represents rotations in 3 dimensional space. More...

#include <frames.hpp>

Public Member Functions
	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)
Rotation &	operator= (const Rotation &arg)
Vector	operator* (const Vector &v) const
	Defines a multiplication R*V between a Rotation R and a Vector V. Complexity : 9M+6A.
double &	operator() (int i, int j)
	Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set.
double	operator() (int i, int j) const
	Access to elements 0..2,0..2, bounds are checked when NDEBUG is not set.
void	SetInverse ()
	Sets the value of *this to its inverse.
Rotation	Inverse () const
	Gives back the inverse rotation matrix of *this.
Vector	Inverse (const Vector &v) const
	The same as R.Inverse()*v but more efficient.
Wrench	Inverse (const Wrench &arg) const
	The same as R.Inverse()*arg but more efficient.
Twist	Inverse (const Twist &arg) const
	The same as R.Inverse()*arg but more efficient.
void	DoRotX (double angle)
	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.
void	DoRotY (double angle)
	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.
void	DoRotZ (double angle)
	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.
Vector	GetRot () const
	Returns a vector with the direction of the equiv. axis and its norm is angle.
double	GetRotAngle (Vector &axis, double eps=epsilon) const
void	GetEulerZYZ (double &alpha, double &beta, double &gamma) const
void	GetQuaternion (double &x, double &y, double &z, double &w) const
	Get the quaternion of this matrix.
void	GetRPY (double &roll, double &pitch, double &yaw) const
void	GetEulerZYX (double &Alfa, double &Beta, double &Gamma) const
Twist	operator* (const Twist &arg) const
	Transformation of the base to which the twist is expressed. Complexity : 18M+12A.
Wrench	operator* (const Wrench &arg) const
	Transformation of the base to which the wrench is expressed. Complexity : 18M+12A.
Vector	UnitX () const
	Access to the underlying unitvectors of the rotation matrix.
void	UnitX (const Vector &X)
	Access to the underlying unitvectors of the rotation matrix.
Vector	UnitY () const
	Access to the underlying unitvectors of the rotation matrix.
void	UnitY (const Vector &X)
	Access to the underlying unitvectors of the rotation matrix.
Vector	UnitZ () const
	Access to the underlying unitvectors of the rotation matrix.
void	UnitZ (const Vector &X)
	Access to the underlying unitvectors of the rotation matrix.

Static Public Member Functions
static Rotation	Identity ()
	Gives back an identity rotaton matrix.
static Rotation	RotX (double angle)
	The Rot... static functions give the value of the appropriate rotation matrix back.
static Rotation	RotY (double angle)
	The Rot... static functions give the value of the appropriate rotation matrix back.
static Rotation	RotZ (double angle)
	The Rot... static functions give the value of the appropriate rotation matrix back.
static Rotation	Rot (const Vector &rotvec, double angle)
	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.
static Rotation	Rot2 (const Vector &rotvec, double angle)
	Along an arbitrary axes. rotvec should be normalized.
static Rotation	EulerZYZ (double Alfa, double Beta, double Gamma)
static Rotation	Quaternion (double x, double y, double z, double w)
	Gives back a rotation matrix specified with Quaternion convention the norm of (x,y,z,w) should be equal to 1.
static Rotation	RPY (double roll, double pitch, double yaw)
static Rotation	EulerZYX (double Alfa, double Beta, double Gamma)

Public Attributes
double	data [9]

Friends
class	Frame
Rotation	operator* (const Rotation &lhs, const Rotation &rhs)
bool	Equal (const Rotation &a, const Rotation &b, double eps=epsilon)
	do not use operator == because the definition of Equal(.,.) is slightly different. It compares whether the 2 arguments are equal in an eps-interval
bool	operator== (const Rotation &a, const Rotation &b)
	The literal equality operator==(), also identical.
bool	operator!= (const Rotation &a, const Rotation &b)
	The literal inequality operator!=().

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

Constructor & Destructor Documentation

◆ Rotation() [1/4]

KDL::Rotation::Rotation ( )

inline

◆ Rotation() [2/4]

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

inline

◆ Rotation() [3/4]

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

inline

◆ Rotation() [4/4]

KDL::Rotation::Rotation ( const Rotation & arg )

inline

Member Function Documentation

◆ DoRotX()

void KDL::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.

◆ DoRotY()

void KDL::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.

◆ DoRotZ()

void KDL::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.

◆ EulerZYX()

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)

◆ 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)

◆ 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.

◆ 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

◆ 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

◆ GetRot()

Vector KDL::Rotation::GetRot ( ) const

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

◆ 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] )

◆ 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

◆ Identity()

Rotation KDL::Rotation::Identity ( )

inlinestatic

Gives back an identity rotaton matrix.

◆ Inverse() [1/4]

Rotation KDL::Rotation::Inverse ( ) const

inline

Gives back the inverse rotation matrix of *this.

◆ Inverse() [2/4]

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

inline

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

◆ Inverse() [3/4]

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

inline

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

◆ Inverse() [4/4]

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

inline

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

◆ operator()() [1/2]

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

inline

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

◆ operator()() [2/2]

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

inline

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

◆ operator*() [1/3]

Twist KDL::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.

◆ operator*() [2/3]

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

inline

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

◆ operator*() [3/3]

Wrench KDL::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.

◆ operator=()

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

inline

◆ 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.

◆ 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.

◆ Rot2()

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

static

Along an arbitrary axes. rotvec should be normalized.

◆ RotX()

Rotation KDL::Rotation::RotX ( double angle )

inlinestatic

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

◆ RotY()

Rotation KDL::Rotation::RotY ( double angle )

inlinestatic

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

◆ RotZ()

Rotation KDL::Rotation::RotZ ( double angle )

inlinestatic

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

◆ 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

◆ SetInverse()

void KDL::Rotation::SetInverse ( )

inline

Sets the value of *this to its inverse.