RobWorkProject
24.8.23-
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A Quaternion \( \mathbf{q}\in \mathbb{R}^4 \) a complex number used to describe rotations in 3-dimensional space. \( q_w+{\bf i}\ q_x+ {\bf j} q_y+ {\bf k}\ q_z \). More...
#include <Quaternion.hpp>
Inherits Rotation3DVector< double >.
Public Types | |
typedef T | value_type |
Value type. | |
Public Member Functions | |
Quaternion () | |
constuct Quaterinion of {0,0,0,1} | |
Quaternion (T qx, T qy, T qz, T qw) | |
Creates a Quaternion. More... | |
Quaternion (const Quaternion< T > &quat) | |
Creates a Quaternion from another Quaternion. More... | |
Quaternion (const rw::math::Rotation3DVector< T > &rot) | |
Creates a Quaternion from another Rotation3DVector type. More... | |
Quaternion (const rw::math::Rotation3D< T > &rot) | |
Extracts a Quaternion from Rotation matrix using setRotation(const Rotation3D<R>& rot) More... | |
Quaternion (const Eigen::Quaternion< T > &r) | |
Creates a Quaternion from a Eigen quaternion. More... | |
template<class R > | |
Quaternion (const Eigen::MatrixBase< R > &r) | |
Creates a Quaternion from vector_expression. More... | |
T | getQx () const |
get method for the x component More... | |
T | getQy () const |
get method for the y component More... | |
T | getQz () const |
get method for the z component More... | |
T | getQw () const |
get method for the w component More... | |
T | operator() (size_t i) const |
Returns reference to Quaternion element. More... | |
T & | operator() (size_t i) |
Returns reference to Quaternion element. More... | |
T & | operator[] (size_t i) |
Returns reference to Quaternion element. More... | |
T | operator[] (size_t i) const |
Returns reference to Quaternion element. More... | |
const rw::math::Rotation3D< T > | toRotation3D () const |
Calculates the \( 3\times 3 \) Rotation matrix. More... | |
template<class R > | |
void | setRotation (const rw::math::Rotation3D< R > &rot) |
Converts a Rotation3D to a Quaternion and saves the Quaternion in this. More... | |
size_t | size () const |
The dimension of the quaternion (i.e. 4). This method is provided to help support generic algorithms using size() and operator[]. | |
Eigen::Quaternion< T > & | e () |
Convert to an Eigen Quaternion. More... | |
const Eigen::Quaternion< T > & | e () const |
Convert to an Eigen Quaternion. More... | |
Eigen::Matrix< T, 4, 1 > | toEigenVector () const |
convert to Eigen Vector More... | |
Quaternion< T > | operator- () const |
Unary minus. | |
Quaternion< T > | operator+ () const |
Unary plus. | |
const Quaternion< T > | operator- (const Quaternion< T > &v) const |
Subtraction. | |
Quaternion< T > | operator* (const Quaternion< T > &r) const |
Multiply-from operator. | |
const Quaternion< T > | operator+ (const Quaternion< T > &v) const |
Addition of two quaternions. | |
const Quaternion< T > | operator* (T s) const |
Scalar multiplication. | |
const Quaternion< T > | operator/ (T s) const |
Scalar Devision. | |
Quaternion< T > | elemDivide (const T &lhs) const |
element whise division More... | |
T | getLength () const |
get length of quaternion \( \sqrt{q_x^2+q_y^2+q_z^2+q_w^2} \) More... | |
T | getLengthSquared () const |
get squared length of quaternion \( q_x^2+q_y^2+q_z^2+q_w^2 \) More... | |
void | normalize () |
normalizes this quaternion so that \( normalze(Q)=\frac{Q}{\sqrt{q_x^2+q_y^2+q_z^2+q_w^2}} \) | |
const Quaternion< T > | slerp (const Quaternion< T > &v, const T t) const |
Calculates a slerp interpolation between this and v. More... | |
Quaternion< T > | exp () const |
Quaternion< T > | inverse () const |
Calculate the inverse Quaternion. More... | |
Quaternion< T > | ln () const |
calculates the natural logerithm of this quaternion More... | |
Quaternion< T > | pow (double power) const |
calculates the quaternion lifted to the power of power More... | |
void | operator= (const Eigen::Quaternion< T > &r) |
copy a boost quaternion to this Quaternion More... | |
const Quaternion< T > | operator*= (T s) |
Scalar multiplication. | |
const Quaternion< T > | operator*= (const Quaternion< T > &r) |
Multiply with operator. | |
const Quaternion< T > | operator+= (const Quaternion< T > &r) |
Add-to operator. | |
const Quaternion< T > | operator-= (const Quaternion< T > &r) |
Subtract-from operator. | |
Quaternion< T > & | operator= (const rw::math::Rotation3D<> &rhs) |
copyfrom rotaion matrix, same as setRotation. More... | |
bool | operator== (const Quaternion< T > &r) const |
Comparison (equals) operator. | |
bool | operator!= (const Quaternion< T > &r) const |
Comparison (not equals) operator. | |
Public Member Functions inherited from Rotation3DVector< double > | |
virtual | ~Rotation3DVector () |
Virtual destructor. | |
Friends | |
const Quaternion< T > | operator* (T s, const Quaternion< T > &v) |
Scalar multiplication. | |
Related Functions | |
(Note that these are not member functions.) | |
template<class T > | |
std::ostream & | operator<< (std::ostream &out, const Quaternion< T > &v) |
Streaming operator. | |
template<> | |
void | write (const rw::math::Quaternion< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id) |
template<> | |
void | write (const rw::math::Quaternion< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id) |
template<> | |
void | read (rw::math::Quaternion< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id) |
template<> | |
void | read (rw::math::Quaternion< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id) |
Additional Inherited Members | |
Protected Member Functions inherited from Rotation3DVector< double > | |
Rotation3DVector (const Rotation3DVector &) | |
Copy Constructor. More... | |
Rotation3DVector () | |
Default Constructor. | |
Rotation3DVector & | operator= (const Rotation3DVector &) |
Assignment operator is protected to force subclasses to implement it by themself. | |
A Quaternion \( \mathbf{q}\in \mathbb{R}^4 \) a complex number used to describe rotations in 3-dimensional space. \( q_w+{\bf i}\ q_x+ {\bf j} q_y+ {\bf k}\ q_z \).
