Study On Two Order Triangular Bézier Curves With Shape Parameters

The value of Computer Aided Geometric Design?CAGD?is self-evident in modern industry.As an important part of CAGD,curve and surface design has become a very valuable research topic.In recent years,trigonometric polynomial is used in curve and surface design,because it hold the advantage which can accurately represent the quadratic curves,which has attracted the attention of scholars.This paper constructs two kinds of Bézier triangular basis function of order two with shape parameters,which add the position parameters and adjustment matrix.Then the tangent point adjustable trigonometric Bézier curve of two order with shape parameters and two order trigonometric Bézier curves with Gⁿ continuity are obtained.They retain the properties of Bézier curves,but also has advantages of adjustability,point adjustable,can accurately represent conic curve.The numerical examples show that the two kinds of curves presented in this paper are very effective in curve and surface design.The main work of this paper is as follows:First,it constructs one or two order trigonometric Bézier function,and natures are discussed.Then,on the basis of the function in first chapter,the tangent point adjustable with shape parameters of two order Bézier triangular basis function are constructed,abd the properties of curve and the geometric meaning of parameterds are analyzed.Curve concection theorem and the theorem of using the curve to express ellipse and circle are provided.Corresponding numerical examples are given.Finally,the trigonometric function is extended to arbitrary order.The order two trigonometric Bézier basis function with Gⁿ continuity by adding paramenter are given and the nature of the basis function are analyzed.The order two trigonometric Bézier curve with Gⁿ continuity are presented.In the same way,the properties of curve and the geometric meaning of parameterds are analyzed.Curve concection theorem and the theorem for expressing ellipse and circle are provided.Relevant numerical examples are given in the end.