Representation of eye position in three dimensions

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Abstract
This chapter provides a short overview of frequently used parameterizations for describing eye positions and eye movements in three dimensions, primarily dealing with coordinate frames, whose purpose is to give clear definitions of motion in three-dimensional space. In addition, Donders' law and Listing's law are briefly described. The chapter informs us that the eye can be treated as a rotating body, for which translatory movements can be neglected. Therefore, its centre of rotation is approximately fixed with respect to the head and three parameters, namely, horizontal, vertical, and torsional components of eye position that suffice to uniquely determine eye position relative to the head. However, rotations in three dimensions do not commute, which means that the order in which they occur determines the final orientation of the rotated body. Several parametrizations have been applied for representing three-dimensional eye position. The chapter also suggests that one has to differentiate between head-fixed coordinate systems and systems in which the coordinate axes move with the eye, as in a gimbal system.

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