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Zbl 0675.65002
Lee, E.T.Y.
Choosing nodes in parametric curve interpolation. (English)
[J] Comput.-Aided Des. 21, No.6, 363-370 (1989). ISSN 0010-4485

Let be given a set of points $P\sb k=(x\sb k,y\sb k)$ $(k=1,...,n)$ in the plane and let $x\sb 1<...<x\sb n$ not necessarily be valid. Parametric curve interpolation means to choose parameters $0=t\sb 1<t\sb 2<...<t\sb n$ and functions $x=x(t)$ and $y=y(t)$ such that $P(t)=(x(t),y(t))$ passes through the given points. The problem is considered how to choose the $t\sb k$. Postponing a normalization $t\sb 1+t\sb 2+...+t\sb n=1$ the usual choice is $t\sb k=t\sb{k-1}+d\sb k$ where $d\sb k=((x\sb k-x\sb{k-1})\sp 2+(y\sb k-y\sb{k-1})\sp 2)\sp{1/2}$ $(k=2,...,n)$. Using a centripedal model the author motivates the choice $t\sb k=t\sb{k-1}+d\sp p\sb k$ with $p=1/2$ and shows (also varying p between 0 and 1) for a number of examples that he gets visually more pleasant curves than for $p=1$.
[H.Späth]

MSC 2000:: *65D05 Interpolation (numerical methods)

Keywords: choosing nodes; Parametric curve interpolation

Cited in: Zbl 1162.41001 Zbl 0836.65014 Zbl 0743.65010

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