Proble 6. 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 surfac); (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. Top Circular plane surface Edge Curved surface Circular plane surface Edge Bottom (base) Cylinder Proble 6. 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 surfac); (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. Top Circular plane surface Edge Curved surface Circular plane surface Edge Bottom (base) Cylinder