Sort matrix of coordinate pairs base of knowledge of adjacent points

I am currently trying to sort airfoil coordinates and I have tried numerous methods to no avail (bottom edge of trailing edge causes issues). I have set of coordinates [nx2] with column 1 being x and column 2 being y. I have determined the distances to all points from one another ([nxn] matrix) and have obtained the indices of the 2 smallest overall distances for each point. How would I go ordering the original [nx2] matrix based off knowing the indices/coordinates adjacent to each point? ( I have put data for a clark-y airfoil since I am not able to share the airfoil data). Any tips or info will be greatly appreciated!

s1 = [0.97                 0.0076868
      0.82                 0.0400245
      0.98                 0.0053335
      0.02                 0.0253735
         0                         0
      0.97                -0.0017011
       0.7                 0.0614329
      0.72                 0.0581599
      0.92                 0.0191156
       0.4                -0.0226341
      0.86                -0.0057408
      0.44                 0.0897175
      0.88                -0.0050063
      0.12                -0.0299633
      0.05                -0.0260452
       0.1                -0.0293786
      0.22                -0.0291445
      0.76                -0.0094133
      0.06                -0.0271277
       0.6                -0.0152893
      0.48                -0.0196986
      0.05                 0.0442753
      0.36                 0.0916266
      0.32                 0.0911857
      0.92                -0.0035373
      0.14                -0.0302404
      0.28                 0.0900016
       0.1                 0.0629981
      0.56                  0.080348
     0.012                 0.0178581
     0.012                -0.0169733
      0.94                -0.0028028
      0.84                -0.0064753
     0.001                -0.0059418
       0.4                 0.0911712
      0.18                 0.0810687
      0.82                -0.0072098
     0.008                  0.013735
      0.03                 0.0330215
      0.86                  0.031974
      0.99                  0.002969
      0.74                -0.0101478
      0.04                -0.0245211
      0.99                -0.0009666
       0.8                 0.0438836
       0.9                 0.0235025
      0.24                -0.0285181
      0.02                -0.0202723
      0.88                 0.0277891
       0.2                -0.0296656
         0                         0
     0.002                -0.0078113
      0.04                 0.0391283
      0.64                 0.0704822
      0.38                -0.0233606
      0.62                 0.0732055
      0.52                 0.0842145
      0.76                 0.0512565
      0.22                 0.0861433
      0.54                 0.0823712
      0.78                 0.0476281
      0.68                 0.0645843
     0.004                 0.0089238
      0.62                -0.0145551
      0.28                -0.0270696
      0.16                 0.0775707
       0.8                -0.0079443
       0.7                -0.0116169
      0.12                 0.0686204
      0.24                 0.0878308
      0.03                -0.0226056
      0.72                -0.0108823
      0.34                 0.0915079
     0.008                -0.0142862
      0.46                -0.0204353
      0.56                -0.0167572
       0.9                -0.0042718
       0.3                 0.0906804
      0.46                 0.0886427
     0.002                 0.0058025
      0.08                -0.0284595
      0.26                  0.089084
       0.6                 0.0757633
      0.74                 0.0547675
      0.42                -0.0219042
    0.0005                  0.002339
      0.38                 0.0915212
      0.68                -0.0123515
      0.84                 0.0360536
      0.34                -0.0248176
         1                -0.0005993
     0.004                -0.0105126
      0.96                -0.0020683
       0.2                 0.0839202
      0.48                 0.0873572
      0.58                 0.0781451
       0.5                 0.0858772
      0.32                -0.0255565
      0.14                  0.073436
      0.26                -0.0278164
      0.36                 -0.024087
      0.78                -0.0086788
       0.3                -0.0263079
      0.66                 0.0676046
    0.0005                  -0.00467
      0.52                -0.0182262
      0.54                -0.0174914
       0.5                -0.0189619
      0.58                -0.0160232
     0.001                 0.0037271
      0.98                -0.0013339
      0.96                 0.0100232
      0.42                 0.0905657
      0.94                 0.0146239
      0.06                 0.0487571
         1                 0.0005993
      0.16                -0.0302546
      0.18                 -0.030049
      0.44                -0.0211708
      0.64                -0.0138207
      0.66                -0.0130862
      0.08                 0.0564308];

for i = 1:length(s1)

    for j = 1:length(s1)

        zz = [ (s1(i,1) - s1(j,1));
                (s1(i,2) - s1(j,2))];
        dist_zz(i,j) = norm(zz);
    end

end
ll = [1:length(s1)]';

bb = [ll dist_zz'];

n=2;
for i = 1:length(s1)
    b_=sortrows(bb,n,"ascend");
    c(:,i)=b_(1);
    n=n+1;
end

%% code to order sort s1

Answer 1

[Umar]

Hi Daniel,

You asked, How would I go ordering the original [nx2] matrix based off knowing the indices/coordinates adjacent to each point?

To order the original [nx2] matrix using the adjacent indices or coordinates, you can utilize the sortrows function in MATLAB. This function sorts the rows of a matrix based on specified columns. By specifying the columns corresponding to the adjacent indices, you can achieve the desired sorting. For more information about this function, please refer to

https://www.mathworks.com/help/matlab/ref/double.sortrows.html

I will also provide an example to help you how to use this function.

>> % Original matrix

A = [4 5; 2 3; 1 2; 3 4];

% Sort based on adjacent indices in the first column

sortedA = sortrows(A, 1);

disp(sortedA);

So, in the above code,sortrows(A, 1) sorts matrix A based on the values in the first column. You can adjust the column index according to the adjacent indices you want to use for sorting.