Direct measurement of the curvature of visual space

We consider the horizontal plane at eye height, that is all objects seen at the horizon. Although this plane visually degenerates into a line in the v isual field, the 'depth' dimension nevertheless gives it a two-dimensional structure. We address the problem of intrinsic curvature of this plane. The classical geometric method is based on Gauss's original definition: The an gular excess in a triangle equals the integral curvature over the area of t he triangle. Angles were directly measured by a novel method of exocentric pointing. Experiments were performed outside, in the natural environment, u nder natural viewing conditions, The observers were instructed not to move from a set location and to maintain eye height, but were otherwise free to perform eye, head, and body movements. We measured the angular excess for e quilateral triangles with sides of 2-20 m, the vantage position at the bary center. We found angular excesses and deficits of up to 30 degrees, From th ese data we constructed the metric. The curvature changes from elliptic in near space to hyperbolic in far space. At very large distances the plane be comes parabolic.