Smooth interpolating curves of prescribed length and minimumc urvature

Joseph W. Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

It is shown that, among all smooth curves of length not exceeding a prescribed upper bound which interpolate a finite set of planar points, there is at least one which minimizes the curvature in the L sense. Thus, we show to be sufficient for the solution of the problem of minimum curvature a condition, viz., prescribed length, which has been known to be necessary for at least a decade. The proof extends immediately to curves in R", n > 2.

Original languageEnglish (US)
Pages (from-to)62-66
Number of pages5
JournalProceedings of the American Mathematical Society
Volume51
Issue number1
DOIs
StatePublished - Aug 1975

Keywords

  • Interpolating
  • Mean square curvature
  • Minimum curvature
  • Nonlinear open spline curve
  • Prescribed length

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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