# Modality with Central Point Definition and Variable Distance Between Control Points

In this modality, the user can choose the position of the central point, which is the fixed one of the device and the software manages the position of the other point. After the selection of the central point position, the Matlab calculates the intervals where it will be possible to place the other control points. The limits of the interval is defined in order to prevent the collision between two adjoined control sectors and Fig. 6.12 Conceptual example of the management of the control points for a generic trajectory in the modality with constant distance between control points Fig. 6.13 Phase 2 - Management of control points, modality with constant distance between control points Fig. 6.14 Conceptual example of the management of the control points for a generic trajectory in the modality with central point definition and variable distance between control points Fig. 6.15 Example of control point in a relative maximum point Fig. 6.16 Phase 2 - Management of control points in the modality with central point definition and variable distance between control points Fig. 6.17 Conceptual example of the management of the control points for a generic trajectory in the modality with interval definition and variable distance between control points

based on the length of the stip. Moreover, it is also possible to manually define the value of this intervals selecting a constant value. After that the software will verify if these ranges respect conditions of collision avoiding and strip length.

Now that the intervals, where to place the control points, are defined, it is possible to perform a function analysis that allows us to identify the presence of:

• • Inflection points;
• • Relative minimum point;
• • Relative maximum point;
• • High values of curvature variation.

These kinds of points are the best solution to place a control point in order to manage the rendered trajectory. Figure6.14 shows conceptual example of the management of the control points for a generic trajectory in the modality with central point definition and variable distance between control points. The picture shows how the control points are chosen, while respecting the constrains concerning the minimum distance needed between two adjoined control points. These constraints are necessary in order to avoid collisions.

If the portion of trajectory does not present inflection point, minimum point or maximum points, the control point will be placed where the value of curvature Fig. 6.18 Normal vector to the surface Fig. 6.19 Management of control points, Modality with interval definition and variable distance between control points

variation is higher. In this particular case, where it is not possible to identify any of these points, as for instance if we consider a flat surface, the system will place the control point using a nominal distance value selected by the user. Figure6.15 shows an example of the selection of a control point in a relative maximum point.

Once the positions of the points are defined, it is possible to calculate the normal vectors to the surface in the obtained points needed for the torsion and the tangency control. This modality is optimal when the user desires to render a portion of surface with a specific position of central point. As shown in Fig.6.16, the coordinates of the points and the values of the calculated angles are the output of Phase 2.