calculate distance matrix for 3D points

I have the lists xA, yA, zA and the lists xB, yB, zB. The contain the the x,y and z coordinates of points of type A and type B. There may be different numbers of type A and type B points.

I would like to calculate a matrix containing the Euclidean distances between points of type A and type B. Of course, I only need to calculate one half of the matrix, since the other half contains duplicate data.

What is the most efficient way to do that?

When I'm done with that, I want to find the points of type B that are closest to one point of type A. How do I then find the coordinates the closest, second closes, third closest and so on points of type B?

Answer 1

[Prahlad Gowtham Katte]

Hello

As per my understanding, you want to create a distance matrix between points of type A and type B. You can do that by creating a matrix and initializing all entries to 0 and using a for loop you can find the distances and update the matrix accordingly. After generating the matrix, you can select a row where all distances would be there from a point in type A and sorting it can give the points with least distance, etc. The following code is just a small illustration for the same.

%Taking values for xA,yA,zA and xB,yB,zB
xA=[1 2 3 4 5];
yA=[1 2 3 4 5];
zA=[1 2 3 4 5];
xB=[5 4 3 2 1];
yB=[5 4 3 2 1];
zB=[5 4 3 2 1];
%Rows and columns of the matrix
M=length(xA);
N=length(xB);
distance_matrix=zeros(M,N);%Initializing the matrix
for i=1:M
    for j=1:N
        d=sqrt((xA(i)-xB(j)).^2+(yA(i)-yB(j)).^2+(zA(i)-zB(j)).^2);
        distance_matrix(i,j)=d;%Updating the distances
    end
end

For more information on how to use sortrows please refer to the following link

Sort rows of matrix or table - MATLAB sortrows (mathworks.com)

Hope it helps.

Answer 2

[Matt J]

Assuming xA, yA, zA, xB, yB, zB are column vectors,

D=pdist2([ xA, yA, zA],[xB, yB, zB])