Abstract
Triangular properties which Blank (1961) proposed are useful in investigating the geometry of visual space. With this method, however, it is not possible to estimate quantitatively the curvature of visual space. In the present article, hyperbolic and elliptic triangles are described with mathematical equations in the two and three dimensional Euclidean maps, and a method is proposed to estimate the curvature with triangular properties. Further, one experiment is conducted to find how the curvature changes according to the experimental conditions. Visual triangles are constructed in an eye level plane, a slanted plane and a horopter plane. The result shows that the curvature is negative in the eye level plane and in the slanted plane, but positive in the horopter plane.
| Original language | English |
|---|---|
| Pages (from-to) | 278-284 |
| Number of pages | 7 |
| Journal | Shinrigaku Kenkyu |
| Volume | 67 |
| Issue number | 4 |
| Publication status | Published - 1996 Oct |
Keywords
- Non-Euclidean geometry
- Visual space
- Visual triangle
ASJC Scopus subject areas
- Psychology(all)
Cite this
The estimation of the curvature of visual space with a visual triangle. / Watanabe, Toshio.
In: Shinrigaku Kenkyu, Vol. 67, No. 4, 10.1996, p. 278-284.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The estimation of the curvature of visual space with a visual triangle
AU - Watanabe, Toshio
PY - 1996/10
Y1 - 1996/10
N2 - Triangular properties which Blank (1961) proposed are useful in investigating the geometry of visual space. With this method, however, it is not possible to estimate quantitatively the curvature of visual space. In the present article, hyperbolic and elliptic triangles are described with mathematical equations in the two and three dimensional Euclidean maps, and a method is proposed to estimate the curvature with triangular properties. Further, one experiment is conducted to find how the curvature changes according to the experimental conditions. Visual triangles are constructed in an eye level plane, a slanted plane and a horopter plane. The result shows that the curvature is negative in the eye level plane and in the slanted plane, but positive in the horopter plane.
AB - Triangular properties which Blank (1961) proposed are useful in investigating the geometry of visual space. With this method, however, it is not possible to estimate quantitatively the curvature of visual space. In the present article, hyperbolic and elliptic triangles are described with mathematical equations in the two and three dimensional Euclidean maps, and a method is proposed to estimate the curvature with triangular properties. Further, one experiment is conducted to find how the curvature changes according to the experimental conditions. Visual triangles are constructed in an eye level plane, a slanted plane and a horopter plane. The result shows that the curvature is negative in the eye level plane and in the slanted plane, but positive in the horopter plane.
KW - Non-Euclidean geometry
KW - Visual space
KW - Visual triangle
UR - http://www.scopus.com/inward/record.url?scp=0030254423&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0030254423&partnerID=8YFLogxK
M3 - Article
VL - 67
SP - 278
EP - 284
JO - Shinrigaku Kenkyu
JF - Shinrigaku Kenkyu
SN - 0021-5236
IS - 4
ER -