fmat::QuaternionT< R > Class Template Reference
Quaternions can be more efficient and more stable for a series of rotations than a corresponding 3x3 matrix, also more compact storage. More...
#include <fmatSpatial.h>
Detailed Description
template<class R = fmatReal>
class fmat::QuaternionT< R >
Quaternions can be more efficient and more stable for a series of rotations than a corresponding 3x3 matrix, also more compact storage.
Definition at line 71 of file fmatSpatial.h.
Public Member Functions | |
| QuaternionT () | |
| Default constructor, initialize to identity (0 rotation). | |
| QuaternionT (R w_, R x_, R y_, R z_) | |
| Explicit construction from elements (careful, does not check normalization!). | |
| template<typename T > | |
| QuaternionT & | importFrom (const T &q) |
| copies from another representation, assuming operator[] is supported and w is index 0 | |
| template<typename T > | |
| T | exportTo () const |
| copies into another representation, assuming operator[] is supported and w is index 0 | |
| template<typename T > | |
| T & | exportTo (T &q) const |
| copies into another representation, assuming operator[] is supported and w is index 0 | |
| template<typename T > | |
| void | exportTo (T &w_, T &x_, T &y_, T &z_) const |
| unpacks into specified storage | |
| template<typename T > | |
| void | exportTo (T &x_, T &y_, T &z_) const |
| unpacks into specified storage, skipping w which can be reconstitued from √(1-x^2-y^2-z^2), see fromAxis() | |
| R | getW () const |
| returns w | |
| R | getX () const |
| returns x | |
| R | getY () const |
| returns y | |
| R | getZ () const |
| returns z | |
| Matrix< 3, 3, R > | toMatrix () const |
| returns a 3x3 rotation matrix representation | |
| operator Matrix< 3, 3, R > () const | |
| allows conversion/assignment to Matrix<3,3> | |
| Column< 3, R > | axis () const |
| return axis of rotation represented by quaternion q (i.e. the axis component of axis-angle representation) | |
| R | angle () const |
| Return angle of rotation (range ±π radians) about the quaternion's native axis (i.e. the angle component for axis-angle representation). | |
| template<class T > | |
| R | axisComponent (const T &v) const |
| Return angle of rotation represented by the quaternion about an arbitrary axis (assumed to already be normalized). | |
| fmat::Column< 3, R > | ypr () const |
| Returns yaw-pitch-roll aka heading-elevation-bank conversion, where roll-pitch-yaw correspond to compounding rotations about the global x, y, and z axis respectively (in that order). | |
| QuaternionT | inverse () const ATTR_must_check |
| Negates just the quaternion axis. | |
| template<typename Rb > | |
| QuaternionT< typename fmat_internal::promotion_trait < R, Rb >::type > | operator* (const QuaternionT< Rb > &q) const |
| multiply quaternions | |
| QuaternionT | operator*= (const QuaternionT &q) |
| multiply quaternions | |
| template<template< size_t H, size_t W, typename Rt > class T, size_t W> | |
| Matrix< 3, W, R > | operator* (const T< 3, W, R > &m) const |
| multiply 3-row matrix by quaternion | |
| TransformT< R > | operator* (const TransformT< R > &m) const |
| multiply Transform by quaternion | |
| Column< 3, R > | operator* (const Column< 3, R > v) const |
| multiply 3-element vector by quaternion | |
| R | sumSq () const |
| returns sum of squares of components; should be "close" to 1, otherwise call normalize() | |
| R | norm () const |
| returns magnitude of quaternion; should be "close" to 1, otherwise call normalize() | |
| R | normalize () |
| Re-normalize the quaternion magnitude to 1 (or 0 if norm is already invalid) and positive W, returns the previous magnitude. | |
Static Public Member Functions | |
| template<typename T > | |
| static QuaternionT | from (const T &q) |
| copies from another representation, assuming operator[] is supported and w is index 0 | |
| static const QuaternionT & | identity () |
| returns a no-op quaternion (0 rotation), the same as the default constructor, but can re-use this instance instead of creating new ones all the time | |
| static QuaternionT< R > | aboutX (R rad) |
| generate quaternion representing rotation of rad radians about X axis | |
| static QuaternionT< R > | aboutY (R rad) |
| generate quaternion representing rotation of rad radians about Y axis | |
| static QuaternionT< R > | aboutZ (R rad) |
| generate quaternion representing rotation of rad radians about Z axis | |
| template<class T > | |
| static QuaternionT | fromAxisAngle (const T &axis, R angle) |
| Generate quaternion from axis-angle representation (angle in radians, axis will be re-normalized if non-zero angle). | |
| template<class T > | |
| static QuaternionT | fromAxis (const T &axis) |
| Generate quaternion from just the axis component of another quaternion (i.e. axis magnitude should be less than 1; 0 magnitude means no rotation). | |
| template<class T > | |
| static QuaternionT | fromMatrix (const T &rot) |
| Generate quaternion from rotation matrix, this assumes the rotation matrix is well-formed. | |
Static Public Attributes | |
| static const QuaternionT | IDENTITY |
| identity instance | |
Protected Member Functions | |
| QuaternionT (const fmat_internal::NoInit &) | |
| no-op constructor for functions which fill in results with additional computation | |
Protected Attributes | |
| R | w |
| R | x |
| R | y |
| R | z |
Friends | |
| std::ostream & | operator<< (std::ostream &os, const QuaternionT< R > &q) |
Constructor & Destructor Documentation
| fmat::QuaternionT< R >::QuaternionT | ( | ) |
Default constructor, initialize to identity (0 rotation).
