
const Matrix<3,3, Precision>& TooN::SO3< Precision >::get_matrix | ( | ) | const |
Returns the SO3 as a Matrix<3>.
static Matrix<3,3, Precision> TooN::SO3< Precision >::generator | ( | int | i | ) | [static] |
Returns the i-th generator.
The generators of a Lie group are the basis for the space of the Lie algebra. For SO3, the generators are three matrices representing the three possible (linearised) rotations.
static Vector<3,Precision> TooN::SO3< Precision >::generator_field | ( | int | i, | |
const Vector< 3, Precision, Base > & | pos | |||
) | [static] |
Returns the i-th generator times pos.
Vector<3, Precision> TooN::SO3< Precision >::adjoint | ( | Vector< 3, Precision, A > | vect | ) | const |
Transfer a vector in the Lie Algebra from one co-ordinate frame to another such that for a matrix , the adjoint
obeys
.
std::ostream & operator<< | ( | std::ostream & | os, | |
const SO3< Precision > & | rhs | |||
) | [related] |
Write an SO3 to a stream.
std::istream & operator>> | ( | std::istream & | is, | |
SO3< Precision > & | rhs | |||
) | [related] |
Read from SO3 to a stream.
Vector< 3, typename Internal::MultiplyType< P, PV >::type > operator * | ( | const SO3< P > & | lhs, | |
const Vector< S, PV, A > & | rhs | |||
) | [related] |
Right-multiply by a Vector.
Vector< 3, typename Internal::MultiplyType< PV, P >::type > operator * | ( | const Vector< S, PV, A > & | lhs, | |
const SO3< P > & | rhs | |||
) | [related] |
Left-multiply by a Vector.
Matrix< 3, C, typename Internal::MultiplyType< P, PM >::type > operator * | ( | const SO3< P > & | lhs, | |
const Matrix< R, C, PM, A > & | rhs | |||
) | [related] |
Right-multiply by a matrix.
Matrix< R, 3, typename Internal::MultiplyType< PM, P >::type > operator * | ( | const Matrix< R, C, PM, A > & | lhs, | |
const SO3< P > & | rhs | |||
) | [related] |
Left-multiply by a matrix.