Abstract: The investigated algorithm named Optimal Method can optimize the process of digital function generation: stepping errors due to the algorithm may be minimized to keep within 1/2 step (accuracy), the path of curve generation is independent of its starting point (uniqueness), the path of curve generation is just the same when its direction is reversed (reversibility), the algorithm suits both 2-dimensional and 3-dimensional curve generation (identity) and the algorithm is simple and practical in use (practicality). As a criterion, Optimal Method traces the given function by searching its minimal absolute value among adjacent candidate mesh points. According to its values of difference functions the X- and Y-axes are assigned to be so called first and second axes or vise versa in order to make mesh point choice quite simple and easy. A compact algorithm is given to determine the beginning direction of function generation and also to change the direction so as to get an accurate and correct bending in the process of curve generation.