Creating 2D spirals from closed curves?

I found this in a search, it’s a little relevant in explaining my goal. That is, going from figure A to figure H, using either a polygonal or curved shape. I know someone has done something like this already, there are probably several discussions on it here and/or the old grasshopper forums but I can’t find anything, I perhaps don’t know the right terminology.

Has anyone seen something like this or have an idea on where to begin?

Thank you!


Hi @closedcurve check this paper.


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Just wanted to give a heads-up that the paper isn’t available anymore. I’ve been reading just about every topic related to the spiraling and it almost always gets mentioned. However, the famous paper has disappeared.

Would anyone have a backup of it somewhere?

Was it this one?

Or this?


I wasn’t aware of the 2nd paper, thankyou for that. I attempted this a few years ago, but stalled out on integrating the nodes together.

Thanks for sharing! Very interesting reads.

Following this discussion

I wanted to give a try to a method to spiralize a convex polygon, I already did this some time ago on this discussion

The algorithm use Clipper for the offset, the departure of the spiral depends on a point
There is 2 types of spiral, the stepped one