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vpThetaUVector Class Reference

#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)
 
 vpThetaUVector (const vpColVector &tu)
 
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)
 
void extract (double &theta, vpColVector &u) const
 
double getTheta () const
 
vpColVector getU () const
 
vpThetaUVectoroperator= (const vpColVector &tu)
 
vpThetaUVectoroperator= (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 $\theta {\bf u}$ 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()
{
// 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
// 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, testPoseRansac2.cpp, testPoseVector.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.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 73 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpPoseVector p)

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

Definition at line 81 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpRotationMatrix R)

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

Definition at line 89 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 99 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 108 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 117 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 126 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 135 of file vpThetaUVector.cpp.

References buildFrom().

vpThetaUVector::vpThetaUVector ( const vpColVector tu)

Copy constructor from a 3-dimension vector.

Definition at line 60 of file vpThetaUVector.cpp.

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

virtual vpThetaUVector::~vpThetaUVector ( )
inlinevirtual

Destructor.

Definition at line 174 of file vpThetaUVector.h.

Member Function Documentation

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 159 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 171 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 221 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 233 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 245 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 258 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 438 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 $ 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>
int main()
{
double theta;
M.getRotationMatrix().getThetaUVector().extract(theta, u);
std::cout << "theta: " << theta << std::endl;
std::cout << "u : " << u.t() << std::endl;
}
See Also
getTheta(), getU()

Definition at line 356 of file vpThetaUVector.cpp.

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

Referenced by vpQuaternionVector::buildFrom().

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.
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>
int main()
{
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 391 of file vpThetaUVector.cpp.

References vpArray2D< double >::data.

Referenced by extract(), and 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>
int main()
{
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 418 of file vpThetaUVector.cpp.

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

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.

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>
int main()
{
v[0] = 0.1;
v[1] = 0.2;
v[2] = 0.3;
tu = v;
// tu is now equal to v : 0.1, 0.2, 0.3
}

Definition at line 316 of file vpThetaUVector.cpp.

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

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()
{
// Initialise the theta U rotation vector
tu = vpMath::rad( 45.f); // All the 3 angles are set to 45 degrees
}

Definition at line 287 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 >::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::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
- [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
- [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().

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 
)
related

Allows to multiply a scalar by rotaion vector.

Definition at line 89 of file vpRotationVector.cpp.

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 57 of file vpGEMM.h.

Member Data Documentation

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(), vpMatrix::euclideanNorm(), vpMatrix::expm(), extract(), getTheta(), 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=(), vpRzyxVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), 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::vpRzyxVector(), vpRzyzVector::vpRzyzVector(), vpThetaUVector(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

unsigned int vpArray2D< double >::rowNum
protectedinherited

Number of rows in the array.

Definition at line 74 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpColVector::extract(), vpMatrix::eye(), vpColVector::infinityNorm(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpMatrix::inverseByLU(), vpMatrix::inverseByQR(), vpRotationMatrix::operator*(), vpTranslationVector::operator*(), vpHomogeneousMatrix::operator*(), vpColVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpTranslationVector::operator*=(), vpColVector::operator*=(), vpMatrix::operator*=(), vpColVector::operator+(), vpColVector::operator+=(), vpMatrix::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpMatrix::operator-=(), vpColVector::operator/(), vpMatrix::operator/(), vpTranslationVector::operator/=(), vpColVector::operator/=(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpColVector::reshape(), vpMatrix::setIdentity(), vpMatrix::stack(), vpColVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpColVector::sum(), vpMatrix::sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpColVector::sumSquare(), vpMatrix::sumSquare(), vpTranslationVector::t(), vpPoseVector::t(), vpColVector::t(), vpMatrix::t(), and vpMatrix::transpose().