We review the work of Evans on graphical proportional analogies, identifying the object mappings that underlie many such comparisons. The limitations of Evans ANALOGY model are investigated. We then establish the role of attributes (colour, shape, pattern etc) in such analogies and identify two distinct mapping algorithms that are required by different classes of geometric analogy problems. We identify the conditions under which the alternate algorithms are required to produce a "best" answer. Finally, we describe a computational model (LUDI) that automatically generates the result for a large number of geometric analogies.