Additive manufacturing, or 3D printing, is the process of building three-dimensional solid shapes by accumulating material laid out in sectional layers. Additive manufacturing has been recognized for enabling production of complex custom parts that are difficult to manufacture otherwise. However, the dependence on build orientation and physical limitations of printing processes invariably lead to geometric deviations between manufactured and designed shapes that are usually evaluated after manufacture. In this paper, we formalize the measurement of such deviations in terms of a printability map that simulates the printing process and partitions each printed layer into disjoint regions with distinct local measures of size. We show that manufacturing capabilities, such as printing resolution, and material specific design recommendations, such as minimal feature sizes, may be coupled in the printability map to evaluate expected deviations before manufacture. Furthermore, we demonstrate how partitions with size measures below required resolutions may be modified using properties of the medial axis transform and use the corrected printability map to construct a representation of the manufactured model. We conclude by discussing several applications of the printability map for additive manufacturing.