A convexity-preservingC
2 parametric rational cubic interpolation |
| |
Authors: | John C Clements |
| |
Institution: | (1) Department of Mathematics, Statistics and Computing Science, Dalhousie University, B3H3J5 Halifax, Nova Scotia, Canada |
| |
Abstract: | Summary AC
2 parametric rational cubic interpolantr(t)=x(t)
i+y(t)
j,tt
1,t
n] to data S={(xj, yj)|j=1,...,n} is defined in terms of non-negative tension parameters
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 exist
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. |
| |
Keywords: | 65D10 |
本文献已被 SpringerLink 等数据库收录! |
|