"Stretch/bend" BitmapData or vector graphics

How would one go about drawing bitmap data or vector shapes to “bend” around in some fashion?

I’m working on a quick “rope/string physics” class, and I want some way to render the result by instead of having several “rectangles” between each point, I want to smooth them out and make them into curves instead.

Anyone done this before or at least have any idea where I could start?