Package Scientific :: Package Geometry :: Module Transformation :: Class Rotation

Class Rotation

     Transformation --+    
                      |    
RigidBodyTransformation --+
                          |
                         Rotation

Rotational transformation

Instance Methods

Scientific.Geometry.Vector

__call__(self, other)
Returns: the transformed vector

__init__(self, *args)
There are two calling patterns:

__mul__(self, other)

asLinearTransformation(self)

Scientific.Geometry.Quaternion.Quaternion

asQuaternion(self)
Returns: a quaternion representing the same rotation

(Scientific.Geometry.Vector, float)

axisAndAngle(self)
Returns: the axis (a normalized vector) and angle (in radians).

Transformation

inverse(self)
Returns: the inverse transformation

Rotation

rotation(self)
Returns: the rotational component

screwMotion(self)
Returns: the four parameters (reference, direction, angle, distance) of a screw-like motion that is equivalent to the transformation.

list of N.array

threeAngles(self, e1, e2, e3, tolerance=1e-07)
Find three angles a1, a2, a3 such that Rotation(a1*e1)*Rotation(a2*e2)*Rotation(a3*e3) is equal to the rotation object.

Translation

translation(self)
Returns: the translational component.

Class Variables
	is_rotation = `1`

Method Details

call(self, other)
(Call operator)

Parameters:

vector - the input vector

Returns: Scientific.Geometry.Vector

the transformed vector

Overrides: Transformation.__call__

(inherited documentation)

init(self, args)
(Constructor)*

There are two calling patterns:

Rotation(tensor), where tensor is a Scientific.Geometry.Tensor of rank 2 containing the rotation matrix.
Rotation(axis, angle), where axis is a Scientific.Geometry.Vector and angle a number (the angle in radians).

asQuaternion(self)

Returns: Scientific.Geometry.Quaternion.Quaternion: a quaternion representing the same rotation

axisAndAngle(self)

Returns: (Scientific.Geometry.Vector, float): the axis (a normalized vector) and angle (in radians). The angle is in the interval (-pi, pi]

inverse(self)

Returns: Transformation: the inverse transformation
Overrides: Transformation.inverse: (inherited documentation)

rotation(self)

Returns: Rotation: the rotational component
Overrides: RigidBodyTransformation.rotation: (inherited documentation)

screwMotion(self)

Returns:: the four parameters (reference, direction, angle, distance) of a screw-like motion that is equivalent to the transformation. The screw motion consists of a displacement of distance (a float) along direction (a normalized Scientific.Geometry.Vector) plus a rotation of angle radians around an axis pointing along direction and passing through the point reference (a Scientific.Geometry.Vector).
Overrides: RigidBodyTransformation.screwMotion: (inherited documentation)

threeAngles(self, e1, e2, e3, tolerance=1e-07)

Find three angles a1, a2, a3 such that Rotation(a1*e1)*Rotation(a2*e2)*Rotation(a3*e3) is equal to the rotation object. e1, e2, and e3 are non-zero vectors. There are two solutions, both of which are computed.

Parameters:

e1 (Scientific.Geometry.Vector) - a rotation axis
e2 (Scientific.Geometry.Vector) - a rotation axis
e3 (Scientific.Geometry.Vector) - a rotation axis

Returns: list of N.array

a list containing two arrays of shape (3,), each containing the three angles of one solution

Raises:

ValueError - if two consecutive axes are parallel

translation(self)

Returns: Translation: the translational component. In the case of a mixed rotation/translation, this translation is executed after the rotation.
Overrides: RigidBodyTransformation.translation: (inherited documentation)