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Unrolling and rolling of curves in non-convex surfaces.

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Muñoz Masqué, Jaime and Pozo Coronado, Luis Miguel (1999) Unrolling and rolling of curves in non-convex surfaces. Inverse Problems, 15 (4). pp. 869-880. ISSN 0266-5611

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Official URL: http://iopscience.iop.org/0266-5611/15/4/303/pdf/0266-5611_15_4_303.pdf


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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.


Item Type:Article
Uncontrolled Keywords:Rolling; unrolling; Levi-Civita connection; Spline interpolation
Subjects:Sciences > Mathematics > Geometry
ID Code:17493
Deposited On:20 Dec 2012 10:55
Last Modified:12 Dec 2018 15:13

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