18 March 2005 A horopter for two-point perspective
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Abstract
Linear perspective is constructed for a particular viewing location with respect to the scene being viewed and, importantly, the location of the canvas between the viewer and the scene. Conversely, both the scene and the center of projection may be reconstructed with some knowledge of the structure of the scene. For example, if it is known that the objects depicted have symmetrical features, such as equiangular corners, the center of projection is constrained to a single line (or point) in space. For one-point perspective (with a single vanishing point for all lines that are not parallel to the canvas plane), the constraint line runs from the vanishing point perpendicular to the canvas. For two-point perspective, in which the objects depicted are oblique to the canvas, the constraint line is a semicircle joining the two vanishing points. A viewer located at any point on the circle will see the depicted objects as rectangular and symmetric, and will have no grounds for knowing that the perspective was not constructed for this viewing location (unless there are objects that are known to be square, i.e., a further symmetry constraint on the object structures). This semi-circular line of rectangular validity forms a kind of horopter for two-point perspective. Moving around this semi-circular line for an architectural scene gives the viewer the odd impression of the architecture reforming itself in credible fashion to form an array of equally plausible structures.
© (2005) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Christopher W. Tyler, "A horopter for two-point perspective", Proc. SPIE 5666, Human Vision and Electronic Imaging X, (18 March 2005); doi: 10.1117/12.602237; https://doi.org/10.1117/12.602237
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