A method for efficiently interpolating sub-span position commands for control of a machine member. The method includes storing a set of coefficients defined by a parametric function relating member position and time, calculating the distance between a target coordinate axis position command and a current coordinate axis position command, generating first and second command modifiers from the stored coefficients, the calculated distance, and a current coordinate axis position command, and summing the current coordinate axis position command and the first and second command modifiers to generate a subspan position command.