Definition at line 74 of file fmatSpatial.h.
Referenced by fmat::QuaternionT< R >::from(), fmat::QuaternionT< R >::fromAxis(), fmat::QuaternionT< R >::fromAxisAngle(), and fmat::QuaternionT< R >::inverse().
| fmat::QuaternionT< R >::QuaternionT | ( | R | w_, | |
| R | x_, | |||
| R | y_, | |||
| R | z_ | |||
| ) |
Explicit construction from elements (careful, does not check normalization!).
Definition at line 77 of file fmatSpatial.h.
| fmat::QuaternionT< R >::QuaternionT | ( | const fmat_internal::NoInit & | ) | [protected] |
no-op constructor for functions which fill in results with additional computation
Definition at line 395 of file fmatSpatial.h.
Member Function Documentation
| static QuaternionT<R> fmat::QuaternionT< R >::aboutX | ( | R | rad | ) | [static] |
generate quaternion representing rotation of rad radians about X axis
Definition at line 102 of file fmatSpatial.h.
| static QuaternionT<R> fmat::QuaternionT< R >::aboutY | ( | R | rad | ) | [static] |
generate quaternion representing rotation of rad radians about Y axis
Definition at line 104 of file fmatSpatial.h.
| static QuaternionT<R> fmat::QuaternionT< R >::aboutZ | ( | R | rad | ) | [static] |
generate quaternion representing rotation of rad radians about Z axis
Definition at line 106 of file fmatSpatial.h.
Referenced by CBracketGrasperPredicate< N >::admissible().
| R fmat::QuaternionT< R >::angle | ( | ) | const |
Return angle of rotation (range ±π radians) about the quaternion's native axis (i.e. the angle component for axis-angle representation).
Handles some slight denormalization gracefully.
Definition at line 225 of file fmatSpatial.h.
Referenced by IKGradientSolver::step().
| Column<3,R> fmat::QuaternionT< R >::axis | ( | ) | const |
return axis of rotation represented by quaternion q (i.e. the axis component of axis-angle representation)
Definition at line 215 of file fmatSpatial.h.
Referenced by IKGradientSolver::step().
| R fmat::QuaternionT< R >::axisComponent | ( | const T & | v | ) | const |
Return angle of rotation represented by the quaternion about an arbitrary axis (assumed to already be normalized).
Definition at line 239 of file fmatSpatial.h.
Referenced by PlanarThreeLinkArm::solve().
| void fmat::QuaternionT< R >::exportTo | ( | T & | x_, | |
| T & | y_, | |||
| T & | z_ | |||
| ) | const |
unpacks into specified storage, skipping w which can be reconstitued from √(1-x^2-y^2-z^2), see fromAxis()
Definition at line 90 of file fmatSpatial.h.
| void fmat::QuaternionT< R >::exportTo | ( | T & | w_, | |
| T & | x_, | |||
| T & | y_, | |||
| T & | z_ | |||
| ) | const |
unpacks into specified storage
Definition at line 88 of file fmatSpatial.h.
| T& fmat::QuaternionT< R >::exportTo | ( | T & | q | ) | const |
copies into another representation, assuming operator[] is supported and w is index 0
Definition at line 86 of file fmatSpatial.h.
copies into another representation, assuming operator[] is supported and w is index 0
Definition at line 84 of file fmatSpatial.h.
| static QuaternionT fmat::QuaternionT< R >::from | ( | const T & | q | ) | [static] |
copies from another representation, assuming operator[] is supported and w is index 0
Definition at line 80 of file fmatSpatial.h.
| static QuaternionT fmat::QuaternionT< R >::fromAxis | ( | const T & | axis | ) | [static] |
Generate quaternion from just the axis component of another quaternion (i.e. axis magnitude should be less than 1; 0 magnitude means no rotation).
