ABSTRACT
This chapter explores some kinematic aspects of gaze control by surveying the most powerful known representations, listing their strong and weak points and shows their interconnections and the origins of their seemingly peculiar properties. The eye has one axis of special functional significance, namely the gaze line, or line of sight. Quaternions and rotation vectors have no gaze channels because information about gaze direction is not fully contained in any two elements, but is distributed across all of them. A perfect representation of eye orientation should reflect the special status of the gaze line. A central fact of life for the oculomotor system, central enough to qualify as the Second Law of Oculodynamics, is that although the eye rotates with three degrees of freedom, gaze direction is only a 2D variable. It takes only two numbers, for example azimuth and elevation, to specify the direction an eye is looking.
