How to fill a 3d volume with non-overlapping structures?

I have a problem that I haven't seem any general solution for in other answers. I need to randomly place arbitrary, irregular shapes (macromolecules, if it matters) into a 3d array volume without overlapping. I don't need packing, but ideally being ale to hit high density is good.

I have a few hamfisted ideas of how to do this, all of which seem inelegant, slow, and error-prone:

1. add a uniform high value to all prospective inputs, check for overlap via finding excessively high values after placement and reverting if an overlap value is generated in the array. Seems the most ideal, as it works well with irregular shapes.
2. randomly choose a centroid, and exhaustively check hundreds-thousands of points within the prospective object's radius to find if anything else is present. place only if nothing is found.
3. generate centroids as plot points, finding the nearest points and checking that the combined radius doesn't overstep the distance

Is there any more simple and reliable way to do this? A function that could do a basic overlap check? something on the file exchange that already accumulates shapes into a 3d volume without overlap? Or just a better strategy?

[yanqi liu]

may be upload some data，such as use isosurface and so on to make 3D object by images

[Matt J]

Are the instances of the shapes all the same size and geometry?

[Carson Purnell]

The shapes are a mixed collection with high variance.

Answer 1

[Carson Purnell]

To answer my own question, I went with #1. it ended up being very efficient, combined with a refactoring of the function I was using to write into the destination array it ended up being a dramatic increase in speed.

Binarize the relevant areas, sum and check for overlap (>1), only write if there is no overlap.

case 'nonoverlap'
        dbin = single(imbinarize(dest(dx,dy,dz))); sbin = single(imbinarize(source(sx,sy,sz)));
        overlap = dbin + sbin;
        if max(max(max(overlap)))>1 %if overlap, record and output original
            overlap = 1; 
        else %if no overlap, add the source to the destination
            dest(dx,dy,dz) = source(sx,sy,sz) + dest(dx,dy,dz); overlap = 0;
        end