A. Shape factors

Recall Equation 204.22, which should be remembered as being the most important one in Section 204:

\[\label{eq1} d^3q^\pm=I^\pm_\nu\cos\theta\,d^2\,\Omega\,d\nu \tag{1}\]

The equation holds for either the radiosity q⁺ or the irradiation q^–, hence the ± notation. This fact has an important result for the shape factor: The shape factor has two equally valid and equally important meanings. (1) The shape factor F_i–j is the fraction of the radiated power leaving diffuse surface i that is intercepted by surface j. (2) The shape factor F_i–j is the fractional weight to be given the radiosity of diffuse surface j in summing up the irradiation upon surface i, or, put another way, it is the fraction of the surrounds of surface i taken up by surface j.

In what immediately follows, the equations will be written without ν or λ subscripts to denote a spectral quantity, but inspection of Equation 204.22 and Equation 204.23 shows that the same expression holds for either spectral or total quantities.