A method is given for representing 3-D shapes. It is based on a hierarchy of stick figures (called 3-D models), where each stick corresponds to an axis in the shape's generalized cone representation. Although the representation of a complete shape may contain many stick figures at different levels of detail, only one stick figure is examined at a time while the representation is being used ot interpret an image. By thus balancing scope of description against detail, the complexity of the computations needed to support the representation is minimized. The method requires (a) a database of stored stick figures; (b) a simple device called the image-space processor for moving between object-centered and viewer-centered coordinate frames; and (c) a process for "relaxing" a stored model onto the image during recognition. The relation of the theory to "mental rotation" phenomena is discussed, and some critical experimental predictions are made.