A quaternion, which can represent a 3D rotation as pair
The elements of the quaternion can be accessed by either:
Users will usually employ the typedef "CQuaternionDouble" instead of this template.
For more information about quaternions, see:
Definition at line 42 of file CQuaternion.h.
#include <mrpt/math/CQuaternion.h>
Public Types | |
typedef T | value_type |
Public Member Functions | |
CQuaternion (TConstructorFlags_Quaternions) | |
Can be used with UNINITIALIZED_QUATERNION as argument, does not initialize the 4 elements of the quaternion (use this constructor when speed is critical). | |
CQuaternion () | |
Default constructor: construct a (1, (0,0,0) ) quaternion representing no rotation. | |
CQuaternion (const T r, const T x, const T y, const T z) | |
Construct a quaternion from its parameters 'r', 'x', 'y', 'z', with q = r + ix + jy + kz. | |
T | r () const |
Return r coordinate of the quaternion. | |
T | x () const |
Return x coordinate of the quaternion. | |
T | y () const |
Return y coordinate of the quaternion. | |
T | z () const |
Return z coordinate of the quaternion. | |
void | r (const T r) |
Set r coordinate of the quaternion. | |
void | x (const T x) |
Set x coordinate of the quaternion. | |
void | y (const T y) |
Set y coordinate of the quaternion. | |
void | z (const T z) |
Set z coordinate of the quaternion. | |
template<class ARRAYLIKE3 > | |
void | fromRodriguesVector (const ARRAYLIKE3 &v) |
Set this quaternion to the rotation described by a 3D (Rodrigues) rotation vector ![]() ![]() ![]() | |
void | crossProduct (const CQuaternion &q1, const CQuaternion &q2) |
Calculate the "cross" product (or "composed rotation") of two quaternion: this = q1 x q2 After the operation, "this" will represent the composed rotations of q1 and q2 (q2 applied "after" q1). | |
void | rotatePoint (const double lx, const double ly, const double lz, double &gx, double &gy, double &gz) const |
Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by this quaternion. | |
void | inverseRotatePoint (const double lx, const double ly, const double lz, double &gx, double &gy, double &gz) const |
Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by the inverse (conjugate) of this quaternion. | |
double | normSqr () const |
Return the squared norm of the quaternion. | |
void | normalize () |
Normalize this quaternion, so its norm becomes the unitity. | |
template<class MATRIXLIKE > | |
void | normalizationJacobian (MATRIXLIKE &J) const |
Calculate the 4x4 Jacobian of the normalization operation of this quaternion. | |
template<class MATRIXLIKE > | |
void | rotationJacobian (MATRIXLIKE &J) const |
Compute the Jacobian of the rotation composition operation ![]() ![]() | |
template<class MATRIXLIKE > | |
void | rotationMatrix (MATRIXLIKE &M) const |
Calculate the 3x3 rotation matrix associated to this quaternion: | |
template<class MATRIXLIKE > | |
void | rotationMatrixNoResize (MATRIXLIKE &M) const |
Fill out the top-left 3x3 block of the given matrix with the rotation matrix associated to this quaternion (does not resize the matrix, for that, see rotationMatrix). | |
void | conj (CQuaternion &q_out) const |
Return the conjugate quaternion | |
CQuaternion | conj () const |
Return the conjugate quaternion | |
void | rpy (T &roll, T &pitch, T &yaw) const |
Return the yaw, pitch & roll angles associated to quaternion. | |
template<class MATRIXLIKE > | |
void | rpy_and_jacobian (T &roll, T &pitch, T &yaw, MATRIXLIKE *out_dr_dq=NULL, bool resize_out_dr_dq_to3x4=true) const |
Return the yaw, pitch & roll angles associated to quaternion, and (optionally) the 3x4 Jacobian of the transformation. | |
CQuaternion | operator* (const T &factor) |
Private Types | |
typedef CArrayNumeric< T, 4 > | Base |
Lie Algebra methods | |
template<class ARRAYLIKE3 > | |
void | ln (ARRAYLIKE3 &out_ln) const |
Logarithm of the 3x3 matrix defined by this pose, generating the corresponding vector in the SO(3) Lie Algebra, which coincides with the so-called "rotation vector" (I don't have space here for the proof ;-). | |
template<class ARRAYLIKE3 > | |
ARRAYLIKE3 | ln () const |
template<class ARRAYLIKE3 > | |
void | ln_noresize (ARRAYLIKE3 &out_ln) const |
Like ln() but does not try to resize the output vector. | |
template<class ARRAYLIKE3 > | |
static CQuaternion< T > | exp (const ARRAYLIKE3 &v) |
Exponential map from the SO(3) Lie Algebra to unit quaternions. | |
template<class ARRAYLIKE3 > | |
static void | exp (const ARRAYLIKE3 &v, CQuaternion< T > &out_quat) |
This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. | |
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Definition at line 44 of file CQuaternion.h.
