Representation of the orientations of shapes

A geometrical model is put forward as underlying superficially quite different data from discrimination and mental transformation tasks and, also, as a possible framework for an eventual account of the perception of shape. The model was evaluated in an experiment in which participants indicated whether two picture-plane views of a polygon with an experimentally determined degree of symmetry under 180° rotation were the same or different in orientation. Multidimensional scaling based on the obtained discriminative reaction times yielded a four-dimensional solution that, in agreement with the proposed model, describes possible transformations of the planar polygons. We suggest that the constraints governing possible transformations of objects have become so internalized that we unconsciously represent these possible motions upon the visual presentation of any object.