__pow__#
- Rotation.__pow__()#
Compose this rotation with itself n times.
Composition of a rotation
p
with itself can be extended to non-integern
by considering the powern
to be a scale factor applied to the angle of rotation about the rotation’s fixed axis. The expressionq = p ** n
can also be expressed asq = Rotation.from_rotvec(n * p.as_rotvec())
.If
n
is negative, then the rotation is inverted before the power is applied. In other words,p ** -abs(n) == p.inv() ** abs(n)
.- Parameters:
- nfloat
The number of times to compose the rotation with itself.
- modulusNone
This overridden argument is not applicable to Rotations and must be
None
.
- Returns:
- power
Rotation
instance If the input Rotation
p
containsN
multiple rotations, then the output will containN
rotations where thei
th rotation is equal top[i] ** n
- power
Notes
For example, a power of 2 will double the angle of rotation, and a power of 0.5 will halve the angle. There are three notable cases: if
n == 1
then the original rotation is returned, ifn == 0
then the identity rotation is returned, and ifn == -1
thenp.inv()
is returned.Note that fractional powers
n
which effectively take a root of rotation, do so using the shortest path smallest representation of that angle (the principal root). This means that powers ofn
and1/n
are not necessarily inverses of each other. For example, a 0.5 power of a +240 degree rotation will be calculated as the 0.5 power of a -120 degree rotation, with the result being a rotation of -60 rather than +120 degrees.Examples
>>> from scipy.spatial.transform import Rotation as R
Raising a rotation to a power:
>>> p = R.from_rotvec([1, 0, 0]) >>> q = p ** 2 >>> q.as_rotvec() array([2., 0., 0.]) >>> r = p ** 0.5 >>> r.as_rotvec() array([0.5, 0., 0.])
Inverse powers do not necessarily cancel out:
>>> p = R.from_rotvec([0, 0, 120], degrees=True) >>> ((p ** 2) ** 0.5).as_rotvec(degrees=True) array([ -0., -0., -60.])