Get all the neighborhood of point x of distance r using matlab

Question

I have a n-dimensional point, and would like to get all its neighborhood of distance r.

I know matlab has rangesearch() to get the neighborhood of distance r in a candidate set, but in my problem I don not have a candidate set.

Is there any matlab code can do this job?

Thanks!

I mean I want to create the subset of the points that are within this ball. For instance, I have a point (3,1) and the radius r is 5, so I want to find all the points within r of 5 to the point (3,1). The incremental would be 1 in this case, which means the possible answer could be point (4,1), (3,2), (5,1)...Am I making myself clear?

Answer 1

You can create a candidate set using ndgrid. In your 2-D example, you want a grid of points with a spacing of 1.

xrange = -10:10;
yrange = -10:10;
[X, Y] = ndgrid(xrange, yrange);

This produces two 2-D matrices of points. To get it into the format expected by rangesearch:

candidate_set = [X(:), Y(:)];

And then you can call rangesearch to find which of these are within the radius of your selected point:

test_pt = [3, 1];
radius = 5;
idx = rangesearch( candidate_set, test_pt, radius );

This returns a cell array (one element for each test point). In your case, you only have a single test point, so we're only interested in idx{1}:

neighborhood = candidate_set(idx{1}, :);

One more note: we could be a bit more clever about generating the candidate set. We know that the neighborhood will be bounded by a hypercube centered around the test point, and so we could start by using the points in the hypercube as the candidate set:

range_min = test_pt - radius;
range_max = test_pt + radius;

And then we can construct a candidate set from this range:

xrange = ceil(range_min(1)):floor(range_max(1));
yrange = ceil(range_min(2)):floor(range_max(2));
[X, Y] = ndgrid(xrange, yrange);
candidate_set = [X(:), Y(:)];

In an arbitrary number of dimensions:

nDims = length(test_pt);
grid_vecs = cell(nDims, 1);
grid_mats = cell(nDims, 1);
for ii = 1:nDims
    grid_vecs{ii} = ceil(range_min(ii)):floor(range_max(ii));
end
[grid_mats{:}] = ndgrid(grid_vecs{:});
for ii = 1:nDims
    grid_mats{ii} = grid_mats{ii}(:);
end
candidate_set = horzcat( grid_mats{:} );