Visual Servoing Platform  version 3.6.1 under development (2024-12-17)
Public Member Functions | Public Attributes | Related Functions | List of all members
vpThetaUVector Class Reference
core: Core module » Mathematics » Transformations

#include <visp3/core/vpThetaUVector.h>

+ Inheritance diagram for vpThetaUVector:

Public Member Functions

 vpThetaUVector ()
 
 vpThetaUVector (const vpThetaUVector &tu)
 
VP_EXPLICIT vpThetaUVector (const vpHomogeneousMatrix &M)
 
VP_EXPLICIT vpThetaUVector (const vpPoseVector &p)
 
VP_EXPLICIT vpThetaUVector (const vpRotationMatrix &R)
 
VP_EXPLICIT vpThetaUVector (const vpRzyxVector &rzyx)
 
VP_EXPLICIT vpThetaUVector (const vpRzyzVector &rzyz)
 
VP_EXPLICIT vpThetaUVector (const vpRxyzVector &rxyz)
 
VP_EXPLICIT vpThetaUVector (const vpQuaternionVector &q)
 
VP_EXPLICIT vpThetaUVector (const vpColVector &tu)
 
VP_EXPLICIT vpThetaUVector (const std::vector< double > &tu)
 
 vpThetaUVector (double tux, double tuy, double tuz)
 
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)
 
vpThetaUVector & buildFrom (const vpColVector &tu)
 
vpThetaUVector & buildFrom (const std::vector< double > &tu)
 
vpThetaUVector & buildFrom (const double &tux, const double &tuy, const double &tuz)
 
void extract (double &theta, vpColVector &u) const
 
double getTheta () const
 
vpColVector getU () const
 
vpThetaUVector & operator= (const vpColVector &tu)
 
vpThetaUVector & operator= (double x)
 
vpThetaUVector operator* (const vpThetaUVector &tu_b) const
 
vpThetaUVector & operator= (const std::initializer_list< double > &list)
 
Inherited functionalities from vpArray2D
unsigned int getCols () const
 
double getMaxValue () const
 
double getMinValue () const
 
unsigned int getRows () const
 
unsigned int size () const
 
void resize (unsigned int nrows, unsigned int ncols, bool flagNullify=true, bool recopy_=true)
 
void reshape (unsigned int nrows, unsigned int ncols)
 
void insert (const vpArray2D< double > &A, unsigned int r, unsigned int c)
 
bool operator== (const vpArray2D< double > &A) const
 
bool operator!= (const vpArray2D< double > &A) const
 
vpArray2D< double > hadamard (const vpArray2D< double > &m) const
 

Public Attributes

double * data
 

Related Functions

(Note that these are not member functions.)

vpColVector operator* (const double &x, const vpRotationVector &v)
 
enum  vpGEMMmethod
 
bool operator== (const vpArray2D< double > &A) const
 
bool operator== (const vpArray2D< float > &A) const
 
bool operator!= (const vpArray2D< double > &A) const
 
void vpGEMM (const vpArray2D< double > &A, const vpArray2D< double > &B, const double &alpha, const vpArray2D< double > &C, const double &beta, vpArray2D< double > &D, const unsigned int &ops=0)
 

Inherited functionalities from vpRotationVector

double & operator[] (unsigned int i)
 
const double & operator[] (unsigned int i) const
 
vpColVector operator* (double x) const
 
vpRotationVector & operator<< (double val)
 
vpRotationVector & operator, (double val)
 
double sumSquare () const
 
vpRowVector t () const
 
std::vector< double > toStdVector () const
 
unsigned int m_index
 

Inherited I/O from vpArray2D with Static Public Member Functions

vpArray2D< double > insert (const vpArray2D< double > &A, const vpArray2D< double > &B, unsigned int r, unsigned int c)
 
unsigned int rowNum
 
unsigned int colNum
 
double ** rowPtrs
 
unsigned int dsize
 
static void insert (const vpArray2D< double > &A, const vpArray2D< double > &B, vpArray2D< double > &C, unsigned int r, unsigned int c)
 
