Everybody knows the brand-new awesome animation inside iOS 7 Calendar app. You can see them in this short video: http://vimeo.com/69247779
I would recreating something like that creating a "modal" rectangle that appear when the user taps on a UIButton. When the user taps on this button the app should move an UIView (actually inside an UITableViewCell) and move it within this rectangle, BUT the original UIView should stay in the same place. It needs to duplicate itself, something alike.
I've created a simple image explaining the concept.

How to implement something like this?