# Bounding Volume Hierarchy-Assisted Fast SAR Image Simulation Based on Spatial Segmentation
## 2 BVH-Assisted Computation of the Target Multiple Backscatter Field
### BVH-Assisted Simulation of Electromagnetic Wave Transmission
Then, the center coordinates of the target model surface facets are arranged in ascending order, and the surface facets can be sorted along the three spatial axes \([X,\,Y,Z]\) of the current node. Then, we perform continuous spatial segmentation one by one and then compare the computational costs of all the segmentation positions and take the position with the lowest computational cost as the optimal segmentation position among the three axes. Take the \(X\)-axis as an example, generate a surface facet set \([Xstar,\,Xend]\) according to the size of the center coordinates of the model surface facets, and choose the method of successive dissections by surface facets \(x\subset[Xstar,\,Xend]\). The spatial surface area corresponding to the left box \(L[Xstar,\,i]\) and the right box \(R[i+1,\,Xend]\) can be calculated in real time and then brought into the SAH computational cost equation. Then, we can determine the dissecting position of the surface facet \(x_{i}\subset[Xstar,\,Xend]\) corresponding to the smallest computational cost as the optimal position of the dissecting along the \(X\)-axis. The other \(Y/Z\)-axes also follow this rule to calculate these optimal profile positions and computational costs. The actual profile location with the smallest computational cost among the three axes is selected as the final actual profile location. Taking the x-axis as an example, the surface area \(S\) of a node corresponding to \(AABB\) can be expressed as follows:  
\[S=2*[(X_{1}-X_{2})(Y_{1}-Y_{2})+(Y_{1}-Y_{2})(Z_{1}-Z_{2})+(X_{1}-X_{2})(Z_{1} -Z_{2})] \tag{5}\]  
where \((X_{1},Y_{1},Z_{1})\) and \((X_{2},Y_{2},Z_{2})\) are the spatial coordinates of the bounding box vertices A and B, respectively. Using Equation (5), calculate the surface area of the left and right child nodes corresponding to the bounding boxes A and B after the arbitrary dissection of a node, and then the cost equation of SAH calculation can be specifically expressed by Equation (6). \[\left\{ \begin{array}{l}\text{Cost}(A,B)=\frac{S_{A}}{S_{C}}N_{A}*\delta+ \frac{S_{B}}{S_{C}}N_{B}*\delta+G_{\text{Cost}}\\ \text{Cost}(X)=\min[\text{Cost}(A,B)]\\ F_{\text{Cost}}=\min[\text{ Cost}(X)\quad\text{Cost}(Y)\quad\text{Cost}(Z)\,\,]\end{array} \right. \tag{6}\]  
where \(\text{Cost}(A,B)\) is the cost of dividing a node; \(\text{Cost}(X)\) is the minimum division cost along the \(X\) axis; \(\delta\) is the cost of intersecting a single surface cell, which can be set to unit 1; \(S_{A}\) is the surface area of the left child node corresponding to the bounding box \(A\); \(S_{B}\) is the surface area of the right child node corresponding to the bounding box \(B\); \(S_{C}\) is the total area of the bounding box corresponding to the node to be divided; \(N_{A}\) is the number of surface  
Figure 3: Process of hitting leaf node assisted by BVH. facets contained in the bounding box \(A\); \(N_{B}\) is the number of surface facets contained in the bounding box \(B\); and \(G_{\text{Cost}}\) is the cost of constructing a binary tree, which can be set to a fixed value. Similarly, the minimum cost \(\text{Cost}(Y)\) and \(\text{Cost}(Z)\) of the \(Y\) and \(Z\) axes are calculated sequentially to find the optimal location of the minimum cost \(F_{\text{Cost}}\), and the internal nodes of the binary tree are constructed recursively by this division method. (b) Lattice radiation area generation and EM wave transmission simulation. As shown in Figure 4, the SAR beam radiation area can be quickly discriminated against with the assistance of the BVH algorithm, and the target facets within the radiation area are converted into lattices. According to the real-time complementary and time-varying characteristics of the radiation area and the shadow area, the real-time shadow area is generated by automatic removal of the beam occluded area or the target parts outside the beam scanning range. The total lattice radiation area can be obtained by a union of the lattice radiation areas determined by the beam scanning plane set.