High quality, physically accurate rendering at interactive rates has widespread application, but is a daunting task. We attempt to bridge the gap between high-quality offline and interactive rendering by using existing environment mapping hardware in combination with a novel Image Based Rendering (IBR) algorithm. The primary contribution lies in performing IBR in reflection space. This method can be applied to ordinary environment maps, but for more physically accurate rendering, we apply reflection space IBR to radiance environment maps. A radiance environment map pre-integrates a Bidirectional Reflection Distribution Function (BRDF) with a lighting environment. Using the reflection-space IBR algorithm on radiance environment maps allows interactive rendering of arbitrary objects with a large class of complex BRDFs in arbitrary lighting environments. The ultimate simplicity of the final algorithm suggests that it will be widely and immediately valuable given the ready availability of hardware assisted environment mapping.