Abstract: We propose a precomputation-based approach for the real-time rendering of scenes that include a number of complex illumination phenomena, such as radiosity and subsurface scattering, and allows interactive modification of camera and lighting parameters. At the heart of our approach lies a novel parameterization of the rendering equation that is inherently supported by the modern GPU. During the pre-computation phase, we build a set of offset transfer maps based on the proposed parameterization, which approximate the complete radiance transfer function for the scene. The rendering phase is then reduced to a set of texture-blending and mapping operations that execute in real-time on the GPU. In contrast to the current state-of-the-art, which employs environment maps to produce global illumination, our approach uses arbitrary first-order lighting to compute a final lighting solution, and fully supports point and spot lights. To discretize the transfer maps, we develop an efficient method for generating and sampling C⁰-continuous probability density functions from unordered data points.We believe that the contributions of this paper offer a significantly different approach to precomputed radiance transfer from those previously proposed.