The traditional radiosity methods discussed so far consider only diffuse reflections, having made it possible to ignore directional variation of the radiation of surfaces, since diffuse reflection generates the same radiant intensity in all directions. To extend the basic method taking into account more terms in the general shading equation, directional dependence has to be built into the model.
The most obvious approach is to place a partitioned sphere on each elemental surface, and to calculate and store the intensity in each solid angle derived from the partition [ICG86]. This partitioning also transforms the integrals of the shading equations to finite sums, and limits the accuracy of the direction of the incoming light beams. Deriving a shading equation for each surface element and elemental solid angle, a linear equation is established, where the unknown variables are the radiant intensities of the surfaces in various solid angles. This linear equation can be solved by similar techniques to those discussed so far. The greatest disadvantage of this approach is that it increases the number of equations and the unknown variables by a factor of the number of partitioning solid angles, making the method prohibitively expensive.
More promising is the combination of the radiosity method with ray tracing, since the respective strong and weak points of the two methods tend to complement each other.