Matlab generating random numbers and overlap check - matlab

Question

I wrote a code for generating random number of rods on Matlab within a specified domain and then saving the output in a text file. I would like to ask for help on adding the following options to the code;
(i) if the randomly generated rod exceeds the specified domain size, the length of that rod should be shortened so that to keep it in that particular domain.
(ii) i would like to avoid the overlapping of the newly generated number (rod) with that of the previous one, in case of overlap generate another place for the new rod.
I can't figure out how shall I do it. It would be of much help if someone may help me write code for these two options.
Thank you
% myrandom.m
% Units are mm.
% domain size
bx = 160;
by = 40;
bz = 40;
lf = 12; % rod length
nf = 500; % Number of rods
rns = rand(nf,3); % Start
rne = rand(nf,3)-0.5; % End
% Start Points
for i = 1:nf
rns(i,1) = rns(i,1)*bx;
rns(i,2) = rns(i,2)*by;
rns(i,3) = rns(i,3)*bz;
end
% Unit Deltas
delta = zeros(nf,1);
for i = 1:nf
temp = rne(i,:);
delta(i) = norm(temp);
end
% Length Deltas
rne = lf*rne./delta;
% End Points
rne = rns + rne;
fileID = fopen('scfibers.txt','w');
for i = 1:nf
fprintf(fileID,'%12.8f %12.8f %12.8f\r\n',rns(i,1),rns(i,2),rns(i,3));
fprintf(fileID,'%12.8f %12.8f %12.8f\r\n\r\n',rne(i,1),rne(i,2),rne(i,3));
end
fclose(fileID);

Answer 1

I would start from writing a function that creates the random rods:
function [rns,rne] = myrandom(domain,len,N)
rns = rand(N,3).*domain; % Start --> rns = bsxfun(#times,rand(N,3),domain)
rne = rand(N,3)-0.5; % End
% Unit Deltas
delta = zeros(N,1);
for k = 1:N
delta(k) = norm(rne(k,:));
end
% Length Deltas
rne = len*rne./delta; % --> rne = len*bsxfun(#rdivide,rne,delta)
% End Points
rne = rns + rne;
% remove rods the exceed the domain:
notValid = any(rne>domain,2); % --> notValid = any(bsxfun(#gt,rne,domain),2);
rns(notValid,:)=[];
rne(notValid,:)=[];
end
This function gets the domain as [bx by bz] and also the length of the rods as len, and N the number of rods to generate. Note that using elementwise multiplication (.*) I have eliminated the first for loop.
In case you use MATLAB version prior to 2016b, you need to use bsxfun:
In MATLAB® R2016b and later, the built-in binary functions listed in this table independently support implicit expansion.
The affected lines are marked with --> in the code (with the alternative).
The last three lines in the function remove from the result all the rodes that exceed the domain size (I hope I got you correctly on this).
Next, I call this function within a script:
% domain size
bx = 160;
by = 40;
bz = 40;
domain = [bx by bz];
lf = 12; % rod length
nf = 500; % Number of rods
[rns,rne] = myrandom(domain,lf,nf);
u = unique([rns rne],'rows');
remain = nf-size(u,1);
while remain>0
[rns_temp,rne_temp] = myrandom(domain,lf,remain);
rns = [rns;rns_temp];
rne = [rne;rne_temp];
u = unique([rns rne],'rows');
remain = nf-size(u,1);
end
After the basic definitions, the function is called and returns rne and rns, which are probably smaller than nf. Then we check for duplicates, and store all unique rods in u. We calculate the rods remain to compute, and we use a while loop to generate new rods as needed. In each iteration of the loop, we add the newly created rods to those we have in rne and rns, and check how many unique vectors we have now, and if there are enough we quit the loop (then you can add printing to the file).
Note that:
I was not sure what you mean by "in case of overlap generate another place for the new rod" - do you want to have more than nf rods if some are duplicates, that from which nf are unique (what the code above does)? or you want to remove the duplicates and remain only with nf unique rods? In the case of the latter option, I would insert the unique function part into the function that creates the rods myrandom.
The wile loop as written above is not efficient since no preallocating of memory is done. I'm not sure that this is possible if you just want to create more rods but keep the duplicates, but if not (the second option in 1 above) and if you are going to use this allot, then preallocating is very recommended.