represents rotations in 3 dimensional space. More...

#include <frames.hpp>

Public Member Functions
void	DoRotX (double angle)

void	DoRotY (double angle)

void	DoRotZ (double angle)

void	GetEulerZYX (double &Alfa, double &Beta, double &Gamma) const

void	GetEulerZYZ (double &alpha, double &beta, double &gamma) const

void	GetQuaternion (double &x, double &y, double &z, double &w) const

Vector	GetRot () const

double	GetRotAngle (Vector &axis, double eps=epsilon) const

void	GetRPY (double &roll, double &pitch, double &yaw) const

Rotation	Inverse () const
	Gives back the inverse rotation matrix of *this. More...

Vector	Inverse (const Vector &v) const
	The same as R.Inverse()*v but more efficient. More...

Wrench	Inverse (const Wrench &arg) const
	The same as R.Inverse()*arg but more efficient. More...

Twist	Inverse (const Twist &arg) const
	The same as R.Inverse()*arg but more efficient. More...

double &	operator() (int i, int j)
	Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set. More...

double	operator() (int i, int j) const
	Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set. More...

Vector	operator* (const Vector &v) const

Twist	operator* (const Twist &arg) const

Wrench	operator* (const Wrench &arg) const

Rotation &	operator= (const Rotation &arg)

	Rotation ()

	Rotation (double Xx, double Yx, double Zx, double Xy, double Yy, double Zy, double Xz, double Yz, double Zz)

	Rotation (const Vector &x, const Vector &y, const Vector &z)

	Rotation (const Rotation &arg)

void	SetInverse ()
	Sets the value of *this to its inverse. More...

Vector	UnitX () const
	Access to the underlying unitvectors of the rotation matrix. More...

void	UnitX (const Vector &X)
	Access to the underlying unitvectors of the rotation matrix. More...

Vector	UnitY () const
	Access to the underlying unitvectors of the rotation matrix. More...

void	UnitY (const Vector &X)
	Access to the underlying unitvectors of the rotation matrix. More...

Vector	UnitZ () const
	Access to the underlying unitvectors of the rotation matrix. More...

void	UnitZ (const Vector &X)
	Access to the underlying unitvectors of the rotation matrix. More...

Static Public Member Functions
static Rotation	EulerZYX (double Alfa, double Beta, double Gamma)

static Rotation	EulerZYZ (double Alfa, double Beta, double Gamma)

static Rotation	Identity ()
	Gives back an identity rotaton matrix. More...

static Rotation	Quaternion (double x, double y, double z, double w)

static Rotation	Rot (const Vector &rotvec, double angle)

static Rotation	Rot2 (const Vector &rotvec, double angle)
	Along an arbitrary axes. rotvec should be normalized. More...

static Rotation	RotX (double angle)
	The Rot... static functions give the value of the appropriate rotation matrix back. More...

static Rotation	RotY (double angle)
	The Rot... static functions give the value of the appropriate rotation matrix back. More...

static Rotation	RotZ (double angle)
	The Rot... static functions give the value of the appropriate rotation matrix back. More...

static Rotation	RPY (double roll, double pitch, double yaw)

Public Attributes
double	data [9]

Friends
bool	Equal (const Rotation &a, const Rotation &b, double eps)

class	Frame

bool	operator!= (const Rotation &a, const Rotation &b)
	The literal inequality operator!=() More...

Rotation	operator* (const Rotation &lhs, const Rotation &rhs)

bool	operator== (const Rotation &a, const Rotation &b)
	The literal equality operator==(), also identical. More...

Detailed Description

represents rotations in 3 dimensional space.

This class represents a rotation matrix with the following conventions :

    Suppose V2 = R*V,                                    (1)
    V is expressed in frame B
    V2 is expressed in frame A
    This matrix R consists of 3 columns [ X,Y,Z ],
    X,Y, and Z contain the axes of frame B, expressed in frame A
    Because of linearity expr(1) is valid.

This class only represents rotational_interpolation, not translation Two interpretations are possible for rotation angles. if you rotate with angle around X frame A to have frame B, then the result of SetRotX is equal to frame B expressed wrt A. In code:

     Rotation R;
     F_A_B = R.SetRotX(angle);

Secondly, if you take the following code :

     Vector p,p2; Rotation R;
     R.SetRotX(angle);
     p2 = R*p;

then the frame p2 is rotated around X axis with (-angle). Analogue reasonings can be applyd to SetRotY,SetRotZ,SetRot

type: Concrete implementation

Definition at line 303 of file frames.hpp.

Constructor & Destructor Documentation

◆ Rotation() [1/4]

KDL::Rotation::Rotation ( )

inline

Definition at line 308 of file frames.hpp.

◆ Rotation() [2/4]

Rotation::Rotation	(	double	Xx,
		double	Yx,
		double	Zx,
		double	Xy,
		double	Yy,
		double	Zy,
		double	Xz,
		double	Yz,
		double	Zz
	)

inline

Definition at line 499 of file frames.hpp.

◆ Rotation() [3/4]

Rotation::Rotation	(	const Vector &	x,
		const Vector &	y,
		const Vector &	z
	)

inline

Definition at line 509 of file frames.hpp.

