The Geometry of Eye Rotations and Listing's Law
نویسندگان
چکیده
We analyse the geometry of eye rotations, and in particular saccades, using basic Lie group theory and differential geometry. Various parameterizations of rotations are related through a unifying mathematical treatment, and transformations between co-ordinate systems are computed using the Campbell-BakerHausdorff formula. Next, we describe Listing's law by means of the Lie algebra so(3). This enables us to demonstrate a direct connection to Donders' law, by showing that eye orientations are restricted to the quotient space 80(3)/80(2). The latter is equivalent to the sphere S2, which is exactly the space of gaze directions. Our analysis provides a mathematical framework for studying the oculomotor system and could also be extended to investigate the geometry of mUlti-joint arm movements .
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