Quaternions can be added and multiplied in a similar way as usual algebraic numbers. Though there are differences. Quaternion multiplication is not commutative which means \( Q\cdot P \neq P\cdot Q \)
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Creates a Quaternion.
qx | [in] \( q_x \) |
qy | [in] \( q_y \) |
qz | [in] \( q_z \) |
qw | [in] \( q_w \) |
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Creates a Quaternion from another Quaternion.
quat | [in] Quaternion |
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Creates a Quaternion from another Rotation3DVector type.
rot | [in] The Rotation3DVector type |
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Extracts a Quaternion from Rotation matrix using setRotation(const Rotation3D<R>& rot)
rot | [in] A 3x3 rotation matrix \( \mathbf{rot} \) |
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Creates a Quaternion from a Eigen quaternion.
r | [in] a boost quaternion |
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Creates a Quaternion from vector_expression.
r | [in] an Eigen Vector |
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Convert to an Eigen Quaternion.
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Convert to an Eigen Quaternion.
Quaternion<T> elemDivide | ( | const T & | lhs | ) | const |
element whise division
lhs | [in] the scalar to devide with |
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get length of quaternion \( \sqrt{q_x^2+q_y^2+q_z^2+q_w^2} \)
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get squared length of quaternion \( q_x^2+q_y^2+q_z^2+q_w^2 \)
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get method for the w component
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get method for the x component
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get method for the y component
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get method for the z component
Quaternion<T> inverse | ( | ) | const |
Calculate the inverse Quaternion.
Quaternion<T> ln | ( | ) | const |
calculates the natural logerithm of this quaternion
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Returns reference to Quaternion element.
i | [in] index in the quaternion \(i\in \{0,1,2,3\} \) |
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Returns reference to Quaternion element.
i | [in] index in the quaternion \(i\in \{0,1,2,3\} \) |
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copy a boost quaternion to this Quaternion
r | [in] - boost quaternion |
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copyfrom rotaion matrix, same as setRotation.
rhs | [in] the rotation that will be copyed |
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Returns reference to Quaternion element.
i | [in] index in the quaternion \(i\in \{0,1,2,3\} \) |
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Returns reference to Quaternion element.
i | [in] index in the quaternion \(i\in \{0,1,2,3\} \) |
Quaternion<T> pow | ( | double | power | ) | const |
calculates the quaternion lifted to the power of power
power | [in] the power the quaternion is lifted to |
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Converts a Rotation3D to a Quaternion and saves the Quaternion in this.
rot | [in] A 3x3 rotation matrix \( \mathbf{R} \) |
\( \begin{array}{c} q_x\\ q_y\\ q_z\\ q_w \end{array} = \left[ \begin{array}{c} \\ \\ \end{array} \right] \)
The conversion method is proposed by Henrik Gordon Petersen. The switching between different cases occur well before numerical instabilities, hence the solution should be more robust, than many of the methods proposed elsewhere.
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Calculates a slerp interpolation between this and v.
The slerp interpolation ensures a constant velocity across the interpolation. For \( t=0\) the result is this and for \( t=1\) it is v.
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Calculates the \( 3\times 3 \) Rotation matrix.
Implements Rotation3DVector< double >.
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Enable read-serialization of class T by overloading this method. Data is read from iarchive and filled into sobject.
sobject | [out] the object in which the data should be streamed into |
iarchive | [in] the InputArchive from which to read data. |
id | [in] The id of the serialized sobject. |
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related |
Enable read-serialization of class T by overloading this method. Data is read from iarchive and filled into sobject.
sobject | [out] the object in which the data should be streamed into |
iarchive | [in] the InputArchive from which to read data. |
id | [in] The id of the serialized sobject. |
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Enable write-serialization of class T by overloading this method. Data is written to oarchive from the sobject.
sobject | [in] the object from which the data should be streamed. |
oarchive | [out] the OutputArchive in which data should be written. |
id | [in] The id of the serialized sobject. |
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related |
Enable write-serialization of class T by overloading this method. Data is written to oarchive from the sobject.
sobject | [in] the object from which the data should be streamed. |
oarchive | [out] the OutputArchive in which data should be written. |
id | [in] The id of the serialized sobject. |