How to create an editable slider like in Osu?

So I’m not looking for someone to give me the code to this but rather someone to give me the theory behind this and how it could work on Unity. If you’ve never seen Osu then the sliders look like this:
55334-osu-slider.png

Each of the 3 little circles in the curve are where the slider can be manipulated to create different curves/shapes. It doesn’t need to be as advanced as this but just being able to move one of the big circles and have the curve adjust accordingly would be nice.

In summary what I’m looking for is to create 2 circular sprites and create a bridge between them that adjusts and stays connected if I move the circles around. If any help could be given into manipulating the curve even more then that would perfect!

Thanks for any help!

Use Bezier Curves… Or Catmull Rom.

You can check my bezier curves as a reference to build your own, or use them if you want.
https://bitbucket.org/eestradalucero/unitycurves