How to create this kind of scherk surface?

I find three pictures on the internet. Any people knows how to do this kind of models?

It is said this is the second Scherk surface and the definition is

sin(z)- sinh(x) * sinh(y) = 0

Attachments:

a.JPG, 145 KB
b.JPG, 141 KB
c.JPG, 154 KB

Replies to This Discussion

Permalink Reply by David Rutten on November 29, 2016 at 2:11pm

There's no way to create surfaces out of implicit equations in standard Grasshopper, though I believe the Millipede and/or Nudibranch plugins may be able to.

Permalink Reply by Laurent DELRIEU on November 29, 2016 at 2:20pm

Look at these links,

http://www.grasshopper3d.com/forum/topics/3d-printing-a-gh-gyroid?x...

https://api.ning.com/files/fboPS79zVdGyo8yP1tRQJeOT4vUp8rmomdr2fdmq...

It is also good to give sources, because the equation is not enough !!!

http://www.twistedmath.com/sculptures/scherk-no2/

It is said "his sculpture is a manipulation of a three period three fold saddle tower, otherwise known as a Scheck's Second Surface, a minimal surface area."

Permalink Reply by Laurent DELRIEU on November 30, 2016 at 2:07pm

Here it is :

Make the isosurface with isosurface and equation above

twist it with Jackalope or twist component in Rhino WIP/GH 1.000

Bend the shape on a torus, I transformed xyz to a radius (unit) and 2 angles.

So I have now a mesh, in order to thicken it I reuse Isosurface.

Permalink Reply by Laurent DELRIEU on November 30, 2016 at 3:27pm

Permalink Reply by Kim hauer on December 1, 2016 at 4:00pm

Hi Laurent:

I was recently looking for help at how this Schek Wall could be made.

Looks like attractors were used to deform the wall? Any hint would be appreciated. :)

http://www.grasshopper3d.com/photo/minsurface03?context=latest

Permalink Reply by Chapulin Colorado on December 1, 2016 at 5:19pm

i am not laurent but it looks like a distortet mesh with a boxmorph

Permalink Reply by federico caputo on February 19, 2017 at 3:04am

Hi,

I'm trying your definition, but i think there are some errors i made somewhere because what i get for now are those surfaces you can see in the image.

Could you please tell me where i'm wrong? thank you

Attachments:

min surf.JPG, 102 KB

Permalink Reply by Laurent DELRIEU on February 19, 2017 at 4:27am

There is no errors in your definition il is just the beginning, you will need to twist it and to bend it in a torus and then to thicken it. I never poster the definition as it was not asked !!!

Permalink Reply by Parivardhan Dangi on February 24, 2017 at 12:21am

Ok, i did get to twist it , but i am still having trouble to "bend" the shape into a torus . What exactly do you mean by this ? i used surface morph, didnt work - naked edges, problem orienting, i used box morph - same issues. im so stuck !

Also, I am not getting a continuous mesh in x & y .I am getting only the Second Schek surface. ie - only in the y direction if i repeat the mesh i get a smooth continuous mesh. If i try to use something like box array, the sides are not aligning perfectly and i am getting naked edges. Can you share the script if possible ?

Permalink Reply by Laurent DELRIEU on February 24, 2017 at 12:30am

Hello, I will put script tonight, no PC at the moment. The transformation in torus doesn't work with bend and other tools. I don't know exactly why. I used a mathematical transformation. It's included in the script I posted in an other discussion. The trick is to transform x y z in 2 angles and one radius. Z is transformed in an angle to place point on the big torus radius. X y are transformed in radius angle to place point on little radius of torus.
http://www.grasshopper3d.com/forum/topics/grasshopper-exercise

Permalink Reply by Laurent DELRIEU on February 24, 2017 at 12:23pm

Here is the script :

Attachments:

second Scherk surface_v2.gh, 30 KB

Permalink Reply by Parivardhan Dangi on February 27, 2017 at 2:55am

Thanks a tonne. Wow thats an elaborate script. I still wonder if there could be a simpler way to achieve the same. @Laurent you are awesome ! How did you decipher the expression ? i kind of understood the transformation that you tried to achieve . . z bent in polar 360 while xy accordingly to the radius of the desired torus. But I dont understand the expression. And i would certainly like to . I am a mech eng. and do have understanding of maths, but the above expression leaves me clueless. May i ask what your profession is Laurent !