Solving system of eqution using vectors

Hi,

I have a problem with solving of equation, where unknown are vectors (coordinates of set of points: seznamX, seznamY, seznamZ) and my part of the program for solving it is:

syms r x y z

[l, m, n, Q] = solve(2*sqrt((seznamX-x).^2+(seznamY-y).^2+(seznamZ-z).^2)==r*ones(1,e),[x,y,z,r]);

It means I want to interpolate these points [seznamX,seznamY,seznamZ] with sphere and find its centre.

After running the program, it stops after the line [l, m, n, Q] , where a work with l. It returns me "Error in sym/subsasgn".

Where is the problem and how could I solve it?

Thank you for reply.

Answer 1

[darova]

You should create a system of equations. You need 4 points and 4 equations

syms x0 y0 z0 r0
eq1 = (x0-x(1))^2 + (y0-y(1))^2 + (z0-z(1))^2 == r0^2;
% ...

[Anezka Koterova]

But the problem is which 4 points, when there is for example 27 points, which the spehre can be fitted.

[darova]

What about fit function? Maybe you should take half of data

[Anezka Koterova]

Yes I tried to do that, which leads to Least square method and this leads to minimizing the distance (of the points from centre) from the radius.

And I don´t know, what you mean "take half of data"?

[darova]

Something like that

ix = z < mean(z);            % take a half
x1 = x(ix);
y1 = y(ix);
z1 = z(ix);
F = @(a,b,c,r,x,y) sqrt( r.^2 - (x-a).^2 - (y-b).^2 ) + c;
f = fit([x1 y1],z1,F);

[Anezka Koterova]

I do not understand this script. what means the first, last and fifth line?