1. A method for determining a position-guided coarse trajectory for a machine drive or tool, comprising the steps of: defining an initial position-guided trajectory, said initial position-guided trajectory defined by an initial function having a scalar trajectory parameter defining a corresponding position on the initial trajectory, said scalar trajectory parameter representing a distance travelled along the initial trajectory, filtering the initial trajectory with a low-pass filter to determine a coarse function, said low-pass filter being a function of the scalar trajectory parameter, inserting the scalar trajectory parameter in the coarse function to determine a position on a coarse trajectory, and determining a distance between the coarse trajectory and the initial position-guided trajectory so that the distance is always smaller than a predetermined threshold value independent of a value of the scalar trajectory parameter.