static bool load (const std::string &filename, vpArray2D< double > &A, bool binary=false, char *header=nullptr)
 
static bool loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=nullptr)
 
static bool save (const std::string &filename, const vpArray2D< double > &A, bool binary=false, const char *header="")
 
static bool saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="")
 
static vpArray2D< double > conv2 (const vpArray2D< double > &M, const vpArray2D< double > &kernel, const std::string &mode)
 
static void conv2 (const vpArray2D< double > &M, const vpArray2D< double > &kernel, vpArray2D< double > &res, const std::string &mode)
 

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 with values in [rad].

You can set values [rad] accessing each element:

vpThetaUVector tu;
tu[0] = M_PI_4;
tu[1] = M_PI_2;
tu[2] = M_PI;
vpThetaUVector
Implementation of a rotation vector as axis-angle minimal representation.
Definition: vpThetaUVector.h:172

You can also initialize the vector using operator<<(double):

tu << M_PI_4, M_PI_2, M_PI;

Or you can also initialize the vector from a list of doubles if ViSP is build with c++11 enabled:

tu = {M_PI_4, M_PI_2, M_PI};

To get the values [rad] use:

double tux = tu[0];
double tuy = tu[1];
double tuz = tu[2];

The code below shows first how to initialize a $\theta {\bf u}$ vector, than how to construct a rotation matrix from a vpThetaUVector and finally 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>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
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;
}
vpMath::rad
static double rad(double deg)
Definition: vpMath.h:129
vpRotationMatrix
Implementation of a rotation matrix and operations on such kind of matrices.
Definition: vpRotationMatrix.h:130
vpRowVector
Implementation of row vector and the associated operations.
Definition: vpRowVector.h:124
vpRowVector::t
vpColVector t() const
Definition: vpRowVector.cpp:532
vpThetaUVector::buildFrom
vpThetaUVector & buildFrom(const vpHomogeneousMatrix &M)
Definition: vpThetaUVector.cpp:115
VISP_NAMESPACE_NAME
Definition: vpEigenConversion.h:44
Examples
calibrate-hand-eye.cpp, catchAprilTag.cpp, catchEigenConversion.cpp, catchNPZ.cpp, catchPoseRansac2.cpp, catchPoseVector.cpp, catchQuaternion.cpp, catchRotation.cpp, exponentialMap.cpp, perfMatrixMultiplication.cpp, servoAfma6AprilTagIBVS.cpp, servoAfma6AprilTagPBVS.cpp, servoAfma6MegaposePBVS.cpp, servoFrankaPBVS.cpp, servoSimu3D_cMcd_CamVelocityWithoutVpServo.cpp, servoSimu3D_cdMc_CamVelocityWithoutVpServo.cpp, servoUniversalRobotsPBVS.cpp, testDisplacement.cpp, testFeature.cpp, testMatrixInitialization.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testXmlParserHomogeneousMatrix.cpp, tutorial-homography-from-points.cpp, tutorial-mb-generic-tracker-full.cpp, tutorial-mb-generic-tracker-read.cpp, and tutorial-mb-generic-tracker-save.cpp.

Definition at line 171 of file vpThetaUVector.h.

Constructor & Destructor Documentation

◆ vpThetaUVector() [1/12]

vpThetaUVector::vpThetaUVector ( )

Default constructor that initialize all the 3 angles to zero.

Definition at line 50 of file vpThetaUVector.cpp.

Referenced by operator*().

◆ vpThetaUVector() [2/12]

vpThetaUVector::vpThetaUVector ( const vpThetaUVector &  tu)

Copy constructor.

Definition at line 52 of file vpThetaUVector.cpp.

