Chaikin basis function ($\beta (t)=\{\begin{array}{ll}3/4-t^2,& |t|\le 1/2,\\ (3/2-|t|{)}^2/2,& 1/2<|t|\le 3/2,\\ 0,& |t|>3/2.\end{array}$)

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 $a{h}^2/4$ in the limit, yielding this basis by extending each three-point neighborhood quadratically.