wrap a line

I would set that kind of work up in Illustrator. The illustration would be a combination of the spiral unwrapping and some straight lines with trim paths added on other layers. Here's how to set up the AI file and turn it into an animation.

By far the easiest way to do what you are trying to do would be to spend a few hours learning how to do wireframe animations in Blender. (http://blender.org). C4D lite that comes with AE does not have the animation tools available to create that kind of animation. Blender does and it's free.

You have to animate the mask/ shape path by hand and in your case you are going to need more than one shape/ mask, anyway. It's all just good old 2D animation and illusion painting.

Mylenium