Grasshopper

algorithmic modeling for Rhino

# voronoi/delaunay diagram on non-planar surface

Hi!

i want to do a voronoi/delaunay diagram on a wavy surface (not a projected diagram, but work in the 2d surface as it were planar). is this possible?

thanks for the interest!

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### Replies to This Discussion

you'll have to solve it in UV space (see attached).

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David Rutten
david@mcneel.com
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hey, thanks a lot. after fiddling with it a bit, i realized how it's done. you transform the uv coordinates in xy coordinates, then apply the manipulation (in ox plane), then input the resulting xy coordinates as uv coordinates for the surface (i'm saying this for others that might be interested, you obviously knew what you were doing ... :)

thanks, great help!
Note that this doesn't generate actual outlines on the surface, it only projects the points back and connects them with straight lines. You'll have to resort to some sort of curve-on-surface interpolation or Geodesics to get a diagram which is coincident with the surface.

Or you could choose to XMorph the entire voronoi diagram from world space back into UV space with the surface morph component.

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David Rutten
david@mcneel.com
i actually need straight lines in this case, so it's all good
I think this previous discussion was also an ongoing saga about similar techniques.

http://www.grasshopper3d.com/forum/topics/flow-along-surface
cheers!

Hey there,

i run into a similar issue but with the delaunay triangulation. The component works great as long as the surface is 'horizontally' oriented. I just can't figure out how to implement it on a 'vertical' surface? (see attached images)

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are you using the method described above?
thanks andrei, should have tried that first...

Hi David,

I'm hoping to accomplish something similar with points on a double curved mesh rather than a nurbs surface... is there some way to parameterize a mesh so the points could be mapped to a 2d plane, solved for the voronoi or delaunay and then mapped back to 3d?

hi thank you for definition and explanation. I could apply this for single and non planar surface but I couldnt apply for the polysurfaces. Here what i did is I extruded curves and cage them in order to have non planar and smooth surfaces (in which im not also succesful) when i want to set the surface it doesnt work. I would be glad if you can help me as

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i didnt check your files, but if you use UV method, you have to understand that each surface has his own UV coordinates so you have to explode the polysurface with "brep components" on singles faces (surfaces) and then apply uv coordinates for each surface...

if you are a beginner, it will be easier if you apply a voronoi 3D directly on points on the surface, and find intersection between voronoi cells and surface.