Background. Spatial neglect affects perception along different dimensions. However, there is limited availability of 3-dimensional (3D) methods that fully map out a patient’s volume of deficit, although this could guide clinical management. Objective. To test whether patients with neglect exhibit simple contralesional versus complex perceptual deficits and whether deficits are best described using Cartesian (rectangular) or polar coordinates. Methods. Seventeen right-hemisphere persons with stroke (8 with a history of neglect) and 9 healthy controls were exposed to a 3D virtual environment. Targets placed in a dense array appeared one at a time in various locations. Results. When tested using rectangular array of targets, subjects in the neglect group exhibited complex asymmetries across several dimensions in both reaction time and target detection rates. Paper-and-pencil tests only detected neglect in 4 of 8 of these patients. When tested using polar array of targets, 2 patients who initially appeared to perform poorly in both left and near space only showed a simple left-side asymmetry that depended almost entirely on the angle from the sagittal plane. A third patient exhibited left neglect irrespective of the arrangements of targets used. An idealized model with pure dependence on the polar angle demonstrated how such deficits could be misconstrued as near neglect if one uses a rectangular array. Conclusions. Such deficits may be poorly detected by paper-and-pencil tests and even by computerized tests that use regular screens. Assessments that incorporate 3D arrangements of targets enable precise mapping of deficient areas and detect subtle forms of neglect whose identification may be relevant to treatment strategies.