Represents a linear interpolation in SO3, using the slerp method provided by Eigen::Quaternion. More...

#include <ndcurves/so3_linear.h>

Inheritance diagram for ndcurves::SO3Linear< Time, Numeric, Safe >:

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Collaboration diagram for ndcurves::SO3Linear< Time, Numeric, Safe >:

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Public Types
typedef Numeric	Scalar

typedef matrix3_t	point_t

typedef point3_t	point_derivate_t

typedef Eigen::Quaternion< Scalar >	quaternion_t

typedef Time	time_t

typedef curve_abc< Time, Numeric, Safe, point_t, point_derivate_t >	curve_abc_t

typedef constant_curve< Time, Numeric, Safe, point_derivate_t >	curve_derivate_t

typedef SO3Linear< Time, Numeric, Safe >	SO3Linear_t

Public Types inherited from ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >
typedef Point	point_t

typedef Point_derivate	point_derivate_t

typedef Time	time_t

typedef Numeric	num_t

typedef curve_abc< Time, Numeric, Safe, point_t, point_derivate_t >	curve_t

typedef curve_abc< Time, Numeric, Safe, point_derivate_t >	curve_derivate_t

typedef std::shared_ptr< curve_t >	curve_ptr_t

Public Member Functions
	SO3Linear ()
	Empty constructor. Curve obtained this way can not perform other class functions.

	SO3Linear (const quaternion_t &init_rot, const quaternion_t &end_rot, const time_t t_min, const time_t t_max)
	constructor with initial and final rotation and time bounds

	SO3Linear (const matrix3_t &init_rot, const matrix3_t &end_rot, const time_t t_min, const time_t t_max)
	constructor with initial and final rotation expressed as rotation matrix and time bounds

	SO3Linear (const quaternion_t &init_rot, const quaternion_t &end_rot)
	constructor with initial and final rotation, time bounds are set to [0;1]

	SO3Linear (const matrix3_t &init_rot, const matrix3_t &end_rot)
	constructor with initial and final rotation expressed as rotation matrix, time bounds are set to [0;1]

virtual	~SO3Linear ()
	Destructor.

	SO3Linear (const SO3Linear &other)

point3_t	computeAngularVelocity (const matrix3_t &init_rot, const matrix3_t &end_rot, const double t_min, const double t_max)

quaternion_t	computeAsQuaternion (const time_t t) const

virtual point_t	operator() (const time_t t) const
	Evaluation of the SO3Linear at time t using Eigen slerp.

bool	isApprox (const SO3Linear_t &other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
	isApprox check if other and *this are approximately equals. Only two curves of the same class can be approximately equals, for comparison between different type of curves see isEquivalent

virtual bool	isApprox (const curve_abc_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision()) const
	isApprox check if other and *this are approximately equal given a precision threshold Only two curves of the same class can be approximately equal, for comparison between different type of curves see isEquivalent.

virtual bool	operator== (const SO3Linear_t &other) const

virtual bool	operator!= (const SO3Linear_t &other) const

virtual point_derivate_t	derivate (const time_t t, const std::size_t order) const
	Evaluation of the derivative of order N of spline at time t.

curve_derivate_t	compute_derivate (const std::size_t order) const

curve_derivate_t *	compute_derivate_ptr (const std::size_t order) const
	Compute the derived curve at order N.

virtual std::size_t	dim () const
	Get dimension of curve.

time_t	min () const
	Get the minimum time for which the curve is defined.

time_t	max () const
	Get the maximum time for which the curve is defined.

virtual std::size_t	degree () const
	Get the degree of the curve.

matrix3_t	getInitRotation () const

matrix3_t	getEndRotation () const

matrix3_t	getInitRotation ()

matrix3_t	getEndRotation ()

template<class Archive >
void	load (Archive &ar, const unsigned int version)

template<class Archive >
void	save (Archive &ar, const unsigned int version) const

point3_t	log3 (const matrix3_t &R)
	Log: SO3 -> so3.

