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A convexity-preserving $C\sp 2$ parametric rational cubic interpolation. (English) Zbl 0763.41001
A $C\sp 2$ parametric rational cubic interpolant $r(t)=x(t)i+y(t)j$, $t\in[t\sb 1,t\sb n]$ to data $S=\{(x\sb j,y\sb j)\mid$ $1,\dots,n\}$ is defined in terms of non-negative tension parameters $\tau\sb j$, $j=1,\dots,n-1$. Let $P$ be the polygonal line defined by the directed line segments joining the points $(x\sb j,y\sb j)$, $j=1,\dots,n$. Sufficient conditions are derived which ensure that $r(t)$ is a strictly convex function on strictly left/right winding polygonal line segments $P$. It is then proved that there always exist $\tau\sb j$, $j=1,\dots,n- 1$ for which $r(t)$ preserves the local left/right winding properties of any polygonal line $P$. An example application is discussed.
Reviewer: J.Clements (Halifax)

41A05Interpolation (approximations and expansions)
Full Text: DOI EuDML
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