Slant underestimation: a model based on the size of the viewing aperture

Abstract

By analyzing the projection plane in terms of the projected size of different elements on a surface, it is shown how the direction of the perpendicular, from the station point to the surface, is an important variable in the derivation of the slant angle. It is also shown that the test surfaces used in traditional slant-perception experiments contain no information about this direction. A model is proposed which is based on the idea that the direction of the line from the eye to one edge of the viewing aperture is mistaken for the perpendicular, and two options are derived to show how the information in the optical array could be interpreted on the basis of the perpendicular lying in this new direction. It is shown that both of these options are dependent upon the size of the field of view of the test surface and both are underestimations as long as half of the angle measuring the field of view is less than the actual slant of the surface. The model is tested against some data from previously reported experiments and is found to provide a close fit.