◆ vpThetaUVector() [3/12]

vpThetaUVector::vpThetaUVector ( const vpHomogeneousMatrix &  M)

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

Definition at line 58 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [4/12]

vpThetaUVector::vpThetaUVector ( const vpPoseVector &  p)

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

Definition at line 62 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [5/12]

vpThetaUVector::vpThetaUVector ( const vpRotationMatrix &  R)

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

Definition at line 66 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [6/12]

vpThetaUVector::vpThetaUVector ( const vpRzyxVector &  rzyx)

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

Definition at line 71 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [7/12]

vpThetaUVector::vpThetaUVector ( const vpRzyzVector &  rzyz)

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

Definition at line 75 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [8/12]

vpThetaUVector::vpThetaUVector ( const vpRxyzVector &  rxyz)

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

Definition at line 79 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [9/12]

vpThetaUVector::vpThetaUVector ( const vpQuaternionVector &  q)

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

Definition at line 83 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [10/12]

vpThetaUVector::vpThetaUVector ( const vpColVector &  tu)

Copy constructor from a 3-dimension vector.

Definition at line 54 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [11/12]

vpThetaUVector::vpThetaUVector ( const std::vector< double > &  tu)

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

Definition at line 110 of file vpThetaUVector.cpp.

References buildFrom().

◆ vpThetaUVector() [12/12]

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

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

#include <visp3/core/vpThetaUVector.cpp>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpThetaUVector tu(0, M_PI_2, M_PI);
std::cout << "tu: " << tu.t() << std::endl;
}

It produces the following printings:

tu: 0 1.570796327 3.141592654

Definition at line 105 of file vpThetaUVector.cpp.

References buildFrom().

Member Function Documentation

◆ buildFrom() [1/10]

vpThetaUVector & 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 300 of file vpThetaUVector.cpp.

References vpArray2D< double >::data.

◆ buildFrom() [2/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const std::vector< double > &  tu)

Build a $\theta {\bf u}$ vector from a 3-dim vectors.

Definition at line 266 of file vpThetaUVector.cpp.

References vpArray2D< double >::data, and vpException::dimensionError.

◆ buildFrom() [3/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const vpColVector &  tu)

Build a $\theta {\bf u}$ vector from a 3-dim vector.

Definition at line 283 of file vpThetaUVector.cpp.

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

◆ buildFrom() [4/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const vpHomogeneousMatrix &  M)

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

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

Definition at line 115 of file vpThetaUVector.cpp.

References vpHomogeneousMatrix::extract().

Referenced by buildFrom(), vpPoseVector::buildFrom(), VISP_NAMESPACE_NAME::eigen2visp(), vpHomogeneousMatrix::extract(), vpRotationMatrix::getThetaUVector(), vpRobotAfma6::getVelocity(), vpRobotViper650::getVelocity(), vpRobotViper850::getVelocity(), vpExponentialMap::inverse(), and vpThetaUVector().

◆ buildFrom() [5/10]

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 128 of file vpThetaUVector.cpp.

References vpArray2D< double >::data.

◆ buildFrom() [6/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const vpQuaternionVector &  q)

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

Definition at line 255 of file vpThetaUVector.cpp.

References buildFrom().

◆ buildFrom() [7/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const vpRotationMatrix &  R)

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

Definition at line 142 of file vpThetaUVector.cpp.

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

◆ buildFrom() [8/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const vpRxyzVector &  rxyz)

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

Definition at line 244 of file vpThetaUVector.cpp.

References buildFrom().

◆ buildFrom() [9/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const vpRzyxVector &  rzyx)

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

Definition at line 224 of file vpThetaUVector.cpp.

References buildFrom().

◆ buildFrom() [10/10]

vpThetaUVector & vpThetaUVector::buildFrom ( const vpRzyzVector &  rzyz)

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

Definition at line 234 of file vpThetaUVector.cpp.

References buildFrom().

◆ conv2() [1/2]

vpArray2D< double > vpArray2D< double >::conv2 ( const vpArray2D< Type > &  M,
const vpArray2D< Type > &  kernel,
const std::string &  mode 
)
staticinherited

Perform a 2D convolution similar to Matlab conv2 function: $ M \star kernel $.

