fit a sphere in matlab

To fit a sphere in MATLAB, we can use the least squares optimization technique. The idea is to minimize the sum of squared distances between the sphere's surface and a set of points.

Here's an example code that generates random points and fits a sphere to them:

main.m
% Generate some random points in 3D space
numPoints = 100;
points = randn(numPoints, 3);

% Define the optimization function to minimize
fun = @(x) sum((sqrt(sum((points - x(1:3)).^2, 2))-x(4)).^2);

% Set some initial guess values for the sphere's center and radius
x0 = [0, 0, 0, 1];

% Perform the optimization
x = fminsearch(fun, x0);

% Extract the center and radius of the fitted sphere
center = x(1:3);
radius = x(4);

% Plot the points and the fitted sphere
[xs, ys, zs] = sphere;
xs = radius*xs + center(1);
ys = radius*ys + center(2);
zs = radius*zs + center(3);
figure;
plot3(points(:,1), points(:,2), points(:,3), 'b.');
hold on;
surf(xs, ys, zs, 'FaceAlpha', 0.2, 'EdgeColor', 'none', 'FaceColor', 'r');
axis equal;
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This code first generates some random points in 3D space using the randn function. Then, it defines the optimization function fun that takes as input a vector x representing the center and radius of the sphere and returns the sum of squared distances between the sphere's surface and the input points.

The optimization is performed using the fminsearch function, which finds the argument x that minimizes fun(x). The initial guess values for x are set to [0, 0, 0, 1].

Finally, the center and radius of the fitted sphere are extracted from the optimal argument x, and the points and fitted sphere are plotted using plot3 and surf functions, respectively.