Recent research and modeling proposes that a closed shape is accurately described by both the curvature and angular location of its parts relative to the shape center, implying that the shape is coded along with its overall orientation. We tested this proposition. Radial frequency (RF) patterns were employed as stimuli as they can represent a range of familiar closed shapes and are processed globally. We measured a RF amplitude aftereffect (RFAAE) as a function of the shape orientation difference between adapt and test patterns of the same RF. For RF3 and RF4, RFAAEs were largest when adapt and test patterns were the same orientation, and then linearly decreased as the adaptor was rotated away from the test. RFAAEs did not, however, reach zero, instead plateauing significantly above zero. On the other hand, when adapt and test were of opposite luminance polarity, RFAAEs, although lower than same luminance-polarity RFAAEs, were invariant to differences between adapt and test orientations. Our findings provide evidence for two global shape mechanisms: one that is selective for shape orientation and luminance polarity, and one that is agnostic to these characteristics.