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I found this image of subdividing a cube based on octree model for the game "Cube 2: Sauerbraten octree". How can such an octree subdivision algorithm can be implemented?

I also need a generalized version of this which can be applicable for any rectangular cuboid having different length, width and height.

How can this be done?

Edit 1:

Consider a volume as

vol = ExampleData[{"TestImage3D", "MRbrain"}];

I can partition it in the following way:

{w, d, h} = ImageDimensions[vol];

Manipulate[ImagePartition[vol, {w/np, d/np, h/np}], {np, 1, 10, 1}]

This gives me a list of all the subvolumes. However, I cannot do the partition into the higher levels and display the partitions in the way as displayed in the mathematica demonstration or in the wikipedia image.

Edit 2:

ImageAssemble[
 ImagePartition[vol, {w/2, d/2, h/2}] /. 
  i_Image3D :> ImagePad[i, 20, 0]];

This gives me

enter image description here

I can break one subpart as

ImageAssemble[
 ImagePartition[
   ImagePartition[vol, {w/2, d/2, h/2}][[1, 1, 2]], {w/4, d/4, 
    h/4}] /. i_Image3D :> ImagePad[i, 20, 0]]

And the corresponding result is:

enter image description here

I am still trying to figure it out how to assemble the second one replacing the corresponding part in the first image.

Edit 2:

Now I can split the volume at the second level.

temp = vol;
{w, d, h} = ImageDimensions[temp];
temp1 = ImagePartition[temp, {Floor[w/2], Floor[d/2], Floor[h/2]}];
temp2 = temp1[[1, 1, 2]];
temp3 = ImagePartition[temp2, {Floor[w/4], Floor[d/4], Floor[h/4]}];
temp3reconstructed = 
  ImageAssemble[temp3 /. i_Image3D :> ImagePad[i, 5, 0]];
temp1[[1, 1, 2]] = 
  ImageResize[
   temp3reconstructed, {Floor[w/2], Floor[d/2], Floor[h/2]}];
temp1reconstructed = 
 ImageAssemble[temp1 /. i_Image3D :> ImagePad[i, 5, 0]]

and the output is:

enter image description here

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  • $\begingroup$ @Kuba I have looked into the quadTree implementation (demonstrations.wolfram.com/QuadtreeSubdivision) and this wikipedia pages (en.wikipedia.org/wiki/Octree; en.wikipedia.org/wiki/Cube_2:_Sauerbraten) $\endgroup$ – Majis Jan 29 '18 at 13:53
  • $\begingroup$ @Kuba The quadTree implementation only works for square images. $\endgroup$ – Majis Jan 29 '18 at 13:54
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    $\begingroup$ Have you tried implementing anything, or do you want us to write the whole thing for you and give you the code? $\endgroup$ – Rahul Jan 29 '18 at 14:41
  • $\begingroup$ @Rahul See my edit. This is what I have done so far and I am still trying to progress further. Whenever I reach up to anything, I will update. $\endgroup$ – Majis Jan 29 '18 at 15:21

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