Grasshopper

algorithmic modeling for Rhino

# Minimal surface for more than 4 boundary curves

Hi Guys,

Would you know how to generate a minimal surface from more than 4boundary curves?

I have tried using this great plugin:

http://www.grasshopper3d.com/profiles/blogs/minimal-surface-plugin?...

but it is limited to 4boundary curves which is not always enough...

Thanks a lot,

Arthur

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### Replies to This Discussion

Thanks Taz,
I have tried these tools, they are great but i m looking for something almost as straightforward as Patch or Network Surface on Rhino in which the input are several curves and the output a surface.
Arthur,

would you be so kind to share how can I install the PlugIn into Grasshopper?

Thanks,

xty
which plugin. if you are talking about the minimal surface plugin just go to www.cerver.org > downloads and download the plugin. there are directions included as well as in the project page
just join the curves together. i have many times used composite curves to get the 4 curves. i can post an example of this if you wish. its "limited" to 4 curves because all surfaces regardless of the shape have 4 sides and only 4 sides.
here is an image showing 8 curves

Thats prerry awesome but are you sure thats a minimal surface? There should be only one solution for a true minimal surface. If you did a physical model of that surface using a soap film would you get that shape? Have you looked at trying to the solve the explicit solution to the minimal surface of a catenoid? What algorithm do you use? DR or something else?
yep i am sure. take a look at the image. i get some stretching at the corners with a mean value of .2 but 99% of the surface has a mean value of 0.0000022557.

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Wonderful!Thanks a lot Robert!
Hmm nice, so are you using geometry is a means of describing the shape? i.e. adjusting the geometry until the sum of the principal curvature at every point is zero? A zero mean curvature is one of the requirements of a stable minimal surface Not the only requirement. For a true unquie stable minimal surface the other requirement is that it is stable - i.e. has the minium surface area betwen given boudaries. If you take a catenoid, there is a certain height above which a minimal surface cannot span between the rings and instead the minimal surface is simply the area of the two surface areas of the rings, i.e it breaks and cannot span bwteen the rings. Im not criticizing the approach, just interested. In fact it doenst really matter as long as you dont want to construct a tensile fabric surface from this geometry. If you do it as it is an unstable geometry it will cause the fabric to wrinkle. If you dont wnat to fabricate it assuming a tensile only load path, i.e. cable net/fabric then it doenst matter.
steve you are correct about the 2 basic requirement area and mean curvature. i do actually meet the second requirement. infact if you set the iteration to 0 the component will auto solve itself to produce 0 mean curvature as well as minimum area. i let you play with the values so you can have "design" control over the surface. so if you set the iteration to 0 you will get the 1 true solution.

also using this to represent a tensile fabric surface will surely produce problems with the real surface because when working with those types material gravity, stiffness, and tension are required to get good results. (unless you are using soap then gravity and surface tension are negligible factors). i will say though that i have done some test with fabric/wire and it is very close

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