In a line generator and a method for determining the individual pixels to be plotted for a line to be drawn in a display system, coded representations of a plurality of lines are stored in a line definition table. The coded representation of each individual line is a string of data items representing the transitions between adjacent pixels to be plotted for drawing the individual line. Preferably, only coded representations of lines up to a predetermined size (i.e. the length of the line in the case of a straight line) are stored in the line definition table. Strings of data items for representing the pixels to be plotted for longer lines to be drawn are still calculated as in the prior art. In this case, control logic determines whether there are coded representations of a line to be drawn in the line definition table, or not, and passes control to appropriate processing logic for determining the pixels to be plotted. In a preferred embodiment, the string of data items forming the coded representation of a line to be drawn is a string of binary digits and the value of each bit in the string represents a transition in one of two directions. This provides a very compact representation of the line.