Parameters
M: First matrix.
kernel: Second matrix.
mode: Convolution mode: "full" (default), "same", "valid".
Convolution mode: full, same, valid (image credit: Theano doc).
Note
This is a very basic implementation that does not use FFT.

Definition at line 1053 of file vpArray2D.h.

◆ conv2() [2/2]

void vpArray2D< double >::conv2 ( const vpArray2D< Type > &  M,
const vpArray2D< Type > &  kernel,
vpArray2D< Type > &  res,
const std::string &  mode 
)
staticinherited

Perform a 2D convolution similar to Matlab conv2 function: $ M \star kernel $.

Parameters
M: First array.
kernel: Second array.
res: Result.
mode: Convolution mode: "full" (default), "same", "valid".
Convolution mode: full, same, valid (image credit: Theano doc).
Note
This is a very basic implementation that does not use FFT.

Definition at line 1067 of file vpArray2D.h.

◆ extract()

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 $ in rad.
u: 3-dim unit vector ${\bf u} = (u_{x},u_{y},u_{z})^{\top} $ representing the rotation axis.

The following example shows how to use this function:

#include <visp3/core/vpThetaUVector.h>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpHomogeneousMatrix M(0, 0, 1., vpMath::rad(10), vpMath::rad(20), vpMath::rad(30));
double theta;
vpColVector u;
M.getRotationMatrix().getThetaUVector().extract(theta, u);
std::cout << "theta: " << theta << std::endl;
std::cout << "u : " << u.t() << std::endl;
}
vpColVector
Implementation of column vector and the associated operations.
Definition: vpColVector.h:191
vpColVector::extract
vpColVector extract(unsigned int r, unsigned int colsize) const
Definition: vpColVector.h:405
vpColVector::t
vpRowVector t() const
Definition: vpColVector.cpp:533
vpHomogeneousMatrix
Implementation of an homogeneous matrix and operations on such kind of matrices.
Definition: vpHomogeneousMatrix.h:221
See also
getTheta(), getU()
Examples
catchRotation.cpp.

Definition at line 417 of file vpThetaUVector.cpp.

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

Referenced by vpQuaternionVector::buildFrom().

◆ getCols()

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

Return the number of columns of the 2D array.

See also
getRows(), size()
Examples
catchAprilTag.cpp, catchArray2D.cpp, catchJsonArrayConversion.cpp, catchLuminanceMapping.cpp, catchMatrixCholesky.cpp, catchPoseVector.cpp, catchRotation.cpp, perfMatrixMultiplication.cpp, perfMatrixTranspose.cpp, servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 337 of file vpArray2D.h.

◆ getMaxValue()

double vpArray2D< double >::getMaxValue
inherited

Return the array max value.

Examples
servoMomentImage.cpp.

Definition at line 339 of file vpArray2D.h.

◆ getMinValue()

double vpArray2D< double >::getMinValue
inherited

Return the array min value.

Examples
servoMomentImage.cpp.

Definition at line 341 of file vpArray2D.h.

◆ getRows()

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

Return the number of rows of the 2D array.

See also
getCols(), size()
Examples
catchAprilTag.cpp, catchArray2D.cpp, catchJsonArrayConversion.cpp, catchLuminanceMapping.cpp, catchMatrixCholesky.cpp, catchParticleFilter.cpp, catchPoseVector.cpp, catchRotation.cpp, mbtGenericTrackingDepth.cpp, mbtGenericTrackingDepthOnly.cpp, perfColVectorOperations.cpp, perfMatrixMultiplication.cpp, perfMatrixTranspose.cpp, testColVector.cpp, testDisplacement.cpp, testGenericTracker.cpp, testGenericTrackerDepth.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 347 of file vpArray2D.h.

