It is just easy follow it as https://au.mathworks.com/help/matlab/ref/sphere.html fun.

You have two options, both use least squares approach:

(1) Using custom equations in curve fitting toolbox.

(2) Using MATLAB's GA. In this approach, you should define the error function manually.

Try ANN with set of evaluated data

Cheers

Try this code (Note that you get better results with more points in the cloud and you may need to adjust the tolerance limit).

function main

function f=Objfun(b)

f=0; re=b(1); xe=b(2); ye=b(3); ze=b(4);

for i=1:n

f=f+ 0.5*( (x(i)-xe)^2 + (y(i)-ye)^2 + (z(i)-ze)^2 - re^2)^2;

end;

end

r=1;

n=500; %number of data points

x=1:1:n; y=x; z=x; %reserve space for vectors x,y and z

%generate some cloud of points

x0=1; y0=0.5; z0=-0.5; %center point of the sphere

%deviation control on the cloud

d=0.1;

for i=1:n

% take a random theta and phi combination in spherical coordinates

theta=rand(1,1)*2*pi; phi=rand(1,1)*2*pi;

x(i)=x0+r*sin(theta)*cos(phi)+(rand(1,1)-0.5)*d*r;

y(i)=y0+r*sin(theta)*sin(phi)+(rand(1,1)-0.5)*d*r;

z(i)=z0+r*cos(theta)+(rand(1,1)-0.5)*d*r;

% Note (rand(1,1)-0.5) geenrates a random number between -0.5 to 0.5

% and the variation is kept between +/- 0.05 of r in x, y and z

%The total variation or disturbance is the resultant of x,y and z

%deviations which changes actual r, theta and phi variables

end

plot3(x,y,z,'o')

%least square fit to obtain unknowns x0,y0,z0 and r

%let the estimated variables be re,xe,ye and ze

b=[1,0,0,0]; %initial estimates

options=optimset('MaxIter',1000000,'MaxFunEvals',1000000,'TolFun',1e-6);

b=fminsearch(@Objfun,b,options);

%Display estimated values re, xe, ye and ze

b

end