RotationMatrix¶

class RotationMatrix(*args, **kwargs)¶

Bases: ArrayDouble2D

Implementation of a rotation matrix and operations on such kind of matrices.

The vpRotationMatrix considers the particular case of a rotation matrix.

The vpRotationMatrix class is derived from vpArray2D<double> .

The code below shows how to create a rotation matrix, set the element values and access them:

#include <visp3/core/vpRotationMatrix.h>

#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif

int main()
{
  vpRotationMatrix R;
  R[0][0] =  0; R[0][1] =  0; R[0][2] = -1;
  R[1][0] =  0; R[1][1] = -1; R[1][2] =  0;
  R[2][0] = -1; R[2][1] =  0; R[2][2] =  0;

  std::cout << "R:" << std::endl;
  for (unsigned int i = 0; i < R.getRows(); ++i) {
    for (unsigned int j = 0; j < R.getCols(); ++j) {
      std::cout << R[i][j] << " ";
    }
    std::cout << std::endl;
  }
}

Once build, this previous code produces the following output:

R:
0 0 -1
0 -1 0
-1 0 0

You can also use operator<< to initialize a rotation matrix as previously:

#include <visp3/core/vpRotationMatrix.h>

#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif

int main()
{
  vpRotationMatrix R;
  R << 0, 0, -1, 0, -1, 0, -1, 0, 0;
  std::cout << "R:\n" << R << std::endl;
}

If ViSP is build with c++11 enabled, you can do the same using:

#include <visp3/code/vpRotationMatrix.h

#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif

int main()
{
  vpRotationMatrix R{ 0, 0, -1, 0, -1, 0, -1, 0, 0 };
  std::cout << "R:\n" << R << std::endl;
}

Overloaded function.

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

Default constructor that initialise a 3-by-3 rotation matrix to identity.

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

Copy constructor that construct a 3-by-3 rotation matrix from another rotation matrix.

__init__(self: visp._visp.core.RotationMatrix, M: visp._visp.core.HomogeneousMatrix) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.ThetaUVector) -> None
__init__(self: visp._visp.core.RotationMatrix, p: visp._visp.core.PoseVector) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.RzyzVector) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.RxyzVector) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.RzyxVector) -> None
__init__(self: visp._visp.core.RotationMatrix, q: visp._visp.core.QuaternionVector) -> None
__init__(self: visp._visp.core.RotationMatrix, R: visp._visp.core.Matrix) -> None
__init__(self: visp._visp.core.RotationMatrix, tux: float, tuy: float, tuz: float) -> None

Construct a 3-by-3 rotation matrix from \(\theta {\bf u}=(\theta u_x, \theta u_y, \theta u_z)^T\) angle representation.

__init__(self: visp._visp.core.RotationMatrix, list: std::initializer_list<double>) -> None
__init__(self: visp._visp.core.RotationMatrix, np_array: numpy.ndarray[numpy.float64]) -> None

Construct a rotation matrix by copying a 2D numpy array. This numpy array should be of dimensions \(3 \times 3\) and be a valid rotation matrix. If it is not a rotation matrix, an exception will be raised.

Parameters:

np_array: The numpy 1D array to copy.

Methods

`__init__`	Overloaded function.
`buildFrom`	Overloaded function.
`eye`	Initialize the rotation matrix as identity.
`getCol`	The following example shows how to use this function:
`getThetaUVector`	Return the \(\theta {\bf u}\) vector that corresponds to the rotation matrix.
`inverse`	Overloaded function.
`isARotationMatrix`	Test if the rotation matrix is really a rotation matrix.
`mean`	Overloaded function.
`numpy`	Numpy view of the underlying array data.
`orthogonalize`	Perform rotation matrix orthogonalization.
`printVector`	Print to std::cout the rotation matrix as a \(\theta {\bf u}\) angle representation vector.
`resize`	Overloaded function.
`t`	Overloaded function.

Inherited Methods

`getMaxValue`	Return the array max value.
`hadamard`	param m: Second matrix;
`insert`	Overloaded function.
`insertStatic`	Insert array B in array A at the given position.
`getRows`	Return the number of rows of the 2D array.
`save`	Overloaded function.
`conv2`	Overloaded function.
`saveYAML`	Save an array in a YAML-formatted file.
`reshape`
`getMinValue`	Return the array min value.
`getCols`	Return the number of columns of the 2D array.
`size`	Return the number of elements of the 2D array.

Operators

`__doc__`
`__getitem__`	Overloaded function.
`__imul__`	Operator that allows to multiply all the elements of a rotation matrix by a scalar.
`__init__`	Overloaded function.
`__module__`
`__mul__`	Overloaded function.

