Vertices and Inflexions of Plane Sections of Surfaces in ℝ3
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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.
KeywordsIsophote curve symmetry set medial axis skeleton vertex inflexion plane curve shape analysis
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