2 00 5 Vertices and inflexions of plane sections of surfaces in R 3
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چکیده
We discuss the behaviour of vertices and inflexions of one-parameter families of plane curves which include a singular member. These arise a 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 (A1), umbilic (A1), hyperbolic (A1), parabolic (A2) and cusp of Gauss (A3) points. This work is preliminary to an investigation of symmetry sets and medial axes for these families of curves, reported elsewhere.
منابع مشابه
2 5 Fe b 20 05 Vertices and inflexions of plane sections of smooth surfaces in R 3 André
We discuss the behaviour of vertices and inflexions on one-parameter families of plane curves, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a smooth surface by parallel planes. This work is preliminary to an investigation of symmetry sets and medial axes for these families of curves, reported elsewhere.
متن کاملVertices and inflexions of plane sections of surfaces in R
We discuss the behaviour of vertices and inflexions of one-parameter families of plane curves which include a singular member. These arise a sectons 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 symme...
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تاریخ انتشار 2005