A methods and processors for generating a 3D-representation of a tooth-specific dental appliance are disclosed. The appliance has a grooved body and a pair of holding arms. The method includes acquiring a 3D-platform representation, acquiring a 3D-grooved body representation, and positioning the 3D-grooved body representation relative to the 3D-platform representation. The method also includes acquiring a first and second 3D-arm representations, each having a respective pair of platform anchor points and a respective adjustment anchor point. The method also includes individually positioning the first and second 3D-arm representations relative to the 3D-platform representation using the respective pairs of platform anchor points, thereby defining preliminary positions of the first and second 3D-arm representations. The method includes individually adjusting the respective preliminary positions relative to the 3D-grooved body representation using the respective adjustment anchor points, thereby defining adjusted positions of the first and second 3D-arm representations.