The Research Of Third-order Trigonometric Bézier

Trigonometric Bézier polynomial function occupies an important position in the ?eld of function approximation, This function is not only inherited many advantages of the polynomial function. At the same time,it overcomes the drawback of polynomial function which cannot approximate transcendental function. In recent years,due to the application requirements,the research of the curve/suiface which is produced by trigonometric Bézier polynomial function is high-pro?led.In this paper, we study the structure of the third-order trigonometric Bézier polynomial and the properties of the curve which is produced by such a polynomial and the problem of its shape adjustment.This paper ?rst comprehensive overview about the trigonometric polynomial function and the current research status of trigonometric polynomial curve, and about some methods and characteristics of the adjustment of curve shape.The second,giving the structure of two class of third-order trigonometric Bézier polynomial basis functions, its main method is comprehensive utilization the expansion of[(1- sin t) + sin t]3combining with the expansion of [(1- cos t) + cos t]3,then respectively composed two class of third-order trigonometric polynomial, and using the two types of basis functions respectively constructing trigonometric polynomial curve and studying the properties of these two kinds of curve.Thirdly,study the problem of adjusting the shape of the triangle Bézier curve shape.The main idea is introducing the control vertices with parameters, in order to reach the purpose of adjusting the shape of the curve.According to the range of the numerical value of these parameters a?ects the geometric meaning of the curve shape adjustment.Finally,study two kinds of third-order Bézier trigonometric polynomial curve in stitching points reach a certain conditions of geometric continuous and parameters continuous,these conditions are related to the control points,thus related to the selection of parameters. Will these two types of curves are compared with those Bernstein polynomial curve,some speci?c application are given.