represents rotations in 3 dimensional space. More...
#include <frames.hpp>
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. |
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
Definition at line 301 of file frames.hpp.
KDL::Rotation::Rotation | ( | ) | [inline] |
Definition at line 306 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] |
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:
Closely related to RPY-convention.
Invariants:
Definition at line 469 of file frames.hpp.
Rotation KDL::Rotation::EulerZYZ | ( | double | Alfa, |
double | Beta, | ||
double | Gamma | ||
) | [static] |
Gives back a rotation matrix specified with EulerZYZ convention :
EulerZYX(alpha,beta,gamma) == EulerZYX(alpha +/- PHI, -beta, gamma +/- 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 :
if beta == PI/2 or beta == -PI/2, multiple solutions for gamma and alpha exist. The solution where gamma==0 is chosen.
Invariants:
Closely related to RPY-convention.
Definition at line 493 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:
if beta==0 or beta==PI, then alpha and gamma are not unique, in this case gamma is chosen to be zero. Invariants:
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
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
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 the rotation angle around the equiv. axis
axis | the 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. |
Definition at line 352 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
convention :
if pitch == PI/2 or pitch == -PI/2, multiple solutions for gamma and alpha exist. The solution where roll==0 is chosen.
Invariants:
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.
Transformation of the base to which the twist is expressed. Complexity : 18M+12A
Transformation of the base to which the wrench is expressed. Complexity : 18M+12A
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
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] |
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:
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 510 of file frames.hpp.
void KDL::Rotation::UnitX | ( | const Vector & | X | ) | [inline] |
Access to the underlying unitvectors of the rotation matrix.
Definition at line 515 of file frames.hpp.
Vector KDL::Rotation::UnitY | ( | ) | const [inline] |
Access to the underlying unitvectors of the rotation matrix.
Definition at line 522 of file frames.hpp.
void KDL::Rotation::UnitY | ( | const Vector & | X | ) | [inline] |
Access to the underlying unitvectors of the rotation matrix.
Definition at line 527 of file frames.hpp.
Vector KDL::Rotation::UnitZ | ( | ) | const [inline] |
Access to the underlying unitvectors of the rotation matrix.
Definition at line 534 of file frames.hpp.
void KDL::Rotation::UnitZ | ( | const Vector & | X | ) | [inline] |
Access to the underlying unitvectors of the rotation matrix.
Definition at line 539 of file frames.hpp.
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 554 of file frames.hpp.
The literal inequality operator!=()
Definition at line 167 of file frames.cpp.
The literal equality operator==(), also identical.
Definition at line 388 of file frames.cpp.
double KDL::Rotation::data[9] |
Definition at line 304 of file frames.hpp.