#include <visp3/core/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)

	vpRzyxVector (const vpColVector &rzyx)

virtual	~vpRzyxVector ()

vpRzyxVector	buildFrom (const vpRotationMatrix &R)

vpRzyxVector	buildFrom (const vpThetaUVector &R)

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

vpRzyxVector &	operator= (const vpColVector &rzyx)

vpRzyxVector &	operator= (double x)

Inherited functionalities from vpRotationVector
double &	operator[] (unsigned int i)

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

vpColVector	operator* (double x) const

double	sumSquare () const

vpRowVector	t () const

Inherited functionalities from vpArray2D
double	getMinValue () const

double	getMaxValue () const

unsigned int	getRows () const

unsigned int	getCols () const

unsigned int	size () const

void	resize (const unsigned int nrows, const unsigned int ncols, const bool flagNullify=true)

Static Public Member Functions
Inherited I/O from vpArray2D with Static Public Member Functions
static bool	load (const std::string &filename, vpArray2D< double > &A, const bool binary=false, char *header=NULL)

static bool	loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=NULL)

static bool	save (const std::string &filename, const vpArray2D< double > &A, const bool binary=false, const char *header="")

static bool	saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="")

Public Attributes
double *	data

Protected Attributes
unsigned int	rowNum

unsigned int	colNum

double **	rowPtrs

unsigned int	dsize

Related Functions
(Note that these are not member functions.)
vpColVector	operator* (const double &x, const vpRotationVector &v)

enum	vpGEMMmethod

Detailed Description

Implementation of a rotation vector as $R(z,y,x)$ Euler angle minimal representation.

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 vpRzyxVector class is derived from vpRotationVector.

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 <visp3/core/vpMath.h>
#include <visp3/core/vpRotationMatrix.h>
#include <visp3/core/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;
}

Examples:: testPoseRansac2.cpp.

Definition at line 152 of file vpRzyxVector.h.

Constructor & Destructor Documentation

vpRzyxVector::vpRzyxVector ( )

Default constructor that initialize all the 3 angles to zero.

Definition at line 51 of file vpRzyxVector.cpp.

vpRzyxVector::vpRzyxVector ( const vpRzyxVector & rzyx )

Copy constructor.

Definition at line 56 of file vpRzyxVector.cpp.

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

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 66 of file vpRzyxVector.cpp.

References buildFrom().

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 77 of file vpRzyxVector.cpp.

References buildFrom().

vpRzyxVector::vpRzyxVector ( const vpThetaUVector & tu )

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

Parameters

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

Definition at line 89 of file vpRzyxVector.cpp.

References buildFrom().

vpRzyxVector::vpRzyxVector ( const vpColVector & rzyx )

Copy constructor from a 3-dimension vector.

Definition at line 96 of file vpRzyxVector.cpp.

References vpArray2D< double >::data, vpException::dimensionError, and vpArray2D< Type >::size().

virtual vpRzyxVector::~vpRzyxVector ( )

inlinevirtual

Destructor.

Definition at line 167 of file vpRzyxVector.h.

Member Function Documentation

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 117 of file vpRzyxVector.cpp.

Referenced by buildFrom(), and vpRzyxVector().

vpRzyxVector vpRzyxVector::buildFrom ( const vpThetaUVector & tu )

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

Parameters

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

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

Definition at line 150 of file vpRzyxVector.cpp.

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

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

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 166 of file vpRzyxVector.cpp.

References vpArray2D< double >::data.

unsigned int vpArray2D< double >::getCols ( ) const

inlineinherited

Return the number of columns of the 2D array.

Examples:: servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, and testTranslationVector.cpp.

Definition at line 154 of file vpArray2D.h.

References vpArray2D< Type >::colNum.

Referenced by vpRowVector::csvPrint(), vpMatrix::csvPrint(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpRowVector::maplePrint(), vpMatrix::maplePrint(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpRowVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), vpMatrix::row(), and vpMatrix::svd().

double vpArray2D< double >::getMaxValue ( ) const

inherited

Return the array max value.

Examples:: servoMomentImage.cpp.

double vpArray2D< double >::getMinValue ( ) const

inherited

Return the array min value.

Examples:: servoMomentImage.cpp.

unsigned int vpArray2D< double >::getRows ( ) const

inlineinherited

Return the number of rows of the 2D array.

Examples:: testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, and testTranslationVector.cpp.

Definition at line 152 of file vpArray2D.h.

References vpArray2D< Type >::rowNum.

