minimal surfaces

hey guys, i got some problems with minimal surfaces. i need you to help me out. how can i define a periodic minimal surface..something like this picture. is there any easy way to build this up? im looking for some expressions or something like that. thx

Attachments:

img10.jpg, 132 KB

Replies to This Discussion

Permalink Reply by Daniel Piker on July 31, 2011 at 8:37am

There's a simple parametric form for this:

x=u

y=v

z=log(cos(u)/cos(v))

Permalink Reply by Behnood Eghbali on July 31, 2011 at 12:44pm

thx, it works. ;)

Permalink Reply by Chris Hanley on August 1, 2011 at 3:35pm

how would that be plugged into GH? I'm not clear on how to define that function?

Permalink Reply by David Rutten on August 2, 2011 at 6:09am

You create an Expression component with 2 inputs (call them u and v to keep things simple). Then the expression would be:

{u, v, Log(Cos(u)/Cos(v))}

the curly brackets mean you're defining a point with x, y and z coordinates. U becomes X, v becomes Y and the equation becomes Z.

since U and V translate directly to X and Y, you could also just generate the elevation with the expression and then plug the three numbers into a XYZ component.

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Chris Hanley on August 2, 2011 at 10:46am

David,

Thanks for the description! Very helpful. I did a little further digging on the forum and found some other very helpful descriptions;

http://www.grasshopper3d.com/forum/topics/function-gets-its-math-wrong

I have to admit, I am more than a little rusty on my trig and need to brush up! With that said, i was able to piece together a reasonable facsimile. One thing I am not sure of is how the domain is defined. Why do the start and end intervals need to be run through a pi component? (sorry for the dumb question...).

Here is the file if anyone is interested but a much better one is available at the link above!

Attachments:

GHScherkSurface2.ghx, 250 KB

Permalink Reply by Behnood Eghbali on August 2, 2011 at 12:48pm

hi chris,

thank u for the link and the definition. that was amazing and very helpful. i think the answer is when we want to define a "continuous function" we should have a domain by pi components.

Permalink Reply by Behnood Eghbali on August 2, 2011 at 12:38pm

hi david,

thx for the description

Permalink Reply by Behnood Eghbali on August 1, 2011 at 10:32pm

here's the incompleted definition..im not so sure about rest of it. somebody help!

Attachments:

minsrf.zip, 3 KB

Permalink Reply by Dedackelzucht on August 2, 2011 at 1:21am

Hey,

here is a modelling version :-) I am sure Daniel has got a smarter version

by the way, moving the PoinCurve component results cool pattern

Best Regards

Dedackel

Attachments:

minsrf_DeDackel2.ghx, 430 KB

Permalink Reply by Behnood Eghbali on August 2, 2011 at 3:47am

@dedackelzucht: thank u so much. ;) that was awesome.

Permalink Reply by Chris K. Palmer on August 2, 2011 at 11:47am

Hi Behnood,

Here is a old one I updated a bit with several common parametric surfaces. You may have to trim and post process the Scherk surface a bit but it is parametrically generated in this definition.

Cheers,

Chris K. Palmer

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