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!

Replies to This Discussion

Permalink Reply by David Rutten on January 6, 2010 at 1:24pm

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

--
David Rutten
david@mcneel.com
Poprad, Slovakia

Attachments:

UVoronoi.zip, 40 KB

Permalink Reply by Andrei Raducanu on January 6, 2010 at 3:03pm

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!

Permalink Reply by David Rutten on January 6, 2010 at 3:16pm

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.

--
David Rutten
david@mcneel.com
Poprad, Slovakia

Permalink Reply by Andrei Raducanu on January 6, 2010 at 3:20pm

i actually need straight lines in this case, so it's all good

Permalink Reply by taz on January 6, 2010 at 4:20pm

I think this previous discussion was also an ongoing saga about similar techniques.

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

Permalink Reply by Andrei Raducanu on January 6, 2010 at 5:17pm

cheers!

Permalink Reply by Max Vomhof on March 25, 2011 at 7:24am

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)

Thanks for your help!

Attachments:

delaunay - horizontal.jpg, 1.5 MB
delaunay - vertical.jpg, 167 KB

Permalink Reply by Andrei Raducanu on March 25, 2011 at 7:39am

are you using the method described above?

Permalink Reply by Max Vomhof on March 26, 2011 at 12:03pm

thanks andrei, should have tried that first...

Permalink Reply by Matt Schmid on June 23, 2011 at 11:36am

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?

Permalink Reply by Sedef Çatalkaya on December 28, 2011 at 2:52am

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

Attachments:

voronoi.3dm, 119 KB
uv_voronoi.ghx, 362 KB

Permalink Reply by Manuel on December 28, 2011 at 5:41am

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.