File:Nusselt analog.svg

English: This diagram depicts the Nusselt analog, or equivalently the projected solid angle, a geometrical way of visualising the view factor (or form factor) which arises in calculations of radiative heat transfer in physics and engineering, and in the radiosity method in 3D computer graphics.

Mathematically, the form factor for energy from an element A_j with a normal vector n_j arriving at a point on an element A_i with a normal vector n_i is given by:

${\displaystyle F_{ij}=\int _{A_{j}}{\frac {\cos(\theta _{i})\cos(\theta _{j})}{\pi r_{ij}^{2}}}\;dA_{j}}$

The Nusselt analog pictures this geometrical factor as equivalent to projecting the area of the element onto the surface of a unit hemisphere (giving the solid angle), and then projecting that in turn onto a unit circle around the point of interest in the plane of A_i. The form factor is equal to the proportion of the unit circle covered by this projection.

See eg: Cohen, M.F., Greenberg, D.P. (1985). The hemi-cube: a radiosity solution for complex environments. Computer Graphics (Proceedings of SIGGRAPH 1985) 19 (3), 31–40. doi:10.1145/325165.325171), figure 3.