scipy.spatial.transform.Rotation.__pow__

Rotation.__pow__()

Compose this rotation with itself n times.

Composition of a rotation p with itself can be extended to non-integer n by considering the power n to be a scale factor applied to the angle of rotation about the rotation’s fixed axis. The expression q = p ** n can also be expressed as q = 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:

powerRotation instance

If the input Rotation p contains N multiple rotations, then the output will contain N rotations where the i th rotation is equal to p[i] ** n

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, if n == 0 then the identity rotation is returned, and if n == -1 then p.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 of n and 1/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

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>>> 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.])

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