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We consider some methods to extract information about the rotator cuff based on magnetic resonance images; the study aims to define an alternative method of display that might facilitate the detection of partial tears in the supraspinatus tendon. Specifically, we are going to use families of ellipsoidal triangular patches to cover the humerus head near the affected area. These patches are going to be textured and displayed with the information of the magnetic resonance images using the trilinear interpolation technique. For the generation of points to texture each patch, we propose a new method that guarantees the uniform distribution of its points using a random statistical method. Its computational cost, defined as the average computing time to generate a fixed number of points, is significantly lower as compared with deterministic and other standard statistical techniques.