Cubic packing?

is it possible to pack inside of a geometry with different sizes of cubes which are not overlapping or not intersecting? i found information about packing spheres but no cubes with my lack of luck :)

i'm aware that i'm no specific about my question but i dunno which information is needed to answer my question, so i'll specify my case with your replies.

Replies to This Discussion

Permalink Reply by Mehmet Ali on December 2, 2010 at 2:19am

I assume you are talking about tesselation. In tessellation geometries are layed on a plane or surface in order to not have a gap in between or overlap each. It is possible with equilateral triangle, square or haxagon in euclidian space for 2 dimensional surfaces. But I think you look for a 3d solution. Tesselation could be a good keyword for this. Also your question made me think of cargo trucks and how to fill them efficiently:)

Permalink Reply by Jon Mirtschin on December 2, 2010 at 3:18am

Hi Ibrahim,

Different sizes (random??) sounds difficult. I've coded various tessellation routines (you probably already know this), if there's a particular repetitive arrangement you want I can possibly add it (normally doesn't take long).

Permalink Reply by Nikitashibby on April 28, 2014 at 8:24pm

would you mind sharing the gh defintion for this?

Permalink Reply by Daniel Piker on December 2, 2010 at 3:59am

Do you want to keep the cubes all oriented parallel to each other ?
(If not I think it is a much more complicated problem)

I know of some studies of a similar problem in 2D:

http://www.emn.fr/z-info/sdemasse/gccat/Ksmallest_rectangle_area.html
http://www.eecs.umich.edu/~mmoffitt/papers/annoperres2010.pdf

It might also be useful to look at some circle packing scripts
http://wiki.mcneel.com/developer/scriptsamples/circlepacking
http://wiki.mcneel.com/developer/sdksamples/2dcirclepacking

You could probably adapt a similar iterative approach to work with cubes

Permalink Reply by ibrahim çağrı uslu on December 2, 2010 at 10:25am

-> Mehmet Ali: exactly as you said, i'm looking for a 3d solution but i haven't searched with the keyword "tesselation" =) I'll go deeper and let you know if i find something similar with cargo truck thing :)

-> Jon Mirtschin: yes, in fact combination of your scripts in GeometryGym and the 2d circle packing definitions on this website emerged the idea of 3d cube packing in my mind. that would be a great solution for the project that i am working on, so i'm trying to achieve the 3d version of Daniel Piker's schematic diagram. I just want to specify the volume (even if it has an irregular shape) and want the packing script fill the space exactly like in the 3d version of that diagram.

-> Daniel Piker: Yes, in my case i want to have parallel oriented cubes. I have already looked the sphere packing and circle packing scripts but I couldn't manage to create a working cube definition yet. now i'm looking the websites that u shared.

I want to thank all of you for your quick and helpful replies, any further help or ideas will be appreciated :) i'll let you know the progress that I made and will share the definition if i manage to make it work.

Permalink Reply by Toni Schade on January 19, 2011 at 2:43am

Hey Ibrahim,

I'm looking for exactly the same thing as you were looking for. Have you found out anything? Would be great if you could share it.

Best Toni

Permalink Reply by pim marsman on March 8, 2011 at 3:56pm

Does the fact this discussion is slowly dying indicate the complexity of the question?

Running into the same quest here, any progress?

I'd like to start looking into it in 2d.

Permalink Reply by Evan C on March 22, 2011 at 9:59pm

I would love to find a 2D solution to this - even getting the algorithm from the link above to work would be great. Has anyone had any luck translating that to GH?

Permalink Reply by Yerko Lucic on March 8, 2011 at 5:28pm

it seem difficult with random size cubes, but maybe you could give it a try with Octrees??

http://dfabnus.wordpress.com/2011/02/09/grasshopper-density-explora...

http://modelab.nu/?p=2734

Permalink Reply by Mish on April 11, 2011 at 11:46pm

Hi, Ibrahim!

Did you find out? I would love to see solutions, if it's possible )

Permalink Reply by ibrahim çağrı uslu on April 11, 2013 at 7:32am

after 2 years, i'm sad to say that i wasn't able to find the solution, neither for 2d nor for 3d. nowadays i'm struggling on a similar issue in 2d, diamond shaped rectangles to be filled now. Daniel's attached image above somehow defines my aim. i am working on it now, if i would be able to finish i'll let you know. any help would be appreciated =)

Permalink Reply by Francisco Lara on October 5, 2013 at 2:21pm