KDL::Rotation Class Reference

represents rotations in 3 dimensional space. More...

#include <src/frames.hpp>

List of all members.

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 & operator= (const Rotation &arg)
Vector operator* (const Vector &v) const
 Defines a multiplication R*V between a Rotation R and a Vector V.
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.
void DoRotY (double angle)
 The DoRot.
void DoRotZ (double angle)
 The DoRot.
Vector GetRot () const
 Returns a vector with the direction of the equiv.
double GetRotAngle (Vector &axis, double eps=epsilon) const
 Returns the rotation angle around the equiv.
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 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
 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.
Twist operator* (const Twist &arg) const
 Transformation of the base to which the twist is expressed.
Wrench operator* (const Wrench &arg) const
 Transformation of the base to which the wrench is expressed.
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.
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 Quaternion (double x, double y, double z, double w)
 Sets the value of this object to a rotation 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)
 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 Equal (const Rotation &a, const Rotation &b, double eps=epsilon)
 do not use operator == because the definition of Equal(.,.
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

Constructor & Destructor Documentation

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

References Identity().

Referenced by RPY().

KDL::Rotation::Rotation ( double  Xx,
double  Yx,
double  Zx,
double  Xy,
double  Yy,
double  Zy,
double  Xz,
double  Yz,
double  Zz 
) [inline]
KDL::Rotation::Rotation ( const Vector &  x,
const Vector &  y,
const Vector &  z 
) [inline]

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

References RPY().

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.

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.

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)

References data.

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
Vector KDL::Rotation::GetRot (  )  const

Returns a vector with the direction of the equiv.

axis and its norm is angle

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] )

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

Referenced by KDL::RotationalInterpolation_SingleAxis::SetStartEnd().

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

Referenced by GetEulerZYX(), and KDL::KDLToolkitPlugin::loadConstructors().

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

Gives back an identity rotaton matrix.

Referenced by Rotation().

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.

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

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

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

Gives back the inverse rotation matrix of *this.

Referenced by KDL::RotationalInterpolation_SingleAxis::SetStartEnd().

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.

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

Rotation & KDL::Rotation::operator= ( const Rotation &  arg  )  [inline]
Rotation KDL::Rotation::Quaternion ( double  x,
double  y,
double  z,
double  w 
) [static]

Sets the value of this object to a rotation specified with Quaternion convention the norm of (x,y,z,w) should be equal to 1.

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.

Referenced by KDL::Path_Line::Path_Line().

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

Along an arbitrary axes. rotvec should be normalized.

Referenced by KDL::Joint::Joint(), KDL::RotationalInterpolation_SingleAxis::Pos(), and KDL::Joint::pose().

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().

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().

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().

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.

References Rotation().

Referenced by EulerZYX().

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

Sets the value of *this to its inverse.

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

Access to the underlying unitvectors of the rotation matrix.

References data.

Vector KDL::Rotation::UnitX (  )  const [inline]

Access to the underlying unitvectors of the rotation matrix.

References data.

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

Access to the underlying unitvectors of the rotation matrix.

References data.

Vector KDL::Rotation::UnitY (  )  const [inline]

Access to the underlying unitvectors of the rotation matrix.

References data.

Referenced by KDL::Path_Circle::Clone(), and KDL::Path_Circle::Write().

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

Access to the underlying unitvectors of the rotation matrix.

References data.

Vector KDL::Rotation::UnitZ (  )  const [inline]

Access to the underlying unitvectors of the rotation matrix.

References data.

Friends And Related Function Documentation

bool Equal ( const Rotation &  a,
const Rotation &  b,
double  eps = epsilon 
) [friend]

do not use operator == because the definition of Equal(.,.

) is slightly different. It compares whether the 2 arguments are equal in an eps-interval

friend class Frame [friend]
bool operator!= ( const Rotation &  a,
const Rotation &  b 
) [friend]

The literal inequality operator!=().

Rotation operator* ( const Rotation &  lhs,
const Rotation &  rhs 
) [friend]
bool operator== ( const Rotation &  a,
const Rotation &  b 
) [friend]

The literal equality operator==(), also identical.

Member Data Documentation

double KDL::Rotation::data[9]

Referenced by KDL::Equal(), GetEulerZYZ(), KDL::Frame::operator*(), KDL::operator*(), KDL::operator+(), UnitX(), UnitY(), and UnitZ().

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