The PME approach to Ewald summation is based on local spline approximation of the complex exponentials appearing in the Ewald reciprocal sum. In this paper we show how the optimal influence function of Hockney and Eastwood can be easily derived using this approach. This result is used to explain why the force-interpolated PME method using least-squares spline approximation has the same accuracy as force-interpolated P3M. ©2000 American Institute of Physics.