Minimal surface for more than 4 boundary curves

Replies to This Discussion

Permalink Reply by taz on April 27, 2010 at 11:17am

Kangaroo has had some demo videos on this...

http://vimeo.com/8842831

http://groups.google.co.uk/group/kangaroophysics

Geometry Gym plug-ins will also do it.

http://www.grasshopper3d.com/forum/topics/grasshopper-plugin

Permalink Reply by Arthur Mamou-Mani on April 27, 2010 at 11:22am

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.

Permalink Reply by taz on April 27, 2010 at 11:28am

Patch

Permalink Reply by christy w on June 18, 2010 at 12:45am

Arthur,

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

Thanks,

xty

Permalink Reply by robert cervellione on June 18, 2010 at 7:15am

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

Permalink Reply by robert cervellione on April 27, 2010 at 3:28pm

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.

Permalink Reply by robert cervellione on April 27, 2010 at 3:47pm

here is an image showing 8 curves

Permalink Reply by Steve Lewis on April 27, 2010 at 4:04pm

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?

Permalink Reply by robert cervellione on April 27, 2010 at 4:19pm

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.

Attachments:

• MINsURFmEAN.jpg, 95 KB

Permalink Reply by Arthur Mamou-Mani on April 27, 2010 at 4:35pm

Wonderful!Thanks a lot Robert!

Permalink Reply by Steve Lewis on April 27, 2010 at 4:55pm

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.

Permalink Reply by robert cervellione on April 27, 2010 at 5:29pm

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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