Grasshopper

algorithmic modeling for Rhino

# Voronoi tesselation on surface

I´m pretty sure someone has tried this before. So please, if anyone would be so kind to share it with me,I´ll be so thankful about it!
I´m looking for a definition wich contains more or less this steps:

1) Pick a surface.
2) Pick a group of points previosuly determined in a 2d "flat" view.
3) Transport those points to the surface.
4) Make the voronoi 3d tesellation around the surface.

That´s it! Thank you all!
Bye!

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hello!
Actually I'm doing my experiments with voronoi algorithm too. And I'still have a some problems with creating of 3d volumes...

What can readily be done is something similar to this approach.

Create a reference surface and use that to map the voronoi coordinates onto a target surface.

A 1-to-1 translation should be straight forward, but translating a voronoi pattern to a polysurface would be a bit trickier.
here ya go...

What this does is transposes the 'catersian-space' voronoi onto 'surface-space' voronoi.

What you mentioned was transposing points and rebuilding the voronoi: the problem with that would be the fact that the new voronoi would still have straight polyline cells, which most likely will not stick to the curvature of the surface, so only your points will truly be on surface.

The image you attached was of a voronoi that 'sticks' to the surface. The definition attached gets around that problem by transposing the built cells instead of the points. Its a simply morph logic.
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Hi... I have been playing around with your definition. It seems that the reference pattern (or plan curves) has to be in the xy plane. I have been trying to use a reference which is in the yz or xz planes? But i can't seem to find the problem? Is it something about the u and v parametres?
hello, i found this theme searching the forum, and thats exactly what i want, transpose the point but not the edges, beacause i want straight edges insted curved...any idea?

Thanks for this, I´ve found it really helpful!!

I had a similar question for David Rutten at a recent user group meeting in NYC. i've used the 3D Voronoi tool in Rhino that exists as part of the pointset reconstruction plugin with good results, but wanted to know how to do this with GH. David (who developed the Rhino plugin as well) seemed to suggest that it would be far too time-consuming a component to include in GH since GH is meant to be a 'real-time' tool, which is why there is only a 2D voronoi component. I'm looking forward to playing with Suryansh's def...
Ivan - thanks for you blog link... New to GH. I was playing around with your def and trying use a polyline attractor instead of the single point attractor. I got it working with a planar surface but when I add it to a curved surface it doesn't work... any ideas? I attached the definition. I'm using this in the context of water canal design. I'm trying to use Voronoi to make the components smaller on the vertical sides of the canal but larger and more open on the bottom and edges to allow for greater water infiltration.
Hey guys,

just has created another discussion about it.
If anyone could help...

http://www.grasshopper3d.com/forum/topics/voronoi-on-organic-surface

R.
Hi All,

Not 100% related to the topic but I'm sure someone knows the answer. Ive tried to build curves from the control points of my offset voronoi diagram but the curves its outputting have corners. Anyone know how to get rid of these?

hi,

maybe it's a stupid question, but did you set P to true so that your curve is closed?

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