Computer-implemented methods to plan, display and evaluate orthodontic treatment plans. A plurality of teeth in a representation on a computer display may be moved simultaneously in accordance with a mathematically defined pattern. Software tools available to generate the treatment path may include adjusting the smile teeth, moving teeth along a curve fit to points in the mandible, individually moving a tooth, cross sectioning to check for interference and simulations of occlusal points, highlighting teeth that have moved from their original position, making notations on the teeth, and generating and saving animation sequences of before and after treatment tooth positions.