Visually recognizing objects at different orientations and distances has been assumed to depend either on extracting from the retinal image a viewpoint–invariant, typically three–dimensional (3D) structure, such as object parts, or on mentally transforming two–dimensional (2D) views. To test how these processes might interact with each other, an experiment was performed in which observers discriminated images of novel, computer–generated, 3D objects, differing by rotations in 3D space and in the number of parts (in principle, a viewpoint–invariant, ‘non–accidental’ property) or in the curvature, length or angle of join of their parts (in principle, each a viewpoint–dependent, metric property), such that the discriminatory cue varied along a common physical scale. Although differences in the number of parts were more readily discriminated than differences in metric properties, they showed almost exactly the same orientation dependence. Overall, visual performance proved remarkably lawful: for both long (2 s) and short (100 ms) display durations, it could be summarized by a simple, compact equation with one term representing generalized viewpoint–invariant parts–based processing of 3D object structure, including metric structure, and another term representing structure–invariant processing of 2D views. Object discriminability was determined by summing signals from these two independent processes.