generating minimal surface in a cube

Hi all

I am trying to generate minimal surfaces in a cube in grasshopper. Please let me know how can I achieve this. The attached image is an example of what I am trying to emulate.

Thank you

Attachments:

ref.jpg, 50 KB

Replies to This Discussion

Permalink Reply by Lars Renklint on July 27, 2009 at 4:16pm

Missed this thread, very interesting. Hope you keep us posted.

There was a similar problem posted in another forum, and Thorolf (who is also a member here) made a video of how he solved it. Based on this I made a definition that creates a Batwing surface.

It seems that it's a bit similar.

The forum thread - Batwing
The video

Permalink Reply by Carlo Beltracchi on August 4, 2009 at 8:31am

It would be nice to link surface evolver with the grasshopper (but also mathematica or k3dsurf)

Permalink Reply by Jon Mirtschin on August 28, 2009 at 2:28am

This is quite an interesting thread that slipped past my attention. I thought it would be an interesting test for the minimal surface solver I've been developing into my plug-in. I'm attaching the initial results for the corner point boundary conditions. Is that surface fixing the free edges along those arcs? The only restraint for the attached file is the corner points. I'll run the solver over the arc boundary conditions over the weekend if you're interested.

Did you mangage to solve this another way?

Cheers,

Jon

Attachments:

090828 jm min surface cube corners.zip, 317 KB

Permalink Reply by Jon Mirtschin on August 29, 2009 at 8:23am

Well, I didn't quite get to the point of a converged solution, but here's the progress.

I'll park this for the time being unless it's interest to someone. I'll be able to progress further if anyone can point me to the best methods (or techniques) to either:
a. Deform a planar surface built with 6 sides to have the arc curve profile (I had my own crude technique for a meshed surface but the mesh gets distorted too far)
or b. Fit a nurbs surface to a mesh of the nature of that shown in the attached image.

I'll try and find out myself, if I can achieve either of the above, I'll be able to "remesh" the partial solution and converge on a better answer. Any rhino related methods would be great.

Cheers,

Jon

Permalink Reply by Abhishek Mathur on August 29, 2009 at 3:20pm

Hi Jon

The problem to me seems that rhino is grasshopper is not able to generate a surface that is derived out of more than 4 curves. Your earlier solution basically transforms a surface into a diagrid mesh which is diffrent from generating a continuous surface.

I have been trying to tackle the problem by first making a surface from 4 edge curves and then chopping it twice to get 6 edge curves. Of course there is little control over the resultant surface but it seems to work in principal.

Thank you for your interest in the posting. Do update me on your progress.

Cheers
Abhishek

Permalink Reply by Jon Mirtschin on August 29, 2009 at 3:33pm

It's an interesting problem, and related to a lot of other work/tools I'm trying to implement in my plug-ins.

It's not a grasshopper solution, but creating a "smooth" nurbs surface is the intent of the exercise as I'm trying to solve it. The interim solution is a "meshed" representation of the solution that I need to solve first. The input is then intended to be a nurbs surface, with a nurbs output that I deform from the "meshed" version results.

Since the earlier posting, I came up with a way of generating the nurbs starting surface with arc edge profiles, but since I haven't written a mesher yet, I need to mesh it using a program at work (and solve the minimal shape on a better computer there). I'll let you know how I fare.

Cheers,

Jon

Permalink Reply by Moshe Nissan on August 11, 2014 at 2:29am

Hi i'm new here in the minimal surfaces world..

i'm working in a very interesting project applying minimal surfaces to big scale precast modules unfortunately i'm finding difficulties in my modeling techniques... i'm an industrial designer... i think for the purpose of this project i will need a math & geometry boost.. anybody can help me giving me some syllabus recommendations for understanding minimal surfaces?

many thanks

idmoshenissan@gmail.com

Permalink Reply by Daniel Piker on August 11, 2014 at 4:12am