generating minimal surface in a cube

Replies to This Discussion

Permalink Reply by Carlo Beltracchi on July 10, 2009 at 5:15am

Why don't you start from a 2 dimensional problem?

That's a problem of calculus of variations...I think you should start from 2d shapes like catenaries or brachistocrone...it's more easy. Then you can switch to catenoids and cycloids...

I'm interested on it...please give a look to my video section...i made a catenary from two points GH definition...but I'm still investigating on it...

Go on with your work ... good luck

Permalink Reply by Abhishek Mathur on July 10, 2009 at 11:50am

thanks carlo..i am on it

Permalink Reply by Daniel Piker on July 10, 2009 at 6:03am

Where is that image from ?
It looks a bit like a piece of a gyroid, but the edges seem to be on the wrong faces of the cube.

Permalink Reply by Carlo Beltracchi on July 10, 2009 at 9:34am

Did u do this with the GH?

Permalink Reply by Daniel Piker on July 10, 2009 at 9:50am

No that's not GH, but I am working on a new GH definition that should be good for modeling this kind of surface. Theres a very nice approximation to the gyroid that can be found by taking the medial surface between the left-handed and right-handed versions of something called the Wells (10,3)-a net.

Permalink Reply by Abhishek Mathur on July 10, 2009 at 11:54am

The image I posted was from a book by Eduardo Catalano 'the constant'. I am not able to emulate this in a Rhino/ grasshopper environment. The Rhino curve network seems to have difficulty in connecting more than 4 curves and this is a 6 curve surface. If I join them, it obviously starts distorting.

The Gyroid is interesting. Did you model this in Rhino? Which software do you use?

Thanks for your comments.

Permalink Reply by Daniel Piker on July 10, 2009 at 1:40pm

To approximate a surface like this with NURBS it helps if you can find a way to divide it into 4-sided patches. In your example I think you would need to look at a larger part of the surface than that contained within the cube.

I started with a mathematically generated mesh (I can't remember which program I used as it was a while back but there are lots out there that can do this sort of thing - mathematica, k3d, dpgraph..) imported into Rhino and then extracted some boundary curves and made surfaces from them.

You might also want to try looking at surface relaxation scripts like this one by Damien Alomar.

Permalink Reply by Jaeman PARK on February 12, 2018 at 5:36am

Hello Daniel,

I'm working on panelizing Gyroid with Nurbs. Currently I found some panel types, but your 4-sided patches are really amazing. Unfortunately all the link you attached is broken or not readable on current GH. Can you give me some information how you extracted and made surfaces?

Thanks,
Jaeman.

Permalink Reply by Carlo Beltracchi on July 10, 2009 at 10:46am

Daniel....brilliant!
My next goal will be to create a medial surfaces algorhytm :)

Permalink Reply by Vicente Soler on July 10, 2009 at 2:24pm

Not sure if it will be useful, but I posted a while ago in the old newsgroup a definition for the marching cubes algorithm, i think it's still there. Marching cubes allows you to create an approximation of many shapes, including gyroids.

This was created from scratch using grasshopper (rendered using brazil for rhino):

It looks dirty since it's a faceted approximation, you can always increase the mesh quality.

Permalink Reply by Luis Fraguada on August 19, 2009 at 8:01am

Hey Vicente...does this exist over on the old forum anymore? I cannot seem to find it...or the link I found says page no longer available...

Permalink Reply by Diana on March 29, 2017 at 5:47am

Hello,

I am quite new with grasshopper and I am trying to recreate the exact shape you posted here in the picture! unfortunately I cannot find tutorials on how to do it... Do you have any suggestion? And, are those surfaces or meshes? 

Thank you very much in advance

Diana

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