#include <visp3/core/vpThetaUVector.h>

Inheritance diagram for vpThetaUVector:

Public Member Functions
	vpThetaUVector ()

	vpThetaUVector (const vpThetaUVector &tu)

	vpThetaUVector (const vpHomogeneousMatrix &M)

	vpThetaUVector (const vpPoseVector &p)

	vpThetaUVector (const vpRotationMatrix &R)

	vpThetaUVector (const vpRzyxVector &rzyx)

	vpThetaUVector (const vpRzyzVector &rzyz)

	vpThetaUVector (const vpRxyzVector &rxyz)

	vpThetaUVector (const vpQuaternionVector &q)

	vpThetaUVector (const double tux, const double tuy, const double tuz)

virtual	~vpThetaUVector ()

vpThetaUVector	buildFrom (const vpHomogeneousMatrix &M)

vpThetaUVector	buildFrom (const vpPoseVector &p)

vpThetaUVector	buildFrom (const vpRotationMatrix &R)

vpThetaUVector	buildFrom (const vpRzyxVector &rzyx)

vpThetaUVector	buildFrom (const vpRzyzVector &zyz)

vpThetaUVector	buildFrom (const vpRxyzVector &xyz)

vpThetaUVector	buildFrom (const vpQuaternionVector &q)

void	buildFrom (const double tux, const double tuy, const double tuz)

vpThetaUVector &	operator= (double x)

void	extract (double &theta, vpColVector &u) const

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 $\theta {\bf u}$ axis-angle minimal representation.

Class that consider the case of the $\theta {\bf u}$ parameterization for the rotation.

The vpThetaUVector class is derived from vpRotationVector.

The $\theta {\bf u}$ representation is one of the minimal representation of a rotation matrix, where ${\bf u} = (u_{x} \; u_{y} \; u_{z})^{\top}$ is a unit vector representing the rotation axis and $\theta$ is the rotation angle.

From the $\theta {\bf u}$ representation it is possible to build the rotation matrix ${\bf R}$ using the Rodrigues formula:

${\bf R} = {\bf I}_{3} + (1 - \cos{ \theta}) \; {\bf u u}^{\top} + \sin{ \theta} \; [{\bf u}]_{\times}$

with ${\bf I}_{3}$ the identity matrix of dimension $3\times3$ and $[{\bf u}]_{\times}$ the skew matrix:

$[{\bf u}]_{\times} = \left( \begin{array}{ccc} 0 & -u_{z} & u_{y} \\ u_{z} & 0 & -u_{x} \\ -u_{y} & u_{x} & 0 \end{array} \right)$

From the implementation point of view, it is nothing more than an array of three floats.

The code below shows first how to initialize a $\theta {\bf u}$ vector, than how to contruct a rotation matrix from a vpThetaUVector and finaly how to extract the theta U angles from the build rotation matrix.

#include <iostream>
#include <visp3/core/vpMath.h>
#include <visp3/core/vpRotationMatrix.h>
#include <visp3/core/vpThetaUVector.h>
int main()
{
  vpThetaUVector tu;
  // Initialise the theta U rotation vector
  tu[0] = vpMath::rad( 45.f); 
  tu[1] = vpMath::rad(-30.f); 
  tu[2] = vpMath::rad( 90.f); 
  // Construct a rotation matrix from the theta U angles
  vpRotationMatrix R(tu);
  // Extract the theta U angles from a rotation matrix
  tu.buildFrom(R);
  // Print the extracted theta U angles. Values are the same than the
  // one used for initialization
  std::cout << tu; 
  // Since the rotation vector is 3 values column vector, the
  // transpose operation produce a row vector.
  vpRowVector tu_t = tu.t();
  
  // Print the transpose row vector
  std::cout << tu_t << std::endl;
}

Examples:: calibrateTsai.cpp, exponentialMap.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, testDisplacement.cpp, testFeature.cpp, testPoseVector.cpp, and tutorial-homography-from-points.cpp.

Definition at line 147 of file vpThetaUVector.h.

Constructor & Destructor Documentation

vpThetaUVector::vpThetaUVector ( )

Default constructor that initialize all the 3 angles to zero.

Definition at line 52 of file vpThetaUVector.cpp.

vpThetaUVector::vpThetaUVector ( const vpThetaUVector & tu )

Copy constructor.

Definition at line 56 of file vpThetaUVector.cpp.

vpThetaUVector::vpThetaUVector ( const vpHomogeneousMatrix & M )

Initialize a $\theta {\bf u}$ vector from an homogeneous matrix.

Definition at line 63 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpPoseVector & p )

Initialize a $\theta {\bf u}$ vector from a pose vector.

Definition at line 71 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpRotationMatrix & R )

Initialize a $\theta {\bf u}$ vector from a rotation matrix.

Definition at line 79 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpRzyxVector & rzyx )

Initialize a $\theta {\bf u}$ vector from an Euler z-y-x representation vector.

Definition at line 89 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpRzyzVector & rzyz )

Initialize a $\theta {\bf u}$ vector from an Euler z-y-z representation vector.

