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

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Sidharth Sanjeev Wazir 2022-11-25

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回答： Aditya 2022-11-29

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.

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Sidharth Sanjeev Wazir 2022-11-25

在 MATLAB Online 中打开

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 2022-11-25

编辑：Sidharth Sanjeev Wazir 2022-11-25

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

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Answer 1

Aditya 2022-11-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1862463-store-midpoint-of-all-the-squares-inside-the-square-of-width-1cm#answer_1114993

在 MATLAB Online 中打开

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:

The number of squares in each column/row is sqrt(n) (=4 in above figure).
The side of a smaller square is of length 1/sqrt(n) (=0.25 in above figure).
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.
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 