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Definition at line 28 of file CArrayNumeric.h.
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Can be used with UNINITIALIZED_QUATERNION as argument, does not initialize the 4 elements of the quaternion (use this constructor when speed is critical).
Definition at line 50 of file CQuaternion.h.
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Default constructor: construct a (1, (0,0,0) ) quaternion representing no rotation.
Definition at line 53 of file CQuaternion.h.
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Construct a quaternion from its parameters 'r', 'x', 'y', 'z', with q = r + ix + jy + kz.
Definition at line 62 of file CQuaternion.h.
References ASSERTMSG_, mrpt::format(), mrpt::math::CQuaternion< T >::normSqr(), mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
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Return the conjugate quaternion
Definition at line 306 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::conj().
Referenced by mrpt::math::CQuaternion< T >::conj().
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Return the conjugate quaternion
Definition at line 297 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
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Calculate the "cross" product (or "composed rotation") of two quaternion: this = q1 x q2 After the operation, "this" will represent the composed rotations of q1 and q2 (q2 applied "after" q1).
Definition at line 179 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::normalize(), mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
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inlinestatic |
Exponential map from the SO(3) Lie Algebra to unit quaternions.
Definition at line 160 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::fromRodriguesVector(), and mrpt::math::UNINITIALIZED_QUATERNION.
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inlinestatic |
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 168 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::fromRodriguesVector().
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Set this quaternion to the rotation described by a 3D (Rodrigues) rotation vector
where
Definition at line 96 of file CQuaternion.h.
References THROW_EXCEPTION, mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
Referenced by mrpt::math::CQuaternion< T >::exp(), and mrpt::math::CQuaternion< T >::exp().
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Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by the inverse (conjugate) of this quaternion.
Definition at line 203 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
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Definition at line 139 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::ln().
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Logarithm of the 3x3 matrix defined by this pose, generating the corresponding vector in the SO(3) Lie Algebra, which coincides with the so-called "rotation vector" (I don't have space here for the proof ;-).
[out] | out_ln | The target vector, which can be: std::vector<>, or mrpt::math::CVectorDouble or any row or column Eigen::Matrix<>. |
Definition at line 132 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::ln_noresize().
Referenced by mrpt::math::CQuaternion< T >::ln().
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Like ln() but does not try to resize the output vector.
Definition at line 147 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r(), mrpt::utils::square(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
Referenced by mrpt::math::CQuaternion< T >::ln().
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Calculate the 4x4 Jacobian of the normalization operation of this quaternion.
The output matrix can be a dynamic or fixed size (4x4) matrix.
Definition at line 231 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::normSqr(), mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
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Normalize this quaternion, so its norm becomes the unitity.
Definition at line 220 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::normSqr().
Referenced by mrpt::poses::CPose3DQuat::CPose3DQuat(), and mrpt::math::CQuaternion< T >::crossProduct().
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Return the squared norm of the quaternion.
Definition at line 213 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r(), mrpt::utils::square(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
Referenced by mrpt::math::CQuaternion< T >::CQuaternion(), mrpt::math::CQuaternion< T >::normalizationJacobian(), and mrpt::math::CQuaternion< T >::normalize().
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Definition at line 398 of file CQuaternion.h.
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Return r coordinate of the quaternion.
Definition at line 75 of file CQuaternion.h.
Referenced by mrpt::math::CQuaternion< T >::conj(), mrpt::math::CQuaternion< T >::CQuaternion(), mrpt::math::CQuaternion< T >::crossProduct(), mrpt::math::CQuaternion< T >::inverseRotatePoint(), mrpt::math::CQuaternion< T >::ln_noresize(), mrpt::math::CQuaternion< T >::normalizationJacobian(), mrpt::math::CQuaternion< T >::normSqr(), mrpt::math::CQuaternion< T >::rotatePoint(), mrpt::math::CQuaternion< T >::rotationJacobian(), mrpt::math::CQuaternion< T >::rotationMatrixNoResize(), and mrpt::math::CQuaternion< T >::rpy_and_jacobian().
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Set r coordinate of the quaternion.
Definition at line 79 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r().
Referenced by mrpt::math::CQuaternion< T >::r().
