algorithmic modeling for Rhino
For the questions below,
the pattern seems direct up, it is because of the stretching imposed by the passage from a torus to a square, it is the same for the map of the world. You can use non uniform scale, there is a slider in my script. You can also change a dimension of the torus.
Here 4 edges can't be seamless, but you can cut, and use symetry/mirror to do that. I think it will not be beautiful.
First, your Voronoi curves are not generated on a torus but projected on a torus so I propose you a more simple way to have a Voronoi on a torus, It will not be a real voronoi on a plane, because it will be curves not lines. But it could be fixed if necessary
1 Generation of a torus
2 Generation of Voronoi in 3d and calculation of intersection between cells and torus
3 Cut of the curves with 2 planes
4 Projection of the curves in XY planes between 0 and 2*PI
5 Scale in X of this pattern and array
It seems quite a simple way to generate a Seamless Voronoi.
Happy ?
For the question about symetry, cut, rotate ... you will have to draw things , seek on internet ... figure it by yourself.
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Grasshopper
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