#include <vpRzyzVector.h>

Inheritance diagram for vpRzyzVector:

Public Member Functions
	vpRzyzVector ()

	vpRzyzVector (const vpRzyzVector &rzyz)

	vpRzyzVector (const double phi, const double theta, const double psi)

	vpRzyzVector (const vpRotationMatrix &R)

	vpRzyzVector (const vpThetaUVector &tu)

void	buildFrom (const double phi, const double theta, const double psi)

vpRzyzVector	buildFrom (const vpRotationMatrix &R)

vpRzyzVector	buildFrom (const vpThetaUVector &R)

vpRzyzVector &	operator= (double x)

double &	operator[] (unsigned int n)

const double &	operator[] (unsigned int n) const

unsigned int	size () const

vpRowVector	t () const

Protected Member Functions
void	init (const unsigned int size)

Protected Attributes
double *	r

unsigned int	_size

Friends
class	vpRotationMatrix

class	vpThetaUVector

Detailed Description

Class that consider the case of the Euler $(\varphi,\theta,\psi)$ angles using the z-y-z convention, where $(\varphi,\theta,\psi)$ are respectively the rotation angles around the $z$ , $y$ and $z$ axis.

$R_{zyz}(\varphi,\theta,\psi) = R_z(\varphi) \; R_y(\theta) \; R_z(\psi)$

with

$R_{z}(\varphi) = \left( \begin{array}{ccc} \cos \varphi & -\sin\varphi & 0\\ \sin\varphi &\cos \varphi& 0 \\ 0 & 0 & 1 \end{array} \right) \; R_{y}(\theta) = \left( \begin{array}{ccc} \cos \theta & 0 & \sin\theta\\ 0 & 1 & 0 \\ -\sin\theta & 0 &\cos \theta \end{array} \right) \; R_{z}(\psi) = \left( \begin{array}{ccc} \cos \psi & -\sin\psi & 0\\ \sin\psi &\cos \psi& 0 \\ 0 & 0 & 1 \end{array} \right)$

The rotation matrix corresponding to the z-y-z convention is given by:

$R_{zyz}(\varphi,\theta,\psi) = \left( \begin{array}{ccc} \cos\varphi \cos\theta \cos\psi - \sin\varphi\sin\psi & -\cos\varphi \cos\theta \sin\psi -\sin\varphi\cos\psi & \cos\varphi \sin\theta \\ \sin\varphi \cos\theta \cos\psi + \cos\varphi\sin\psi & -\sin\varphi \cos\theta \sin\psi +\cos\varphi\cos\psi & \sin\varphi \sin\theta \\ -\sin\theta \cos\psi & \sin\theta \sin\psi & \cos\theta \end{array} \right)$

The code below shows first how to initialize this representation of Euler angles, than how to contruct a rotation matrix from a vpRzyzVector and finaly how to extract the vpRzyzVector Euler angles from the build rotation matrix.

#include <visp/vpMath.h>
#include <visp/vpRotationMatrix.h>
#include <visp/vpRzyzVector.h>
int main()
{
  vpRzyzVector rzyz;
  // Initialise the Euler angles
  rzyz[0] = vpMath::rad( 45.f); // phi   angle in rad/s around z axis 
  rzyz[1] = vpMath::rad(-30.f); // theta angle in rad/s around y axis
  rzyz[2] = vpMath::rad( 90.f); // psi   angle in rad/s around z axis
  // Construct a rotation matrix from the Euler angles
  vpRotationMatrix R(rzyz);
  // Extract the Euler angles around z,y,z axis from a rotation matrix
  rzyz.buildFrom(R);
  // Print the extracted Euler angles. Values are the same than the
  // one used for initialization
  std::cout << rzyz; 
  // Since the rotation vector is 3 values column vector, the
  // transpose operation produce a row vector.
  vpRowVector rzyz_t = rzyz.t();
  
  // Print the transpose row vector
  std::cout << rzyz_t << std::endl;
}

Examples:: testRobotViper850.cpp, and testViper850.cpp.

Definition at line 150 of file vpRzyzVector.h.

Constructor & Destructor Documentation

vpRzyzVector::vpRzyzVector ( )

inline

Default constructor that initialize all the angles to zero.

Definition at line 157 of file vpRzyzVector.h.

vpRzyzVector::vpRzyzVector ( const vpRzyzVector & rzyz )

inline

Copy constructor.

