Grasshopper

algorithmic modeling for Rhino

Hi,  I been always had a problem with sphere surface subdivisions and box morphing the image below  is something i am trying to do. But its obvious that points converge at ends of sphere. i want to panel a sphere with all same unit .  

something like this ....

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AS seen the Panels(geometry) skew at at both tip of sphere. 

i would make a mesh box in rhino with one face per side then use catmull clark. then from here i would weld with remove overlapping vertices. then offset the vertices and create a twisted box. Or if I'm not mistaken paneling tools may have a solution for this.

The problem with this solution is that the facets are not all the same shape and size. However, subdivision is generally the right direction - Complex, regular geometric forms like this one are usually derived from simpler polyhedral forms. There are a bunch of ways you could break down the form shown into the image, but the cleanest one I can see is a shape called a "snub dodecahedron"

http://en.wikipedia.org/wiki/Snub_dodecahedron

If you place triangles in the pentagons as I've done, you can see that the shape inside each triangle is always the same. 

Here's a definition that attempts to reproduce the shape shown. I apologize; it's a bit of a mess and relies on some custom user object clusters and plug ins (lunchbox, hdt utilities tree frog, I think that's all) to achieve the desired result. Also I just eyeballed the amount of rotation on the snub dodecahedron - you could probably use galapagos on the rotation parameter to get equilateral triangles. Please ask if there are any questions!

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on further reflection, I don't think they actually are (or can be) identical if they're approximating a sphere. but perhaps you could get it down to two similar units? just speculating...

Yea, I knew it was very involved :). I was thinking even wb icosahedron but still there is slight variance.

THanks   Michael Pryor  and Andrew Heumann  . I m huge fan of u guys...  thanks for the response. u people inspire me greatly.

Andrew guess i m missing out somepluginn. what did u use for Tiling Snub Dodecahedron ?

Andrew i see so many cluster components :O .   cant this get simpler .  ..?? 

well i can use area to find center of each face and scale them  how can i planar surface ?? is it having problem with duplicate edges ??

I get only few faces with that triangle removed after planar surfacing. what better ways can i do it ??

Is that you want Sridhar ?

Made with 'Geodome', from Jon Mirtschin's great plugin 'Geometrygym'

Hope it helps !

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