IMAGINING PROJECTIVE TRANSFORMATIONS - ALIGNED ORIENTATIONS IN SPATIAL-ORGANIZATION

Four experiments were conducted to investigate whether variations in o rientation that profoundly affect the ability to imagine rotations als o affect the ability to imagine projective transformations. For a basi c rectilinear object and the three simpler Platonic Solids, imagining projective transformations (e.g., the casting of a shadow) was quite s uccessful when the objects were aligned with the direction of projecti on. For the solids, this alignment occurred when the objects were gene ralized cylinders about axes aligned with the projection. As the objec ts were made more oblique to the projection, performance deteriorated markedly. When the objects were moderately aligned with the projection , performance depended on the orientation of the object and the orient ation of the projection to the environment. We suggest that the imagin ation of projection and of rotation is a type of problem solving in wh ich spatial structures are organized in relation to initially given pr operties of the objects and transformations. When there is alignment a mong the various structural components, this process of imagination wo rks efficiently. Without such alignment, nonexperts often fail. We sug gest that aligned (i.e., parallel and perpendicular) orientations are effective in spatial imagination because they are categorically distin ct and singular, and they provide a critical form of redundancy. (C) 1 996 Academic Press, Inc.