## 2 Methodology
According to this model, the global solar irradiance, \(I\), on an inclined plane at an angle \(\beta\) is the sum of the direct, diffuse, and reflected irradiance on an inclined plane, which, in turn, depends on the direct irradiance, \(I_{B}\), and diffuse, \(I_{D}\), on a horizontal surface, according to Equation (7), where \(\theta\) is the angle between the normal vector and the collector plane \(\left(\overset{\rightarrow}{n}\right)\) and the solar vector \(\left(\overset{\rightarrow}{s}\right)\), \(\theta_{z}\) is the zenith angle, \(\rho\) is the albedo of the surface of incidence of the irradiance before being reflected towards the collector, \(a\) and \(b\) are parameters given by Equations (8) and (9), and \(F_{1}\) and \(F_{2}\) are the weighting factors for the decomposition of the inclined diffuse radiation, the second addition, in the three subcomponents considered by the authors: isotropic diffuse, circumsolar diffuse, and diffuse from the horizon ([PERSON] et al., 1990). \[I=\frac{\cos\theta}{\cos\theta_{z}}I_{B}+\left[(1-F_{1})\frac{1+\cos\beta}{2}+F _{1}\frac{a}{b}+F_{2}\sin\beta\right]I_{D}+\rho\frac{1-\cos\beta}{2}(I_{B}+I_{D}) \tag{7}\]  
\[a=\max(\cos\theta,\,0) \tag{8}\]  
\[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]0  
\[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]1  
\[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]2  
\[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]3  
From expression (20), given that \(\overrightarrow{d}_{i}\) is a vector included in the collector plane \(\psi\), Equations (24) and (25) allow for determination of the components of this vector in the OXY reference system contained in the plane \(\psi\) and defined by the vectors \(\overrightarrow{u}\) y \(\overrightarrow{v}\). \[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]4  
\[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]5  
\[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]6 Astronomical and geometric magnitudes considered. Knowing \(\overset{\rightarrow}{d}_{i}\) and its components \(d_{Xi}\) and \(d_{Yi}\), the dichotomous criterion proposed by [PERSON] et al. [38], based on [PERSON]'s algebra [44; 45; 46] and whose validity is demonstrated in Appendix A, it is established that there will be an intersection of the polygons \(\Pi_{0}\) and \(\Pi^{\prime}_{i}\). Therefore, mutual shading between the panels \(\Pi_{0}\) y \(\Pi_{i}\), if, when representing vector \(d_{i}\) from the origin of coordinates, the end of the vector is included within the plane curve \(\Sigma\), which is obtained as the envelope of the family of all polygons that can be drawn on the plane \(\psi\) by translating the polygon \(\Pi_{0}\) with the condition that its perimeter is in contact with the coordinate origin of the reference system contained in \(\psi\) (Figure 3). It is important to note that, since photovoltaic collectors are built by annexing rectangular photovoltaic modules, the resulting geometric shape for the collector is, in general, a closed polygon in which all sides of the perimeter are contained in two directions perpendicular to each other, as shown by the orange line in \[\delta(rad)=0.006918-0.399912\cos(\Gamma)+0.070257\sin(\Gamma)-0.006758\cos(2 \Gamma)+0.00907\sin(2\Gamma) \tag{2}\]7 This fact leads to the determination of the envelope \(\Sigma\) being simplified and able to be performed analytically. Furthermore, this envelope (blue trace in Figure 4) will also be a closed polygon with the sides parallel and perpendicular to the directions of the perimeter of the collectors (Figure 4).