Spiral effect from a polygon

Grasshopper
1

Hello,

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.

spiral

Thanks in advance!

2

you could do it that way:

poly
poly1450×689 72.6 KB

poly.gh (6.2 KB)

4 Likes
3

Check this as well…

Canvas%20at%2003%3B59%3B39
Canvas at 03;59;39.jpg1471×699 210 KB
PolygonalSpiral_re.gh (11.3 KB)

4 Likes
4

Just for fun, one with recursion.

growingNgon
growingNgon1325×754 96 KB

growingNgon.gh (10.1 KB)

4 Likes
5

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.

1
1.jpg1220×402 191 KB

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)

spiral
spiral.png1019×723 85.1 KB

Edit: Tim’s is the same (geometrically) as Kim’s
2

6

i think @HS_Kim’s is correct :slight_smile:

7

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!

8

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:

polygon-spiral
polygon-spiral.gif638×602 1.52 MB

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
polygon-spiral.png837×478 84.7 KB

polygon-spiral.gh (10.4 KB)

Edit: This is a “involute spiral”.

9 Likes
9

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

10

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

11

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.

2 Likes
12

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

4 Likes