Numerische Mathematik

, Volume 63, Issue 1, pp 165-171

First online:

A convexity-preservingC 2 parametric rational cubic interpolation

  • John C. ClementsAffiliated withDepartment of Mathematics, Statistics and Computing Science, Dalhousie University

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AC 2 parametric rational cubic interpolantr(t)=x(t) i+y(t) j,t∈[t 1,t n] to data S={(xj, yj)|j=1,...,n} is defined in terms of non-negative tension parametersτ j ,j=1,...,n−1. LetP be the polygonal line defined by the directed line segments joining the points (x j ,y j ),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 existτ j ,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)