## 4 Discussion: Finding of the Global Form Factor
### Determination Procedures  
It has been proved by the author [34; 35] that the form factor amounts to the average over the domain of the emitting surface of the configuration factor previously obtained on a point-to-point basis, as it precisely represents the integral extended to this second area. It is possible by any numerical automated procedure to obtain the mean value of all the point factors for any sort of figure contained in the said transferring field. For instance, in the nephograph in Figure 14 with the results of Equation (13) by virtue of the seventh postulate, we have automatically calculated the form factor F\({}_{21}\) from a rectangle of 8 m by 5 m to a triangle of 5 m height by 5 m width; it amounts to 0.090. In Figure 15, we can see the radiative field in plan of the triangle over the rectangle; the curves of received radiation are more pronounced in the left lower part of the nephograph due to the higher altitude of the triangle in that area as it nears its upper vertex. In Figure 16, we have represented the same field in a three-dimensional view to understand better how the exchanges are manifested, for example, in luminous emissions such as windows or LED devices. With a similar approach, the total form factors can be found for the usual sets of precincts, such as prisms or oblique cuboids. Inter-reflection within the so-generated  
Figure 14: Average for a triangle of 5 m by 5 m over a horizontal rectangle of length 8 m. The form factor F\({}_{21}\) from the rectangle (2) to the triangle (1) is equal in this case to 0.090. Figure 15: Nephograph in plan of the radiative field from the triangle to the rectangle. volumes is also an issue that we have to foresee; in the case of triangular prisms, we would require a set of five equations with five unknowns, which is detailed in the Appendix A[36]. For example, when designing and solving inclined slats, the triangles that appear are not right, but usually they appear as obtuse or acute angles; in these situations, we cannot employ the already solved form factor for perpendicular rectangles [5]; instead, we need to resort to different extended formulas developed by the author [37] to take into account the exchanges between inclined rectangles. Let us proceed to explain how the twenty form factors Fij with i and j from 1 to 5 but excluding the dummy sub-indexes like F11, F22, as all surfaces are planar. With the first direct integration using Equation (13) and detailed in Figures 14-16, we obtain the exchange between the horizontal surface (4) and the side triangles (surfaces 1 and 2 in Figure 17), by symmetry,  
\[\text{F}_{41}=\text{F}_{42} \tag{76}\]  
But by reciprocity (Equation (1))  
\[\text{A}_{4}\text{F}_{41}=\text{A}_{1}\text{F}_{14} \tag{77}\]  
\[\text{F}_{14}=\text{F}_{24}=\text{A}_{4}\text{F}_{41}/\text{A}_{1} \tag{78}\]  
Figure 16: Nephograph of radiative distribution for the same case in 3D. Figure 17: The five surfaces of the volume of a triangular prism ending in right triangles. F\({}_{43}\) and F\({}_{34}\) are known, since we have deducted the expression for perpendicular rectangles with a common edge [38]. The form factor algebra demonstrated elsewhere [1; 5; 34; 35] states that,  
\[\text{F}_{12}+\text{F}_{13}+\ldots\text{F}_{\text{IJ}}=1 \tag{79}\]  
Consequently,  
\[\text{F}_{41}+\text{F}_{42}+\text{F}_{43}+\text{F}_{45}=1 \tag{80}\]  
\[\text{F}_{45}=1-2\text{F}_{41}-\text{F}_{43} \tag{81}\]  
As F\({}_{41}\) and F\({}_{43}\) are known, we can extract F\({}_{45}\),  
Figure 15:0  
Once we know F\({}_{54}\), we can write,  
Figure 15:1  
Figure 15:2  
F\({}_{51}\) is unknown, but similarly to Equation (76), rotating the triangles to the vertical side of the prism (Surf.