Piecewise polynomial spaces and geometric continuity of curves

Nira Dyn*, Charles A. Micchelli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

We say that a curve has geometric continuity if its curvatures and Frenet frame are continuous. In this paper we introduce spaces of piecewise polynomials which can be used to model space curves which have geometric continuity. We show that the basic theoretical properties of ordinary spline functions also hold for these spaces. These results extend and unify recent work on Beta-splines and Nu-splines which are used as a design tool in computer-aided geometric design of free form curves and surfaces.

Original languageEnglish
Pages (from-to)319-337
Number of pages19
JournalNumerische Mathematik
Volume54
Issue number3
DOIs
StatePublished - May 1989

Keywords

  • Subject Classifications: AMS(MOS): 65D07, CR: G 1.2

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