Abstract
Many authors contend that the perception of 2-D drawings of a 3-D object is governed by polar projective geometry. A problem for this position is that observers accept parallel projections, which are not produced with polar projective geometry, as accurate representations of 3-D objects. In Experiments 1 and 2, we used two different standards of comparison to study the perceptions of three line drawings of cubes—correct polar projections of cubes with subtenses of 15° and 35°, and a parallel projection—at five different angular subtenses. In Experiment 1, 14 observers judged each drawing when it subtended about 35°, 15°, 5°, 4°, and 2° in width. Subjects used an 8-point rating scale to compare each drawing with a correct polar projection of a cube subtending 35°, viewed with the drawing subtending 15°. As predicted, both polar projections had their highest ratings at their correct vantage points. Ratings for the parallel projection were highest at small angular subtenses and decreased when it subtended 35°. These findings were supported by a second experiment in which the 15° polar projection was set at a 5° viewing angle as a standard. In Experiment 3, 15 observers compared the three drawings, viewed at a second set of angular subtenses (30°, 35°, 40°, 45°, and 50°), with a standard, the 35° polar set at 45°. Ratings fell with increases in viewing angle, and the parallel projection was rated lowest. The results indicate that parallel projections are assessed as polar projections that are correct for objects at a small angular subtense. Furthermore, projections at a small angular subtense are robust; that is, they are acceptable over a wide range of angular subtenses. We suggest that robustness can be explained by the modest variability in the proportions of pictures of cubes subtending small angles.
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References
Arnheim, R. (1974).Art and visual perception (2nd ed.). Berkeley & Los Angeles: University of California Press.
Arnheim, R. (1977). Perception of perspective pictorial space from different viewing points.Leonardo,10, 283–288.
Bengston, J. K., Stergios, J. C., Ward, J. L., &Jester, R. E. (1980). Optic array determinants of apparent distance and size in pictures.Journal of Experimental Psychology: Human Perception & Performance,6, 751–759.
Busey, T. A., Brady, N. P., &Cutting, J. E. (1990). Compensation is unnecessary for the perception of faces in slanted pictures.Perception & Psychophysics.48, 1–11.
Cutting, J. E. (1986).Perception with an eye for motion. Cambridge, MA: MIT Press.
Cutting, J. E. (1987). Rigidity in cinema seen from the front row, side aisle.Journal of Experimental Psychology: Human Perception & Performance,13, 323–334.
Dubery, F., &Willats, J. (1983).Perspective and other drawing systems. London: Herbert Press.
Edgerton, S. Y. (1975).The Renaissance rediscovery of linear perspective. New York: Basic Books.
Farber, J., &Rosinski, R.R. (1978). Geometric transformations of pictured space.Perception,7, 269–282.
Gibson, J. (1979).The ecological approach to visual perception. Boston: Houghton-Mifflin.
Goldstein, E. B. (1987). Spatial layout, orientation relative to the observer, and perceived projection in pictures viewed at an angle.Journal of Experimental Psychology: Human Perception & Performance,13, 256–266.
Hagen, M. A. (1980). Generative theory: A perceptual theory of pictorial representation. In M. A. Hagen, (Ed.),The perception of pictures (Vol. 2, pp. 3–46). New York: Academic Press.
Hagen, Ma. (1985). There is no development in art. In N. H. Freeman & M. V. Cox (Eds.),Visual order (pp. 59–77). Cambridge: Cambridge University Press.
Hagen, M. A. (1986).Varieties of realism. Cambridge: Cambridge University Press.
Kubovy, M. (1986).The psychology of perspective and Renaissance art. Cambridge: Cambridge University Press.
Lumsden, E. A. (1980). Problems of magnification and minification: An explanation of the distortions of distance, slant, shape and velocity. Im. A. Hagen (Ed.),The perception of pictures (Vol. I, pp. 91–135). New York: Academic Press.
McGreevy, M. W., &Ellis, S. R. (1986). The effect of perspective geometry on judged direction in spatial information instruments.Human Factors,28, 439–456.
Nicholls, A. L., & Kennedy, J, M. (1992, June).Perspective robustness and optical infinity. Paper presented at the meeting of the Canadian Society for Brain, Behavioural and Cognitive Sciences, Quebec City.
Pirenne, M. H. (1970).Optics, painting and photography. Cambridge: Cambridge University Press.
Rosinski, R. R., &Farber, J. (1980). Compensation for viewing point in the perception of pictured space. In M. A. Hagen (Ed.), The perception of pictures (Vol. l, pp. 137–176). New York: Academic Press.
Rosinski, R. R., Mulholland, T., Degelman, D., &Farber, J. (1980). Picture perceptios: An analysis of visual compensation.Perception & Psychophysics,28, 521–526.
Sedgwick, H. A. (1980). The geometry of spatial layout in pictorial representation. In M. A. Hagen (Ed.),The perception of pictures (Vol. 1, pp. 33–90). New York: Academic Press.
Sedgwick, H. A. (1991). The effects of viewpoint on the virtual space of pictures. In S. R. Ellis (Ed.),Pictorial communication in virtual and real environments (pp. 460–479). New York: Taylor & Francis.
Smith, O. W. (1958). Judgments of size and distance in photographs.American Journal of Psychohgy,71, 529–538.
Smith, O. W., &Gruber, H. (1958). Perception of depth in photographs.Perceptual & Motor Skills,8, 307–313.
Veltman, K. H. (1987).Studies on Leonardo da Vinci I: Linear perspective and the visual dimensions of art and science. Munich: Deutscher Kunstverlag.
Wallach, H., &Marshall, F. J. (1986). Shape constancy in pictorial representation.Perception & Psychophysics,39, 233–235.
White, J. (1967).The birth and rebirth of pictorial space. Somerset, U.K.: Butler & Tanner.
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This work was supported by a grant from the National Science and Engineering Research Committee, Ottawa.
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Nicholls, A.L., Kennedy, J.M. Angular subtense effects on perception of polar and parallel projections of cubes. Perception & Psychophysics 54, 763–772 (1993). https://doi.org/10.3758/BF03211801
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DOI: https://doi.org/10.3758/BF03211801