Piecewise Trigonometric Polynomial Curve Study

The paper mainly discusses some contents of Computer Aided Geometry Design. In CAGD, most of the curves are generated by the polynomials, such as Bézier curves and B spline curves, but they have some defects. Many scholars want to construct basic functions by other methods, such as trigonometric polynomials functions. The methods of constructing basic functions by trigonometric polynomials are discussed in the paper.Two groups of trigonometric polynomial curves on five-point piecewise scheme are presented in the paper. Weighted trigonometric polynomial curves are given. The given trigonometric polynomial curves of degree 1 and 2 are G~1 continuous. The given trigonometric polynomial curves of degree 2 and 3 are G~3 continuous and G~2 continuous. By choosing the shape parameter, the trigonometric polynomial curves can approach to the given control polygon in a different way. Therefore, the construction method of the trigonometric polynomial curves is simple and useful for curve design.Two groups of trigonometric polynomial curves are extended, original curves are the special form of extended curves. Extended curves inherit good characters of original curves and import variable parameter so bring flexibility to design.Furthermore, trigonometric Bézier curves with all edges tangent to a given control polygon are given in the paper, we can adjust the shape of curves by the parameter of trigonometric Bézier polynomial curves to approach the polygon. The method can improve the continuity and decrease the additional points. Many graphics examples in thesis show that they are efficient design methods.