Public Member Functions | Static Public Member Functions | Public Attributes | Friends
KDL::Rotation Class Reference

represents rotations in 3 dimensional space. More...

#include <frames.hpp>

List of all members.

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.
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.
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.
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)
void SetInverse ()
 Sets the value of *this to its inverse.
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 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.
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.
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 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!=()
Rotation operator* (const Rotation &lhs, const Rotation &rhs)
bool operator== (const Rotation &a, const Rotation &b)
 The literal equality operator==(), also identical.

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 292 of file frames.hpp.

Constructor & Destructor Documentation

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

Definition at line 297 of file frames.hpp.

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]

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 460 of file frames.hpp.

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 256 of file frames.cpp.

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 484 of file frames.hpp.

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 269 of file frames.cpp.

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 198 of file frames.cpp.

Vector KDL::Rotation::GetRot ( ) const

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

Definition at line 330 of file frames.cpp.

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

Returns the rotation angle around the equiv. axis

Parameters:
axisthe 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 Taken from Wikipedia http://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation

Parameters:
axisthe rotation axis is returned in this variable
eps: in the case of angle == 0 : rot axis is undefined and choosen to be the 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 355 of file frames.cpp.

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 243 of file frames.cpp.

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

Gives back an identity rotaton matrix.

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

Gives back the inverse rotation matrix of *this.

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

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

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

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

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

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

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

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

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.

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.
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.
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

Definition at line 184 of file frames.cpp.

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 287 of file frames.cpp.

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

Along an arbitrary axes. rotvec should be normalized.

Definition at line 297 of file frames.cpp.

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

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

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

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

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

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

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 yaw

Invariants:

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

Definition at line 231 of file frames.cpp.

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

Sets the value of *this to its inverse.

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

Access to the underlying unitvectors of the rotation matrix.

Definition at line 501 of file frames.hpp.

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

Access to the underlying unitvectors of the rotation matrix.

Definition at line 506 of file frames.hpp.

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

Access to the underlying unitvectors of the rotation matrix.

Definition at line 513 of file frames.hpp.

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

Access to the underlying unitvectors of the rotation matrix.

Definition at line 518 of file frames.hpp.

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

Access to the underlying unitvectors of the rotation matrix.

Definition at line 525 of file frames.hpp.

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

Access to the underlying unitvectors of the rotation matrix.

Definition at line 530 of file frames.hpp.

Friends And Related Function Documentation

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

Definition at line 153 of file frames.cpp.

friend class Frame [friend]

Definition at line 545 of file frames.hpp.

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

The literal inequality operator!=()

Rotation operator* ( const Rotation &  lhs,
const Rotation &  rhs 
) [friend]

Definition at line 167 of file frames.cpp.

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

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

Definition at line 372 of file frames.cpp.

Member Data Documentation

double KDL::Rotation::data[9]

Definition at line 295 of file frames.hpp.

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

orocos_kdl
Author(s): Ruben Smits, Erwin Aertbelien, Orocos Developers
autogenerated on Sat Dec 28 2013 17:17:26