Interlocking Shapes On A Sphere

Replies to This Discussion

Permalink Reply by Julian Buhagiar on March 13, 2017 at 2:53pm

I'm currently trying to build a platonic shape maker natively in Grasshopper (without kangaroo or lunchbox) where you can specify the number of faces and the shape can construct. its tricky, but if I get it working you can then substitute the fixed lunch box shapes, for any shape you like.

Permalink Reply by Ol OneEye on March 13, 2017 at 4:05pm

Woah Cool!! This is dope! So I tried to recreate the item using your logic, and with my own  GH script. I also wanted to 'project' onto the surface, so the lines were curved (not sure, in your example are the lines actually on the sphere?) I am close, but when I 'project' it projects on  both sides (ugh!), how do I fix that?

Thanks!

Attachments:

• demo1.3dm, 153 KB
• demo1.gh, 27 KB

Permalink Reply by Julian Buhagiar on March 14, 2017 at 7:46am

ah right, the project direction that you used is taking both lines from opposite sides of the DoDecahedron, and projecting twice onto the sphere.

For example, both path 18;0 and 27;0 have identical points. The clean way to do it is try and work out how to get the closest line to the surface to project in the correct direction. The messy way to do it is to try and create a filter that omits one of the results after the projection.

Permalink Reply by Ol OneEye on March 14, 2017 at 6:04am

Now the real question. How can one do the same thing, but with a poly surface shape such as this attached. Is that even possible? I have a theory I am working on, curious if you have any ideas??

Thanks!

Attachments:

• demo1.gh, 34 KB

Permalink Reply by Julian Buhagiar on March 14, 2017 at 8:03am

In terms of the polysurface, yes I believe it may be possible and I'm working on a way of creating regular faced shapes that can construct such an object.

Its easy to conceptualise the 2D version using methods of splitting a circle and into regular shapes. But expecting to do the same in 3D with a sphere makes a very complex task and I found that steradians don't help like radian in 2D do. Instead I'm tackling it from a different basis which seems like a positive approach so far. 

The additional dimension adds the complexity where there may be several regular faced shapes that have the same number of faces (Cube>Tetrahdron) and as you get into higher numbers the complexity increases. I'm exploring this at the moment so that multiple solutions are producable.

Permalink Reply by Ol OneEye on March 14, 2017 at 9:59am

Cool!, out of curiosity what logic's are you thinking about?

Permalink Reply by Julian Buhagiar on March 14, 2017 at 11:58am

essentially using mirrors to cast an array of reflections of a single point. The angle, (or angles increase the more points you need but they are at very predictable positions, therefore they can be generated with a slider input)

Once you have the point positions, these can represent either vertices or centre positions of lines, or centre points of faces...This is why it gets very complex very quickly, but its a very good starting point for setting up to scaffolding onto which you create the platonic geometry.

Ill share the GH definition when I have it a little more refined.

Permalink Reply by Ol OneEye on March 15, 2017 at 12:56pm

Woah Cool! I am excited to see what you come up with Julian. I want to increase the sides of my dodecahedron  so I have more surface divisions. Any ideas on  that? obviously it wouldnt be a dodecahedron. Maybe I have to find the 'math' of a dodecahedron and write a custom script?

Permalink Reply by Ol OneEye on March 21, 2017 at 7:19am

hey julian,

how is your project going? I'd be stoked to see your current GH script..

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