Researches On Shape Preserving Interpolation Curves

This paper makes mainly researches on shape preserving interpolation curves, and presents new methods of constructing curves which possess good shape preserving and smoothing properties. It contains four chapters and it is organized as follows. In chapter 1, after briefly reviewing the development and present conditions of curves and surfaces modeling in CAGD, the paper introduces generalized Ball curves and T-B trigonometric spline with their properties related, and briefly introduces the main contents of this paper. In chapter 2, a sort of quadratic generalized Ball interpolation curves are constructed. The corresponding curves are G 2-continuous and shape preserving. The local modifications of the curves are possible. The shape of these curves can be modified by changing the parameters. Finally, corresponding graph examples for different conditions are given respectively; and G 2-continuous Beta constrained conditions and detailed constructing process for generalized Ball curves of arbitrary degree are presented. There is another method of constructing interpolation curves in chapter 3: a sort of interpolation curves with the properties of convexity preserving, C 3continuous are constructed by using the T-B triangular bases, and the shape of these curves can also be modified locally. In addition, the shape preserving conditions of these curves are given. Finally, some corresponding graph examples are respectively given. It gives brief summary for the whole paper and presents some questions which is worthwhile to explore and research in chapter 4.