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!

Attachments:

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

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/...

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.

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

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?

Permalink Reply by dani bas on December 6, 2010 at 2:18pm

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?

Permalink Reply by Luis Angel on November 20, 2013 at 8:58am

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

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...

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

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.

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.

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?