Phase 1: Surface Definition and Import
This is the initial stage of the process and it allows the user to communicate the surface data to the software, as shown in Fig. 6.9.
In order to obtain a flexible and customizable process, the software is able to receive these data in two different ways: symbolic expressions or data files. By means of symbolic formulation, the user can provide the software with the mathematical function of the surface, such as implicit equation or parametric equation. On the other hand, by exporting the designed surface from a 3D CAD software or Surface Modeller, by means of a format supported by Matlab, it is possible to choose the data file import option. Thanks to this feature, the user is able to import in Matlab the file that contains the surface information. These data are used by Matlab to analyse and store in the memory the surface. The analysis could be performed in a symbolic way or in a discrete way. Although the first one requires more memory resources rather, it allows us to perform an analysis on a continuous surface formulation, which is very accurate. On the other hand, the discrete definition simplifies the surface in a mash of points that reduces the stored data, thus allowing fast analysis. The drawback is that it introduces an approximation on the surface data. The user can define the mash coarseness in order to set the resolution of the surface definition to his/her needs. The definition of the surface by mathematical function allows us to perform the analysis by means of the symbolic procedure or the discrete approach. Figure 6.10 shows the same surface generated by discrete approach with low accuracy mesh (a), with high accuracy mesh (b) and with the symbolic approach (c). As regards the surfaces imported by data file, these can be defined in Matlab only by means of the discrete approach.
When the data of the surface are stored in Matlab, it is possible to choose a cutting plane, which allow us to obtain the trajectory that the strip has to represent, with the approximation illustrated in Fig. 4.1, as shown in Fig. 6.11. If the user has selected the symbolic approach, the trajectory obtained is expressed by means of a mathematical equation, that means with a continued formulation. On the contrary, by choosing the discrete approach, also the obtained trajectory is represented by means of a discrete set of points. The information obtained from Phase 1 are used as input for Phase 2.
Fig. 6.9 Phase 1 - Surface definition/import
Fig. 6.10 Surface definition
Fig. 6.11 Cutting plane and resulting trajectory