Variational Interpolation of Subsets

Johannes Wallner*, Helmut Pottmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)233-248
Number of pages16
JournalConstructive Approximation
Issue number2
StatePublished - 2004
Externally publishedYes


  • Cubic splines
  • Variational interpolation

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Computational Mathematics


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