Representing and comparing two-dimensional shapes is an important problem. Our hypothesis about human representations is that that people utilize two representations of shape: an abstract, qualitative representation of the spatial relations between the shape's parts, and a detailed, quantitative representation. The advantage of relational, qualitative representations is that they facilitate shape comparison: two shapes can be compared via structural alignment processes which have been used to model similarity and analogy more broadly. This comparison process plays an important role in determining when two objects share the same shape, or in identifying transformations (rotations and reflections) between two shapes. Based on our hypothesis, we have built a computational model which automatically constructs both qualitative and quantitative representations and uses them to compare two-dimensional shapes in visual scenes. We demonstrate the effectiveness of our model by summarizing a series of studies which have simulated human spatial reasoning.