کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4035404 | 1263524 | 2006 | 5 صفحه PDF | دانلود رایگان |

Our 3-D percept of the world is constructed from the two-dimensional visual images on the retina of each eye, but these images and the relationships between them are affected by the 3-D rotations of each eye. These 3-D eye rotations are constrained to patterns such as Listing’s law, or its generalisation ‘L2’, according to the context. Our understanding of the patterns of such three-dimensional eye rotations, and their effect on the retinal images, has been greatly advanced by the development of algebraic methods (Haustein, 1989, Tweed and Vilis, 1987 and Westheimer, 1957) for calculating the effect of eye rotations. But not many would say, with Dirac, that they understand the equations describing the 3-D geometry in the sense that they have “a way of figuring out the characteristic of its solution without actually solving it” (Dirac, according to Feynman, Leighton, & Sands, 1964). I show here how the geometry of 3-D rotations of the eye and their visual effects can be made easier to understand by use of the principle that a rotation through angle α can be achieved by a pair of reflections in planes with an angular separation α/2, and a common line that is the rotation axis ( Tweed, 1997b and Tweed et al., 1990). Mathematically (see Appendix A), the method is equivalent to decomposing the unit quaternions so successfully used to study three-dimensional eye rotations ( Tweed and Vilis, 1987 and Westheimer, 1957) into pairs of pure quaternions (ones whose scalar part is zero) which represent the reflections (Coxeter, 1946).
Journal: Vision Research - Volume 46, Issue 22, October 2006, Pages 3862–3866