Find the centre position and the radius of the sphere

Assignment Help MATLAB Programming

Reference no: EM133236676

MATLAB Programming Assignment -

Task & Requirements -

(1) Understand the optimisation problem;

(2) Develop the mathematical model;

(3) Applying the required optimisation techniques to solve the problem (if the optimisation techniques are not specified in the problem, then any optimisation software, program or toolbox can be used);

(4) Perform other tasks as required.

(5) Write a project report.

Problem - Sphere surface model fitting

Suppose there are N points given in the format of (x,y,z) positions. Knowing the points are from a sphere surface, find the centre position and the radius of the sphere such that the N three dimensional (3D) points best fit the sphere surface.

(1) Generate the 3D points using a given sphere: you can choose any N, centre position and radius of the sphere, the number N should be more than 50;

(2) Assuming you only know the 3D points, formulating the optimisation problem to minimise the fitting error (using the centre position and the radius as design variables);

(3) Solve the problem wing at least two methods;

(4) Add some small noises on the 3D points, solve the problem again.

(5) Use different sphere parameters to royal the data generation, problem formulation and problem solving process.

(6) Discuss the maths, such as when the optimisation method works well, when the method does not work well etc.

Note - Need 400 words report (calculation) + MATLAB code + result.

Reference no: EM133236676

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