Spiral effect from a polygon


I’m would like to create an spiral effect from any polygon in grasshopper, but I have no idea where to start with it. It has to be something like the following image.Can anybody point me in the right direction… video, tutorial, script, etc.


Thanks in advance!

you could do it that way:

poly.gh (6.2 KB)


Check this as well…

PolygonalSpiral_re.gh (11.3 KB)


Just for fun, one with recursion.

growingNgon.gh (10.1 KB)


I love these challenges that show you that you might think you know something but you actually don’t.

I tried to create what you asked based on the archimedean spiral. I thought that If I defined vertexes for specific angles and with a fixed radial step, the edges would by definition be parallel. They are not. After some head-scratching and looking at the other guys’ definitions I came to this conclusion:

You can only have 2 of 3:

  • vertexes will have a fixed radial step
  • vertexes will have a fixed offset step from the center
  • edges (of the same side) will be parallel

Kim sacrificed the radial step, Baris sacrificed the offset step and I sacrificed the parallelity of the edges.

From what I understand each approach has its merits, as long as you know what you are getting!
-and just to support the archimedean approach, the edges are not parallel in the beginning but approach parallelity as you add more turns-

spiral.gh (10.0 KB)

Edit: Tim’s is the same (geometrically) as Kim’s

i think @HS_Kim’s is correct :slight_smile:

Hello everyone!

Thanks for your help! I think all the approaches are right! I think that the one that I’ll use will be Kim’s approach as it is for cut something in CNC and it is easier to modify for different tools if you can control the offset.

Thanks again for your help!

Hi guys!

… what about a solution that (almost) respect all of those 3 points?
The red lines you drawn, Aris, shouldn’t intersect to a central point, but to a polygon.
I can’t explain better than this gif:

So, vertexes have a fixed radial step, edges are parallel, and the whole shape is a costant progression from the center.
Math was a bit tricky to make.

polygon-spiral.gh (10.4 KB)

Edit: This is a “involute spiral”.


Yes! this is it!
(and very nice animation too)

Wooooow! I just got to see this one! This is amazing! Thanks for sharing!

involute spiral 7.31.18.gh (17.1 KB)
Hi, I was also interested in this challenge but also wanted to avoid the tricky math that Riccardo so elegantly used.


involute spiral 7.31.18 v2.gh (22.7 KB)
This is an improved version with edges now being parallel. Multiple shapes now possible.