Public Member Functions inherited from ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >
	curve_abc ()
	Constructor.

virtual	~curve_abc ()
	Destructor.

bool	isEquivalent (const curve_t *other, const Numeric prec=Eigen::NumTraits< Numeric >::dummy_precision(), const size_t order=5) const
	isEquivalent check if other and *this are approximately equal by values, given a precision threshold. This test is done by discretizing both curves and evaluating them and their derivatives.

std::pair< time_t, time_t >	timeRange ()

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Public Member Functions inherited from ndcurves::serialization::Serializable
template<class Derived >
void	loadFromText (const std::string &filename)
	Loads a Derived object from a text file.

template<class Derived >
void	saveAsText (const std::string &filename) const
	Saved a Derived object as a text file.

template<class Derived >
void	loadFromXML (const std::string &filename, const std::string &tag_name)
	Loads a Derived object from an XML file.

template<class Derived >
void	saveAsXML (const std::string &filename, const std::string &tag_name) const
	Saved a Derived object as an XML file.

template<class Derived >
void	loadFromBinary (const std::string &filename)
	Loads a Derived object from an binary file.

template<class Derived >
void	saveAsBinary (const std::string &filename) const
	Saved a Derived object as an binary file.

Public Attributes
std::size_t	dim_

quaternion_t	init_rot_

quaternion_t	end_rot_

point3_t	angular_vel_

time_t	T_min_

time_t	T_max_

Friends
class	boost::serialization::access

Detailed Description

template<typename Time = double, typename Numeric = Time, bool Safe = false>
class ndcurves::SO3Linear< Time, Numeric, Safe >

Represents a linear interpolation in SO3, using the slerp method provided by Eigen::Quaternion.

Member Typedef Documentation

◆ curve_abc_t

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef curve_abc<Time, Numeric, Safe, point_t, point_derivate_t> ndcurves::SO3Linear< Time, Numeric, Safe >::curve_abc_t

◆ curve_derivate_t

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef constant_curve<Time, Numeric, Safe, point_derivate_t> ndcurves::SO3Linear< Time, Numeric, Safe >::curve_derivate_t

◆ point_derivate_t

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef point3_t ndcurves::SO3Linear< Time, Numeric, Safe >::point_derivate_t

◆ point_t

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef matrix3_t ndcurves::SO3Linear< Time, Numeric, Safe >::point_t

◆ quaternion_t

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef Eigen::Quaternion<Scalar> ndcurves::SO3Linear< Time, Numeric, Safe >::quaternion_t

◆ Scalar

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef Numeric ndcurves::SO3Linear< Time, Numeric, Safe >::Scalar

◆ SO3Linear_t

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef SO3Linear<Time, Numeric, Safe> ndcurves::SO3Linear< Time, Numeric, Safe >::SO3Linear_t

◆ time_t

template<typename Time = double, typename Numeric = Time, bool Safe = false>

typedef Time ndcurves::SO3Linear< Time, Numeric, Safe >::time_t

Constructor & Destructor Documentation

◆ SO3Linear() [1/6]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

ndcurves::SO3Linear< Time, Numeric, Safe >::SO3Linear ( )

inline

Empty constructor. Curve obtained this way can not perform other class functions.

◆ SO3Linear() [2/6]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

ndcurves::SO3Linear< Time, Numeric, Safe >::SO3Linear	(	const quaternion_t &	init_rot,
		const quaternion_t &	end_rot,
		const time_t	t_min,
		const time_t	t_max
	)

inline

constructor with initial and final rotation and time bounds

◆ SO3Linear() [3/6]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

ndcurves::SO3Linear< Time, Numeric, Safe >::SO3Linear	(	const matrix3_t &	init_rot,
		const matrix3_t &	end_rot,
		const time_t	t_min,
		const time_t	t_max
	)

inline

constructor with initial and final rotation expressed as rotation matrix and time bounds

◆ SO3Linear() [4/6]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

ndcurves::SO3Linear< Time, Numeric, Safe >::SO3Linear	(	const quaternion_t &	init_rot,
		const quaternion_t &	end_rot
	)

inline

constructor with initial and final rotation, time bounds are set to [0;1]

◆ SO3Linear() [5/6]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

ndcurves::SO3Linear< Time, Numeric, Safe >::SO3Linear	(	const matrix3_t &	init_rot,
		const matrix3_t &	end_rot
	)

inline

constructor with initial and final rotation expressed as rotation matrix, time bounds are set to [0;1]

◆ ~SO3Linear()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual ndcurves::SO3Linear< Time, Numeric, Safe >::~SO3Linear ( )

inlinevirtual

Destructor.

