Reach and Offset
摘要
In this chapter, we study the medial axis, bottlenecks, and offset hypersurfaces. These notions are intuitive and important for many applications. They will also lead to a better understanding of the geometry of the reach, which was introduced in Definition 6.19. The last section is devoted to the offset discriminant of a variety. This offers a direct link between the ED problem in Chapter 2 and differential geometric concepts we saw in the previous chapter, namely the second fundamental form (6.9) and the Weingarten map (6.10).