The holographic visualization of three-dimensional object geometry still represents a major challenge in computational holography research. Besides the development of suitable holographic display devices, the fast calculation of the hologram’s interference pattern for complex-shaped three-dimensional objects is an important pre-requisite of any interactive holographic display system. We present a fast method for rendering full-parallax holograms using a standard PC with a consumer-market graphics card. To calculate the hologram of a 3D object, scaled and translated versions of the interference pattern of simple primitives, e.g. point sources, are superimposed. The hologram is built up completely on-board the graphics card. To avoid numerical inaccuracies due to limited frame-buffer resolution, we use a hierarchical approach. Using an NVidia Geforce4 graphics card, the proposed algorithm takes 1.0 second to calculate the 512x512-pixel hologram of 1024 primitives.