◆ getTheta()

double vpThetaUVector::getTheta ( ) const

Get the rotation angle $ \theta $ from the $ \theta {\bf u} $ representation.

Returns
Rotation angle $ \theta $ in rad.

The following example shows how to use this function:

#include <visp3/core/vpThetaUVector.h>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpHomogeneousMatrix M(0, 0, 1., vpMath::rad(10), vpMath::rad(20), vpMath::rad(30));
std::cout << "theta: " << M.getRotationMatrix().getThetaUVector().getTheta() << std::endl;
std::cout << "u : " << M.getRotationMatrix().getThetaUVector().getU().t() << std::endl;
}
See also
getTheta(), extract()

Definition at line 459 of file vpThetaUVector.cpp.

References vpArray2D< double >::data.

Referenced by extract(), getU(), operator*(), and VISP_NAMESPACE_NAME::visp2eigen().

◆ getU()

vpColVector vpThetaUVector::getU ( ) const

Get the unit vector $\bf u $ from the $ \theta {\bf u} $ representation.

Returns
3-dim unit vector ${\bf u} = (u_{x},u_{y},u_{z})^{\top} $ representing the rotation axis.

The following example shows how to use this function:

#include <visp3/core/vpThetaUVector.h>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpHomogeneousMatrix M(0, 0, 1., vpMath::rad(10), vpMath::rad(20), pMath::rad(30));
std::cout << "theta: " << M.getRotationMatrix().getThetaUVector().getTheta() << std::endl;
std::cout << "u : " << M.getRotationMatrix().getThetaUVector().getU().t() << std::endl;
}
See also
getTheta(), extract()

Definition at line 494 of file vpThetaUVector.cpp.

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

Referenced by operator*(), and VISP_NAMESPACE_NAME::visp2eigen().

◆ hadamard()

vpArray2D< double > vpArray2D< double >::hadamard ( const vpArray2D< Type > &  m) const
inherited

Compute the Hadamard product (element wise matrix multiplication).

Parameters
m: Second matrix;
Returns
m1.hadamard(m2) The Hadamard product : $ m1 \circ m2 = (m1 \circ m2)_{i,j} = (m1)_{i,j} (m2)_{i,j} $

Definition at line 641 of file vpArray2D.h.

◆ insert() [1/2]

vpArray2D< double > vpArray2D< double >::insert ( const vpArray2D< Type > &  A,
const vpArray2D< Type > &  B,
unsigned int  r,
unsigned int  c 
)
inherited

Insert array B in array A at the given position.

Parameters
A: Main array.
B: Array to insert.
r: Index of the row where to add the array.
c: Index of the column where to add the array.
Returns
Array with B insert in A.
Warning
Throw exception if the sizes of the arrays do not allow the insertion.

Definition at line 1081 of file vpArray2D.h.

◆ insert() [2/2]

void vpArray2D< double >::insert ( const vpArray2D< Type > &  A,
unsigned int  r,
unsigned int  c 
)
inlineinherited

Insert array A at the given position in the current array.

Warning
Throw vpException::dimensionError if the dimensions of the matrices do not allow the operation.
Parameters
A: The array to insert.
r: The index of the row to begin to insert data.
c: The index of the column to begin to insert data.

Definition at line 497 of file vpArray2D.h.

◆ load()

static bool vpArray2D< double >::load ( const std::string &  filename,
vpArray2D< Type > &  A,
bool  binary = false,
char *  header = nullptr 
)
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 669 of file vpArray2D.h.

◆ loadYAML()

static bool vpArray2D< double >::loadYAML ( const std::string &  filename,
vpArray2D< Type > &  A,
char *  header = nullptr 
)
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()
Examples
servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoUniversalRobotsIBVS.cpp, servoUniversalRobotsPBVS.cpp, tutorial-flir-ptu-ibvs.cpp, tutorial-hsv-segmentation-pcl-viewer.cpp, tutorial-hsv-segmentation-pcl.cpp, and tutorial-hsv-segmentation.cpp.

