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| | SE3 () |
| | Default constructor. Initialises the the rotation to zero (the identity) and the translation to zero. More...
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| template<int S, typename P , typename A > |
| | SE3 (const SO3< Precision > &R, const Vector< S, P, A > &T) |
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| template<int S, typename P , typename A > |
| | SE3 (const Vector< S, P, A > &v) |
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| template<class IP , int S, typename P , typename A > |
| | SE3 (const Operator< Internal::Identity< IP > > &, const Vector< S, P, A > &T) |
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| SO3< Precision > & | get_rotation () |
| | Returns the rotation part of the transformation as a SO3. More...
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| const SO3< Precision > & | get_rotation () const |
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| Vector< 3, Precision > & | get_translation () |
| | Returns the translation part of the transformation as a Vector. More...
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| const Vector< 3, Precision > & | get_translation () const |
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| Vector< 6, Precision > | ln () const |
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| SE3 | inverse () const |
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| SE3 & | operator*= (const SE3 &rhs) |
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| template<typename P > |
| SE3< typename Internal::MultiplyType< Precision, P >::type > | operator* (const SE3< P > &rhs) const |
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| SE3 & | left_multiply_by (const SE3 &left) |
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| template<int S, typename P2 , typename Accessor > |
| Vector< 6, Precision > | adjoint (const Vector< S, P2, Accessor > &vect) const |
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| template<int S, typename P2 , typename Accessor > |
| Vector< 6, Precision > | trinvadjoint (const Vector< S, P2, Accessor > &vect) const |
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| template<int R, int C, typename P2 , typename Accessor > |
| Matrix< 6, 6, Precision > | adjoint (const Matrix< R, C, P2, Accessor > &M) const |
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| template<int R, int C, typename P2 , typename Accessor > |
| Matrix< 6, 6, Precision > | trinvadjoint (const Matrix< R, C, P2, Accessor > &M) const |
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| template<int S, typename P , typename VA > |
| SE3< Precision > | exp (const Vector< S, P, VA > &mu) |
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| template<int S, typename P , typename A > |
| static SE3 | exp (const Vector< S, P, A > &vect) |
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| static Vector< 6, Precision > | ln (const SE3 &se3) |
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| static Matrix< 4, 4, Precision > | generator (int i) |
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| template<typename Base > |
| static Vector< 4, Precision > | generator_field (int i, const Vector< 4, Precision, Base > &pos) |
| | Returns the i-th generator times pos. More...
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(Note that these are not member functions.)
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| template<typename Precision > |
| std::ostream & | operator<< (std::ostream &os, const SE3< Precision > &rhs) |
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| template<typename Precision > |
| std::istream & | operator>> (std::istream &is, SE3< Precision > &rhs) |
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| template<int S, typename PV , typename A , typename P > |
| Vector< 4, typename Internal::MultiplyType< P, PV >::type > | operator* (const SE3< P > &lhs, const Vector< S, PV, A > &rhs) |
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| template<typename PV , typename A , typename P > |
| Vector< 3, typename Internal::MultiplyType< P, PV >::type > | operator* (const SE3< P > &lhs, const Vector< 3, PV, A > &rhs) |
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| template<int S, typename PV , typename A , typename P > |
| Vector< 4, typename Internal::MultiplyType< P, PV >::type > | operator* (const Vector< S, PV, A > &lhs, const SE3< P > &rhs) |
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| template<int R, int Cols, typename PM , typename A , typename P > |
| Matrix< 4, Cols, typename Internal::MultiplyType< P, PM >::type > | operator* (const SE3< P > &lhs, const Matrix< R, Cols, PM, A > &rhs) |
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| template<int Rows, int C, typename PM , typename A , typename P > |
| Matrix< Rows, 4, typename Internal::MultiplyType< PM, P >::type > | operator* (const Matrix< Rows, C, PM, A > &lhs, const SE3< P > &rhs) |
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template<typename Precision = double>
class TooN::SE3< Precision >
Represent a three-dimensional Euclidean transformation (a rotation and a translation). This can be represented by a 
matrix operating on a homogeneous co-ordinate, so that a vector 
is transformed to a new location 
by
![\[\begin{aligned}\underline{x}' &= E\times\underline{x}\\ \begin{bmatrix}x'\\y'\\z'\end{bmatrix} &= \begin{pmatrix}r_{11} & r_{12} & r_{13} & t_1\\r_{21} & r_{22} & r_{23} & t_2\\r_{31} & r_{32} & r_{33} & t_3\end{pmatrix}\begin{bmatrix}x\\y\\z\\1\end{bmatrix}\end{aligned}\]](../../form_106.png)
This transformation is a member of the Special Euclidean Lie group SE3. These can be parameterised six numbers (in the space of the Lie Algebra). In this class, the first three parameters are a translation vector while the second three are a rotation vector, whose direction is the axis of rotation and length the amount of rotation (in radians), as for SO3
Definition at line 50 of file se3.h.
template<typename Precision >
template<int S, typename P2 , typename Accessor >
Transfer a matrix in the Lie Algebra from one co-ordinate frame to another. This is the operation such that for a matrix 
, 
- Parameters
-
Definition at line 168 of file se3.h.
template<typename Precision >
template<int R, int C, typename P2 , typename Accessor >
| Matrix< 6, 6, Precision > TooN::SE3< Precision >::adjoint |
( |
const Matrix< R, C, P2, Accessor > & |
M | ) |
const |
|
inline |
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
Definition at line 193 of file se3.h.
template<typename Precision >
template<int S, typename P2 , typename Accessor >
| Vector< 6, Precision > TooN::SE3< Precision >::trinvadjoint |
( |
const Vector< S, P2, Accessor > & |
vect | ) |
const |
|
inline |
Transfer covectors between frames (using the transpose of the inverse of the adjoint) so that trinvadjoint(vect1) * adjoint(vect2) = vect1 * vect2
Definition at line 182 of file se3.h.
template<typename Precision >
template<int R, int C, typename P2 , typename Accessor >
| Matrix< 6, 6, Precision > TooN::SE3< Precision >::trinvadjoint |
( |
const Matrix< R, C, P2, Accessor > & |
M | ) |
const |
|
inline |
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.
Definition at line 209 of file se3.h.
1.8.9.1
