Cubic Non-uniform Trigonometric Polynomial Curves With Multiple Shape Parameters

This thesis makes mainly researches on cubic non-uniform trigonometric polynomial curves with multiple shape parameters, It contains five chapters and is organized as follows.In chapter 1, after briefly reviewing the development and present conditions of curves and surfaces modeling in CAGD, the main contents of this thesis are given. The second chapter focuses on the B spline curve's definition and properties. The third chapter recommends C~3-continuous trigonometric spline curves presented by Wu xiaoqin and Han xuli, a class of trigonometric spline curves on four-point piecewise scheme by Han xuli and the uniform trigonometric polynomial B spline curves by Liu yonggang et al. The fourth chapter introduces a class of trigonometric polynomial curves with one shape parameter and theirs properties. It is convenient to adjust totally the shape of curves by changing the values of the shape parameters. In the fifth chapter, the author constructs cubic non-uniform trigonometric polynomial curves with multiple shape parameters, whose shape can be adjusted totally or locally by changing the values of the shape parameters.