Voronoi on multi curved surface

Hey there,

I'm trying to make a voronoi structure on a multi curved surface but can't seem to find a way. Does anyone know how to do this? all ideas are welcome.

Cheers

Replies to This Discussion

Permalink Reply by djordje on September 22, 2013 at 9:18am

Hi Marinus,

If a Multi curved surface is a double curved surface, then you can create the voronoi on a flat rectangle bellow or above the surface. After that interest those 2d voronoi curves with surface.

Permalink Reply by David Rutten on September 22, 2013 at 9:18am

Two basic approaches you can take; 3D and UV.

Either solve a 3D voronoi and intersect it with the surface. The problem here might be that if the surface has detail that is significantly smaller than the voronoi cells, you can get weird intersections. Also the edges of open surfaces could be problematic. This approach also requires 3D voronoi and Brep|Brep intersections, which are both slow operations.

The other approach means you 'unfold' the surface, solve the voronoi in the flat plane and then push it back onto the original surface. Problem here is that it doesn't work well on closed surface seams (as far as the voronoi diagram is concerned, the surface stops at the edge) and that surface parameterization can distort the solution. If the surface is very stretched in one location and very compressed in the other, the voronoi edges will reflect that.

Ideally you'd solve the diagram in 2D while using a 3D carthesian distance metric rather than a 2D UV nurbs metric. But there is no algorithm in Grasshopper that does that.

David Rutten

david@mcneel.com

Tirol, Austria

Attachments:

Voronoi3D.gh, 8 KB
VoronoiUV.gh, 13 KB

Permalink Reply by Marinus van Hall on September 22, 2013 at 9:22am

Thanks David! this is almost exactly what I was looking for. Many thanks!

Permalink Reply by Lee Souder on December 11, 2013 at 7:34pm

How would you then turn these stray lines into cells or faces? I am guessing since each cell would share neighboring polylines this would not be possible. Any ideas?

Permalink Reply by Lee Souder on December 11, 2013 at 8:21pm

Actually, there are 2 lines on top of each other. How can I find the lines of a cell and connect them?

Also I used the UV method from above

Permalink Reply by Lee Souder on December 12, 2013 at 1:44pm

Weaverbird somewhat solved my problem except the holes are uneven. Is there another setup I could use?

Permalink Reply by djordje on December 12, 2013 at 2:03pm

Hi Lee,

Do you want to have each of these voronoi cells on the curved surface, in form of separate surfaces?

If that is so, then try the attached definition.

Attachments: