How does null function works?

Hi guys,

I'm doing a project in which I have to find the circle that describes the intersection of 2 spheres. I found in the internet a cool matlab algorithm that works really well but I don't understand how it works.

Let C1 = [x1,y1,z1] and C2 = [x2,y2,z2] be two row vectors defining the spheres' centers and r1 and r2 their respective radii.

    C21 = C2-C1;

    d2 = dot(C21,C21);

    C0 = (C1+C2)/2+(r1^2-r2^2)/(2*d2)*C21;

    R = sqrt(((r1+r2)^2-d2)*(d2-(r2-r1)^2)/(4*d2));

    N = null(C21).';

    T = linspace(0,2*pi).';

    V = bsxfun(@plus,C0,R*[cos(T),sin(T)]*N);

In particular, I would like to understand how does the null function works.

I understand what is the result if I use the function as null(matrix,'r') but if I use null(matrix) I don't understand what it does.

I hope I have explained myself well. Thanks for your help ;)

Ana

Answer 1

[Matt J]

I understand what is the result if I use the function as null(matrix,'r') but if I use null(matrix) I don't understand what it does.

The difference between null(matrix,'r') and null(matrix) is that the latter produces an orthonormal basis for the null space, whereas you may not get orthonormality from null(matrix,'r').

[Ana]

Thanks for you answer, but do you know how exactly are the calculations done?

[Matt J]

There are some steps. You can view the contents of null.m by doing

>>type null