Store midpoint of all the squares inside the square of width 1cm.

There is a square of width 1cm.Discretize it in n squares and find the midpoint of all the square.Plot it

Donot use any pde tools or inbuilt function.

[KSSV]

What have you attempted?

[Sidharth Sanjeev Wazir]

NN=150;

x1=0;     y1=0; 
x2=1;     y2=0; 
x3=1;     y3=1;
x4=0;     y4=1;


% For Bottom Line
 
L1 = [0,0,0;5,0,0]

R1 = pdist(L1,'euclidean')

for N = 1:NN
    delL1 = R1/N; %small increment on loop1

        for m = 1:N
            R12 = delL1*m
            
        end
    end

%For Top Line

L2 = [5,5,0;0,5,0];

R2 = pdist(L2,'euclidean')

for N = 1:NN
    delL2 = R2/N; %small increment on loop1
        for m = 1:N
            R34 = delL2*m
        end
end

%Mapping top and bottom line
%for i=2:NN-1;
 %   for j=2:NN-1;
%L3=[R34(i+1);R12(j+1)]
 %       for N=1:NN
   %         R1234 = pdist(L3,'euclidean')
  %          delL3=R1234/N
     %            for m=1:N
    %                   R1234=delL3*m
      %           end
       % end
   % end
%end  

[Sidharth Sanjeev Wazir]

I divided the lne how to find all the midpoints between the two lines

Answer 1

[Aditya]

Hi,

I understand that you are trying to divide a square of side 1 into n squares and find mid points of all these smaller squares.

A basic approach is to divide the larger square into rows and columns and proceed as follows:

1. The number of squares in each column/row is sqrt(n) (=4 in above figure).
2. The side of a smaller square is of length 1/sqrt(n) (=0.25 in above figure).
3. Find the mid-point of first square (0.25/2, 0.25/2) and keep incrementing by side of square (0.25) to get mid points along an axis.
4. Once, we have mid points along a side, we can use meshgrid to generate all points.

Here is a simple function that does that:

function discretize_square(n) 
    % n has to be a perfect square.
    assert(mod(sqrt(n), 1) == 0, "n not a perfect square"); 
    
    side_divs = sqrt(n); 
    delta = 1/side_divs; 
    midpts = delta/2: delta:1; 
    [x,y]= meshgrid(midpts, midpts); 
    scatter(x,y);
    xlim([0, 1]); 
    ylim([0,1]); 
    
end 

A few points for above code:

1. This will work only is n is a perfect square.
2. Notice the colon operator for creating array of mid points along a side.