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- W2138045758 abstract "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-Baker-Hausdorff 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 SO(3)/SO(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." @default.
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- W2138045758 date "1995-11-27" @default.
- W2138045758 modified "2023-09-24" @default.
- W2138045758 title "The Geometry of Eye Rotations and Listing's Law" @default.
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