This method requires only basic operations on the input type, so you can pass a raw array or plist::Point...
Definition at line 124 of file fmatSpatial.h.
Referenced by LinkComponent::computeOwnAABB(), LinkComponent::getCollisionModelTransform(), LinkComponent::getModelTransform(), and LinkComponent::getObstacle().
| static QuaternionT fmat::QuaternionT< R >::fromAxisAngle | ( | const T & | axis, | |
| R | angle | |||
| ) | [static] |
Generate quaternion from axis-angle representation (angle in radians, axis will be re-normalized if non-zero angle).
If axis is 0 length, initializes to identity (0 rotation)
Definition at line 111 of file fmatSpatial.h.
Referenced by IKSolver::Parallel::computeErrorGradient(), and GaitedFootsteps::expand().
| static QuaternionT fmat::QuaternionT< R >::fromMatrix | ( | const T & | rot | ) | [static] |
Generate quaternion from rotation matrix, this assumes the rotation matrix is well-formed.
This implementation is based on cross pollination between "Angel"'s code on this page: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm and the Ogre3D Quaternion implementation, which itself references: Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes article "Quaternion Calculus and Fast Animation".
Definition at line 149 of file fmatSpatial.h.
Referenced by ArmController::ArmController(), Grasper::computeGoalStates(), and KinematicJoint::getQuaternion().
| R fmat::QuaternionT< R >::getW | ( | ) | const |
returns w
Definition at line 92 of file fmatSpatial.h.
| R fmat::QuaternionT< R >::getX | ( | ) | const |
| R fmat::QuaternionT< R >::getY | ( | ) | const |
| R fmat::QuaternionT< R >::getZ | ( | ) | const |
| static const QuaternionT& fmat::QuaternionT< R >::identity | ( | ) | [static] |
returns a no-op quaternion (0 rotation), the same as the default constructor, but can re-use this instance instead of creating new ones all the time
Definition at line 98 of file fmatSpatial.h.
Referenced by KinematicJoint::getQuaternion().
| QuaternionT& fmat::QuaternionT< R >::importFrom | ( | const T & | q | ) |
copies from another representation, assuming operator[] is supported and w is index 0
Definition at line 82 of file fmatSpatial.h.
| QuaternionT fmat::QuaternionT< R >::inverse | ( | ) | const |
Negates just the quaternion axis.
Definition at line 277 of file fmatSpatial.h.
Referenced by fmat::crossProduct(), KinematicJoint::getQuaternion(), and fmat::invert().
| R fmat::QuaternionT< R >::norm | ( | ) | const |
returns magnitude of quaternion; should be "close" to 1, otherwise call normalize()
Definition at line 362 of file fmatSpatial.h.
| R fmat::QuaternionT< R >::normalize | ( | ) |
Re-normalize the quaternion magnitude to 1 (or 0 if norm is already invalid) and positive W, returns the previous magnitude.
Definition at line 365 of file fmatSpatial.h.
Referenced by IKGradientSolver::step().
| fmat::QuaternionT< R >::operator Matrix< 3, 3, R > | ( | ) | const |
allows conversion/assignment to Matrix<3,3>
Definition at line 212 of file fmatSpatial.h.
| Column<3,R> fmat::QuaternionT< R >::operator* | ( | const Column< 3, R > | v | ) | const |
multiply 3-element vector by quaternion
Definition at line 341 of file fmatSpatial.h.
| TransformT<R> fmat::QuaternionT< R >::operator* | ( | const TransformT< R > & | m | ) | const |
multiply Transform by quaternion
Definition at line 321 of file fmatSpatial.h.
| Matrix<3,W,R> fmat::QuaternionT< R >::operator* | ( | const T< 3, W, R > & | m | ) | const |
multiply 3-row matrix by quaternion
Definition at line 301 of file fmatSpatial.h.
| QuaternionT<typename fmat_internal::promotion_trait<R,Rb>::type> fmat::QuaternionT< R >::operator* | ( | const QuaternionT< Rb > & | q | ) | const |
multiply quaternions
Definition at line 287 of file fmatSpatial.h.
| QuaternionT fmat::QuaternionT< R >::operator*= | ( | const QuaternionT< R > & | q | ) |
multiply quaternions
Definition at line 297 of file fmatSpatial.h.
| R fmat::QuaternionT< R >::sumSq | ( | ) | const |
returns sum of squares of components; should be "close" to 1, otherwise call normalize()
Definition at line 359 of file fmatSpatial.h.
