Abstract: Surface mapping and/or generation device is provided, with a device for mapping 3D data of at least one denture base object such as a tooth stump or an implantation abutment, and an environment thereof, as well as with a device for the data-based generation and production of a denture part incorporating the 3D data of the denture base object. Additionally provided are a device for determining and/or defining a placement direction of the denture part that is to be slipped onto the denture base object, and a device for determining and producing a primary part that is to be slipped onto the denture base object before the denture part and that yields a desired placement direction for the denture part which is different from the placement direction that exists for slipping the primary part onto the denture base object. The device for data-based generation and production of a denture part is designed to generate and produce the latter by incorporating the 3D data of the primary part.