Still trying to understand the research. Essentially I want to use the same method shown in image two but on a dome or appropriate 3d Structure. (But instead of sphere collide use â€śTangentInCirclesâ€ť). The issue im having trouble solving is making sure that the angles y change proportionally and maintain the structure. If it was planar i would just scale from the base mesh to achieve the shrinking.

Hey Daniel, Amazing help! I played around with the script you have provided to work with circle packing using the vertices as the circle centers and works well however a bit of tolerance is lost as the circle packing is not perfect, Any suggestions on improving/tightening the tolerance (The original circle packing optimisation script can be found in the original post)? Regardless i imagine the joint/connection i design will accommodate such tolerances. TriMesh-CirclePacking_scissorlinkage_deploy1.gh (15.7 KB)

The aim would to be to make the structure more compactable compared to the constant angle version which can be calculated by scaling the entire group proportionally. I can manage it in 2 dimensions or â€śArrayedâ€ť systems but I was looking for a similar flexibility to that of the one you provided. Any help is appreciated!

Note that it is the incircle packing (in blue below) we need to use to make the linkage.
These can easily be made tangent to a very high degree of accuracy.
You just need to make sure that all other goals are turned off before getting the final geometry out.
(since for example also keeping the vertices exactly on a surface would likely conflict with the tangent incircles property by some amount and make it less accurate. You can use it for the initial shaping, but to strictly enforce tangent incircles turn everything else off)

The red circles on the other hand cannot possibly be perfectly tangent, except in the very specific case of a Koebe polyhedron where the mesh edges are all tangent to a single sphere.
For freeform meshes, when the faces are optimised for tangent incircles, there will be a set of tangent spheres centered at the mesh vertices, but the points of intersection of these spheres with the incircles will not form a circle.

Ah i see, so its not possible unless using Koebe Polyhedrons. Is the same said for using the â€śPolar Methodâ€ť for the scissor structure on a free form mesh, is it simply not possible? Are there any other readings you can suggest for the topic?