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The geometry of the Wigner caustic and affine equidistants of planar curves. (arXiv:1605.05361v2 [math.DG] UPDATED)

来源于:arXiv
In this paper we study global properties of the Wigner caustic and affine equidistants of parameterized closed planar curves. We find new results about their geometry and singular points. In particular, we consider these objects for regular closed parameterized curves with non-vanishing curvature. We present an algorithm to describe smooth branches of the Wigner caustic and affine equidistants of parameterized planar curves. By this algorithm we can find the number of smooth branches, the rotation number, the number of inflexion points and the parity of the number of cusp singularities of each branch. We also study the global properties of the Wigner caustic on shell (the branch of the Wigner caustic connecting two inflexion points of a curve). 查看全文>>