Abstract: Several types of methods precompute or capture light transport operators in either virtual or real scenes. Precomputed radiance transfer methods interactively render realistic images of static scenes under dynamic incident illumination, while reflectance field techniques capture an appearance model of a real scene for relighting purposes. In this article we present a unifying mathematical framework for methods that precompute or capture light transport operators, and characterize a large body of earlier work in its terms. The framework is given in the form of an operator equation that extends the rendering equation to account for a constrained space of emissions. The connections between traditional global illumination methods and precomputed transfer techniques become apparent through the explicit equation. Based on insight provided by the unifying view, we outline possibilities for new methods, particularly the wider adaptation of previous, hierarchical finite element techniques for efficient computation of the transport operators.