Create Flat Voronoi plane between 2 specimen with common vertex sharing

I want to create a flat surface between top and bottom box, where the vertex of Voronoi will be common between these 2 box. Please follow the below GH script and rhino file.
Thanks in advance for your help.

GHscript_Re2_Atik_Col+base_chk.gh (26.9 KB)
Untitled.3dm (84.9 KB)

In the current script the Voronoi of bottom box become diverged and common vertex also missing in several points.

could you please clarify what you are trying to achieve? maybe with a sketch?

Thanks for your kind response. Please check the figure below. please ask me if it is still unclear.

If I understand correctly, the voronoi cells should be identical in the overlap of the two faces of the parallelepipeds.


Thanks for the solution. Yes, the overlap of Voronoi surfaces are required. Could you please share with me the GH script.

GHscript_Re2_Atik_Col+base_chk a.gh (33.7 KB)

Thanks for sharing the script. Regarding the mesh number, the input value (now set to 500) is for each part? or it is for whole specimen? Please kindly response according to your free time. Thanks again.

The number of points is proportional to the volume of the two solids.

Thanks. If there are 3 specimens rather than 2 as above, any suggestion to solve the script? Now the division command has only 2 parts A and B. Sorry for bothering you.
3_parts.3dm (78.1 KB)
GHscript_Re2_Atik_Col+base_chk_3p.gh (23.4 KB)

Here, try this definition, it should be what you are looking for.
I used100 points just for brevity of execution.

GHscript_Re2_Atik_Col+base_chk_3p a.gh (35.3 KB)

Thanks. It will solve the problem for meshing multiple specimens.

In this script, if the input seed number is 100, the output become larger like around 300. Is it possible to make the output seed number to 100 in total for all 3 specimens? Thanks

Do you mean a total of 100 points?
GHscript_Re2_Atik_Col+base_chk_3p b.gh (39.2 KB)

Yes total seed point will be 100