Referenced by vpMatrix::column(), vpColVector::cppPrint(), vpMatrix::cppPrint(), vpColVector::csvPrint(), vpMatrix::csvPrint(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpColVector::maplePrint(), vpMatrix::maplePrint(), vpColVector::matlabPrint(), vpMatrix::matlabPrint(), vpColVector::operator+(), vpColVector::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpPoseVector::print(), vpColVector::print(), vpMatrix::print(), and vpMatrix::pseudoInverse().

static bool vpArray2D< double >::load	(	const std::string &	filename,
		vpArray2D< double > &	A,
		const bool	binary = `false`,
		char *	header = `NULL`
	)

inlinestaticinherited

Load a matrix from a file.

Parameters

filename	: Absolute file name.
A	: Array to be loaded
binary	: If true the matrix is loaded from a binary file, else from a text file.
header	: Header of the file is loaded in this parameter.

Returns: Returns true if success.

See Also: save()

Definition at line 308 of file vpArray2D.h.

References vpException::badValue, and vpArray2D< Type >::resize().

static bool vpArray2D< double >::loadYAML	(	const std::string &	filename,
		vpArray2D< double > &	A,
		char *	header = `NULL`
	)

inlinestaticinherited

Load an array from a YAML-formatted file.

Parameters

filename	: absolute file name.
A	: array to be loaded from the file.
header	: header of the file is loaded in this parameter.

Returns: Returns true on success.

See Also: saveYAML()

Definition at line 417 of file vpArray2D.h.

References vpArray2D< Type >::resize().

vpColVector vpRotationVector::operator* ( double x ) const

inherited

Operator that allows to multiply each element of a rotation vector by a scalar.

Parameters

x	: The scalar.

Returns: The rotation vector multiplied by the scalar as a column vector. The current rotation vector (*this) is unchanged.

Definition at line 76 of file vpRotationVector.cpp.

References vpArray2D< double >::dsize.

vpRzyxVector & vpRzyxVector::operator= ( const vpColVector & rzyx )

Copy operator that initializes a $R_{zyx}=(\varphi,\theta,\psi)$ Euler angles vector from a 3-dimension column vector.

Parameters

rzyx	: 3-dimension vector containing the values of the rotation vector.

#include <visp3/core/vpRzyxVector.h>
int main()
{
  vpColVector v(3);
  v[0] = 0.1;
  v[1] = 0.2;
  v[2] = 0.3;
  vpRzyxVector rzyx;
  rzyx = v;
  // rzyx is now equal to v : 0.1, 0.2, 0.3
}

Definition at line 222 of file vpRzyxVector.cpp.

References vpArray2D< double >::data, vpException::dimensionError, and vpArray2D< Type >::size().

vpRzyxVector & vpRzyxVector::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 <visp3/core/vpMath.h>
#include <visp3/core/vpRzyxVector.h>
int main()
{
  vpRzyxVector v;
  // Initialise the rotation vector
  v = vpMath::rad( 45.f); // All the 3 angles are set to 45 degrees
}

Definition at line 192 of file vpRzyxVector.cpp.

References vpArray2D< double >::data, and vpArray2D< double >::dsize.

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

inlineinherited

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

Definition at line 126 of file vpRotationVector.h.

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

inlineinherited

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

Definition at line 131 of file vpRotationVector.h.

void vpArray2D< double >::resize	(	const unsigned int	nrows,
		const unsigned int	ncols,
		const bool	flagNullify = `true`
	)

inlineinherited

Set the size of the array and initialize all the values to zero.

Parameters

nrows	: number of rows.
ncols	: number of column.
flagNullify	: if true, then the array is re-initialized to 0 after resize. If false, the initial values from the common part of the array (common part between old and new version of the array) are kept. Default value is true.

Examples:: testArray2D.cpp, testMatrix.cpp, testMatrixInverse.cpp, and testSvd.cpp.

Definition at line 167 of file vpArray2D.h.

References vpArray2D< Type >::colNum, vpArray2D< Type >::data, vpArray2D< Type >::dsize, vpException::memoryAllocationError, vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::diag(), vpMatrix::eye(), vpMatrix::init(), and vpMatrix::operator=().

static bool vpArray2D< double >::save	(	const std::string &	filename,
		const vpArray2D< double > &	A,
		const bool	binary = `false`,
		const char *	header = `""`
	)

inlinestaticinherited

Save a matrix to a file.

Parameters

filename	: Absolute file name.
A	: Array to be saved.
binary	: If true the matrix is saved in a binary file, else a text file.
header	: Optional line that will be saved at the beginning of the file.

Returns: Returns true if success.

Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.

