A digital orthodontic treatment planning system provides a practitioner with a digital representation of at least a part of a tooth of a patient within a three-dimensional environment. The practitioner may provide input indicative of a desired movement for a tooth of a patient via a user interface. Based on the desired movement for the tooth, a position of a virtual orthodontic appliance is calculated. The digital representation of the tooth may be moved in accordance with the adjusted position of the virtual orthodontic appliance. In this way, the system provides the practitioner with the perception that the input is being directly applied to the tooth, whereas the input is being indirectly applied to the tooth.