How to plot only selected spheres?

I have plotted spheres in space from known coordinates and radius. All the spheres are randomly distributed in space. I want to plot only those spheres which are intersecting with each other from top to bottom along the z-axis. I dont want to plot the rest of spheres. Is there any way to do it? I am doing it manually which is wasting a lot of my time. I see only for those spheres which are in continuity and deleting the rest spheres manually which is quite frustrating. Your help and suggestions would be highly appreciated.

Answer 1

[Image Analyst]

For each sphere, compute the distance of it's center to the centers of all the other spheres. If the distance is less than the sum or their two radii, then those two spheres overlap, and record/log that pair of spheres. Then, once all overlapping pairs have been identified, clear the axes or use a new one and plot only those spheres that had overlap. Code should be straightfoward. Let me know if you can't figure it out. Here's a start, assuming you have an array xyzr with one row for every sphere

numSpheres = size(xyzr, 1);
for k = 1 : numSpheres
    distances = sqrt((xyzr(:, 1) - xyzr(k, 1))^2 + (xyzr(:, 2) - xyzr(k, 2))^2 + (xyzr(:, 3) - xyzr(k, 3))^2)
    sumOfRadii = xyzr(k, 4) + xyzr(:, 4);
    overlaps = distances < sumOfRadii;
    indexes = find(................
end
% etc.

That should be a good start. See if you can finish it.

[Muhammad Khan]

Thanks for your ans Image Analyst. I have already calculated the distances and sum of radii to calculate Matrix M. Matrix M is giving me intersection volume of intersecting spheres. Intersection volume is zero for spheres distance > sum of radii and different values for distance <sum of radii. The only thing i want now is to select only those spheres which are intersecting continuously from top to bottom along the z-axis.

[Image Analyst]

Each sphere has an index - some kind of ID number to identify it. Why didn't you just keep track of those that had the distance less than the sum of the radii?

overlaps = distances < sumOfRadii;
indexes = find(overlaps); % Keep track of indexes that overlap the k'th sphere.