Definition at line 783 of file vpArray2D.h.

◆ operator!=()

bool operator!= ( const vpArray2D< Type > &  A) const
inherited

Not equal to comparison operator of a 2D array.

Definition at line 523 of file vpArray2D.h.

◆ operator*() [1/2]

vpThetaUVector vpThetaUVector::operator* ( const vpThetaUVector &  tu_b) const

Perform rotation chaining / rotation multiplication using the theta.u rotation representation. See: this answer for some details about the maths.

Definition at line 515 of file vpThetaUVector.cpp.

References vpColVector::crossProd(), vpColVector::dotProd(), getTheta(), getU(), and vpThetaUVector().

◆ operator*() [2/2]

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 89 of file vpRotationVector.cpp.

References vpArray2D< double >::dsize.

◆ operator,()

vpRotationVector & vpRotationVector::operator, ( double  val)
inherited

Set vector second and third element values.

Parameters
val: Value of the vector element [rad].
Returns
An updated vector.

The following example shows how to initialize a $\theta_u$ vector from a list of 3 values [rad].

#include <visp3/core/vpThetaUVector.h>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpThetaUVector tu;
tu << 0, M_PI_2, M_PI;
std::cout << "tu: " << tu.t() << std::endl;
}
vpRotationVector::t
vpRowVector t() const
Definition: vpRotationVector.cpp:53

It produces the following printings:

tu: 0 1.570796327 3.141592654
See also
operator<<()

Definition at line 160 of file vpRotationVector.cpp.

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

◆ operator<<()

vpRotationVector & vpRotationVector::operator<< ( double  val)
inherited

Set vector first element value.

Parameters
val: Value of the vector first element [rad].
Returns
An updated vector.

The following example shows how to initialize a $\theta_u$ vector from a list of 3 values [rad].

#include <visp3/core/vpThetaUVector.h>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpThetaUVector tu;
tu << 0, M_PI_2, M_PI;
std::cout << "tu: " << tu.t() << std::endl;
}

It produces the following printings:

tu: 0 1.570796327 3.141592654
See also
operator,()

Definition at line 126 of file vpRotationVector.cpp.

References vpArray2D< double >::data, and vpRotationVector::m_index.

◆ operator=() [1/3]

vpThetaUVector & vpThetaUVector::operator= ( const std::initializer_list< double > &  list)

Set vector from a list of 3 double angle values in radians.

#include <visp3/core/vpThetaUVector.cpp>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpThetaUVector tu = {M_PI, 0, M_PI_2};
std::cout << "tu: " << tu.t() << std::endl;
}

It produces the following printings:

tu: 3.141592654 0 1.570796327
See also
operator<<()

Definition at line 554 of file vpThetaUVector.cpp.

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

◆ operator=() [2/3]

vpThetaUVector & vpThetaUVector::operator= ( const vpColVector &  tu)

Copy operator that initializes a $\theta {\bf u}$ vector from a 3-dimension column vector tu.

Parameters
tu: 3-dimension vector containing the values of the $\theta {\bf u}$ vector.
#include <visp3/core/vpThetaUVector.h>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
int main()
{
vpColVector v(3);
v[0] = 0.1;
v[1] = 0.2;
v[2] = 0.3;
vpThetaUVector tu;
tu = v;
// tu is now equal to v : 0.1, 0.2, 0.3
}

Definition at line 370 of file vpThetaUVector.cpp.

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

◆ operator=() [3/3]

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>
#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif
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 335 of file vpThetaUVector.cpp.

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

◆ operator==()

bool vpArray2D< double >::operator== ( const vpArray2D< Type > &  A) const
inherited

Equal to comparison operator of a 2D array.

Definition at line 519 of file vpArray2D.h.

◆ operator[]() [1/2]

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 124 of file vpRotationVector.h.

◆ operator[]() [2/2]

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 129 of file vpRotationVector.h.

