Spiral effect from a polygon

jesus.villarreal.wrk · July 16, 2018, 6:34pm

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!

Baris · July 16, 2018, 6:59pm

you could do it that way:

poly.gh (6.2 KB)

HS_Kim · July 16, 2018, 7:02pm

Check this as well…

PolygonalSpiral_re.gh (11.3 KB)

tim.stark · July 16, 2018, 7:31pm

Just for fun, one with recursion.

growingNgon.gh (10.1 KB)

anikolo · July 16, 2018, 10:36pm

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

jeff_hammond · July 16, 2018, 11:42pm

i think @HS_Kim’s is correct

jesus.villarreal.wrk · July 17, 2018, 10:00am

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!

maje90 · July 18, 2018, 12:59am

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”.

anikolo · July 21, 2018, 9:39am

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

jesus.villarreal.wrk · July 30, 2018, 10:58pm

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

dripps · July 31, 2018, 5:04pm

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.

dripps · July 31, 2018, 5:23pm

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