Interactive, computer based orthodontist treatment planning, appliance design and appliance manufacturing is described. A scanner is described which acquires images of the dentition which are converted to three-dimensional frames of data. The data from the several frames are registered to each other to provide a complete three-dimensional virtual model of the dentition. Individual tooth objects are obtained from the virtual model. A computer-interactive software program provides for treatment planning, diagnosis and appliance from the virtual tooth models. A desired occlusion for the patient is obtained from the treatment planning software. The virtual model of the desired occlusion and the virtual model of the original dentition provide a base of information for custom manufacture of an orthodontic appliance. A variety of possible appliance and appliance manufacturing systems are contemplated, including customized archwires and customized devices for placement of off-the shelf brackets on the archwires, and removable orthodontic appliances.