The Extension Research Of Bezier Curves

Bezier curves and surfaces are one of the important components for computer aided geometric design. They are widely applied in computer graphics and industrial products. Because of their many good properties in shape controlling, they have drown wide attentions of many people.In recent years, one of the main studies for Bezier curves is how to adjust the shape of the curves without the changing of control polygon. In this paper, a new extending method of Be zier curves will be discussed based on the idea of the linear combination of basic functions. By introducing parameters in the basic functions and changing the value of the parameters, the shape of the curves can be adjusted freely.The paper includes the following parts.In part â… , the research background and main content of this thesis are introduced. In part â…¡, the basic concepts of Bezier curves and some achievements on extended Bezier curves are given. And three main extended Bezier curves are analyzed and compared with each other. In part â…¢ and â…£, a new extended form of quadratic and cubic Bezier curves is discussed in details based on the idea of the linear combination of basic functions. The extended curve keeps the form of quadratic and cubic polynomial and shows some better properties than the traditional extension form of Bezier curves.Finally, our work is summarized and some problems should be studied in the future are given.