Perspective Using Curved Projection Rays and its Computer Application

The author describes a novel way for generating line drawings of 3-dimensional objects and describes a computer programme that he used in plotting such drawings. Instead of being confined by the rules of linear perspective, which governs retinal and photographic images, he employs a more general mathematical model that provides a family of perspectives. Each member of the family is designated individually by a numerical value (between 0 and 1)for its index i. The lowest value, i=0, leads to the linear equation that applies to linear perspective; application of the highest value, i = 1, results in axonometric projection. Sometimes linear perspective leads to a drawing or to a photographic image that seems grossly distorted in comparison with what one perceives in looking at an object. The author’s method, employed with fractional values for i and with the same viewpoint, may be used to produce more acceptable drawings.

[1]  On Gibson’s and Goodman’s Accounts of Depiction , 1973 .

[2]  J. Hochberg,et al.  Art, Perception, and Reality , 1972 .

[3]  R. Gregory,et al.  Illusion in Nature and Art , 1980 .

[4]  M. Vernon.  The psychology of perception , 1962 .

[5]  Kenneth R. Adams.  Perspective and the Viewpoint , 1972 .

[6]  James J. Gibson,et al.  The Information Available in Pictures , 1971 .

[7]  Perceptual constancy or perceptual compromise , 1972 .

[8]  R. Gregory.  The intelligent eye , 1970 .

[9]  Size constancy and the problem of perceptual spaces , 1972 .

[10]  Gyorgy Kepes,et al.  Language of Vision , 1944 .

[11]  R. Thouless.  INDIVIDUAL DIFFERENCES IN PHENOMENAL REGRESSION , 1932 .

[12]  Robert H. Thouless,et al.  Phenomenal Regression to the Real Object , 1931, Nature.

[13]  J. Gibson.  The Senses Considered As Perceptual Systems , 1967 .

[14]  R. Thouless.  Phenomenal Regression to the Real Object , 1933, Nature.

[15]  N. Goodman.  Languages of Art , 1968 .

[16]  R. Hansen.  This Curving World: Hyperbolic Linear Perspective , 1973 .

[17]  W. Mauch,et al.  Contents , 2007, European Neuropsychopharmacology.

[18]  John White.  The birth and rebirth of pictorial space , 1958 .

[19]  John M. Kennedy,et al.  Optics Painting and Photography , 1970 .

[20]  Cézanne and the Average Effect of Foreshortening on Shape , 1975 .

[21]  R. L. GREGORY,et al.  Measuring Visual Constancy for Stationary or Moving Objects , 1961, Nature.

[22]  E. Gombrich.  Art and Illusion , 1962 .

[23]  Nicholas Negroponte,et al.  Recent advances in sketch recognition , 1973, AFIPS National Computer Conference.

[24]  Robert F. Sproull,et al.  Principles in interactive computer graphics , 1973 .

[25]  H. Ridley.  Eye and Brain , 1973 .

[26]  Paul M. Laporte,et al.  Mathematical Analysis of Binocular Vision , 1950 .