1. A method for manufacturing a physical dental model, comprising: (A) providing a trimmed first virtual model part and a trimmed second virtual model part corresponding to at least one dental site comprising: providing to a computer processor, data of a 3D virtual model of at least a portion of an intraoral cavity comprising a preparation having a finish line, wherein at least a portion of the finish line is obscured; and configuring said computer processor to: manipulate data of said obscured portion of said finish line of the 3D virtual model in a virtual manner to create an auxiliary 3D virtual model that is displayable on a computer screen and corresponds to said obscured portion of said finish line; provide topographical data of the finish line from the 3D virtual model and the auxiliary 3D virtual model; identify in said 3D virtual model a first virtual model part representing a dental site comprising said preparation and a second virtual model part representing at least soft tissues in abutting virtual contact with said first virtual model part; manipulate said 3D virtual model to separate said first virtual model part from said second virtual model part; manipulate said first virtual model part to create said auxiliary 3D virtual model; creating a trimmed first model part comprising said first virtual model part and said auxiliary 3D virtual model; manipulating said second model part to remove surface data thereof corresponding to said auxiliary 3D virtual model and creating a trimmed second model part; manipulating said trimmed first model part to include a virtual model base projecting therefrom, and manipulating said trimmed second model part to include a virtual model well substantially complementary to said virtual model base; (B) preparing computer instructions for controlling operation of a computer controlled manufacturing machine for creating physical models corresponding to said trimmed first and second virtual model parts respectively including said virtual model base and said virtual model well; and (C) executing said computer instructions on said computer controlled manufacturing machine and creating a set of physical models comprising a trimmed first physical model part and a trimmed second physical model part corresponding to said trimmed first and second virtual model parts respectively including said virtual model base and said virtual model well.