Changing point coordinates in a file to closest ones in another file

I have a file M1 containing a matrix from this form, for example

1 10 45
2 32 56
3 12 50
4 28 67

The second and third column are x and y coordinates of nodes and the first column is the id of the node. And another one M2 containing another matrix, for example

10 50
30 60

These columns are coordinates of, let's say, reference nodes

What I want to do is to change the coordinates in the first file to the closest one to them in the second file. So my result, will be something like this:

1 10 50
2 30 60
3 10 50
4 30 60

Any hints or ideas how to do it?

Answer 1

[Guillaume]

If you have the statistics toolbox, you can use pdist2 to calculate your distance matrix:

Dist = pdist2(M1(:, [2 3]), M2, 'cityblock'); %You used the cityblock distance in your code. Wouldn't 'euclidean' be better?

If not, you can still avoid the loops with:

Dist = abs(bsxfun(@minus, M1(:, 2), M2(:, 1).')) + abs(bsxfun(@minus, M1(:, 3), M2(:, 2).')); %for cityblock
DistSquared = abs(bsxfun(@minus, M1(:, 2), M2(:, 1).').^2) + abs(bsxfun(@minus, M1(:, 3), M2(:, 2).').^2); %for euclidean

You also don't need a loop to create your final matrix:

[~, closestidx] = min(Dist, [], 2);
M3 = [M1(:, 1), M2(closestidx, [1 2])];

To find the rows of M2 that do not appear in M3:

notpresent = ~ismember(M2, M3(:, [2 3]), 'rows');

To remove these rows from M2:

M2(notpresent, :) = [];

[etudiant_is]

Thanks a lot for your answer. For the distance, yes i used the Manhattan distance which is what i need in my problem.

Answer 2

[etudiant_is]

I did it like this

[rows1, ~] = size(M1);
[rows2 , ~] = size(M2);

   for i=1:rows1
  for j=1:rows2
    Dist (i,j) = abs(M1 (i,2) - M2 (j,1)) + abs(M1 (i,3) - M2 (j,2));
  end
   end

   [MinDist, MinDistInd]= min(Dist');
   for i=1:rows1
      M3(i,1)=i;
      M3(i,2)=M2 (MinDistInd(i),1);
      M3(i,3)=M2 (MinDistInd(i),2);

    end

I get the result I want, but then I notice that some reference points are not picked at all, so how can I remove them from M2 and keep only those which were used? Besides, is there a shorted way to do it because my first matrices has like 10000 elements inside of it?