Definition at line 159 of file vpRzyzVector.h.

vpRzyzVector::vpRzyzVector	(	const double	phi,
		const double	theta,
		const double	psi
	)

inline

Constructor from 3 angles (in radian).

Parameters

phi	: $\varphi$ angle around the axis.
theta	: $\theta$ angle around the axis.
psi	: $\psi$ angle around the axis.

Definition at line 167 of file vpRzyzVector.h.

References vpRotationVector::r.

vpRzyzVector::vpRzyzVector ( const vpRotationMatrix & R )

Constructor that initialize $R_{zyz}=(\varphi,\theta,\psi)$ Euler angles from a rotation matrix.

Parameters

R	: Rotation matrix used to initialize the Euler angles.

Definition at line 59 of file vpRzyzVector.cpp.

References buildFrom().

vpRzyzVector::vpRzyzVector ( const vpThetaUVector & tu )

Constructor that initialize $R_{zyz}=(\varphi,\theta,\psi)$ Euler angles vector from a $\theta u$ vector.

Parameters

tu	: $\theta u$ representation of a rotation used here as input to initialize the Euler angles.

Definition at line 70 of file vpRzyzVector.cpp.

References buildFrom().

Member Function Documentation

void vpRzyzVector::buildFrom	(	const double	phi,
		const double	theta,
		const double	psi
	)

inline

Construction from 3 angles (in radian).

Parameters

phi	: $\varphi$ angle around the axis.
theta	: $\theta$ angle around the axis.
psi	: $\psi$ angle around the axis.

Examples:: testRobotViper850.cpp, and testViper850.cpp.

Definition at line 182 of file vpRzyzVector.h.

References vpRotationVector::r.

Referenced by buildFrom(), and vpRzyzVector().

vpRzyzVector vpRzyzVector::buildFrom ( const vpRotationMatrix & R )

Convert a rotation matrix into a $R_{zyz}=(\varphi,\theta,\psi)$ Euler angles vector.

Parameters

R	: Rotation matrix used as input.

Returns: $R_{zyz}=(\varphi,\theta,\psi)$ Euler angles vector.

Definition at line 84 of file vpRzyzVector.cpp.

References vpRotationVector::r.

vpRzyzVector vpRzyzVector::buildFrom ( const vpThetaUVector & tu )

Convert a $\theta u$ vector into a $R_{zyz}=(\varphi,\theta,\psi)$ Euler angles vector.

Parameters

tu	: $\theta u$ representation of a rotation used here as input.

Returns: $R_{zyz}=(\varphi,\theta,\psi)$ Euler angles vector.

Definition at line 114 of file vpRzyzVector.cpp.

References vpRotationMatrix::buildFrom(), and buildFrom().

void vpRotationVector::init ( const unsigned int size )

protectedinherited

Definition at line 117 of file vpRotationVector.cpp.

References vpRotationVector::_size, and vpRotationVector::r.

vpRzyzVector & vpRzyzVector::operator= ( double v )

Initialize each element of the vector to the same angle value v.

Parameters

v	: Angle value to set for each element of the vector.

#include <visp/vpMath.h>
#include <visp/vpRzyzVector.h>
int main()
{
  vpRzyzVector r;
  // Initialise the rotation vector
  r = vpMath::rad( 45.f); // All the 3 angles are set to 45 degrees
}

Definition at line 143 of file vpRzyzVector.cpp.

References vpRotationVector::r.

double& vpRotationVector::operator[] ( unsigned int n )

inlineinherited

Operator that allows to set the value of an element of the rotation vector: r[i] = value

Definition at line 130 of file vpRotationVector.h.

const double& vpRotationVector::operator[] ( unsigned int n ) const

inlineinherited

Operator that allows to get the value of an element of the rotation vector: value = r[i]

Definition at line 135 of file vpRotationVector.h.

unsigned int vpRotationVector::size ( ) const

inherited

Returns the size of the rotation vector

Size of the rotation vector: number of double values describing the rotation. Common sizes are 4 for a quaternion and 3 for angle-based rotation vectors.

Definition at line 71 of file vpRotationVector.cpp.

References vpRotationVector::_size.

Referenced by vpRotationVector::operator=().

vpRowVector vpRotationVector::t ( ) const

inherited

Return the transpose of the rotation vector.