Approssimazione "Meshfree" per la modellazione di maschere per l'ossigeno

Given a set of points, sampled on a face surface and some oxygens masks of the same typology but with different shapes, which are used in the health sector in the equipment for sleep apnea, we need to suggest to the customer which of these is the most appropriate to his face shape. The best choice will ensure that there are no leaks between the mask and the face, and therefore its effect will be maximized. In the first two chapters the mathematical tools that will be used for solving our problem are presented and analyzed. In particolar, we will use the RBF-PUM Interpolation. The third chapter is dedicated to the mask modeling through the use of a 3D scanner. Finally, in the fourth chapter it is explained how to apply such methods to the detected data in order to find the most suitable mask. A practical example is also presented by implementing MATLAB codes for the different phases of the problem resolution.