This paper presents the scan-line algorithm which has been implemented on the Lisp Machine. The scan-line algorithm resides beneath a library of primitive software routines which draw more fundamental objects: lines, triangles and rectangles. This routine, implemented in microcode, applies the A(BC)*D approach to word boundary alignments in order to create an extremely fast, efficient, and general purpose drawing primitive. The scan-line algorithm improves on previous methodologies by limiting the number of CPU intensive instructions and by minimizing the number of words referenced. This paper will describe how to draw scan-lines and the constraints imposed upon the scan-line algorithm by the Lisp Machine's hardware and software.