MATLAB: Deleting X-Y points that are not near other points on a field of data points

for loop

I have a set of data. This data is around 900 rows of two columns. Each row has an X and a Y value which specifies a point on the X-Y plane. The X-Y plane is from 0 to 100 and 0 to 100 respectively. All of these points are randomly scattered throughout the X-Y plane. My problem is there are too many X-Y points cluttering up the scatter plot. So what I want to do is have Matlab look at each point and say: Is this point a distance of 10 or less to another point. If it is then keep it. If it isn’t then delete the row containing that X, Y value. A shortened example of my data:
X=[1 2 3 4 20];
Y=[1 3 4 3 59];
Since (20,59) is more than a distance of 10 away from the other points, delete it and return the following:
X2=[1 2 3 4];
Y2=[1 3 4 3];
If anyone knows how I could do this, It would be a very great thing.

Best Answer

See Doug's video Advanced: making a 2d or 3d histogram to visualize data density and search the FEX for "hist2"
I failed to find a solution in the FEX. Here is a naive code with "10" hard-coded in the magic number "100".
    X=[1,2,3,4,20];
    Y=[1,3,4,3,59];
    to_be_removed = false(size(X));
    for ii = 1 : length(X)
        is = (X-X(ii)).^2+(Y-Y(ii)).^2 <= 100; 
        is(ii) = false;
        if not( any( is ) )
            to_be_removed(ii) = true;
        end
    end
    X(to_be_removed)=[];
    Y(to_be_removed)=[];
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