write code to fit a sphere in matlab

To fit a sphere in MATLAB, we can use optimization techniques. First, we need to define the function that evaluates the quality of the proposed sphere's fit to our data points. We will use the sum of square distances between the points and the sphere as our cost function.

Assuming we have N data points stored in a 3 x N matrix data, the function can be defined like this:

main.m
function cost = sphereCost(x, data)
% x is a vector of sphere parameters: the center coordinates (x,y,z) and the radius r
% data is a 3 x N matrix of data points

% Compute the distance of each point to the sphere
d = sqrt(sum((data - x(1:3)').^2, 2)) - x(4);

% Compute the sum of squared distances
cost = sum(d.^2);
end
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Next, we can use an optimization algorithm to find the best sphere parameters that minimize the cost function. Here we will use the fminsearch function:

main.m
% Define initial guess for sphere parameters
x0 = [0, 0, 0, 1];

% Find the best-fit sphere parameters
x = fminsearch(@(x) sphereCost(x, data), x0);

% Extract the sphere center and radius
center = x(1:3);
radius = x(4);
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The resulting center and radius variables will give us the best-fit sphere for our data points.