On each of three frontoparallel planes at distances of about 98, 186, and 276 cm from the subject, two series of light points running horizontally in the dark, one above the other, were constructed by six subjects: a P-alley in which the two series appear as two straight lines that are parallel, and a D-alley in which each pair of points appear equally separated in the vertical direction. Luneburg's mapping functions between visual space and physical space have been used to obtain estimates of K (curvature) and sigma (a constant related to depth perception). In addition, ratios of perceptual distances were assessed by four out of the six subjects with eleven triplets of points on the alleys and values of K were estimated (and the fits of theoretical equations were tested) without the use of the mapping functions. In contrast to experiments with P-alleys and D-alleys on the horizontal plane, K was not unequivocally negative in either of the two experiments.