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

coordinates nearest value

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?

Best Answer

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, :) = [];
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