Abstract: Multidimensional lightcuts is a new scalable method for efficiently rendering rich visual effects such as motion blur, participating media, depth of field, and spatial anti-aliasing in complex scenes. It introduces a flexible, general rendering framework that unifies the handling of such effects by discretizing the integrals into large sets of gather and light points and adaptively approximating the sum of all possible gather-light pair interactions.We create an implicit hierarchy, the product graph, over the gather-light pairs to rapidly and accurately approximate the contribution from hundreds of millions of pairs per pixel while only evaluating a tiny fraction (e.g., 200--1,000). We build upon the techniques of the prior Lightcuts method for complex illumination at a point, however, by considering the complete pixel integrals, we achieve much greater efficiency and scalability.Our example results demonstrate efficient handling of volume scattering, camera focus, and motion of lights, cameras, and geometry. For example, enabling high quality motion blur with 256x temporal sampling requires only a 6.7x increase in shading cost in a scene with complex moving geometry, materials, and illumination.