## 2 Design Methods Based on TO and GD Tools  
According to a conventional engineering design approach, the process starts in the conceptual stage by developing the functional specifications, over the user needs, that are adopted in the subsequent modeling stage to be translated into geometric shapes by means of a CAD system. In particular, the CAD system is used to perform a detailed 3D representation of the final object and create accurate technical drawings. The three-dimensional models are then validated with simulation tools, i.e., CAE (Computer Aided Engineering) and CAM (Computer Aided Manufacturing) tools, by means of analysis and testing activities, before being transferred into manufacturing equipment, such as machining centers, lathes, or mill machines, to make the product. By using such an approach, if on the one hand, the CAx (Computer Aided Technologies) systems [10] support and simplify designers' jobs, on the other hand, they can influence the design process and limit their creativity [11]. This is mainly because the current CAD systems allow designers to create 3D models according to a feature-based parametric modeling approach that was introduced at the end of the 1980s. The main advantage introduced by this technique was its capability to produce very flexible designs defined by its design variables and parametric features. In the following years, the CAD systems were enriched with further modeling functions and specific features, and were integrated with CAE and CAM modules to allow engineers to operate within a single environment. In particular, CAE modules allow to perform finite element analysis (FEA) in which structural problems are solved by defining the geometry, boundary conditions, and initial conditions [12], while CAM are used to assess manufacturability of the geometry created in the CAD part. When tools and tool paths are found satisfactory CNC (computer numerical control)-code can be generated and used in a real machine to manufacture the geometry, if a CNC-coder for the machine has been implemented in the CAD/CAM software [13]. Nevertheless, the modeling approach has remained essentially unchanged and fails in supporting designers to build complex geometry and high functional performance models [1]. The advent of AM has broken down the technological constraints of subtractive manufacturing and therefore it has offered designers enormous potential for the realization of geometries that were impossible to achieve until a few years ago. Despite growing awareness of these potentials, as abovementioned, current CAD systems do not put engineers and designers in a position to fully exploit them. This is because designers and design engineers must adapt the functionalities conceived for conventional manufacturing methods to generate very complex geometries. In fact, CAD systems use the same terminology for these features as those used in manufacturing and design. These features refer then to specific conventional manufacturing processes developed to form them efficiently. It is therefore clear that the use of the actual CAD functionalities for a design oriented to AM is a tedious and labor-intensive activity, the result of which depends a lot on the individual skills and experience of the modelers [14]. In this context, it results evident that TO and GD tools could be an efficient and useful aid not only for the analysis and optimization of the geometry but especially to support engineers, in the conceptual and modeling stages, for defining the geometry of the 3D models. Unlike the traditional design approach, in which CAD systems are adopted to generate a detailed geometry that follows the designer's indications, the introduction of TO and GD tools allows designers to focus primarily on the function, instead of the form, delegating optimization tools to generate design alternatives. In fact, as depicted in Figure 1, the first stage, common to both approaches, provides the adoption of the CAD system but for the definition of the functional surfaces only.