Hello everyone, I am still a beginner with Rhino. If there are any issues with my question or code, I would greatly appreciate your corrections. Thank you.
Thank you for your reply. Since I hope to incorporate the formulas from the paper (as mentioned earlier) once I become more proficient, I really appreciate it.
Thank you for your reply, but I hope to use this program to derive similar results, as I intend to incorporate the formulas from the aforementioned paper in the future to analyze the effects of different grid structures.
Here is the reference; this method uses Galapagos for optimization to find the grid with the lowest curvature. You can see that the output grid is composed of curves.
I may not have expressed myself clearly enough. My ultimate goal is to implement the second and third types of grids shown in the image in Rhino using the Variational Method. (The following content is excerpted from Elisa Lafuente Hernández’s paper On the Design and Construction of Elastic Gridshells with Irregular Meshes). It doesn’t necessarily have to be done with scripting—if it can be achieved using Kangaroo or other methods, that would also be great. I would really appreciate it!
Hi, I’ve studied it. This component rotates the mesh points on the surface, which may not achieve my goal, although it looks very similar… Thanks for your input, I will keep trying!
if I make any progress, I will share my findings (if you’re interested…). My goal is to figure out the method for generating the irregular grid on the spherical surface that I mentioned earlier.
If your goal is curves on a sphere then why post a hyperbolic paraboloid (saddle surface)?
Yeah, I’d be very surprised if my artistic doodles have anything in common with your goals.
Still, I made some improvements.
Instead of centroids of SubSrf fragments, I’m now using their corner points.
Added orange group to reduce fragments affected, which helps avoid weird effects when rotating the grid and points go off the surface. (best seen in Top view)
Added a Graph Mapper to accelerate rotation angles for points further from the center.
Hi, I spent some time studying your component, and I learned a lot from it. Thank you very much!
I chose the saddle shape because I want to compare it with an asymptotic grid in the future. However, I might need to first implement it on a spherical surface. Therefore, I modified your component to conduct the following experiment.
This is interesting, but there are also some issues:
The projection method does not work well in nearly vertical areas.
I’m still not very familiar with the UV mapping on a sphere…
The points become denser as they get closer to the rotation center (which, in this case, is the top of the sphere). However, when compared to the results in the paper, the points at the top of the sphere are actually more spaced out (similar to a geodesic grid).
Hi, thank you for your responses over the past few days. I just finished studying your GH code.
I only made a simple modification (the part for selecting mesh faces).
gride_with_galapago.gh (43.7 KB)
It may not be possible for all points to rotate in the same direction… but it’s already very close. (The density can still be adjusted.)
The discussions over the past few days have been very beneficial to me. Thank you again!!!
Or are taking me seriously 
