of the sending elements in turn in its main outermost loop for each update, rather than each of the receiving patches. This is known as the shooting variant of the algorithm, as opposed to the gathering variant. Using the view factor reciprocity, Ai Fij = Aj Fji, the update equation can also be re-written in terms of the view factor Fji seen by each sending patch Aj: This is sometimes known as the "power" formulation, since it is now the total transmitted power of each element that is being updated, rather than its radiosity. The view factor Fij itself can be calculated in a number of ways. Early methods used a hemicube (an imaginary cube centered upon the first surface to which the second surface was projected, devised by Michael F. Cohen and Donald P. Greenberg in 1985). The surface of the hemicube was divided into pixel-like squares, for each of which a view factor can be readily calculated analytically. The full form factor could then be approximated by adding up the contribution from each of the pixel-like squares. The projection onto the hemicube, which could be adapted from standard methods for determining the visibility of polygons, also solved the problem of intervening patches partially obscuring those behind. However all this was quite computationally expensive, because ideally form factors must be derived for every possible pair of patches, leading to a quadratic increase in computation as the number of patches increased. This can be reduced somewhat by using a binary space partitioning tree to reduce the amount of time spent determining which patches are completely hidden from others in complex scenes; but even so, the time spent to determine the form factor still typically scales as n log n. New methods include adaptive integration. Sampling approaches The form factors Fij themselves are not in fact explicitly needed in either of the update equations; neither to estimate the total intensity Σj Fij Bj gathered from the whole view, nor to estimate how the power Aj Bj being radiated is distributed. Instead, these updates can be estimated by sampling methods, without ever having to calculate form factors explicitly. Since the mid 1990s such sampling approaches have been the methods most predominantly used for practical radiosity calculations. The gathered intensity can be estimated by generating a set of samples in the unit circle, lifting these onto the hemisphere, and then seeing what was