International Journal of CAD/CAM

Society for Computational Design and Engineering (한국CDE학회)
권호 표지

An Accelerated Simulated Annealing Method for B-spline Curve Fitting to Strip-shaped Scattered Points

  • Javidrad, Farhad (Center for Postgraduate Studies, Aeronautical University of Science and Technology)
  • Published : 2012.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

Generation of optimum planar B-spline curve in terms of minimum deviation and required fairness to approximate a target shape defined by a strip-shaped unorganized 2D point cloud is studied. It is proposed to use the location of control points as variables within the geometric optimization framework of point distance minimization. An adaptive simulated annealing heuristic optimization algorithm is developed to iteratively update an initial approximate curve towards the target shape. The new implementation comprises an adaptive cooling procedure in which the temperature change is adaptively dependent on the objective function evolution. It is shown that the proposed method results in an improved convergence speed when compared to the standard simulated annealing method. A couple of examples are included to show the applicability of the proposed method in the surface model reconstruction directly from point cloud data.

Keywords

References

  1. Li, L., Schemeauer, N., Peng, X., Zeng, Y. and Gu, P. (2002), A reverse engineering system for rapid manufacturing of complex objects, Robotics and Computer Integrated Manufacturing, 18, 53-67. https://doi.org/10.1016/S0736-5845(01)00026-6
  2. Bi, Z.M. and Wang, L. (2010), Advances in 3D data acquisition and processing for industrial applications, Robotics and Computer Integrated Manufacturing, 26, 403-413. https://doi.org/10.1016/j.rcim.2010.03.003
  3. Azariadis, P. and Sapidis, N. (2007), Product design using point-cloud surfaces: A recursive subdivision technique for point parameterization, Computers in Industry, 58, 832-843. https://doi.org/10.1016/j.compind.2007.03.001
  4. Hahmann, S. and Konz, S. (1997), Fairing bicubic Bspline surfaces using simulated annealing, Curves and Surfaces with Applications in CAGD Conference Proceedings, 159-168.
  5. Lin, H., Chen, W. and Wang, G. (2005), Curve reconstruction based on an interval B-spline curve, Visual Computing, 21, 1-10. https://doi.org/10.1007/s00371-004-0243-5
  6. Liu, G.H., Wong, Y.S., Zhang, Y.F. and Loh, H.T. (2003), Modelling cloud data for prototype manufacturing, Journal of Material Processing and Technology, 138, 53- 57. https://doi.org/10.1016/S0924-0136(03)00048-7
  7. Javidrad, F. and Pourmoayed, A.R. (2011), Contour curve reconstruction from cloud data for rapid prototyping, Robotics and Computer Integrated Manufacturing, 27, 397-404. https://doi.org/10.1016/j.rcim.2010.08.008
  8. Wang, W., Pottmann, H. and Liu Y. (2004), Fitting Bspline curves to point clouds by squared distance minimization, HKU CS Tech Report TR-2004-11, University of Hong Kong, Hong Kong.
  9. Wang, W., Pottmann, H. and Liu, Y. (2006), Fitting Bspline curves to point clouds by curvature-based squared distance minimization, ACM Transactions on Graphics (TOG), 25, 214-238. https://doi.org/10.1145/1138450.1138453
  10. Hoschek, J. (1988), Intrinsic parameterization for approximation. Computer Aided Geometric Design, 5, 27-31. https://doi.org/10.1016/0167-8396(88)90017-9
  11. Weiss, V., Andor, L., Renner, G. and Varady, T. (2002), Advanced surface fitting techniques, Computer Aided Geometric Design, 19, 19-42. https://doi.org/10.1016/S0167-8396(01)00086-3
  12. Kin-Sing, D., Wang, W., Qin, H., Wong, K.-Y., Yang, H. and Liu, Y. (2007), Design and analysis of optimization methods for subdivision surface fitting, IEEE Transactions on Visual Computer Graphics, 13, 878-890. https://doi.org/10.1109/TVCG.2007.1064
  13. Kelly, C.T. (1999), Iterative methods for optimization, Frontiers in applied mathematics, 18, SIAM publications, Philadelphia.
  14. Flöry, S. and Hofer, M. (2008), Constrained curve fitting on manifolds, Computer- Aided Design, 40, 25-34. https://doi.org/10.1016/j.cad.2007.01.012
  15. Pottmann, H., Leopoldseder, S. and Hofer, M. (2003), A concept for parametric surface fitting which avoids the parameterization problem, Computer Aided Geometric Design, 20, 343-362. https://doi.org/10.1016/S0167-8396(03)00078-5
  16. Liu, Y., Pottmann, H. and Wang, W. (2006), Constrained 3D shape reconstruction using a combination of surface fitting and registration, Computer- Aided Design, 38, 572- 583. https://doi.org/10.1016/j.cad.2006.01.014
  17. Flöry, S. (2009), Fitting curves and surfaces to point clouds in the presence of obstacles, Computer Aided Geometric Design, 26, 192-202. https://doi.org/10.1016/j.cagd.2008.04.003
  18. Kirkpatrick, S., Galatt, C.D. and Vecchi, M.P. (1983), Optimization by simulated annealing, Science, 220, 671- 680.
  19. Hajek, B. (1988), Cooling schedules for optimal annealing, Mathematical Operation Research, 13, 311-329. https://doi.org/10.1287/moor.13.2.311
  20. Hammerlin, G.J. and Hoffmann, K.H. (1991), Numerical Mathematics, Springer-Verlag, New York.
  21. Bartels, R.H., Beatty, J.C. and Barsky, B.A. (1987), An introduction to splines for use in computer graphics and geometric modeling, Morgan Kaufmann Publishers, California, USA.
  22. Chen, X.-D., Yong, J.-H., Paul, J.-C. and Xu, G. (2008), Computing the minimum distance between a point and a NURBS curve, Computer- Aided Design, 40, 1051-1054. https://doi.org/10.1016/j.cad.2008.06.008
  23. Mullineux, G. and Robinson, S.T. (2007), Fairing point sets using curvature, Computer- Aided Design, 39, 27-34. https://doi.org/10.1016/j.cad.2006.09.002
  24. Li, W., Xu, S., Zheng, J. and Zhao, G. (2004), Target curvature driven fairing algorithm for planar cubic Bspline curves, Computer Aided Geometric Design, 21, 499-513. https://doi.org/10.1016/j.cagd.2004.03.004