The common assumption that the brain maps visual space using a spatially additive operation, which combines retinal representations of visual stimulus with 2-D eye position, does not account for the rotatory nature of 3-D eye orientation and its effect on stimulation sites on the retina. Projections of lines onto the retina curve as a function of 3-D eye orientation, such that geometrically correct measures of retinal error (RE) for horizontal lines at different elevations in space do not stimulate purely horizontal points on the retina. Instead these RE's tilt out in a fan-like pattern as the eye is rotated away from primary position (Crawford & Guitton, 1997). Previous research has shown that the brain does perform the 3-D reference frame transformation to compute correct eye displacements when reading 2-D retinal information (Klier & Crawford, 1998). We wanted to determine if the arm movement system makes the same corrections when pointing between horizontally displaced targets while looking up or down. If pointing responses are accurate or any minor mistakes resemble those of the eye, this would suggest that eye and arm share a common or similar neural mechanism.

Methods: Seven right-handed subjects participated in this experiment in complete darkness with their heads fixed. They were asked to point toward a LED target briefly flashed 40° to 80° to the right of fixation, across 5 elevations over a vertical range of ±30° from eye level. 3-D eye and arm orientations and oculocentric target directions (RE) were computed from the search coil signals from the right eye and arm. These results were compared with controls where subject pointed toward peripherally-viewed LED's in dim light (with feedback).

Results: Subjects showed a consistent vertical offset when pointing toward the remembered target, but showed little or no systematic error as a function of eye position. Moreover, pointing responses did not follow the fanning out predictions of an additive spatial model. When actual vertical pointing errors were compared to those predicted, the averaged slope across subjects was -0.035 (±0.101 SD). The findings show that the visuomotor transformation for pointing does account for 3-D eye orientation in correcting for retinal curvature of space. This requires that the mechanism for comparison between RE and eye position be rotatory (i.e. multiplicative) rather than additive.