◆ Rotation() [4/4]

Rotation::Rotation ( const Rotation & arg )

inline

Definition at line 516 of file frames.hpp.

Member Function Documentation

◆ DoRotX()

void Rotation::DoRotX ( double angle )

inline

The DoRot... functions apply a rotation R to *this,such that *this = *this * Rot.. DoRot... functions are only defined when they can be executed more efficiently

Definition at line 557 of file frames.hpp.

◆ DoRotY()

void Rotation::DoRotY ( double angle )

inline

The DoRot... functions apply a rotation R to *this,such that *this = *this * Rot.. DoRot... functions are only defined when they can be executed more efficiently

Definition at line 573 of file frames.hpp.

◆ DoRotZ()

void Rotation::DoRotZ ( double angle )

inline

The DoRot... functions apply a rotation R to *this,such that *this = *this * Rot.. DoRot... functions are only defined when they can be executed more efficiently

Definition at line 589 of file frames.hpp.

◆ EulerZYX()

static Rotation KDL::Rotation::EulerZYX	(	double	Alfa,
		double	Beta,
		double	Gamma
	)

inlinestatic

EulerZYX constructs a Rotation from the Euler ZYX parameters:

First rotate around Z with alfa,
then around the new Y with beta,
then around new X with gamma.

Closely related to RPY-convention.

Invariants:

EulerZYX(alpha,beta,gamma) == EulerZYX(alpha +/- PI, PI-beta, gamma +/- PI)
(angle + 2*k*PI)

Definition at line 471 of file frames.hpp.

◆ EulerZYZ()

Rotation KDL::Rotation::EulerZYZ	(	double	Alfa,
		double	Beta,
		double	Gamma
	)

static

Gives back a rotation matrix specified with EulerZYZ convention :

First rotate around Z with alfa,
then around the new Y with beta,
then around new Z with gamma. Invariants:

EulerZYX(alpha,beta,gamma) == EulerZYX(alpha +/- PHI, -beta, gamma +/- PI)

(angle + 2*k*PI)

Definition at line 262 of file frames.cpp.

◆ GetEulerZYX()

void KDL::Rotation::GetEulerZYX	(	double &	Alfa,
		double &	Beta,
		double &	Gamma
	)		const

inline

GetEulerZYX gets the euler ZYX parameters of a rotation : First rotate around Z with alfa, then around the new Y with beta, then around new X with gamma.

Range of the results of GetEulerZYX :

-PI <= alfa <= PI
-PI <= gamma <= PI
-PI/2 <= beta <= PI/2

if beta == PI/2 or beta == -PI/2, multiple solutions for gamma and alpha exist. The solution where gamma==0 is chosen.

Invariants:

EulerZYX(alpha,beta,gamma) == EulerZYX(alpha +/- PI, PI-beta, gamma +/- PI)
and also (angle + 2*k*PI)

Closely related to RPY-convention.

Definition at line 495 of file frames.hpp.

◆ GetEulerZYZ()

void KDL::Rotation::GetEulerZYZ	(	double &	alpha,
		double &	beta,
		double &	gamma
	)		const

Gives back the EulerZYZ convention description of the rotation matrix : First rotate around Z with alpha, then around the new Y with beta, then around new Z with gamma.

Variables are bound by:

(-PI < alpha <= PI),
(0 <= beta <= PI),
(-PI < gamma <= PI)

if beta==0 or beta==PI, then alpha and gamma are not unique, in this case gamma is chosen to be zero. Invariants:

EulerZYX(alpha,beta,gamma) == EulerZYX(alpha +/- PI, -beta, gamma +/- PI)
angle + 2*k*PI

Definition at line 275 of file frames.cpp.

◆ GetQuaternion()

void KDL::Rotation::GetQuaternion	(	double &	x,
		double &	y,
		double &	z,
		double &	w
	)		const

Get the quaternion of this matrix

Postcondition: the norm of (x,y,z,w) is 1

Definition at line 204 of file frames.cpp.

◆ GetRot()

Vector KDL::Rotation::GetRot ( ) const

Returns a vector with the direction of the equiv. axis and its norm is angle

Definition at line 336 of file frames.cpp.

◆ GetRotAngle()

double KDL::Rotation::GetRotAngle	(	Vector &	axis,
		double	eps = `epsilon`
	)		const

Returns the rotation angle around the equiv. axis

Parameters

axis	the rotation axis is returned in this variable
eps	: in the case of angle == 0 : rot axis is undefined and chosen to be +/- Z-axis in the case of angle == PI : 2 solutions, positive Z-component of the axis is chosen.

Returns: returns the rotation angle (between [0..PI] )

Returns the rotation angle around the equiv. axis

Parameters

axis	the rotation axis is returned in this variable
eps	: in the case of angle == 0 : rot axis is undefined and chosen to be the Z-axis in the case of angle == PI : 2 solutions, positive Z-component of the axis is chosen.

Returns: returns the rotation angle (between [0..PI] ) /todo : Check corresponding routines in rframes and rrframes

Definition at line 358 of file frames.cpp.

