Exocentric Directions in Egocentric Space

Observers had to direct a pointer (using a radio link for remote control) at some location towards a beacon at another location such that the pointer appeared to point straight at the beacon. Experiments were done in the natural landscape under broad daylight with the subjects using natural (binocular) vision. Distances were in the range of 1 – 24 m. The location of the vantage point was prescribed, but the observers were allowed (indeed needed) to make eye, head, and body movements, including placement of the feet. Only one or two beacons were visible at any time, but positions were taken from configurations composed of many points. In this way samples of the nexus of pregeodesics of visual space were obtained. The results are interpreted in terms of a curvature of optical space, and in terms of a nonlinear range — depth relation. The results are in conflict with constant-curvature models (such as Luneburg's) of optical space: the curvature is elliptical in near space and changes to hyperbolical in far space. The nexus of pregeodesics does not necessarily involve a metric at all and is thus a more primitive structure of optical space than conventionally considered in the literature.