◆ SO3Linear() [6/6]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

ndcurves::SO3Linear< Time, Numeric, Safe >::SO3Linear ( const SO3Linear< Time, Numeric, Safe > & other )

inline

Member Function Documentation

◆ compute_derivate()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

curve_derivate_t ndcurves::SO3Linear< Time, Numeric, Safe >::compute_derivate ( const std::size_t order ) const

inline

◆ compute_derivate_ptr()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

curve_derivate_t * ndcurves::SO3Linear< Time, Numeric, Safe >::compute_derivate_ptr ( const std::size_t order ) const

inlinevirtual

Compute the derived curve at order N.

Parameters

order : order of derivative.

Returns: A pointer to \(\frac{d^Nx(t)}{dt^N}\) derivative order N of the curve.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ computeAngularVelocity()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

point3_t ndcurves::SO3Linear< Time, Numeric, Safe >::computeAngularVelocity	(	const matrix3_t &	init_rot,
		const matrix3_t &	end_rot,
		const double	t_min,
		const double	t_max
	)

inline

◆ computeAsQuaternion()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

quaternion_t ndcurves::SO3Linear< Time, Numeric, Safe >::computeAsQuaternion ( const time_t t ) const

inline

◆ degree()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual std::size_t ndcurves::SO3Linear< Time, Numeric, Safe >::degree ( ) const

inlinevirtual

Get the degree of the curve.

Returns: \(degree\), the degree of the curve.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ derivate()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual point_derivate_t ndcurves::SO3Linear< Time, Numeric, Safe >::derivate	(	const time_t	t,
		const std::size_t	order
	)		const

inlinevirtual

Evaluation of the derivative of order N of spline at time t.

Parameters

t	: the time when to evaluate the spline.
order	: order of derivative.

Returns: \(\frac{d^Nx(t)}{dt^N}\) point corresponding on derivative spline at time t.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ dim()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual std::size_t ndcurves::SO3Linear< Time, Numeric, Safe >::dim ( ) const

inlinevirtual

Get dimension of curve.

Returns: dimension of curve.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ getEndRotation() [1/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

matrix3_t ndcurves::SO3Linear< Time, Numeric, Safe >::getEndRotation ( )

inline

◆ getEndRotation() [2/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

matrix3_t ndcurves::SO3Linear< Time, Numeric, Safe >::getEndRotation ( ) const

inline

◆ getInitRotation() [1/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

matrix3_t ndcurves::SO3Linear< Time, Numeric, Safe >::getInitRotation ( )

inline

◆ getInitRotation() [2/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

matrix3_t ndcurves::SO3Linear< Time, Numeric, Safe >::getInitRotation ( ) const

inline

◆ isApprox() [1/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual bool ndcurves::SO3Linear< Time, Numeric, Safe >::isApprox	(	const curve_abc_t *	other,
		const Numeric	prec = `Eigen::NumTraits< Numeric >::dummy_precision()`
	)		const

inlinevirtual

isApprox check if other and *this are approximately equal given a precision threshold Only two curves of the same class can be approximately equal, for comparison between different type of curves see isEquivalent.

Parameters

other	the other curve to check
prec	the precision threshold, default Eigen::NumTraits<Numeric>::dummy_precision()

Returns: true if the two curves are approximately equal

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ isApprox() [2/2]

template<typename Time = double, typename Numeric = Time, bool Safe = false>

bool ndcurves::SO3Linear< Time, Numeric, Safe >::isApprox	(	const SO3Linear_t &	other,
		const Numeric	prec = `Eigen::NumTraits<Numeric>::dummy_precision()`
	)		const

inline

isApprox check if other and *this are approximately equals. Only two curves of the same class can be approximately equals, for comparison between different type of curves see isEquivalent

Parameters

other	the other curve to check
prec	the precision threshold, default Eigen::NumTraits<Numeric>::dummy_precision()

Returns: true is the two curves are approximately equals

◆ load()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

template<class Archive >

void ndcurves::SO3Linear< Time, Numeric, Safe >::load	(	Archive &	ar,
		const unsigned int	version
	)

inline

◆ log3()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

point3_t ndcurves::SO3Linear< Time, Numeric, Safe >::log3 ( const matrix3_t & R )

inline

Log: SO3 -> so3.

Pseudo-inverse of log from \( SO3 -> { v \in so3, ||v|| \le pi } \).

