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A method for generating optimal arch forms for a patient's dental arch is presented. The method comprises: receiving first positional digital data for one or more teeth from a reconstructed 3D digital volume of the patient dental arch;(b) generating second positional digital data for the one or more teeth according to a desired dental arch form for the patient;(c) calculating a first displacement data for one or more teeth according to the first positional and second positional digital data;(d) detecting teeth collision values based on the first displacement data;(e) calculating a second displacement data for one or more teeth based on the detected teeth collision values; and (f) reporting a combination of the first displacement data and second displacement data for repositioning one tooth or more teeth of the dental arch.