Cone Visibility Decomposition Cone Visibility Decomposition Cone Visibility Decomposition Cone Visibility Decomposition Cone Visibility Decomposition Cone Visibility Decomposition

(a) (b) Figure 8: The nal set of directions from that covers G S in thick gray lines. Two views are provided with (a) presents the regular view of Figures 5 to 7 and (b) shows the entire Gauss map. See also Figure 1. (a) (b) Figure 6: The boundary and central silhouettes of G S in thick dark gray lines is projected onto the plane z = 1 in thick light gray lines, in (a). In (b), The convex hull in thick dark gray lines is shown for the projected G S in light gray, again computed in the plane z = 1. (a) (b) Figure 5: The unnormalized normal eld of the propeller section from Figure 4, along with its boundary and central silhouette in thick light gray lines are presented in (a). In (b), the projection onto S 2 of the boundary and central silhouette of the unnormalized normal eld is shown in thick dark gray. Figure 4: This freeform surface which is a portion of a propeller is used as a test case in this work. Two diierent views are provided. Finally, 8 shows two views of the axes in the coverage that are also found to be in the ooset of the convex hull of boundaries and central silhouettes of the normal eld of S. The exploitation of the convex hull of G S instead of G S signiicantly simpliied the computation, because the exact boundaries of G S were never computed. Nevertheless, the last stage of the algorithm , when one gures out the regions of S that are-sensible from a given direction ~ A i (Section 4), can be used to eliminate the directions that yields empty such regions. Every direction, ~ A i , such that F(u;v) = 0 in Equation (7) yields the empty set can be purged away. The resulting set of directions, while still not optimal, will typically be signiicantly smaller. 6 Conclusion We have presented a method to decompose a freeform surface into regions, so that each region is-sensible from a selected direction. The selection of the directions is made out of an almost optimal relaxed distribution of points on S 2 and guarantee a complete coverage of the surface. In this work, we did not address the question of the scanner's position, only its orientation. Once a region R i of surface S is known to be-sensible …