Abstract: We develop a radiance formulation for discrete three point transport, and a new measure and description of reflectance:area reflectance. This formulation and associated reflectance allow an estimate of error in the computation of radiance across triples of surface elements, and lead directly to a hierarchical refinement algorithm for global illumination. We have implemented and analyzed this algorithm over surfaces exhibiting glossy specular and diffuse reflection. Theoretical growth in light transport computation is shown to be $<$i$>$O(n + k$<$sup$>$3$<$/sup$>$)$<$/i$>$ for sufficient refinement, where n is the number of elements at the finest level of subdivision over an environment consisting of k input polygonal patches - this growth is exhibited in experimental trials. Naive application of three point transport would require computation over $<$i$>$O(n$<$sup$>$3$<$/sup$>$)$<$/i$>$ element-triple interactions.