International Journal of CAD/CAM

Society for Computational Design and Engineering (한국CDE학회)
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Geometric Hermite Curves Based on Curvature Variation Minimization

  • Chi, Jing (Department of Computer Science and Technology, Shandong Economic University) ;
  • Zhang, Caiming (Department of Computer Science and Technology, Shandong Economic University) ;
  • Wu, Xiaoming (Shandong Computer Science Center)
  • Published : 2006.12.31
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Abstract

Based on the smoothness criterion of minimum curvature variation of the curve, tangent angle constraints guaranteeing an optimized geometric Hermite (OGH) curve both mathematically and geometrically smooth is given, and new methods for constructing composite optimized geometric Hermite (COH) curves are presented in this paper. The comparison of the new methods with Yong and Cheng's methods based on strain energy minimization is included.

Keywords

References

  1. Chen, Y., Beier, K.-P., Papageorgiou, D.(1997), Direct highlight line modification on NURBS surfaces, Computer Aided Geometric Design, Vol. 14 (6), pp. 583–601 https://doi.org/10.1016/S0167-8396(96)00048-9
  2. de Boor, C., Hollig, K., Sabin, M. (1987), High accuracy geometric Hermite interpolation, Computer Aided Geometric Design, Vol. 4, pp. 269–278
  3. Farouki, R.T., Neff, C.A. (1995), Hermite interpolation by Pythagorean hodograph quintics, Math. Comput, Vol. 64 (212), pp. 1589–1609
  4. Farouki, R.T., Sakkalis, T. (1990), Pythagorean hodographs, IBM J. Res. Develop. 34, 736–752
  5. Hollig, K., Koch, J. (1995), Geometric Hermite interpolation, Computer Aided Geometric Design, Vol.12 (6), pp. 567–580
  6. Meek, D.S., Walton, D.J. (1997a), Geometric Hermite interpolation with Tschirnhausen cubics, J. Comput. Appl. Math, Vol. 81 (2), pp. 299-309 https://doi.org/10.1016/S0377-0427(97)00066-6
  7. Meek, D.S., Walton, D.J. (1997b), Hermite interpolation with Tschirnhausen cubic spirals, Computer Aided Geometric Design, Vol. 14 (7), pp. 619–635
  8. Reif, U. (1999), On the local existence of the quadratic geometric Hermite interpolant, Computer Aided Geometric Design, Vol. 16 (3), pp. 217–221
  9. Yong, J., Cheng, F. (2004), Geometric Hermite curves with minimum strain energy, Computer Aided Geometric Design, Vol. 21, pp. 281-301 https://doi.org/10.1016/j.cagd.2003.08.003
  10. Yong, J.-H., Hu, S.-M., Sun, J.-G. (1999), A note on approximation of discrete data by G1 arc splines, Computer-Aided Design 31 (14), 911–915 https://doi.org/10.1016/S0010-4485(99)00076-7
  11. Zhang, C., Cheng, F. (1998), Removing local irregularities of NURBS surfaces by modifying highlight lines, Computer-Aided Design 30 (12), 923–930 https://doi.org/10.1016/S0010-4485(98)00048-7
  12. Zhang, C., Zhang, P., Cheng, F. (2001), Fairing spline curves and surfaces by minimizing energy, Computer-Aided Design 33 (13), 913–923 https://doi.org/10.1016/S0010-4485(00)00114-7