A Class Of Uniform Trigonometric Splines And Interpolation Curves With Shape Parameters

This thesis make mainly researches on a class of uniform trigonometric splines and interpolation curves with shape parameters, it contains five 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 article introduces some kinds of non-polynomial splines, and gives the main contents of this thesis. In chapter 2, it introduces some kinds of trigonometric splines on three-point piecewise scheme. In chapter 3, it constructs some kinds of uniform trigonometric spline curves with shape parameters on three-point piecewise scheme by the trigonometric splines given in chapter 2, then combined the graphics examples, their characters are discussed. In chapter 4, first, it constructs α-trigonometric spline interpolation curves by the method of constructing α-B spline interpolation curves, then constructs particularly a class of α -trigonometric spline interpolation curves with one or two shape parameters on three-point piecewise scheme, its characters are discussed combining the graphics examples. α-B₃ spline interpolation curve on four-point piecewise scheme is shown in chapter 5, its characters and advantages and disadvantages are also discussed in this chapter.