Abstract

In Euclidean spaces of an arbitrary number n of dimensions metrics are defined which are invariant with respect to affine transformations of the coordinates. These metrics are closely related to non-Euclidean distances in spaces of negative constant curvature. Special cases are discussed. The logarithmic scale results for n=1. The case n=2 occurs in the solution of a colorimetric problem. The most important case n=3 is connected to the color space and to Luneburg’s geometry of the space of binocular vision.

© 1956 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Experimental Test of Luneburg’s Theory. Horopter and Alley Experiments*

A. Zajaczkowska
J. Opt. Soc. Am. 46(7) 514-527 (1956)

Concept of Distance in Affine Geometry

P. J. van Heerden
J. Opt. Soc. Am. 46(11) 1000-1000 (1956)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (44)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription