Convex surface ray tracing based on adaptive cutting surface adjustment under exact normal vector
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摘要:
针对电大尺寸目标难以精确解析表达带来的一致性几何绕射算法应用难问题，提出了基于三角网格、适用于任意凸曲面的射线寻迹（TM-tracing）算法。应用工程中较易获取的三角网格及其协议，设计了一种满足快速多边搜索条件的网状数据存储链表；提出了满足寻迹要求的高精度法矢求解算法；采用切割面自适应调整的弧形拟合寻迹方法实现了爬行波寻迹算法；结合一致性几何绕射理论（UTD）实现了暗区场值求解算法。任意网格曲面射线寻迹结果表明：本文提出的寻迹算法适用于包括球、柱和锥在内的任意光滑凸曲面，寻迹偏差小于1.61%，寻迹速度为2.8 s，具有一定的工程应用价值。
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关键词:
- 三角网格 /
- 一致性几何绕射理论(UTD) /
- 射线寻迹 /
- 短程线 /
- 爬行波
Abstract:Electrical large targets are difficult to be accurately and analytically expressed and thus it is difficult to use uniform geometrical theory of diffraction (UTD) method for field computation. Aimed at this problem, a novel creeping ray triangular mesh tracing (TM-tracing) algorithm for arbitrary convex surface was proposed. Based on practical engineering triangular mesh and its protocol, a net-like triangular mesh data storage list which meets the rapid multilateral search criteria was designed. A high accuracy normal vector algorithm was proposed to satisfy the tracing requirement. Then a dynamic adjustment of the arc cutting surface fitting tracing method was proposed to realize creeping wave tracing algorithm. Finally, combined with UTD, shadow field value solving algorithm was realized. Aircraft-based ray tracing results show that TM-tracing algorithm can be applied to arbitrary smooth convex surfaces including sphere, cylinder and cone. Tracing speed is 2.8 seconds and deviation is less than 1.61%. It shows that the proposed algorithm has an application value in engineering.
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图 2 三角网格模型的数学几何表达
Figure 2. Mathematic and geometrical expression of triangle mesh model
图 3 凸曲面爬行波示意图
sd1，sd2-入射采样点和出射点；ni-顶点连接的第i个三角片的单位法矢；t1，t2-初始传播方向和出射方向；ρ-射线焦散距离。
Figure 3. Schematic diagram of convex surface creeping wave
图 6 切割面调整寻迹方法示意图
S′2-未修正的传播交点；n′S2-未修正传播交点的法向量。
Figure 6. Schematic diagram of cutting surface adjustment tracing method
图 9 柱体表面、球体表面、锥体表面及复杂结构爬行波寻迹
Figure 9. Creeping wave tracing on cylinder surface, sphere surface, cone surface and complex structure
图 10 理想导体圆柱面绕射场求解配置图
Figure 10. Configuration diagram of diffraction field solve on a perfect electric conductor cylinder surface
表 1 法矢计算精度对比
Table 1. Computation precision of normal vector
参量 x/m y/m z/m 模长/m 理论 -0.0074 0.1002 0.9877 1 本文算法 -0.0016 0.1222 0.9925 0.99999165 
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表 2 球体上短程线寻迹结果对比
Table 2. Comparison of geodesic tracing results on a sphere
方法 长度/m 偏差/m 误差/% 时间开销/s 理论方法 3.1237 0.0496 1.61 2.8 最小夹角法[5] 3.6925 0.6184 20.11 1.2 本文算法 3.0741
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