The perceptual and sensorimotor mechanisms that guide our abilities at localizing and orienting in space integrate sensory information from vision and from a "body-referenced mechanism" that itself makes use of extraretinal signals regarding eye position relative to the head and head orientation relative to the body and to gravity. The experiments and theoretical treatment center on two perceptual dimensions: the visual perception of elevation and of orientation within the frontoparallel plane. Several experiments measuring localization in the horizontal plane are also treated. The experiments involve measurements of the physical elevation of visually perceived eye level (VPEL, a norm for perceived elevation), measurements of the physical orientation within the frontoparallel plane corresponding to visually perceived vertical (VPV), and measurements of the direction within a horizontal plane perceived as straight ahead (VPSA). VPEL and VPV are each significantly and systematically influenced by both the pitch and the roll of visual fields, and it is these influences that provide the basis for experimentally isolating the contributions of vision from those of the body-referenced mechanism. The VPEL discrimination is nearly invariant with variation in head and eye orientation. The possibility that influences from vision and from the body-referenced mechanism combine linearly is well supported. The visual influences on VPEL and VPV are controlled by the action of individual lines, and the same pitched-from-vertical lines (from pitched planes) or oblique lines within erect planes influence both discriminations. The Great Circle Model (GCM) accounts for the influences of individual lines, and contains rules for the influence of combinations of lines on both VPEL and VPV. GCM is interpreted by a 3-dimensional vector treatment in "egocentric orientation space."