## 2 Materials and Methods
### Calculation of the Shadow Area of Human Obstacles under Multiple Light Sources  
#### 2.2.1 Full Shadow Calculation of Human Obstacles  
If the size of the receiving plane is \(N(m)\times N(m)\) and it is divided into \(M\times M\) rectangular grids, then the area of each rectangular grid is \(S_{rect}\). The circular arc of the top surface of the cylinder was equally divided into units of 1 degree, and multiple shadow line segments \(FG\) were generated on the receiving plane by the vertical line segment (\(QF\) in Figure 3a) where the light source \(L\) and each discrete circular arc point located are calculated. The total number of Rectangular Grids \(R_{total}\) passed by the Shadow Segment \(FG\) was counted and \(R_{total}\) represent the number of total receivers located in the shadow area. Therefore, the shadow area \(S_{shadow}\) of the human obstacle could be expressed as:  
\[S_{shadow}=R_{total}\times S_{rect} \tag{6}\]  
The specific solution process for the shadow area of human obstacles can be described as follows. It can be assumed that Point \(Q\) is the \(k\)-th discrete point of the circular arc on the  
Figure 3: (**a**) Three-dimensional position relation diagram of a single light source and obstacle. (**b**) Two-dimensional projection diagram of a single light source and obstacle shadow. top surface of a cylinder. From the geometric relation in Figure 3a, it can be seen that the angle between the positive semiaxis of the \(x\)-axis and \(NQ\) is:  
\[\theta=\frac{1}{360^{\circ}}\times k \tag{7}\]  
Then, the coordinates \((x_{Q},y_{Q},z_{Q})\) of Point \(Q\) can be obtained by the following formula:  
\[\left\{ \begin{array}{l}x_{Q}=X_{n}+r\cos\theta\\ y_{Q}=Y_{n}+r\sin\theta\\ z_{Q}=Z_{n}\end{array} \right. \tag{8}\]  
The Euclidean distance between Point \(L\) and Point \(Q\) in position space was:  
\[d_{QL}=\|l_{Q}-l_{L}\| \tag{9}\]  
where \(l_{Q}\) represents the position of Point \(Q\) and \(l_{L}\) represents the LED position of the light source. From \(d_{QL}\), we know that the unit vector of \(LQ\) was:  
\[\mathbf{e}_{LQ}=\frac{(\mathbf{Q}-\mathbf{L})}{d_{QL}} \tag{10}\]  
The length \(d_{LG}\) of the Line Segment \(LG\) could be obtained from the relation of similar triangles \(\Delta QGF\) and \(\Delta LGO\). \[d_{LG}=\frac{d_{QL}d_{LO}}{d_{LO}-d_{QF}} \tag{11}\]  
where \(d_{LO}\) and \(d_{QF}\) are the lengths of Vector \(\overset{\rightarrow}{LO}\) and Vector \(\overset{\rightarrow}{QF}\), respectively. Vector \(\mathbf{G}\) can be expressed as:  
\[\mathbf{G}=\mathbf{L}+d_{LG}\times\mathbf{e}_{LQ} \tag{12}\]  
Then, the shadow length generated by the Line Segment \(QF\) on the XOY plane under Light Source \(L\) was:  
\[d_{FG}=\|l_{F}-l_{G}\| \tag{13}\]  
where \(l_{F}\) represents the position of \(F\) and \(l_{G}\) represents the position of \(G\). After the length of the shadow line segment, \(FG\) was calculated according to the above derivation process, the shadow line segment \(FG\) was discretized according to the size of the rectangular grid, and the position of each discrete shadow point in the shadow area and its corresponding rectangular grid was marked. After marking according to the above steps, the shadow matrix \(A\) of the receiving plane under the occlusion of a single light source and a single obstacle could be obtained. Then, the total number of Shadow Grids \(R_{total}\) marked in the shadow matrix \(A\) (i.e., the rectangular grid marked as 1 in the shadow matrix) could be counted and substituted into Formula (6) to obtain the shadow area generated by the single body obstacle of a single light source.