Abstract
We discuss the behavior of vertices and inflexions of one-parameter families of plane curves which include a singular member. These arise as sections of smooth surfaces by families of planes parallel to the tangent plane at a given point. We cover all the generic cases, namely elliptic, umbilic, hyperbolic, parabolic and cusp of Gauss points. This work is preliminary to an investigation of symmetry sets and medial axes for these families of curves, reported elsewhere.
This work is a part of the DSSCV project supported by the IST Programme of the European Union (IST-2001-35443.) The first author was supported and the second author partially supported by this grant. We are also very grateful to Terry Wall, Bill Bruce and Vladimir Zakalyukin for helpful suggestions.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Diatta, A., Giblin, P. (2006). Vertices and Inflexions of Plane Sections of Surfaces in ℝ3 . In: Brasselet, JP., Ruas, M.A.S. (eds) Real and Complex Singularities. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7776-2_7
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DOI: https://doi.org/10.1007/978-3-7643-7776-2_7
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