Calculating distance of all the points in a region with each other

问题

I have a region with about 144 points. What i want to achieve is to measure the distance of a point with all others and store it in an array. I want to do this for all the points. If possible i would like to store this data in such a manner that there in no repetition. And i should be able to make queries like- All the distances between all the points without repetition, sum of all the distances for point no56 etc.

I have a 3*144 array with two columns storing the coordinates of the points.

回答1:

A possible solution (I am not really clear with what you mean by no repetition, though):

 X are your points with coordinates x = X(:,1), y = X(:,2)


 dist = sqrt(bsxfun(@minus,X(:,1),X(:,1)').^2 + bsxfun(@minus,X(:,2),X(:,2)').^2)

so

dist(i,j) is the euclidean distance between i and j

of course the matrix is symmetric. You can easily reduce the complexity involved.

回答2:

Let's say your array is A, where each column stores the coordinates of a single point. To obtain the combinations of all point pairs (without repetitions), use nchoosek:

pairs = nchoosek(1:size(A, 2), 2)

Then calculate the Euclidean distance like so:

dist = sqrt(sum((A(:, pairs(:, 1)) - A(:, pairs(:, 2))) .^ 2, 1))

If you have the Statistics Toolbox installed, you can use pdist(A) instead for the same effect.

回答3:

If you have the statistics toolbox, and if you have all your data in the array X, then

D = pdist(X)

gives all the pairwise distances between all points in X.

来源：https://stackoverflow.com/questions/14483468/calculating-distance-of-all-the-points-in-a-region-with-each-other