# An Intelligent Measurement Method and System for Vehicle Passing Angles
## 3 Measurement Method
### Parameter Calculation  
After building the point cloud, it is necessary to align it with national regulations to identify target points and calculate the parameters. Several parameters of vehicle chassis can be calculated rapidly by rotating and segmenting the overall point cloud collected by this paper. Here, we focus on solving the passing angles, which currently have the lowest degree of automated detection and the poorest data consistency in Algorithm 2. An iterative algorithm is employed to determine the target points during the calculation of passing angles, as shown in Figure 6. The point cloud belonging to the vehicle body and the point clouds associated with the tires are separated using the RANSAC method, which utilizes a planar model for the body and a cylindrical model for the tires. Subsequently, these point clouds are projected onto suitable surfaces for further analysis. ```
1:Input: L1, L2, L3, T1, T2
2:Output:\(\alpha\), \(\beta\), \(\lambda\)
3: Select a point \(A_{o}\) in L1 and a point \(B_{o}\) in T1 as init. 4: for traverse the point \(A_{o}\) in L1 do
5: Choose the point \(A\) so that it satisfies Equation (8). 6: end for
7: for traverse the point \(B_{o}\) in T1 do
8: Choose the point \(B\) so that it satisfies Equation (9). 9: end for
10: Calculate the approach angle \(\alpha\) as Equation (10). 11: Select a point \(G_{o}\) in L3,  and a point \(F_{o}\) in T2 as init. 12: for traverse the point \(G_{o}\) in L3 do
13: Choose the point \(G\) so that it satisfies Equation (11). 14: end for
15: for traverse the point \(F_{o}\) in T2 do
16: Choose the point \(F\) so that it satisfies Equation (12). 17: end for
18: Calculate the departure angle \(\lambda\) as Equation (13). 19: Select a point \(C_{o}\) in L2,  a point \(D_{o}\) in T1 and a point \(E_{o}\) in T2 as init do
20: for traverse the point \(C_{o}\) in L2 do
21: Choose the points \(D_{p}\) and \(E_{p}\) so that it satisfies Equation (14). 22: end for
23: Calculate angle \(\beta_{o}\) as Equation (16). 24: if \(\beta_{o}\) is minimum then
25: Calculate the ramp break angle \(\beta=\beta_{o}\), as Equation (15). 26: end if
27: end for
28: return \(\alpha\), \(\beta\), \(\lambda\)
```  
**Algorithm 2**Parameters calculation  
The cylindrical model is used to segment the tire point clouds, allowing for the extraction of parameters such as the circle center and radius. Additionally, based on these parameters and the Z-axis coordinates, the lower portion of the tire point clouds, referred to as T1 and T2, can be extracted to reduce computational overhead. Similarly, the body point cloud can be segmented into LI, L2 and L3 using these parameters. The approach angle, ramp break-over angle and departure angle are then calculated according to the standard definition [1]. In Algorithm 2, certain points should be selected randomly. As shown in Figure 6, points \(B_{o}\), \(D_{o}\), \(E_{o}\) and \(F_{o}\) represent the initial random selection points in the edge part of the tire point clouds. Additionally, points \(A_{o}\), \(G_{o}\) and \(C_{o}\) represent the traversal points in the point cloud of the body. The target point \(A\) for the approach angle can be obtained by traversing as:  
Figure 6: Diagram of angle calculation. \[\frac{z_{A}-z_{B_{o}}}{y_{A}-y_{B_{o}}}=\min\left\{\frac{z_{A_{o}}-z_{B_{o}}}{y_{A_ {o}}-y_{B_{o}}}\right\} \tag{8}\]  
Another target point for the approach angle is \(B\), that is, the tangent point between the ray of the target point A and the tire. This tangent point can be found by traversing T1, where the line connecting T1 to the center of the tire is perpendicular to the line connecting T1 to point A. The process can be described as:  
\[\left|\overrightarrow{BO_{1}}\times\overrightarrow{BA}\right|=0 \tag{9}\]  
Additionally, the approach angle can be obtained as:  
\[\alpha=\arctan(\frac{z_{A}-z_{B}}{y_{A}-y_{B}}) \tag{10}\]  
The calculation of the departure angle is similar to that of the approach angle. The difference lies in traversing the L3 points and the rear tire point cloud T2.