Alleys on an apparent frontoparallel plane
type: Item
instance of: scholarly article
title: Alleys on an apparent frontoparallel plane
zbMATH Open document ID: 0653.92023
DOI: 10.1016/0022-2496(88)90012-0
author: Tarow Indow
published in: Journal of Mathematical Psychology
publication date: 1988-01-01T00:00:00Z
review text: In the author's article, ibid. 19, 221-258 (1979; Zbl 0441.92024), equations were presented for a plane appearing frontopaallel in the three-dimensional visual space and for two alleys on that plane which run horizontally in the following way: an alley that appears straight and parallel (Hh) and an alley that appears to be separated by a constant interval (Dh). This is an extension of traditional parallel and equidistant alleys which run toward the subject on the horizontal plane. As was done by \textit{R. K. Luneburg} [see: Mathematical analysis of binocular vision. Princeton (1947); and Studies and essays, pres. to Courant, 215-240 (1948; Zbl 0033.090)] for these alleys, the equations were defined in the Euclidean map (EM) under the assumption that visual space is a Riemannian space of constant curvature K. In the present article, the general definition of perceptually straight lines in EM is discussed and, on the basis of this representation, new equations for Hh and Dh are given. Previous and present sets of equations give the same qualitative predictions as to the behavior of Hh and Dh, but two predictions are quantitatively different.
Mathematics Subject Classification ID: 91E30
zbMATH DE Number: 4066703
zbMATH Keywords: geodesics
zbMATH Keywords: three-dimensional visual space
zbMATH Keywords: alleys
zbMATH Keywords: Euclidean map
zbMATH Keywords: general definition of perceptually straight lines
zbMATH Keywords: EM
zbMATH Keywords: Hh
zbMATH Keywords: Dh
MaRDI profile type: Publication
full work available at URL: 0022-2496(88)90012-0
OpenAlex ID: W1967976277
cites work: Q5822835
cites work: Alleys in visual space
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cites work: Landkarten der nichteuklidischen Ebene
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cites work: Q5788995
cites work: Gravitational collapse: The role of general relativity
cites work: Q4130032
cites work: Q3869915
cites work: Q3258630
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description: scientific article; zbMATH DE number 4066703