Reported is a formal study on the visual quality of rasterized lines and the optimality of Bresenham-type line generators. A straight line is rendered as a sequence of pixels on raster displays. Due to the finite resolution of raster devices quantization errors are inevitable in the rendering, often causing visually objectionable jagged digital lines. Different rasterization schemes will generate different digital lines. Thus a question of both theoretical and practical importance arises: is there an optimal line rasterization scheme different from the existing ones which can render visually most pleasing digital lines for the given device resolution? This paper will give an answer to this open question.