◆ reshape()

void vpArray2D< double >::reshape ( unsigned int  nrows,
unsigned int  ncols 
)
inlineinherited
Examples
testMatrixInitialization.cpp.

Definition at line 456 of file vpArray2D.h.

◆ resize()

void vpArray2D< double >::resize ( unsigned int  nrows,
unsigned int  ncols,
bool  flagNullify = true,
bool  recopy_ = 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.
recopy_: if true, will perform an explicit recopy of the old data.
Examples
catchArray2D.cpp, catchJsonArrayConversion.cpp, catchParticleFilter.cpp, perfMatrixMultiplication.cpp, perfMatrixTranspose.cpp, testMatrix.cpp, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 362 of file vpArray2D.h.

◆ save()

static bool vpArray2D< double >::save ( const std::string &  filename,
const vpArray2D< Type > &  A,
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 874 of file vpArray2D.h.

◆ saveYAML()

static bool vpArray2D< double >::saveYAML ( const std::string &  filename,
const vpArray2D< Type > &  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");
vpArray2D::saveYAML
static bool saveYAML(const std::string &filename, const vpArray2D< Type > &A, const char *header="")
Definition: vpArray2D.h:972

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]
vpArray2D< double >::data
double * data
Address of the first element of the data array.
Definition: vpArray2D.h:148

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 972 of file vpArray2D.h.

◆ size()

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

Return the number of elements of the 2D array.

Examples
catchJsonArrayConversion.cpp, catchLuminanceMapping.cpp, catchParticleFilter.cpp, catchPoseVector.cpp, catchRotation.cpp, perfColVectorOperations.cpp, testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInitialization.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testTranslationVector.cpp, testTukeyEstimator.cpp, testUniversalRobotsGetData.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-mb-generic-tracker-rgbd-realsense-json.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, tutorial-mb-generic-tracker-rgbd-structure-core.cpp, tutorial-pf.cpp, tutorial-ukf.cpp, ukf-nonlinear-complex-example.cpp, and ukf-nonlinear-example.cpp.

Definition at line 349 of file vpArray2D.h.

◆ sumSquare()

double vpRotationVector::sumSquare ( ) const
inherited

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

Returns
The value

\[\sum{i=0}^{m} r_i^{2}\]

.
Examples
servoAfma6AprilTagPBVS.cpp, servoAfma6MegaposePBVS.cpp, servoFrankaPBVS.cpp, and servoUniversalRobotsPBVS.cpp.

Definition at line 179 of file vpRotationVector.cpp.

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

◆ t()

BEGIN_VISP_NAMESPACE vpRowVector vpRotationVector::t ( ) const
inherited

Return the transpose of the rotation vector.

Examples
calibrate-hand-eye.cpp, catchEigenConversion.cpp, testMatrixInitialization.cpp, testMocapQualisys.cpp, testMocapVicon.cpp, testViper650.cpp, testViper850.cpp, and tutorial-pose-from-qrcode-image.cpp.

Definition at line 53 of file vpRotationVector.cpp.

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

Referenced by vpQuaternionVector::lerp(), vpQuaternionVector::nlerp(), and vpQuaternionVector::slerp().

◆ toStdVector()

std::vector< double > vpRotationVector::toStdVector ( ) const
inherited

Converts the vpRotationVector to a std::vector.

Returns
The corresponding std::vector<double>.

Definition at line 68 of file vpRotationVector.cpp.

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

Friends And Related Function Documentation

◆ insert()

void vpArray2D< double >::insert ( const vpArray2D< Type > &  A,
const vpArray2D< Type > &  B,
vpArray2D< Type > &  C,
unsigned int  r,
unsigned int  c 
)
related

Insert array B in array A at the given position.

Parameters
A: Main array.
B: Array to insert.
C: Result array.
r: Index of the row where to insert array B.
c: Index of the column where to insert array B.
Warning
Throw exception if the sizes of the arrays do not allow the insertion.

Definition at line 1096 of file vpArray2D.h.

