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What is the Rodrigues' formula

If you want to rotate a point by an angle around a specific axis, you will most likely think about Quaternions. But what if I told you there is another way? Rodrigues' formula is as simple as it can be. I never benchmarked it, and chances are, for our needs, it's slower than over-optimized quaternions. But I find it pretty interesting, and hey, it's always nice to have alternatives =]

Implementation

There is not much more to say about it, so I'll just go ahead and provide a python snippet

    import numpy as np
    def rodrigues_formula(point: list, angle: float, vector: list):
        return point*np.cos(angle) + \
                np.cross(vector, point) * np.sin(angle) + \
                vector * np.dot(vector, point) * (1-np.cos(angle))

And to use it:

    # create an input locator, randomly placed
    input_point = cmds.spaceLocator(n='input_point')[0]
    v = np.random.rand(3)
    cmds.setAttr(f'{input_point}.t', *v)

    angle = np.pi/4. # let's do 45 deg because why not
    k = np.array((1, 0, 0))  # rotate around the X axis
    result = rodrigues_formula(point=v, angle=angle, vector=k)
    # now let's see how it looks
    loc = cmds.spaceLocator()[0]
    cmds.setAttr(loc + '.t', *result)

Voila, we just rotated our input locator by 45 degrees around the X axis.
Just for fun, I did the same operation with a quaternion, and we can see the result is identical

    from maya.api.OpenMaya import *
    quat = MQuaternion()
    quat.setValue(MVector(k), angle)
    point = MPoint(v)
    rotated = point * quat.asMatrix()
    loc = cmds.spaceLocator()[0]
    cmds.setAttr(loc + '.t', rotated.x, rotated.y, rotated.z)