Publication: Unrolling and rolling of curves in non-convex surfaces.
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Publication Date
1999
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Iop science
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Abstract
The notion of unrolling of a spherical curve is proved to coincide with its development into the tangent plane. The development of a curve in an arbitrary surface in the Euclidean 3-space is then studied from the point of view of unrolling. The inverse operation, called the rolling of a curve onto a surface, is also analysed and the relationship of such notions with the functional defined by the square of curvature is stated. An application to the construction of nonlinear splines on Riemannian surfaces is suggested.
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Bryant R and Griffiths P 1986 Reduction for constrained variational problems and the integral of the squared curvature Am. J. Math. 108 525–70
Courant R and Hilbert D 1970 Methods of Mathematical Physics vol I (New York: Interscience)
Jupp P E and Kent J T 1987 Fitting smooth paths to spherical data Appl. Stat. 36 34–46
Kobayashi S and Nomizu K 1963 Foundations of Differential Geometry vol I (New York: Interscience)
Langer J and Singer D A 1984 The total squared curvature of closed curves J. Diff. Geom. 20 1–22
Malcolm M A 1977 On the computation of nonlinear spline functions SIAM J. Num. Anal. 14 254–82
O’Neill B 1983 Semi-Riemannian geometry with applications to relativity (New York: Academic)
Smale S 1958 Regular curves on Riemannian manifolds Trans. Am. Math. Soc. 87 492–512