See Also: load()

Definition at line 499 of file vpArray2D.h.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

static bool vpArray2D< double >::saveYAML	(	const std::string &	filename,
		const vpArray2D< double > &	A,
		const char *	header = `""`
	)

inlinestaticinherited

Save an array in a YAML-formatted file.

Parameters

filename	: absolute file name.
A	: array to be saved in the file.
header	: optional lines that will be saved at the beginning of the file. Should be YAML-formatted and will adapt to the indentation if any.

Returns: Returns true if success.

Here is an example of outputs.

vpArray2D<double> M(3,4);
vpArray2D::saveYAML("matrix.yml", M, "example: a YAML-formatted header");
vpArray2D::saveYAML("matrixIndent.yml", M, "example:\n    - a YAML-formatted header\n    - with inner indentation");

Content of matrix.yml:

example: a YAML-formatted header
rows: 3
cols: 4
data:
  - [0, 0, 0, 0]
  - [0, 0, 0, 0]
  - [0, 0, 0, 0]

Content of matrixIndent.yml:

example:
    - a YAML-formatted header
    - with inner indentation
rows: 3
cols: 4
data:
    - [0, 0, 0, 0]
    - [0, 0, 0, 0]
    - [0, 0, 0, 0]

See Also: loadYAML()

Definition at line 588 of file vpArray2D.h.

References vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

unsigned int vpArray2D< double >::size ( ) const

inlineinherited

Return the number of elements of the 2D array.

Examples:: testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testPoseVector.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testThread2.cpp, testTranslationVector.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, and tutorial-ibvs-4pts-wireframe-robot-viper.cpp.

Definition at line 156 of file vpArray2D.h.

References vpArray2D< Type >::colNum, and vpArray2D< Type >::rowNum.

Referenced by vpRowVector::insert(), vpColVector::insert(), and vpColVector::operator*().

double vpRotationVector::sumSquare ( ) const

inherited

Return the sum square of all the elements $r_{i}$ of the rotation vector r(m).

Returns: The value
$\sum{i=0}^{m} r_i^{2}$
.

Definition at line 101 of file vpRotationVector.cpp.

References vpArray2D< double >::rowNum, and vpArray2D< double >::rowPtrs.

vpRowVector vpRotationVector::t ( ) const

inherited

Return the transpose of the rotation vector.

Examples:: testViper650.cpp, and testViper850.cpp.

Definition at line 57 of file vpRotationVector.cpp.

References vpArray2D< double >::data, and vpArray2D< double >::dsize.

Friends And Related Function Documentation

vpColVector operator*	(	const double &	x,
		const vpRotationVector &	v
	)

Definition at line 89 of file vpRotationVector.cpp.

enum vpGEMMmethod

Operations are :

VP_GEMM_A_T to use the transpose matrix of A instead of the matrix A
VP_GEMM_B_T to use the transpose matrix of B instead of the matrix B
VP_GEMM_C_T to use the transpose matrix of C instead of the matrix C

Definition at line 57 of file vpGEMM.h.

Member Data Documentation

unsigned int vpArray2D< double >::colNum

protectedinherited

Number of columns in the array.

Definition at line 76 of file vpArray2D.h.

double * vpArray2D< double >::data

inherited

Address of the first element of the data array.

Examples:: testDisplacement.cpp, testMatrix.cpp, testPoseVector.cpp, and testTranslationVector.cpp.

Definition at line 84 of file vpArray2D.h.

Referenced by vpMatrix::AtA(), vpHomogeneousMatrix::buildFrom(), vpRzyzVector::buildFrom(), buildFrom(), vpRxyzVector::buildFrom(), vpThetaUVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), vpMatrix::euclideanNorm(), vpMatrix::expm(), vpThetaUVector::extract(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpColVector::operator*(), vpHomography::operator*(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpColVector::operator/(), vpHomography::operator/(), vpHomography::operator/=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpRzyzVector::operator=(), operator=(), vpRxyzVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpThetaUVector::operator=(), vpColVector::operator[](), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), vpMatrix::stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpQuaternionVector::vpQuaternionVector(), vpRxyzVector::vpRxyzVector(), vpRzyxVector(), vpRzyzVector::vpRzyzVector(), vpThetaUVector::vpThetaUVector(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

unsigned int vpArray2D< double >::dsize

protectedinherited

unsigned int vpArray2D< double >::rowNum

protectedinherited

Number of rows in the array.

Definition at line 74 of file vpArray2D.h.

double ** vpArray2D< double >::rowPtrs

protectedinherited

Address of the first element of each rows.

Definition at line 78 of file vpArray2D.h.

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Attributes

Related Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation