We introduce reconfigurable image projection (RIP) holograms and a method for computing RIP holograms of three-dimensional (3-D) scenes. RIP holograms project one or more series of parallax views of a 3-D scene through one or more holographically reconstructed projection surfaces. Projection surfaces are defined at locations at which the hologram reconstructs a variable number of real or virtual images, called holographic primitives, which collectively compose the surface and constitute exit pupils for the view pixel information. RIP holograms are efficiently assembled by combining a sweep of 2-D parallax views of a scene with instances of one or more precomputed diffractive elements, which are permitted to overlap on the hologram, and which reconstruct the holographic primitives. The technique improves on the image quality of conventional stereograms while affording similar efficient computation: it incorporates realistic computer graphic rendering or high-quality optical capture of a scene, it eliminates some artifacts often present in conventional computed stereograms, and its basic multiply-and-accumulate operations are suitable for hardware implementation. The RIP approach offers flexible tuning of capture and projection together, according to the sampling requirements of the scene and the constraints of a given display architecture.