Interlocking Shapes On A Sphere

Hello all,

I made a spherical rhododendron by projecting one onto a sphere, and rejoin the points. The next step would be to make some MC escher like interlocking shapes instead of a simple rhododendron... confused as to how I would go about that. Any ideas? Basically they do not interlock now, but I would like to see these parts interlock in cool ways..

Attachments:

blob chair 2.gh, 22 KB

Replies to This Discussion

Permalink Reply by Julian Buhagiar on March 10, 2017 at 12:24pm

https://3dwarehouse.sketchup.com/collection.html?id=8f0e8922-36a2-4...

MCEscher... A favourite of mine... I produced these in the sketchup warehouse.

I'll help once I've taken a look.

Permalink Reply by Julian Buhagiar on March 10, 2017 at 12:27pm

seems like the starting shape isn't internalised. any chance you can internalise it?

Permalink Reply by Ol OneEye on March 11, 2017 at 7:45am

hey i just checked, it is internalized? Anyway these are some examples of what i am trying to create. More like a 'sphere puzzle,' where the shapes interlock in cool ways. I am projecting from an interior object, so I am not sure whether to project the design or what...

Thanks

Attachments:

1f5b3d08c2464ca96f8d84c7e2800330.jpg, 108 KB
keychain-6pc-ball-crop1.jpg, 26 KB
Full+rev+2+assembly.JPG, 167 KB

Permalink Reply by Ol OneEye on March 11, 2017 at 8:22am

In terms of surface tessellation, is this the best method? Project from the interior, reconstruct on the surface, and then extrude back down?

Permalink Reply by Julian Buhagiar on March 11, 2017 at 3:59pm

It looks like a fun object. I'll give it some thought. As for the internalisation - it was because I didn't have Lunchbox installed and therefore didn't have the dodecahedron. Got lunchbox now though.

Permalink Reply by Ol OneEye on March 12, 2017 at 8:49am

Okay cool. I can do this no problem on a 2D surface. Making puzzles using voronoi or the similiar. But on a sphere is much more tricky.... projecting interior shapes seems to be the only way to get 'equal' pieces on a sphere.

Permalink Reply by Julian Buhagiar on March 13, 2017 at 6:30am

I agree, uv mapping only works for polar tessellation providing you correct for distortion at the poles. a uv method might work for the first image, but for the other two images, the approach you're doing seems reasonable.

I've suggested to do the tessellation before the projection in the attached file. There may be a more elegant mathematical way to do it though.

Attachments:

Tesselation.gh, 34 KB

Permalink Reply by Julian Buhagiar on March 13, 2017 at 6:47am

Surprisingly, it works for crazy lines as well if you change the last component to an interpolate crv. ( I was expecting something to break somewhere)

Permalink Reply by Julian Buhagiar on March 13, 2017 at 6:52am

And more surprisingly, the pathmapping hasn't broken when changing the shape to an icosahedron.

Permalink Reply by Julian Buhagiar on March 13, 2017 at 7:03am

...and for what its worth, this was the original idea I explored using polar mapping

Attachments:

polarTesselation.gh, 25 KB

Permalink Reply by Julian Buhagiar on March 13, 2017 at 2:45pm

Attachments:

Tesselation.gh, 32 KB

Permalink Reply by Julian Buhagiar on March 13, 2017 at 3:01pm

maybe some modification for the edge definition to be done... To ensure the shape to be identical to its neighbours, The line would need to be rotationally symmetrical.

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