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Rotate a 3D point (lx,ly,lz) -> (gx,gy,gz) as described by this quaternion.
Definition at line 192 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
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Compute the Jacobian of the rotation composition operation
The output matrix can be a dynamic or fixed size (4x4) matrix.
Definition at line 261 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
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Calculate the 3x3 rotation matrix associated to this quaternion:
Definition at line 280 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::rotationMatrixNoResize().
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Fill out the top-left 3x3 block of the given matrix with the rotation matrix associated to this quaternion (does not resize the matrix, for that, see rotationMatrix).
Definition at line 288 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::r(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
Referenced by mrpt::math::CQuaternion< T >::rotationMatrix(), and mrpt::poses::CPose3D::setFromXYZQ().
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Return the yaw, pitch & roll angles associated to quaternion.
Definition at line 317 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::rpy_and_jacobian().
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Return the yaw, pitch & roll angles associated to quaternion, and (optionally) the 3x4 Jacobian of the transformation.
Note that both the angles and the Jacobian have one set of normal equations, plus other special formulas for the degenerated cases of |pitch|=90 degrees.
Definition at line 328 of file CQuaternion.h.
References M_PI, mrpt::math::CQuaternion< T >::r(), mrpt::utils::square(), mrpt::math::CQuaternion< T >::x(), mrpt::math::CQuaternion< T >::y(), and mrpt::math::CQuaternion< T >::z().
Referenced by mrpt::math::CQuaternion< T >::rpy().
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Return x coordinate of the quaternion.
Definition at line 76 of file CQuaternion.h.
Referenced by mrpt::math::CQuaternion< T >::conj(), mrpt::math::CQuaternion< T >::CQuaternion(), mrpt::math::CQuaternion< T >::crossProduct(), mrpt::math::CQuaternion< T >::fromRodriguesVector(), mrpt::math::CQuaternion< T >::inverseRotatePoint(), mrpt::math::CQuaternion< T >::ln_noresize(), mrpt::math::CQuaternion< T >::normalizationJacobian(), mrpt::math::CQuaternion< T >::normSqr(), mrpt::math::CQuaternion< T >::rotatePoint(), mrpt::math::CQuaternion< T >::rotationJacobian(), mrpt::math::CQuaternion< T >::rotationMatrixNoResize(), and mrpt::math::CQuaternion< T >::rpy_and_jacobian().
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Set x coordinate of the quaternion.
Definition at line 80 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::x().
Referenced by mrpt::math::CQuaternion< T >::x().
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Return y coordinate of the quaternion.
Definition at line 77 of file CQuaternion.h.
Referenced by mrpt::math::CQuaternion< T >::conj(), mrpt::math::CQuaternion< T >::CQuaternion(), mrpt::math::CQuaternion< T >::crossProduct(), mrpt::math::CQuaternion< T >::fromRodriguesVector(), mrpt::math::CQuaternion< T >::inverseRotatePoint(), mrpt::math::CQuaternion< T >::ln_noresize(), mrpt::math::CQuaternion< T >::normalizationJacobian(), mrpt::math::CQuaternion< T >::normSqr(), mrpt::math::CQuaternion< T >::rotatePoint(), mrpt::math::CQuaternion< T >::rotationJacobian(), mrpt::math::CQuaternion< T >::rotationMatrixNoResize(), and mrpt::math::CQuaternion< T >::rpy_and_jacobian().
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Set y coordinate of the quaternion.
Definition at line 81 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::y().
Referenced by mrpt::math::CQuaternion< T >::y().
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Return z coordinate of the quaternion.
Definition at line 78 of file CQuaternion.h.
Referenced by mrpt::math::CQuaternion< T >::conj(), mrpt::math::CQuaternion< T >::CQuaternion(), mrpt::math::CQuaternion< T >::crossProduct(), mrpt::math::CQuaternion< T >::fromRodriguesVector(), mrpt::math::CQuaternion< T >::inverseRotatePoint(), mrpt::math::CQuaternion< T >::ln_noresize(), mrpt::math::CQuaternion< T >::normalizationJacobian(), mrpt::math::CQuaternion< T >::normSqr(), mrpt::math::CQuaternion< T >::rotatePoint(), mrpt::math::CQuaternion< T >::rotationJacobian(), mrpt::math::CQuaternion< T >::rotationMatrixNoResize(), and mrpt::math::CQuaternion< T >::rpy_and_jacobian().
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Set z coordinate of the quaternion.
Definition at line 82 of file CQuaternion.h.
References mrpt::math::CQuaternion< T >::z().
Referenced by mrpt::math::CQuaternion< T >::z().
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