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

class RotationVector(*args, **kwargs)¶

Bases: pybind11_object

Overloaded function.

__init__(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector, axis: numpy.ndarray[numpy.float64[3, 1]], angle: ostk::mathematics::geometry::Angle) -> None
Create a rotation vector from axis and angle.
Args:
axis (numpy.array): The rotation axis (will be normalized). angle (Angle): The rotation angle around the axis.

Example:
>>> axis = numpy.array([0.0, 0.0, 1.0]) >>> angle = Angle.degrees(90.0) >>> rot_vector = RotationVector(axis, angle)
__init__(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector, vector: numpy.ndarray[numpy.float64[3, 1]], angle_unit: ostk::mathematics::geometry::Angle::Unit) -> None
Create a rotation vector from a vector representation.
Args:
vector (numpy.array): The rotation vector (magnitude represents angle). angle_unit (Angle.Unit): The unit of the angle in the vector magnitude.

Example:
>>> vector = numpy.array([0.0, 0.0, 1.5708]) # π/2 in z-axis >>> rot_vector = RotationVector(vector, Angle.Unit.Radian)

Methods

`euler_angle`	Create a rotation vector from Euler angles.
`get_angle`	Get the rotation angle.
`get_axis`	Get the rotation axis vector.
`is_defined`	Check if the rotation vector is defined.
`quaternion`	Create a rotation vector from a quaternion.
`rectify`	Rectify the rotation vector in-place (ensure angle is in [0, π]).
`rotation_matrix`	Create a rotation vector from a rotation matrix.
`to_string`	Overloaded function.
`undefined`	Create an undefined rotation vector.
`unit`	Create a unit rotation vector (no rotation).
`x`	Create a rotation vector around the x-axis.
`y`	Create a rotation vector around the y-axis.
`z`	Create a rotation vector around the z-axis.

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

Create a rotation vector from Euler angles.

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

Example

>>> ea = EulerAngle.zyx(Angle.degrees(30), Angle.degrees(45), Angle.degrees(60))
>>> rot_vector = RotationVector.euler_angle(ea)

get_angle( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector, ) → ostk::mathematics::geometry::Angle¶

Get the rotation angle.

Returns:: The rotation angle around the axis.
Return type:: Angle

Example

>>> rot_vector = RotationVector(axis, Angle.degrees(90.0))
>>> angle = rot_vector.get_angle()  # 90 degrees

get_axis( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector, ) → numpy.ndarray[numpy.float64[3, 1]]¶

Get the rotation axis vector.

Returns:: The normalized rotation axis.
Return type:: Vector3d

Example

>>> rot_vector = RotationVector(numpy.array([1.0, 0.0, 0.0]), angle)
>>> axis = rot_vector.get_axis()  # [1.0, 0.0, 0.0]

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

Check if the rotation vector is defined.

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

Example

>>> rot_vector = RotationVector(axis, angle)
>>> rot_vector.is_defined()  # True

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

Create a rotation vector from a quaternion.

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

Example

>>> q = Quaternion.unit()
>>> rot_vector = RotationVector.quaternion(q)

rectify( self: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector, ) → None¶

Rectify the rotation vector in-place (ensure angle is in [0, π]).

Example

>>> rot_vector = RotationVector(axis, Angle.degrees(270.0))
>>> rot_vector.rectify()  # Converts to equivalent rotation with angle ≤ π

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

Create a rotation vector from a rotation matrix.

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

Example

>>> rm = RotationMatrix.identity()
>>> rot_vector = RotationVector.rotation_matrix(rm)

to_string(*args, **kwargs)¶

Overloaded function.

to_string(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector) -> ostk.core.type.String
Convert the rotation vector to string representation.
Returns:
str: String representation of the rotation vector.

Example:
>>> rot_vector = RotationVector.unit() >>> rot_vector.to_string()
to_string(self: ostk.mathematics.geometry.d3.transformation.rotation.RotationVector, precision: ostk.core.type.Integer) -> ostk.core.type.String
Convert the rotation vector to string representation with specified precision.
Args:
precision (int): The precision for floating point numbers.

Returns:
str: String representation of the rotation vector.

Example:
>>> rot_vector = RotationVector.unit() >>> rot_vector.to_string(3)

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

Create an undefined rotation vector.

Returns:: An undefined rotation vector.
Return type:: RotationVector

Example

>>> undefined_vector = RotationVector.undefined()
>>> undefined_vector.is_defined()  # False

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

Create a unit rotation vector (no rotation).

Returns:: A rotation vector representing no rotation.
Return type:: RotationVector

Example

>>> unit_vector = RotationVector.unit()
>>> angle = unit_vector.get_angle()  # 0 degrees

static x( angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationVector¶

Create a rotation vector around the x-axis.

Parameters:: angle (Angle) -- The rotation angle around the x-axis.
Returns:: A rotation vector around the x-axis.
Return type:: RotationVector

Example

>>> rot_vector = RotationVector.x(Angle.degrees(90.0))

static y( angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationVector¶

Create a rotation vector around the y-axis.

Parameters:: angle (Angle) -- The rotation angle around the y-axis.
Returns:: A rotation vector around the y-axis.
Return type:: RotationVector

Example

>>> rot_vector = RotationVector.y(Angle.degrees(90.0))

static z( angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.RotationVector¶

Create a rotation vector around the z-axis.

Parameters:: angle (Angle) -- The rotation angle around the z-axis.
Returns:: A rotation vector around the z-axis.
Return type:: RotationVector

Example

>>> rot_vector = RotationVector.z(Angle.degrees(90.0))