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

__imul__(self, x: float) → visp._visp.core.RotationMatrix¶: Operator that allows to multiply all the elements of a rotation matrix by a scalar.

__init__(*args, **kwargs)¶

Overloaded function.

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

Default constructor that initialise a 3-by-3 rotation matrix to identity.

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

Copy constructor that construct a 3-by-3 rotation matrix from another rotation matrix.

__init__(self: visp._visp.core.RotationMatrix, M: visp._visp.core.HomogeneousMatrix) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.ThetaUVector) -> None
__init__(self: visp._visp.core.RotationMatrix, p: visp._visp.core.PoseVector) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.RzyzVector) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.RxyzVector) -> None
__init__(self: visp._visp.core.RotationMatrix, r: visp._visp.core.RzyxVector) -> None
__init__(self: visp._visp.core.RotationMatrix, q: visp._visp.core.QuaternionVector) -> None
__init__(self: visp._visp.core.RotationMatrix, R: visp._visp.core.Matrix) -> None
__init__(self: visp._visp.core.RotationMatrix, tux: float, tuy: float, tuz: float) -> None

Construct a 3-by-3 rotation matrix from \(\theta {\bf u}=(\theta u_x, \theta u_y, \theta u_z)^T\) angle representation.

__init__(self: visp._visp.core.RotationMatrix, list: std::initializer_list<double>) -> None
__init__(self: visp._visp.core.RotationMatrix, np_array: numpy.ndarray[numpy.float64]) -> None

Parameters:

np_array: The numpy 1D array to copy.

__mul__(*args, **kwargs)¶

Overloaded function.

__mul__(self: visp._visp.core.RotationMatrix, tv: visp._visp.core.TranslationVector) -> visp._visp.core.TranslationVector

Multiply a rotation matrix by a translation vector and return the resulting translation vector.

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

Compute the product between two rotation matrices.

__mul__(self: visp._visp.core.RotationMatrix, M: visp._visp.core.HomogeneousMatrix) -> visp._visp.core.HomogeneousMatrix

Operator that allows to multiply a rotation matrix by a homogeneous matrix.

The following snippet shows how to use this method:

vpRotationMatrix c1_R_c2;
vpHomogeneousMatrix c2_M_c3;
vpHomogeneousMatrix c1_M_c3 = c1_R_c2 * c2_M_c3;

Parameters:

M: Homogeneous matrix.

Returns:

The product between the rotation matrix and the homogeneous matrix M .

__mul__(self: visp._visp.core.RotationMatrix, M: visp._visp.core.Matrix) -> visp._visp.core.Matrix

Operator that allows to multiply a rotation matrix by a 3-by-3 matrix. Allows for example to multiply a rotation matrix by a skew matrix.

The following snippet shows how to use this method:

vpRotationMatrix R;
vpTranslationVector t;
vpMatrix M = t.skew();
vpMatrix RM = R * M;

Parameters:

M: 3-by-3 matrix.

Returns:

The product between the rotation matrix and the 3-by-3 matrix M .

__mul__(self: visp._visp.core.RotationMatrix, v: visp._visp.core.ColVector) -> visp._visp.core.ColVector

Operator that allows to multiply a rotation matrix by a 3 dimension column vector.

The code below shows how to use this operator.

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpRotationMatrix.h>

#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif

int main()
{
  vpColVector p1(3), p2(3);
  vpRotationMatrix R;

  p2 = R * p1;

  return 0;
}

Parameters:

v: Three dimension column vector.

Returns:

The product of the rotation matrix by the column vector

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

Operator that allows to multiply all the elements of a rotation matrix by a scalar.

__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.RotationMatrix, M: visp._visp.core.HomogeneousMatrix) -> visp._visp.core.RotationMatrix

Build a rotation matrix from an homogeneous matrix.

buildFrom(self: visp._visp.core.RotationMatrix, v: visp._visp.core.ThetaUVector) -> visp._visp.core.RotationMatrix

Transform a \(\theta {\bf u}\) angle representation into a rotation matrix.

The rotation is computed using :

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

buildFrom(self: visp._visp.core.RotationMatrix, p: visp._visp.core.PoseVector) -> visp._visp.core.RotationMatrix

Build a rotation matrix from a pose vector.

