Grasshopper

algorithmic modeling for Rhino

Please, i'm student in architecture and I would like to create a geodesic dome based on a triangular grid, and a recursive generation, like in the image. I'm really lost please ! Capture%20d%E2%80%99%C3%A9cran%202016-03-18%20%C3%A0%2013.15.53.png

The goal is to construct in real life with balloons, in order to calculate and optimize the dimensions of the dome. It is possible to do that in grasshopper? 

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Thank you for your help, 

Nastia 

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Search the forum with keyword like geodesic dome or icosahedrons
You will have plenty script
You have also many component to subdivide triangle
After each subdivision you. Will have to reparametrize coordinate on the radius you need.

Well ... I have good, bad and ugly news

Good: see this attached that does geo-domes (unfortunately the other far more capable versions are classified strictly as internals in my practice - for obvious reasons).

Bad: It's not a component (the "long" thingy that does the job, that is [see the other one as well]). In fact is not AT ALL suitable for a novice ... but it doesn't bite either, he he.In fact it's not written for making balloons (or thickened meshes): is written for creating AEC domes with MERO type of trusses and other freaky things.

Here's what I mean:

Ugly: Using the known "cut-and-paste" technique I've added 2 ways to "thicken" the wires: (a) ExoW (very tricky, rather try Intralattice) and (b) some other that is taken from truss cases (for helping users in this forum, I don't do business with components). But ... if you play with the Loft options (and the position of the profiles) ... well ... you can approximate the balloon effect that you are after.

ExoW (the inverse effect):

Mero type of stuff ...er... used the wrong way:

best, Lord of Darkness

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THHHANNNK YYYOOOUU ! I will try to understand, i miss also some plug in to read the definition entirely (exoskeleton, wavebird). Your definition is very playful.  

Have a good day, 

Best, Nastia 

Nastia? This means what it means?

BTW: these types of things (collections of something that make ...er ...something) require what we call connectivity trees (what is connected with what): I have N codes for that ... but in order to make things "palatable": get Sandbox and feed it with the (rather chaotic) no duplicates Line List > start getting the gist of the most important thingy in engineering. 

BTW: Why use balloons and not xxx sausages (made in Frankfurt) > that way the whole thingy could be literally delicious. 

If you're happy to use a plugin, Bullant has a geodesic dome generator.  http://www.geometrygym.com/downloads  Example is attached.

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Starting from scratch in order to learn, we first construct an icosahedron by intersecting unit radius spheres placed on the vertices of a pentagon of unit edge length:

That gave us equilateral triangles automatically at the right angle to form the cap of an icosahedron.

To complete the full icosahedron, we consider just the six points we already know, the five pentagon vertices and the raised pyramid tip and reorient one of the vertices using three-point transformation so it obtains the exact same relationship between vertices only one more stage beyond our little cap pyramid, and we do a five-fold polar array:

I used a password-protected cluster I ran into one the forum somewhere to reproduce Rhino's 3-point orient command:

A final 3-point orientation transforms in space the original pyramid tip down to the bottom:

Now we can create a convex hull which gives an icosahedron mesh:

So that's how you build an icosahedron in Rhino from scratch, only using rather long winded Grasshopper.

Now we use the Weaverbird plug-in to subdivide the faces and then project the vertices out onto a sphere via finding the closest points to a sphere and then recreating a convex hull to make a geodesic dome mesh:

Subdividing two times works fine but 3 times blows up convex hull, so I'll just have due with the the subdivision step and leave out projecting back to a sphere, since the algorithm already gives a nice spherical result that you can see inside this disaster:

Now you know what a standard geodescic dome is, just an icosahedron with faces divided into smaller triangles, projected out to a sphere.

Actually, the mere subdivision is just a bit blobby instead of a sphere, damn it, so I'll have to topologically recreate the mesh after projecting the points indeed back onto our sphere.

Using a subdivision plug-in may be slightly throwing the perfect result off, so manually creating subdivision points on each mesh face may be in order, doing them flat against each icosahedron face:

You can also start with the two other triangulated Platonic solids but those give less regular triangles:

Thanks, it's possible to have the two definitions ? I'm a beginner and i do not recognize all the symbols of the boxes... 

Best, 

Nastia 

... and simpler algorithm for a beginner understanding with WeaverBird add-on.

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Oh, I see, only even numbers of subdivisions afford a flat equator that can act as a dome base. The odd subdivision models would require chopping triangles off at a plane.

And indeed even with a good equator there still a slight artifact from my subdivision use and Igor's use of Split Triangles avoids that, as I hoped it would.

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Thank, it's easier for understanding :) 

Best, 

Nastia 

Why it appears this error? I've downloaded the mesh edit component

Thanks

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Hi all,

In this coffee&gh challenge you can find many more ways to create a regular icosahedron:

http://www.grasshopper3d.com/group/coffee-and-grasshopper/forum/top...

cheers, Nikos

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