Mirror symmetry and parallelism: two opposite rules for the identity transform in space perception and their unified treatment by the Great Circle Model.

Two opposite rules control the contributions of individual lines to the perceptual processing of two different spatial dimensions of egocentric localization and orientation. For lines restricted to the frontal plane, a tilted line on one side of the median plane induces a rotation of the orientation visually perceived as vertical (VPV) identical to that induced by the same tilt on the other side of the median plane, but the influences exerted on the elevation of visually perceived eye level (VPEL) are mirror symmetric. The rule for VPV fits our intuitions; the rule for VPEL does not. However, the reverse peculiarity holds when the inducing lines are rotated within sagittal planes (pitched): Two parallel, pitched-from-vertical lines on opposite sides of the median plane generate identical effects on VPEL but mirror symmetric effects on VPV. These counterintuitive symmetry reversals are reconciled by the Great Circle Model of spatial orientation (GCM), in which line orientations are represented by the great circle coordinates of their images on a sphere centered at the nodal point of the eye via central projection.