algorithmic modeling for Rhino

How to create tetrahedron for any given angle in grasshopper?



I would like to create a tetrahedron like the one in the image where my lines are centerpoints of its faces.


I would be grateful for your help and suggestions.

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You could try using a FacetDome. It limits the solution to a polyhedron that is constrained to a sphere, but it might be enough...




David Rutten

Poprad, Slovakia

Here's a start that at least gives the right topology


I'm assuming this is related to this discussion

in which case I guess its mainly the topology you are after.

(it needs the lines to all start at your node - so you might need to flip some of them)


There's probably a better option than using the same curve parameter for all lines - some way of weighting them so that it stays centred on the node.


Another option would be to intersect all the normal planes



Daniel, thank you very much for your reply!

Yes, it is related to my previous discussion :) 


Your definition is exactly what I am looking for, however I would like the direction of  the faces of the tetrahedron to be the same as the direction vectors of the curves around which it is created. Do you think that would be possible?



You could just boolean some boxes from the normal planes to the curves, but you'd end up with some fairly spiky tetrahedra when the angles were irregular.

It might be better to use the outer tetrahedron in the definition above, and truncate it with planes normal to the curves. Splitting along lines from edge midpts to the centre could then give you the quads you need for subdivision and relaxation.

Nodes with 3 legs should be easy, but nodes with 5 or more would be quite a bit trickier.

Thank you for your suggestions. I will try both methods and see which one works best for unrolling and casting with concrete. I will post my result soon :)
Also can I use this logic for 3 and 5 legs?






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