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)
void	setValue (float *oglmat)
void	getValue (float *oglmat) const
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.
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.
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.
void	Ortho ()
Vector	GetRot () const
	Returns a vector with the direction of the equiv. axis and its norm is angle.
Vector2	GetXZRot () const
	Returns a 2D vector representing the equivalent rotation in the XZ plane that brings the Y axis onto the Matrix Y axis and its norm is angle.
double	GetRotAngle (Vector &axis, double eps=epsilon) const
void	GetEulerZYZ (double &alfa, double &beta, double &gamma) const
	Gives back the EulerZYZ convention description of the rotation matrix : First rotate around Z with alfa, then around the new Y with beta, then around new Z with gamma.
void	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.
void	GetEulerZYX (double &Alfa, double &Beta, double &Gamma) const
	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.
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 &rotaxis, double angle)
	Along an arbitrary axes. It is not necessary to normalize rotaxis. returns identity rotation matrix in the case that the norm of rotaxis is too 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)
	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.
static Rotation	RPY (double roll, double pitch, double yaw)
	Sets the value of this object to a rotation specified with RPY convention: first rotate around X with roll, then around the old Y with pitch, then around old Z with alfa.
static Rotation	EulerZYX (double Alfa, double Beta, double Gamma)
	Gives back a rotation matrix specified with EulerZYX convention : First rotate around Z with alfa, then around the new Y with beta, then around new X with gamma.

Public Attributes
double	data [9]

Friends
class	Frame
Rotation	operator* (const Rotation &lhs, const Rotation &rhs)
bool	operator== (const Rotation &a, const Rotation &b)
	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 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 collumns [ 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 298 of file frames.hpp.

Constructor & Destructor Documentation

◆ Rotation() [1/3]

KDL::Rotation::Rotation ( )

inline

Definition at line 303 of file frames.hpp.

◆ Rotation() [2/3]

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

inline

Definition at line 508 of file frames.hpp.

◆ Rotation() [3/3]

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

inline

Definition at line 518 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 561 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 577 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 593 of file frames.hpp.

◆ EulerZYX()

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

inlinestatic

Gives back a rotation matrix specified with EulerZYX convention : First rotate around Z with alfa, then around the new Y with beta, then around new X with gamma.

closely related to RPY-convention

Definition at line 435 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.

Definition at line 220 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

Closely related to RPY-convention.

Definition at line 450 of file frames.hpp.

◆ GetEulerZYZ()

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

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

Variables are bound by (-PI <= alfa <= PI), (0 <= beta <= PI), (-PI <= alfa <= PI)

Definition at line 233 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 297 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 choosen to be +/- Z-axis in the case of angle == PI : 2 solutions, positive Z-component of the axis is choosen.

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 choosen to be +/- Z-axis in the case of angle == PI : 2 solutions, positive Z-component of the axis is choosen.

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

Definition at line 354 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 alfa

Definition at line 207 of file frames.cpp.

◆ getValue()

void Rotation::getValue ( float * oglmat ) const

inline

Definition at line 665 of file frames.hpp.

◆ GetXZRot()

Vector2 KDL::Rotation::GetXZRot ( ) const

Returns a 2D vector representing the equivalent rotation in the XZ plane that brings the Y axis onto the Matrix Y axis and its norm is angle.

Definition at line 330 of file frames.cpp.

◆ Identity()

Rotation Rotation::Identity ( )

inlinestatic

Gives back an identity rotaton matrix.

Definition at line 557 of file frames.hpp.

◆ Inverse() [1/4]

Rotation Rotation::Inverse ( ) const

inline

Gives back the inverse rotation matrix of *this.

Definition at line 642 of file frames.hpp.

◆ Inverse() [2/4]

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

inline

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

Definition at line 201 of file frames.hpp.

◆ Inverse() [3/4]

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

inline

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

Definition at line 649 of file frames.hpp.

◆ Inverse() [4/4]

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

inline

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

Definition at line 196 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 498 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 503 of file frames.hpp.

◆ operator*() [1/3]

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 540 of file frames.hpp.

◆ operator*() [2/3]

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 531 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 549 of file frames.hpp.

◆ operator=()

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

inline

Definition at line 525 of file frames.hpp.

◆ Ortho()

void KDL::Rotation::Ortho ( )

Definition at line 169 of file frames.cpp.

◆ Rot()

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

static

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

Definition at line 250 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 273 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 610 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 615 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 620 of file frames.hpp.

◆ RPY()

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

static

Sets the value of this object to a rotation specified with RPY convention: first rotate around X with roll, then around the old Y with pitch, then around old Z with alfa.

Definition at line 195 of file frames.cpp.

◆ SetInverse()

void Rotation::SetInverse ( )

inline

Sets the value of *this to its inverse.

Definition at line 673 of file frames.hpp.

◆ setValue()

void Rotation::setValue ( float * oglmat )

inline

Definition at line 657 of file frames.hpp.