Question

I have a vector of coordinates called x. I want to get the element(s) with the min y coordinate:

a = find(x(:,2)==min(x(:,2))); % Contains indices

This returns the indexes of the elements with the smallest y coordinates. I say element*s* because sometimes this would return more than 1 value (e.g. (10,2) and (24,2) both have 2 as y coordinate and if 2 is the min y coordinate…).

Anyway, my next step is to sort (ascending) the elements with the min y coordinates according to their x coordinates. First I do:

b = sort(x(a,1));

The above operation might rearrange the elements with min y coordinates so I want to apply this rearrangement to a as well. So I do:

[v i] = ismember(b, x(:, 1));

Unfortunately, if there are elements with the same x value but different y values and one of these elements turns out to be a member of a (i.e. b) then the above matrix chooses it. For example if (10,2) and (24,2) are the elements with smallest y coordinates and there is a 3rd element (24, 13) then it will mess up the above operation. Is there a better way? I wrote my script using loops and everything was fine but in line with Matlab’s methodology I rewrote it and I fear my unfamiliarity with matlab is causing this error.

Answer 1

Sorry, I might have misunderstood your question but lemme rephrase what I think you want here:
You have a set of 2D coordinates:

x = [24,2; 10,2; 24,13];

You want the pairs of coordinates to stay together (24,2) (10,2) and (24,13). And you want to find the pairs of coordinates that has the min y-coordinate and if there are multiples, then you want to sort them by x-coordinate. And you want the row indices of what those coordinate pairs were in the original matrix x. So in other words, you want a final answer of:

v = [10,2; 24,2];
i = [2,1];

If I understood correctly, then this is how you can do it:

(Note: I changed x to have one more pair (40,13) to illustrate the difference between idx(i) and i)

>> x = [40,13; 24,2; 10,2; 24,13];
>> idx = find(x(:,2)==min(x(:,2))) %Same as what you've done before.

idx =

     2
     3

>> [v,i] = sortrows(x(idx,:)) %Use sortrows to sort by x-coord while preserving pairings

v =

    10     2
    24     2


i = % The indices in x(idx,:)

     2
     1

>> idx(i) %The row indices in the original matrix x

ans =

     3
     2

And finally, if this is not what you wanted, can you indicate what you think your answer [v,i] should be in the example you gave?