Computing Geometric Transformations of Irregular Teeth Sets for Orthodontic Treatment

This research evaluates the feasibility of assisting orthodontists to treat irregularities in teeth by computing the geometric transformations to move each tooth to its ideal position. The intent is to help orthodontists craft a precise and specific treatment plan for each patient. The inputs for finding the transformations are the patient’s teeth mold and dental arch templates. A 3D laser scanner is used to generate a point cloud data representation of the patient’s teeth mold. A commercial solid modeler is used to construct a non-uniform rational B-spline surface from this point cloud. Transformations are then computed by establishing a multiple scan registration, matching the axis of the patient’s teeth model and dental arch templates, and computation of initial and final positions of the teeth. The steps in the process and the algorithms developed were implemented in the scripting language of the solid modeler. Details of the algorithms are provided, and a case study is presented to demonstrate the process.