Fig. 1. Algorithm global flow chart

Fig. 2. Tube bending point cloud uniform downsampling

Fig. 3. Schematic of main direction on the surface of cylinder

Fig. 4. Schematic of principal direction perpendicular to normal at a point on a cylindrical surface

Fig. 5. Main direction update process. (a) Neighborhood point of the plane πi; (b) main direction iterative update

Fig. 6. Main direction angle changes at a point during iteration

Fig. 7. Main direction of tube bending point cloud

Fig. 8. Ambiguity of orientation of principal direction

Fig. 9. Diagram of directed distance from a point to a plane

Fig. 10. Spatially discontinuous but satisfying the first condition

Fig. 11. Schematic diagram of clustering process

Fig. 12. Tube bending segmentation effect

Fig. 13. A geometric model of a cylinder

Fig. 14. Tube bending axis reconstruction effect diagram

Fig. 15. Schematic diagram of curvature change of tube bending axis

Fig. 16. Axis node curvature calculation diagram

Fig. 17. Space circle fitting is carried out for curvedsection nodes

Fig. 18. XTOM-MATRIX-QC

Fig. 19. Experimental system diagram

Fig. 20. Tube bending and point cloud data. (a)(b) T1 physical object and point cloud; (c)(d) T2 physical object and point cloud

Fig. 21. Cylindricity diagram

Fig. 22. A partial cylindrical point cloud taken from a curved section. (a) T1; (b) T2

Fig. 23. Cylindricity experiment results. (a) Cylindricity of the bending section with radius of 120 mm; (b) cylindricity of the bending section with radius of 60 mm

Fig. 24. Measuring object. (a) T1; (b) T2