Unroll a planar curve

[AntoineSfx]

Is there a clever way to unroll a planar curve, of course in a progressive way ?

The effect I'm trying to achieve is a rug unrolling after an initial impulse , or with the effect  of a constant force in a fixed direction.

So far, I've tried to stitch curves created to the specifications explicitly (one line + 1 Archimedean spiral) but it's neither very stable nor procedural. This is highly dependent on the parametric equation of the initial curve.

I was thinking of doing something like this:  once I have the resampled curve as polygon, I could define the whole curve as a n-uple of (vector, angle), angle being the relative angle to the next point. Then flatten the curve by changing all the angles to zero, in a nice ease in / ease out, several points at a time.

[mestela]

Quite a few answers come up if you search for 'unroll' here. Several solutions in this thread:

http://forums.odforce.net/topic/31600-spiral-unrolling-rolling-animation/?do=findComment&comment=174963

 

 

[AntoineSfx]

Thanks. BTW the search function used by Invision is confusing. I didn't find it for some reason and I almost sent another Hawaii’s missile alert.