Creating Scutoid cells in Grasshopper- based on voronoi cell diagram

Hello all,
right now I am focusing on developing a 3-dimensional geometry based on Scutoids (original article: https://www.nature.com/articles/s41467-018-05376-1 ; wiki: https://en.wikipedia.org/wiki/Scutoid).

Based on the articles and the definition, I started working on a script. So far I just created a diagram how the geometry can be visualized - using the Voronoi 2D component.
My Apical (A) geometry is just series of Populate 2D points, which I am moving in Z direction and then scaling in one direction to achieve different distribution of Voronoi cells - Basal geometry (B).
Then, I am layering this gradient of Voronoi cells in Z-direction and here already I can see that it is creating sctutoid-like geometry. (I enclosed file ScutoidDiagram.gh)
What I have now seems not to be enough, because:

  • I cannot define this one point of transition where the topological change happens (basically, the point where the triangle is defined). (enclosed file PointsOfTransition.png)
  • When lofting those layers, Grasshopper/Rhino cannot read it correctly, because of this point of transition, where one point splits into two and then creates a triangle. When taking one lofted cell then, I can see that the loft was not done correctly (enclosed LoftedCell.png; LoftedGroupOfCells.png).

For now, I would also like to extract those specific moments, where the transition (triangulation) is happening so I can continue working with it furthermore, but so far I cannot see how.

If anyone would have a tip, how to fix any of my issues which I have decribed, I would be superrhappy and grateful.
Thank you very much for any help with the script!

Cheers,
Veronika

ScutoidDiagram.gh (10.3 KB)

Hi Veronika,

First, I think maybe this Developer category is not so good to be reached by everyone (just developers)
I guess is better to swith to “Grasshopper” to get more feedback.

Well, Scutoids are new for me, I just knew them a couple of day ago, but it sounds very interesting and challenging.

I understand your approach, but maybe first is better to understand how a polygon with N-sides morphs to a polygon with N+1-sides.
I’ve seen some aproaches using trigonommetry, but always resolving a regular pentagon to a regular hexagon, like the more popular example of Scutoids.
But I think the problem is a bit more complex since voronoi will generate N-side polygons. So the thing is how to create that stage in between the basal and apical voronoi tesselation to start the bifurcation (or the topological change as you said).

My last attempt has the double deck Voronoi and changing the scale on X-axis I can see the branches how they change in the N-sides, but I can not find the way to turn a switch on when that happens and also creating the extra triangle is needed.

This weekend I will study about Data Trees and I hope to get better knowledge to handle this.

I hope it helps you somehow. Let’s see how it goes.
Good luck!

ScutoidRM.gh (33.7 KB)

Maybe tagging some people who know more could help. @HS_Kim @flatform @laurent_delrieu @fraguada @dale @DanielPiker

Any ideas? Thank you

I need that Scutoid cell for my design project, but me also couldnt make it. Any ideas to design it?

I just browsed through this paper and it’s highly complex. And by the look of it this will be impossible to recreate with just grasshopper components. It would need to be programmed with proper Object Oriented design and a good technical understanding of the principals of what the paper is explaining.

My first impression is that probably this patterns are not generated geometrically speaking but rather more on a mathematical level, think of a reaction diffusion system ( just google Karl sims reaction diffusion) those patterns are emergent from a set of rules and are not constructed on geometrical manipulations. Now if you would try to Make a reaction diffusion in 3D it would just be a matter of layering the values over time and then visualizing the geometry with a marching cubes algorithm. The Beauty about natural phenomena is how complexity emerges from simple rules of interaction.

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