MATLAB: Count number of points around points in a list

Question

Dear;

I have two list of points defined by to array vectors xyz1 and xyz2, both of them are Nx3, where N is the number of points (different in xyz1 and xyz2) and 3 are the cartesian coordinates.

I would like to count the number of xyz2 particles in a neighborhood of each xyz1 particles, where the neighborhood is defined as a sphere of radio "h" around each element in xyz1.

I code the following:

Countxyz=zeros(size(xyz1,1),1);
h2=h*h;
for i=1:size(xyz1,1)
    Dstxyz=sum((xyz2-repnat(xyz1(i,:),1)).^2,2);
    Countxyz(i)=sum(Dstxyz<=h2);
end

As the number of elements in both xyz1 and xyz2 are large (more tham 10000 or 1000000) the code takes time to calculate the counts.

Is there any way to vectorize the main for loop and speed up the code?

Thanks in advance,

Answer 1

I feel the following functions will be help ful for you. Read about knnsearch, rangesearch.