A simple, fast, and approximate voxel-based approach to 6-DOF haptic rendering is presented. It can reliably sustain a 1000 Hz haptic refresh rate without resorting to asynchronous physics and haptic rendering loops. It enables the manipulation of a modestly complex rigid object within an arbitrarily complex environment of static rigid objects. It renders a short-range force field surrounding the static objects, which repels the manipulated object and strives to maintain a voxel-scale minimum separation distance that is known to preclude exact surface interpenetration. Force discontinuities arising from the use of a simple penalty force model are mitigated by a dynamic simulation based on virtual coupling. A generalization of octree improves voxel memory efficiency. In a preliminary implementation, a commercially available 6-DOF haptic prototype device is driven at a constant 1000 Hz haptic refresh rate from one dedicated haptic processor, with a separate processor for graphics. This system yields stable and convincing force feedback for a wide range of user controlled motion inside a large, complex virtual environment, with very few surface interpenetration events. This level of performance appears suited to applications such as certain maintenance and assembly task simulations that can tolerate voxel-scale minimum separation distances.