Abstract: Existing radiosity rendering algorithms achieve interactivity or high fidelity, but not both. Most radiosity renderers optimize interactivity by converting to a polygonal representation and Gouraud interpolating shading samples, thus sacrificing visual fidelity. A few renderers achieve improved fidelity by performing a per-pixel irradiance "gather" operation, much as in ray-tracing. This approach does not achieve interactive frame rates on existing hardware. This paper bridges the gap, by describing a data structure and algorithm which enable interactive, high-fidelity rendering of radiosity solutions. Our algorithm "factors" the radiosity rendering computation into two components: an offline phase, in which a per-surface representation of irradiance is constructed, and an online phase, in which this representation is rapidly queried, in parallel, to produce a radiosity value at each pixel. The key components of the offline phase are a heuristic discontinuity ranking algorithm, which identifies the strongest discontinuities, and a hybrid quadtree-mesh data structure which prevents combinatorial interactions between most discontinuities. The online phase involves a novel use of perspective-correct texture-mapping hardware to produce nonlinear, analytic shading effects.