= Chaikin basis function
{c}
{title2=$\beta(t)=\begin{cases}3/4-t^2,&|t|\leq1/2,\\(3/2-|t|)^2/2,&1/2<|t|\leq3/2,\\0,&|t|>3/2.\end{cases}$}
This centered <quadratic cardinal B-spline> weights each original control ordinate at its uniformly spaced abscissa. Its translates sum to one. It and its first <derivative> match at half-integer knots, while the second <derivative> can jump. The limit graph is $\sum_i y_i\beta((x-x_i)/h)$; one ordinate influences exactly three original intervals. Refinement of a quadratic adds $ah^2/4$ in the limit, yielding this basis by extending each three-point neighborhood quadratically.
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