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
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)
void	DoRotY (double angle)
void	DoRotZ (double angle)
void	Ortho ()
Vector	GetRot () const
Vector2	GetXZRot () const
double	GetRotAngle (Vector &axis, double eps=epsilon) const
void	GetEulerZYZ (double &alfa, double &beta, double &gamma) const
void	GetRPY (double &roll, double &pitch, double &yaw) const
void	GetEulerZYX (double &Alfa, double &Beta, double &Gamma) const
Twist	operator* (const Twist &arg) const
Wrench	operator* (const Wrench &arg) const
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)
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	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)
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 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 296 of file frames.hpp.

Constructor & Destructor Documentation

KDL::Rotation::Rotation ( ) [inline]

Definition at line 301 of file frames.hpp.

References Identity().

Referenced by EulerZYZ(), Rot(), Rot2(), KDL::RotationVel::RotX(), KDL::RotationVel::RotY(), KDL::RotationVel::RotZ(), and RPY().

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.inl.

References data.

Rotation::Rotation	(	const Vector &	x,
		const Vector &	y,
		const Vector &	z
	)		`[inline]`

Definition at line 509 of file frames.inl.

References KDL::Vector::data, and data.

Member Function Documentation

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

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

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

static Rotation KDL::Rotation::EulerZYX	(	double	Alfa,
		double	Beta,
		double	Gamma
	)		`[inline, static]`

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 433 of file frames.hpp.

References RPY().

Referenced by posrandom(), and random().

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.

References KDL::cos(), Rotation(), and KDL::sin().

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 448 of file frames.hpp.

References GetRPY().

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.

References KDL::atan2(), data, KDL::epsilon, fabs(), KDL::PI, KDL::sqr(), and KDL::sqrt().

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.

References KDL::atan2(), KDL::Vector::data, data, KDL::epsilon, KDL::Vector::Norm(), and KDL::PI.

Referenced by GetJointRotation().

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.

References KDL::acos(), angle(), data, KDL::PI, KDL::sin(), and KDL::sqrt().

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.

References KDL::atan2(), data, KDL::epsilon, fabs(), KDL::PI, KDL::sign(), KDL::sqr(), and KDL::sqrt().

Referenced by GetEulerZYX().

void KDL::Rotation::getValue ( float * oglmat ) const [inline]

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.

References KDL::acos(), data, KDL::epsilon, norm(), KDL::Vector2::Normalize(), and KDL::PI.

Referenced by GetJointRotation().

static Rotation KDL::Rotation::Identity ( ) [inline, static]

Gives back an identity rotaton matrix.

Referenced by Rotation().

Rotation KDL::Rotation::Inverse ( ) const [inline]

Gives back the inverse rotation matrix of *this.

Referenced by base_callback(), iTaSC::updateJoint(), and iTaSC::MovingFrame::updateKinematics().

Vector KDL::Rotation::Inverse ( const Vector & v ) const [inline]

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

Twist KDL::Rotation::Inverse ( const Twist & arg ) const [inline]

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

Wrench KDL::Rotation::Inverse ( const Wrench & arg ) const [inline]

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

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.inl.

References data, and FRAMES_CHECKI.

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.

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.

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

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.

Rotation& KDL::Rotation::operator= ( const Rotation & arg ) [inline]

void KDL::Rotation::Ortho ( )

Definition at line 169 of file frames.cpp.

References data, credits_svn_gen::e, KDL::sqr(), and KDL::sqrt().

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 to small to be used.

Definition at line 250 of file frames.cpp.

References KDL::cos(), KDL::Vector::Normalize(), Rotation(), and KDL::sin().

Referenced by KDL::Frame2::Integrate().

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.

References KDL::cos(), Rotation(), and KDL::sin().

static Rotation KDL::Rotation::RotX ( double angle ) [inline, static]

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

Referenced by KDL::Joint::pose(), and RemoveEulerAngleFromMatrix().

static Rotation KDL::Rotation::RotY ( double angle ) [inline, static]

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

Referenced by KDL::Joint::pose(), and RemoveEulerAngleFromMatrix().

static Rotation KDL::Rotation::RotZ ( double angle ) [inline, static]

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

Referenced by KDL::Joint::pose(), and RemoveEulerAngleFromMatrix().

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.

References KDL::cos(), Rotation(), and KDL::sin().

Referenced by EulerZYX().

void KDL::Rotation::SetInverse ( ) [inline]

Sets the value of *this to its inverse.

void KDL::Rotation::setValue ( float * oglmat ) [inline]

Referenced by convert_pose().

void KDL::Rotation::UnitX ( const Vector & X ) [inline]