Abstract
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).
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Breiding, P., Kohn, K., Sturmfels, B. (2024). Reach and Offset. In: Metric Algebraic Geometry. Oberwolfach Seminars, vol 53. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-51462-3_7
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DOI: https://doi.org/10.1007/978-3-031-51462-3_7
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-51461-6
Online ISBN: 978-3-031-51462-3
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