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

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Sidharth Sanjeev Wazir
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
Sidharth Sanjeev Wazir 2022-11-25
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

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回答（1 个）

Aditya
Aditya 2022-11-29
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.

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