Referenced by fmat::QuaternionT< R >::normalize().
| Matrix<3,3,R> fmat::QuaternionT< R >::toMatrix | ( | ) | const |
returns a 3x3 rotation matrix representation
implemented by simplified version of operator*(*this, Matrix<3,3>::identity())
Definition at line 188 of file fmatSpatial.h.
Referenced by LinkComponent::getObstacle(), and fmat::QuaternionT< R >::operator Matrix< 3, 3, R >().
| fmat::Column<3,R> fmat::QuaternionT< R >::ypr | ( | ) | const |
Returns yaw-pitch-roll aka heading-elevation-bank conversion, where roll-pitch-yaw correspond to compounding rotations about the global x, y, and z axis respectively (in that order).
From the "driver's seat" positive heading is turning to the left (z is up, using right hand rule, not compass heading), positive pitch is looking down, and positive roll is spinning clockwise. Within this frame-oriented view, we apply rotation axes in the 'reverse' order: first z, then y, then x.
You can reconstruct a Quaternion from these values by: q · v = aboutZ(yaw) * aboutY(pitch) * aboutX(roll) · v Note we right-multiply v to apply the rotation, so x is applied to an incoming vector first, then y, then z.
With thanks to http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/ (note that page uses different axis mapping however!)
Definition at line 259 of file fmatSpatial.h.
Referenced by MoCapLogger::gotMoCapGUI(), and fmat::ypr().
Friends And Related Function Documentation
| std::ostream& operator<< | ( | std::ostream & | os, | |
| const QuaternionT< R > & | q | |||
| ) | [friend] |
Definition at line 389 of file fmatSpatial.h.
Member Data Documentation
const QuaternionT< T > fmat::QuaternionT< T >::IDENTITY [static] |
identity instance
Definition at line 99 of file fmatSpatial.h.
Referenced by fmat::TransformT< R >::identity(), and fmat::QuaternionT< R >::identity().
R fmat::QuaternionT< R >::w [protected] |
Definition at line 392 of file fmatSpatial.h.
Referenced by fmat::QuaternionT< R >::angle(), fmat::QuaternionT< R >::axisComponent(), fmat::QuaternionT< R >::exportTo(), fmat::QuaternionT< R >::fromMatrix(), fmat::QuaternionT< R >::getW(), fmat::QuaternionT< R >::importFrom(), fmat::QuaternionT< R >::inverse(), fmat::QuaternionT< R >::norm(), fmat::QuaternionT< R >::normalize(), fmat::QuaternionT< R >::operator*(), fmat::QuaternionT< R >::sumSq(), fmat::QuaternionT< R >::toMatrix(), and fmat::QuaternionT< R >::ypr().
R fmat::QuaternionT< R >::x [protected] |
Definition at line 392 of file fmatSpatial.h.
Referenced by fmat::QuaternionT< R >::exportTo(), fmat::QuaternionT< R >::fromMatrix(), fmat::QuaternionT< R >::getX(), fmat::QuaternionT< R >::importFrom(), fmat::QuaternionT< R >::operator*(), and fmat::QuaternionT< R >::toMatrix().
R fmat::QuaternionT< R >::y [protected] |
Definition at line 392 of file fmatSpatial.h.
Referenced by fmat::QuaternionT< R >::exportTo(), fmat::QuaternionT< R >::fromMatrix(), fmat::QuaternionT< R >::getY(), fmat::QuaternionT< R >::importFrom(), fmat::QuaternionT< R >::operator*(), and fmat::QuaternionT< R >::toMatrix().
R fmat::QuaternionT< R >::z [protected] |
Definition at line 392 of file fmatSpatial.h.
Referenced by fmat::QuaternionT< R >::exportTo(), fmat::QuaternionT< R >::fromMatrix(), fmat::QuaternionT< R >::getZ(), fmat::QuaternionT< R >::importFrom(), fmat::QuaternionT< R >::operator*(), and fmat::QuaternionT< R >::toMatrix().
The documentation for this class was generated from the following files:
