Abstract: We introduce a new approach for the computation of view-independent solutions to the diffuse global illumination problem in polyhedral environments. The approach combines ideas from hierarchical radiosity and discontinuity meshing to yield solutions that are accurate both numerically and visually. First, we describe a modified hierarchical radiosity algorithm that uses a discontinuity-driven subdivision strategy to achieve better numerical accuracy and faster convergence. Second, we present a new algorithm based on discontinuity meshing that uses the hierarchical solution to reconstruct an object-space approximation to the radiance function that is visually accurate. Our results show significant improvements over both hierarchical radiosity and discontinuity meshing algorithms.