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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)
Publication Information
International Journal of CAD/CAM / v.6, no.1, 2006 , pp. 65-71 More about this Journal
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
Curvature variation; Geometric smoothness; Hermite;
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1 Farouki, R.T., Neff, C.A. (1995), Hermite interpolation by Pythagorean hodograph quintics, Math. Comput, Vol. 64 (212), pp. 1589–1609
2 Farouki, R.T., Sakkalis, T. (1990), Pythagorean hodographs, IBM J. Res. Develop. 34, 736–752
3 Meek, D.S., Walton, D.J. (1997a), Geometric Hermite interpolation with Tschirnhausen cubics, J. Comput. Appl. Math, Vol. 81 (2), pp. 299-309   DOI   ScienceOn
4 Zhang, C., Cheng, F. (1998), Removing local irregularities of NURBS surfaces by modifying highlight lines, Computer-Aided Design 30 (12), 923–930   DOI   ScienceOn
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. (1997b), Hermite interpolation with Tschirnhausen cubic spirals, Computer Aided Geometric Design, Vol. 14 (7), pp. 619–635
7 Yong, J., Cheng, F. (2004), Geometric Hermite curves with minimum strain energy, Computer Aided Geometric Design, Vol. 21, pp. 281-301   DOI   ScienceOn
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.-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   DOI   ScienceOn
10 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   DOI   ScienceOn
11 Zhang, C., Zhang, P., Cheng, F. (2001), Fairing spline curves and surfaces by minimizing energy, Computer-Aided Design 33 (13), 913–923   DOI   ScienceOn
12 de Boor, C., Hollig, K., Sabin, M. (1987), High accuracy geometric Hermite interpolation, Computer Aided Geometric Design, Vol. 4, pp. 269–278