#include <vpRzyxVector.h>

Inheritance diagram for vpRzyxVector:

Public Member Functions
	vpRzyxVector ()

	vpRzyxVector (const vpRzyxVector &rzyx)

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

	vpRzyxVector (const vpRotationMatrix &R)

	vpRzyxVector (const vpThetaUVector &tu)

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

vpRzyxVector	buildFrom (const vpRotationMatrix &R)

vpRzyxVector	buildFrom (const vpThetaUVector &R)

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 $(\varphi,\theta,\psi)$ angle using the z-y-x convention, where $(\varphi,\theta,\psi)$ are respectively the rotation angles around the $z$ , $y$ and $x$ axis.

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

with

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

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

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

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

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

Definition at line 151 of file vpRzyxVector.h.

Constructor & Destructor Documentation

vpRzyxVector::vpRzyxVector ( )

inline

Default constructor that initialize all the angles to zero.

Definition at line 158 of file vpRzyxVector.h.

vpRzyxVector::vpRzyxVector ( const vpRzyxVector & rzyx )

inline

Copy constructor.

Definition at line 160 of file vpRzyxVector.h.

vpRzyxVector::vpRzyxVector	(	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 168 of file vpRzyxVector.h.

References vpRotationVector::r.

vpRzyxVector::vpRzyxVector ( const vpRotationMatrix & R )

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

Parameters

R	: Rotation matrix used to initialize the Euler angles.

Definition at line 59 of file vpRzyxVector.cpp.

References buildFrom().

vpRzyxVector::vpRzyxVector ( const vpThetaUVector & tu )

Constructor that initialize $R_{zyx}=(\varphi,\theta,\psi)$ 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 71 of file vpRzyxVector.cpp.

References buildFrom().

Member Function Documentation

void vpRzyxVector::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.

Definition at line 183 of file vpRzyxVector.h.

References vpRotationVector::r.

Referenced by buildFrom(), and vpRzyxVector().

vpRzyxVector vpRzyxVector::buildFrom ( const vpRotationMatrix & R )

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

Source: R. Paul, Robot Manipulators: Mathematics, Programming, and Control. MIT Press, 1981, p. 71

Parameters

R	: Rotation matrix used as input.

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

Definition at line 87 of file vpRzyxVector.cpp.

References vpRotationVector::r.

vpRzyxVector vpRzyxVector::buildFrom ( const vpThetaUVector & tu )

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

Parameters

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

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

Definition at line 122 of file vpRzyxVector.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.

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.