The visual environment is distorted with respect to the physical environment. Luneburg [1947, Mathematical Analysis of Binocular Vision (Princeton, NJ: Princeton University Press)] assumed that visual space could be described by a Riemannian space of constant curvature. Such a space is described by a metric which defines the distance between any two points. It is uncertain, however, whether such a metric description is valid. Two experiments are reported in which subjects were asked to set two bars parallel to each other in a horizontal plane. The backdrop consisted of wrinkled black plastic sheeting, and the floor and ceiling were hidden by means of a horizontal aperture restricting the visual field of the subject vertically to 10 deg. We found that large deviations (of up to 40°) occur and that the deviations are proportional to the separation angle: on average, the proportion is 30%. These deviations occur for 30°, 60°, 120°, and 150° reference orientations, but not for 0° and 90° reference orientations; there the deviation is approximately 0° for most subjects. A Riemannian space of constant curvature, therefore, cannot be an adequate description. If it were, then the deviation between the orientation of the test and the reference bar would be independent of the reference orientation. Furthermore, we found that the results are independent of the distance of the bars from the subject, which suggests either that visual space has a zero mean curvature, or that the parallelity task is essentially a monocular task. The fact that the deviations vanish for a 0° and 90° orientation is reminiscent of the oblique effect reported in the literature. However, the 'oblique effect' reported here takes place in a horizontal plane at eye height, not in a frontoparallel plane.