# Reflection Propagation Law of Electromagnetic Waves in U-Shaped Roadway
## 3 U-Shaped Roadway Model and Reflection Path Validity
### Reflection Path Validity
#### 3.2.3 Six-Time Valid Reflection Paths  
Figure 8 shows the two-dimensional six-time valid reflection paths, where the combination of points T to P as a secondary reflection and points P to R as a quaternary reflection are used as an example.  
* Create a primary mirror of the emission point T with respect to plane \(m_{1}\) to obtain the primary mirror point I\({}_{1}\).
* Set I\({}_{1}\) as the base point, and a secondary mirror is made in plane \(m_{2}\) to obtain the secondary mirror point I\({}_{12}\).
* Connect point I\({}_{12}\) with point P, and the intersection point of \(m_{2}\) in the plane is C\({}_{12}\).
* Connect the point C\({}_{12}\) with point I\({}_{1}\), and the intersection point \(m_{1}\) in the plane is C\({}_{1}\).
* Connect points T, C\({}_{1}\), and C\({}_{12}\) in turn to form a secondary valid reflection path.  
* Relay node \(P\) is mirrored with respect to plane \(m_{5}\) to obtain the first-level mirror point I\({}_{5}\).
* With I\({}_{5}\) as the base point, it is mirrored in plane \(m_{2}\) to obtain the second-level mirror point I\({}_{52}\).
* With I\({}_{52}\) as the base point, it is mirrored in plane \(m_{3}\) to obtain the third-level mirror point I\({}_{523}\).
* Finally, with I\({}_{523}\) as the base point, it is mirrored in plane \(m_{6}\) to obtain the fourth-level mirror point I\({}_{5236}\).
* The I\({}_{5236}\) point and R point connection in plane \(m_{6}\) intersect at C\({}_{5236}\).
* The C\({}_{5236}\) point and I\({}_{523}\) point are connected to the plane \(m_{3}\) intersection for C\({}_{523}\).
* The C\({}_{523}\) point and I\({}_{52}\) point are connected to the plane \(m_{2}\) intersection for C\({}_{52}\).
* Finally, points C\({}_{52}\) and I\({}_{5}\) are connected to the plane \(m_{5}\) intersection for C\({}_{5}\).
* Sequentially connect points P, C\({}_{5}\), C\({}_{52}\), C\({}_{523}\), C\({}_{5236}\), and R.  
Figure 8: Two-dimensional diagram of six-time valid reflection paths.  
Points P, C\({}_{5}\), C\({}_{52}\), C\({}_{523}\), C\({}_{5236}\), and R form a quaternary valid reflection path.  
This shows that the transmitting point T to the relay node \(P\) theoretically has 30 secondary mirror points, that is, 30 reflection lines, and the relay node \(P\) to the receiving point \(R\) theoretically has 750 quadruple mirror points, that is, 750 reflection lines; therefore, there are 780 mirror points and 22,500 reflection lines in this combination. Similarly, for the combination of transmitting point T to relay node \(P\) as a quadruple reflection, and relay node \(P\) to receiving point \(R\) as a secondary reflection, there are 780 mirror points and 22,500 reflection lines. When the combination of transmitting point T to relay node \(P\) is one reflection and relay node \(P\) to receiving point \(R\) is five reflections, and when the combination of transmitting point T to relay node \(P\) is five reflections and relay node \(P\) to receiving point \(R\) is one reflection, there are theoretically 3756 mirror points and 22,500 reflection lines. For the combination of three reflections from transmitting point T to relay node \(P\), and three reflections from relay node \(P\) to receiving point \(R\), there are theoretically 300 mirror points and 22,500 reflection lines. Therefore, all combinations of the six-time reflection paths theoretically have a total of 9372 mirror points and 112,500 reflection lines.