FORESHORTENING AND THE PERCEPTION OF PARALLEL PROJECTIONS

Does picture perception follow polar projective geometry? Parallel pro jection drawings, which are not produced by using rules of polar proje ction, are widely regarded as visually acceptable representations of t hree-dimensional (3-D) objects in free viewing. One explanation is tha t they are perceived by means of a system in which there is no foresho rtening. If so, edges of a 3-D block in 1:1 proportions should be deno ted by lines in 1:1 proportions on the picture surface. However, three experiments suggest that the perception of parallel projections of a block involves foreshortening. In Experiment 1, 90 subjects were shown a set of parallel projections of a cube, in which each drawing depict ed three sides of the cube, drawn as a square with obliques-a frontal square with receding edges shown by parallel obliques of various lengt hs. The subjects preferred a drawing with a receding side length that was considerably foreshortened in relation to the front side. In Exper iments 2 and 3, subjects viewed drawings of three blocks that differed in the ratios of the lengths of their receding edges to their frontal edges (1:l, 1:2, and 1:0.65). In Experiment 2, the subjects were show n square-with-obliques drawings of the three blocks with receding edge s shown by parallel obliques of various lengths. Again, the subjects p referred drawings with a receding side that was foreshortened. In Expe riment 3, the drawings showed two sides of a block. The receding dimen sion was drawn with parallel or converging lines. The preferred foresh ortening was not a fixed ratio of the dimensions of the 3-D blocks. We suggest that square-with-obliques parallel projections showing cubes are taken by vision to be approximations to projections using foreshor tening. We suggest also that as the line showing the receding edge elo ngates, foreshortening becomes less of a factor.