An algorithm for reprojection of 3D data, called the fast Fourier projection (FFP), is presented. Its input data are in the spatial-frequency domain, which in most cases requires an initial 3D Fourier transformation, but the FFP generates arbitrary views in significantly less computation time than previous methods. The theoretical basis of the method, including implications for image quality and artifacts, is presented. It may be implemented easily on conventional workstations and may be expected to run between 10 and 40 times as fast as ray-casting methods on a given processor. The user may freely zoom and rotate the view, the system filling in intermediate views quickly enough to provide motion-related depth cues (e.g., parallax) which aid visualization of 3D structures. A prototype software implementation and its performance are described.ETX