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

class RotationMatrix(*args, **kwargs)

Bases: pybind11_object

Overloaded function.

1. __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)
   

2. __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).

__mul__(*args, **kwargs)

Overloaded function.

1. __mul__(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix, arg0: ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix) -> ostk.mathematics.geometry.d3.transformation.rotation.RotationMatrix

2. __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