How do I modify the interpolation of control point animations?

It can be done (to a certain extent), but it would help to know exactly how you want to implement the animation? Is it a specific keyframing situation or an automatic animation of some type?

The "trick" to get something like this to work is to use a Track Points for the one point to be animated and *another* Track Points to "stick" all the other points in the Shape to a "still" point (do not Reset the attached points but DO set the Transform to Attach to Source).

Track Points ONLY works with images (it cannot be used with other shapes.) The most common tracker image is the Crosshair Minute.png (in the Content Library).

(For this demo, an Oscillate behavior was applied to the Crosshair image, but it can also be set up to be controlled by an OnScreen Control or simply keyframe the position.)

Hello CrispOne

Interpolation is not possible when points are directly key framed this way. You still have options available to you.

If you are aware of how to use the track point behavior, you can isolate points by tracking them to individual layers, with the interpolation applied to the layers. The practicality of that method depend entirely on the animation you want to achieve. It is not reliable in many cases and in general, it is not the intended use case for the track point behavior, however in some situations, it can be effective.

You also have various distortion filters available that you can work with.

You should also consider using multiple shape layers to work together. You might find with by combining shape layers, using masks and animating by geometry and by scale that you can achieve the result you are looking for.

It would be ideal if you could post some kind of visual reference/story board for the result you want. That way we can better help you.