Problem - Cylindrical surface model fitting
Suppose there are N points given in the format of (x,y,z) positions. Knowing the points are from a cylindrical surface, find the centre position, the radius and the height of the cylinder such that the N 3D points best fit the cuboid surface.
(1) Generate the 3D points using a given cylinder; you can choose any N, centre position and radius/height of the cylinder, the number N should be more than 60 (at least 20 per surface);
(2) Formulate the optimisation problem to minimise the fitting error;
(3) Solve the problem using any method;
(4) Add some small noises on the 3D points, solve the problem again.
