ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

class RotationMatrix(*args, **kwargs)¶

Bases: pybind11_object

Overloaded function.

__init__(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, matrix: numpy.ndarray[numpy.float64[3, 3]]) -> None
Create a rotation matrix from a 3x3 matrix.
Args:
matrix (Matrix3d): A 3x3 matrix representing the rotation.

Example:
>>> matrix = Matrix3d.identity() >>> rotation_matrix = RotationMatrix(matrix)
__init__(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, first_coefficient: ostk.core.type.Real, second_coefficient: ostk.core.type.Real, third_coefficient: ostk.core.type.Real, fourth_coefficient: ostk.core.type.Real, fifth_coefficient: ostk.core.type.Real, sixth_coefficient: ostk.core.type.Real, seventh_coefficient: ostk.core.type.Real, eighth_coefficient: ostk.core.type.Real, ninth_coefficient: ostk.core.type.Real) -> None
Create a rotation matrix from nine coefficients (row-major order).
Args:
first_coefficient (float): Matrix element (0,0). second_coefficient (float): Matrix element (0,1). third_coefficient (float): Matrix element (0,2). fourth_coefficient (float): Matrix element (1,0). fifth_coefficient (float): Matrix element (1,1). sixth_coefficient (float): Matrix element (1,2). seventh_coefficient (float): Matrix element (2,0). eighth_coefficient (float): Matrix element (2,1). ninth_coefficient (float): Matrix element (2,2).

Example:
>>> rot_matrix = RotationMatrix(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0)

Methods

`columns`	Create a rotation matrix from column vectors.
`euler_angle`	Create a rotation matrix from Euler angles.
`get_column_at`	Get a column of the rotation matrix at specified index.
`get_matrix`	Get the underlying 3x3 matrix.
`get_row_at`	Get a row of the rotation matrix at specified index.
`is_defined`	Check if the rotation matrix is defined.
`quaternion`	Create a rotation matrix from a quaternion.
`rotation_vector`	Create a rotation matrix from a rotation vector.
`rows`	Create a rotation matrix from row vectors.
`rx`	Create a rotation matrix for rotation around the X-axis.
`ry`	Create a rotation matrix for rotation around the Y-axis.
`rz`	Create a rotation matrix for rotation around the Z-axis.
`to_transposed`	Get the transpose of this rotation matrix.
`transpose`	Transpose the rotation matrix in place.
`undefined`	Create an undefined rotation matrix.
`unit`	Create a unit rotation matrix (identity matrix).
`vector_basis`	Create a rotation matrix from two pairs of vectors.

__mul__(*args, **kwargs)¶

Overloaded function.

__mul__(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, arg0: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix) -> ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix
__mul__(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, arg0: numpy.ndarray[numpy.float64[3, 1]]) -> numpy.ndarray[numpy.float64[3, 1]]

static columns( first_column: numpy.ndarray[numpy.float64[3, 1]], second_column: numpy.ndarray[numpy.float64[3, 1]], third_column: numpy.ndarray[numpy.float64[3, 1]], ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix from column vectors.

Parameters:

first_column (Vector3d) -- The first column of the rotation matrix.
second_column (Vector3d) -- The second column of the rotation matrix.
third_column (Vector3d) -- The third column of the rotation matrix.

Returns:

A rotation matrix from column vectors.

Return type:

RotationMatrix

Example

>>> rot_matrix = RotationMatrix.columns(Vector3d(1.0, 0.0, 0.0), Vector3d(0.0, 1.0, 0.0), Vector3d(0.0, 0.0, 1.0))

static euler_angle( euler_angle: ostk::mathematics::geometry::d3::transformation::rotation::EulerAngle, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix from Euler angles.

Parameters:: euler_angle (EulerAngle) -- The Euler angles to convert.
Returns:: The equivalent rotation matrix.
Return type:: RotationMatrix

Example

>>> euler = EulerAngle.unit()
>>> rot_matrix = RotationMatrix.euler_angle(euler)

get_column_at( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, index: int, ) → numpy.ndarray[numpy.float64[3, 1]]¶

Get a column of the rotation matrix at specified index.

Parameters:: index (int) -- The column index (0, 1, or 2).
Returns:: The column vector at the specified index.
Return type:: Vector3d

Example

>>> rot_matrix = RotationMatrix.unit()
>>> first_column = rot_matrix.get_column_at(0)  # [1, 0, 0]

get_matrix( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, ) → numpy.ndarray[numpy.float64[3, 3]]¶

Get the underlying 3x3 matrix.

Returns:: The 3x3 rotation matrix.
Return type:: Matrix3d

Example

>>> rot_matrix = RotationMatrix.unit()
>>> matrix = rot_matrix.get_matrix()

get_row_at( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, index: int, ) → numpy.ndarray[numpy.float64[3, 1]]¶

Get a row of the rotation matrix at specified index.

Parameters:: index (int) -- The row index (0, 1, or 2).
Returns:: The row vector at the specified index.
Return type:: Vector3d

Example

>>> rot_matrix = RotationMatrix.unit()
>>> first_row = rot_matrix.get_row_at(0)  # [1, 0, 0]

is_defined( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, ) → bool¶

Check if the rotation matrix is defined.

