1. A computer-implemented method for prosthesis manipulation in dental prosthesis design, comprising: presenting, via a computer-implemented interface, a virtual multi-tooth prosthesis, said virtual multi-tooth prosthesis comprising two or more 3D models of individual teeth, said virtual multi-tooth prosthesis being presented relative to a 3D representation of a multi-tooth area of a patient's mouth that is to be reconstructed, said computer-implemented interface running on one or more computing devices; receiving a command to manipulate a subset of the teeth in the virtual multi-tooth prosthesis, from an operator, via the computer-implemented interface; modifying, using one or more computing devices, based on the manipulation command, one or more parameters for the shape of the virtual multi-tooth prosthesis, said one or more parameters being related to the subset of teeth; and generating production data related to the virtual multi-tooth prosthesis.