Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices

Phillip Barry, Ronald N. Goldman, Charles A. Micchelli

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

We show that many fundamental algorithms and techniques for B-spline curves extend to geometrically continuous splines. The algorithms, which are all related to knot insertion, include recursive evaluation, differentiation, and change of basis. While the algorithms for geometrically continuous splines are not as computationally simple as those for B-spline curves, they share the same general structure. The techniques we investigate include knot insertion, dual functionals, and polar forms; these prove to be useful theoretical tools for studying geometrically continuous splines.

Original languageEnglish (US)
Pages (from-to)139-171
Number of pages33
JournalAdvances in Computational Mathematics
Volume1
Issue number2
DOIs
StatePublished - Jun 1 1993

Keywords

  • B-spline
  • connection matrix
  • differentiation
  • dual functional
  • geometric continuity
  • knot insertion
  • polar form

Fingerprint Dive into the research topics of 'Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices'. Together they form a unique fingerprint.

  • Cite this