Note

See buildFrom(const vpThetaUVector &)

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

Transform a vector representing the Euler angle into a rotation matrix. Rzyz( \(\phi, \theta , \psi\) ) = Rot( \(z,\phi\) ) Rot( \(y,\theta\) ) Rot( \(z,\psi\) )

buildFrom(self: visp._visp.core.RotationMatrix, v: visp._visp.core.RxyzVector) -> visp._visp.core.RotationMatrix

Transform a vector representing the Rxyz angle into a rotation matrix. Rxyz( \(\phi,\theta, \psi\) ) = Rot( \(x, \psi\) ) Rot( \(y, \theta\) ) Rot( \(z,\phi\) )

buildFrom(self: visp._visp.core.RotationMatrix, v: visp._visp.core.RzyxVector) -> visp._visp.core.RotationMatrix

Transform a vector representing the Rzyx angle into a rotation matrix. Rxyz( \(\phi, \theta , \psi\) ) = Rot( \(z, \psi\) ) Rot( \(y, \theta\) )Rot( \(x, \phi\) )

buildFrom(self: visp._visp.core.RotationMatrix, q: visp._visp.core.QuaternionVector) -> visp._visp.core.RotationMatrix

Construct a 3-by-3 rotation matrix from a quaternion representation.

buildFrom(self: visp._visp.core.RotationMatrix, tux: float, tuy: float, tuz: float) -> visp._visp.core.RotationMatrix

Construct a 3-by-3 rotation matrix from \(\theta {\bf u}=(\theta u_x, \theta u_y, \theta u_z)^T\) angle representation.

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”.

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”.

eye(self) → None¶: Initialize the rotation matrix as identity.

Note

See setIdentity()

getCol(self, j: int) → visp._visp.core.ColVector¶

The following example shows how to use this function:

#include <visp3/core/vpColVector.h>
#include <visp3/core/vpRotationMatrix.h>

#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif

int main()
{
  vpRotationMatrix R;

  vpColVector r = R.getCol(2);
  std::cout << "Last column: \n" << r << std::endl;
}

It produces the following output:

Last column:
0
0
1

Parameters:

j: int¶: Index of the column to extract. If j=0, the first column is extracted.

Returns:

The extracted column vector.

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()

getThetaUVector(self) → visp._visp.core.ThetaUVector¶: Return the \(\theta {\bf u}\) vector that corresponds to the rotation matrix.

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.

inverse(*args, **kwargs)¶

Overloaded function.

inverse(self: visp._visp.core.RotationMatrix) -> visp._visp.core.RotationMatrix

Return the rotation matrix inverse which is also the transpose of the rotation matrix.

Note

See t()

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

Inverse the rotation matrix.

#include <visp3/core/vpRotationMatrix.h>

#ifdef ENABLE_VISP_NAMESPACE
using namespace VISP_NAMESPACE_NAME;
#endif

int main()
{
  vpRotationMatrix R, Rinv;
  // ... Update rotation matrix R
  // Compute the inverse in Rinv
  R.inverse(Rinv);
}

Parameters:

R: (output): Inverted rotation matrix.

isARotationMatrix(self, threshold: float = 1e-6) → bool¶

Test if the rotation matrix is really a rotation matrix.

Returns:: true if the matrix is a rotation matrix, false otherwise.

static mean(*args, **kwargs)¶

Overloaded function.

mean(vec_M: list[visp._visp.core.HomogeneousMatrix]) -> visp._visp.core.RotationMatrix

Compute the Euclidean mean of the rotation matrices extracted from a vector of homogeneous matrices following Moakher’s method (SIAM 2002).

Note

See vpTranslationVector::mean()

Parameters:

vec_M: Set of homogeneous matrices.

Returns:

The Euclidean mean of the rotation matrices.

mean(vec_R: list[visp._visp.core.RotationMatrix]) -> visp._visp.core.RotationMatrix

Compute the Euclidean mean of the rotation matrices following Moakher’s method (SIAM 2002).

Note

See vpTranslationVector::mean()

Parameters:

vec_R: Set of rotation matrices.

Returns:

The Euclidean mean of the rotation matrices.

numpy(self) → numpy.ndarray[numpy.float64]¶: Numpy view of the underlying array data. This numpy view cannot be modified. If you try to modify the array, an exception will be raised.

orthogonalize(self) → None¶: Perform rotation matrix orthogonalization.

printVector(self) → None¶: Print to std::cout the rotation matrix as a \(\theta {\bf u}\) angle representation vector.

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

resize(*args, **kwargs)¶

Overloaded function.

resize(self: visp._visp.core.RotationMatrix, nrows: int, ncols: int, flagNullify: bool = true) -> None

This function is not applicable to a rotation matrix that is always a 3-by-3 matrix.

resize(self: visp._visp.core.ArrayDouble2D, 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: 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.

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.

t(*args, **kwargs)¶

Overloaded function.

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

Return the rotation matrix transpose which is also the inverse of the rotation matrix.

Note

See inverse()

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

Compute the transpose of the array.

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

__hash__ = None¶