Hello evryone

Am new in grasshooper am trying to creat a 3d random voronoi cell with the same volume for all cells and the result am getting is always diffrnet volumes of 3d voronoi cells

So is there any way to set an equal volume for all cell and how can i control it?

Thank u

random 3d voronoi cells ( diffrent volumes).gh (13.6 KB)

Assigned to Grasshopper category.

Yes it is possible, use evenly distributed points. On a cubic grid or surely with dense packing of sphere.

So if you want that you better use tools that generate polygons that could be packed

Triangles extrude

square extruded (cubes also)

Hexagon extruded

…

Avoid random.

I want it to be random destribution of the polyhedron and in same time the polyhedrons are all the same volumes is that possible ?

Based on the voronoi tesselation principe i guess the way to creat polyhedrons (the voronoi 3d cells) with the same volume is to set random 3d points but with the same distance between theme but i cant find a way to do that. All i get each time is random point with diffrent distances between theme. So is there any solution?

Thank you

If you want Voronoi Tesselation I am sure it is not possible as there is just one tesselation given a set of points.

It is possible to have the same volume you just have to scale all polyhedron depending on their volume. But it will be no more a Voronoi Tessellation.

If you want to keep the point distribution truly random, then as Laurent says, this is impossible.

I’m guessing though that what you’re really after is something not completely regular, but with less variation in spacing than a random distribution.

One way to do this is to iteratively move the points to the centroids of their cells.

It won’t give identical volumes, but they will become more similar than with a random distribution.

lloyds2d.gh (9.7 KB)

naughtyLoop.gh (13.8 KB)

This dirty double data dam trick (gets round GH’s restriction on cyclic data streams without plugins) can be fun to play with, but isn’t really recommended for anything serious, and is likely to cause crashes - use at your own risk!

Thank you so much it helped me