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 three dimensional (3D) points best fit the cylinder surface. (1) Generate the 3D points using a given cylinder; you can choose any centre position and radius/height as the cylinder parameters, the number of points N should be more than 60 (at least 20 per surface); (2) Formulate the optimisation problem to minimise the fitting error (with the centre position, radius and height as design variables); you can assume that it is know that which point is on which of the three surfaces; (3) Solve the problem using any method; (4) Add some small noises on the 3D points, solve the problem again. (5) Use different cylinder parameters to repeat the data generation, problem formulation and problem solving process. (6) Discuss the results, such as when the optimisation method works well, when the method does not work well, etc.

Problem 6. Cylindrical surface model fitting (Difficulty level: 2) 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 three dimensional (3D) points best fit the cylinder surface. (1) Generate the 3D points using a given cylinder, you can choose any centre position and radius/height as the cylinder parameters, the number of points N should be more than 60 (at least 20 per surface); (2) Formulate the optimisation problem to minimise the fitting error (with the centre position, radius and height as design variables); you can assume that it is know that which point is on which of the three surfaces; (3) Solve the problem using any method; (4) Add some small noises on the 3D points, solve the problem again. (5) Use different cylinder parameters to repeat the data generation, problem formulation and problem solving process. (6) Discuss the results, such as when the optimisation method works well, when the method does not work well, etc. Top Circular plane surface Edge Curved surface Circular plane surface Edge Bottom (base) Cylinder Problem 6. Cylindrical surface model fitting (Difficulty level: 2) 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 three dimensional (3D) points best fit the cylinder surface. (1) Generate the 3D points using a given cylinder, you can choose any centre position and radius/height as the cylinder parameters, the number of points N should be more than 60 (at least 20 per surface); (2) Formulate the optimisation problem to minimise the fitting error (with the centre position, radius and height as design variables); you can assume that it is know that which point is on which of the three surfaces; (3) Solve the problem using any method; (4) Add some small noises on the 3D points, solve the problem again. (5) Use different cylinder parameters to repeat the data generation, problem formulation and problem solving process. (6) Discuss the results, such as when the optimisation method works well, when the method does not work well, etc. Top Circular plane surface Edge Curved surface Circular plane surface Edge Bottom (base) Cylinder