Quaternion that are used for singularity free joints. More...

#include <Quaternion.h>

Inheritance diagram for RobotDynamics::Math::Quaternion:

Public Member Functions
Quaternion	conjugate () const

EIGEN_STRONG_INLINE double	getScalarPart () const
	Get scalar part. More...

Quaternion	operator* (const double &s) const
	Method to scale the elements of a quaternion by a constant. Normalization is NOT performed. More...

Quaternion	operator* (const Quaternion &q) const
	Quaternion multiplication. More...

Quaternion &	operator*= (const Quaternion &q)
	Overloaded *= operator for quaternion multiplication. More...

Quaternion &	operator= (const Eigen::Quaterniond &q)

Quaternion &	operator= (const RobotDynamics::Math::Quaternion &q)

Quaternion &	operator= (const Vector4d &q)

Quaternion &	operator= (const Matrix3d &E)

Quaternion &	operator= (const AxisAngle &axis_angle)

	Quaternion ()
	Constructor. More...

	Quaternion (const Eigen::Quaterniond &q)

	Quaternion (const RobotDynamics::Math::Quaternion &q)

	Quaternion (const RobotDynamics::Math::Matrix3d &E)

	Quaternion (const Vector4d &q)

	Quaternion (const AxisAngle &axis_angle)

	Quaternion (const Vector3d &axis, double angle)

	Quaternion (double x, double y, double z, double w)
	Constructor. More...

Vector3d	rotate (const Vector3d &vec) const

void	sanitize ()
	sanitize the quaternion by negating each element if the w element is less than zero More...

void	set (double x, double y, double z, double w)

void	set (const Matrix3d &E)

void	set (const Quaternion &q)

void	set (const AxisAngle &axis_angle)

void	set (Vector3d axis, double angle)

Quaternion	slerp (double alpha, const Quaternion &quat) const
	From Wikipedia: In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1. More...

void	swingTwistDecomposition (const Vector3d &twist_axis, Quaternion &swing, Quaternion &twist)
	Decompose a quaternion into a swing then twist quaternion where the twist is about the given axis. More...

Quaternion	timeStep (const Vector3d &omega, double dt)

void	transform (const RobotDynamics::Math::SpatialTransform &X)
	Pure virtual object. This object forces objects that inherit from it to have a method that tells how that object is transformed. More...

EIGEN_STRONG_INLINE Vector3d	vec () const
	Get vector part. More...

EIGEN_STRONG_INLINE double &	w ()

EIGEN_STRONG_INLINE double	w () const

EIGEN_STRONG_INLINE double &	x ()

EIGEN_STRONG_INLINE double	x () const

EIGEN_STRONG_INLINE double &	y ()

EIGEN_STRONG_INLINE double	y () const

EIGEN_STRONG_INLINE double &	z ()

EIGEN_STRONG_INLINE double	z () const

Public Member Functions inherited from RobotDynamics::Math::Vector4d
template<typename OtherDerived >
Vector4d &	operator= (const Eigen::MatrixBase< OtherDerived > &other)

void	set (const double &v0, const double &v1, const double &v2, const double &v3)

template<typename OtherDerived >
	Vector4d (const Eigen::MatrixBase< OtherDerived > &other)

EIGEN_STRONG_INLINE	Vector4d ()

EIGEN_STRONG_INLINE	Vector4d (const double &v0, const double &v1, const double &v2, const double &v3)

Private Member Functions
Quaternion	fromAxisAngle (const Vector3d &axis, double angle_rad)

Quaternion	toQuaternion (const Matrix3d &mat)

Additional Inherited Members
Public Types inherited from RobotDynamics::Math::Vector4d
typedef Eigen::Vector4d	Base

Detailed Description

Quaternion that are used for singularity free joints.

order: x,y,z,w

Definition at line 25 of file Quaternion.h.

Constructor & Destructor Documentation

RobotDynamics::Math::Quaternion::Quaternion ( )

inline

Constructor.

Definition at line 31 of file Quaternion.h.

RobotDynamics::Math::Quaternion::Quaternion ( const Eigen::Quaterniond & q )

inline

Definition at line 36 of file Quaternion.h.

RobotDynamics::Math::Quaternion::Quaternion ( const RobotDynamics::Math::Quaternion & q )

inline

Definition at line 41 of file Quaternion.h.

RobotDynamics::Math::Quaternion::Quaternion ( const RobotDynamics::Math::Matrix3d & E )

inline

Definition at line 46 of file Quaternion.h.

RobotDynamics::Math::Quaternion::Quaternion ( const Vector4d & q )

inline

Definition at line 51 of file Quaternion.h.

RobotDynamics::Math::Quaternion::Quaternion ( const AxisAngle & axis_angle )

inline

Definition at line 56 of file Quaternion.h.

RobotDynamics::Math::Quaternion::Quaternion	(	const Vector3d &	axis,
		double	angle
	)

inline

Definition at line 60 of file Quaternion.h.

RobotDynamics::Math::Quaternion::Quaternion	(	double	x,
		double	y,
		double	z,
		double	w
	)

inline

Constructor.

Parameters

x
y
z
w

Definition at line 72 of file Quaternion.h.

