Virtual reality systems commonly include both monocular and binocular depth cues, which have the potential to provide viewers with a realistic impression of spatial properties of the virtual environment. However, when multiple viewers share the same display, only one viewer typically receives the projectively correct images. All other viewers experience the same images despite displacement from the center of projection (CoP). Three experiments evaluated perceptual distortions caused by displacement from the CoP and compared those percepts to predictions of models based on monocular and binocular viewing geometry. Leftward and rightward displacement from the CoP caused virtual angles on the ground plane to be judged as larger and smaller, respectively, compared to judgments from the CoP. Backward and forward displacement caused rectangles on the ground plane to be judged as larger and smaller in depth, respectively, compared to judgments from the CoP. Judgment biases were in the same direction as cue-based model predictions but of smaller magnitude. Displacement from the CoP had asymmetric effects on perceptual judgments, unlike model predictions. Perceptual distortion occurred with monocular cues alone but was exaggerated when binocular cues were added. The results are grounded in terms of practical implications for multiuser virtual environments.