New computer display is being designed to project the large images to the walls of buildings. This works by reflecting a laser beam off a mirror mounted on the pair of loudspeaker coils. Two analogue signals control the horizontal and vertical deflection of the laser beam through driving the coils. The third digital signal turns the laser on and off. The deflection coils can be driven up to a frequency of 20 kHz and the laser can be turned on and off at a frequency of 10 MHz. Two approaches are being considered: Raster scan and calligraphic.

problem 1: Illustrate whether the resolution of two-level (on/off) raster display could support the hardware?

problem 2: How might grey levels be given? What resolution raster display could the hardware support if eight levels of grey were needed?

problem 3: The alternative approach would be a random scan calligraphic display that drew lines by deflecting the mirrors to the starting of a line, turning the laser on, deflecting the mirrors to the end of the line (making sure that the intermediate deflections lay all along a straight line), and turning the laser off again. How many lines could be drawn on this calligraphic display before the image flickered?

problem 4: The analogue signals controlling the horizontal and vertical deflection coils are generated by fast digital-to-analogue converters with 10-bit inputs. Present an algorithm for producing intermediate coordinates all along the line to make sure that lines drawn on the calligraphic display are straight and as well evenly illuminated.

problem 5: How could the algorithm be adapted to draw the arcs of circles?

problem 6: What additional hardware might be helpful to help with producing the intermediate coordinates from the end-points of lines?