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

class EulerAngle(*args, **kwargs)¶

Bases: pybind11_object

Overloaded function.

__init__(self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle, phi: ostk::mathematics::geometry::Angle, theta: ostk::mathematics::geometry::Angle, psi: ostk::mathematics::geometry::Angle, axis_sequence: ostk::mathematics::geometry::d3::transformation::rotation::EulerAngle::AxisSequence) -> None
Create Euler angles from three angle components and axis sequence.
Args:
phi (Angle): The first rotation angle. theta (Angle): The second rotation angle. psi (Angle): The third rotation angle. axis_sequence (EulerAngle.AxisSequence): The axis sequence (XYZ, ZXY, ZYX).

Example:
>>> phi = Angle.degrees(30.0) >>> theta = Angle.degrees(45.0) >>> psi = Angle.degrees(60.0) >>> euler = EulerAngle(phi, theta, psi, EulerAngle.AxisSequence.XYZ)
__init__(self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle, vector: numpy.ndarray[numpy.float64[3, 1]], angle_unit: ostk::mathematics::geometry::Angle::Unit, axis_sequence: ostk::mathematics::geometry::d3::transformation::rotation::EulerAngle::AxisSequence) -> None
Create Euler angles from a 3D vector with specified angle unit and axis sequence.
Args:
vector (numpy.array): Vector containing the three angle values. angle_unit (Angle.Unit): The unit of the angles in the vector. axis_sequence (EulerAngle.AxisSequence): The axis sequence.

Example:
>>> vector = numpy.array([30.0, 45.0, 60.0]) >>> euler = EulerAngle(vector, Angle.Unit.Degree, EulerAngle.AxisSequence.XYZ)

Methods

`is_defined`	Check if the Euler angle is defined.
`is_near`	Check if this Euler angle is near another Euler angle within tolerance.
`is_unitary`	Check if the Euler angle represents a unit rotation.
`quaternion`	Create Euler angles from a quaternion with specified axis sequence.
`rotation_matrix`
`rotation_vector`
`to_string`	Overloaded function.
`to_vector`	Convert the Euler angle to a 3D vector with specified unit.
`undefined`	Create an undefined Euler angle.
`unit`	Create a unit Euler angle (no rotation).
`xyz`	Create Euler angles with XYZ axis sequence.
`zxy`	Create Euler angles with ZXY axis sequence.
`zyx`	Create Euler angles with ZYX axis sequence.

Attributes

`axis_sequence`
`phi`
`psi`
`theta`

class AxisSequence( self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle.AxisSequence, value: int, )¶

Bases: pybind11_object

Members:

Undefined

XYZ

ZXY

ZYX

property name¶

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

Check if the Euler angle is defined.

Returns:: True if the Euler angle is defined, False otherwise.
Return type:: bool

Example

>>> euler = EulerAngle(phi, theta, psi, EulerAngle.AxisSequence.XYZ)
>>> euler.is_defined()  # True

is_near( self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle, euler_angle: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle, angular_tolerance: ostk::mathematics::geometry::Angle, ) → bool¶

Check if this Euler angle is near another Euler angle within tolerance.

Parameters:

euler_angle (EulerAngle) -- The Euler angle to compare with.
angular_tolerance (Angle) -- The angular tolerance for comparison.

Returns:

True if angles are within tolerance, False otherwise.

Return type:

bool

Example

>>> euler1 = EulerAngle(phi1, theta1, psi1, sequence)
>>> euler2 = EulerAngle(phi2, theta2, psi2, sequence)
>>> euler1.is_near(euler2, Angle.degrees(1.0))

is_unitary( self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle, ) → bool¶

Check if the Euler angle represents a unit rotation.

Returns:: True if the Euler angle is unitary, False otherwise.
Return type:: bool

Example

>>> euler = EulerAngle.unit()
>>> euler.is_unitary()  # True

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

Create Euler angles from a quaternion with specified axis sequence.

Parameters:

quaternion (Quaternion) -- The quaternion to convert.
axis_sequence (EulerAngle.AxisSequence) -- The desired axis sequence.

Returns:

The equivalent Euler angles.

Return type:

EulerAngle

Example

>>> quat = Quaternion.unit()
>>> euler = EulerAngle.quaternion(quat, EulerAngle.AxisSequence.XYZ)

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

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

to_string(*args, **kwargs)¶

Overloaded function.

to_string(self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle) -> ostk.core.type.String
to_string(self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle, angle_unit: ostk::mathematics::geometry::Angle::Unit) -> ostk.core.type.String

to_vector( self: ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle, angle_unit: ostk::mathematics::geometry::Angle::Unit, ) → numpy.ndarray[numpy.float64[3, 1]]¶

Convert the Euler angle to a 3D vector with specified unit.

Parameters:: angle_unit (Angle.Unit) -- The unit for the output vector angles.
Returns:: A vector containing [phi, theta, psi] in the specified unit.
Return type:: Vector3d

Example

>>> euler = EulerAngle(phi, theta, psi, EulerAngle.AxisSequence.XYZ)
>>> vector = euler.to_vector(Angle.Unit.Degree)

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

Create an undefined Euler angle.

Returns:: An undefined Euler angle object.
Return type:: EulerAngle

Example

>>> undefined_euler = EulerAngle.undefined()
>>> undefined_euler.is_defined()  # False

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

Create a unit Euler angle (no rotation).

Returns:: A unit Euler angle representing no rotation.
Return type:: EulerAngle

Example

>>> unit_euler = EulerAngle.unit()
>>> unit_euler.is_unitary()  # True

static xyz( phi: ostk::mathematics::geometry::Angle, theta: ostk::mathematics::geometry::Angle, psi: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle¶

Create Euler angles with XYZ axis sequence.

Parameters:

phi (Angle) -- The first rotation angle around X-axis.
theta (Angle) -- The second rotation angle around Y-axis.
psi (Angle) -- The third rotation angle around Z-axis.

Returns:

An Euler angle with XYZ sequence.

Return type:

EulerAngle

Example

>>> euler = EulerAngle.xyz(Angle.degrees(30.0), Angle.degrees(45.0), Angle.degrees(60.0))

static zxy( phi: ostk::mathematics::geometry::Angle, theta: ostk::mathematics::geometry::Angle, psi: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle¶

Create Euler angles with ZXY axis sequence.

Parameters:

phi (Angle) -- The first rotation angle around Z-axis.
theta (Angle) -- The second rotation angle around X-axis.
psi (Angle) -- The third rotation angle around Y-axis.

Returns:

An Euler angle with ZXY sequence.

Return type:

EulerAngle

Example

>>> euler = EulerAngle.zxy(Angle.degrees(30.0), Angle.degrees(45.0), Angle.degrees(60.0))

static zyx( phi: ostk::mathematics::geometry::Angle, theta: ostk::mathematics::geometry::Angle, psi: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d3.transformation.rotation.EulerAngle¶

Create Euler angles with ZYX axis sequence.

Parameters:

phi (Angle) -- The first rotation angle around Z-axis.
theta (Angle) -- The second rotation angle around Y-axis.
psi (Angle) -- The third rotation angle around X-axis.

Returns:

An Euler angle with ZYX sequence.

Return type:

EulerAngle

Example

>>> euler = EulerAngle.zyx(Angle.degrees(30.0), Angle.degrees(45.0), Angle.degrees(60.0))