Fig. 1.

Axes of sinusoidal translations for characterization of the 3-dimensional translational vestibulo-ocular reflex. A: the chinchilla was oriented ~50° nose-down to put the horizontal canals approximately in the Earth-horizontal plane (Hullar and Williams 2006). The +X, +Y, and +Z axes of the coordinate system shown correspond, respectively, to (θ, φ) = (0°, 90°), (90°, 90°), and (0°, 0°). For translation along an axis, those 3 cardinal axes represent surge (fore-aft, positive anterior), lateral (interaural, positive leftward), and heave (up-down, positive up). For rotations about an axis, the same 3 axes represent roll, pitch, and yaw, respectively, with positive rotations defined by a right-hand rule (curved white arrows). B–D: sinusoidal translation stimuli at 1 Hz were delivered along each of 8 axes in the Earth-horizontal plane (B), 8 axes in the coronal plane (C), and 8 axes in the sagittal plane (D). Note that in spherical coordinates, θ is the azimuth referenced to +X, φ is the always-positive polar angle referenced to +Z, and (90 – φ) is the elevation from the XY plane.