I feel a bit confused about the use of $F_{ij}$ and $F_{ji}$ in Radiosity papers. $F_{ij}$ should be the fraction of energy leaving patch $i$ that arrives at patch $j$.

If you take the original radiosity paper ("Modeling the Interaction of Light Between Diffuse Surfaces", by Goral, Torrance, Greenberg, and Battaile, at SIGGRAPH 84), the radiosity equation is expressed as: $$ B_{j} = E_{j} + \rho_{j} \sum\limits_{i=1}^n B_{i} F_{ij} $$ and they explicitly mention that all radiosities are measured in $W/m^2$ and that $F_{ij}$ is the "form factor and represents the fraction of radiant energy leaving surface i and impinging on surface j" (sic).

Now if you take another famous paper ("The Hemi-Cube. A Radiosity solution for complex environments", by Cohen and Greenberg, at SIGGRAPH 85) you see that their equation 1 is: $$ B_{i} = E_{i} + \rho_{i} \sum\limits_{j=1}^n B_{j} F_{ij} $$ and they also explicitly say that radiosities are expressed in $W/m^2$ and that $F_{ij}$ is the "the fraction of the energy leaving one surface which lands on another surface" (sic).

Yes, I didn't make a mistake, both papers use $F_{ij}$ even if they switched the $i$ and $j$ indices and even if they're formulating the classical gathering radiosity (the shooting-based progressive refinement approach came later, in SIGGRAPH 88).

Moreover, to add more into the confusion, some books follow the SIGGRAPH 84 paper equation (Foley, van Dam, Feiner, Hugues, for example), while others use the SIGGRAPH 85 paper equation (Sillion & Puech, for example).

I know $F_{ij}$ and $F_{ji}$ get reversed if you express the equation in radiant energy $(W)$ instead of radiosities $(W/m^2)$ because of the reciprocity relationship $F_{ij}A_{i}=F_{ji}A_{j}$, but however, both equations above are explicitly radiosity-based, in $W/m^2$.

Is there any mistake in radiosity papers? In that case, what equation is right? Or maybe I'm missing some piece in this puzzle?



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