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!

Tags: grasshopper, voronoi

Attachments:

gusano.bmp, 1.5 MB
lon2.bmp, 1.9 MB

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Replies to This Discussion

Permalink Reply by Dmytro Lutsak on November 2, 2009 at 8:36am: hello!
Actually I'm doing my experiments with voronoi algorithm too. And I'still have a some problems with creating of 3d volumes...
I'm tring to reach something like Zaha's "Mesa Table" http://www.ultrafeel.tv/wp-content/uploads/image/design/zaha-hadid/...; ▶ Reply to This

Permalink Reply by taz on November 2, 2009 at 9:49am: I was thinking about this the other day...

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.; ▶ Reply to This

Permalink Reply by Suryansh Chandra on November 2, 2009 at 10:53am

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.

Attachments:

FlowAlongSurface.zip, 63 KB

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Permalink Reply by Rasmus Holst on November 19, 2009 at 12:59pm: 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?; ▶ Reply to This

Permalink Reply by dave lee on November 17, 2009 at 2:14pm: 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...; ▶ Reply to This

Permalink Reply by Ivan Kiryakov on November 19, 2009 at 1:11pm: Hi
maybe this will help
http://bfxlog.blogspot.com/2009/08/voronoi-attractor.html; ▶ Reply to This

Permalink Reply by David Wooden on December 5, 2009 at 2:01pm: 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.; ▶ Reply to This

Permalink Reply by Rafael Martin on January 13, 2010 at 11:46am: Hey guys,

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

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

Thanks in advance.
R.; ▶ Reply to This

Permalink Reply by Mickey on February 7, 2010 at 6:23am: 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?; ▶ Reply to This

Permalink Reply by Tudor Cosmatu on February 7, 2010 at 7:55am: hi,

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

Permalink Reply by Jon Mirtschin on February 7, 2010 at 8:48am: I just posted to the other voronoi post referenced above. If you want a bubble diagram with curves offset a particular distance and filleted corners, I've written the algorithm into my Rhino plug-in. I'll look at whether it can be called from Grasshopper. If it sounds of interest, feel free to get in touch.

Cheers,

Jon; ▶ Reply to This

Permalink Reply by Alina Diga on February 21, 2010 at 10:03am: Hi Mickey,

I am trying to do the same thing you are showing. How were you able to generate the curves inside the polygons? As far as removing the corners, did you try to use trim?

Thanks; ▶ Reply to This