Grasshopper

algorithmic modeling for Rhino

Actually a toy definition ...

A 4-dimension cube centered at the origin is built

and then rotated on an arbitrary sequence of

planes ( ? ).

Finally it is, obviously, projected to 3D.

Wire frame and mesh output.

 

No warranties on the correctness of calculations.

I just _guessed_ how to rotate 4D stuff and

project it to 3D space ...

 

Emilio

 

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Great idea! What about a component that creates cubic lattices of arbitrary dimensions (slider to choose), and projects them onto a plane (or 3d basis) of your choice. This would create the whole range of aperiodic lattices.....!

Yes, that would be cool ...

but also much more complex, I think.

I'm not going to work on that, sorry.

Thanks

Cheers

Emilio

I've loaded the hyper.ghx function into Grasshopper (8.0007) and no lines or meshes are visible. Is there a seed input necessary? Do I need a particular c# runtime? What am I doing wrong here?

I only tested that on 8.0004, no input should be needed.

Trying the definition on 8.0007 raises an error here about a missing dependency

Maybe my .NET framework is too old ... sorry

 

Emilio

 

Thanks Emilio:   That sometimes happens on a moving target but that's the price we pay for progress.  By the way. I find that if I bake either the lines or the mesh that they produce a viable rhino object.  

Al

That's annoying, I mean not being able to see what will be baked ...

Should you like to keep testing, I attach a simpler definition,

just in case any of the geometric objects might work as they do in 8.0004 ...

Not much logic behind that ... just trying something.

Thansk Al, cheers.

Emilio

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where did you load this component?

On a similar note - years ago I wrote some Rhinoscript for 4D rotation of objects, along with stereographic projection to and from a 3-sphere

I just dropped the same code into a GH component, attached here in case anyone wants to play with it.

The t parameter controls the amount of rotation (so you can also supply a range of values to sweep objects around to get things like the lawson klein bottle and sudanese mobius band, or the Hopf fibration). A value of pi gives a simple inversion in a sphere.

p and q are the different components of the 4D rotation. When they are equal it is isoclinic.

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Thanks for sharing that, Daniel !

Your code is very interesting, and also the link to 4D rotations.

Emilio

been working on this topic with a partner, hoping to input more than just a hypercube.

i attached an earlier study with just a hypercube, we're hoping to define a hypercone now but struggling with it

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