How can I divide area into 12 sectors and deploy its nodes_locations ?

Hi,

Below is the Matlab-code to equally divided Area into 8 parts as in the picture below

% %Inputs:  nodes_location: the coordinates of the nodes.
%         Tx: Transmission powers of the nodes.
%         threshold: the chosen threshold for clustering.

%Outputs: CH_I: Index of cluster heads.
%         CH_T: Transmission powers of cluster heads.
%         CM_T: Transmission powers of cluster members.
%         CM_I: Index of cluster members.
%         clusters: Indicates the size of each cluster.

function [CH_I , CH_T , CM_T , CM_I , clusters] = clustering(nodes_location , Tx , threshold)%H i add ce and cnn

global cluster_size 
index = find(Tx > threshold);
cn = nodes_location(index , :);
clusters = zeros(8 , 50);
CH_I = [];
CH_T = [];
CM_L = [];
CM_T = [];

%Sector 1
index_s1 = find(cn(: , 1) >= 0 & cn(: , 1) <= cn(: , 2) & cn(: , 2) >= 0);
a_index_s1 = index(index_s1);
sector1 = cn(index_s1 , :); 
Tx_sector1 = Tx(a_index_s1);

%Sector 2
index_s2 = find(cn(: , 1) >= 0 & cn(: , 1) > cn(: , 2) & cn(: , 2) >= 0);
a_index_s2 = index(index_s2);
sector2 = cn(index_s2 , :);
Tx_sector2 = Tx(a_index_s2);

%Sector 8
index_s8 = find(cn(: , 1) < 0 & abs(cn(: , 1)) <= cn(: , 2) & cn(: , 2) >= 0);
a_index_s8 = index(index_s8);
sector8 = cn(index_s8 , :);
Tx_sector8 = Tx(a_index_s8);

%Sector 7
index_s7 = find(cn(: , 1) < 0 & abs(cn(: , 1)) > cn(: , 2) & cn(: , 2) >= 0);
a_index_s7 = index(index_s7);
sector7 = cn(index_s7 , :);
Tx_sector7 = Tx(a_index_s7);

%Sector 3
index_s3 = find(cn(: , 1) >= 0 & cn(: , 1) > abs(cn(: , 2)) & cn(: , 2) < 0);
a_index_s3 = index(index_s3);
sector3 = cn(index_s3 , :);
Tx_sector3 = Tx(a_index_s3);

%Sector 4
index_s4 = find(cn(: , 1) >= 0 & cn(: , 1) <= abs(cn(: , 2)) & cn(: , 2) < 0);
a_index_s4 = index(index_s4);
sector4 = cn(index_s4 , :);
Tx_sector4 = Tx(a_index_s4);

%Sector 5
index_s5 = find(cn(: , 1) < 0 & abs(cn(: , 1)) <= abs(cn(: , 2)) & cn(: , 2) < 0);
a_index_s5 = index(index_s5);
sector5 = cn(index_s5 , :);
Tx_sector5 = Tx(a_index_s5);

%Sector 6
index_s6 = find(cn(: , 1) < 0 & abs(cn(: , 1)) > abs(cn(: , 2)) & cn(: , 2) < 0);
a_index_s6 = index(index_s6);
sector6 = cn(index_s6 , :);
Tx_sector6 = Tx(a_index_s6);

How the area can be split and deploy nodes into more parts, for instance (12) like pic below

%

[Tamoor Shafique]

did you get the answer to this?

[Walter Roberson]

yes I posted code below https://www.mathworks.com/matlabcentral/answers/393205-how-can-i-divide-area-into-12-sectors-and-deploy-its-nodes_locations#comment_554235

Answer 1

[Walter Roberson]

I would suggest converting into polar form relative to the center of the circle, and then dividing according to groups of 2*pi/12 radians.

[Hassan Al-Khateeb]

if I have this code... How can I split it into 12 parts

clear all
close all

Nmax=1000;
r=1;
R=5;

for n=1:Nmax

      %wrong method
      r1(n)=r+R*rand(1,1);
      theta1(n)=2*pi*rand(1,1);

      % right method
      % pdf_r(r)=(2/R^2) * r
      % cumulative pdf_r is F_r = (2/R^2)* (r^2)/2
      % inverse cumulative pdf is r = R*sqrt(F_r)
      % so we generate the correct r as
      r2(n) = r+R*sqrt(rand(1,1));
      % and theta as before:
      theta2(n)=2*pi*rand(1,1)./h;

      % convert to cartesian
      x1(n)=r1(n)*cos(theta1(n));
      y1(n)=r1(n)*sin(theta1(n));
      x2(n)=r2(n)*cos(theta2(n));
      y2(n)=r2(n)*sin(theta2(n));
  end

subplot(1,2,1)
plot(x1,y1,'r.')
axis([-1.1*R 1.1*R -1.1*R 1.1*R])
axis square
title('Wrong')
subplot(1,2,2)
plot(x2,y2,'g.')
axis([-1.1*R 1.1*R -1.1*R 1.1*R])
axis square
title('Right')

Thanks

Answer 2

[Hassan Al-Khateeb]

Thank you Mr.Walter Roberson Could you explain how can divide it into 2*pi/12 ? (MATLAB CODE or any source if it is possible )

Regards,

[Walter Roberson]

[th, r] = cart2pol( x - xc, y - yc );
sector_number = mod(floor(th / (2*pi/12) ) - 1, 12) + 1;