Author Affiliations
College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao , Shandong 266590, Chinashow less
Fig. 1. Flow chart of 3D axis extraction
Fig. 2. Boundary points extraction
Fig. 3. Comparison of fitting accuracy. (a) Boundary lines with different degrees of deviation; (b) root mean square error of fitting with different components as independent variable
Fig. 4. Sketch of 3D axis points extraction
Fig. 5. Solving normal vector of cross-section by infinitesimal method
Fig. 6. Experimental data. (a) Data Ⅰ; (b) data Ⅱ; (c) data Ⅲ
Fig. 7. Comparison of boundary points extracted by two methods. (a) Our method; (b) traditional method
Fig. 8. Comparison of horizontal 2D midline extracted by two methods. (a) Our method; (b) method in Ref. [
4]
Fig. 9. Extraction of 3D central axis and cross-section of two sets of data. (a) Data Ⅰ; (b) data Ⅱ
Fig. 10. Top view of two cross-sections with the same inner diameter and different longitudinal slopes
Fig. 11. Sketch of cross-section extraction error
Parameter | Value |
---|
| (160°, 200°) | /cm | 1.0 | | | | 80% | l /cm | 0.1 | e /cm | 2.5 |
|
Table 1. Main setting parameters
Method | Data Ⅰ | Data Ⅱ | Data Ⅲ |
---|
Time /s | number | Time /s | number | Time /s | number |
---|
Our method | 4.6 | 5154 | 4.2 | 2527 | 0.9 | 928 | Traditional method | 25.6 | 6351 | 26.0 | 4987 | 5.4 | 1090 |
|
Table 2. Comparison of extraction results of two methods
Error | Our method | Ref.[4] |
---|
| 2.7 | 177.1 | | 4.5 | 571.8 | | 0.3 | 0.004 | | 2.4 | 72.6 |
|
Table 3. Comparison of extraction errors between two methods
f | | Section 1 | Section 2 | Section 3 | /mm |
---|
/mm | /mm | ε /% | /mm | /mm | ε /% | /mm | /mm | ε /% |
---|
0 | 0.00 | 0.11 | 0.11 | / | 0.10 | 0.10 | / | 0.11 | 0.11 | / | 0.11 | 1% | 50.00 | 49.39 | 0.61 | 1.22 | 49.32 | 0.68 | 1.36 | 49.74 | 0.26 | 0.52 | 0.52 | 2% | 100.00 | 98.04 | 1.96 | 1.96 | 98.10 | 1.90 | 1.90 | 98.15 | 1.85 | 1.85 | 1.90 | 3% | 150.00 | 146.42 | 3.58 | 2.39 | 146.40 | 3.60 | 2.40 | 146.46 | 3.54 | 2.36 | 3.57 | 4% | 200.00 | 195.81 | 4.19 | 2.10 | 195.96 | 4.04 | 2.02 | 195.96 | 4.04 | 2.02 | 4.09 | 5% | 250.00 | 242.40 | 7.60 | 3.04 | 242.35 | 7.65 | 3.06 | 242.47 | 7.53 | 3.01 | 7.59 |
|
Table 4. Analysis of the accuracy of tunnel cross-sections extraction