Automate re-creating this shape that looks like a paper sphere template

This is the 1977 “Charles Ross: Light Placed” poster by Jacqueline Casey and it’s insane.

"Charles Ross - Light Placed" by Jacqueline Casey

I was wondering how would one re-create a similar shape in Illustrator relatively easily. Just to clarify: I’m talking specifically about the shape which appears like a template for making a paper sphere, and not the contents.

Here’s what I tried:

  • creating

    1. a 100×100mm circle with the inner stroke of 20mm and
    2. a 20×314mm rectangle (h=2×PI×r)

    and then blending the two – didn’t work

  • image-tracing an existing template – too limited

  • drawing the shape manually using pen tool – too time consuming and not precise enough; also not flexible
  • creating a small and a big circles then blending the two – this may work only when knowing which circle sizes to use, I couldn’t figure out how to calculate

I feel like there’s an easy way which I’m missing. Please share any ideas you may have

Answer

My approach would be modeling a 3D sphere using Blender and converting it into a 3D craftable paper model using this: https://tamasoft.co.jp/pepakura-en/order/index.html (No affiliation here)


A slower, but a free method, would be taking the initial 3D model, and extracting a base polygon of each row aligning it with the camera viewport. https://blender.stackexchange.com/questions/15045/how-do-i-align-the-viewport-to-a-face-normal

enter image description here

enter image description here

Another option would be manually marking the seams of the 3D model and unwrapping it. The process is a bit specific, so look at some tutorials online pls.

https://en.wikibooks.org/wiki/Blender_3D:_Noob_to_Pro/UV_Map_Basics

This is the result of partial work… Just a test.

But unwrapping can produce not exact shapes, that potentially do not assemble well on a real paper model, so use the previous method, face per face one.

enter image description here

But a more exact way would be taking the mathematical approach @user287001 uses.

Attribution
Source : Link , Question Author : WhatHiFi , Answer Author : Rafael

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