◆ GetRPY()

void KDL::Rotation::GetRPY	(	double &	roll,
		double &	pitch,
		double &	yaw
	)		const

Gives back a vector in RPY coordinates, variables are bound by

-PI <= roll <= PI
-PI <= Yaw <= PI
-PI/2 <= PITCH <= PI/2

convention :

first rotate around X with roll,
then around the old Y with pitch,
then around old Z with yaw

if pitch == PI/2 or pitch == -PI/2, multiple solutions for gamma and alpha exist. The solution where roll==0 is chosen.

Invariants:

RPY(roll,pitch,yaw) == RPY( roll +/- PI, PI-pitch, yaw +/- PI )
angles + 2*k*PI

Definition at line 249 of file frames.cpp.

◆ Identity()

Rotation Rotation::Identity ( )

inlinestatic

Gives back an identity rotaton matrix.

Definition at line 553 of file frames.hpp.

◆ Inverse() [1/4]

Rotation Rotation::Inverse ( ) const

inline

Gives back the inverse rotation matrix of *this.

Definition at line 638 of file frames.hpp.

◆ Inverse() [2/4]

Vector Rotation::Inverse ( const Vector & v ) const

inline

The same as R.Inverse()*v but more efficient.

Definition at line 645 of file frames.hpp.

◆ Inverse() [3/4]

Wrench Rotation::Inverse ( const Wrench & arg ) const

inline

The same as R.Inverse()*arg but more efficient.

Definition at line 176 of file frames.hpp.

◆ Inverse() [4/4]

Twist Rotation::Inverse ( const Twist & arg ) const

inline

The same as R.Inverse()*arg but more efficient.

Definition at line 181 of file frames.hpp.

◆ operator()() [1/2]

double & Rotation::operator()	(	int	i,
		int	j
	)

inline

Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set.

Definition at line 489 of file frames.hpp.

◆ operator()() [2/2]

double Rotation::operator()	(	int	i,
		int	j
	)		const

inline

Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set.

Definition at line 494 of file frames.hpp.

◆ operator*() [1/3]

Vector Rotation::operator* ( const Vector & v ) const

inline

Defines a multiplication R*V between a Rotation R and a Vector V. Complexity : 9M+6A

Definition at line 527 of file frames.hpp.

◆ operator*() [2/3]

Twist Rotation::operator* ( const Twist & arg ) const

inline

Transformation of the base to which the twist is expressed. Complexity : 18M+12A

See also: Frame*Twist for a transformation that also transforms the velocity reference point.

Definition at line 536 of file frames.hpp.

◆ operator*() [3/3]

Wrench Rotation::operator* ( const Wrench & arg ) const

inline

Transformation of the base to which the wrench is expressed. Complexity : 18M+12A

See also: Frame*Wrench for a transformation that also transforms the force reference point.

Definition at line 545 of file frames.hpp.

◆ operator=()

Rotation & Rotation::operator= ( const Rotation & arg )

inline

Definition at line 521 of file frames.hpp.

◆ Quaternion()

Rotation KDL::Rotation::Quaternion	(	double	x,
		double	y,
		double	z,
		double	w
	)

static

Gives back a rotation matrix specified with Quaternion convention the norm of (x,y,z,w) should be equal to 1

Definition at line 190 of file frames.cpp.

◆ Rot()

Rotation KDL::Rotation::Rot	(	const Vector &	rotvec,
		double	angle
	)

static

Along an arbitrary axes. It is not necessary to normalize rotvec. returns identity rotation matrix in the case that the norm of rotvec is to small to be used.

Definition at line 293 of file frames.cpp.

◆ Rot2()

Rotation KDL::Rotation::Rot2	(	const Vector &	rotvec,
		double	angle
	)

static

Along an arbitrary axes. rotvec should be normalized.

Definition at line 303 of file frames.cpp.

◆ RotX()

Rotation Rotation::RotX ( double angle )

inlinestatic

The Rot... static functions give the value of the appropriate rotation matrix back.

Definition at line 606 of file frames.hpp.

◆ RotY()

Rotation Rotation::RotY ( double angle )

inlinestatic

The Rot... static functions give the value of the appropriate rotation matrix back.

Definition at line 611 of file frames.hpp.

◆ RotZ()

Rotation Rotation::RotZ ( double angle )

inlinestatic

The Rot... static functions give the value of the appropriate rotation matrix back.

Definition at line 616 of file frames.hpp.

◆ RPY()

Rotation KDL::Rotation::RPY	(	double	roll,
		double	pitch,
		double	yaw
	)

static

Gives back a rotation matrix specified with RPY convention: first rotate around X with roll, then around the old Y with pitch, then around old Z with yaw

Invariants:

RPY(roll,pitch,yaw) == RPY( roll +/- PI, PI-pitch, yaw +/- PI )
angles + 2*k*PI

Definition at line 237 of file frames.cpp.

◆ SetInverse()

void Rotation::SetInverse ( )

inline

Sets the value of *this to its inverse.

Definition at line 654 of file frames.hpp.