Returns:: True if the rotation matrix is defined, False otherwise.
Return type:: bool

Example

>>> rot_matrix = RotationMatrix(Matrix3d.identity())
>>> rot_matrix.is_defined()  # True

static quaternion( quaternion: ostk.mathematics.geometry.d3.transformation.rotation.Quaternion, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix from a quaternion.

Parameters:: quaternion (Quaternion) -- The quaternion to convert.
Returns:: The equivalent rotation matrix.
Return type:: RotationMatrix

Example

>>> quat = Quaternion.unit()
>>> rot_matrix = RotationMatrix.quaternion(quat)

static rotation_vector( rotation_vector: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix from a rotation vector.

Parameters:: rotation_vector (RotationVector) -- The rotation vector to convert.
Returns:: The equivalent rotation matrix.
Return type:: RotationMatrix

Example

>>> rot_vector = RotationVector.unit()
>>> rot_matrix = RotationMatrix.rotation_vector(rot_vector)

static rows( first_row: numpy.ndarray[numpy.float64[3, 1]], second_row: numpy.ndarray[numpy.float64[3, 1]], third_row: numpy.ndarray[numpy.float64[3, 1]], ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix from row vectors.

Parameters:

first_row (Vector3d) -- The first row of the rotation matrix.
second_row (Vector3d) -- The second row of the rotation matrix.
third_row (Vector3d) -- The third row of the rotation matrix.

Returns:

A rotation matrix from row vectors.

Return type:

RotationMatrix

Example

>>> rot_matrix = RotationMatrix.rows(Vector3d(1.0, 0.0, 0.0), Vector3d(0.0, 1.0, 0.0), Vector3d(0.0, 0.0, 1.0))

static rx( rotation_angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix for rotation around the X-axis.

Parameters:: rotation_angle (Angle) -- The angle of rotation around X-axis.
Returns:: A rotation matrix for X-axis rotation.
Return type:: RotationMatrix

Example

>>> rot_x = RotationMatrix.rx(Angle.degrees(90.0))

static ry( rotation_angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix for rotation around the Y-axis.

Parameters:: rotation_angle (Angle) -- The angle of rotation around Y-axis.
Returns:: A rotation matrix for Y-axis rotation.
Return type:: RotationMatrix

Example

>>> rot_y = RotationMatrix.ry(Angle.degrees(90.0))

static rz( rotation_angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix for rotation around the Z-axis.

Parameters:: rotation_angle (Angle) -- The angle of rotation around Z-axis.
Returns:: A rotation matrix for Z-axis rotation.
Return type:: RotationMatrix

Example

>>> rot_z = RotationMatrix.rz(Angle.degrees(90.0))

to_transposed( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Get the transpose of this rotation matrix.

Returns:: The transposed rotation matrix.
Return type:: RotationMatrix

Example

>>> rot_matrix = RotationMatrix.rx(Angle.degrees(90.0))
>>> transposed = rot_matrix.to_transposed()

transpose( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, ) → None¶

Transpose the rotation matrix in place.

Example

>>> rot_matrix = RotationMatrix.rx(Angle.degrees(90.0))
>>> rot_matrix.transpose()

static undefined() → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create an undefined rotation matrix.

Returns:: An undefined rotation matrix.
Return type:: RotationMatrix

Example

>>> undefined_matrix = RotationMatrix.undefined()
>>> undefined_matrix.is_defined()  # False

static unit() → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a unit rotation matrix (identity matrix).

Returns:: The 3x3 identity rotation matrix.
Return type:: RotationMatrix

Example

>>> unit_matrix = RotationMatrix.unit()
>>> matrix = unit_matrix.get_matrix()  # 3x3 identity matrix

static vector_basis( source_vectors: tuple[numpy.ndarray[numpy.float64[3, 1]], numpy.ndarray[numpy.float64[3, 1]]], destination_vectors: tuple[numpy.ndarray[numpy.float64[3, 1]], numpy.ndarray[numpy.float64[3, 1]]], ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix¶

Create a rotation matrix from two pairs of vectors.

Constructs orthonormal basis frames from each pair of vectors and returns the rotation matrix that transforms from the source basis to the destination basis. The first vector defines the primary direction, and the second vector is used to determine the orientation of the basis (via cross product).

Parameters:

source_vectors (tuple[numpy.array, numpy.array]) -- A pair of 3-dimensional source vectors.
destination_vectors (tuple[numpy.array, numpy.array]) -- A pair of 3-dimensional destination vectors.

Returns:

Rotation matrix transforming from source to destination basis.

Return type:

RotationMatrix

Example

>>> # Identity rotation
>>> source1 = numpy.array([1.0, 0.0, 0.0])
>>> source2 = numpy.array([0.0, 1.0, 0.0])
>>> rot = RotationMatrix.vector_basis((source1, source2), (source1, source2))

>>> # 90-degree rotation around Z-axis
>>> dest1 = numpy.array([0.0, 1.0, 0.0])
>>> dest2 = numpy.array([-1.0, 0.0, 0.0])
>>> rot = RotationMatrix.vector_basis((source1, source2), (dest1, dest2))