Finding a centre and plotting a sphere

Hi, I'm new to matlab and completely lost on this one. I have to make a function which evaluates Euclidean distances between two sets of points, finds a sphere with centre at the middle-point between two most distant points and calculate its radius.

Basically I have 2 sets of points, from which I form the distance matrix D by using

D = sqrt( bsxfun(@plus,sum(P.^2,2),sum(R.^2,2)') - 2*(P*R') )

centre of the sphere should be between the 2 points with the largest distance between them. How to find that point?

Answer 1

[David Hill]

M=0;%point sets p and q assumed to be in matrix form, for example [1 2 3;4 5 6]
for k=1:size(q,1)
    [m,idx]=max(sqrt(sum((p-q(k,:)).^2,2)));
    if m>M
        M=m;
        points=[p(idx,:);q(k,:)];
    end
end
radius=M/2;
center=sum(points)/2;

[Adin Adac]

This works perfectly, thank you!

Answer 2

[Matt J]

Maybe you can use minboundsphere, distributed at,

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects