RzyzVector¶

class RzyzVector(*args, **kwargs)¶

Bases: RotationVector

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

Class that consider the case of the Euler \((\varphi,\theta,\psi)\) angles using the z-y-z convention, where \((\varphi,\theta,\psi)\) are respectively the rotation angles around the \(z\) , \(y\) and \(z\) axis.

\[R_{zyz}(\varphi,\theta,\psi) = R_z(\varphi) \; R_y(\theta) \; R_z(\psi)\]

with

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

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

\[\begin{split}R_{zyz}(\varphi,\theta,\psi) = \left( \begin{array}{ccc} \cos\varphi \cos\theta \cos\psi - \sin\varphi\sin\psi & -\cos\varphi \cos\theta \sin\psi -\sin\varphi\cos\psi & \cos\varphi \sin\theta \\\sin\varphi \cos\theta \cos\psi + \cos\varphi\sin\psi & -\sin\varphi \cos\theta \sin\psi +\cos\varphi\cos\psi & \sin\varphi \sin\theta \\-\sin\theta \cos\psi & \sin\theta \sin\psi & \cos\theta \end{array} \right) \end{split}\]

The vpRzyzVector class is derived from vpRotationVector .

From the implementation point of view, it is nothing more than an array of three doubles with values in [rad].

You can set values [rad] accessing each element:

vpRzyzVector rzyz;
rzyz[0] = M_PI_4;
rzyz[1] = M_PI_2;
rzyz[2] = M_PI;

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

rzyz << 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:

rzyz = {M_PI_4, M_PI_2, M_PI};

To get the values [rad] use:

double r1 = rzyz[0];
double r2 = rzyz[1];
double r3 = rzyz[2];

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

#include <visp3/core/vpMath.h>
#include <visp3/core/vpRotationMatrix.h>
#include <visp3/core/vpRzyzVector.h>

int main()
{
  vpRzyzVector rzyz;

  // Initialise the Euler angles
  rzyz[0] = vpMath::rad( 45.f); // phi   angle in rad/s around z axis
  rzyz[1] = vpMath::rad(-30.f); // theta angle in rad/s around y axis
  rzyz[2] = vpMath::rad( 90.f); // psi   angle in rad/s around z axis

  // Construct a rotation matrix from the Euler angles
  vpRotationMatrix R(rzyz);

  // Extract the Euler angles around z,y,z axis from a rotation matrix
  rzyz.buildFrom(R);

  // Print the extracted Euler angles. Values are the same than the
  // one used for initialization
  std::cout << rzyz;

  // Since the rotation vector is 3 values column vector, the
  // transpose operation produce a row vector.
  vpRowVector rzyz_t = rzyz.t();

  // Print the transpose row vector
  std::cout << rzyz_t << std::endl;
}

Overloaded function.

__init__(self: visp._visp.core.RzyzVector) -> None

Default constructor that initialize all the 3 angles to zero.

__init__(self: visp._visp.core.RzyzVector, rzyz: visp._visp.core.RzyzVector) -> None

Copy constructor.

__init__(self: visp._visp.core.RzyzVector, R: visp._visp.core.RotationMatrix) -> None

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

Parameters:

R: Rotation matrix used to initialize the Euler angles.

__init__(self: visp._visp.core.RzyzVector, tu: visp._visp.core.ThetaUVector) -> None

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

Parameters:

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

__init__(self: visp._visp.core.RzyzVector, phi: float, theta: float, psi: float) -> None

Constructor from 3 angles (in radian).

Parameters:

phi: math:varphi angle around the \(z\) axis.
theta: math:theta angle around the \(y\) axis.
psi: math:psi angle around the \(z\) axis.

__init__(self: visp._visp.core.RzyzVector, rzyz: visp._visp.core.ColVector) -> None

Copy constructor from a 3-dimension vector.

__init__(self: visp._visp.core.RzyzVector, rzyz: list[float]) -> None

Copy constructor from a 3-dimension vector.

Methods

`__init__`	Overloaded function.
`buildFrom`	Overloaded function.

Inherited Methods

`insert`	Overloaded function.
`getCols`	Return the number of columns of the 2D array.
`insertStatic`	Insert array B in array A at the given position.
`toStdVector`	return: The corresponding std::vector<double>.
`save`	Overloaded function.
`reshape`
`getRows`	Return the number of rows of the 2D array.
`size`	Return the number of elements of the 2D array.
`getMinValue`	Return the array min value.
`sumSquare`	Return the sum square of all the elements \(r_{i}\) of the rotation vector r(m).
`getMaxValue`	Return the array max value.
`hadamard`	param m: Second matrix;
`saveYAML`	Save an array in a YAML-formatted file.
`conv2`	Overloaded function.
`t`	Overloaded function.
`numpy`	Numpy view of the underlying array data.
`resize`	Set the size of the array and initialize all the values to zero.

