Add .pow(exponent) and .multiplyByExponentiatedQuaternion(quat2, exponent) methods to the Quaternion class

Is your feature request related to a problem? Please describe.

Hello! I want to be able to handle rotations in my engine in similar way to the positions - I can write position.addScaledVector(velocity, timePassed) if I want to program moving with some velocity frame-by-frame and I want to be able to do similar thing for quaternions (or at least thing similar to position.add(velocity.clone().scale(timePassed))), i.e. rotation.multiplyByExponentiatedQuaternion(rotationalVelocity, timePassed) (or rotation.multiply(rotationalVelocity.clone().pow(timePassed))).

Describe the solution you’d like

I suggest that methods .pow(exponent) and .multiplyByExponentiatedQuaternion(quat2, exponent) would be added to the Quaternion class.

Describe alternatives you’ve considered

These methods could be added just by monkey-patching the prototype of the Quaternion class (and it is how I do it currently).

Additional context

The methods could be implemented similar to glMatrix’s pow(out, a, b) function: https://github.com/toji/gl-matrix/blob/master/src/quat.js#L280.

[WestLangley]

@Mugen87 Conceptually, quaternion.pow() is the same as

const _vec3 = new THREE.Vector3();
const _vec4 = new THREE.Vector4();

//

_vec4.setAxisAngleFromQuaternion( q );

q.setFromAxisAngle( _vec3.set( _vec4.x, _vec4.y, _vec4.z ), _vec4.w * alpha );

Add pow() if you want, if it can be made efficient. I would not support adding the other method.

[Mugen87]

see https://github.com/mrdoob/three.js/pull/22970#issuecomment-991583290