Member Function Documentation

Quaternion RobotDynamics::Math::Quaternion::conjugate ( ) const

inline

Definition at line 285 of file Quaternion.h.

Quaternion RobotDynamics::Math::Quaternion::fromAxisAngle	(	const Vector3d &	axis,
		double	angle_rad
	)

inlineprivate

Definition at line 353 of file Quaternion.h.

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::getScalarPart ( ) const

inline

Get scalar part.

Deprecated:

Returns: Vector part

Definition at line 138 of file Quaternion.h.

Quaternion RobotDynamics::Math::Quaternion::operator* ( const double & s ) const

inline

Method to scale the elements of a quaternion by a constant. Normalization is NOT performed.

Parameters

s

Returns: Scaled quaternion

Definition at line 192 of file Quaternion.h.

Quaternion RobotDynamics::Math::Quaternion::operator* ( const Quaternion & q ) const

inline

Quaternion multiplication.

Parameters

q	Quaternion to multiply by

Returns: New multiplied quaternion result

Definition at line 202 of file Quaternion.h.

Quaternion& RobotDynamics::Math::Quaternion::operator*= ( const Quaternion & q )

inline

Overloaded *= operator for quaternion multiplication.

Parameters

q	Quaternion to multiply by

Returns: Modified result of the multiplication

Definition at line 214 of file Quaternion.h.

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const Eigen::Quaterniond & q )

inline

Definition at line 141 of file Quaternion.h.

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const RobotDynamics::Math::Quaternion & q )

inline

Definition at line 163 of file Quaternion.h.

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const Vector4d & q )

inline

Definition at line 169 of file Quaternion.h.

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const Matrix3d & E )

inline

Definition at line 175 of file Quaternion.h.

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const AxisAngle & axis_angle )

inline

Definition at line 181 of file Quaternion.h.

Vector3d RobotDynamics::Math::Quaternion::rotate ( const Vector3d & vec ) const

inline

Definition at line 297 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::sanitize ( )

inline

sanitize the quaternion by negating each element if the w element is less than zero

Definition at line 150 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::set	(	double	x,
		double	y,
		double	z,
		double	w
	)

inline

Definition at line 116 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::set ( const Matrix3d & E )

inline

Definition at line 221 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::set ( const Quaternion & q )

inline

Definition at line 226 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::set ( const AxisAngle & axis_angle )

inline

Definition at line 231 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::set	(	Vector3d	axis,
		double	angle
	)

inline

Definition at line 236 of file Quaternion.h.

Quaternion RobotDynamics::Math::Quaternion::slerp	(	double	alpha,
		const Quaternion &	quat
	)		const

inline

From Wikipedia: In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1.

Note: Only unit quaternions are valid rotations, so make sure to normalize

Parameters

alpha	Interpolation parameter. Should be between 0 and 1
quat	Quaternion to interpolate between

Returns: Interpolated quaternion

Definition at line 258 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::swingTwistDecomposition	(	const Vector3d &	twist_axis,
		Quaternion &	swing,
		Quaternion &	twist
	)

inline

Decompose a quaternion into a swing then twist quaternion where the twist is about the given axis.

twist_axis Unit vector for the axis of the twist, e.g. (0., 0., 1.) for the z-axis
swing Modified. Location for the resulting swing quaternion to be stored
twist Modified. Location for the resulting twist quaternion to be stored

Note: This implementation can be found in PRZEMYSLAW DOBROWOLSKI's thesis titled, "SWING-TWIST DECOMPOSITION IN CLIFFORD ALGEBRA"

Definition at line 316 of file Quaternion.h.

Quaternion RobotDynamics::Math::Quaternion::timeStep	(	const Vector3d &	omega,
		double	dt
	)

inline

Definition at line 290 of file Quaternion.h.

Quaternion RobotDynamics::Math::Quaternion::toQuaternion ( const Matrix3d & mat )

inlineprivate

Definition at line 327 of file Quaternion.h.

void RobotDynamics::Math::Quaternion::transform ( const RobotDynamics::Math::SpatialTransform & X )

inlinevirtual

Pure virtual object. This object forces objects that inherit from it to have a method that tells how that object is transformed.

Parameters

X	SpatialTransform

Implements RobotDynamics::Math::TransformableGeometricObject.

Definition at line 243 of file Quaternion.h.

EIGEN_STRONG_INLINE Vector3d RobotDynamics::Math::Quaternion::vec ( ) const

inline

Get vector part.

Returns: Vector part

Definition at line 128 of file Quaternion.h.

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::w ( )

inline

Definition at line 106 of file Quaternion.h.

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::w ( ) const

inline

Definition at line 111 of file Quaternion.h.

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::x ( )

inline

Definition at line 76 of file Quaternion.h.

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::x ( ) const

inline

Definition at line 81 of file Quaternion.h.

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::y ( )

inline

Definition at line 86 of file Quaternion.h.

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::y ( ) const

inline

Definition at line 91 of file Quaternion.h.

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::z ( )

inline

Definition at line 96 of file Quaternion.h.

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::z ( ) const

inline

Definition at line 101 of file Quaternion.h.

The documentation for this class was generated from the following file:

Quaternion.h

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation