The basis function theory of spatial representations explains how neurons in the parietal cortex can perform nonlinear transformations from sensory to motor coordinates. The authors present computer simulations showing that unilateral parietal lesions leading to a neuronal gradient in basis function maps can account for the behavior of patients with hemineglect, including (a) neglect in line cancellation and line bisection experiments; (b) neglect in multiple frames of reference simultaneously; (c) relative neglect, a form of what is sometime called object-centered neglect; and (d) neglect without optic ataxia. Contralateral neglect arises in the model because the lesion produces an imbalance in the salience of stimuli that is modulated by the orientation of the body in space. These results strongly support the basis function theory for spatial representations in humans and provide a computational model of hemineglect at the single-cell level.