How to roll up a plane/create a rolled yoga mat? [duplicate]

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I'm trying to create a rolled up yoga mat. I thought I could use the cloth simulator and run a physics animation to make a subdivided mesh roll itself up but I couldn't get it to work. Everything I tried just resulted in a cloth that was bent in lots of different directions.

So then I thought maybe I could run an animation to make the mesh roll itself around a cylinder. I guess for this to work I'd need to be able to pin the mesh to the cylinder, and then animate the cylinder rotating a few times. I guess I can rotate the cylinder by creating keyframes with 0 degrees of rotation then say 10 * 360 degrees rotation. But how can I parent one end of the mesh to the cylinder in the first place?

Or is there a better way to do this?

I'd also like to be able to have the corners of the mat slightly curled up when it's flat (e.g. like this but less pronounced) which makes me think perhaps physics is the way to go after all?

Answer 1

Here is a possible way:

First create a bezier like this:

which has control points like

then add the mat in a convenient position (I used a subdivided plane with solidify and subsurf) then use a curve modifier to the above bezier

if you animate the bezier along X you get this:

There could be other ways of course but I hope it helps you.