algorithmic modeling for Rhino

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

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There's a simple parametric form for this:




thx, it works. ;)
how would that be plugged into GH?  I'm not clear on how to define that function?

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

Poprad, Slovakia



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


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!



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.

hi david,

thx for the description

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



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




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

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. 




Chris K. Palmer


hi chris,

thank u so much for helping me. that's what i need. ;)






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