Integrated Expression Of Several Sub-algorithms

Discrete subdivision is an important theme of constructing curves and surfaces,it isalso an important issue in the function approximation theory and applied research, whoseprocess is simple, from discrete to discrete, providing a fast method to generate curvesand surfaces. However, due to the diference of the convergence and stability each otherof subdivision, the efect and performance is not the same. Many subdivision method cangenerate the curve of good efect, such as the method of cutting polygon’s angle gradually.In considering of the methods to generate interpolating curves, scholars have created aclassic four-point method. Its main idea is to get a new control point by using the originalcontrol point According to a particular rule, and then to connect these new vertices toget a new control polygon, through adjusting parameters to control the shape of the limitcurve. Its forms of expression is simple, and the maximum order of convergence is up tofour, which can generate an order continuous limit curve, so it is the classical subdivisionalgorithm in CAGD. The four-point method is a important interpolation algorithm, whosepropose has play an important role in promoting the development of the segments. So onthis basis, many scholars of the four-Point method to get the limit curve has the desiredproperties, such as the number of higher order of convergence, relatively quick convergencespeed.On the basis of analysis of the four-point method algorithm carefully, our gives asubdivision algorithm, this algorithm is a Promotion of four-point method. There are fourparameters to control the subdivision process, increase the freedom of control the shape ofthe curve. Through give diferent values of the four parameters can be subdivided formatof diferent shapes limit curves When these parameters are given certain values,the methodcan obtain several subdivision formats as follow: Dyn.N classic four-point method, non-uniform four-point method, Hassan ternary four-point method, and given in the form of the theorem, made a detailed proof. fnally gives some practical examples.