, Volume 63, Issue 1, pp 165-171

A convexity-preservingC 2 parametric rational cubic interpolation

Purchase on Springer.com

$39.95 / €34.95 / £29.95*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Summary

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.

This research was supported in part by the natural Sciences and Engineering Research Council of Canada.