How to find minimum distance from one set of points to another set of points in matlab?

Question

I have distributed 100 random points(nodes) in an area by using following code

n=100; xm=100;ym=100;
    for i = 1 : 1 :n
    S(i).xd = rand(1,1)*xm ;
    S(i).yd = rand (1,1)*ym ;
    xd(i) = S(i).xd ;
    yd(i) = S(i).yd ;
    S(i).id = i;
    S(i).type = 0;
    S(i).g = 0 ;
    S(i).E = Eo ;
    S(i).type = 0 ;

end

Next I have fixed 10 gateway nodes at the edge of the area using following code

 for i=1:1:10
    Sg(i).xd= 2+100*rand(1,1);
      Sg(i).yd=100;
    xd(i)=Sg(i).xd;
    yd(i)=Sg(i).yd;
    Sg(i).id=i;
     plot(Sg(i).xd,Sg(i).yd,'*k')
grid on;
hold on;   
end

Now I have formed cluster heads using LEACH protocol from 100 nodes.

I have to find min distance gateway node from a CH. As there are 10 gateway nodes, I have to find which is closer to a CH in the area.

To determine CH I have used following code

for all nodes in the area


    temp_rand1=rand;
                if(temp_rand1<= (p/(1-p*mod(r,round(1/p)))))
                    countCHs1=countCHs1+1;

                    S3(i).type=1;
                    S3(i).g=round(1/p)-1;
                    C1(cluster1).xd=S3(i).xd;
                    C1(cluster1).yd=S3(i).yd;

         **distance1=sqrt((S3(i).xd-(gw_node.x) )^2 + (S3(i).yd-(gw_node.y) )^2 );**
                    C1(cluster1).distance1=distance1;
                    C1(cluster1).id=i;
                    X(cluster1)=S3(i).xd;
                    Y(cluster1)=S3(i).yd;
                    cluster1=cluster1+1; 
end

I know how to determine distance between a CH and one gateway node, But I do not know how to find closet gateway node from a set of gateway nodes. Thanks in advance

Please reply

Answer 1

Not too sure what you are asking for but I think you want to find the two closest points.

This is how you could do it.

%// Generate some points
n = 3;    xm = 1:n;    ym =1:n;
m = [xm' ym']; %// This is the line
xd = [    2    8   3]; 
yd = [    1    4   3];
d = [xd' yd']; %// These are the random points
drep = repmat(d,n,1); %// This will repeat the matrix d n times
B= ones(n,1); 
mrep = kron(m,B); %// This will repeat each value in m n times        
distances = bsxfun(@minus,mrep,drep);  %// The distance from each point to every other point       
C_squared = sum(distances.^2,2)
[min_dist,idx] = min(sum(distances.^2,2)) %// Find the minimum distance

value_in_m = mrep(idx,:)

ans =

   3   3

value_in_d = drep(idx,:)
ans =

   3   3

---

Explanation

% Generate some points
n = 3;
xm = 1:n;
ym =1:n;
m = [xm' ym']; %// This is the line. Each row is a point
xd = [    2    8   3]; 
yd = [    1    4   3];
d = [xd' yd']; %// These are the random points

We want to calculate the distance from one point to every other point so we repeat the points nxn times

Below is just one way of getting repeated elements. More suggestions are here: https://stackoverflow.com/a/16269185

drep = repmat(d,n,1); %// This will repeat the matrix d n times
B= ones(n,1); 
mrep = kron(m,B); %// This will repeat each value in m n times

We are basing this on Pythagoras theorem so (m_x-d_x)^2 + (m_y-d_y)^2 = C^2

distances = bsxfun(@minus,mrep,drep);  %// The distance from each point to every other point       
C_squared = sum(distances.^2,2)

Find the minimum distance

[min_dist,idx] = min(sum(distances.^2,2)); 

Find the points with the minimum distance

value_in_m = mrep(idx,:)
ans =

   3   3

value_in_d = drep(idx,:)
ans =

   3   3

Answer 2

Not sure what you are asking. I assume you have set of fixed points in a straight line (marked blue) and set of random points (marked red). You want the Minimal distance between one fixed and one random point.

Try this code:

si = randi([0,100],10,2);    %// Random points (red)
sg(:,1) = randi([0,100],10,1);  %// fixed points x param (blue)
sg(:,2) = ones(10,1)*50;    %// fixed points y param (blue) r const, to make them a st. line

sgc = mat2cell(sg,ones(1,size(sg,1)),size(sg,2)); %// converting to cell array
sic = mat2cell(si,ones(1,size(si,1)),size(si,2)); %// converting to cell array

%// distMat gives n*n matrix of all the dist between each fixed point with every other point.
distMat = cellfun(@(x,y) pdist2(x,y),repmat(sic,1,size(sgc,1)),repmat(sgc',size(sic,1),1));

figure; axis('image');
plot(si(:,1),si(:,2),'r.');
text(si(:,1),si(:,2),[repmat('  ',size(si,1),1), num2str((1:size(si,1))')]);
hold on
plot(sg(:,1),sg(:,2),'b.');
text(sg(:,1),sg(:,2),[repmat('  ',size(sg,1),1), num2str((1:size(sg,1))')]);
hold off

[mdist, index] = min(distMat(:));
[randomP, fixedP] = ind2sub(size(distMat),index)

Plot:

output:

randomP =

 2


fixedP =

 2

>> mdist

mdist =

6.7082