This thesis presents a method for generating a parameter domain (more precisely the trimming curves defining it) for the construction of a trimmed surface, whose boundary curve interpolates a given closed space curve and that interpolates given tangent planes at the boundary. An appropriate domain is essential to constructs such trimmed surfaces. Our aim is to construct trimming curves that have a similar shape as the given loop. For that purpose we study the shape properties of the given closed space curve and establish an optimization problem in order to obtain a suitable domain. We conducted experiments and used the obtained trimming curves to fit trimmed surfaces.