A system automatically determines positions of orthodontic objects, such as teeth and/or orthodontic appliances, along an archwire within a three-dimensional (3D) environment based on a proposed orthodontic prescription. The resulting placement of the orthodontic objects in the dentition predicts a final occlusion that may result from the proposed orthodontic prescription. An orthodontic practitioner may interact with the system to enter a proposed orthodontic prescription, or the system may choose the proposed orthodontic prescription from a number of standardized prescriptions stored in a database. The system may also display a digital representation of the orthodontic objects at the determined positions. The practitioner may modify the proposed prescription and view the resulting placement of the orthodontic objects until a desired result is obtained.