Operators

`__doc__`
`__init__`	Overloaded function.
`__module__`

Attributes

`__annotations__`
`__hash__`

__eq__(*args, **kwargs)¶

Overloaded function.

__eq__(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D) -> bool

Equal to comparison operator of a 2D array.

__eq__(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D) -> bool

Equal to comparison operator of a 2D array.

__eq__(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D) -> bool

Equal to comparison operator of a 2D array.

__getitem__(*args, **kwargs)¶

Overloaded function.

__getitem__(self: visp._visp.core.ArrayDouble2D, arg0: tuple[int, int]) -> float
__getitem__(self: visp._visp.core.ArrayDouble2D, arg0: int) -> numpy.ndarray[numpy.float64]
__getitem__(self: visp._visp.core.ArrayDouble2D, arg0: slice) -> numpy.ndarray[numpy.float64]
__getitem__(self: visp._visp.core.ArrayDouble2D, arg0: tuple) -> numpy.ndarray[numpy.float64]

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: visp._visp.core.RzyzVector) -> None

Default constructor that initialize all the 3 angles to zero.

__init__(self: visp._visp.core.RzyzVector, rzyz: visp._visp.core.RzyzVector) -> None

Copy constructor.

__init__(self: visp._visp.core.RzyzVector, R: visp._visp.core.RotationMatrix) -> None

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

Parameters:

R: Rotation matrix used to initialize the Euler angles.

__init__(self: visp._visp.core.RzyzVector, tu: visp._visp.core.ThetaUVector) -> None

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

Parameters:

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

__init__(self: visp._visp.core.RzyzVector, phi: float, theta: float, psi: float) -> None

Constructor from 3 angles (in radian).

Parameters:

phi: math:varphi angle around the \(z\) axis.
theta: math:theta angle around the \(y\) axis.
psi: math:psi angle around the \(z\) axis.

__init__(self: visp._visp.core.RzyzVector, rzyz: visp._visp.core.ColVector) -> None

Copy constructor from a 3-dimension vector.

__init__(self: visp._visp.core.RzyzVector, rzyz: list[float]) -> None

Copy constructor from a 3-dimension vector.

__mul__(*args, **kwargs)¶

Overloaded function.

__mul__(self: visp._visp.core.RotationVector, x: float) -> visp._visp.core.ColVector

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.

__mul__(self: visp._visp.core.RotationVector, x: float) -> visp._visp.core.ColVector

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.

__mul__(self: visp._visp.core.RotationVector, x: float) -> visp._visp.core.ColVector

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.

__ne__(*args, **kwargs)¶

Overloaded function.

__ne__(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D) -> bool

Not equal to comparison operator of a 2D array.

__ne__(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D) -> bool

Not equal to comparison operator of a 2D array.

__ne__(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D) -> bool

Not equal to comparison operator of a 2D array.

buildFrom(*args, **kwargs)¶

Overloaded function.

buildFrom(self: visp._visp.core.RzyzVector, R: visp._visp.core.RotationMatrix) -> visp._visp.core.RzyzVector

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

Parameters:

R: Rotation matrix used as input.

Returns:

\(R_{zyz}=(\varphi,\theta,\psi)\) Euler angles vector.

buildFrom(self: visp._visp.core.RzyzVector, R: visp._visp.core.ThetaUVector) -> visp._visp.core.RzyzVector

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

buildFrom(self: visp._visp.core.RzyzVector, rxyz: visp._visp.core.ColVector) -> visp._visp.core.RzyzVector

Construct a \(R_{zyz}=(\varphi,\theta,\psi)\) Euler angles vectorfrom a 3-dim vector.

buildFrom(self: visp._visp.core.RzyzVector, rxyz: list[float]) -> visp._visp.core.RzyzVector

Construct a \(R_{zyx}=(\varphi,\theta,\psi)\) Euler angles vector from a 3-dim vector.

buildFrom(self: visp._visp.core.RzyzVector, phi: float, theta: float, psi: float) -> None

Construction from 3 angles (in radian).

