CODEWITHSUNDEEP
matlab
Learner
Learner

Reputation: 960

How to generate points with distance between them above some thershold?

I need to generate(in matlab) L points in d-dimensional space which has to satisfies the condition that distance between any two points in the set D (defined below) is above some given threshold r.

The set D ={ L Union Combination of L}. The other various combination of L are generated as its average. For example, the combination of point 1,5,6 is generated as (point_1 + point_5 + point_6)/3, similarly the combination 1,2,5,6 is generated as (point_1 + point_2 + point_5 + point_6)/4.

In general, the set D will have $\sum_{i=1}^{L} L C_{i}$ points.

Upvotes: 1

Views: 885

Answers (1)

Oli
Oli

Reputation: 16035

I made a code that (I think) do what you explain, tell me what you think.

nL=6;
d=2;
r=0.1;
L=rand(d,nL); %%% generate nL random d-dimentional points

Lfinal=[];
for nn=1:nL %% for all passible size of subset of (1:nL)
  sets=nchoosek(1:nL,nn); %% all sub-set of 1:nL of size nn
  Ls=reshape(L(:,sets'),d,nn,[]); %% the corresponding Ls
  newL=squeeze(sum(Ls,2))/nn; %% their sums
  Lfinal=[Lfinal newL]; %% concatante to the final set of Ls.
end

L=Lfinal;
dists=pdist2(L',L'); %%% compute the distances between each point
dists(dists==0)=inf; %%% fill the diagonal with infinity to not use the distance between a point and it self
L=L*r/min(dists(:)); %%% multiply the points by "r/min(dists(:))" to make sure all points are at leat at distance r

L

Upvotes: 1

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