Abstract: In engineering, Archimedes and involute curves are widely used, but algorithms for generating this sort of curves by now were rarely studied, especially the pixel-level algorithms. New approaches for generating them are presented, and an efficient method to determine their step-lengths are formulated. In each iteration, no trigonometric function is used and only two multiplications are required By taking the advantage of symmetry, only the points in an octant need to be generated. Furthermore, the error is no more than \frac\overline22 pixel.