Sir I Want to place some target point in a reign of 100x100 and then cover them with Some sensor node like this given diagram, How I can do this?

[Walter Roberson]

This is not clear. Are the sensors to be placed at random? Is there a particular algorithm to place the sensors? If you want some kind of optimization, then why not just use kmeans clustering using the number of sensors as the number of clusters, and then place the sensors at the cluster centroids?

[Aqeel Awan]

Sensors are placed randomly. and now i wants that these sensor cover all targets

N=4;
Trange=1;   
area=[5,5];
nodes.pos=area(1).*rand(N,2);
%% plot the nodes deployment
% -----------------------------------------------------
plot(nodes.pos(:,1),nodes.pos(:,2),'.','color','b');
hold on
for ii=1:N                   % plot the circular transmission range
    [nodes.circle.x(ii,:),nodes.circle.y(ii,:)]=circle(nodes.pos(ii,1),nodes.pos(ii,2),Trange);
   disp(circle(nodes.pos(ii,1),nodes.pos(ii,2),Trange));
    F6=fill(nodes.circle.x(ii,:),nodes.circle.y(ii,:),[0.25,0.25,0.25]);
    alpha 0.1
    hold on
end
axis on
xlabel('x(m)')
ylabel('y(m)')
title('Initial Placement of Nodes with circular transmission range')

% -----------------------------------------------------
% plot the targets
% -----------------------------------------------------
N1=4;
coords = area(1).*rand(N1,2);
plot(coords(:,1),coords(:,2),'*','color','r');
hold on
% -----------------------------------------------------
function [xunit,yunit] = circle(x,y,r)
hold on
th = 0:pi/50:2*pi;
xunit = r * cos(th) + x;
yunit = r * sin(th) + y;
% h = plot(xunit, yunit);
% hold off
end

[Walter Roberson]

So what is the question? You have locations for all of the sensors.

If the sensors have a maximum detection radius, then there is a possibility that you are missing out on some node -- for example the sensors could have all randomly been placed in the top right corner, and the nodes could have all randomly been placed in the bottom left corner (if this is not a possible outcome, then the distribution is not Uniform Random. Uniform Random might have a low probability of that kind of placement, but it will always be possible with Uniform Random.)

You can detect whether every node is within range of some sensor by using pdist2(), assuming that the nodes do not interfere with each other. But the question ends there: you do not ask for the sensors to be relocated under any conditions, so the placement is either good or it is not.

[Aqeel Awan]

I just want to reallocate the sensors until all the targets are in the range of these sensors and no one target should be left without any sensor range

[Walter Roberson]

ok so what is the sensor range? Is that the variable designated by Trange?

[Aqeel Awan]

yes Trange variable is the sensor range...

[Walter Roberson]

Here is an example of re-arranging and cleaning up your code a bit, and using the positions of the targets to try to figure out good positions for nodes.

In this case I use the kmeans() algorithm to try to find placements.

This is a good example because we can see that the placement was unsuccessful, but we can also see that circles could have been placed to cover all of the targets. As you increase the number of nodes relative to the number of targets you increase the probability that it will not be possible to place the nodes to cover all of the targets. When you compare NN * pi*Trange^2 to prod(area) you can see that once you have filled more than that fraction with targets then you might not be able to cover all of them.

So, using kmeans() by itself is not the solution, but this arrangement of code will give you a better framework on how to construct a solution.

NN = 4;  %number of nodes
NT = 10;  %number of targets

Trange = 1;   
area = [5,5];

% -----------------------------------------------------
% plot the targets
% -----------------------------------------------------

coords = area.*rand(NT,2);
plot(coords(:,1),coords(:,2),'*','color','r');
hold on

axis on equal
xlabel('x(m)')
ylabel('y(m)')
title('Initial Placement of Nodes with circular transmission range')

%place the nodes AFTER you have the target

nodes.pos=area(1).*rand(NT,2);

[~, nodes.pos] = kmeans(coords, NT, 'start', 'uniform')

nodes = struct with fields:
    pos: [10×2 double]

%% plot the nodes deployment
% -----------------------------------------------------
plot(nodes.pos(:,1),nodes.pos(:,2),'.','color','b');
for ii=1:NN                   % plot the circular transmission range
    [nodes.circle.x(ii,:),nodes.circle.y(ii,:)] = circle(nodes.pos(ii,1),nodes.pos(ii,2),Trange);
    F6 = fill(nodes.circle.x(ii,:),nodes.circle.y(ii,:),[0.25,0.25,0.25]);
    alpha 0.1
end

% -----------------------------------------------------
function [xunit,yunit] = circle(x,y,r)
hold on
th = 0:pi/50:2*pi;
xunit = r * cos(th) + x;
yunit = r * sin(th) + y;
% h = plot(xunit, yunit);
% hold off
end