Find closest sphere in a cluster with random spheres having different diameters

Hi,

I am making clusters of spheres using random number generator. Some of the spheres are connected and some of them are not connected. I want to exclude the not connected ones, so I only get the clusters/connected spheres .I have random spheres having random diameters between 0.1 and 0.5.

here is my code till now

%% Data for Agglomerates
N = 50; % number of spheres
a = 0.1 ; % lowest diameter of sphere
b = 0.5 ; % highest diameter of sphere
Diam = a + (b-a).*rand(N,1);


const = ((1+sqrt(5))/2); % golden ratio bsed on fibonacci sequence

aaa= 0;     % minimum center x and y coordinate limit for spheres
bbb= 2 ;  % maximum center x and y coordinat limit for sphere
% bbb= N*const;  % maximum center x and y coordinat limit for sphere
M=3  ;
Axes= zeros(N,M);
Axes(:,1)=aaa+(bbb-aaa)*rand(N,1);
for k=2:M
    aaa=randperm(N);
    Axes(:,k)=Axes(aaa,1);
end
Axes_Label ={'X axis','Y axis','Z axis'};
Data_agglo = [Diam Axes];
Data_Label ={'Diameter','X axis','Y axis','Z axis'};

R = Diam ./2;
%% generate mesh

dipS = 0.01;
xmin = min(Data_agglo(:,2)-R);
xmax = max(Data_agglo(:,2)+R);

ymin = min(Data_agglo(:,3)-R);
ymax = max(Data_agglo(:,3)+R);

zmin = min(Data_agglo(:,4)-R);
zmax = max(Data_agglo(:,4)+R);


[Xgrid,Ygrid,Zgrid]= ndgrid((xmin:dipS:xmax)-(xmin+xmax)/2,(ymin:dipS:ymax)-(ymin+ymax)/2,(zmin:dipS:zmax)-(zmin+zmax)/2);

Data_agglo(:,2:4) = Data_agglo(:,2:4) - [(xmin+xmax)/2,(ymin+ymax)/2,(zmin+zmax)/2];

% plot3(Xgrid(:),Ygrid(:), Zgrid(:),'.','MarkerFaceColor','blue');
% hold all

%% get active dipoles
tic
active = false(size(Xgrid));
for i =1:1:size(Data_agglo,1)
    
    active = active | (((Xgrid - Data_agglo(i,2)).^2 + (Ygrid - Data_agglo(i,3)).^2 + (Zgrid - Data_agglo(i,4)).^2) <= R(i).^2);
     
end

plot3(Xgrid(active),Ygrid(active),Zgrid(active),'o','MarkerFaceColor','red');
toc
active_dip = sum(sum(sum(active)));
volume = active_dip * dipS^3;

Before I generate the mesh, I get the data set called " Data_agglo", which has the diameter and the x,y,z center coordinates of the spheres data, which I later plot.

I have to find a way to exclude the spheres which are not in the cluster before plotting using the data " Data_agglo".

Does any one know?

Answer 1

[Image Analyst]

What defines "connected" for a bunch of points? If the centers are within a certain distance of each other? Then you can use dbscan

https://en.wikipedia.org/wiki/DBSCAN

It groups points into a cluster if there can be a path between the points that is less than some distance. See attached demo.

In the above figure on the right you can see the cluster distance parameter of 60 indicated by the red bar and the yellow circle. Now see the points connected/outlined in colored polygons? Those points are all within 60 pixels of at least one other pixel in the cluster. The red points are all NOT in any cluster because they are further than 60 from any other point. It sounds like those are the ones you'd want to exclude from your data set. Learn how dbscan (in the Statistics and Machine Learning Toolbox) can be used in your program.

[Chris Dan]

Hii,

thank you for the answer. connected here is when the distance between the center points of two spheres is less than the sum of their radii

d < r1+r2

[Chris Dan]

I have to find all the spheres which satisfy this condition and keep them in the data set and eliminate those from the data set which dont satisfy

[Image Analyst]

Use pdist2() and look for distances greater than diam

distances = pdist2(xy, xy);
goodDistances = distances == 0 || distances >= Diam;
[rows, columns] = find(goodDistances);
xyGood = unique([columns(:), rows(:)], 'rows')

[Chris Dan]

Hi Image Analyst,

Is there any way it can be done without dbscan and the statistical and machine learning toolbox ?

[Image Analyst]

You can get the distances from a particular point (x0,y0) to all other (x,y) points like

distances = sqrt((x-x0).^2 + (y-y0).^2);
% Find min distance that's not zero (to prevent the particle itself being the closest particle).
minDistance = min(nonzeros(distances))
% Get indexes of coordinates that have this min distance.
indexes = find(distances == minDistance)