Abstract
We report results from an experiment showing that a tall pillar with a triangular base evokes radically different three-dimensional (3D) percepts depending on the vantage point from which it is observed. The base of the pillar is an isosceles right triangle, but the pillar is perceived as just a thin plane when viewed from some vantage points. Viewed from other vantage points, the perceived 3D shape of the pillar corresponds to a square or rectangular base. In general, our results suggest that the visual system uses a preference for rectangularity (or symmetry) to determine the 3D shape of objects. The amodal impressions of the invisible backside of the pillar are often quite compelling, and the corresponding illusions persist even when the observers know the true shape of the pillar. Interestingly, though, the compellingness and definiteness of the amodal impression of the pillar's backside depends on the vantage point. This is reflected in corresponding differences in the interobserver variability of the 3D shape judgments. We also discuss how variants of this illusion are used as a powerful tool in the art of magic.