Numerische Mathematik

, Volume 63, Issue 1, pp 165–171

A convexity-preservingC2 parametric rational cubic interpolation

  • John C. Clements

DOI: 10.1007/BF01385853

Cite this article as:
Clements, J.C. Numer. Math. (1992) 63: 165. doi:10.1007/BF01385853


AC2 parametric rational cubic interpolantr(t)=x(t)i+y(t)j,t∈[t1,tn] to data S={(xj, yj)|j=1,...,n} is defined in terms of non-negative tension parametersτj,j=1,...,n−1. LetP be the polygonal line defined by the directed line segments joining the points (xj,yj),t=1,...,n. Sufficient conditions are derived which ensure thatr(t) is a strictly convex function on strictly left/right winding polygonal line segmentsP. It is then proved that there always existτj,j=1,...,n−1 for whichr(t) preserves the local left/righ winding properties of any polygonal lineP. An example application is discussed.

Mathematics Subject Classification (1991)


Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • John C. Clements
    • 1
  1. 1.Department of Mathematics, Statistics and Computing ScienceDalhousie UniversityHalifaxCanada