Definition at line 98 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpRxyzVector & rxyz )

Initialize a $\theta {\bf u}$ vector from an Euler x-y-z representation vector.

Definition at line 107 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpQuaternionVector & q )

Initialize a $\theta {\bf u}$ vector from a quaternion representation vector.

Definition at line 116 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector	(	const double	tux,
		const double	tuy,
		const double	tuz
	)

Build a $\theta {\bf u}$ vector from 3 angles in radian.

Definition at line 125 of file vpThetaUVector.cpp.

References buildFrom().

virtual vpThetaUVector::~vpThetaUVector ( )

inlinevirtual

Destructor.

Definition at line 173 of file vpThetaUVector.h.

Member Function Documentation

vpThetaUVector vpThetaUVector::buildFrom ( const vpHomogeneousMatrix & M )

Converts an homogeneous matrix into a $\theta {\bf u}$ vector.

Examples:: exponentialMap.cpp, and tutorial-homography-from-points.cpp.

Definition at line 135 of file vpThetaUVector.cpp.

References vpHomogeneousMatrix::extract().

Referenced by vpPoseVector::buildFrom(), buildFrom(), vpHomogeneousMatrix::extract(), vpRotationMatrix::getThetaUVector(), vpRobotAfma6::getVelocity(), vpRobotViper850::getVelocity(), vpRobotViper650::getVelocity(), vpExponentialMap::inverse(), vpSimulatorAfma6::setPosition(), and vpThetaUVector().

vpThetaUVector vpThetaUVector::buildFrom ( const vpPoseVector & p )

Converts a pose vector into a $\theta {\bf u}$ vector copying the $\theta {\bf u}$ values contained in the pose vector.

Definition at line 149 of file vpThetaUVector.cpp.

References vpArray2D< double >::data.

vpThetaUVector vpThetaUVector::buildFrom ( const vpRotationMatrix & R )

Converts a rotation matrix into a $\theta {\bf u}$ vector.

Definition at line 161 of file vpThetaUVector.cpp.

References vpArray2D< double >::data, and vpMath::sinc().

vpThetaUVector vpThetaUVector::buildFrom ( const vpRzyxVector & rzyx )

Build a $\theta {\bf u}$ vector from an Euler z-y-x representation vector.

Definition at line 211 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector vpThetaUVector::buildFrom ( const vpRzyzVector & rzyz )

Build a $\theta {\bf u}$ vector from an Euler z-y-z representation vector.

Definition at line 223 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector vpThetaUVector::buildFrom ( const vpRxyzVector & rxyz )

Build a $\theta {\bf u}$ vector from an Euler x-y-z representation vector.

Definition at line 235 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector vpThetaUVector::buildFrom ( const vpQuaternionVector & q )

Build a $\theta {\bf u}$ vector from a quaternion representation vector.

Definition at line 248 of file vpThetaUVector.cpp.

References buildFrom().

void vpThetaUVector::buildFrom	(	const double	tux,
		const double	tuy,
		const double	tuz
	)

Build a $\theta {\bf u}$ vector from 3 angles in radian.

Definition at line 315 of file vpThetaUVector.cpp.

References vpArray2D< double >::data.

void vpThetaUVector::extract	(	double &	theta,
		vpColVector &	u
	)		const

Extract the rotation angle $\theta$ and the unit vector $\bf u$ from the $\theta {\bf u}$ representation.

Parameters

theta	: Rotation angle $\theta$ .
u	: Unit vector ${\bf u} = (u_{x},u_{y},u_{z})^{\top}$ representing the rotation axis.

Definition at line 297 of file vpThetaUVector.cpp.

References vpArray2D< double >::data, and vpColVector::resize().

Referenced by vpQuaternionVector::buildFrom().

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 vpMatrix::csvPrint(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpMatrix::maplePrint(), vpRowVector::operator*(), vpRowVector::operator+(), vpRowVector::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpForceTwistMatrix::print(), vpVelocityTwistMatrix::print(), vpRowVector::print(), vpMatrix::print(), vpMatrix::pseudoInverse(), 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::cppPrint(), vpMatrix::csvPrint(), vpRotationMatrix::getCol(), vpHomogeneousMatrix::getCol(), vpMatrix::getCol(), vpMatrix::getRow(), vpMatrix::inverseByCholeskyLapack(), vpMatrix::inverseByQRLapack(), vpMatrix::kernel(), vpMatrix::maplePrint(), 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 392 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.

vpThetaUVector & vpThetaUVector::operator= ( double v )

Initialize each element of the $\theta {\bf u}$ vector to the same angle value v.

Parameters

v	: Angle value to set for each element of the $\theta {\bf u}$ vector.

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

Definition at line 277 of file vpThetaUVector.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 >::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 468 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 560 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, testRowVector.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 >::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:: 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(), vpRzyxVector::buildFrom(), vpRzyzVector::buildFrom(), vpRxyzVector::buildFrom(), buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), vpColVector::euclideanNorm(), vpMatrix::euclideanNorm(), vpMatrix::expm(), extract(), 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=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpRzyxVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpMatrix::operator=(), operator=(), vpColVector::operator[](), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), vpMatrix::stackRows(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), 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