number of nearest neighbous around each element of a matrix

I have a matrix that contain coordinates I=[x y z]. I need to find the number of nearest neighbors for each point in the matrix within a radius R. Thanks a lot!

Jack,

Answer 1

[Image Analyst]

How about just a brute force approach (though slightly vectorized):

% Set up / initialize.
numberOfCoordinates = 100;
m = rand(numberOfCoordinates, 3); % Don't us I because I is a bad name.
radius = 0.5;
% Check each point for others within radius.
for row = 1 : numberOfCoordinates
  % Get the distance of every point to this point.
  distances = sqrt((m(row,1) - m(:, 1)).^2 + ...
    (m(row, 2) - m(:, 2)).^2 + ...
    (m(row, 3) - m(:, 3)).^2);
  % Count the number of points that are
  % greater than 0 (to exclude this point itself)
  % but less than or equal to the radius.
  counts(row) = sum(distances > 0 & distances <= radius);
end
% Report to the command line the counts:
counts

[jack]

Thank you! This works great.

Answer 2

[Youssef Khmou]

This problem can be solved using the equation of radius in three dimensional space such as if x²+y²+z² < R² then the point is inside the sphere, let us elaborate an example :

M=randn(300,3);
R=0.5;
for n=1:300

   if sqrt((M(n,1)^2)+(M(n,2)^2)+(M(n,3)^2))<= R

           C(n,:)=M(n,:);
  end

 end

[jack]

Thanks!