# 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
where \(\theta_{s}\) is the equivalent rotation angle; \(L_{s}\) is the synthetic aperture length; \(R_{0}\) is the slant range of scene center; \(\theta_{s-strip}\) is the beamwidth with stripmap mode; \(\lambda\) is the wavelength; and \(D_{a}\) is the azimuthal length of real aperture. (b) As shown in Figure 2, the zero Doppler scanning plane does not consider the dynamic occlusion relationship between the target and the sensor within the corresponding synthetic aperture time and has not yet been able to reproduce the time-varying radar beam radiation area and the shadow area. According to beam pointing characteristics in different SAR imaging modes, the SAR equivalent beam rotation angle can be calculated using the synthetic aperture length and slant range of the scene's center. Then, the zero Doppler plane is used as the scanning reference plane. The platform flight direction is taken as the positive direction, and the connection line between the sensor and the nadir point is taken as the central axis ST. The half of the equivalent beam rotation angle is taken as the positive or negative angle to rotate the scanning reference plane and coincide with the beam's front or backward edge. The equivalent beam front and backward edge planes and zero Doppler planes generated by each PRT are taken as the beam scanning plane set. \[\left\{ \begin{array}{l}F\left[\overrightarrow{v}\right]=\left[\overrightarrow {v}_{0}\right]\cdot\left[\begin{array}{ccc}\cos(\theta_{s})&\sin(\theta_{ s})&0\\ -\sin(\theta_{s})&\cos(\theta_{s})&0\\ 0&0&1\end{array}\right]\\ \\ M\left[\overrightarrow{v}\right]=\left[\overrightarrow{v}_{0}\right]\cdot \left[\begin{array}{ccc}1&0&0\\ 0&1&0\\ 0&0&1\end{array}\right]\\ \\ B\left[\overrightarrow{v}\right]=\left[\overrightarrow{v}_{0}\right]\cdot \left[\begin{array}{ccc}\cos(\theta_{s})&-\sin(\theta_{s})&0\\ \sin(\theta_{s})&\cos(\theta_{s})&0\\ 0&0&1\end{array}\right]\\ \end{array} \right. \tag{4}\]  
where \(F\left[\overrightarrow{v}\right]\) is the beam's front edge; \(M\left[\overrightarrow{v}\right]\) is the zero Doppler plane; and \(B\left[\overrightarrow{v}\right]\) is the beam's backward edge. (3): BVH-assisted EM wave transmission simulation. The main idea of the BVH algorithm is that if the EM wave cannot hit the bounding box of a node, then it must not hit the facets inside the box, and the invalid facets in the corresponding bounding box of the node can be directly eliminated. If the EM wave does not hit the outermost bounding box corresponding to the root node, it means that the EM wave has no direct interaction with the target model. The construction process of the bounding box is to generate a binary tree by dividing the root node from top to bottom, as shown in Figure 3. The internal node does not contain facet information but provides spatial boundary information, and only the leaf node contains a few facets. (a) BVH assists the EM wave to intersect with the target model. As shown in Figure 3, according to the spatial boundary relationship between EM waves and internal nodes at all levels, the direction of the corresponding branches of nodes at all levels in the binary tree is determined step by step, and the internal nodes containing the intersecting surface facet are constantly hit. The leaf node contains only a small number of facets, which is the last level node, and the calculation amount of traversing the facets of the leaf node is small. The more compact the space of the bounding box corresponding to the internal nodes of the same level, the smaller the overlap degree, which can reduce the calculation cost of traversing the bounding box, corresponding to the nodes of the same level. The key points of BVH that assist the EM wave to intersect with the target model are as follows. The axis-aligned bounding box (\(AABB\)) is used for efficiently handling query operations on a large number of internal nodes.