Parameters:

phi: math:varphi angle around the \(z\) axis.
theta: math:theta angle around the \(y\) axis.
psi: math:psi angle around the \(z\) axis.

static conv2(*args, **kwargs)¶

Overloaded function.

conv2(M: visp._visp.core.ArrayDouble2D, kernel: visp._visp.core.ArrayDouble2D, mode: str) -> visp._visp.core.ArrayDouble2D

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

Note

This is a very basic implementation that does not use FFT.

Parameters:

M: First matrix.
kernel: Second matrix.
mode: Convolution mode: “full” (default), “same”, “valid”.

conv2(M: visp._visp.core.ArrayDouble2D, kernel: visp._visp.core.ArrayDouble2D, res: visp._visp.core.ArrayDouble2D, mode: str) -> None

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

Note

This is a very basic implementation that does not use FFT.

Parameters:

M: First array.
kernel: Second array.
res: Result.
mode: Convolution mode: “full” (default), “same”, “valid”.

getCols(self) → int¶: Return the number of columns of the 2D array.

Note

See getRows() , size()

getMaxValue(self) → float¶: Return the array max value.

getMinValue(self) → float¶: Return the array min value.

getRows(self) → int¶: Return the number of rows of the 2D array.

Note

See getCols() , size()

hadamard(self, m: visp._visp.core.ArrayDouble2D) → visp._visp.core.ArrayDouble2D¶

Parameters:

m: visp._visp.core.ArrayDouble2D¶: Second matrix;

Returns:

m1.hadamard(m2) The Hadamard product : \(m1 \circ m2 = (m1 \circ m2)_{i,j} = (m1)_{i,j} (m2)_{i,j}\)

insert(*args, **kwargs)¶

Overloaded function.

insert(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D, r: int, c: int) -> None

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.

insert(self: visp._visp.core.ArrayDouble2D, A: visp._visp.core.ArrayDouble2D, B: visp._visp.core.ArrayDouble2D, r: int, c: int) -> visp._visp.core.ArrayDouble2D

Insert array B in array A at the given position.

Warning

Throw exception if the sizes of the arrays do not allow the insertion.

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.

static insertStatic(A: visp._visp.core.ArrayDouble2D, B: visp._visp.core.ArrayDouble2D, C: visp._visp.core.ArrayDouble2D, r: int, c: int) → None¶

Insert array B in array A at the given position.

Warning

Throw exception if the sizes of the arrays do not allow the insertion.

Parameters:

A: visp._visp.core.ArrayDouble2D¶: Main array.
B: visp._visp.core.ArrayDouble2D¶: Array to insert.
C: visp._visp.core.ArrayDouble2D¶: Result array.
r: int¶: Index of the row where to insert array B.
c: int¶: Index of the column where to insert array B.

numpy(self) → numpy.ndarray[numpy.float64]¶: Numpy view of the underlying array data. This numpy view can be used to directly modify the array.

reshape(self, nrows: int, ncols: int) → None¶

resize(self, nrows: int, ncols: int, flagNullify: bool = true, recopy_: bool = true) → None¶

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

Parameters:

nrows: int¶: number of rows.
ncols: int¶: number of column.
flagNullify: bool = true¶: 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_: bool = true¶: if true, will perform an explicit recopy of the old data.

static save(*args, **kwargs)¶

Overloaded function.

save(filename: str, A: visp._visp.core.ArrayDouble2D, binary: bool = false, header: str = ) -> bool

Save a matrix to a file.

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

Note

See load()

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.

save(filename: str, A: visp._visp.core.ArrayDouble2D, binary: bool = false, header: str = ) -> bool

Save a matrix to a file.

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

Note

See load()

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.

save(filename: str, A: visp._visp.core.ArrayDouble2D, binary: bool = false, header: str = ) -> bool

Save a matrix to a file.

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

Note

See load()

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.

static saveYAML(filename: str, A: visp._visp.core.ArrayDouble2D, header: str =) → bool¶

Save an array in a YAML-formatted file.

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]

Note

See loadYAML()

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.

size(self) → int¶: Return the number of elements of the 2D array.

sumSquare(self) → float¶

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

Returns:: The value

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

t(*args, **kwargs)¶

Overloaded function.

t(self: visp._visp.core.RotationVector) -> visp._visp.core.RowVector

Return the transpose of the rotation vector.

t(self: visp._visp.core.ArrayDouble2D) -> visp._visp.core.ArrayDouble2D

Compute the transpose of the array.

Returns:: vpArray2D<Type> C = A^T

toStdVector(self) → list[float]¶

Returns:: The corresponding std::vector<double>.

__hash__ = None¶