Code from pinocchio.

Parameters

[in] R the rotation matrix. ///

Returns: The angular velocity vector associated to the rotation matrix.

◆ max()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

time_t ndcurves::SO3Linear< Time, Numeric, Safe >::max ( ) const

inlinevirtual

Get the maximum time for which the curve is defined.

Returns: \(t_{max}\) upper bound of time range.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ min()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

time_t ndcurves::SO3Linear< Time, Numeric, Safe >::min ( ) const

inlinevirtual

Get the minimum time for which the curve is defined.

Returns: \(t_{min}\) lower bound of time range.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ operator!=()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual bool ndcurves::SO3Linear< Time, Numeric, Safe >::operator!= ( const SO3Linear_t & other ) const

inlinevirtual

◆ operator()()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual point_t ndcurves::SO3Linear< Time, Numeric, Safe >::operator() ( const time_t t ) const

inlinevirtual

Evaluation of the SO3Linear at time t using Eigen slerp.

Parameters

t	: time when to evaluate the spline.

Returns: \(x(t)\) point corresponding on spline at time t.

Implements ndcurves::curve_abc< Time, Numeric, Safe, Point, Point_derivate >.

◆ operator==()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

virtual bool ndcurves::SO3Linear< Time, Numeric, Safe >::operator== ( const SO3Linear_t & other ) const

inlinevirtual

◆ save()

template<typename Time = double, typename Numeric = Time, bool Safe = false>

template<class Archive >

void ndcurves::SO3Linear< Time, Numeric, Safe >::save	(	Archive &	ar,
		const unsigned int	version
	)		const

inline

Friends And Related Symbol Documentation

◆ boost::serialization::access

template<typename Time = double, typename Numeric = Time, bool Safe = false>

friend class boost::serialization::access

friend

Member Data Documentation

◆ angular_vel_

template<typename Time = double, typename Numeric = Time, bool Safe = false>

point3_t ndcurves::SO3Linear< Time, Numeric, Safe >::angular_vel_

◆ dim_

template<typename Time = double, typename Numeric = Time, bool Safe = false>

std::size_t ndcurves::SO3Linear< Time, Numeric, Safe >::dim_

◆ end_rot_

template<typename Time = double, typename Numeric = Time, bool Safe = false>

quaternion_t ndcurves::SO3Linear< Time, Numeric, Safe >::end_rot_

◆ init_rot_

template<typename Time = double, typename Numeric = Time, bool Safe = false>

quaternion_t ndcurves::SO3Linear< Time, Numeric, Safe >::init_rot_

◆ T_max_

template<typename Time = double, typename Numeric = Time, bool Safe = false>

time_t ndcurves::SO3Linear< Time, Numeric, Safe >::T_max_

◆ T_min_

template<typename Time = double, typename Numeric = Time, bool Safe = false>

time_t ndcurves::SO3Linear< Time, Numeric, Safe >::T_min_

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

include/ndcurves/fwd.h
include/ndcurves/so3_linear.h

Public Types

Public Member Functions

Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ curve_abc_t

◆ curve_derivate_t

◆ point_derivate_t

◆ point_t

◆ quaternion_t

◆ Scalar

◆ SO3Linear_t

◆ time_t

Constructor & Destructor Documentation

◆ SO3Linear() [1/6]

◆ SO3Linear() [2/6]

◆ SO3Linear() [3/6]

◆ SO3Linear() [4/6]

◆ SO3Linear() [5/6]

◆ ~SO3Linear()

◆ SO3Linear() [6/6]

Member Function Documentation

◆ compute_derivate()

◆ compute_derivate_ptr()

◆ computeAngularVelocity()

◆ computeAsQuaternion()

◆ degree()

◆ derivate()

◆ dim()

◆ getEndRotation() [1/2]

◆ getEndRotation() [2/2]

◆ getInitRotation() [1/2]

◆ getInitRotation() [2/2]

◆ isApprox() [1/2]

◆ isApprox() [2/2]

◆ load()

◆ log3()

◆ max()

◆ min()

◆ operator!=()

◆ operator()()

◆ operator==()

◆ save()

Friends And Related Symbol Documentation

◆ boost::serialization::access

Member Data Documentation

◆ angular_vel_

◆ dim_

◆ end_rot_

◆ init_rot_

◆ T_max_

◆ T_min_