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