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Variational Interpolation of Subsets

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Constructive Approximation Aims and scope

Abstract

We consider the problem of the variational interpolation of subsets of Euclidean spaces by curves such that the L2 norm of the second derivative is minimized. It is well-known that the resulting curves are cubic spline curves. We study geometric boundary conditions arising for various types of subsets such as subspaces, polyhedra, and submanifolds, and we indicate how solutions can be computed in the case of convex polyhedra.

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Authors and Affiliations

  1. Institut für Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/113 A 1040 Wien, Austria

    Johannes Wallner & Helmut Pottmann

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  1. Johannes Wallner
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  2. Helmut Pottmann
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Correspondence to Johannes Wallner or Helmut Pottmann.

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Wallner, J., Pottmann, H. Variational Interpolation of Subsets. Constr Approx 20, 233–248 (2004). https://doi.org/10.1007/s00365-003-0554-1

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  • DOI: https://doi.org/10.1007/s00365-003-0554-1

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