◆ operator!=()

bool operator!= ( const vpArray2D< Type > &  A) const
related

Definition at line 1351 of file vpArray2D.h.

◆ operator*()

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

Allows to multiply a scalar by rotaion vector.

Definition at line 195 of file vpRotationVector.cpp.

◆ operator==() [1/2]

bool operator== ( const vpArray2D< double > &  A) const
related

Definition at line 1313 of file vpArray2D.h.

◆ operator==() [2/2]

bool operator== ( const vpArray2D< float > &  A) const
related

Definition at line 1332 of file vpArray2D.h.

◆ vpGEMM()

void vpGEMM ( const vpArray2D< double > &  A,
const vpArray2D< double > &  B,
const double &  alpha,
const vpArray2D< double > &  C,
const double &  beta,
vpArray2D< double > &  D,
const unsigned int &  ops = 0 
)
related

This function performs generalized matrix multiplication: D = alpha*op(A)*op(B) + beta*op(C), where op(X) is X or X^T. Operation on A, B and C matrices is described by enumeration vpGEMMmethod().

For example, to compute D = alpha*A^T*B^T+beta*C we need to call :

vpGEMM(A, B, alpha, C, beta, D, VP_GEMM_A_T + VP_GEMM_B_T);
vpArray2D< double >::vpGEMM
void vpGEMM(const vpArray2D< double > &A, const vpArray2D< double > &B, const double &alpha, const vpArray2D< double > &C, const double &beta, vpArray2D< double > &D, const unsigned int &ops=0)
Definition: vpGEMM.h:414

If C is not used, vpGEMM must be called using an empty array null. Thus to compute D = alpha*A^T*B, we have to call:

vpGEMM(A, B, alpha, null, 0, D, VP_GEMM_B_T);
Exceptions
vpException::incorrectMatrixSizeErrorif the sizes of the matrices do not allow the operations.
Parameters
A: An array that could be a vpMatrix.
B: An array that could be a vpMatrix.
alpha: A scalar.
C: An array that could be a vpMatrix.
beta: A scalar.
D: The resulting array that could be a vpMatrix.
ops: A scalar describing operation applied on the matrices. Possible values are the one defined in vpGEMMmethod(): VP_GEMM_A_T, VP_GEMM_B_T, VP_GEMM_C_T.

Definition at line 414 of file vpGEMM.h.

◆ vpGEMMmethod

enum vpGEMMmethod
related

Enumeration of the operations applied on matrices in vpGEMM() function.

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 53 of file vpGEMM.h.

Member Data Documentation

◆ colNum

unsigned int vpArray2D< double >::colNum
protectedinherited

Number of columns in the array.

Definition at line 1103 of file vpArray2D.h.

◆ data

double * vpArray2D< double >::data
inherited

Address of the first element of the data array.

Examples
catchArray2D.cpp, catchQuaternion.cpp, catchRotation.cpp, perfMatrixMultiplication.cpp, testDisplacement.cpp, testMatrix.cpp, testTranslationVector.cpp, testUniversalRobotsGetData.cpp, tutorial-bridge-opencv-matrix.cpp, and tutorial-matlab.cpp.

Definition at line 148 of file vpArray2D.h.

◆ dsize

unsigned int vpArray2D< double >::dsize
protectedinherited

Current array size (rowNum * colNum)

Definition at line 1107 of file vpArray2D.h.

◆ m_index

unsigned int vpRotationVector::m_index
protectedinherited

Definition at line 159 of file vpRotationVector.h.

Referenced by vpRotationVector::operator,(), and vpRotationVector::operator<<().

◆ rowNum

unsigned int vpArray2D< double >::rowNum
protectedinherited

Number of rows in the array.

Definition at line 1101 of file vpArray2D.h.

◆ rowPtrs

double ** vpArray2D< double >::rowPtrs
protectedinherited

Address of the first element of each rows.

Definition at line 1105 of file vpArray2D.h.