Foreshortening and the perception of parallel projections.

Does picture perception follow polar projective geometry? Parallel projection drawings, which are not produced by using rules of polar projection, are widely regarded as visually acceptable representations of three-dimensional (3-D) objects in free viewing. One explanation is that they are perceived by means of a system in which there is no foreshortening. If so, edges of a 3-D block in 1:1 proportions should be denoted 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 depicted three sides of the cube, drawn as a square with obliques--a frontal square with receding edges shown by parallel obliques of various lengths. The subjects preferred a drawing with a receding side length that was considerably foreshortened in relation to the front side. In Experiments 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 (1:1, 1:2, and 1:0.65). In Experiment 2, the subjects were shown square-with-obliques drawings of the three blocks with receding edges shown by parallel obliques of various lengths. Again, the subjects preferred drawings with a receding side that was foreshortened. In Experiment 3, the drawings showed two sides of a block. The receding dimension was drawn with parallel or converging lines. The preferred foreshortening 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 foreshortening. We suggest also that as the line showing the receding edge elongates, foreshortening becomes less of a factor.