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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

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